## Begin on: Sat Oct 19 08:02:58 CEST 2019 ENUMERATION No. of records: 1408 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 42 (38 non-degenerate) 2 [ E3b] : 170 (128 non-degenerate) 2* [E3*b] : 170 (128 non-degenerate) 2ex [E3*c] : 3 (3 non-degenerate) 2*ex [ E3c] : 3 (3 non-degenerate) 2P [ E2] : 27 (20 non-degenerate) 2Pex [ E1a] : 2 (2 non-degenerate) 3 [ E5a] : 798 (437 non-degenerate) 4 [ E4] : 68 (38 non-degenerate) 4* [ E4*] : 68 (38 non-degenerate) 4P [ E6] : 29 (14 non-degenerate) 5 [ E3a] : 13 (11 non-degenerate) 5* [E3*a] : 13 (11 non-degenerate) 5P [ E5b] : 2 (2 non-degenerate) E15.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, S^2, S^-1 * A * S * B, S^-1 * B * S * A, S^-1 * Z * S * Z, Z^15, (Z^-1 * A * B^-1 * A^-1 * B)^15 ] Map:: R = (1, 17, 32, 47, 2, 19, 34, 49, 4, 21, 36, 51, 6, 23, 38, 53, 8, 25, 40, 55, 10, 27, 42, 57, 12, 29, 44, 59, 14, 30, 45, 60, 15, 28, 43, 58, 13, 26, 41, 56, 11, 24, 39, 54, 9, 22, 37, 52, 7, 20, 35, 50, 5, 18, 33, 48, 3, 16, 31, 46) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, B^-1 * A^-1 * B^-1, A^3, S * B * S * A, Z * B^-1 * Z^-1 * A, (S * Z)^2, A * Z^-1 * B^-1 * Z, Z^-2 * B^-1 * Z^-3 ] Map:: R = (1, 17, 32, 47, 2, 21, 36, 51, 6, 27, 42, 57, 12, 26, 41, 56, 11, 20, 35, 50, 5, 23, 38, 53, 8, 29, 44, 59, 14, 30, 45, 60, 15, 24, 39, 54, 9, 18, 33, 48, 3, 22, 37, 52, 7, 28, 43, 58, 13, 25, 40, 55, 10, 19, 34, 49, 4, 16, 31, 46) L = (1, 33)(2, 37)(3, 35)(4, 39)(5, 31)(6, 43)(7, 38)(8, 32)(9, 41)(10, 45)(11, 34)(12, 40)(13, 44)(14, 36)(15, 42)(16, 50)(17, 53)(18, 46)(19, 56)(20, 48)(21, 59)(22, 47)(23, 52)(24, 49)(25, 57)(26, 54)(27, 60)(28, 51)(29, 58)(30, 55) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, B^3, A * B * A, (S * Z)^2, S * A * S * B, (A^-1, Z), Z^3 * B^-1 * Z^2 ] Map:: R = (1, 17, 32, 47, 2, 21, 36, 51, 6, 27, 42, 57, 12, 24, 39, 54, 9, 18, 33, 48, 3, 22, 37, 52, 7, 28, 43, 58, 13, 30, 45, 60, 15, 26, 41, 56, 11, 20, 35, 50, 5, 23, 38, 53, 8, 29, 44, 59, 14, 25, 40, 55, 10, 19, 34, 49, 4, 16, 31, 46) L = (1, 33)(2, 37)(3, 35)(4, 39)(5, 31)(6, 43)(7, 38)(8, 32)(9, 41)(10, 42)(11, 34)(12, 45)(13, 44)(14, 36)(15, 40)(16, 50)(17, 53)(18, 46)(19, 56)(20, 48)(21, 59)(22, 47)(23, 52)(24, 49)(25, 60)(26, 54)(27, 55)(28, 51)(29, 58)(30, 57) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ S^2, A * B^-1, (S * Z)^2, A^-1 * Z^-1 * B * Z, S * B * S * A, Z * B^-1 * Z * B^-1 * Z, A^5, Z^-1 * A^-1 * Z^-1 * A^-2 * Z^-1, Z^15 ] Map:: R = (1, 17, 32, 47, 2, 21, 36, 51, 6, 24, 39, 54, 9, 30, 45, 60, 15, 27, 42, 57, 12, 20, 35, 50, 5, 23, 38, 53, 8, 25, 40, 55, 10, 18, 33, 48, 3, 22, 37, 52, 7, 29, 44, 59, 14, 28, 43, 58, 13, 26, 41, 56, 11, 19, 34, 49, 4, 16, 31, 46) L = (1, 33)(2, 37)(3, 39)(4, 40)(5, 31)(6, 44)(7, 45)(8, 32)(9, 43)(10, 36)(11, 38)(12, 34)(13, 35)(14, 42)(15, 41)(16, 50)(17, 53)(18, 46)(19, 57)(20, 58)(21, 55)(22, 47)(23, 56)(24, 48)(25, 49)(26, 60)(27, 59)(28, 54)(29, 51)(30, 52) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A^-1 * Z^-3, (A^-1, Z^-1), S * B * S * A, (S * Z)^2, A^5 ] Map:: R = (1, 17, 32, 47, 2, 21, 36, 51, 6, 20, 35, 50, 5, 23, 38, 53, 8, 27, 42, 57, 12, 26, 41, 56, 11, 29, 44, 59, 14, 30, 45, 60, 15, 24, 39, 54, 9, 28, 43, 58, 13, 25, 40, 55, 10, 18, 33, 48, 3, 22, 37, 52, 7, 19, 34, 49, 4, 16, 31, 46) L = (1, 33)(2, 37)(3, 39)(4, 40)(5, 31)(6, 34)(7, 43)(8, 32)(9, 41)(10, 45)(11, 35)(12, 36)(13, 44)(14, 38)(15, 42)(16, 50)(17, 53)(18, 46)(19, 51)(20, 56)(21, 57)(22, 47)(23, 59)(24, 48)(25, 49)(26, 54)(27, 60)(28, 52)(29, 58)(30, 55) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ S^2, B * A^-1, A * Z^-3, (S * Z)^2, S * B * S * A, (A^-1, Z^-1), A^5 ] Map:: R = (1, 17, 32, 47, 2, 21, 36, 51, 6, 18, 33, 48, 3, 22, 37, 52, 7, 27, 42, 57, 12, 24, 39, 54, 9, 28, 43, 58, 13, 30, 45, 60, 15, 26, 41, 56, 11, 29, 44, 59, 14, 25, 40, 55, 10, 20, 35, 50, 5, 23, 38, 53, 8, 19, 34, 49, 4, 16, 31, 46) L = (1, 33)(2, 37)(3, 39)(4, 36)(5, 31)(6, 42)(7, 43)(8, 32)(9, 41)(10, 34)(11, 35)(12, 45)(13, 44)(14, 38)(15, 40)(16, 50)(17, 53)(18, 46)(19, 55)(20, 56)(21, 49)(22, 47)(23, 59)(24, 48)(25, 60)(26, 54)(27, 51)(28, 52)(29, 58)(30, 57) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {15, 15}) Quotient :: toric Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A^-1 * Z^-1, B^-1 * Z^-1, (S * Z)^2, S * A * S * B, B^15, Z^15, Z^7 * A^-8 ] Map:: R = (1, 17, 32, 47, 2, 19, 34, 49, 4, 21, 36, 51, 6, 23, 38, 53, 8, 25, 40, 55, 10, 27, 42, 57, 12, 29, 44, 59, 14, 30, 45, 60, 15, 28, 43, 58, 13, 26, 41, 56, 11, 24, 39, 54, 9, 22, 37, 52, 7, 20, 35, 50, 5, 18, 33, 48, 3, 16, 31, 46) L = (1, 33)(2, 31)(3, 35)(4, 32)(5, 37)(6, 34)(7, 39)(8, 36)(9, 41)(10, 38)(11, 43)(12, 40)(13, 45)(14, 42)(15, 44)(16, 47)(17, 49)(18, 46)(19, 51)(20, 48)(21, 53)(22, 50)(23, 55)(24, 52)(25, 57)(26, 54)(27, 59)(28, 56)(29, 60)(30, 58) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z * A^2, (S * Z)^2, S * A * S * B, Z^8, (B * A)^8 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 26, 42, 58, 10, 30, 46, 62, 14, 29, 45, 61, 13, 25, 41, 57, 9, 20, 36, 52, 4, 17, 33, 49)(3, 21, 37, 53, 5, 23, 39, 55, 7, 27, 43, 59, 11, 31, 47, 63, 15, 32, 48, 64, 16, 28, 44, 60, 12, 24, 40, 56, 8, 19, 35, 51) L = (1, 35)(2, 37)(3, 36)(4, 40)(5, 33)(6, 39)(7, 34)(8, 41)(9, 44)(10, 43)(11, 38)(12, 45)(13, 48)(14, 47)(15, 42)(16, 46)(17, 53)(18, 55)(19, 49)(20, 51)(21, 50)(22, 59)(23, 54)(24, 52)(25, 56)(26, 63)(27, 58)(28, 57)(29, 60)(30, 64)(31, 62)(32, 61) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C16 (small group id <16, 1>) Aut = QD32 (small group id <32, 19>) |r| :: 2 Presentation :: [ S^2, A * Z * B, A * B * Z, S * A * S * B, A^2 * B^-2, (S * Z)^2, Z^2 * A^-1 * Z * A^-1, Z^2 * B^-1 * Z * B^-1, Z^8 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 24, 40, 56, 8, 27, 43, 59, 11, 29, 45, 61, 13, 32, 48, 64, 16, 31, 47, 63, 15, 21, 37, 53, 5, 17, 33, 49)(3, 23, 39, 55, 7, 26, 42, 58, 10, 30, 46, 62, 14, 20, 36, 52, 4, 22, 38, 54, 6, 25, 41, 57, 9, 28, 44, 60, 12, 19, 35, 51) L = (1, 35)(2, 39)(3, 43)(4, 37)(5, 44)(6, 33)(7, 45)(8, 42)(9, 34)(10, 48)(11, 46)(12, 40)(13, 36)(14, 47)(15, 41)(16, 38)(17, 55)(18, 58)(19, 61)(20, 49)(21, 51)(22, 50)(23, 64)(24, 62)(25, 56)(26, 63)(27, 52)(28, 59)(29, 54)(30, 53)(31, 60)(32, 57) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ S^2, A^2, B^-1 * A, A * Z * A * Z^-1, (S * Z)^2, S * A * S * B, Z^8 ] Map:: R = (1, 18, 34, 50, 2, 21, 37, 53, 5, 25, 41, 57, 9, 29, 45, 61, 13, 28, 44, 60, 12, 24, 40, 56, 8, 20, 36, 52, 4, 17, 33, 49)(3, 22, 38, 54, 6, 26, 42, 58, 10, 30, 46, 62, 14, 32, 48, 64, 16, 31, 47, 63, 15, 27, 43, 59, 11, 23, 39, 55, 7, 19, 35, 51) L = (1, 35)(2, 38)(3, 33)(4, 39)(5, 42)(6, 34)(7, 36)(8, 43)(9, 46)(10, 37)(11, 40)(12, 47)(13, 48)(14, 41)(15, 44)(16, 45)(17, 51)(18, 54)(19, 49)(20, 55)(21, 58)(22, 50)(23, 52)(24, 59)(25, 62)(26, 53)(27, 56)(28, 63)(29, 64)(30, 57)(31, 60)(32, 61) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.11 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ S^2, B * A^-1, A^4, A^4, (S * Z)^2, S * A * S * B, Z^-1 * B * Z * A^-1, Z^-2 * A^2 * Z^-2 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 25, 41, 57, 9, 32, 48, 64, 16, 27, 43, 59, 11, 20, 36, 52, 4, 17, 33, 49)(3, 23, 39, 55, 7, 30, 46, 62, 14, 28, 44, 60, 12, 21, 37, 53, 5, 24, 40, 56, 8, 31, 47, 63, 15, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 46)(7, 48)(8, 34)(9, 37)(10, 45)(11, 47)(12, 36)(13, 44)(14, 43)(15, 38)(16, 40)(17, 53)(18, 56)(19, 49)(20, 60)(21, 57)(22, 63)(23, 50)(24, 64)(25, 51)(26, 52)(27, 62)(28, 61)(29, 58)(30, 54)(31, 59)(32, 55) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.12 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 x C2 (small group id <16, 5>) Aut = (C8 x C2) : C2 (small group id <32, 42>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, A * Z^-1 * A * Z, (B * A)^2, (S * Z)^2, B * Z * B * Z^-1, S * B * S * A, Z^-1 * B * A * Z^-3 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 25, 41, 57, 9, 32, 48, 64, 16, 28, 44, 60, 12, 21, 37, 53, 5, 17, 33, 49)(3, 23, 39, 55, 7, 30, 46, 62, 14, 27, 43, 59, 11, 20, 36, 52, 4, 24, 40, 56, 8, 31, 47, 63, 15, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 33)(4, 41)(5, 42)(6, 46)(7, 34)(8, 48)(9, 36)(10, 37)(11, 45)(12, 47)(13, 43)(14, 38)(15, 44)(16, 40)(17, 52)(18, 56)(19, 57)(20, 49)(21, 59)(22, 63)(23, 64)(24, 50)(25, 51)(26, 61)(27, 53)(28, 62)(29, 58)(30, 60)(31, 54)(32, 55) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.13 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 x C2 (small group id <16, 5>) Aut = (C8 x C2) : C2 (small group id <32, 42>) |r| :: 2 Presentation :: [ S^2, A^-1 * B^-1, B * A, B^-1 * A^-1, B * A^-3, S * B * S * A, (A^-1, Z^-1), (Z, B^-1), (S * Z)^2, Z^-1 * A^2 * Z^-3 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 25, 41, 57, 9, 32, 48, 64, 16, 28, 44, 60, 12, 21, 37, 53, 5, 17, 33, 49)(3, 23, 39, 55, 7, 30, 46, 62, 14, 27, 43, 59, 11, 20, 36, 52, 4, 24, 40, 56, 8, 31, 47, 63, 15, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 41)(4, 33)(5, 42)(6, 46)(7, 48)(8, 34)(9, 36)(10, 45)(11, 37)(12, 47)(13, 43)(14, 44)(15, 38)(16, 40)(17, 51)(18, 55)(19, 57)(20, 49)(21, 58)(22, 62)(23, 64)(24, 50)(25, 52)(26, 61)(27, 53)(28, 63)(29, 59)(30, 60)(31, 54)(32, 56) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.14 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, (B * A)^2, B * Z * A * Z^-1, S * B * S * A, (S * Z)^2, Z^-1 * A * Z * B, Z^-1 * B * Z^-1 * B * Z^-2, B * A * Z^-1 * A * B * Z ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 25, 41, 57, 9, 32, 48, 64, 16, 28, 44, 60, 12, 21, 37, 53, 5, 17, 33, 49)(3, 24, 40, 56, 8, 30, 46, 62, 14, 27, 43, 59, 11, 20, 36, 52, 4, 23, 39, 55, 7, 31, 47, 63, 15, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 33)(4, 41)(5, 43)(6, 46)(7, 34)(8, 48)(9, 36)(10, 45)(11, 37)(12, 47)(13, 42)(14, 38)(15, 44)(16, 40)(17, 52)(18, 56)(19, 57)(20, 49)(21, 58)(22, 63)(23, 64)(24, 50)(25, 51)(26, 53)(27, 61)(28, 62)(29, 59)(30, 60)(31, 54)(32, 55) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.15 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, A * B * Z^-2, (S * Z)^2, S * B * S * A, B * Z * A * Z^-1, Z^8 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 28, 44, 60, 12, 32, 48, 64, 16, 31, 47, 63, 15, 27, 43, 59, 11, 21, 37, 53, 5, 17, 33, 49)(3, 25, 41, 57, 9, 20, 36, 52, 4, 23, 39, 55, 7, 30, 46, 62, 14, 24, 40, 56, 8, 29, 45, 61, 13, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 33)(4, 43)(5, 40)(6, 45)(7, 34)(8, 37)(9, 44)(10, 47)(11, 36)(12, 41)(13, 38)(14, 48)(15, 42)(16, 46)(17, 52)(18, 56)(19, 54)(20, 49)(21, 58)(22, 51)(23, 60)(24, 50)(25, 63)(26, 53)(27, 62)(28, 55)(29, 64)(30, 59)(31, 57)(32, 61) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.16 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.16 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, S * B * S * A, Z^-2 * B * A, A * Z * B * Z^-1, (S * Z)^2, Z * B * A * Z^5 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 28, 44, 60, 12, 32, 48, 64, 16, 31, 47, 63, 15, 25, 41, 57, 9, 21, 37, 53, 5, 17, 33, 49)(3, 24, 40, 56, 8, 30, 46, 62, 14, 23, 39, 55, 7, 29, 45, 61, 13, 27, 43, 59, 11, 20, 36, 52, 4, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 33)(4, 38)(5, 43)(6, 36)(7, 34)(8, 44)(9, 46)(10, 47)(11, 37)(12, 40)(13, 48)(14, 41)(15, 42)(16, 45)(17, 52)(18, 56)(19, 57)(20, 49)(21, 55)(22, 61)(23, 53)(24, 50)(25, 51)(26, 60)(27, 63)(28, 58)(29, 54)(30, 64)(31, 59)(32, 62) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.15 Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.17 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ S^2, B^-1 * A^-1, Z * B^-1 * Z^-1 * B^-1, A * B^-3, A^4, S * B * S * A, (S * Z)^2, A^-1 * Z^-1 * B * Z, Z^-1 * A * Z * B^-1, A^-2 * Z * A^-2 * Z^-1, Z^-1 * B^2 * Z^-3 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 25, 41, 57, 9, 32, 48, 64, 16, 28, 44, 60, 12, 21, 37, 53, 5, 17, 33, 49)(3, 24, 40, 56, 8, 30, 46, 62, 14, 27, 43, 59, 11, 20, 36, 52, 4, 23, 39, 55, 7, 31, 47, 63, 15, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 41)(4, 33)(5, 43)(6, 46)(7, 48)(8, 34)(9, 36)(10, 37)(11, 45)(12, 47)(13, 42)(14, 44)(15, 38)(16, 40)(17, 51)(18, 55)(19, 57)(20, 49)(21, 59)(22, 62)(23, 64)(24, 50)(25, 52)(26, 53)(27, 61)(28, 63)(29, 58)(30, 60)(31, 54)(32, 56) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.18 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A^-1 * B, S * A * S * B, (A^-1 * B^-1)^2, (S * Z)^2, Z * A * Z * B, A * Z^-1 * B * Z^-1, Z^-1 * A^-1 * Z * A * Z^-2 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 26, 42, 58, 10, 32, 48, 64, 16, 28, 44, 60, 12, 20, 36, 52, 4, 17, 33, 49)(3, 25, 41, 57, 9, 31, 47, 63, 15, 23, 39, 55, 7, 21, 37, 53, 5, 27, 43, 59, 11, 30, 46, 62, 14, 24, 40, 56, 8, 19, 35, 51) L = (1, 35)(2, 39)(3, 42)(4, 43)(5, 33)(6, 46)(7, 48)(8, 34)(9, 36)(10, 37)(11, 45)(12, 47)(13, 41)(14, 44)(15, 38)(16, 40)(17, 53)(18, 56)(19, 49)(20, 57)(21, 58)(22, 63)(23, 50)(24, 64)(25, 61)(26, 51)(27, 52)(28, 62)(29, 59)(30, 54)(31, 60)(32, 55) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.19 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = QD16 (small group id <16, 8>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ S^2, A^-1 * B^-1, (A * B^-1)^2, (S * Z)^2, Z^-1 * B * Z^-1 * A^-1, Z^-1 * A * Z^-1 * B^-1, B^2 * A^-2, S * B * S * A, Z^-1 * B * A^-1 * Z^-3 ] Map:: non-degenerate R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 29, 45, 61, 13, 26, 42, 58, 10, 32, 48, 64, 16, 28, 44, 60, 12, 21, 37, 53, 5, 17, 33, 49)(3, 25, 41, 57, 9, 31, 47, 63, 15, 23, 39, 55, 7, 20, 36, 52, 4, 27, 43, 59, 11, 30, 46, 62, 14, 24, 40, 56, 8, 19, 35, 51) L = (1, 35)(2, 39)(3, 42)(4, 33)(5, 43)(6, 46)(7, 48)(8, 34)(9, 37)(10, 36)(11, 45)(12, 47)(13, 41)(14, 44)(15, 38)(16, 40)(17, 51)(18, 55)(19, 58)(20, 49)(21, 59)(22, 62)(23, 64)(24, 50)(25, 53)(26, 52)(27, 61)(28, 63)(29, 57)(30, 60)(31, 54)(32, 56) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.20 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, (S * Z)^2, Z^-2 * A^-2, S * B * S * A, (A * Z^-1)^2, A^8 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 28, 44, 60, 12, 32, 48, 64, 16, 31, 47, 63, 15, 26, 42, 58, 10, 20, 36, 52, 4, 17, 33, 49)(3, 25, 41, 57, 9, 21, 37, 53, 5, 27, 43, 59, 11, 29, 45, 61, 13, 23, 39, 55, 7, 30, 46, 62, 14, 24, 40, 56, 8, 19, 35, 51) L = (1, 35)(2, 39)(3, 42)(4, 43)(5, 33)(6, 37)(7, 36)(8, 34)(9, 44)(10, 46)(11, 47)(12, 40)(13, 38)(14, 48)(15, 41)(16, 45)(17, 53)(18, 56)(19, 49)(20, 55)(21, 54)(22, 61)(23, 50)(24, 60)(25, 63)(26, 51)(27, 52)(28, 57)(29, 64)(30, 58)(31, 59)(32, 62) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.21 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {8, 8}) Quotient :: toric Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, B * A^-1, A^2 * Z^-2, S * A * S * B, (S * Z)^2, (Z^-1 * A^-1)^2, A^8 ] Map:: R = (1, 18, 34, 50, 2, 22, 38, 54, 6, 28, 44, 60, 12, 32, 48, 64, 16, 31, 47, 63, 15, 27, 43, 59, 11, 20, 36, 52, 4, 17, 33, 49)(3, 25, 41, 57, 9, 29, 45, 61, 13, 24, 40, 56, 8, 30, 46, 62, 14, 23, 39, 55, 7, 21, 37, 53, 5, 26, 42, 58, 10, 19, 35, 51) L = (1, 35)(2, 39)(3, 38)(4, 40)(5, 33)(6, 45)(7, 44)(8, 34)(9, 36)(10, 47)(11, 37)(12, 42)(13, 48)(14, 43)(15, 41)(16, 46)(17, 53)(18, 56)(19, 49)(20, 57)(21, 59)(22, 51)(23, 50)(24, 52)(25, 63)(26, 60)(27, 62)(28, 55)(29, 54)(30, 64)(31, 58)(32, 61) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.22 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C21 (small group id <21, 2>) Aut = C7 x S3 (small group id <42, 3>) |r| :: 2 Presentation :: [ S^2, B^-1 * A^-1, Z^3, (S * Z)^2, S * B * S * A, (B^-1, Z^-1), (A^-1, Z^-1), A^4 * B^-3 ] Map:: non-degenerate R = (1, 23, 44, 65, 2, 26, 47, 68, 5, 22, 43, 64)(3, 27, 48, 69, 6, 30, 51, 72, 9, 24, 45, 66)(4, 28, 49, 70, 7, 32, 53, 74, 11, 25, 46, 67)(8, 33, 54, 75, 12, 36, 57, 78, 15, 29, 50, 71)(10, 34, 55, 76, 13, 38, 59, 80, 17, 31, 52, 73)(14, 39, 60, 81, 18, 41, 62, 83, 20, 35, 56, 77)(16, 40, 61, 82, 19, 42, 63, 84, 21, 37, 58, 79) L = (1, 45)(2, 48)(3, 50)(4, 43)(5, 51)(6, 54)(7, 44)(8, 56)(9, 57)(10, 46)(11, 47)(12, 60)(13, 49)(14, 58)(15, 62)(16, 52)(17, 53)(18, 61)(19, 55)(20, 63)(21, 59)(22, 66)(23, 69)(24, 71)(25, 64)(26, 72)(27, 75)(28, 65)(29, 77)(30, 78)(31, 67)(32, 68)(33, 81)(34, 70)(35, 79)(36, 83)(37, 73)(38, 74)(39, 82)(40, 76)(41, 84)(42, 80) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 7 e = 42 f = 7 degree seq :: [ 12^7 ] E15.23 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^3, S * B * S * A, (S * Z)^2, (A, Z), A^3 * B * A^3 ] Map:: R = (1, 23, 44, 65, 2, 25, 46, 67, 4, 22, 43, 64)(3, 27, 48, 69, 6, 30, 51, 72, 9, 24, 45, 66)(5, 28, 49, 70, 7, 31, 52, 73, 10, 26, 47, 68)(8, 33, 54, 75, 12, 36, 57, 78, 15, 29, 50, 71)(11, 34, 55, 76, 13, 37, 58, 79, 16, 32, 53, 74)(14, 39, 60, 81, 18, 41, 62, 83, 20, 35, 56, 77)(17, 40, 61, 82, 19, 42, 63, 84, 21, 38, 59, 80) L = (1, 45)(2, 48)(3, 50)(4, 51)(5, 43)(6, 54)(7, 44)(8, 56)(9, 57)(10, 46)(11, 47)(12, 60)(13, 49)(14, 59)(15, 62)(16, 52)(17, 53)(18, 61)(19, 55)(20, 63)(21, 58)(22, 68)(23, 70)(24, 64)(25, 73)(26, 74)(27, 65)(28, 76)(29, 66)(30, 67)(31, 79)(32, 80)(33, 69)(34, 82)(35, 71)(36, 72)(37, 84)(38, 77)(39, 75)(40, 81)(41, 78)(42, 83) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 7 e = 42 f = 7 degree seq :: [ 12^7 ] E15.24 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 3}) Quotient :: toric Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Z^2, S^2, B^2, A^2, S * A * S * B, (S * Z)^2, (B * A)^3, Z * A * Z * A * B * Z * B ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 25, 49, 73)(3, 31, 55, 79, 7, 27, 51, 75)(4, 33, 57, 81, 9, 28, 52, 76)(5, 35, 59, 83, 11, 29, 53, 77)(6, 37, 61, 85, 13, 30, 54, 78)(8, 41, 65, 89, 17, 32, 56, 80)(10, 45, 69, 93, 21, 34, 58, 82)(12, 40, 64, 88, 16, 36, 60, 84)(14, 43, 67, 91, 19, 38, 62, 86)(15, 44, 68, 92, 20, 39, 63, 87)(18, 46, 70, 94, 22, 42, 66, 90)(23, 48, 72, 96, 24, 47, 71, 95) L = (1, 51)(2, 53)(3, 49)(4, 58)(5, 50)(6, 62)(7, 63)(8, 66)(9, 67)(10, 52)(11, 68)(12, 70)(13, 69)(14, 54)(15, 55)(16, 71)(17, 72)(18, 56)(19, 57)(20, 59)(21, 61)(22, 60)(23, 64)(24, 65)(25, 76)(26, 78)(27, 80)(28, 73)(29, 84)(30, 74)(31, 88)(32, 75)(33, 92)(34, 90)(35, 89)(36, 77)(37, 87)(38, 94)(39, 85)(40, 79)(41, 83)(42, 82)(43, 96)(44, 81)(45, 95)(46, 86)(47, 93)(48, 91) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.25 Transitivity :: VT+ Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.25 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 3}) Quotient :: toric Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, Z^3, B * Z^-1 * A * Z, S * A * S * B, A * Z * B * Z^-1, (S * Z)^2, (B * A * Z^-1)^2, (B * A)^3 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 29, 53, 77, 5, 25, 49, 73)(3, 31, 55, 79, 7, 33, 57, 81, 9, 27, 51, 75)(4, 34, 58, 82, 10, 36, 60, 84, 12, 28, 52, 76)(6, 37, 61, 85, 13, 39, 63, 87, 15, 30, 54, 78)(8, 41, 65, 89, 17, 43, 67, 91, 19, 32, 56, 80)(11, 45, 69, 93, 21, 38, 62, 86, 14, 35, 59, 83)(16, 44, 68, 92, 20, 46, 70, 94, 22, 40, 64, 88)(18, 48, 72, 96, 24, 47, 71, 95, 23, 42, 66, 90) L = (1, 51)(2, 54)(3, 49)(4, 59)(5, 60)(6, 50)(7, 64)(8, 66)(9, 67)(10, 68)(11, 52)(12, 53)(13, 65)(14, 71)(15, 69)(16, 55)(17, 61)(18, 56)(19, 57)(20, 58)(21, 63)(22, 72)(23, 62)(24, 70)(25, 76)(26, 79)(27, 80)(28, 73)(29, 85)(30, 86)(31, 74)(32, 75)(33, 92)(34, 93)(35, 90)(36, 94)(37, 77)(38, 78)(39, 91)(40, 95)(41, 96)(42, 83)(43, 87)(44, 81)(45, 82)(46, 84)(47, 88)(48, 89) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.24 Transitivity :: VT+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.26 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^14 ] Map:: R = (1, 30, 58, 86, 2, 29, 57, 85)(3, 33, 61, 89, 5, 31, 59, 87)(4, 34, 62, 90, 6, 32, 60, 88)(7, 37, 65, 93, 9, 35, 63, 91)(8, 38, 66, 94, 10, 36, 64, 92)(11, 41, 69, 97, 13, 39, 67, 95)(12, 48, 76, 104, 20, 40, 68, 96)(14, 50, 78, 106, 22, 42, 70, 98)(15, 51, 79, 107, 23, 43, 71, 99)(16, 52, 80, 108, 24, 44, 72, 100)(17, 53, 81, 109, 25, 45, 73, 101)(18, 54, 82, 110, 26, 46, 74, 102)(19, 55, 83, 111, 27, 47, 75, 103)(21, 56, 84, 112, 28, 49, 77, 105) L = (1, 59)(2, 60)(3, 57)(4, 58)(5, 63)(6, 64)(7, 61)(8, 62)(9, 67)(10, 68)(11, 65)(12, 66)(13, 70)(14, 69)(15, 76)(16, 78)(17, 79)(18, 80)(19, 81)(20, 71)(21, 82)(22, 72)(23, 73)(24, 74)(25, 75)(26, 77)(27, 84)(28, 83)(29, 87)(30, 88)(31, 85)(32, 86)(33, 91)(34, 92)(35, 89)(36, 90)(37, 95)(38, 96)(39, 93)(40, 94)(41, 98)(42, 97)(43, 104)(44, 106)(45, 107)(46, 108)(47, 109)(48, 99)(49, 110)(50, 100)(51, 101)(52, 102)(53, 103)(54, 105)(55, 112)(56, 111) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 14 e = 56 f = 14 degree seq :: [ 8^14 ] E15.27 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * B * S * A, (S * Z)^2, A * Z * B^-1 * Z, B^7 * A^-7 ] Map:: non-degenerate R = (1, 30, 58, 86, 2, 29, 57, 85)(3, 34, 62, 90, 6, 31, 59, 87)(4, 33, 61, 89, 5, 32, 60, 88)(7, 38, 66, 94, 10, 35, 63, 91)(8, 37, 65, 93, 9, 36, 64, 92)(11, 42, 70, 98, 14, 39, 67, 95)(12, 41, 69, 97, 13, 40, 68, 96)(15, 46, 74, 102, 18, 43, 71, 99)(16, 45, 73, 101, 17, 44, 72, 100)(19, 50, 78, 106, 22, 47, 75, 103)(20, 49, 77, 105, 21, 48, 76, 104)(23, 54, 82, 110, 26, 51, 79, 107)(24, 53, 81, 109, 25, 52, 80, 108)(27, 56, 84, 112, 28, 55, 83, 111) L = (1, 59)(2, 61)(3, 63)(4, 57)(5, 65)(6, 58)(7, 67)(8, 60)(9, 69)(10, 62)(11, 71)(12, 64)(13, 73)(14, 66)(15, 75)(16, 68)(17, 77)(18, 70)(19, 79)(20, 72)(21, 81)(22, 74)(23, 83)(24, 76)(25, 84)(26, 78)(27, 80)(28, 82)(29, 87)(30, 89)(31, 91)(32, 85)(33, 93)(34, 86)(35, 95)(36, 88)(37, 97)(38, 90)(39, 99)(40, 92)(41, 101)(42, 94)(43, 103)(44, 96)(45, 105)(46, 98)(47, 107)(48, 100)(49, 109)(50, 102)(51, 111)(52, 104)(53, 112)(54, 106)(55, 108)(56, 110) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 14 e = 56 f = 14 degree seq :: [ 8^14 ] E15.28 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2}) Quotient :: toric Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ Z^2, S^2, S * B * S * A, (S * Z)^2, (B^-1 * A^-1)^2, A * Z * A^-1 * B * A, Z * A^2 * B^2, A^-1 * B^-2 * Z * B, (Z * B * A)^2, A^3 * B^-1 * A * B^-2, A^7, A^2 * B^-3 * A * B^-1 ] Map:: polytopal non-degenerate R = (1, 58, 114, 170, 2, 57, 113, 169)(3, 67, 123, 179, 11, 59, 115, 171)(4, 71, 127, 183, 15, 60, 116, 172)(5, 75, 131, 187, 19, 61, 117, 173)(6, 78, 134, 190, 22, 62, 118, 174)(7, 81, 137, 193, 25, 63, 119, 175)(8, 83, 139, 195, 27, 64, 120, 176)(9, 85, 141, 197, 29, 65, 121, 177)(10, 86, 142, 198, 30, 66, 122, 178)(12, 79, 135, 191, 23, 68, 124, 180)(13, 82, 138, 194, 26, 69, 125, 181)(14, 80, 136, 192, 24, 70, 126, 182)(16, 84, 140, 196, 28, 72, 128, 184)(17, 77, 133, 189, 21, 73, 129, 185)(18, 76, 132, 188, 20, 74, 130, 186)(31, 106, 162, 218, 50, 87, 143, 199)(32, 112, 168, 224, 56, 88, 144, 200)(33, 107, 163, 219, 51, 89, 145, 201)(34, 92, 148, 204, 36, 90, 146, 202)(35, 93, 149, 205, 37, 91, 147, 203)(38, 101, 157, 213, 45, 94, 150, 206)(39, 100, 156, 212, 44, 95, 151, 207)(40, 99, 155, 211, 43, 96, 152, 208)(41, 98, 154, 210, 42, 97, 153, 209)(46, 105, 161, 217, 49, 102, 158, 214)(47, 104, 160, 216, 48, 103, 159, 215)(52, 110, 166, 222, 54, 108, 164, 220)(53, 111, 167, 223, 55, 109, 165, 221) L = (1, 115)(2, 119)(3, 124)(4, 128)(5, 113)(6, 135)(7, 136)(8, 140)(9, 114)(10, 126)(11, 143)(12, 146)(13, 118)(14, 148)(15, 125)(16, 123)(17, 120)(18, 116)(19, 144)(20, 121)(21, 117)(22, 162)(23, 164)(24, 166)(25, 163)(26, 122)(27, 138)(28, 137)(29, 168)(30, 145)(31, 149)(32, 134)(33, 147)(34, 161)(35, 158)(36, 152)(37, 155)(38, 139)(39, 127)(40, 150)(41, 129)(42, 151)(43, 130)(44, 141)(45, 131)(46, 156)(47, 132)(48, 157)(49, 133)(50, 167)(51, 165)(52, 154)(53, 153)(54, 159)(55, 160)(56, 142)(57, 174)(58, 178)(59, 182)(60, 169)(61, 184)(62, 192)(63, 191)(64, 170)(65, 196)(66, 180)(67, 201)(68, 203)(69, 171)(70, 205)(71, 200)(72, 190)(73, 172)(74, 176)(75, 181)(76, 173)(77, 177)(78, 219)(79, 221)(80, 223)(81, 218)(82, 175)(83, 224)(84, 198)(85, 194)(86, 199)(87, 204)(88, 179)(89, 202)(90, 209)(91, 210)(92, 216)(93, 215)(94, 183)(95, 195)(96, 185)(97, 206)(98, 186)(99, 207)(100, 187)(101, 197)(102, 188)(103, 212)(104, 189)(105, 213)(106, 222)(107, 220)(108, 214)(109, 217)(110, 211)(111, 208)(112, 193) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.29 Transitivity :: VT+ Graph:: simple v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.29 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2}) Quotient :: toric Aut^+ = (C2 x C2 x C2) : C7 (small group id <56, 11>) Aut = C2 x ((C2 x C2 x C2) : C7) (small group id <112, 41>) |r| :: 2 Presentation :: [ Z, S^2, S * B * S * A, (S * Z)^2, (A^-1 * B^-1)^2, A^7, A^2 * B^-1 * A * B^-3, A^2 * B^-2 * A * B^-1 * A, B^7, (Z^-1 * A^2 * B^2)^2 ] Map:: polytopal non-degenerate R = (1, 57, 113, 169)(2, 58, 114, 170)(3, 59, 115, 171)(4, 60, 116, 172)(5, 61, 117, 173)(6, 62, 118, 174)(7, 63, 119, 175)(8, 64, 120, 176)(9, 65, 121, 177)(10, 66, 122, 178)(11, 67, 123, 179)(12, 68, 124, 180)(13, 69, 125, 181)(14, 70, 126, 182)(15, 71, 127, 183)(16, 72, 128, 184)(17, 73, 129, 185)(18, 74, 130, 186)(19, 75, 131, 187)(20, 76, 132, 188)(21, 77, 133, 189)(22, 78, 134, 190)(23, 79, 135, 191)(24, 80, 136, 192)(25, 81, 137, 193)(26, 82, 138, 194)(27, 83, 139, 195)(28, 84, 140, 196)(29, 85, 141, 197)(30, 86, 142, 198)(31, 87, 143, 199)(32, 88, 144, 200)(33, 89, 145, 201)(34, 90, 146, 202)(35, 91, 147, 203)(36, 92, 148, 204)(37, 93, 149, 205)(38, 94, 150, 206)(39, 95, 151, 207)(40, 96, 152, 208)(41, 97, 153, 209)(42, 98, 154, 210)(43, 99, 155, 211)(44, 100, 156, 212)(45, 101, 157, 213)(46, 102, 158, 214)(47, 103, 159, 215)(48, 104, 160, 216)(49, 105, 161, 217)(50, 106, 162, 218)(51, 107, 163, 219)(52, 108, 164, 220)(53, 109, 165, 221)(54, 110, 166, 222)(55, 111, 167, 223)(56, 112, 168, 224) L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 126)(6, 128)(7, 117)(8, 133)(9, 135)(10, 137)(11, 115)(12, 142)(13, 116)(14, 147)(15, 150)(16, 146)(17, 120)(18, 138)(19, 155)(20, 119)(21, 139)(22, 145)(23, 161)(24, 152)(25, 154)(26, 157)(27, 122)(28, 156)(29, 123)(30, 163)(31, 159)(32, 124)(33, 158)(34, 125)(35, 143)(36, 127)(37, 141)(38, 140)(39, 144)(40, 130)(41, 148)(42, 129)(43, 136)(44, 166)(45, 131)(46, 165)(47, 132)(48, 134)(49, 149)(50, 151)(51, 167)(52, 160)(53, 168)(54, 153)(55, 162)(56, 164)(57, 173)(58, 176)(59, 169)(60, 177)(61, 183)(62, 186)(63, 170)(64, 190)(65, 192)(66, 171)(67, 193)(68, 172)(69, 198)(70, 205)(71, 207)(72, 196)(73, 174)(74, 200)(75, 175)(76, 211)(77, 199)(78, 197)(79, 218)(80, 216)(81, 219)(82, 178)(83, 213)(84, 179)(85, 212)(86, 210)(87, 180)(88, 215)(89, 181)(90, 214)(91, 195)(92, 182)(93, 201)(94, 202)(95, 194)(96, 184)(97, 185)(98, 204)(99, 191)(100, 187)(101, 222)(102, 188)(103, 221)(104, 189)(105, 203)(106, 206)(107, 220)(108, 208)(109, 209)(110, 224)(111, 217)(112, 223) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.28 Transitivity :: VT+ Graph:: simple v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.30 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^5 * Y2, (Y3^-1 * Y1^-1)^16, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 12, 28, 11, 27, 5, 21, 8, 24, 14, 30, 16, 32, 15, 31, 9, 25, 3, 19, 7, 23, 13, 29, 10, 26, 4, 20)(33, 49, 35, 51, 40, 56, 34, 50, 39, 55, 46, 62, 38, 54, 45, 61, 48, 64, 44, 60, 42, 58, 47, 63, 43, 59, 36, 52, 41, 57, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.31 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-5, (Y3 * Y2^-1)^16, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 12, 28, 10, 26, 3, 19, 7, 23, 13, 29, 16, 32, 15, 31, 9, 25, 5, 21, 8, 24, 14, 30, 11, 27, 4, 20)(33, 49, 35, 51, 41, 57, 36, 52, 42, 58, 47, 63, 43, 59, 44, 60, 48, 64, 46, 62, 38, 54, 45, 61, 40, 56, 34, 50, 39, 55, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.32 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^-1 * Y2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^-1 * Y1^3 * Y3, Y1 * Y3 * Y1^2 * Y2^-1, Y2 * Y1^2 * Y2 * Y3 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 11, 27, 16, 32, 6, 22, 10, 26, 13, 29, 4, 20, 9, 25, 12, 28, 3, 19, 8, 24, 14, 30, 15, 31, 5, 21)(33, 49, 35, 51, 42, 58, 34, 50, 40, 56, 45, 61, 39, 55, 46, 62, 36, 52, 43, 59, 47, 63, 41, 57, 48, 64, 37, 53, 44, 60, 38, 54) L = (1, 36)(2, 41)(3, 43)(4, 33)(5, 45)(6, 46)(7, 44)(8, 48)(9, 34)(10, 47)(11, 35)(12, 39)(13, 37)(14, 38)(15, 42)(16, 40)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.33 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1 * Y2^-2, (Y1^-1, Y2), (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y2^-1 * Y1^2 * Y3 * Y2^-1, Y1^2 * Y2 * Y1 * Y3 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 15, 31, 13, 29, 3, 19, 8, 24, 14, 30, 4, 20, 9, 25, 11, 27, 6, 22, 10, 26, 12, 28, 16, 32, 5, 21)(33, 49, 35, 51, 43, 59, 37, 53, 45, 61, 41, 57, 48, 64, 47, 63, 36, 52, 44, 60, 39, 55, 46, 62, 42, 58, 34, 50, 40, 56, 38, 54) L = (1, 36)(2, 41)(3, 44)(4, 33)(5, 46)(6, 47)(7, 43)(8, 48)(9, 34)(10, 45)(11, 39)(12, 35)(13, 42)(14, 37)(15, 38)(16, 40)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.34 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y1, Y1 * Y3 * Y2, Y1^-1 * Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^4, Y1^4 * Y3^-1 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 14, 30, 4, 20, 6, 22, 9, 25, 12, 28, 13, 29, 15, 31, 11, 27, 3, 19, 7, 23, 10, 26, 16, 32, 5, 21)(33, 49, 35, 51, 41, 57, 34, 50, 39, 55, 44, 60, 40, 56, 42, 58, 45, 61, 46, 62, 48, 64, 47, 63, 36, 52, 37, 53, 43, 59, 38, 54) L = (1, 36)(2, 38)(3, 37)(4, 45)(5, 46)(6, 47)(7, 33)(8, 41)(9, 43)(10, 34)(11, 48)(12, 35)(13, 39)(14, 44)(15, 42)(16, 40)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.35 Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.35 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y1 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1 * Y2^-3, (R * Y2)^2, Y1^2 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 15, 31, 7, 23, 6, 22, 10, 26, 11, 27, 13, 29, 16, 32, 12, 28, 3, 19, 4, 20, 9, 25, 14, 30, 5, 21)(33, 49, 35, 51, 42, 58, 34, 50, 36, 52, 43, 59, 40, 56, 41, 57, 45, 61, 47, 63, 46, 62, 48, 64, 39, 55, 37, 53, 44, 60, 38, 54) L = (1, 36)(2, 41)(3, 43)(4, 45)(5, 35)(6, 34)(7, 33)(8, 46)(9, 48)(10, 40)(11, 47)(12, 42)(13, 39)(14, 44)(15, 37)(16, 38)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.34 Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.36 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2, Y2^2 * Y3, Y1 * Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-2 * Y2 * Y1^-3, Y3^8, (Y3^-1 * Y1^-1)^16 ] Map:: non-degenerate R = (1, 17, 2, 18, 8, 24, 14, 30, 11, 27, 3, 19, 4, 20, 9, 25, 15, 31, 13, 29, 7, 23, 6, 22, 10, 26, 16, 32, 12, 28, 5, 21)(33, 49, 35, 51, 39, 55, 37, 53, 43, 59, 45, 61, 44, 60, 46, 62, 47, 63, 48, 64, 40, 56, 41, 57, 42, 58, 34, 50, 36, 52, 38, 54) L = (1, 36)(2, 41)(3, 38)(4, 42)(5, 35)(6, 34)(7, 33)(8, 47)(9, 48)(10, 40)(11, 39)(12, 43)(13, 37)(14, 45)(15, 44)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.37 Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.37 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 16, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, Y2^2 * Y3, (Y2^-1, Y3), (Y2^-1, Y1), (Y1^-1 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3^-3, (Y2 * Y1)^8 ] Map:: non-degenerate R = (1, 17, 2, 18, 7, 23, 10, 26, 16, 32, 14, 30, 15, 31, 6, 22, 9, 25, 3, 19, 8, 24, 11, 27, 12, 28, 13, 29, 4, 20, 5, 21)(33, 49, 35, 51, 39, 55, 43, 59, 48, 64, 45, 61, 47, 63, 37, 53, 41, 57, 34, 50, 40, 56, 42, 58, 44, 60, 46, 62, 36, 52, 38, 54) L = (1, 36)(2, 37)(3, 38)(4, 44)(5, 45)(6, 46)(7, 33)(8, 41)(9, 47)(10, 34)(11, 35)(12, 40)(13, 43)(14, 42)(15, 48)(16, 39)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.36 Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (Y3^-1, Y1^-1), (R * Y1)^2, R * Y2 * R * Y3^-1, (Y2^-1, Y1^-1), Y3^-3 * Y1^2, Y2^3 * Y1^2, Y1^6, Y1^2 * Y3 * Y1^2 * Y2^-2, Y1^-12, (Y3 * Y2^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 14, 32, 13, 31, 5, 23)(3, 21, 7, 25, 11, 29, 16, 34, 18, 36, 10, 28)(4, 22, 8, 26, 15, 33, 17, 35, 9, 27, 12, 30)(37, 55, 39, 57, 45, 63, 49, 67, 54, 72, 51, 69, 42, 60, 47, 65, 40, 58)(38, 56, 43, 61, 48, 66, 41, 59, 46, 64, 53, 71, 50, 68, 52, 70, 44, 62) L = (1, 40)(2, 44)(3, 37)(4, 47)(5, 48)(6, 51)(7, 38)(8, 52)(9, 39)(10, 41)(11, 42)(12, 43)(13, 45)(14, 53)(15, 54)(16, 50)(17, 46)(18, 49)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E15.51 Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 12^3, 18^2 ] E15.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), Y2^-3 * Y1^2, Y3 * Y1 * Y3 * Y1 * Y2^-1, Y1^6, Y1^6, Y1^2 * Y2 * Y1^2 * Y3^-2, (Y3 * Y2^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 14, 32, 13, 31, 5, 23)(3, 21, 7, 25, 15, 33, 17, 35, 11, 29, 10, 28)(4, 22, 8, 26, 9, 27, 16, 34, 18, 36, 12, 30)(37, 55, 39, 57, 45, 63, 42, 60, 51, 69, 54, 72, 49, 67, 47, 65, 40, 58)(38, 56, 43, 61, 52, 70, 50, 68, 53, 71, 48, 66, 41, 59, 46, 64, 44, 62) L = (1, 40)(2, 44)(3, 37)(4, 47)(5, 48)(6, 45)(7, 38)(8, 46)(9, 39)(10, 41)(11, 49)(12, 53)(13, 54)(14, 52)(15, 42)(16, 43)(17, 50)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E15.50 Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 12^3, 18^2 ] E15.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y3 * Y1^2 * Y2, (Y1, Y3^-1), Y1 * Y2 * Y1 * Y3, Y1^-2 * Y2^-1 * Y3^-1, (R * Y1)^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-3 * Y1 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 18, 36, 13, 31, 5, 23)(3, 21, 9, 27, 7, 25, 12, 30, 15, 33, 14, 32)(4, 22, 10, 28, 6, 24, 11, 29, 17, 35, 16, 34)(37, 55, 39, 57, 40, 58, 49, 67, 51, 69, 53, 71, 44, 62, 43, 61, 42, 60)(38, 56, 45, 63, 46, 64, 41, 59, 50, 68, 52, 70, 54, 72, 48, 66, 47, 65) L = (1, 40)(2, 46)(3, 49)(4, 51)(5, 52)(6, 39)(7, 37)(8, 42)(9, 41)(10, 50)(11, 45)(12, 38)(13, 53)(14, 54)(15, 44)(16, 48)(17, 43)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E15.52 Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 12^3, 18^2 ] E15.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-2, (Y1^-1, Y3^-1), Y2^-1 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y1^2, (R * Y2)^2, Y3^3 * Y1^2, (Y3 * Y2)^3 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 18, 36, 14, 32, 5, 23)(3, 21, 9, 27, 13, 31, 16, 34, 7, 25, 12, 30)(4, 22, 10, 28, 17, 35, 15, 33, 6, 24, 11, 29)(37, 55, 39, 57, 40, 58, 44, 62, 49, 67, 53, 71, 50, 68, 43, 61, 42, 60)(38, 56, 45, 63, 46, 64, 54, 72, 52, 70, 51, 69, 41, 59, 48, 66, 47, 65) L = (1, 40)(2, 46)(3, 44)(4, 49)(5, 47)(6, 39)(7, 37)(8, 53)(9, 54)(10, 52)(11, 45)(12, 38)(13, 50)(14, 42)(15, 48)(16, 41)(17, 43)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E15.48 Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 12^3, 18^2 ] E15.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1^2 * Y2^-1 * Y3^-1, (Y1^-1, Y2^-1), (Y3, Y1^-1), Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-3 * Y1^-2, (Y3 * Y2)^3 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 18, 36, 14, 32, 5, 23)(3, 21, 9, 27, 17, 35, 16, 34, 7, 25, 12, 30)(4, 22, 10, 28, 13, 31, 15, 33, 6, 24, 11, 29)(37, 55, 39, 57, 49, 67, 50, 68, 43, 61, 40, 58, 44, 62, 53, 71, 42, 60)(38, 56, 45, 63, 51, 69, 41, 59, 48, 66, 46, 64, 54, 72, 52, 70, 47, 65) L = (1, 40)(2, 46)(3, 44)(4, 39)(5, 47)(6, 43)(7, 37)(8, 49)(9, 54)(10, 45)(11, 48)(12, 38)(13, 53)(14, 42)(15, 52)(16, 41)(17, 50)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E15.53 Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 12^3, 18^2 ] E15.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, (Y1^-1, Y2), Y3 * Y1 * Y2 * Y1, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^3 * Y3 * Y2, Y1 * Y2^-1 * Y1 * Y2^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 18, 36, 14, 32, 5, 23)(3, 21, 9, 27, 7, 25, 12, 30, 17, 35, 15, 33)(4, 22, 10, 28, 6, 24, 11, 29, 13, 31, 16, 34)(37, 55, 39, 57, 49, 67, 44, 62, 43, 61, 40, 58, 50, 68, 53, 71, 42, 60)(38, 56, 45, 63, 52, 70, 54, 72, 48, 66, 46, 64, 41, 59, 51, 69, 47, 65) L = (1, 40)(2, 46)(3, 50)(4, 39)(5, 52)(6, 43)(7, 37)(8, 42)(9, 41)(10, 45)(11, 48)(12, 38)(13, 53)(14, 49)(15, 54)(16, 51)(17, 44)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) } Outer automorphisms :: reflexible Dual of E15.49 Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 12^3, 18^2 ] E15.44 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1, Y1 * Y2^2, (Y2, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^-4, (Y3^-1 * Y1^-1)^6, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 12, 30, 3, 21, 6, 24, 10, 28, 15, 33, 5, 23)(4, 22, 9, 27, 17, 35, 13, 31, 11, 29, 14, 32, 18, 36, 16, 34, 7, 25)(37, 55, 39, 57, 41, 59, 48, 66, 51, 69, 44, 62, 46, 64, 38, 56, 42, 60)(40, 58, 47, 65, 43, 61, 49, 67, 52, 70, 53, 71, 54, 72, 45, 63, 50, 68) L = (1, 40)(2, 45)(3, 47)(4, 38)(5, 43)(6, 50)(7, 37)(8, 53)(9, 44)(10, 54)(11, 42)(12, 49)(13, 39)(14, 46)(15, 52)(16, 41)(17, 48)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E15.46 Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 18^4 ] E15.45 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^2, (Y3^-1 * Y2^-1)^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-2 * Y2^2, Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 9, 27, 15, 33, 11, 29, 13, 31, 3, 21, 5, 23)(4, 22, 8, 26, 17, 35, 14, 32, 18, 36, 7, 25, 10, 28, 12, 30, 16, 34)(37, 55, 39, 57, 47, 65, 45, 63, 38, 56, 41, 59, 49, 67, 51, 69, 42, 60)(40, 58, 48, 66, 43, 61, 50, 68, 44, 62, 52, 70, 46, 64, 54, 72, 53, 71) L = (1, 40)(2, 44)(3, 48)(4, 51)(5, 52)(6, 53)(7, 37)(8, 47)(9, 50)(10, 38)(11, 43)(12, 42)(13, 46)(14, 39)(15, 54)(16, 45)(17, 49)(18, 41)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E15.47 Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 18^4 ] E15.46 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y2^-2, Y1^-1 * Y2 * Y1^-2, Y3 * Y1^-1 * Y2^-2, Y1 * Y3^2 * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3^-2 * Y2^-1, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (R * Y3)^2, Y1 * Y3^-2 * Y1 * Y3^-1 * Y1, Y3 * Y1^-1 * Y2^4 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 3, 21, 9, 27, 16, 34, 13, 31, 4, 22, 10, 28, 17, 35, 14, 32, 7, 25, 12, 30, 18, 36, 15, 33, 6, 24, 11, 29, 5, 23)(37, 55, 39, 57, 49, 67, 53, 71, 48, 66, 42, 60)(38, 56, 45, 63, 40, 58, 50, 68, 54, 72, 47, 65)(41, 59, 44, 62, 52, 70, 46, 64, 43, 61, 51, 69) L = (1, 40)(2, 46)(3, 50)(4, 51)(5, 49)(6, 45)(7, 37)(8, 53)(9, 43)(10, 42)(11, 52)(12, 38)(13, 54)(14, 41)(15, 39)(16, 48)(17, 47)(18, 44)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^12 ), ( 18^36 ) } Outer automorphisms :: reflexible Dual of E15.44 Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.47 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y2^-1 * Y1^-3, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y3 * Y2^-1)^9, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 5, 23, 8, 26, 12, 30, 11, 29, 14, 32, 17, 35, 15, 33, 18, 36, 16, 34, 9, 27, 13, 31, 10, 28, 3, 21, 7, 25, 4, 22)(37, 55, 39, 57, 45, 63, 51, 69, 47, 65, 41, 59)(38, 56, 43, 61, 49, 67, 54, 72, 50, 68, 44, 62)(40, 58, 46, 64, 52, 70, 53, 71, 48, 66, 42, 60) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 41)(7, 40)(8, 48)(9, 49)(10, 39)(11, 50)(12, 47)(13, 46)(14, 53)(15, 54)(16, 45)(17, 51)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^12 ), ( 18^36 ) } Outer automorphisms :: reflexible Dual of E15.45 Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.48 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2, Y2^2 * Y3, (Y1^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y2^-1), Y1 * Y3^-4, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 16, 34, 12, 30, 13, 31, 4, 22, 5, 23)(3, 21, 8, 26, 11, 29, 17, 35, 18, 36, 14, 32, 15, 33, 6, 24, 9, 27)(37, 55, 39, 57, 43, 61, 47, 65, 52, 70, 54, 72, 49, 67, 51, 69, 41, 59, 45, 63, 38, 56, 44, 62, 46, 64, 53, 71, 48, 66, 50, 68, 40, 58, 42, 60) L = (1, 40)(2, 41)(3, 42)(4, 48)(5, 49)(6, 50)(7, 37)(8, 45)(9, 51)(10, 38)(11, 39)(12, 46)(13, 52)(14, 53)(15, 54)(16, 43)(17, 44)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E15.41 Graph:: bipartite v = 3 e = 36 f = 5 degree seq :: [ 18^2, 36 ] E15.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^9, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 10, 28, 14, 32, 17, 35, 13, 31, 9, 27, 4, 22)(3, 21, 5, 23, 7, 25, 11, 29, 15, 33, 18, 36, 16, 34, 12, 30, 8, 26)(37, 55, 39, 57, 40, 58, 44, 62, 45, 63, 48, 66, 49, 67, 52, 70, 53, 71, 54, 72, 50, 68, 51, 69, 46, 64, 47, 65, 42, 60, 43, 61, 38, 56, 41, 59) L = (1, 38)(2, 42)(3, 41)(4, 37)(5, 43)(6, 46)(7, 47)(8, 39)(9, 40)(10, 50)(11, 51)(12, 44)(13, 45)(14, 53)(15, 54)(16, 48)(17, 49)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E15.43 Graph:: bipartite v = 3 e = 36 f = 5 degree seq :: [ 18^2, 36 ] E15.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y3^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-4 * Y3 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 13, 31, 4, 22, 7, 25, 11, 29, 14, 32, 5, 23)(3, 21, 9, 27, 16, 34, 15, 33, 6, 24, 10, 28, 17, 35, 18, 36, 12, 30)(37, 55, 39, 57, 43, 61, 46, 64, 38, 56, 45, 63, 47, 65, 53, 71, 44, 62, 52, 70, 50, 68, 54, 72, 49, 67, 51, 69, 41, 59, 48, 66, 40, 58, 42, 60) L = (1, 40)(2, 43)(3, 42)(4, 41)(5, 49)(6, 48)(7, 37)(8, 47)(9, 46)(10, 39)(11, 38)(12, 51)(13, 50)(14, 44)(15, 54)(16, 53)(17, 45)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E15.39 Graph:: bipartite v = 3 e = 36 f = 5 degree seq :: [ 18^2, 36 ] E15.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y2^2 * Y1^-2, (Y3^-1, Y2^-1), (Y2, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^-4 * Y3, Y3 * Y2 * Y1^-1 * Y3 * Y2, Y1^18 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 14, 32, 4, 22, 7, 25, 11, 29, 16, 34, 5, 23)(3, 21, 9, 27, 15, 33, 18, 36, 12, 30, 13, 31, 17, 35, 6, 24, 10, 28)(37, 55, 39, 57, 44, 62, 51, 69, 40, 58, 48, 66, 47, 65, 53, 71, 41, 59, 46, 64, 38, 56, 45, 63, 50, 68, 54, 72, 43, 61, 49, 67, 52, 70, 42, 60) L = (1, 40)(2, 43)(3, 48)(4, 41)(5, 50)(6, 51)(7, 37)(8, 47)(9, 49)(10, 54)(11, 38)(12, 46)(13, 39)(14, 52)(15, 53)(16, 44)(17, 45)(18, 42)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E15.38 Graph:: bipartite v = 3 e = 36 f = 5 degree seq :: [ 18^2, 36 ] E15.52 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1 * Y3 * Y1, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3^4 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 9, 27, 15, 33, 12, 30, 13, 31, 4, 22, 5, 23)(3, 21, 6, 24, 8, 26, 14, 32, 16, 34, 17, 35, 18, 36, 10, 28, 11, 29)(37, 55, 39, 57, 41, 59, 47, 65, 40, 58, 46, 64, 49, 67, 54, 72, 48, 66, 53, 71, 51, 69, 52, 70, 45, 63, 50, 68, 43, 61, 44, 62, 38, 56, 42, 60) L = (1, 40)(2, 41)(3, 46)(4, 48)(5, 49)(6, 47)(7, 37)(8, 39)(9, 38)(10, 53)(11, 54)(12, 45)(13, 51)(14, 42)(15, 43)(16, 44)(17, 50)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E15.40 Graph:: bipartite v = 3 e = 36 f = 5 degree seq :: [ 18^2, 36 ] E15.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (Y2, Y1), (R * Y3)^2, Y2^-4 * Y1, Y1 * Y2 * Y1^3 * Y2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 14, 32, 13, 31, 9, 27, 17, 35, 11, 29, 4, 22)(3, 21, 7, 25, 15, 33, 12, 30, 5, 23, 8, 26, 16, 34, 18, 36, 10, 28)(37, 55, 39, 57, 45, 63, 44, 62, 38, 56, 43, 61, 53, 71, 52, 70, 42, 60, 51, 69, 47, 65, 54, 72, 50, 68, 48, 66, 40, 58, 46, 64, 49, 67, 41, 59) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 45)(14, 49)(15, 48)(16, 54)(17, 47)(18, 46)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) } Outer automorphisms :: reflexible Dual of E15.42 Graph:: bipartite v = 3 e = 36 f = 5 degree seq :: [ 18^2, 36 ] E15.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 12, 30, 10, 28, 4, 22)(3, 21, 7, 25, 13, 31, 17, 35, 15, 33, 9, 27)(5, 23, 8, 26, 14, 32, 18, 36, 16, 34, 11, 29)(37, 55, 39, 57, 44, 62, 38, 56, 43, 61, 50, 68, 42, 60, 49, 67, 54, 72, 48, 66, 53, 71, 52, 70, 46, 64, 51, 69, 47, 65, 40, 58, 45, 63, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 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, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 6, 24, 12, 30, 11, 29, 4, 22)(3, 21, 7, 25, 13, 31, 17, 35, 16, 34, 10, 28)(5, 23, 8, 26, 14, 32, 18, 36, 15, 33, 9, 27)(37, 55, 39, 57, 45, 63, 40, 58, 46, 64, 51, 69, 47, 65, 52, 70, 54, 72, 48, 66, 53, 71, 50, 68, 42, 60, 49, 67, 44, 62, 38, 56, 43, 61, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 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, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, Y3^3, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (Y3 * Y1^-1)^2, (Y2, Y3^-1) ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 4, 22, 5, 23)(3, 21, 8, 26, 13, 31, 17, 35, 11, 29, 12, 30)(6, 24, 9, 27, 16, 34, 18, 36, 14, 32, 15, 33)(37, 55, 39, 57, 45, 63, 38, 56, 44, 62, 52, 70, 43, 61, 49, 67, 54, 72, 46, 64, 53, 71, 50, 68, 40, 58, 47, 65, 51, 69, 41, 59, 48, 66, 42, 60) L = (1, 40)(2, 41)(3, 47)(4, 43)(5, 46)(6, 50)(7, 37)(8, 48)(9, 51)(10, 38)(11, 49)(12, 53)(13, 39)(14, 52)(15, 54)(16, 42)(17, 44)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 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, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E15.57 Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.57 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3 * Y1, (Y2, Y3), Y1^-1 * Y2^-3, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 4, 22, 5, 23)(3, 21, 8, 26, 14, 32, 17, 35, 12, 30, 13, 31)(6, 24, 9, 27, 16, 34, 18, 36, 15, 33, 11, 29)(37, 55, 39, 57, 47, 65, 41, 59, 49, 67, 51, 69, 40, 58, 48, 66, 54, 72, 46, 64, 53, 71, 52, 70, 43, 61, 50, 68, 45, 63, 38, 56, 44, 62, 42, 60) L = (1, 40)(2, 41)(3, 48)(4, 43)(5, 46)(6, 51)(7, 37)(8, 49)(9, 47)(10, 38)(11, 54)(12, 50)(13, 53)(14, 39)(15, 52)(16, 42)(17, 44)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 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, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E15.56 Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.58 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, (Y2^-1, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^4, Y1^-2 * Y3^-1 * Y2^2, Y1^-2 * Y3 * Y2^-2, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^5, (Y3 * Y2^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 17, 37, 14, 34)(4, 24, 10, 30, 13, 33, 16, 36)(6, 26, 11, 31, 15, 35, 18, 38)(7, 27, 12, 32, 20, 40, 19, 39)(41, 61, 43, 63, 53, 73, 60, 80, 46, 66)(42, 62, 49, 69, 56, 76, 59, 79, 51, 71)(44, 64, 47, 67, 55, 75, 48, 68, 57, 77)(45, 65, 54, 74, 50, 70, 52, 72, 58, 78) L = (1, 44)(2, 50)(3, 47)(4, 46)(5, 56)(6, 57)(7, 41)(8, 53)(9, 52)(10, 51)(11, 54)(12, 42)(13, 55)(14, 59)(15, 43)(16, 58)(17, 60)(18, 49)(19, 45)(20, 48)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40, 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E15.67 Graph:: bipartite v = 9 e = 40 f = 3 degree seq :: [ 8^5, 10^4 ] E15.59 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, (Y1, Y3), (R * Y2)^2, Y1^4, Y1^-2 * Y3 * Y2^2, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1, Y1^-2 * Y3^-1 * Y2^-2, Y2^5, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 20, 40, 15, 35)(4, 24, 10, 30, 19, 39, 16, 36)(6, 26, 11, 31, 14, 34, 17, 37)(7, 27, 12, 32, 13, 33, 18, 38)(41, 61, 43, 63, 53, 73, 59, 79, 46, 66)(42, 62, 49, 69, 58, 78, 56, 76, 51, 71)(44, 64, 54, 74, 48, 68, 60, 80, 47, 67)(45, 65, 55, 75, 52, 72, 50, 70, 57, 77) L = (1, 44)(2, 50)(3, 54)(4, 43)(5, 56)(6, 47)(7, 41)(8, 59)(9, 57)(10, 49)(11, 52)(12, 42)(13, 48)(14, 53)(15, 51)(16, 55)(17, 58)(18, 45)(19, 60)(20, 46)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40, 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E15.69 Graph:: bipartite v = 9 e = 40 f = 3 degree seq :: [ 8^5, 10^4 ] E15.60 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2^-2, (Y2, Y1^-1), Y3 * Y2 * Y1^-2, Y2 * Y1^-1 * Y3 * Y1^-1, Y2^-1 * Y1^-2 * Y3^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y1^-2, Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^5, Y2^2 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 7, 27, 12, 32)(4, 24, 10, 30, 6, 26, 11, 31)(13, 33, 17, 37, 14, 34, 18, 38)(15, 35, 19, 39, 16, 36, 20, 40)(41, 61, 43, 63, 53, 73, 55, 75, 46, 66)(42, 62, 49, 69, 57, 77, 59, 79, 51, 71)(44, 64, 48, 68, 47, 67, 54, 74, 56, 76)(45, 65, 52, 72, 58, 78, 60, 80, 50, 70) L = (1, 44)(2, 50)(3, 48)(4, 55)(5, 51)(6, 56)(7, 41)(8, 46)(9, 45)(10, 59)(11, 60)(12, 42)(13, 47)(14, 43)(15, 54)(16, 53)(17, 52)(18, 49)(19, 58)(20, 57)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40, 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E15.68 Graph:: bipartite v = 9 e = 40 f = 3 degree seq :: [ 8^5, 10^4 ] E15.61 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1 * Y3, Y2 * Y1^-1 * Y2, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^5, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 13, 33, 5, 25)(3, 23, 9, 29, 16, 36, 14, 34, 6, 26)(4, 24, 10, 30, 17, 37, 19, 39, 12, 32)(7, 27, 11, 31, 18, 38, 20, 40, 15, 35)(41, 61, 43, 63, 42, 62, 49, 69, 48, 68, 56, 76, 53, 73, 54, 74, 45, 65, 46, 66)(44, 64, 51, 71, 50, 70, 58, 78, 57, 77, 60, 80, 59, 79, 55, 75, 52, 72, 47, 67) L = (1, 44)(2, 50)(3, 51)(4, 43)(5, 52)(6, 47)(7, 41)(8, 57)(9, 58)(10, 49)(11, 42)(12, 46)(13, 59)(14, 55)(15, 45)(16, 60)(17, 56)(18, 48)(19, 54)(20, 53)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E15.64 Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 10^4, 20^2 ] E15.62 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y2 * Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-1 * Y3 * Y2^-1, Y1^5, (Y3^-1 * Y1^-1)^4, (Y2^-1 * Y1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 14, 34, 5, 25)(3, 23, 6, 26, 10, 30, 17, 37, 12, 32)(4, 24, 9, 29, 16, 36, 19, 39, 13, 33)(7, 27, 11, 31, 18, 38, 20, 40, 15, 35)(41, 61, 43, 63, 45, 65, 52, 72, 54, 74, 57, 77, 48, 68, 50, 70, 42, 62, 46, 66)(44, 64, 47, 67, 53, 73, 55, 75, 59, 79, 60, 80, 56, 76, 58, 78, 49, 69, 51, 71) L = (1, 44)(2, 49)(3, 47)(4, 46)(5, 53)(6, 51)(7, 41)(8, 56)(9, 50)(10, 58)(11, 42)(12, 55)(13, 43)(14, 59)(15, 45)(16, 57)(17, 60)(18, 48)(19, 52)(20, 54)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E15.65 Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 10^4, 20^2 ] E15.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y1, Y3^-1), Y2^2 * Y1^-2, Y3^-2 * Y2^-1 * Y1^-1, (R * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y2^2 * Y1^3, Y2 * Y3^-1 * Y1^2 * Y3^-1, Y3^-3 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 18, 38, 5, 25)(3, 23, 9, 29, 15, 35, 6, 26, 11, 31)(4, 24, 10, 30, 19, 39, 14, 34, 16, 36)(7, 27, 12, 32, 17, 37, 20, 40, 13, 33)(41, 61, 43, 63, 48, 68, 55, 75, 45, 65, 51, 71, 42, 62, 49, 69, 58, 78, 46, 66)(44, 64, 53, 73, 59, 79, 52, 72, 56, 76, 60, 80, 50, 70, 47, 67, 54, 74, 57, 77) L = (1, 44)(2, 50)(3, 53)(4, 55)(5, 56)(6, 57)(7, 41)(8, 59)(9, 47)(10, 46)(11, 60)(12, 42)(13, 45)(14, 43)(15, 52)(16, 49)(17, 48)(18, 54)(19, 51)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E15.66 Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 10^4, 20^2 ] E15.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y2)^2, (Y3, Y2), Y2^4, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y3^-5 * Y2, Y1^-1 * Y2 * Y3^-1 * Y1^-3, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 13, 33, 10, 30, 3, 23, 7, 27, 14, 34, 19, 39, 17, 37, 9, 29, 16, 36, 20, 40, 18, 38, 12, 32, 5, 25, 8, 28, 15, 35, 11, 31, 4, 24)(41, 61, 43, 63, 49, 69, 45, 65)(42, 62, 47, 67, 56, 76, 48, 68)(44, 64, 50, 70, 57, 77, 52, 72)(46, 66, 54, 74, 60, 80, 55, 75)(51, 71, 53, 73, 59, 79, 58, 78) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 53)(7, 54)(8, 55)(9, 56)(10, 43)(11, 44)(12, 45)(13, 50)(14, 59)(15, 51)(16, 60)(17, 49)(18, 52)(19, 57)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 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 E15.61 Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y1^2, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^2 * Y1 * Y3, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3^-1, Y2), Y3 * Y2 * Y1^2, (Y1, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y1^-1 * Y3^2 * Y2^-1, Y1^5 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 17, 37, 15, 35, 3, 23, 9, 29, 7, 27, 12, 32, 19, 39, 13, 33, 20, 40, 16, 36, 4, 24, 10, 30, 6, 26, 11, 31, 18, 38, 14, 34, 5, 25)(41, 61, 43, 63, 53, 73, 46, 66)(42, 62, 49, 69, 60, 80, 51, 71)(44, 64, 54, 74, 57, 77, 52, 72)(45, 65, 55, 75, 59, 79, 50, 70)(47, 67, 56, 76, 58, 78, 48, 68) L = (1, 44)(2, 50)(3, 54)(4, 49)(5, 56)(6, 52)(7, 41)(8, 46)(9, 45)(10, 47)(11, 59)(12, 42)(13, 57)(14, 60)(15, 58)(16, 43)(17, 51)(18, 53)(19, 48)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 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 E15.62 Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y1^-1, (Y3, Y1^-1), Y3^-1 * Y1^-3, Y2 * Y3 * Y1^-2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y1)^2, Y2^4, (R * Y2)^2, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2, (Y3 * Y2^-1)^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 7, 27, 12, 32, 3, 23, 9, 29, 17, 37, 14, 34, 19, 39, 13, 33, 18, 38, 16, 36, 20, 40, 15, 35, 6, 26, 11, 31, 4, 24, 10, 30, 5, 25)(41, 61, 43, 63, 53, 73, 46, 66)(42, 62, 49, 69, 58, 78, 51, 71)(44, 64, 48, 68, 57, 77, 56, 76)(45, 65, 52, 72, 59, 79, 55, 75)(47, 67, 54, 74, 60, 80, 50, 70) L = (1, 44)(2, 50)(3, 48)(4, 55)(5, 51)(6, 56)(7, 41)(8, 45)(9, 47)(10, 46)(11, 60)(12, 42)(13, 57)(14, 43)(15, 58)(16, 59)(17, 52)(18, 54)(19, 49)(20, 53)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 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, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E15.63 Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2, Y3^-1 * Y1^3, Y3 * Y1 * Y3^2, (R * Y3)^2, (Y3, Y2), (Y3, Y1), (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y3^-1 * Y2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 4, 24, 10, 30, 18, 38, 14, 34, 7, 27, 11, 31, 5, 25)(3, 23, 9, 29, 15, 35, 12, 32, 19, 39, 20, 40, 17, 37, 13, 33, 16, 36, 6, 26)(41, 61, 43, 63, 42, 62, 49, 69, 48, 68, 55, 75, 44, 64, 52, 72, 50, 70, 59, 79, 58, 78, 60, 80, 54, 74, 57, 77, 47, 67, 53, 73, 51, 71, 56, 76, 45, 65, 46, 66) L = (1, 44)(2, 50)(3, 52)(4, 54)(5, 48)(6, 55)(7, 41)(8, 58)(9, 59)(10, 47)(11, 42)(12, 57)(13, 43)(14, 45)(15, 60)(16, 49)(17, 46)(18, 51)(19, 53)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E15.58 Graph:: bipartite v = 3 e = 40 f = 9 degree seq :: [ 20^2, 40 ] E15.68 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, (Y3, Y2^-1), Y3^-1 * Y1^-3, Y3 * Y1^-1 * Y3^2, (Y3, Y2^-1), (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1^-2 * Y3)^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 7, 27, 11, 31, 18, 38, 15, 35, 4, 24, 9, 29, 5, 25)(3, 23, 6, 26, 10, 30, 14, 34, 17, 37, 19, 39, 20, 40, 12, 32, 16, 36, 13, 33)(41, 61, 43, 63, 45, 65, 53, 73, 49, 69, 56, 76, 44, 64, 52, 72, 55, 75, 60, 80, 58, 78, 59, 79, 51, 71, 57, 77, 47, 67, 54, 74, 48, 68, 50, 70, 42, 62, 46, 66) L = (1, 44)(2, 49)(3, 52)(4, 51)(5, 55)(6, 56)(7, 41)(8, 45)(9, 58)(10, 53)(11, 42)(12, 57)(13, 60)(14, 43)(15, 47)(16, 59)(17, 46)(18, 48)(19, 50)(20, 54)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E15.60 Graph:: bipartite v = 3 e = 40 f = 9 degree seq :: [ 20^2, 40 ] E15.69 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y1 * Y2 * Y1^2 * Y2, (R * Y2 * Y3^-1)^2, Y2^-6 * Y1, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 13, 33, 15, 35, 20, 40, 17, 37, 9, 29, 11, 31, 4, 24)(3, 23, 7, 27, 12, 32, 5, 25, 8, 28, 14, 34, 19, 39, 16, 36, 18, 38, 10, 30)(41, 61, 43, 63, 49, 69, 56, 76, 55, 75, 48, 68, 42, 62, 47, 67, 51, 71, 58, 78, 60, 80, 54, 74, 46, 66, 52, 72, 44, 64, 50, 70, 57, 77, 59, 79, 53, 73, 45, 65) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 53)(7, 52)(8, 54)(9, 51)(10, 43)(11, 44)(12, 45)(13, 55)(14, 59)(15, 60)(16, 58)(17, 49)(18, 50)(19, 56)(20, 57)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E15.59 Graph:: bipartite v = 3 e = 40 f = 9 degree seq :: [ 20^2, 40 ] E15.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2^-1, Y1^-1), Y2 * Y1 * Y2^2 * Y1 * Y3^-2, Y1^-2 * Y2^2 * Y3^-3, Y3 * Y1 * Y3 * Y1 * Y2^-3, Y2^10, (Y3 * Y2^-1)^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 5, 25)(3, 23, 7, 27, 13, 33, 10, 30)(4, 24, 8, 28, 14, 34, 12, 32)(9, 29, 15, 35, 19, 39, 18, 38)(11, 31, 16, 36, 17, 37, 20, 40)(41, 61, 43, 63, 49, 69, 57, 77, 54, 74, 46, 66, 53, 73, 59, 79, 51, 71, 44, 64)(42, 62, 47, 67, 55, 75, 60, 80, 52, 72, 45, 65, 50, 70, 58, 78, 56, 76, 48, 68) L = (1, 44)(2, 48)(3, 41)(4, 51)(5, 52)(6, 54)(7, 42)(8, 56)(9, 43)(10, 45)(11, 59)(12, 60)(13, 46)(14, 57)(15, 47)(16, 58)(17, 49)(18, 50)(19, 53)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E15.75 Graph:: bipartite v = 7 e = 40 f = 5 degree seq :: [ 8^5, 20^2 ] E15.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y2^-1, Y2^-3 * Y3, (Y1^-1, Y2), (Y3, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4, (Y2, Y3), Y3 * Y1 * Y3 * Y1 * Y2^-1, Y2 * Y1^2 * Y3^-2, Y2 * Y1 * Y2 * Y3 * Y1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 17, 37, 15, 35)(4, 24, 10, 30, 16, 36, 18, 38)(6, 26, 11, 31, 14, 34, 19, 39)(7, 27, 12, 32, 13, 33, 20, 40)(41, 61, 43, 63, 53, 73, 44, 64, 54, 74, 48, 68, 57, 77, 47, 67, 56, 76, 46, 66)(42, 62, 49, 69, 60, 80, 50, 70, 59, 79, 45, 65, 55, 75, 52, 72, 58, 78, 51, 71) L = (1, 44)(2, 50)(3, 54)(4, 57)(5, 58)(6, 53)(7, 41)(8, 56)(9, 59)(10, 55)(11, 60)(12, 42)(13, 48)(14, 47)(15, 51)(16, 43)(17, 46)(18, 49)(19, 52)(20, 45)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E15.73 Graph:: bipartite v = 7 e = 40 f = 5 degree seq :: [ 8^5, 20^2 ] E15.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1 * Y3^2, Y3^-1 * Y2^-3, (Y1^-1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y3^-1, Y1^-1), (Y2^-1, Y3^-1), Y2 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y1 * Y2 * Y3 * Y1, Y3 * Y1^2 * Y2^-2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 9, 29, 18, 38, 15, 35)(4, 24, 10, 30, 13, 33, 17, 37)(6, 26, 11, 31, 16, 36, 19, 39)(7, 27, 12, 32, 14, 34, 20, 40)(41, 61, 43, 63, 53, 73, 47, 67, 56, 76, 48, 68, 58, 78, 44, 64, 54, 74, 46, 66)(42, 62, 49, 69, 57, 77, 52, 72, 59, 79, 45, 65, 55, 75, 50, 70, 60, 80, 51, 71) L = (1, 44)(2, 50)(3, 54)(4, 56)(5, 57)(6, 58)(7, 41)(8, 53)(9, 60)(10, 59)(11, 55)(12, 42)(13, 46)(14, 48)(15, 52)(16, 43)(17, 51)(18, 47)(19, 49)(20, 45)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 40, 10, 40, 10, 40, 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40, 10, 40 ) } Outer automorphisms :: reflexible Dual of E15.74 Graph:: bipartite v = 7 e = 40 f = 5 degree seq :: [ 8^5, 20^2 ] E15.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y2^2 * Y3^2, (R * Y1)^2, (Y2^-1, Y1^-1), R * Y2 * R * Y3^-1, (Y3^-1, Y1^-1), Y3^-4 * Y1, Y1^5, (Y3 * Y2^-1)^10, Y2^20 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 13, 33, 5, 25)(3, 23, 7, 27, 14, 34, 18, 38, 10, 30)(4, 24, 8, 28, 15, 35, 19, 39, 12, 32)(9, 29, 11, 31, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 52, 72, 45, 65, 50, 70, 57, 77, 59, 79, 53, 73, 58, 78, 60, 80, 55, 75, 46, 66, 54, 74, 56, 76, 48, 68, 42, 62, 47, 67, 51, 71, 44, 64) L = (1, 44)(2, 48)(3, 41)(4, 51)(5, 52)(6, 55)(7, 42)(8, 56)(9, 43)(10, 45)(11, 47)(12, 49)(13, 59)(14, 46)(15, 60)(16, 54)(17, 50)(18, 53)(19, 57)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 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, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E15.71 Graph:: bipartite v = 5 e = 40 f = 7 degree seq :: [ 10^4, 40 ] E15.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-3, Y2 * Y3 * Y1^-2, Y2^-1 * Y1 * Y3^-1 * Y1, Y1^2 * Y2^-1 * Y3^-1, (R * Y1)^2, (Y1, Y3^-1), (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y2^-1 * Y1^-2 * Y3^-1, Y1 * Y3 * Y2^-1 * Y3^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 16, 36, 5, 25)(3, 23, 9, 29, 18, 38, 7, 27, 12, 32)(4, 24, 10, 30, 17, 37, 6, 26, 11, 31)(13, 33, 19, 39, 15, 35, 14, 34, 20, 40)(41, 61, 43, 63, 53, 73, 44, 64, 48, 68, 58, 78, 55, 75, 57, 77, 45, 65, 52, 72, 60, 80, 51, 71, 42, 62, 49, 69, 59, 79, 50, 70, 56, 76, 47, 67, 54, 74, 46, 66) L = (1, 44)(2, 50)(3, 48)(4, 55)(5, 51)(6, 53)(7, 41)(8, 57)(9, 56)(10, 54)(11, 59)(12, 42)(13, 58)(14, 43)(15, 52)(16, 46)(17, 60)(18, 45)(19, 47)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 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, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E15.72 Graph:: bipartite v = 5 e = 40 f = 7 degree seq :: [ 10^4, 40 ] E15.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 5, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y3, (R * Y2)^2, Y3^2 * Y2^-1 * Y3, (R * Y3)^2, (R * Y1)^2, Y1^5, (Y1 * Y2^2)^2, Y1^-1 * Y2^-4 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 14, 34, 5, 25)(3, 23, 9, 29, 18, 38, 16, 36, 7, 27)(4, 24, 10, 30, 19, 39, 15, 35, 6, 26)(11, 31, 20, 40, 17, 37, 13, 33, 12, 32)(41, 61, 43, 63, 51, 71, 59, 79, 54, 74, 56, 76, 53, 73, 44, 64, 42, 62, 49, 69, 60, 80, 55, 75, 45, 65, 47, 67, 52, 72, 50, 70, 48, 68, 58, 78, 57, 77, 46, 66) L = (1, 44)(2, 50)(3, 42)(4, 52)(5, 46)(6, 53)(7, 41)(8, 59)(9, 48)(10, 51)(11, 49)(12, 43)(13, 47)(14, 55)(15, 57)(16, 45)(17, 56)(18, 54)(19, 60)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 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, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E15.70 Graph:: bipartite v = 5 e = 40 f = 7 degree seq :: [ 10^4, 40 ] E15.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^5 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 17, 37)(12, 32, 16, 36, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 60, 80, 54, 74, 46, 66, 53, 73, 59, 79, 58, 78, 51, 71, 44, 64, 50, 70, 57, 77, 52, 72, 45, 65) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y1^4, Y2^-5 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^20 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 18, 38)(12, 32, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 57, 77, 51, 71, 44, 64, 50, 70, 58, 78, 60, 80, 54, 74, 46, 66, 53, 73, 59, 79, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 52, 72, 45, 65) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.78 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y3 * Y1, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, Y2^3 * Y1^-1 * Y2^2 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 5, 25)(3, 23, 7, 27, 10, 30, 11, 31)(6, 26, 8, 28, 12, 32, 13, 33)(9, 29, 15, 35, 17, 37, 18, 38)(14, 34, 16, 36, 19, 39, 20, 40)(41, 61, 43, 63, 49, 69, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 59, 79, 52, 72, 44, 64, 50, 70, 57, 77, 60, 80, 53, 73, 45, 65, 51, 71, 58, 78, 54, 74, 46, 66) L = (1, 44)(2, 45)(3, 50)(4, 41)(5, 42)(6, 52)(7, 51)(8, 53)(9, 57)(10, 43)(11, 47)(12, 46)(13, 48)(14, 59)(15, 58)(16, 60)(17, 49)(18, 55)(19, 54)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.79 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 20, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y2 * Y1 * Y2^-2 * Y1^-1 * Y2, Y2^-5 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 4, 24, 5, 25)(3, 23, 7, 27, 10, 30, 11, 31)(6, 26, 8, 28, 12, 32, 13, 33)(9, 29, 15, 35, 18, 38, 19, 39)(14, 34, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 57, 77, 53, 73, 45, 65, 51, 71, 59, 79, 60, 80, 52, 72, 44, 64, 50, 70, 58, 78, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 54, 74, 46, 66) L = (1, 44)(2, 45)(3, 50)(4, 41)(5, 42)(6, 52)(7, 51)(8, 53)(9, 58)(10, 43)(11, 47)(12, 46)(13, 48)(14, 60)(15, 59)(16, 57)(17, 56)(18, 49)(19, 55)(20, 54)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 40, 8, 40, 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 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 selfdual Graph:: bipartite v = 6 e = 40 f = 6 degree seq :: [ 8^5, 40 ] E15.80 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), Y2^7, (Y3 * Y2^-1)^7, Y3^-21 ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 6, 27, 9, 30)(4, 25, 7, 28, 11, 32)(8, 29, 12, 33, 15, 36)(10, 31, 13, 34, 17, 38)(14, 35, 18, 39, 20, 41)(16, 37, 19, 40, 21, 42)(43, 64, 45, 66, 50, 71, 56, 77, 58, 79, 52, 73, 46, 67)(44, 65, 48, 69, 54, 75, 60, 81, 61, 82, 55, 76, 49, 70)(47, 68, 51, 72, 57, 78, 62, 83, 63, 84, 59, 80, 53, 74) L = (1, 46)(2, 49)(3, 43)(4, 52)(5, 53)(6, 44)(7, 55)(8, 45)(9, 47)(10, 58)(11, 59)(12, 48)(13, 61)(14, 50)(15, 51)(16, 56)(17, 63)(18, 54)(19, 60)(20, 57)(21, 62)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E15.91 Graph:: bipartite v = 10 e = 42 f = 4 degree seq :: [ 6^7, 14^3 ] E15.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y1^3, Y2 * Y3^3, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3^3 * Y2, (R * Y2)^2, (Y1, Y3^-1) ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 8, 29, 13, 34)(4, 25, 9, 30, 15, 36)(6, 27, 10, 31, 16, 37)(7, 28, 11, 32, 17, 38)(12, 33, 18, 39, 20, 41)(14, 35, 19, 40, 21, 42)(43, 64, 45, 66, 46, 67, 54, 75, 56, 77, 49, 70, 48, 69)(44, 65, 50, 71, 51, 72, 60, 81, 61, 82, 53, 74, 52, 73)(47, 68, 55, 76, 57, 78, 62, 83, 63, 84, 59, 80, 58, 79) L = (1, 46)(2, 51)(3, 54)(4, 56)(5, 57)(6, 45)(7, 43)(8, 60)(9, 61)(10, 50)(11, 44)(12, 49)(13, 62)(14, 48)(15, 63)(16, 55)(17, 47)(18, 53)(19, 52)(20, 59)(21, 58)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E15.92 Graph:: bipartite v = 10 e = 42 f = 4 degree seq :: [ 6^7, 14^3 ] E15.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y1^3, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y2 * Y3^-3, (R * Y2)^2, 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 ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 8, 29, 12, 33)(4, 25, 9, 30, 14, 35)(6, 27, 10, 31, 16, 37)(7, 28, 11, 32, 17, 38)(13, 34, 18, 39, 20, 41)(15, 36, 19, 40, 21, 42)(43, 64, 45, 66, 49, 70, 55, 76, 57, 78, 46, 67, 48, 69)(44, 65, 50, 71, 53, 74, 60, 81, 61, 82, 51, 72, 52, 73)(47, 68, 54, 75, 59, 80, 62, 83, 63, 84, 56, 77, 58, 79) L = (1, 46)(2, 51)(3, 48)(4, 55)(5, 56)(6, 57)(7, 43)(8, 52)(9, 60)(10, 61)(11, 44)(12, 58)(13, 45)(14, 62)(15, 49)(16, 63)(17, 47)(18, 50)(19, 53)(20, 54)(21, 59)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E15.90 Graph:: bipartite v = 10 e = 42 f = 4 degree seq :: [ 6^7, 14^3 ] E15.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, Y1^3, (Y3^-1, Y1), (Y2^-1, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-3, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 8, 29, 13, 34)(4, 25, 9, 30, 15, 36)(6, 27, 10, 31, 16, 37)(7, 28, 11, 32, 17, 38)(12, 33, 18, 39, 20, 41)(14, 35, 19, 40, 21, 42)(43, 64, 45, 66, 54, 75, 46, 67, 49, 70, 56, 77, 48, 69)(44, 65, 50, 71, 60, 81, 51, 72, 53, 74, 61, 82, 52, 73)(47, 68, 55, 76, 62, 83, 57, 78, 59, 80, 63, 84, 58, 79) L = (1, 46)(2, 51)(3, 49)(4, 48)(5, 57)(6, 54)(7, 43)(8, 53)(9, 52)(10, 60)(11, 44)(12, 56)(13, 59)(14, 45)(15, 58)(16, 62)(17, 47)(18, 61)(19, 50)(20, 63)(21, 55)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E15.93 Graph:: bipartite v = 10 e = 42 f = 4 degree seq :: [ 6^7, 14^3 ] E15.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1^3, (Y1, Y3^-1), (Y1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2^-3 * Y3^-1, (R * Y1)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 ] Map:: non-degenerate R = (1, 22, 2, 23, 5, 26)(3, 24, 8, 29, 14, 35)(4, 25, 9, 30, 15, 36)(6, 27, 10, 31, 16, 37)(7, 28, 11, 32, 17, 38)(12, 33, 18, 39, 20, 41)(13, 34, 19, 40, 21, 42)(43, 64, 45, 66, 54, 75, 49, 70, 46, 67, 55, 76, 48, 69)(44, 65, 50, 71, 60, 81, 53, 74, 51, 72, 61, 82, 52, 73)(47, 68, 56, 77, 62, 83, 59, 80, 57, 78, 63, 84, 58, 79) L = (1, 46)(2, 51)(3, 55)(4, 45)(5, 57)(6, 49)(7, 43)(8, 61)(9, 50)(10, 53)(11, 44)(12, 48)(13, 54)(14, 63)(15, 56)(16, 59)(17, 47)(18, 52)(19, 60)(20, 58)(21, 62)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14, 42, 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) } Outer automorphisms :: reflexible Dual of E15.89 Graph:: bipartite v = 10 e = 42 f = 4 degree seq :: [ 6^7, 14^3 ] E15.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y3^-1 * Y2^-1 * Y3^-2, (Y1^-1, Y3), (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-3, (R * Y2)^2, (Y1^-1 * Y3^-1)^3, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 3, 24, 6, 27, 10, 31, 5, 26)(4, 25, 9, 30, 18, 39, 12, 33, 16, 37, 21, 42, 15, 36)(7, 28, 11, 32, 19, 40, 13, 34, 14, 35, 20, 41, 17, 38)(43, 64, 45, 66, 47, 68, 50, 71, 52, 73, 44, 65, 48, 69)(46, 67, 54, 75, 57, 78, 60, 81, 63, 84, 51, 72, 58, 79)(49, 70, 55, 76, 59, 80, 61, 82, 62, 83, 53, 74, 56, 77) L = (1, 46)(2, 51)(3, 54)(4, 56)(5, 57)(6, 58)(7, 43)(8, 60)(9, 62)(10, 63)(11, 44)(12, 49)(13, 45)(14, 48)(15, 55)(16, 53)(17, 47)(18, 59)(19, 50)(20, 52)(21, 61)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E15.88 Graph:: bipartite v = 6 e = 42 f = 8 degree seq :: [ 14^6 ] E15.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, Y3^-1 * Y2 * Y3^-2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), (R * Y1)^2, (Y3^-1, Y1^-1), Y2 * Y1^3, (Y1^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 6, 27, 3, 24, 9, 30, 5, 26)(4, 25, 10, 31, 18, 39, 15, 36, 12, 33, 20, 41, 14, 35)(7, 28, 11, 32, 19, 40, 17, 38, 13, 34, 21, 42, 16, 37)(43, 64, 45, 66, 44, 65, 51, 72, 50, 71, 47, 68, 48, 69)(46, 67, 54, 75, 52, 73, 62, 83, 60, 81, 56, 77, 57, 78)(49, 70, 55, 76, 53, 74, 63, 84, 61, 82, 58, 79, 59, 80) L = (1, 46)(2, 52)(3, 54)(4, 55)(5, 56)(6, 57)(7, 43)(8, 60)(9, 62)(10, 63)(11, 44)(12, 53)(13, 45)(14, 59)(15, 49)(16, 47)(17, 48)(18, 58)(19, 50)(20, 61)(21, 51)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E15.87 Graph:: bipartite v = 6 e = 42 f = 8 degree seq :: [ 14^6 ] E15.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^2, (Y2^-1, Y3^-1), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^2 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 14, 35, 12, 33, 21, 42, 17, 38, 6, 27, 11, 32, 18, 39, 7, 28, 4, 25, 10, 31, 13, 34, 3, 24, 9, 30, 20, 41, 19, 40, 15, 36, 16, 37, 5, 26)(43, 64, 45, 66, 48, 69)(44, 65, 51, 72, 53, 74)(46, 67, 54, 75, 57, 78)(47, 68, 55, 76, 59, 80)(49, 70, 56, 77, 61, 82)(50, 71, 62, 83, 60, 81)(52, 73, 63, 84, 58, 79) L = (1, 46)(2, 52)(3, 54)(4, 44)(5, 49)(6, 57)(7, 43)(8, 55)(9, 63)(10, 50)(11, 58)(12, 51)(13, 56)(14, 45)(15, 53)(16, 60)(17, 61)(18, 47)(19, 48)(20, 59)(21, 62)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14^6 ), ( 14^42 ) } Outer automorphisms :: reflexible Dual of E15.86 Graph:: bipartite v = 8 e = 42 f = 6 degree seq :: [ 6^7, 42 ] E15.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1 * Y2 * Y3 * Y1, Y1^2 * Y3 * Y2, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (R * Y1)^2, Y3 * Y1 * Y3^3, Y1^-1 * Y2 * Y3 * Y1^-2 * Y3, Y1^14 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 20, 41, 17, 38, 4, 25, 10, 31, 6, 27, 11, 32, 15, 36, 16, 37, 19, 40, 18, 39, 14, 35, 3, 24, 9, 30, 7, 28, 12, 33, 21, 42, 13, 34, 5, 26)(43, 64, 45, 66, 48, 69)(44, 65, 51, 72, 53, 74)(46, 67, 55, 76, 60, 81)(47, 68, 56, 77, 52, 73)(49, 70, 57, 78, 50, 71)(54, 75, 58, 79, 62, 83)(59, 80, 63, 84, 61, 82) L = (1, 46)(2, 52)(3, 55)(4, 58)(5, 59)(6, 60)(7, 43)(8, 48)(9, 47)(10, 61)(11, 56)(12, 44)(13, 62)(14, 63)(15, 45)(16, 51)(17, 57)(18, 54)(19, 49)(20, 53)(21, 50)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14^6 ), ( 14^42 ) } Outer automorphisms :: reflexible Dual of E15.85 Graph:: bipartite v = 8 e = 42 f = 6 degree seq :: [ 6^7, 42 ] E15.89 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, Y1^-3 * Y2^3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^-1 * Y2^-6, Y1^7, (Y3^-1 * Y1^-1)^7 ] Map:: non-degenerate R = (1, 22, 2, 23, 6, 27, 14, 35, 19, 40, 11, 32, 4, 25)(3, 24, 7, 28, 15, 36, 21, 42, 13, 34, 18, 39, 10, 31)(5, 26, 8, 29, 16, 37, 9, 30, 17, 38, 20, 41, 12, 33)(43, 64, 45, 66, 51, 72, 56, 77, 63, 84, 54, 75, 46, 67, 52, 73, 58, 79, 48, 69, 57, 78, 62, 83, 53, 74, 60, 81, 50, 71, 44, 65, 49, 70, 59, 80, 61, 82, 55, 76, 47, 68) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 61)(15, 63)(16, 51)(17, 62)(18, 52)(19, 53)(20, 54)(21, 55)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E15.84 Graph:: bipartite v = 4 e = 42 f = 10 degree seq :: [ 14^3, 42 ] E15.90 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2), Y1^-2 * Y3^-1 * Y1^-1, Y2 * Y1 * Y2^2 * Y1, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 7, 28, 4, 25, 10, 31, 5, 26)(3, 24, 9, 30, 18, 39, 15, 36, 13, 34, 21, 42, 14, 35)(6, 27, 11, 32, 20, 41, 19, 40, 16, 37, 12, 33, 17, 38)(43, 64, 45, 66, 54, 75, 52, 73, 63, 84, 61, 82, 49, 70, 57, 78, 53, 74, 44, 65, 51, 72, 59, 80, 47, 68, 56, 77, 58, 79, 46, 67, 55, 76, 62, 83, 50, 71, 60, 81, 48, 69) L = (1, 46)(2, 52)(3, 55)(4, 44)(5, 49)(6, 58)(7, 43)(8, 47)(9, 63)(10, 50)(11, 54)(12, 62)(13, 51)(14, 57)(15, 45)(16, 53)(17, 61)(18, 56)(19, 48)(20, 59)(21, 60)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E15.82 Graph:: bipartite v = 4 e = 42 f = 10 degree seq :: [ 14^3, 42 ] E15.91 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1, (R * Y2)^2, Y1^-3 * Y3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2), (Y1^-1, Y2), Y1 * Y2^3 * Y3^-1, Y2 * Y1^-1 * Y2^2 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 4, 25, 7, 28, 11, 32, 5, 26)(3, 24, 9, 30, 20, 41, 13, 34, 15, 36, 18, 39, 14, 35)(6, 27, 10, 31, 12, 33, 16, 37, 19, 40, 21, 42, 17, 38)(43, 64, 45, 66, 54, 75, 50, 71, 62, 83, 61, 82, 49, 70, 57, 78, 59, 80, 47, 68, 56, 77, 52, 73, 44, 65, 51, 72, 58, 79, 46, 67, 55, 76, 63, 84, 53, 74, 60, 81, 48, 69) L = (1, 46)(2, 49)(3, 55)(4, 47)(5, 50)(6, 58)(7, 43)(8, 53)(9, 57)(10, 61)(11, 44)(12, 63)(13, 56)(14, 62)(15, 45)(16, 59)(17, 54)(18, 51)(19, 48)(20, 60)(21, 52)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E15.80 Graph:: bipartite v = 4 e = 42 f = 10 degree seq :: [ 14^3, 42 ] E15.92 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, Y2^2 * Y1^-1 * Y2, Y2 * Y1^-1 * Y2^2, Y1 * Y3^-3, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 7, 28, 10, 31, 14, 35, 4, 25, 5, 26)(3, 24, 8, 29, 13, 34, 18, 39, 20, 41, 11, 32, 12, 33)(6, 27, 9, 30, 17, 38, 19, 40, 21, 42, 15, 36, 16, 37)(43, 64, 45, 66, 51, 72, 44, 65, 50, 71, 59, 80, 49, 70, 55, 76, 61, 82, 52, 73, 60, 81, 63, 84, 56, 77, 62, 83, 57, 78, 46, 67, 53, 74, 58, 79, 47, 68, 54, 75, 48, 69) L = (1, 46)(2, 47)(3, 53)(4, 52)(5, 56)(6, 57)(7, 43)(8, 54)(9, 58)(10, 44)(11, 60)(12, 62)(13, 45)(14, 49)(15, 61)(16, 63)(17, 48)(18, 50)(19, 51)(20, 55)(21, 59)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E15.81 Graph:: bipartite v = 4 e = 42 f = 10 degree seq :: [ 14^3, 42 ] E15.93 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 7, 7, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^2, Y1^-1 * Y3^-3, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 4, 25, 9, 30, 15, 36, 7, 28, 5, 26)(3, 24, 8, 29, 12, 33, 18, 39, 21, 42, 14, 35, 13, 34)(6, 27, 10, 31, 16, 37, 19, 40, 20, 41, 17, 38, 11, 32)(43, 64, 45, 66, 53, 74, 47, 68, 55, 76, 59, 80, 49, 70, 56, 77, 62, 83, 57, 78, 63, 84, 61, 82, 51, 72, 60, 81, 58, 79, 46, 67, 54, 75, 52, 73, 44, 65, 50, 71, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 57)(5, 44)(6, 58)(7, 43)(8, 60)(9, 49)(10, 61)(11, 52)(12, 63)(13, 50)(14, 45)(15, 47)(16, 62)(17, 48)(18, 56)(19, 59)(20, 53)(21, 55)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E15.83 Graph:: bipartite v = 4 e = 42 f = 10 degree seq :: [ 14^3, 42 ] E15.94 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2^11, Y3^22, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 5, 27)(4, 26, 6, 28)(7, 29, 9, 31)(8, 30, 10, 32)(11, 33, 13, 35)(12, 34, 14, 36)(15, 37, 17, 39)(16, 38, 18, 40)(19, 41, 21, 43)(20, 42, 22, 44)(45, 67, 47, 69, 51, 73, 55, 77, 59, 81, 63, 85, 64, 86, 60, 82, 56, 78, 52, 74, 48, 70)(46, 68, 49, 71, 53, 75, 57, 79, 61, 83, 65, 87, 66, 88, 62, 84, 58, 80, 54, 76, 50, 72) L = (1, 48)(2, 50)(3, 45)(4, 52)(5, 46)(6, 54)(7, 47)(8, 56)(9, 49)(10, 58)(11, 51)(12, 60)(13, 53)(14, 62)(15, 55)(16, 64)(17, 57)(18, 66)(19, 59)(20, 63)(21, 61)(22, 65)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.113 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.95 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y3^-2 * Y2^-1 * Y3^-3 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 15, 37)(12, 34, 16, 38)(13, 35, 17, 39)(14, 36, 18, 40)(19, 41, 21, 43)(20, 42, 22, 44)(45, 67, 47, 69, 48, 70, 55, 77, 56, 78, 63, 85, 64, 86, 58, 80, 57, 79, 50, 72, 49, 71)(46, 68, 51, 73, 52, 74, 59, 81, 60, 82, 65, 87, 66, 88, 62, 84, 61, 83, 54, 76, 53, 75) L = (1, 48)(2, 52)(3, 55)(4, 56)(5, 47)(6, 45)(7, 59)(8, 60)(9, 51)(10, 46)(11, 63)(12, 64)(13, 49)(14, 50)(15, 65)(16, 66)(17, 53)(18, 54)(19, 58)(20, 57)(21, 62)(22, 61)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.118 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y3^5 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 15, 37)(12, 34, 16, 38)(13, 35, 17, 39)(14, 36, 18, 40)(19, 41, 21, 43)(20, 42, 22, 44)(45, 67, 47, 69, 50, 72, 55, 77, 58, 80, 63, 85, 64, 86, 56, 78, 57, 79, 48, 70, 49, 71)(46, 68, 51, 73, 54, 76, 59, 81, 62, 84, 65, 87, 66, 88, 60, 82, 61, 83, 52, 74, 53, 75) L = (1, 48)(2, 52)(3, 49)(4, 56)(5, 57)(6, 45)(7, 53)(8, 60)(9, 61)(10, 46)(11, 47)(12, 63)(13, 64)(14, 50)(15, 51)(16, 65)(17, 66)(18, 54)(19, 55)(20, 58)(21, 59)(22, 62)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.116 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y3^4 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 17, 39)(12, 34, 18, 40)(13, 35, 19, 41)(14, 36, 20, 42)(15, 37, 21, 43)(16, 38, 22, 44)(45, 67, 47, 69, 55, 77, 48, 70, 56, 78, 60, 82, 58, 80, 59, 81, 50, 72, 57, 79, 49, 71)(46, 68, 51, 73, 61, 83, 52, 74, 62, 84, 66, 88, 64, 86, 65, 87, 54, 76, 63, 85, 53, 75) L = (1, 48)(2, 52)(3, 56)(4, 58)(5, 55)(6, 45)(7, 62)(8, 64)(9, 61)(10, 46)(11, 60)(12, 59)(13, 47)(14, 57)(15, 49)(16, 50)(17, 66)(18, 65)(19, 51)(20, 63)(21, 53)(22, 54)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.114 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.98 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y3^4, Y3^-1 * Y2 * Y3^-2 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 17, 39)(12, 34, 18, 40)(13, 35, 19, 41)(14, 36, 20, 42)(15, 37, 21, 43)(16, 38, 22, 44)(45, 67, 47, 69, 55, 77, 50, 72, 57, 79, 58, 80, 60, 82, 59, 81, 48, 70, 56, 78, 49, 71)(46, 68, 51, 73, 61, 83, 54, 76, 63, 85, 64, 86, 66, 88, 65, 87, 52, 74, 62, 84, 53, 75) L = (1, 48)(2, 52)(3, 56)(4, 58)(5, 59)(6, 45)(7, 62)(8, 64)(9, 65)(10, 46)(11, 49)(12, 60)(13, 47)(14, 55)(15, 57)(16, 50)(17, 53)(18, 66)(19, 51)(20, 61)(21, 63)(22, 54)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.119 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.99 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2 * Y3^-2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y2^2 * Y3 * Y2, Y3^-1 * Y2^4 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 17, 39)(12, 34, 18, 40)(13, 35, 19, 41)(14, 36, 20, 42)(15, 37, 21, 43)(16, 38, 22, 44)(45, 67, 47, 69, 55, 77, 58, 80, 48, 70, 56, 78, 60, 82, 50, 72, 57, 79, 59, 81, 49, 71)(46, 68, 51, 73, 61, 83, 64, 86, 52, 74, 62, 84, 66, 88, 54, 76, 63, 85, 65, 87, 53, 75) L = (1, 48)(2, 52)(3, 56)(4, 57)(5, 58)(6, 45)(7, 62)(8, 63)(9, 64)(10, 46)(11, 60)(12, 59)(13, 47)(14, 50)(15, 55)(16, 49)(17, 66)(18, 65)(19, 51)(20, 54)(21, 61)(22, 53)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.112 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y2 * Y3 * Y2^3, Y3^-1 * Y2^2 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 17, 39)(12, 34, 18, 40)(13, 35, 19, 41)(14, 36, 20, 42)(15, 37, 21, 43)(16, 38, 22, 44)(45, 67, 47, 69, 55, 77, 58, 80, 50, 72, 57, 79, 59, 81, 48, 70, 56, 78, 60, 82, 49, 71)(46, 68, 51, 73, 61, 83, 64, 86, 54, 76, 63, 85, 65, 87, 52, 74, 62, 84, 66, 88, 53, 75) L = (1, 48)(2, 52)(3, 56)(4, 58)(5, 59)(6, 45)(7, 62)(8, 64)(9, 65)(10, 46)(11, 60)(12, 50)(13, 47)(14, 49)(15, 55)(16, 57)(17, 66)(18, 54)(19, 51)(20, 53)(21, 61)(22, 63)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.117 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y3 * Y2^-5 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 15, 37)(12, 34, 16, 38)(13, 35, 17, 39)(14, 36, 18, 40)(19, 41, 21, 43)(20, 42, 22, 44)(45, 67, 47, 69, 55, 77, 63, 85, 57, 79, 48, 70, 50, 72, 56, 78, 64, 86, 58, 80, 49, 71)(46, 68, 51, 73, 59, 81, 65, 87, 61, 83, 52, 74, 54, 76, 60, 82, 66, 88, 62, 84, 53, 75) L = (1, 48)(2, 52)(3, 50)(4, 49)(5, 57)(6, 45)(7, 54)(8, 53)(9, 61)(10, 46)(11, 56)(12, 47)(13, 58)(14, 63)(15, 60)(16, 51)(17, 62)(18, 65)(19, 64)(20, 55)(21, 66)(22, 59)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.115 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^-5 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24)(3, 25, 7, 29)(4, 26, 8, 30)(5, 27, 9, 31)(6, 28, 10, 32)(11, 33, 15, 37)(12, 34, 16, 38)(13, 35, 17, 39)(14, 36, 18, 40)(19, 41, 21, 43)(20, 42, 22, 44)(45, 67, 47, 69, 55, 77, 63, 85, 58, 80, 50, 72, 48, 70, 56, 78, 64, 86, 57, 79, 49, 71)(46, 68, 51, 73, 59, 81, 65, 87, 62, 84, 54, 76, 52, 74, 60, 82, 66, 88, 61, 83, 53, 75) L = (1, 48)(2, 52)(3, 56)(4, 47)(5, 50)(6, 45)(7, 60)(8, 51)(9, 54)(10, 46)(11, 64)(12, 55)(13, 58)(14, 49)(15, 66)(16, 59)(17, 62)(18, 53)(19, 57)(20, 63)(21, 61)(22, 65)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22, 44, 22, 44 ), ( 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E15.111 Graph:: bipartite v = 13 e = 44 f = 3 degree seq :: [ 4^11, 22^2 ] E15.103 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, Y2^-3 * Y1^-1, (Y3^-1, Y2), (R * Y1)^2, Y3^2 * Y1^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-2 * Y2^-2, Y3^-2 * Y1 * Y2^-2, Y3^-1 * Y1 * Y2 * Y3^-1 * Y1, Y3^-2 * Y2 * Y3^-2, (Y2 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 13, 35, 6, 28, 11, 33, 15, 37, 3, 25, 9, 31, 17, 39, 5, 27)(4, 26, 10, 32, 7, 29, 12, 34, 19, 41, 22, 44, 20, 42, 14, 36, 21, 43, 16, 38, 18, 40)(45, 67, 47, 69, 57, 79, 49, 71, 59, 81, 52, 74, 61, 83, 55, 77, 46, 68, 53, 75, 50, 72)(48, 70, 58, 80, 56, 78, 62, 84, 64, 86, 51, 73, 60, 82, 66, 88, 54, 76, 65, 87, 63, 85) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 62)(6, 63)(7, 45)(8, 51)(9, 65)(10, 49)(11, 66)(12, 46)(13, 56)(14, 55)(15, 64)(16, 47)(17, 60)(18, 53)(19, 52)(20, 50)(21, 59)(22, 57)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E15.108 Graph:: bipartite v = 4 e = 44 f = 12 degree seq :: [ 22^4 ] E15.104 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y1^-1 * Y3^-1)^2, (Y1^-1, Y3), Y2^2 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, (Y1^-1, Y2), Y1 * Y2 * Y1 * Y2 * Y1, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y2^-1 * Y1^2 * Y3^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 14, 36, 3, 25, 9, 31, 19, 41, 6, 28, 11, 33, 16, 38, 5, 27)(4, 26, 10, 32, 7, 29, 12, 34, 13, 35, 21, 43, 15, 37, 18, 40, 22, 44, 20, 42, 17, 39)(45, 67, 47, 69, 55, 77, 46, 68, 53, 75, 60, 82, 52, 74, 63, 85, 49, 71, 58, 80, 50, 72)(48, 70, 57, 79, 66, 88, 54, 76, 65, 87, 64, 86, 51, 73, 59, 81, 61, 83, 56, 78, 62, 84) L = (1, 48)(2, 54)(3, 57)(4, 60)(5, 61)(6, 62)(7, 45)(8, 51)(9, 65)(10, 49)(11, 66)(12, 46)(13, 52)(14, 56)(15, 47)(16, 64)(17, 55)(18, 53)(19, 59)(20, 50)(21, 58)(22, 63)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E15.110 Graph:: bipartite v = 4 e = 44 f = 12 degree seq :: [ 22^4 ] E15.105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2, Y3^2 * Y2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), (R * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2^5, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 3, 25, 8, 30, 11, 33, 17, 39, 19, 41, 16, 38, 15, 37, 6, 28, 5, 27)(4, 26, 9, 31, 7, 29, 10, 32, 12, 34, 18, 40, 20, 42, 22, 44, 21, 43, 14, 36, 13, 35)(45, 67, 47, 69, 55, 77, 63, 85, 59, 81, 49, 71, 46, 68, 52, 74, 61, 83, 60, 82, 50, 72)(48, 70, 51, 73, 56, 78, 64, 86, 65, 87, 57, 79, 53, 75, 54, 76, 62, 84, 66, 88, 58, 80) L = (1, 48)(2, 53)(3, 51)(4, 50)(5, 57)(6, 58)(7, 45)(8, 54)(9, 49)(10, 46)(11, 56)(12, 47)(13, 59)(14, 60)(15, 65)(16, 66)(17, 62)(18, 52)(19, 64)(20, 55)(21, 63)(22, 61)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E15.109 Graph:: bipartite v = 4 e = 44 f = 12 degree seq :: [ 22^4 ] E15.106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-2, Y2 * Y3^-2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y1 * Y2^-5 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 9, 31, 15, 37, 17, 39, 20, 42, 11, 33, 13, 35, 3, 25, 5, 27)(4, 26, 8, 30, 7, 29, 10, 32, 16, 38, 18, 40, 22, 44, 19, 41, 21, 43, 12, 34, 14, 36)(45, 67, 47, 69, 55, 77, 61, 83, 53, 75, 46, 68, 49, 71, 57, 79, 64, 86, 59, 81, 50, 72)(48, 70, 56, 78, 63, 85, 62, 84, 54, 76, 52, 74, 58, 80, 65, 87, 66, 88, 60, 82, 51, 73) L = (1, 48)(2, 52)(3, 56)(4, 47)(5, 58)(6, 51)(7, 45)(8, 49)(9, 54)(10, 46)(11, 63)(12, 55)(13, 65)(14, 57)(15, 60)(16, 50)(17, 62)(18, 53)(19, 61)(20, 66)(21, 64)(22, 59)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E15.107 Graph:: bipartite v = 4 e = 44 f = 12 degree seq :: [ 22^4 ] E15.107 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-1, Y1^-1 * Y2 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-4 * Y2 * Y1^5 * Y2 * Y3^-1, Y1^-4 * Y2 * Y3^-1 * Y1^-6, (Y3^-1 * Y1^-1)^11, (Y3 * Y2)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 5, 27, 9, 31, 13, 35, 17, 39, 21, 43, 19, 41, 15, 37, 11, 33, 7, 29, 3, 25, 6, 28, 10, 32, 14, 36, 18, 40, 22, 44, 20, 42, 16, 38, 12, 34, 8, 30, 4, 26)(45, 67, 47, 69)(46, 68, 50, 72)(48, 70, 51, 73)(49, 71, 54, 76)(52, 74, 55, 77)(53, 75, 58, 80)(56, 78, 59, 81)(57, 79, 62, 84)(60, 82, 63, 85)(61, 83, 66, 88)(64, 86, 65, 87) L = (1, 46)(2, 49)(3, 50)(4, 45)(5, 53)(6, 54)(7, 47)(8, 48)(9, 57)(10, 58)(11, 51)(12, 52)(13, 61)(14, 62)(15, 55)(16, 56)(17, 65)(18, 66)(19, 59)(20, 60)(21, 63)(22, 64)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22^4 ), ( 22^44 ) } Outer automorphisms :: reflexible Dual of E15.106 Graph:: bipartite v = 12 e = 44 f = 4 degree seq :: [ 4^11, 44 ] E15.108 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1^-1, Y3^-1), Y2 * Y1 * Y2 * Y1^-1, Y3^-2 * Y1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^2 * Y3^-1 * Y1 * Y2 * Y1, Y3 * Y2 * Y1^-4 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 17, 39, 11, 33, 21, 43, 16, 38, 6, 28, 10, 32, 20, 42, 12, 34, 3, 25, 8, 30, 18, 40, 14, 36, 4, 26, 9, 31, 19, 41, 13, 35, 22, 44, 15, 37, 5, 27)(45, 67, 47, 69)(46, 68, 52, 74)(48, 70, 55, 77)(49, 71, 56, 78)(50, 72, 57, 79)(51, 73, 62, 84)(53, 75, 65, 87)(54, 76, 66, 88)(58, 80, 61, 83)(59, 81, 64, 86)(60, 82, 63, 85) L = (1, 48)(2, 53)(3, 55)(4, 54)(5, 58)(6, 45)(7, 63)(8, 65)(9, 64)(10, 46)(11, 66)(12, 61)(13, 47)(14, 50)(15, 62)(16, 49)(17, 57)(18, 60)(19, 56)(20, 51)(21, 59)(22, 52)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22^4 ), ( 22^44 ) } Outer automorphisms :: reflexible Dual of E15.103 Graph:: bipartite v = 12 e = 44 f = 4 degree seq :: [ 4^11, 44 ] E15.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y1, (Y3, Y1), Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y1^-4, Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 17, 39, 13, 35, 22, 44, 15, 37, 4, 26, 9, 31, 19, 41, 12, 34, 3, 25, 8, 30, 18, 40, 14, 36, 6, 28, 10, 32, 20, 42, 11, 33, 21, 43, 16, 38, 5, 27)(45, 67, 47, 69)(46, 68, 52, 74)(48, 70, 55, 77)(49, 71, 56, 78)(50, 72, 57, 79)(51, 73, 62, 84)(53, 75, 65, 87)(54, 76, 66, 88)(58, 80, 61, 83)(59, 81, 64, 86)(60, 82, 63, 85) L = (1, 48)(2, 53)(3, 55)(4, 58)(5, 59)(6, 45)(7, 63)(8, 65)(9, 50)(10, 46)(11, 61)(12, 64)(13, 47)(14, 49)(15, 62)(16, 66)(17, 56)(18, 60)(19, 54)(20, 51)(21, 57)(22, 52)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22^4 ), ( 22^44 ) } Outer automorphisms :: reflexible Dual of E15.105 Graph:: bipartite v = 12 e = 44 f = 4 degree seq :: [ 4^11, 44 ] E15.110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), Y2 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y1^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^-2, Y3^-1 * Y1^-1 * Y3^-4, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, Y3^2 * Y1^18 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 15, 37, 12, 34, 17, 39, 22, 44, 19, 41, 13, 35, 6, 28, 10, 32, 3, 25, 8, 30, 4, 26, 9, 31, 16, 38, 21, 43, 20, 42, 14, 36, 18, 40, 11, 33, 5, 27)(45, 67, 47, 69)(46, 68, 52, 74)(48, 70, 51, 73)(49, 71, 54, 76)(50, 72, 55, 77)(53, 75, 59, 81)(56, 78, 60, 82)(57, 79, 62, 84)(58, 80, 63, 85)(61, 83, 65, 87)(64, 86, 66, 88) L = (1, 48)(2, 53)(3, 51)(4, 56)(5, 52)(6, 45)(7, 60)(8, 59)(9, 61)(10, 46)(11, 47)(12, 64)(13, 49)(14, 50)(15, 65)(16, 66)(17, 58)(18, 54)(19, 55)(20, 57)(21, 63)(22, 62)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22^4 ), ( 22^44 ) } Outer automorphisms :: reflexible Dual of E15.104 Graph:: bipartite v = 12 e = 44 f = 4 degree seq :: [ 4^11, 44 ] E15.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y2, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y2^-2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^4 * Y1 * Y2^6, (Y3^-1 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 11, 33, 15, 37, 19, 41, 21, 43, 17, 39, 13, 35, 9, 31, 4, 26)(3, 25, 7, 29, 12, 34, 16, 38, 20, 42, 22, 44, 18, 40, 14, 36, 10, 32, 5, 27, 8, 30)(45, 67, 47, 69, 50, 72, 56, 78, 59, 81, 64, 86, 65, 87, 62, 84, 57, 79, 54, 76, 48, 70, 52, 74, 46, 68, 51, 73, 55, 77, 60, 82, 63, 85, 66, 88, 61, 83, 58, 80, 53, 75, 49, 71) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 55)(7, 56)(8, 47)(9, 48)(10, 49)(11, 59)(12, 60)(13, 53)(14, 54)(15, 63)(16, 64)(17, 57)(18, 58)(19, 65)(20, 66)(21, 61)(22, 62)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.102 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3, Y1^-1 * Y2^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-3 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 15, 37, 7, 29, 4, 26, 10, 32, 19, 41, 13, 35, 5, 27)(3, 25, 9, 31, 18, 40, 22, 44, 16, 38, 12, 34, 11, 33, 20, 42, 21, 43, 14, 36, 6, 28)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 62, 84, 61, 83, 66, 88, 59, 81, 60, 82, 51, 73, 56, 78, 48, 70, 55, 77, 54, 76, 64, 86, 63, 85, 65, 87, 57, 79, 58, 80, 49, 71, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 46)(5, 51)(6, 56)(7, 45)(8, 63)(9, 64)(10, 52)(11, 53)(12, 47)(13, 59)(14, 60)(15, 49)(16, 50)(17, 57)(18, 65)(19, 61)(20, 62)(21, 66)(22, 58)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.99 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-2, Y2 * Y1 * Y2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-5 * Y3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 14, 36, 4, 26, 7, 29, 10, 32, 19, 41, 15, 37, 5, 27)(3, 25, 6, 28, 9, 31, 18, 40, 21, 43, 11, 33, 13, 35, 16, 38, 20, 42, 22, 44, 12, 34)(45, 67, 47, 69, 49, 71, 56, 78, 59, 81, 66, 88, 63, 85, 64, 86, 54, 76, 60, 82, 51, 73, 57, 79, 48, 70, 55, 77, 58, 80, 65, 87, 61, 83, 62, 84, 52, 74, 53, 75, 46, 68, 50, 72) L = (1, 48)(2, 51)(3, 55)(4, 49)(5, 58)(6, 57)(7, 45)(8, 54)(9, 60)(10, 46)(11, 56)(12, 65)(13, 47)(14, 59)(15, 61)(16, 50)(17, 63)(18, 64)(19, 52)(20, 53)(21, 66)(22, 62)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.94 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (Y2, Y1^-1), (Y3^-1 * Y2)^2, Y3^2 * Y2^-2, Y3 * Y2^2 * Y1^-1, (R * Y3)^2, Y2^2 * Y3 * Y1^-1, (R * Y1)^2, Y1^3 * Y2^2, Y1 * Y3 * Y1 * Y3 * Y1, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 4, 26, 10, 32, 18, 40, 7, 29, 12, 34, 16, 38, 5, 27)(3, 25, 9, 31, 17, 39, 6, 28, 11, 33, 19, 41, 22, 44, 14, 36, 20, 42, 21, 43, 13, 35)(45, 67, 47, 69, 56, 78, 64, 86, 54, 76, 63, 85, 52, 74, 61, 83, 49, 71, 57, 79, 51, 73, 58, 80, 48, 70, 55, 77, 46, 68, 53, 75, 60, 82, 65, 87, 62, 84, 66, 88, 59, 81, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 56)(5, 59)(6, 58)(7, 45)(8, 62)(9, 63)(10, 60)(11, 64)(12, 46)(13, 50)(14, 47)(15, 51)(16, 52)(17, 66)(18, 49)(19, 65)(20, 53)(21, 61)(22, 57)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.97 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1 * Y2, Y2^-2 * Y3^-1 * Y1^-1, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2), (R * Y2)^2, Y1^3 * Y2^-2, Y1^2 * Y3^-1 * Y1 * Y3^-1, (Y1^-1 * Y3^-1)^11, Y2^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 13, 35, 7, 29, 12, 34, 17, 39, 4, 26, 10, 32, 18, 40, 5, 27)(3, 25, 9, 31, 19, 41, 21, 43, 16, 38, 20, 42, 22, 44, 14, 36, 6, 28, 11, 33, 15, 37)(45, 67, 47, 69, 57, 79, 65, 87, 61, 83, 66, 88, 62, 84, 55, 77, 46, 68, 53, 75, 51, 73, 60, 82, 48, 70, 58, 80, 49, 71, 59, 81, 52, 74, 63, 85, 56, 78, 64, 86, 54, 76, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 57)(5, 61)(6, 60)(7, 45)(8, 62)(9, 50)(10, 51)(11, 64)(12, 46)(13, 49)(14, 65)(15, 66)(16, 47)(17, 52)(18, 56)(19, 55)(20, 53)(21, 59)(22, 63)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.101 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y3 * Y1^-3, (R * Y1)^2, (Y2^-1, Y1^-1), Y3^-2 * Y2^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y3 * Y1, Y2^-4 * Y1, Y3 * Y1^-1 * Y3 * Y2^2, (Y3^-1 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 19, 41, 13, 35, 18, 40, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 20, 42, 14, 36, 17, 39, 6, 28, 11, 33, 21, 43, 16, 38, 22, 44, 15, 37)(45, 67, 47, 69, 57, 79, 55, 77, 46, 68, 53, 75, 62, 84, 65, 87, 52, 74, 64, 86, 51, 73, 60, 82, 48, 70, 58, 80, 56, 78, 66, 88, 54, 76, 61, 83, 49, 71, 59, 81, 63, 85, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 57)(5, 52)(6, 60)(7, 45)(8, 63)(9, 61)(10, 62)(11, 66)(12, 46)(13, 56)(14, 55)(15, 64)(16, 47)(17, 65)(18, 49)(19, 51)(20, 50)(21, 59)(22, 53)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.96 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y1^-1 * Y3^-1 * Y1^-2, Y2^2 * Y3^-2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y2^-2 * Y1^2 * Y3^-1, Y1^-1 * Y3^-4, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 13, 35, 19, 41, 17, 39, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 21, 43, 16, 38, 22, 44, 18, 40, 6, 28, 11, 33, 14, 36, 20, 42, 15, 37)(45, 67, 47, 69, 57, 79, 62, 84, 49, 71, 59, 81, 56, 78, 66, 88, 54, 76, 64, 86, 51, 73, 60, 82, 48, 70, 58, 80, 52, 74, 65, 87, 61, 83, 55, 77, 46, 68, 53, 75, 63, 85, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 57)(5, 61)(6, 60)(7, 45)(8, 49)(9, 64)(10, 63)(11, 66)(12, 46)(13, 52)(14, 62)(15, 55)(16, 47)(17, 56)(18, 65)(19, 51)(20, 50)(21, 59)(22, 53)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.100 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y1, Y3^-2 * Y2^2, (Y3, Y2^-1), (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3 * Y2^4 * Y1^-1, Y3^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 17, 39, 19, 41, 21, 43, 11, 33, 15, 37, 4, 26, 5, 27)(3, 25, 8, 30, 14, 36, 16, 38, 6, 28, 9, 31, 18, 40, 20, 42, 22, 44, 12, 34, 13, 35)(45, 67, 47, 69, 55, 77, 64, 86, 54, 76, 60, 82, 49, 71, 57, 79, 65, 87, 62, 84, 51, 73, 58, 80, 48, 70, 56, 78, 63, 85, 53, 75, 46, 68, 52, 74, 59, 81, 66, 88, 61, 83, 50, 72) L = (1, 48)(2, 49)(3, 56)(4, 55)(5, 59)(6, 58)(7, 45)(8, 57)(9, 60)(10, 46)(11, 63)(12, 64)(13, 66)(14, 47)(15, 65)(16, 52)(17, 51)(18, 50)(19, 54)(20, 53)(21, 61)(22, 62)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.95 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 11, 11, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y1, Y3^2 * Y2^-2, (Y3 * Y2^-1)^2, (Y1, Y2), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y3^-5 * Y1^-1, Y2^-2 * Y1^-1 * Y3^-1 * Y2^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 11, 33, 19, 41, 22, 44, 17, 39, 16, 38, 7, 29, 5, 27)(3, 25, 8, 30, 12, 34, 20, 42, 21, 43, 18, 40, 15, 37, 6, 28, 10, 32, 14, 36, 13, 35)(45, 67, 47, 69, 55, 77, 65, 87, 60, 82, 54, 76, 46, 68, 52, 74, 63, 85, 62, 84, 51, 73, 58, 80, 48, 70, 56, 78, 66, 88, 59, 81, 49, 71, 57, 79, 53, 75, 64, 86, 61, 83, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 55)(5, 46)(6, 58)(7, 45)(8, 64)(9, 63)(10, 57)(11, 66)(12, 65)(13, 52)(14, 47)(15, 54)(16, 49)(17, 51)(18, 50)(19, 61)(20, 62)(21, 59)(22, 60)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E15.98 Graph:: bipartite v = 3 e = 44 f = 13 degree seq :: [ 22^2, 44 ] E15.120 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y2^2 * Y1^2 * Y2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 16, 40, 11, 35)(5, 29, 14, 38, 10, 34, 15, 39)(7, 31, 17, 41, 12, 36, 18, 42)(8, 32, 19, 43, 13, 37, 20, 44)(21, 45, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 58, 82, 54, 78, 64, 88, 53, 77)(50, 74, 55, 79, 61, 85, 52, 76, 60, 84, 56, 80)(57, 81, 67, 91, 70, 94, 59, 83, 68, 92, 69, 93)(62, 86, 71, 95, 65, 89, 63, 87, 72, 96, 66, 90) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.121 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y2^-3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 16, 40, 11, 35)(5, 29, 14, 38, 10, 34, 15, 39)(7, 31, 17, 41, 12, 36, 18, 42)(8, 32, 19, 43, 13, 37, 20, 44)(21, 45, 23, 47, 22, 46, 24, 48)(49, 73, 51, 75, 58, 82, 54, 78, 64, 88, 53, 77)(50, 74, 55, 79, 61, 85, 52, 76, 60, 84, 56, 80)(57, 81, 68, 92, 70, 94, 59, 83, 67, 91, 69, 93)(62, 86, 71, 95, 66, 90, 63, 87, 72, 96, 65, 89) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.122 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = (C12 x C2) : C2 (small group id <48, 14>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2 * Y2, Y2^2 * Y1^2, Y1^4, Y3 * Y2^-1 * Y3 * Y2, (Y1^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y1^-1 * Y3^-2, Y3^-1 * Y1 * Y3^2 * Y2^-1, (Y3 * Y1^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 11, 35, 20, 44, 7, 31)(2, 26, 10, 34, 14, 38, 3, 27, 13, 37, 12, 36)(5, 29, 18, 42, 17, 41, 6, 30, 19, 43, 16, 40)(8, 32, 21, 45, 24, 48, 9, 33, 23, 47, 22, 46)(49, 50, 56, 53)(51, 57, 54, 59)(52, 60, 69, 64)(55, 58, 70, 66)(61, 72, 67, 63)(62, 71, 65, 68)(73, 75, 80, 78)(74, 81, 77, 83)(76, 86, 93, 89)(79, 85, 94, 91)(82, 96, 90, 87)(84, 95, 88, 92) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.130 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.123 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = (C12 x C2) : C2 (small group id <48, 14>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y1, Y2 * Y1^2 * Y2, Y1^4, Y1 * Y3 * Y1^-1 * Y3, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2^2 * Y3^-2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 8, 32, 20, 44, 7, 31)(2, 26, 10, 34, 16, 40, 5, 29, 18, 42, 12, 36)(3, 27, 13, 37, 17, 41, 6, 30, 19, 43, 14, 38)(9, 33, 21, 45, 23, 47, 11, 35, 24, 48, 22, 46)(49, 50, 56, 53)(51, 57, 54, 59)(52, 60, 68, 64)(55, 58, 63, 66)(61, 70, 67, 71)(62, 69, 65, 72)(73, 75, 80, 78)(74, 81, 77, 83)(76, 86, 92, 89)(79, 85, 87, 91)(82, 94, 90, 95)(84, 93, 88, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.129 Graph:: bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.124 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x C4 x S3 (small group id <48, 35>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y3^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 11, 35, 19, 43, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 22, 46, 16, 40, 8, 32)(3, 27, 9, 33, 17, 41, 23, 47, 18, 42, 10, 34)(6, 30, 13, 37, 20, 44, 24, 48, 21, 45, 14, 38)(49, 50, 54, 51)(52, 56, 61, 58)(53, 55, 62, 57)(59, 64, 68, 66)(60, 63, 69, 65)(67, 70, 72, 71)(73, 75, 78, 74)(76, 82, 85, 80)(77, 81, 86, 79)(83, 90, 92, 88)(84, 89, 93, 87)(91, 95, 96, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.131 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.125 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y1^4, Y3^6, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 17, 41, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 22, 46, 16, 40, 8, 32)(4, 28, 11, 35, 19, 43, 23, 47, 18, 42, 10, 34)(6, 30, 13, 37, 20, 44, 24, 48, 21, 45, 14, 38)(49, 50, 54, 52)(51, 56, 61, 58)(53, 55, 62, 59)(57, 64, 68, 66)(60, 63, 69, 67)(65, 70, 72, 71)(73, 74, 78, 76)(75, 80, 85, 82)(77, 79, 86, 83)(81, 88, 92, 90)(84, 87, 93, 91)(89, 94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.132 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.126 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, Y1^-1 * Y3^-2 * Y2^-1, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y2^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y1^-1 * Y3^2, Y3 * Y2 * Y3 * Y1^-1, R * Y1 * R * Y2, Y3^4, Y3 * Y1 * Y3 * Y2^-1, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 9, 33, 7, 31)(2, 26, 10, 34, 6, 30, 12, 36)(3, 27, 14, 38, 5, 29, 16, 40)(8, 32, 18, 42, 11, 35, 20, 44)(13, 37, 21, 45, 15, 39, 22, 46)(17, 41, 23, 47, 19, 43, 24, 48)(49, 50, 56, 65, 61, 53)(51, 57, 54, 59, 67, 63)(52, 64, 69, 71, 66, 58)(55, 62, 70, 72, 68, 60)(73, 75, 85, 91, 80, 78)(74, 81, 77, 87, 89, 83)(76, 84, 90, 96, 93, 86)(79, 82, 92, 95, 94, 88) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.133 Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.127 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y1^6, Y2^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 12, 36, 5, 29)(2, 26, 7, 31, 16, 40, 8, 32)(3, 27, 10, 34, 19, 43, 11, 35)(6, 30, 14, 38, 22, 46, 15, 39)(9, 33, 17, 41, 23, 47, 18, 42)(13, 37, 20, 44, 24, 48, 21, 45)(49, 50, 54, 61, 57, 51)(52, 58, 65, 68, 62, 55)(53, 59, 66, 69, 63, 56)(60, 64, 70, 72, 71, 67)(73, 75, 81, 85, 78, 74)(76, 79, 86, 92, 89, 82)(77, 80, 87, 93, 90, 83)(84, 91, 95, 96, 94, 88) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.134 Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.128 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y2^-1 * Y1^-1, Y1^-1 * Y2^-1, (R * Y3)^2, Y3^4, R * Y1 * R * Y2, (Y3 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^6, Y2^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 12, 36, 5, 29)(2, 26, 7, 31, 16, 40, 8, 32)(3, 27, 10, 34, 19, 43, 11, 35)(6, 30, 14, 38, 22, 46, 15, 39)(9, 33, 17, 41, 23, 47, 18, 42)(13, 37, 20, 44, 24, 48, 21, 45)(49, 50, 54, 61, 57, 51)(52, 59, 65, 69, 62, 56)(53, 58, 66, 68, 63, 55)(60, 64, 70, 72, 71, 67)(73, 75, 81, 85, 78, 74)(76, 80, 86, 93, 89, 83)(77, 79, 87, 92, 90, 82)(84, 91, 95, 96, 94, 88) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.135 Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.129 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = (C12 x C2) : C2 (small group id <48, 14>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2 * Y2, Y2^2 * Y1^2, Y1^4, Y3 * Y2^-1 * Y3 * Y2, (Y1^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y1^-1 * Y3^-2, Y3^-1 * Y1 * Y3^2 * Y2^-1, (Y3 * Y1^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 11, 35, 59, 83, 20, 44, 68, 92, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 14, 38, 62, 86, 3, 27, 51, 75, 13, 37, 61, 85, 12, 36, 60, 84)(5, 29, 53, 77, 18, 42, 66, 90, 17, 41, 65, 89, 6, 30, 54, 78, 19, 43, 67, 91, 16, 40, 64, 88)(8, 32, 56, 80, 21, 45, 69, 93, 24, 48, 72, 96, 9, 33, 57, 81, 23, 47, 71, 95, 22, 46, 70, 94) L = (1, 26)(2, 32)(3, 33)(4, 36)(5, 25)(6, 35)(7, 34)(8, 29)(9, 30)(10, 46)(11, 27)(12, 45)(13, 48)(14, 47)(15, 37)(16, 28)(17, 44)(18, 31)(19, 39)(20, 38)(21, 40)(22, 42)(23, 41)(24, 43)(49, 75)(50, 81)(51, 80)(52, 86)(53, 83)(54, 73)(55, 85)(56, 78)(57, 77)(58, 96)(59, 74)(60, 95)(61, 94)(62, 93)(63, 82)(64, 92)(65, 76)(66, 87)(67, 79)(68, 84)(69, 89)(70, 91)(71, 88)(72, 90) 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 E15.123 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.130 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = (C12 x C2) : C2 (small group id <48, 14>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y1, Y2 * Y1^2 * Y2, Y1^4, Y1 * Y3 * Y1^-1 * Y3, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2^2 * Y3^-2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 8, 32, 56, 80, 20, 44, 68, 92, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 16, 40, 64, 88, 5, 29, 53, 77, 18, 42, 66, 90, 12, 36, 60, 84)(3, 27, 51, 75, 13, 37, 61, 85, 17, 41, 65, 89, 6, 30, 54, 78, 19, 43, 67, 91, 14, 38, 62, 86)(9, 33, 57, 81, 21, 45, 69, 93, 23, 47, 71, 95, 11, 35, 59, 83, 24, 48, 72, 96, 22, 46, 70, 94) L = (1, 26)(2, 32)(3, 33)(4, 36)(5, 25)(6, 35)(7, 34)(8, 29)(9, 30)(10, 39)(11, 27)(12, 44)(13, 46)(14, 45)(15, 42)(16, 28)(17, 48)(18, 31)(19, 47)(20, 40)(21, 41)(22, 43)(23, 37)(24, 38)(49, 75)(50, 81)(51, 80)(52, 86)(53, 83)(54, 73)(55, 85)(56, 78)(57, 77)(58, 94)(59, 74)(60, 93)(61, 87)(62, 92)(63, 91)(64, 96)(65, 76)(66, 95)(67, 79)(68, 89)(69, 88)(70, 90)(71, 82)(72, 84) 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 E15.122 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.131 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x C4 x S3 (small group id <48, 35>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y3^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 11, 35, 59, 83, 19, 43, 67, 91, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 15, 39, 63, 87, 22, 46, 70, 94, 16, 40, 64, 88, 8, 32, 56, 80)(3, 27, 51, 75, 9, 33, 57, 81, 17, 41, 65, 89, 23, 47, 71, 95, 18, 42, 66, 90, 10, 34, 58, 82)(6, 30, 54, 78, 13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93, 14, 38, 62, 86) L = (1, 26)(2, 30)(3, 25)(4, 32)(5, 31)(6, 27)(7, 38)(8, 37)(9, 29)(10, 28)(11, 40)(12, 39)(13, 34)(14, 33)(15, 45)(16, 44)(17, 36)(18, 35)(19, 46)(20, 42)(21, 41)(22, 48)(23, 43)(24, 47)(49, 75)(50, 73)(51, 78)(52, 82)(53, 81)(54, 74)(55, 77)(56, 76)(57, 86)(58, 85)(59, 90)(60, 89)(61, 80)(62, 79)(63, 84)(64, 83)(65, 93)(66, 92)(67, 95)(68, 88)(69, 87)(70, 91)(71, 96)(72, 94) 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 E15.124 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.132 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y1^4, Y3^6, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75, 9, 33, 57, 81, 17, 41, 65, 89, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 15, 39, 63, 87, 22, 46, 70, 94, 16, 40, 64, 88, 8, 32, 56, 80)(4, 28, 52, 76, 11, 35, 59, 83, 19, 43, 67, 91, 23, 47, 71, 95, 18, 42, 66, 90, 10, 34, 58, 82)(6, 30, 54, 78, 13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93, 14, 38, 62, 86) L = (1, 26)(2, 30)(3, 32)(4, 25)(5, 31)(6, 28)(7, 38)(8, 37)(9, 40)(10, 27)(11, 29)(12, 39)(13, 34)(14, 35)(15, 45)(16, 44)(17, 46)(18, 33)(19, 36)(20, 42)(21, 43)(22, 48)(23, 41)(24, 47)(49, 74)(50, 78)(51, 80)(52, 73)(53, 79)(54, 76)(55, 86)(56, 85)(57, 88)(58, 75)(59, 77)(60, 87)(61, 82)(62, 83)(63, 93)(64, 92)(65, 94)(66, 81)(67, 84)(68, 90)(69, 91)(70, 96)(71, 89)(72, 95) 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 E15.125 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.133 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, Y1^-1 * Y3^-2 * Y2^-1, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y2^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y1^-1 * Y3^2, Y3 * Y2 * Y3 * Y1^-1, R * Y1 * R * Y2, Y3^4, Y3 * Y1 * Y3 * Y2^-1, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 9, 33, 57, 81, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 6, 30, 54, 78, 12, 36, 60, 84)(3, 27, 51, 75, 14, 38, 62, 86, 5, 29, 53, 77, 16, 40, 64, 88)(8, 32, 56, 80, 18, 42, 66, 90, 11, 35, 59, 83, 20, 44, 68, 92)(13, 37, 61, 85, 21, 45, 69, 93, 15, 39, 63, 87, 22, 46, 70, 94)(17, 41, 65, 89, 23, 47, 71, 95, 19, 43, 67, 91, 24, 48, 72, 96) L = (1, 26)(2, 32)(3, 33)(4, 40)(5, 25)(6, 35)(7, 38)(8, 41)(9, 30)(10, 28)(11, 43)(12, 31)(13, 29)(14, 46)(15, 27)(16, 45)(17, 37)(18, 34)(19, 39)(20, 36)(21, 47)(22, 48)(23, 42)(24, 44)(49, 75)(50, 81)(51, 85)(52, 84)(53, 87)(54, 73)(55, 82)(56, 78)(57, 77)(58, 92)(59, 74)(60, 90)(61, 91)(62, 76)(63, 89)(64, 79)(65, 83)(66, 96)(67, 80)(68, 95)(69, 86)(70, 88)(71, 94)(72, 93) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.126 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.134 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y1^6, Y2^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 16, 40, 64, 88, 8, 32, 56, 80)(3, 27, 51, 75, 10, 34, 58, 82, 19, 43, 67, 91, 11, 35, 59, 83)(6, 30, 54, 78, 14, 38, 62, 86, 22, 46, 70, 94, 15, 39, 63, 87)(9, 33, 57, 81, 17, 41, 65, 89, 23, 47, 71, 95, 18, 42, 66, 90)(13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93) L = (1, 26)(2, 30)(3, 25)(4, 34)(5, 35)(6, 37)(7, 28)(8, 29)(9, 27)(10, 41)(11, 42)(12, 40)(13, 33)(14, 31)(15, 32)(16, 46)(17, 44)(18, 45)(19, 36)(20, 38)(21, 39)(22, 48)(23, 43)(24, 47)(49, 75)(50, 73)(51, 81)(52, 79)(53, 80)(54, 74)(55, 86)(56, 87)(57, 85)(58, 76)(59, 77)(60, 91)(61, 78)(62, 92)(63, 93)(64, 84)(65, 82)(66, 83)(67, 95)(68, 89)(69, 90)(70, 88)(71, 96)(72, 94) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.127 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.135 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y2^-1 * Y1^-1, Y1^-1 * Y2^-1, (R * Y3)^2, Y3^4, R * Y1 * R * Y2, (Y3 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^6, Y2^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 16, 40, 64, 88, 8, 32, 56, 80)(3, 27, 51, 75, 10, 34, 58, 82, 19, 43, 67, 91, 11, 35, 59, 83)(6, 30, 54, 78, 14, 38, 62, 86, 22, 46, 70, 94, 15, 39, 63, 87)(9, 33, 57, 81, 17, 41, 65, 89, 23, 47, 71, 95, 18, 42, 66, 90)(13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93) L = (1, 26)(2, 30)(3, 25)(4, 35)(5, 34)(6, 37)(7, 29)(8, 28)(9, 27)(10, 42)(11, 41)(12, 40)(13, 33)(14, 32)(15, 31)(16, 46)(17, 45)(18, 44)(19, 36)(20, 39)(21, 38)(22, 48)(23, 43)(24, 47)(49, 75)(50, 73)(51, 81)(52, 80)(53, 79)(54, 74)(55, 87)(56, 86)(57, 85)(58, 77)(59, 76)(60, 91)(61, 78)(62, 93)(63, 92)(64, 84)(65, 83)(66, 82)(67, 95)(68, 90)(69, 89)(70, 88)(71, 96)(72, 94) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.128 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2^6, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 8, 32, 13, 37, 10, 34)(5, 29, 7, 31, 14, 38, 11, 35)(9, 33, 16, 40, 20, 44, 18, 42)(12, 36, 15, 39, 21, 45, 19, 43)(17, 41, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 57, 81, 65, 89, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 59, 83, 67, 91, 71, 95, 66, 90, 58, 82)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y2)^2, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 5, 29)(3, 27, 8, 32, 10, 34, 11, 35)(6, 30, 7, 31, 12, 36, 13, 37)(9, 33, 16, 40, 18, 42, 19, 43)(14, 38, 15, 39, 20, 44, 21, 45)(17, 41, 22, 46, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 65, 89, 62, 86, 54, 78)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 58, 82, 66, 90, 71, 95, 68, 92, 60, 84)(53, 77, 61, 85, 69, 93, 72, 96, 67, 91, 59, 83) L = (1, 52)(2, 53)(3, 58)(4, 49)(5, 50)(6, 60)(7, 61)(8, 59)(9, 66)(10, 51)(11, 56)(12, 54)(13, 55)(14, 68)(15, 69)(16, 67)(17, 71)(18, 57)(19, 64)(20, 62)(21, 63)(22, 72)(23, 65)(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) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y2 * Y1 * Y2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y1^4, (R * Y2)^2, Y3 * Y2^-3 * Y1^-2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 10, 34, 18, 42, 13, 37)(4, 28, 9, 33, 19, 43, 14, 38)(6, 30, 8, 32, 20, 44, 16, 40)(11, 35, 24, 48, 15, 39, 22, 46)(12, 36, 23, 47, 17, 41, 21, 45)(49, 73, 51, 75, 59, 83, 67, 91, 65, 89, 54, 78)(50, 74, 56, 80, 69, 93, 62, 86, 72, 96, 58, 82)(52, 76, 60, 84, 68, 92, 55, 79, 66, 90, 63, 87)(53, 77, 64, 88, 71, 95, 57, 81, 70, 94, 61, 85) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 67)(8, 70)(9, 50)(10, 71)(11, 68)(12, 51)(13, 69)(14, 53)(15, 54)(16, 72)(17, 66)(18, 65)(19, 55)(20, 59)(21, 61)(22, 56)(23, 58)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.142 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y3^3, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y2)^2, Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 18, 42, 14, 38)(4, 28, 12, 36, 19, 43, 15, 39)(6, 30, 9, 33, 20, 44, 16, 40)(7, 31, 10, 34, 21, 45, 17, 41)(13, 37, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 52, 76, 61, 85, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 70, 94, 60, 84, 59, 83)(53, 77, 64, 88, 65, 89, 71, 95, 63, 87, 62, 86)(56, 80, 66, 90, 67, 91, 72, 96, 69, 93, 68, 92) L = (1, 52)(2, 58)(3, 61)(4, 55)(5, 65)(6, 51)(7, 49)(8, 67)(9, 70)(10, 60)(11, 57)(12, 50)(13, 54)(14, 64)(15, 53)(16, 71)(17, 63)(18, 72)(19, 69)(20, 66)(21, 56)(22, 59)(23, 62)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^-2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (Y2^-1, Y3), (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^4, (R * Y2)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-2, Y3 * Y1 * Y2 * Y1 * Y2^-1, Y3^-2 * Y1^2 * Y3^-1, Y1^-2 * Y2^2 * Y3^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 19, 43, 15, 39)(4, 28, 12, 36, 13, 37, 18, 42)(6, 30, 9, 33, 16, 40, 20, 44)(7, 31, 10, 34, 17, 41, 21, 45)(14, 38, 22, 46, 23, 47, 24, 48)(49, 73, 51, 75, 61, 85, 71, 95, 65, 89, 54, 78)(50, 74, 57, 81, 69, 93, 72, 96, 66, 90, 59, 83)(52, 76, 62, 86, 55, 79, 64, 88, 56, 80, 67, 91)(53, 77, 68, 92, 58, 82, 70, 94, 60, 84, 63, 87) L = (1, 52)(2, 58)(3, 62)(4, 65)(5, 69)(6, 67)(7, 49)(8, 61)(9, 70)(10, 66)(11, 68)(12, 50)(13, 55)(14, 54)(15, 57)(16, 51)(17, 56)(18, 53)(19, 71)(20, 72)(21, 60)(22, 59)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^-2, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y2^-1, Y3^-1), Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2 * Y1^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2)^2, Y3^6, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 7, 31, 10, 34)(4, 28, 12, 36, 6, 30, 9, 33)(13, 37, 19, 43, 14, 38, 20, 44)(15, 39, 17, 41, 16, 40, 18, 42)(21, 45, 23, 47, 22, 46, 24, 48)(49, 73, 51, 75, 61, 85, 69, 93, 63, 87, 54, 78)(50, 74, 57, 81, 65, 89, 71, 95, 67, 91, 59, 83)(52, 76, 56, 80, 55, 79, 62, 86, 70, 94, 64, 88)(53, 77, 60, 84, 66, 90, 72, 96, 68, 92, 58, 82) L = (1, 52)(2, 58)(3, 56)(4, 63)(5, 59)(6, 64)(7, 49)(8, 54)(9, 53)(10, 67)(11, 68)(12, 50)(13, 55)(14, 51)(15, 70)(16, 69)(17, 60)(18, 57)(19, 72)(20, 71)(21, 62)(22, 61)(23, 66)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.143 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.142 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, Y1^4, Y2^-1 * Y1^2 * Y2^-2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 10, 34, 17, 41, 13, 37)(4, 28, 9, 33, 18, 42, 14, 38)(6, 30, 8, 32, 11, 35, 16, 40)(12, 36, 20, 44, 24, 48, 22, 46)(15, 39, 19, 43, 21, 45, 23, 47)(49, 73, 51, 75, 59, 83, 55, 79, 65, 89, 54, 78)(50, 74, 56, 80, 61, 85, 53, 77, 64, 88, 58, 82)(52, 76, 60, 84, 69, 93, 66, 90, 72, 96, 63, 87)(57, 81, 67, 91, 70, 94, 62, 86, 71, 95, 68, 92) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 66)(8, 67)(9, 50)(10, 68)(11, 69)(12, 51)(13, 70)(14, 53)(15, 54)(16, 71)(17, 72)(18, 55)(19, 56)(20, 58)(21, 59)(22, 61)(23, 64)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.138 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.143 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x (C3 : C4) (small group id <24, 7>) Aut = C2 x ((C6 x C2) : C2) (small group id <48, 43>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2^-2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, Y2^-1 * Y1^2 * Y2^-2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1, (Y2^-1 * Y3)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 17, 41, 15, 39)(4, 28, 12, 36, 16, 40, 18, 42)(6, 30, 9, 33, 13, 37, 20, 44)(7, 31, 10, 34, 19, 43, 21, 45)(14, 38, 22, 46, 23, 47, 24, 48)(49, 73, 51, 75, 61, 85, 56, 80, 65, 89, 54, 78)(50, 74, 57, 81, 63, 87, 53, 77, 68, 92, 59, 83)(52, 76, 62, 86, 55, 79, 64, 88, 71, 95, 67, 91)(58, 82, 70, 94, 60, 84, 69, 93, 72, 96, 66, 90) L = (1, 52)(2, 58)(3, 62)(4, 65)(5, 69)(6, 67)(7, 49)(8, 64)(9, 70)(10, 68)(11, 66)(12, 50)(13, 55)(14, 54)(15, 60)(16, 51)(17, 71)(18, 53)(19, 56)(20, 72)(21, 57)(22, 59)(23, 61)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.141 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.144 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y3 * Y1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3 * Y2^-1, Y3^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 11, 35, 19, 43, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 22, 46, 16, 40, 8, 32)(3, 27, 9, 33, 17, 41, 23, 47, 18, 42, 10, 34)(6, 30, 13, 37, 20, 44, 24, 48, 21, 45, 14, 38)(49, 50, 54, 51)(52, 57, 61, 55)(53, 58, 62, 56)(59, 63, 68, 65)(60, 64, 69, 66)(67, 71, 72, 70)(73, 75, 78, 74)(76, 79, 85, 81)(77, 80, 86, 82)(83, 89, 92, 87)(84, 90, 93, 88)(91, 94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.148 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.145 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y3 * Y1 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y3^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 11, 35, 19, 43, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 22, 46, 16, 40, 8, 32)(3, 27, 9, 33, 17, 41, 23, 47, 18, 42, 10, 34)(6, 30, 13, 37, 20, 44, 24, 48, 21, 45, 14, 38)(49, 50, 54, 51)(52, 58, 61, 56)(53, 57, 62, 55)(59, 64, 68, 66)(60, 63, 69, 65)(67, 71, 72, 70)(73, 75, 78, 74)(76, 80, 85, 82)(77, 79, 86, 81)(83, 90, 92, 88)(84, 89, 93, 87)(91, 94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.149 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.146 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y3^-1 * Y2 * Y3 * Y1^-1, (Y3^-1 * Y2^-1)^2, Y3^2 * Y1^-1 * Y2^-1, Y2^-1 * Y1^-2 * Y2^-1, Y1^-2 * Y2^2, (Y2^-1 * Y3)^2, Y3^2 * Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, (Y1^-1 * Y2^-1)^3, Y3^2 * Y2 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 4, 28, 13, 37, 23, 47, 9, 33, 7, 31)(2, 26, 10, 34, 21, 45, 17, 41, 6, 30, 12, 36)(3, 27, 14, 38, 5, 29, 18, 42, 22, 46, 16, 40)(8, 32, 19, 43, 15, 39, 24, 48, 11, 35, 20, 44)(49, 50, 56, 53)(51, 61, 54, 63)(52, 62, 67, 60)(55, 66, 68, 58)(57, 69, 59, 70)(64, 72, 65, 71)(73, 75, 80, 78)(74, 81, 77, 83)(76, 89, 91, 88)(79, 84, 92, 86)(82, 96, 90, 95)(85, 94, 87, 93) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.150 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.147 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, (Y3 * Y1^-1)^2, Y3^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y3^2 * Y1^-1, Y1^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 9, 33, 7, 31)(2, 26, 10, 34, 6, 30, 12, 36)(3, 27, 14, 38, 5, 29, 16, 40)(8, 32, 18, 42, 11, 35, 20, 44)(13, 37, 21, 45, 15, 39, 22, 46)(17, 41, 23, 47, 19, 43, 24, 48)(49, 50, 56, 65, 61, 53)(51, 57, 54, 59, 67, 63)(52, 62, 69, 72, 66, 60)(55, 64, 70, 71, 68, 58)(73, 75, 85, 91, 80, 78)(74, 81, 77, 87, 89, 83)(76, 82, 90, 95, 93, 88)(79, 84, 92, 96, 94, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.151 Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.148 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y3 * Y1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3 * Y2^-1, Y3^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 11, 35, 59, 83, 19, 43, 67, 91, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 15, 39, 63, 87, 22, 46, 70, 94, 16, 40, 64, 88, 8, 32, 56, 80)(3, 27, 51, 75, 9, 33, 57, 81, 17, 41, 65, 89, 23, 47, 71, 95, 18, 42, 66, 90, 10, 34, 58, 82)(6, 30, 54, 78, 13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93, 14, 38, 62, 86) L = (1, 26)(2, 30)(3, 25)(4, 33)(5, 34)(6, 27)(7, 28)(8, 29)(9, 37)(10, 38)(11, 39)(12, 40)(13, 31)(14, 32)(15, 44)(16, 45)(17, 35)(18, 36)(19, 47)(20, 41)(21, 42)(22, 43)(23, 48)(24, 46)(49, 75)(50, 73)(51, 78)(52, 79)(53, 80)(54, 74)(55, 85)(56, 86)(57, 76)(58, 77)(59, 89)(60, 90)(61, 81)(62, 82)(63, 83)(64, 84)(65, 92)(66, 93)(67, 94)(68, 87)(69, 88)(70, 96)(71, 91)(72, 95) 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 E15.144 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.149 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y3 * Y1 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y3^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 11, 35, 59, 83, 19, 43, 67, 91, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 15, 39, 63, 87, 22, 46, 70, 94, 16, 40, 64, 88, 8, 32, 56, 80)(3, 27, 51, 75, 9, 33, 57, 81, 17, 41, 65, 89, 23, 47, 71, 95, 18, 42, 66, 90, 10, 34, 58, 82)(6, 30, 54, 78, 13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93, 14, 38, 62, 86) L = (1, 26)(2, 30)(3, 25)(4, 34)(5, 33)(6, 27)(7, 29)(8, 28)(9, 38)(10, 37)(11, 40)(12, 39)(13, 32)(14, 31)(15, 45)(16, 44)(17, 36)(18, 35)(19, 47)(20, 42)(21, 41)(22, 43)(23, 48)(24, 46)(49, 75)(50, 73)(51, 78)(52, 80)(53, 79)(54, 74)(55, 86)(56, 85)(57, 77)(58, 76)(59, 90)(60, 89)(61, 82)(62, 81)(63, 84)(64, 83)(65, 93)(66, 92)(67, 94)(68, 88)(69, 87)(70, 96)(71, 91)(72, 95) 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 E15.145 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.150 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y3^-1 * Y2 * Y3 * Y1^-1, (Y3^-1 * Y2^-1)^2, Y3^2 * Y1^-1 * Y2^-1, Y2^-1 * Y1^-2 * Y2^-1, Y1^-2 * Y2^2, (Y2^-1 * Y3)^2, Y3^2 * Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, (Y1^-1 * Y2^-1)^3, Y3^2 * Y2 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 13, 37, 61, 85, 23, 47, 71, 95, 9, 33, 57, 81, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 21, 45, 69, 93, 17, 41, 65, 89, 6, 30, 54, 78, 12, 36, 60, 84)(3, 27, 51, 75, 14, 38, 62, 86, 5, 29, 53, 77, 18, 42, 66, 90, 22, 46, 70, 94, 16, 40, 64, 88)(8, 32, 56, 80, 19, 43, 67, 91, 15, 39, 63, 87, 24, 48, 72, 96, 11, 35, 59, 83, 20, 44, 68, 92) L = (1, 26)(2, 32)(3, 37)(4, 38)(5, 25)(6, 39)(7, 42)(8, 29)(9, 45)(10, 31)(11, 46)(12, 28)(13, 30)(14, 43)(15, 27)(16, 48)(17, 47)(18, 44)(19, 36)(20, 34)(21, 35)(22, 33)(23, 40)(24, 41)(49, 75)(50, 81)(51, 80)(52, 89)(53, 83)(54, 73)(55, 84)(56, 78)(57, 77)(58, 96)(59, 74)(60, 92)(61, 94)(62, 79)(63, 93)(64, 76)(65, 91)(66, 95)(67, 88)(68, 86)(69, 85)(70, 87)(71, 82)(72, 90) 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 E15.146 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.151 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, (Y3 * Y1^-1)^2, Y3^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y3^2 * Y1^-1, Y1^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 9, 33, 57, 81, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 6, 30, 54, 78, 12, 36, 60, 84)(3, 27, 51, 75, 14, 38, 62, 86, 5, 29, 53, 77, 16, 40, 64, 88)(8, 32, 56, 80, 18, 42, 66, 90, 11, 35, 59, 83, 20, 44, 68, 92)(13, 37, 61, 85, 21, 45, 69, 93, 15, 39, 63, 87, 22, 46, 70, 94)(17, 41, 65, 89, 23, 47, 71, 95, 19, 43, 67, 91, 24, 48, 72, 96) L = (1, 26)(2, 32)(3, 33)(4, 38)(5, 25)(6, 35)(7, 40)(8, 41)(9, 30)(10, 31)(11, 43)(12, 28)(13, 29)(14, 45)(15, 27)(16, 46)(17, 37)(18, 36)(19, 39)(20, 34)(21, 48)(22, 47)(23, 44)(24, 42)(49, 75)(50, 81)(51, 85)(52, 82)(53, 87)(54, 73)(55, 84)(56, 78)(57, 77)(58, 90)(59, 74)(60, 92)(61, 91)(62, 79)(63, 89)(64, 76)(65, 83)(66, 95)(67, 80)(68, 96)(69, 88)(70, 86)(71, 93)(72, 94) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.147 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ 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, Y2^6, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 7, 31)(5, 29, 11, 35, 14, 38, 8, 32)(10, 34, 15, 39, 20, 44, 17, 41)(12, 36, 16, 40, 21, 45, 19, 43)(18, 42, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 57, 81, 65, 89, 71, 95, 67, 91, 59, 83)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.153 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 8, 32)(5, 29, 11, 35, 14, 38, 7, 31)(10, 34, 16, 40, 20, 44, 17, 41)(12, 36, 15, 39, 21, 45, 19, 43)(18, 42, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 59, 83, 67, 91, 71, 95, 65, 89, 57, 81)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.154 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^-2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y1 * Y2 * Y1 * Y2^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 5, 29)(3, 27, 9, 33, 11, 35, 7, 31)(6, 30, 13, 37, 12, 36, 8, 32)(10, 34, 15, 39, 19, 43, 17, 41)(14, 38, 16, 40, 20, 44, 21, 45)(18, 42, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 62, 86, 54, 78)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 59, 83, 67, 91, 72, 96, 68, 92, 60, 84)(53, 77, 57, 81, 65, 89, 71, 95, 69, 93, 61, 85) L = (1, 52)(2, 53)(3, 59)(4, 49)(5, 50)(6, 60)(7, 57)(8, 61)(9, 55)(10, 67)(11, 51)(12, 54)(13, 56)(14, 68)(15, 65)(16, 69)(17, 63)(18, 72)(19, 58)(20, 62)(21, 64)(22, 71)(23, 70)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.155 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^-2, (R * Y2)^2, (R * Y3)^2, (Y1 * Y2^-1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (Y1^-1 * Y2^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 5, 29)(3, 27, 9, 33, 11, 35, 8, 32)(6, 30, 13, 37, 12, 36, 7, 31)(10, 34, 16, 40, 19, 43, 17, 41)(14, 38, 15, 39, 20, 44, 21, 45)(18, 42, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 62, 86, 54, 78)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 59, 83, 67, 91, 72, 96, 68, 92, 60, 84)(53, 77, 61, 85, 69, 93, 71, 95, 65, 89, 57, 81) L = (1, 52)(2, 53)(3, 59)(4, 49)(5, 50)(6, 60)(7, 61)(8, 57)(9, 56)(10, 67)(11, 51)(12, 54)(13, 55)(14, 68)(15, 69)(16, 65)(17, 64)(18, 72)(19, 58)(20, 62)(21, 63)(22, 71)(23, 70)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.156 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y3^-1 * Y2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1, (R * Y2)^2, (Y2 * Y1)^2, Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 18, 42, 11, 35)(4, 28, 12, 36, 19, 43, 15, 39)(6, 30, 16, 40, 20, 44, 9, 33)(7, 31, 10, 34, 21, 45, 17, 41)(14, 38, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 52, 76, 62, 86, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 70, 94, 60, 84, 59, 83)(53, 77, 64, 88, 65, 89, 71, 95, 63, 87, 61, 85)(56, 80, 66, 90, 67, 91, 72, 96, 69, 93, 68, 92) L = (1, 52)(2, 58)(3, 62)(4, 55)(5, 65)(6, 51)(7, 49)(8, 67)(9, 70)(10, 60)(11, 57)(12, 50)(13, 64)(14, 54)(15, 53)(16, 71)(17, 63)(18, 72)(19, 69)(20, 66)(21, 56)(22, 59)(23, 61)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.157 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y2^-2, Y1^4, (R * Y2)^2, (Y1 * Y2)^2, (Y2^-1 * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^-2 * Y2^2 * Y3^-1, Y3^-2 * Y1^2 * Y3^-1, Y3 * Y1 * Y2 * Y1^-1 * Y2^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 13, 37, 19, 43, 11, 35)(4, 28, 12, 36, 14, 38, 18, 42)(6, 30, 20, 44, 16, 40, 9, 33)(7, 31, 10, 34, 17, 41, 21, 45)(15, 39, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 62, 86, 72, 96, 65, 89, 54, 78)(50, 74, 57, 81, 69, 93, 71, 95, 66, 90, 59, 83)(52, 76, 63, 87, 55, 79, 64, 88, 56, 80, 67, 91)(53, 77, 68, 92, 58, 82, 70, 94, 60, 84, 61, 85) L = (1, 52)(2, 58)(3, 63)(4, 65)(5, 69)(6, 67)(7, 49)(8, 62)(9, 70)(10, 66)(11, 68)(12, 50)(13, 57)(14, 55)(15, 54)(16, 51)(17, 56)(18, 53)(19, 72)(20, 71)(21, 60)(22, 59)(23, 61)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.158 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = C6 x D8 (small group id <48, 45>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y1^6, Y2^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 12, 36, 5, 29)(2, 26, 7, 31, 16, 40, 8, 32)(3, 27, 10, 34, 19, 43, 11, 35)(6, 30, 14, 38, 22, 46, 15, 39)(9, 33, 17, 41, 23, 47, 18, 42)(13, 37, 20, 44, 24, 48, 21, 45)(49, 50, 54, 61, 57, 51)(52, 56, 62, 69, 65, 59)(53, 55, 63, 68, 66, 58)(60, 64, 70, 72, 71, 67)(73, 75, 81, 85, 78, 74)(76, 83, 89, 93, 86, 80)(77, 82, 90, 92, 87, 79)(84, 91, 95, 96, 94, 88) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.159 Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.159 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = C6 x D8 (small group id <48, 45>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y1^6, Y2^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 12, 36, 60, 84, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 16, 40, 64, 88, 8, 32, 56, 80)(3, 27, 51, 75, 10, 34, 58, 82, 19, 43, 67, 91, 11, 35, 59, 83)(6, 30, 54, 78, 14, 38, 62, 86, 22, 46, 70, 94, 15, 39, 63, 87)(9, 33, 57, 81, 17, 41, 65, 89, 23, 47, 71, 95, 18, 42, 66, 90)(13, 37, 61, 85, 20, 44, 68, 92, 24, 48, 72, 96, 21, 45, 69, 93) L = (1, 26)(2, 30)(3, 25)(4, 32)(5, 31)(6, 37)(7, 39)(8, 38)(9, 27)(10, 29)(11, 28)(12, 40)(13, 33)(14, 45)(15, 44)(16, 46)(17, 35)(18, 34)(19, 36)(20, 42)(21, 41)(22, 48)(23, 43)(24, 47)(49, 75)(50, 73)(51, 81)(52, 83)(53, 82)(54, 74)(55, 77)(56, 76)(57, 85)(58, 90)(59, 89)(60, 91)(61, 78)(62, 80)(63, 79)(64, 84)(65, 93)(66, 92)(67, 95)(68, 87)(69, 86)(70, 88)(71, 96)(72, 94) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.158 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.160 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 7, 31, 13, 37, 10, 34)(5, 29, 8, 32, 14, 38, 11, 35)(9, 33, 15, 39, 20, 44, 18, 42)(12, 36, 16, 40, 21, 45, 19, 43)(17, 41, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 57, 81, 65, 89, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 58, 82, 66, 90, 71, 95, 67, 91, 59, 83)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.161 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^2, (Y1^-1, Y2^-1), Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 5, 29)(3, 27, 7, 31, 10, 34, 11, 35)(6, 30, 8, 32, 12, 36, 13, 37)(9, 33, 15, 39, 18, 42, 19, 43)(14, 38, 16, 40, 20, 44, 21, 45)(17, 41, 22, 46, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 65, 89, 62, 86, 54, 78)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 58, 82, 66, 90, 71, 95, 68, 92, 60, 84)(53, 77, 59, 83, 67, 91, 72, 96, 69, 93, 61, 85) L = (1, 52)(2, 53)(3, 58)(4, 49)(5, 50)(6, 60)(7, 59)(8, 61)(9, 66)(10, 51)(11, 55)(12, 54)(13, 56)(14, 68)(15, 67)(16, 69)(17, 71)(18, 57)(19, 63)(20, 62)(21, 64)(22, 72)(23, 65)(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) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.162 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^4, (Y2^-1, Y1), Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y3, (R * Y2)^2, Y1^-1 * Y2^-3 * Y3 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 8, 32, 18, 42, 13, 37)(4, 28, 9, 33, 19, 43, 14, 38)(6, 30, 10, 34, 20, 44, 16, 40)(11, 35, 21, 45, 15, 39, 23, 47)(12, 36, 22, 46, 17, 41, 24, 48)(49, 73, 51, 75, 59, 83, 67, 91, 65, 89, 54, 78)(50, 74, 56, 80, 69, 93, 62, 86, 72, 96, 58, 82)(52, 76, 60, 84, 68, 92, 55, 79, 66, 90, 63, 87)(53, 77, 61, 85, 71, 95, 57, 81, 70, 94, 64, 88) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 67)(8, 70)(9, 50)(10, 71)(11, 68)(12, 51)(13, 72)(14, 53)(15, 54)(16, 69)(17, 66)(18, 65)(19, 55)(20, 59)(21, 64)(22, 56)(23, 58)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.163 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.163 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 6}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^4, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^-3 * Y1^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 8, 32, 17, 41, 13, 37)(4, 28, 9, 33, 18, 42, 14, 38)(6, 30, 10, 34, 11, 35, 16, 40)(12, 36, 19, 43, 24, 48, 22, 46)(15, 39, 20, 44, 21, 45, 23, 47)(49, 73, 51, 75, 59, 83, 55, 79, 65, 89, 54, 78)(50, 74, 56, 80, 64, 88, 53, 77, 61, 85, 58, 82)(52, 76, 60, 84, 69, 93, 66, 90, 72, 96, 63, 87)(57, 81, 67, 91, 71, 95, 62, 86, 70, 94, 68, 92) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 66)(8, 67)(9, 50)(10, 68)(11, 69)(12, 51)(13, 70)(14, 53)(15, 54)(16, 71)(17, 72)(18, 55)(19, 56)(20, 58)(21, 59)(22, 61)(23, 64)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.162 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.164 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 6, 6, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3, Y3^-1 * Y2^-1 * Y3 * Y1, Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y2^-1 * Y3 * Y2, Y2^-1 * Y1 * Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y2^6, Y1^6, Y3^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 15, 39, 22, 46, 21, 45, 7, 31)(2, 26, 9, 33, 24, 48, 18, 42, 17, 41, 11, 35)(3, 27, 13, 37, 8, 32, 20, 44, 19, 43, 5, 29)(6, 30, 16, 40, 14, 38, 12, 36, 23, 47, 10, 34)(49, 50, 56, 70, 66, 53)(51, 59, 58, 68, 72, 62)(52, 61, 71, 69, 67, 64)(54, 57, 63, 60, 65, 55)(73, 75, 84, 94, 92, 78)(74, 76, 86, 90, 93, 82)(77, 89, 95, 80, 81, 88)(79, 83, 85, 87, 96, 91) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^6 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E15.167 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 6^8, 12^4 ] E15.165 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 6, 6, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y1 * Y3 * Y1^-2 * Y3, Y2^6, (Y3 * Y1^-1)^3, Y1^6, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 3, 27, 5, 29)(2, 26, 7, 31, 8, 32)(4, 28, 11, 35, 13, 37)(6, 30, 17, 41, 9, 33)(10, 34, 19, 43, 21, 45)(12, 36, 15, 39, 23, 47)(14, 38, 20, 44, 22, 46)(16, 40, 24, 48, 18, 42)(49, 50, 54, 64, 60, 52)(51, 57, 68, 72, 61, 58)(53, 62, 55, 66, 69, 63)(56, 67, 65, 71, 70, 59)(73, 74, 78, 88, 84, 76)(75, 81, 92, 96, 85, 82)(77, 86, 79, 90, 93, 87)(80, 91, 89, 95, 94, 83) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^6 ) } Outer automorphisms :: reflexible Dual of E15.166 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 6^16 ] E15.166 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 6, 6, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3, Y3^-1 * Y2^-1 * Y3 * Y1, Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y2^-1 * Y3 * Y2, Y2^-1 * Y1 * Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y2^6, Y1^6, Y3^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 15, 39, 63, 87, 22, 46, 70, 94, 21, 45, 69, 93, 7, 31, 55, 79)(2, 26, 50, 74, 9, 33, 57, 81, 24, 48, 72, 96, 18, 42, 66, 90, 17, 41, 65, 89, 11, 35, 59, 83)(3, 27, 51, 75, 13, 37, 61, 85, 8, 32, 56, 80, 20, 44, 68, 92, 19, 43, 67, 91, 5, 29, 53, 77)(6, 30, 54, 78, 16, 40, 64, 88, 14, 38, 62, 86, 12, 36, 60, 84, 23, 47, 71, 95, 10, 34, 58, 82) L = (1, 26)(2, 32)(3, 35)(4, 37)(5, 25)(6, 33)(7, 30)(8, 46)(9, 39)(10, 44)(11, 34)(12, 41)(13, 47)(14, 27)(15, 36)(16, 28)(17, 31)(18, 29)(19, 40)(20, 48)(21, 43)(22, 42)(23, 45)(24, 38)(49, 75)(50, 76)(51, 84)(52, 86)(53, 89)(54, 73)(55, 83)(56, 81)(57, 88)(58, 74)(59, 85)(60, 94)(61, 87)(62, 90)(63, 96)(64, 77)(65, 95)(66, 93)(67, 79)(68, 78)(69, 82)(70, 92)(71, 80)(72, 91) local type(s) :: { ( 6^24 ) } Outer automorphisms :: reflexible Dual of E15.165 Transitivity :: VT+ Graph:: v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.167 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 6, 6, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y1 * Y3 * Y1^-2 * Y3, Y2^6, (Y3 * Y1^-1)^3, Y1^6, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 8, 32, 56, 80)(4, 28, 52, 76, 11, 35, 59, 83, 13, 37, 61, 85)(6, 30, 54, 78, 17, 41, 65, 89, 9, 33, 57, 81)(10, 34, 58, 82, 19, 43, 67, 91, 21, 45, 69, 93)(12, 36, 60, 84, 15, 39, 63, 87, 23, 47, 71, 95)(14, 38, 62, 86, 20, 44, 68, 92, 22, 46, 70, 94)(16, 40, 64, 88, 24, 48, 72, 96, 18, 42, 66, 90) L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 38)(6, 40)(7, 42)(8, 43)(9, 44)(10, 27)(11, 32)(12, 28)(13, 34)(14, 31)(15, 29)(16, 36)(17, 47)(18, 45)(19, 41)(20, 48)(21, 39)(22, 35)(23, 46)(24, 37)(49, 74)(50, 78)(51, 81)(52, 73)(53, 86)(54, 88)(55, 90)(56, 91)(57, 92)(58, 75)(59, 80)(60, 76)(61, 82)(62, 79)(63, 77)(64, 84)(65, 95)(66, 93)(67, 89)(68, 96)(69, 87)(70, 83)(71, 94)(72, 85) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E15.164 Transitivity :: VT+ Graph:: v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y3^3, Y1^3, Y3 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y2 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 14, 38)(4, 28, 15, 39, 8, 32)(6, 30, 19, 43, 11, 35)(7, 31, 17, 41, 20, 44)(9, 33, 22, 46, 16, 40)(10, 34, 23, 47, 18, 42)(13, 37, 21, 45, 24, 48)(49, 73, 51, 75, 52, 76, 61, 85, 55, 79, 54, 78)(50, 74, 56, 80, 57, 81, 69, 93, 59, 83, 58, 82)(53, 77, 64, 88, 60, 84, 72, 96, 66, 90, 65, 89)(62, 86, 71, 95, 63, 87, 68, 92, 70, 94, 67, 91) L = (1, 52)(2, 57)(3, 61)(4, 55)(5, 60)(6, 51)(7, 49)(8, 69)(9, 59)(10, 56)(11, 50)(12, 66)(13, 54)(14, 63)(15, 70)(16, 72)(17, 64)(18, 53)(19, 71)(20, 67)(21, 58)(22, 62)(23, 68)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^6 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E15.170 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 6^8, 12^4 ] E15.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3, Y1^3, (R * Y1^-1)^2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y3^4, Y1 * Y3^-2 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 11, 35, 13, 37)(4, 28, 6, 30, 16, 40)(7, 31, 12, 36, 22, 46)(8, 32, 9, 33, 23, 47)(10, 34, 21, 45, 24, 48)(14, 38, 15, 39, 17, 41)(18, 42, 19, 43, 20, 44)(49, 73, 51, 75, 60, 84, 63, 87, 66, 90, 54, 78)(50, 74, 55, 79, 69, 93, 65, 89, 52, 76, 57, 81)(53, 77, 58, 82, 59, 83, 62, 86, 56, 80, 67, 91)(61, 85, 71, 95, 70, 94, 68, 92, 72, 96, 64, 88) L = (1, 52)(2, 56)(3, 53)(4, 63)(5, 66)(6, 68)(7, 49)(8, 65)(9, 64)(10, 50)(11, 72)(12, 61)(13, 54)(14, 51)(15, 55)(16, 69)(17, 58)(18, 62)(19, 71)(20, 60)(21, 70)(22, 57)(23, 59)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^6 ), ( 12^12 ) } Outer automorphisms :: reflexible Dual of E15.171 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 6^8, 12^4 ] E15.170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y3^3, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y2 * Y1 * Y3^-1 * Y1, (R * Y2)^2, (R * Y3)^2, Y3 * Y1^2 * Y3 * Y1^-1, Y1^3 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 18, 42, 5, 29)(3, 27, 13, 37, 22, 46, 7, 31, 19, 43, 15, 39)(4, 28, 16, 40, 12, 36, 6, 30, 21, 45, 9, 33)(10, 34, 23, 47, 17, 41, 11, 35, 24, 48, 20, 44)(49, 73, 51, 75, 52, 76, 62, 86, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 66, 90, 60, 84, 59, 83)(53, 77, 65, 89, 61, 85, 56, 80, 68, 92, 67, 91)(63, 87, 71, 95, 64, 88, 70, 94, 72, 96, 69, 93) L = (1, 52)(2, 58)(3, 62)(4, 55)(5, 61)(6, 51)(7, 49)(8, 67)(9, 66)(10, 60)(11, 57)(12, 50)(13, 68)(14, 54)(15, 64)(16, 72)(17, 56)(18, 59)(19, 65)(20, 53)(21, 71)(22, 69)(23, 70)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E15.168 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3^-1, Y1^2 * Y2^-1 * Y3^-1, (R * Y3)^2, Y2^2 * Y3^-1 * Y1^-1, (R * Y1)^2, Y3^4, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 16, 40, 18, 42, 5, 29)(3, 27, 4, 28, 15, 39, 21, 45, 7, 31, 13, 37)(6, 30, 14, 38, 9, 33, 10, 34, 12, 36, 20, 44)(11, 35, 24, 48, 22, 46, 19, 43, 23, 47, 17, 41)(49, 73, 51, 75, 58, 82, 64, 88, 69, 93, 54, 78)(50, 74, 57, 81, 67, 91, 66, 90, 68, 92, 59, 83)(52, 76, 56, 80, 70, 94, 55, 79, 53, 77, 65, 89)(60, 84, 63, 87, 72, 96, 62, 86, 61, 85, 71, 95) L = (1, 52)(2, 58)(3, 60)(4, 64)(5, 59)(6, 50)(7, 49)(8, 67)(9, 71)(10, 66)(11, 56)(12, 69)(13, 65)(14, 51)(15, 70)(16, 55)(17, 63)(18, 54)(19, 53)(20, 72)(21, 62)(22, 61)(23, 68)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E15.169 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, Y1 * Y3^-3, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y1^4, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 17, 41, 6, 30)(4, 28, 10, 34, 23, 47, 15, 39)(7, 31, 11, 35, 24, 48, 18, 42)(12, 36, 22, 46, 21, 45, 19, 43)(13, 37, 16, 40, 14, 38, 20, 44)(49, 73, 51, 75, 50, 74, 57, 81, 56, 80, 65, 89, 53, 77, 54, 78)(52, 76, 62, 86, 58, 82, 68, 92, 71, 95, 61, 85, 63, 87, 64, 88)(55, 79, 69, 93, 59, 83, 67, 91, 72, 96, 60, 84, 66, 90, 70, 94) L = (1, 52)(2, 58)(3, 60)(4, 59)(5, 63)(6, 67)(7, 49)(8, 71)(9, 70)(10, 72)(11, 50)(12, 64)(13, 51)(14, 65)(15, 55)(16, 57)(17, 69)(18, 53)(19, 61)(20, 54)(21, 68)(22, 62)(23, 66)(24, 56)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E15.175 Graph:: bipartite v = 9 e = 48 f = 11 degree seq :: [ 8^6, 16^3 ] E15.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1, Y3^3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 6, 30, 10, 34, 13, 37)(4, 28, 9, 33, 23, 47, 16, 40)(7, 31, 11, 35, 24, 48, 18, 42)(12, 36, 19, 43, 21, 45, 22, 46)(14, 38, 20, 44, 15, 39, 17, 41)(49, 73, 51, 75, 53, 77, 61, 85, 56, 80, 58, 82, 50, 74, 54, 78)(52, 76, 63, 87, 64, 88, 68, 92, 71, 95, 62, 86, 57, 81, 65, 89)(55, 79, 69, 93, 66, 90, 67, 91, 72, 96, 60, 84, 59, 83, 70, 94) L = (1, 52)(2, 57)(3, 60)(4, 59)(5, 64)(6, 67)(7, 49)(8, 71)(9, 72)(10, 69)(11, 50)(12, 68)(13, 70)(14, 51)(15, 58)(16, 55)(17, 61)(18, 53)(19, 63)(20, 54)(21, 65)(22, 62)(23, 66)(24, 56)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E15.174 Graph:: bipartite v = 9 e = 48 f = 11 degree seq :: [ 8^6, 16^3 ] E15.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y3, Y2), Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y3^-4 * Y2, Y3^-1 * Y1^-1 * Y3 * Y1 * Y2^-1, Y3^-1 * Y2 * Y1^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 23, 47, 24, 48, 17, 41, 5, 29)(3, 27, 11, 35, 19, 43, 12, 36, 21, 45, 16, 40, 4, 28, 14, 38)(6, 30, 9, 33, 7, 31, 20, 44, 15, 39, 18, 42, 13, 37, 10, 34)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 61, 85, 65, 89)(53, 77, 58, 82, 62, 86)(55, 79, 56, 80, 67, 91)(60, 84, 70, 94, 68, 92)(63, 87, 71, 95, 69, 93)(64, 88, 72, 96, 66, 90) L = (1, 52)(2, 58)(3, 61)(4, 63)(5, 66)(6, 65)(7, 49)(8, 51)(9, 62)(10, 64)(11, 53)(12, 50)(13, 71)(14, 72)(15, 56)(16, 70)(17, 69)(18, 60)(19, 54)(20, 59)(21, 55)(22, 57)(23, 67)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.173 Graph:: bipartite v = 11 e = 48 f = 9 degree seq :: [ 6^8, 16^3 ] E15.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y2^3, Y1^2 * Y3^-1 * Y2, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y1)^2, (Y3^-1, Y2^-1), Y1 * Y2 * Y3 * Y1^-1 * Y3^-1, Y1^2 * Y3^3, Y1^8 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 23, 47, 24, 48, 14, 38, 5, 29)(3, 27, 11, 35, 4, 28, 15, 39, 21, 45, 18, 42, 19, 43, 12, 36)(6, 30, 9, 33, 13, 37, 10, 34, 16, 40, 20, 44, 7, 31, 17, 41)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 61, 85, 56, 80)(53, 77, 65, 89, 60, 84)(55, 79, 62, 86, 67, 91)(58, 82, 63, 87, 70, 94)(64, 88, 71, 95, 69, 93)(66, 90, 72, 96, 68, 92) L = (1, 52)(2, 58)(3, 61)(4, 64)(5, 57)(6, 56)(7, 49)(8, 69)(9, 63)(10, 66)(11, 70)(12, 50)(13, 71)(14, 51)(15, 72)(16, 62)(17, 59)(18, 53)(19, 54)(20, 60)(21, 55)(22, 68)(23, 67)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.172 Graph:: bipartite v = 11 e = 48 f = 9 degree seq :: [ 6^8, 16^3 ] E15.176 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 12}) Quotient :: edge^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y2^4, Y3^2 * Y2^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, R * Y1 * R * Y2, Y1^-1 * Y3^-2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^2 * Y2, (R * Y3)^2, (Y2^-1 * Y1^-1)^3, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1 * Y2 ] Map:: non-degenerate R = (1, 25, 4, 28, 8, 32, 7, 31)(2, 26, 10, 34, 5, 29, 12, 36)(3, 27, 14, 38, 6, 30, 16, 40)(9, 33, 18, 42, 11, 35, 20, 44)(13, 37, 21, 45, 15, 39, 22, 46)(17, 41, 23, 47, 19, 43, 24, 48)(49, 50, 56, 53)(51, 61, 54, 63)(52, 60, 55, 58)(57, 65, 59, 67)(62, 70, 64, 69)(66, 72, 68, 71)(73, 75, 80, 78)(74, 81, 77, 83)(76, 88, 79, 86)(82, 92, 84, 90)(85, 91, 87, 89)(93, 95, 94, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^8 ) } Outer automorphisms :: reflexible Dual of E15.179 Graph:: bipartite v = 18 e = 48 f = 2 degree seq :: [ 4^12, 8^6 ] E15.177 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 12}) Quotient :: edge^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-1 * Y1, Y3 * Y2 * Y1^-1 * Y3, Y2^2 * Y1^2, Y1^4, Y2^4, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, Y2^2 * Y1^-2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-2 * Y2 * Y1^-1, (Y1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 4, 28, 11, 35, 24, 48, 13, 37, 20, 44, 8, 32, 19, 43, 9, 33, 22, 46, 15, 39, 7, 31)(2, 26, 10, 34, 3, 27, 14, 38, 21, 45, 16, 40, 5, 29, 17, 41, 6, 30, 18, 42, 23, 47, 12, 36)(49, 50, 56, 53)(51, 61, 54, 63)(52, 60, 67, 64)(55, 58, 68, 65)(57, 69, 59, 71)(62, 72, 66, 70)(73, 75, 80, 78)(74, 81, 77, 83)(76, 82, 91, 89)(79, 86, 92, 90)(84, 94, 88, 96)(85, 95, 87, 93) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^4 ), ( 16^24 ) } Outer automorphisms :: reflexible Dual of E15.178 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.178 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 12}) Quotient :: loop^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y2^4, Y3^2 * Y2^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, R * Y1 * R * Y2, Y1^-1 * Y3^-2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^2 * Y2, (R * Y3)^2, (Y2^-1 * Y1^-1)^3, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1 * Y2 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 8, 32, 56, 80, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 5, 29, 53, 77, 12, 36, 60, 84)(3, 27, 51, 75, 14, 38, 62, 86, 6, 30, 54, 78, 16, 40, 64, 88)(9, 33, 57, 81, 18, 42, 66, 90, 11, 35, 59, 83, 20, 44, 68, 92)(13, 37, 61, 85, 21, 45, 69, 93, 15, 39, 63, 87, 22, 46, 70, 94)(17, 41, 65, 89, 23, 47, 71, 95, 19, 43, 67, 91, 24, 48, 72, 96) L = (1, 26)(2, 32)(3, 37)(4, 36)(5, 25)(6, 39)(7, 34)(8, 29)(9, 41)(10, 28)(11, 43)(12, 31)(13, 30)(14, 46)(15, 27)(16, 45)(17, 35)(18, 48)(19, 33)(20, 47)(21, 38)(22, 40)(23, 42)(24, 44)(49, 75)(50, 81)(51, 80)(52, 88)(53, 83)(54, 73)(55, 86)(56, 78)(57, 77)(58, 92)(59, 74)(60, 90)(61, 91)(62, 76)(63, 89)(64, 79)(65, 85)(66, 82)(67, 87)(68, 84)(69, 95)(70, 96)(71, 94)(72, 93) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.177 Transitivity :: VT+ Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.179 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 12}) Quotient :: loop^2 Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-1 * Y1, Y3 * Y2 * Y1^-1 * Y3, Y2^2 * Y1^2, Y1^4, Y2^4, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, Y2^2 * Y1^-2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-2 * Y2 * Y1^-1, (Y1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 11, 35, 59, 83, 24, 48, 72, 96, 13, 37, 61, 85, 20, 44, 68, 92, 8, 32, 56, 80, 19, 43, 67, 91, 9, 33, 57, 81, 22, 46, 70, 94, 15, 39, 63, 87, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 3, 27, 51, 75, 14, 38, 62, 86, 21, 45, 69, 93, 16, 40, 64, 88, 5, 29, 53, 77, 17, 41, 65, 89, 6, 30, 54, 78, 18, 42, 66, 90, 23, 47, 71, 95, 12, 36, 60, 84) L = (1, 26)(2, 32)(3, 37)(4, 36)(5, 25)(6, 39)(7, 34)(8, 29)(9, 45)(10, 44)(11, 47)(12, 43)(13, 30)(14, 48)(15, 27)(16, 28)(17, 31)(18, 46)(19, 40)(20, 41)(21, 35)(22, 38)(23, 33)(24, 42)(49, 75)(50, 81)(51, 80)(52, 82)(53, 83)(54, 73)(55, 86)(56, 78)(57, 77)(58, 91)(59, 74)(60, 94)(61, 95)(62, 92)(63, 93)(64, 96)(65, 76)(66, 79)(67, 89)(68, 90)(69, 85)(70, 88)(71, 87)(72, 84) 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 ) } Outer automorphisms :: reflexible Dual of E15.176 Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 18 degree seq :: [ 48^2 ] E15.180 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y2^2, Y1^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y3^-2 * Y1^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y3)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^-2 * Y1^-1, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, R * Y2 * R * Y2^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1, (Y1 * Y3^-1 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 6, 30, 9, 33)(4, 28, 15, 39, 7, 31, 16, 40)(10, 34, 19, 43, 12, 36, 20, 44)(13, 37, 21, 45, 14, 38, 22, 46)(17, 41, 24, 48, 18, 42, 23, 47)(49, 73, 51, 75, 56, 80, 54, 78)(50, 74, 57, 81, 53, 77, 59, 83)(52, 76, 62, 86, 55, 79, 61, 85)(58, 82, 66, 90, 60, 84, 65, 89)(63, 87, 69, 93, 64, 88, 70, 94)(67, 91, 72, 96, 68, 92, 71, 95) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 62)(7, 49)(8, 55)(9, 65)(10, 53)(11, 66)(12, 50)(13, 54)(14, 51)(15, 71)(16, 72)(17, 59)(18, 57)(19, 69)(20, 70)(21, 68)(22, 67)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.183 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.181 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y2^-1 * Y3^-2 * Y2^-1, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2^2 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4, R * Y2 * R * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 6, 30, 9, 33)(4, 28, 15, 39, 7, 31, 16, 40)(10, 34, 19, 43, 12, 36, 20, 44)(13, 37, 21, 45, 14, 38, 22, 46)(17, 41, 23, 47, 18, 42, 24, 48)(49, 73, 51, 75, 56, 80, 54, 78)(50, 74, 57, 81, 53, 77, 59, 83)(52, 76, 62, 86, 55, 79, 61, 85)(58, 82, 66, 90, 60, 84, 65, 89)(63, 87, 69, 93, 64, 88, 70, 94)(67, 91, 71, 95, 68, 92, 72, 96) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 62)(7, 49)(8, 55)(9, 65)(10, 53)(11, 66)(12, 50)(13, 54)(14, 51)(15, 71)(16, 72)(17, 59)(18, 57)(19, 70)(20, 69)(21, 67)(22, 68)(23, 64)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.182 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^4, (Y3^-1, Y1^-1), Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y1^4, Y2 * Y1^-2 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 21, 45, 7, 31, 12, 36, 14, 38, 17, 41, 4, 28, 10, 34, 19, 43, 5, 29)(3, 27, 13, 37, 22, 46, 23, 47, 16, 40, 11, 35, 6, 30, 20, 44, 15, 39, 24, 48, 18, 42, 9, 33)(49, 73, 51, 75, 62, 86, 54, 78)(50, 74, 57, 81, 65, 89, 59, 83)(52, 76, 64, 88, 56, 80, 66, 90)(53, 77, 61, 85, 60, 84, 68, 92)(55, 79, 63, 87, 67, 91, 70, 94)(58, 82, 71, 95, 69, 93, 72, 96) L = (1, 52)(2, 58)(3, 63)(4, 55)(5, 65)(6, 70)(7, 49)(8, 67)(9, 68)(10, 60)(11, 61)(12, 50)(13, 72)(14, 56)(15, 64)(16, 51)(17, 69)(18, 54)(19, 62)(20, 71)(21, 53)(22, 66)(23, 57)(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) :: { ( 8^8 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E15.181 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y3 * Y2^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^-2 * Y2^2, Y1 * Y2 * Y1 * Y2^-1, R * Y2 * R * Y2^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3, (R * Y1)^2, Y2^-1 * Y3^-2 * Y2^-1, Y2 * Y1^-2 * Y3 * Y1, Y3 * Y1^-3 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 16, 40, 22, 46, 23, 47, 14, 38, 21, 45, 24, 48, 15, 39, 18, 42, 5, 29)(3, 27, 13, 37, 10, 34, 4, 28, 17, 41, 11, 35, 6, 30, 19, 43, 12, 36, 7, 31, 20, 44, 9, 33)(49, 73, 51, 75, 62, 86, 54, 78)(50, 74, 57, 81, 69, 93, 59, 83)(52, 76, 64, 88, 55, 79, 63, 87)(53, 77, 61, 85, 71, 95, 67, 91)(56, 80, 68, 92, 72, 96, 65, 89)(58, 82, 70, 94, 60, 84, 66, 90) L = (1, 52)(2, 58)(3, 63)(4, 62)(5, 65)(6, 64)(7, 49)(8, 61)(9, 66)(10, 69)(11, 70)(12, 50)(13, 72)(14, 55)(15, 54)(16, 51)(17, 71)(18, 59)(19, 56)(20, 53)(21, 60)(22, 57)(23, 68)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E15.180 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^2, (R * Y2)^2, Y2^2 * Y1^2, (Y2^-1, Y1^-1), Y1^4, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (Y3 * Y1^-2)^2, Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, (Y1^-1 * Y2 * Y3)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 8, 32, 6, 30, 10, 34)(4, 28, 12, 36, 16, 40, 13, 37)(9, 33, 18, 42, 15, 39, 19, 43)(11, 35, 21, 45, 14, 38, 22, 46)(17, 41, 24, 48, 20, 44, 23, 47)(49, 73, 51, 75, 55, 79, 54, 78)(50, 74, 56, 80, 53, 77, 58, 82)(52, 76, 59, 83, 64, 88, 62, 86)(57, 81, 65, 89, 63, 87, 68, 92)(60, 84, 69, 93, 61, 85, 70, 94)(66, 90, 72, 96, 67, 91, 71, 95) L = (1, 52)(2, 57)(3, 59)(4, 49)(5, 63)(6, 62)(7, 64)(8, 65)(9, 50)(10, 68)(11, 51)(12, 71)(13, 72)(14, 54)(15, 53)(16, 55)(17, 56)(18, 69)(19, 70)(20, 58)(21, 66)(22, 67)(23, 60)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.186 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y3 * Y2^-1 * Y3, Y1^2 * Y2^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y2), Y1^4, (R * Y1)^2, Y3 * Y2^2 * Y3 * Y1^-2, Y2^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 8, 32, 6, 30, 10, 34)(4, 28, 12, 36, 16, 40, 13, 37)(9, 33, 18, 42, 15, 39, 19, 43)(11, 35, 21, 45, 14, 38, 22, 46)(17, 41, 23, 47, 20, 44, 24, 48)(49, 73, 51, 75, 55, 79, 54, 78)(50, 74, 56, 80, 53, 77, 58, 82)(52, 76, 59, 83, 64, 88, 62, 86)(57, 81, 65, 89, 63, 87, 68, 92)(60, 84, 69, 93, 61, 85, 70, 94)(66, 90, 71, 95, 67, 91, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 49)(5, 63)(6, 62)(7, 64)(8, 65)(9, 50)(10, 68)(11, 51)(12, 71)(13, 72)(14, 54)(15, 53)(16, 55)(17, 56)(18, 70)(19, 69)(20, 58)(21, 67)(22, 66)(23, 60)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.187 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1^-1)^2, Y3 * Y2 * Y3 * Y2^-1, (Y1^-1 * Y2^-1)^2, Y1 * Y2 * Y1^-2 * Y3, Y1 * Y3 * Y2 * Y1^2, Y1 * Y3 * Y1 * Y2^-2 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 16, 40, 22, 46, 23, 47, 12, 36, 20, 44, 24, 48, 13, 37, 19, 43, 5, 29)(3, 27, 11, 35, 15, 39, 4, 28, 14, 38, 8, 32, 6, 30, 17, 41, 9, 33, 21, 45, 18, 42, 10, 34)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 68, 92, 58, 82)(52, 76, 61, 85, 69, 93, 64, 88)(53, 77, 65, 89, 71, 95, 59, 83)(55, 79, 66, 90, 72, 96, 62, 86)(57, 81, 67, 91, 63, 87, 70, 94) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 66)(6, 64)(7, 59)(8, 67)(9, 50)(10, 70)(11, 55)(12, 69)(13, 51)(14, 71)(15, 68)(16, 54)(17, 72)(18, 53)(19, 56)(20, 63)(21, 60)(22, 58)(23, 62)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E15.184 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y1^-1 * Y2^-1)^2, (Y2 * Y1^-1)^2, Y1 * Y3 * Y1^-1 * Y2 * Y1, Y2 * Y1^-3 * Y3, (Y3 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 13, 37, 21, 45, 24, 48, 12, 36, 20, 44, 23, 47, 16, 40, 19, 43, 5, 29)(3, 27, 11, 35, 9, 33, 22, 46, 18, 42, 8, 32, 6, 30, 17, 41, 15, 39, 4, 28, 14, 38, 10, 34)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 68, 92, 58, 82)(52, 76, 61, 85, 70, 94, 64, 88)(53, 77, 65, 89, 72, 96, 59, 83)(55, 79, 62, 86, 71, 95, 66, 90)(57, 81, 69, 93, 63, 87, 67, 91) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 66)(6, 64)(7, 65)(8, 69)(9, 50)(10, 67)(11, 71)(12, 70)(13, 51)(14, 72)(15, 68)(16, 54)(17, 55)(18, 53)(19, 58)(20, 63)(21, 56)(22, 60)(23, 59)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E15.185 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y3^-1, Y2^-1), (Y1, Y2^-1), (Y3^-1, Y1^-1), Y3^-2 * Y2^2 * Y1^-1, Y2 * Y1 * Y2 * Y3^2, Y3^-4 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, (Y1^-1 * Y3^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 14, 38)(4, 28, 9, 33, 17, 41)(6, 30, 10, 34, 19, 43)(7, 31, 11, 35, 20, 44)(12, 36, 22, 46, 16, 40)(13, 37, 21, 45, 24, 48)(15, 39, 23, 47, 18, 42)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 70, 94, 58, 82)(52, 76, 61, 85, 68, 92, 66, 90)(53, 77, 62, 86, 64, 88, 67, 91)(55, 79, 63, 87, 57, 81, 69, 93)(59, 83, 71, 95, 65, 89, 72, 96) L = (1, 52)(2, 57)(3, 61)(4, 64)(5, 65)(6, 66)(7, 49)(8, 69)(9, 60)(10, 63)(11, 50)(12, 68)(13, 67)(14, 72)(15, 51)(16, 59)(17, 70)(18, 62)(19, 71)(20, 53)(21, 54)(22, 55)(23, 56)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.191 Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^3 * Y1^-1, (Y3^-1, Y1^-1), Y2^2 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1^-1, Y1^4, Y3^-1 * Y2^2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y2^6, (Y3 * Y1)^3, Y3 * Y2^2 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 19, 43, 14, 38)(4, 28, 10, 34, 20, 44, 15, 39)(6, 30, 11, 35, 21, 45, 16, 40)(7, 31, 12, 36, 22, 46, 17, 41)(13, 37, 23, 47, 18, 42, 24, 48)(49, 73, 51, 75, 58, 82, 71, 95, 65, 89, 54, 78)(50, 74, 57, 81, 68, 92, 66, 90, 55, 79, 59, 83)(52, 76, 61, 85, 70, 94, 64, 88, 53, 77, 62, 86)(56, 80, 67, 91, 63, 87, 72, 96, 60, 84, 69, 93) L = (1, 52)(2, 58)(3, 61)(4, 60)(5, 63)(6, 62)(7, 49)(8, 68)(9, 71)(10, 70)(11, 51)(12, 50)(13, 69)(14, 72)(15, 55)(16, 67)(17, 53)(18, 54)(19, 66)(20, 65)(21, 57)(22, 56)(23, 64)(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) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E15.190 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 8^6, 12^4 ] E15.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^2 * Y3^-2, (Y3^-1, Y1^-1), (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y3^4 * Y2^-1, Y2^-1 * Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 3, 27, 9, 33, 21, 45, 18, 42, 6, 30, 11, 35, 17, 41, 5, 29)(4, 28, 10, 34, 15, 39, 23, 47, 13, 37, 22, 46, 20, 44, 24, 48, 16, 40, 19, 43, 7, 31, 12, 36)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 61, 85, 64, 88)(53, 77, 62, 86, 66, 90)(55, 79, 63, 87, 68, 92)(56, 80, 69, 93, 65, 89)(58, 82, 70, 94, 67, 91)(60, 84, 71, 95, 72, 96) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 64)(7, 49)(8, 63)(9, 70)(10, 62)(11, 67)(12, 50)(13, 69)(14, 71)(15, 51)(16, 65)(17, 55)(18, 72)(19, 53)(20, 54)(21, 68)(22, 66)(23, 57)(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) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.189 Graph:: bipartite v = 10 e = 48 f = 10 degree seq :: [ 6^8, 24^2 ] E15.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (Y2, Y3^-1), Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y2^5 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3^-1 * Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 17, 41, 5, 29)(3, 27, 9, 33, 20, 44, 16, 40, 4, 28, 10, 34)(6, 30, 11, 35, 7, 31, 12, 36, 21, 45, 18, 42)(13, 37, 22, 46, 15, 39, 24, 48, 14, 38, 23, 47)(49, 73, 51, 75, 61, 85, 69, 93, 65, 89, 52, 76, 62, 86, 55, 79, 56, 80, 68, 92, 63, 87, 54, 78)(50, 74, 57, 81, 70, 94, 66, 90, 53, 77, 58, 82, 71, 95, 60, 84, 67, 91, 64, 88, 72, 96, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 63)(5, 64)(6, 65)(7, 49)(8, 51)(9, 71)(10, 72)(11, 53)(12, 50)(13, 55)(14, 54)(15, 69)(16, 70)(17, 68)(18, 67)(19, 57)(20, 61)(21, 56)(22, 60)(23, 59)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.188 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^3, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (Y2^-1, Y3^-1), (Y2 * Y1^-1)^2, (R * Y2)^2, Y1 * Y3^-4, (Y2^-1 * Y3)^4, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 6, 30, 9, 33)(4, 28, 8, 32, 14, 38)(7, 31, 10, 34, 16, 40)(11, 35, 15, 39, 20, 44)(12, 36, 17, 41, 21, 45)(13, 37, 19, 43, 18, 42)(22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 53, 77, 57, 81, 50, 74, 54, 78)(52, 76, 59, 83, 62, 86, 68, 92, 56, 80, 63, 87)(55, 79, 60, 84, 64, 88, 69, 93, 58, 82, 65, 89)(61, 85, 70, 94, 66, 90, 71, 95, 67, 91, 72, 96) L = (1, 52)(2, 56)(3, 59)(4, 61)(5, 62)(6, 63)(7, 49)(8, 67)(9, 68)(10, 50)(11, 70)(12, 51)(13, 58)(14, 66)(15, 72)(16, 53)(17, 54)(18, 55)(19, 64)(20, 71)(21, 57)(22, 65)(23, 60)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.193 Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 6^8, 12^4 ] E15.193 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 6, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^3 * Y1^-1, Y3 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-2 * Y2^-2, (Y2^-1 * Y3^-1)^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y1^4, (Y3 * Y1)^3, Y3^-1 * Y2^8 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 18, 42, 15, 39)(4, 28, 10, 34, 19, 43, 13, 37)(6, 30, 11, 35, 20, 44, 16, 40)(7, 31, 12, 36, 21, 45, 17, 41)(14, 38, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 61, 85, 71, 95, 65, 89, 68, 92, 56, 80, 66, 90, 58, 82, 70, 94, 60, 84, 54, 78)(50, 74, 57, 81, 52, 76, 62, 86, 55, 79, 64, 88, 53, 77, 63, 87, 67, 91, 72, 96, 69, 93, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 61)(6, 57)(7, 49)(8, 67)(9, 70)(10, 69)(11, 66)(12, 50)(13, 55)(14, 54)(15, 71)(16, 51)(17, 53)(18, 72)(19, 65)(20, 63)(21, 56)(22, 59)(23, 64)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E15.192 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8, 12}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y3^-1 * Y2 * Y3^-1, R * Y2 * Y3 * R * Y2^-1, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^4 * Y1, Y3^2 * Y2^-2 * Y3, Y2 * Y3^2 * Y2 * Y3^-1, (Y2^-2 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 18, 42)(12, 36, 20, 44)(13, 37, 14, 38)(15, 39, 23, 47)(16, 40, 19, 43)(17, 41, 21, 45)(22, 46, 24, 48)(49, 73, 51, 75, 59, 83, 57, 81, 50, 74, 55, 79, 66, 90, 53, 77)(52, 76, 62, 86, 72, 96, 67, 91, 56, 80, 61, 85, 70, 94, 64, 88)(54, 78, 68, 92, 63, 87, 65, 89, 58, 82, 60, 84, 71, 95, 69, 93) L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 65)(6, 49)(7, 68)(8, 71)(9, 69)(10, 50)(11, 72)(12, 64)(13, 51)(14, 55)(15, 59)(16, 57)(17, 61)(18, 70)(19, 53)(20, 67)(21, 62)(22, 54)(23, 66)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E15.196 Graph:: bipartite v = 15 e = 48 f = 5 degree seq :: [ 4^12, 16^3 ] E15.195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8, 12}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * R * Y2^-1 * R, Y2^-1 * Y1 * Y3^-1 * Y2 * Y3^-1, Y2^4 * Y1, Y2^2 * Y3^3, Y2 * Y3 * Y2 * Y3^-2, (Y2^2 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 18, 42)(12, 36, 20, 44)(13, 37, 14, 38)(15, 39, 23, 47)(16, 40, 19, 43)(17, 41, 21, 45)(22, 46, 24, 48)(49, 73, 51, 75, 59, 83, 57, 81, 50, 74, 55, 79, 66, 90, 53, 77)(52, 76, 62, 86, 70, 94, 67, 91, 56, 80, 61, 85, 72, 96, 64, 88)(54, 78, 68, 92, 71, 95, 65, 89, 58, 82, 60, 84, 63, 87, 69, 93) L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 65)(6, 49)(7, 68)(8, 71)(9, 69)(10, 50)(11, 70)(12, 67)(13, 51)(14, 55)(15, 66)(16, 57)(17, 62)(18, 72)(19, 53)(20, 64)(21, 61)(22, 54)(23, 59)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E15.197 Graph:: bipartite v = 15 e = 48 f = 5 degree seq :: [ 4^12, 16^3 ] E15.196 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8, 12}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-2, (Y3, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y2 * Y1^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-2, Y1 * Y3^-1 * Y1 * Y3 * Y2, Y3^-2 * Y1^2 * Y2^-1, Y1^8, Y2^9 * Y1^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 23, 47, 16, 40, 24, 48, 20, 44, 5, 29)(3, 27, 12, 36, 22, 46, 17, 41, 4, 28, 11, 35, 21, 45, 15, 39)(6, 30, 10, 34, 13, 37, 18, 42, 7, 31, 9, 33, 14, 38, 19, 43)(49, 73, 51, 75, 61, 85, 56, 80, 70, 94, 55, 79, 64, 88, 52, 76, 62, 86, 68, 92, 69, 93, 54, 78)(50, 74, 57, 81, 63, 87, 71, 95, 67, 91, 60, 84, 72, 96, 58, 82, 65, 89, 53, 77, 66, 90, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 61)(5, 67)(6, 64)(7, 49)(8, 69)(9, 65)(10, 63)(11, 72)(12, 50)(13, 68)(14, 56)(15, 53)(16, 51)(17, 71)(18, 60)(19, 59)(20, 70)(21, 55)(22, 54)(23, 66)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 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 E15.194 Graph:: bipartite v = 5 e = 48 f = 15 degree seq :: [ 16^3, 24^2 ] E15.197 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8, 12}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1^-1, Y3 * Y1 * Y2 * Y1^-1, (Y2^-1, Y3^-1), Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y3^-3 * Y1, Y1^8, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * 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, 25, 2, 26, 8, 32, 23, 47, 16, 40, 24, 48, 20, 44, 5, 29)(3, 27, 12, 36, 21, 45, 17, 41, 4, 28, 11, 35, 22, 46, 15, 39)(6, 30, 10, 34, 14, 38, 18, 42, 7, 31, 9, 33, 13, 37, 19, 43)(49, 73, 51, 75, 61, 85, 68, 92, 70, 94, 55, 79, 64, 88, 52, 76, 62, 86, 56, 80, 69, 93, 54, 78)(50, 74, 57, 81, 65, 89, 53, 77, 66, 90, 60, 84, 72, 96, 58, 82, 63, 87, 71, 95, 67, 91, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 61)(5, 67)(6, 64)(7, 49)(8, 70)(9, 63)(10, 65)(11, 72)(12, 50)(13, 56)(14, 68)(15, 53)(16, 51)(17, 71)(18, 59)(19, 60)(20, 69)(21, 55)(22, 54)(23, 66)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 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 E15.195 Graph:: bipartite v = 5 e = 48 f = 15 degree seq :: [ 16^3, 24^2 ] E15.198 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, Y3^3, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2, Y3), (R * Y1)^2, Y2^-4 * Y3^-1, (Y2^-1 * Y3)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 7, 31, 5, 29)(3, 27, 8, 32, 12, 36, 20, 44, 14, 38, 13, 37)(6, 30, 10, 34, 15, 39, 21, 45, 18, 42, 16, 40)(11, 35, 19, 43, 17, 41, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 59, 83, 66, 90, 55, 79, 62, 86, 72, 96, 63, 87, 52, 76, 60, 84, 65, 89, 54, 78)(50, 74, 56, 80, 67, 91, 64, 88, 53, 77, 61, 85, 71, 95, 69, 93, 57, 81, 68, 92, 70, 94, 58, 82) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 50)(6, 63)(7, 49)(8, 68)(9, 53)(10, 69)(11, 65)(12, 62)(13, 56)(14, 51)(15, 66)(16, 58)(17, 72)(18, 54)(19, 70)(20, 61)(21, 64)(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) :: { ( 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 E15.202 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.199 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^-2 * Y3^-2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (Y3, Y2^-1), (R * Y2)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y1^-4 * Y3^2, Y3^6, Y3^-2 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 15, 39, 5, 29)(3, 27, 6, 30, 10, 34, 20, 44, 23, 47, 13, 37)(4, 28, 9, 33, 7, 31, 11, 35, 21, 45, 16, 40)(12, 36, 17, 41, 14, 38, 18, 42, 22, 46, 24, 48)(49, 73, 51, 75, 53, 77, 61, 85, 63, 87, 71, 95, 67, 91, 68, 92, 56, 80, 58, 82, 50, 74, 54, 78)(52, 76, 60, 84, 64, 88, 72, 96, 69, 93, 70, 94, 59, 83, 66, 90, 55, 79, 62, 86, 57, 81, 65, 89) L = (1, 52)(2, 57)(3, 60)(4, 63)(5, 64)(6, 65)(7, 49)(8, 55)(9, 53)(10, 62)(11, 50)(12, 71)(13, 72)(14, 51)(15, 69)(16, 67)(17, 61)(18, 54)(19, 59)(20, 66)(21, 56)(22, 58)(23, 70)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 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 E15.204 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.200 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-2, Y3 * Y2^2 * Y1^-1, (Y3, Y1^-1), Y2^-2 * Y1 * Y3^-1, (Y3^-1, Y2), Y2 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-6, Y2^-1 * Y3^2 * Y2 * Y1^2, Y1^6, Y2^-2 * Y3 * Y1^-3, Y2^-12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 15, 39, 5, 29)(3, 27, 9, 33, 20, 44, 17, 41, 24, 48, 13, 37)(4, 28, 10, 34, 7, 31, 12, 36, 22, 46, 16, 40)(6, 30, 11, 35, 21, 45, 14, 38, 23, 47, 18, 42)(49, 73, 51, 75, 60, 84, 71, 95, 63, 87, 72, 96, 58, 82, 69, 93, 56, 80, 68, 92, 64, 88, 54, 78)(50, 74, 57, 81, 70, 94, 66, 90, 53, 77, 61, 85, 55, 79, 62, 86, 67, 91, 65, 89, 52, 76, 59, 83) L = (1, 52)(2, 58)(3, 59)(4, 63)(5, 64)(6, 65)(7, 49)(8, 55)(9, 69)(10, 53)(11, 72)(12, 50)(13, 54)(14, 51)(15, 70)(16, 67)(17, 71)(18, 68)(19, 60)(20, 62)(21, 61)(22, 56)(23, 57)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.205 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, (Y3 * Y1)^2, Y1^2 * Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y1^-2 * Y3^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 15, 39, 5, 29)(3, 27, 9, 33, 18, 42, 22, 46, 23, 47, 14, 38)(4, 28, 10, 34, 7, 31, 12, 36, 21, 45, 16, 40)(6, 30, 11, 35, 20, 44, 24, 48, 13, 37, 17, 41)(49, 73, 51, 75, 52, 76, 61, 85, 63, 87, 71, 95, 69, 93, 68, 92, 56, 80, 66, 90, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 65, 89, 53, 77, 62, 86, 64, 88, 72, 96, 67, 91, 70, 94, 60, 84, 59, 83) L = (1, 52)(2, 58)(3, 61)(4, 63)(5, 64)(6, 51)(7, 49)(8, 55)(9, 65)(10, 53)(11, 57)(12, 50)(13, 71)(14, 72)(15, 69)(16, 67)(17, 62)(18, 54)(19, 60)(20, 66)(21, 56)(22, 59)(23, 68)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 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 E15.203 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.202 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y1^4, (Y1^-1 * Y3^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 14, 38, 4, 28, 9, 33, 18, 42, 16, 40, 6, 30, 10, 34, 15, 39, 5, 29)(3, 27, 8, 32, 17, 41, 21, 45, 11, 35, 19, 43, 24, 48, 23, 47, 13, 37, 20, 44, 22, 46, 12, 36)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 65, 89)(57, 81, 67, 91)(58, 82, 68, 92)(62, 86, 69, 93)(63, 87, 70, 94)(64, 88, 71, 95)(66, 90, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 54)(5, 62)(6, 49)(7, 66)(8, 67)(9, 58)(10, 50)(11, 61)(12, 69)(13, 51)(14, 64)(15, 55)(16, 53)(17, 72)(18, 63)(19, 68)(20, 56)(21, 71)(22, 65)(23, 60)(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) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.198 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.203 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 8, 32, 14, 38, 16, 40, 20, 44, 21, 45, 12, 36, 13, 37, 4, 28, 5, 29)(3, 27, 7, 31, 11, 35, 15, 39, 19, 43, 22, 46, 23, 47, 24, 48, 17, 41, 18, 42, 9, 33, 10, 34)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 57, 81)(53, 77, 58, 82)(54, 78, 59, 83)(56, 80, 63, 87)(60, 84, 65, 89)(61, 85, 66, 90)(62, 86, 67, 91)(64, 88, 70, 94)(68, 92, 71, 95)(69, 93, 72, 96) L = (1, 52)(2, 53)(3, 57)(4, 60)(5, 61)(6, 49)(7, 58)(8, 50)(9, 65)(10, 66)(11, 51)(12, 68)(13, 69)(14, 54)(15, 55)(16, 56)(17, 71)(18, 72)(19, 59)(20, 62)(21, 64)(22, 63)(23, 67)(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) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.201 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.204 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y2 * Y3^-1, Y1^-2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^6, Y3^-1 * Y1^8 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 14, 38, 18, 42, 23, 47, 21, 45, 12, 36, 17, 41, 11, 35, 5, 29)(3, 27, 8, 32, 6, 30, 10, 34, 16, 40, 22, 46, 20, 44, 24, 48, 19, 43, 13, 37, 4, 28, 9, 33)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 57, 81)(54, 78, 55, 79)(58, 82, 63, 87)(60, 84, 67, 91)(61, 85, 65, 89)(62, 86, 64, 88)(66, 90, 70, 94)(68, 92, 71, 95)(69, 93, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 60)(5, 61)(6, 49)(7, 51)(8, 53)(9, 65)(10, 50)(11, 67)(12, 68)(13, 69)(14, 54)(15, 56)(16, 55)(17, 72)(18, 58)(19, 71)(20, 62)(21, 70)(22, 63)(23, 64)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.199 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.205 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1^2 * Y3^-2, Y3^-2 * Y1^-4, Y3^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 19, 43, 18, 42, 12, 36, 3, 27, 8, 32, 14, 38, 22, 46, 16, 40, 5, 29)(4, 28, 9, 33, 20, 44, 17, 41, 6, 30, 10, 34, 11, 35, 21, 45, 24, 48, 23, 47, 13, 37, 15, 39)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 62, 86)(57, 81, 69, 93)(58, 82, 63, 87)(64, 88, 66, 90)(65, 89, 71, 95)(67, 91, 70, 94)(68, 92, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 62)(5, 63)(6, 49)(7, 68)(8, 69)(9, 70)(10, 50)(11, 55)(12, 58)(13, 51)(14, 72)(15, 56)(16, 61)(17, 53)(18, 54)(19, 65)(20, 64)(21, 67)(22, 71)(23, 60)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.200 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.206 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 6, 12, 12}) Quotient :: edge^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, R * Y1 * R * Y2, (Y2, Y1), Y2^-5 * Y1^-1, Y1^12, Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y2^-2 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 4, 28)(2, 26, 9, 33)(3, 27, 11, 35)(5, 29, 13, 37)(6, 30, 12, 36)(7, 31, 18, 42)(8, 32, 19, 43)(10, 34, 20, 44)(14, 38, 21, 45)(15, 39, 22, 46)(16, 40, 23, 47)(17, 41, 24, 48)(49, 50, 55, 64, 63, 54, 58, 51, 56, 65, 62, 53)(52, 59, 66, 72, 70, 61, 68, 57, 67, 71, 69, 60)(73, 75, 79, 89, 87, 77, 82, 74, 80, 88, 86, 78)(76, 81, 90, 95, 94, 84, 92, 83, 91, 96, 93, 85) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.209 Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.207 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 6, 12, 12}) Quotient :: edge^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1^-1), Y3^-1 * Y1 * Y3 * Y2^-1, Y3^2 * Y1^-1 * Y2^-1, Y2^2 * Y1^-2, (Y3 * Y1^-1)^2, Y1 * Y2 * Y3^-2, R * Y1 * R * Y2, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y2 * Y1)^3, Y1^-1 * Y3^-4 * Y2^-1, Y2^2 * Y1^10 ] Map:: non-degenerate R = (1, 25, 4, 28, 9, 33, 23, 47, 16, 40, 7, 31)(2, 26, 10, 34, 20, 44, 18, 42, 6, 30, 12, 36)(3, 27, 13, 37, 19, 43, 17, 41, 5, 29, 14, 38)(8, 32, 21, 45, 15, 39, 24, 48, 11, 35, 22, 46)(49, 50, 56, 67, 64, 54, 59, 51, 57, 68, 63, 53)(52, 61, 69, 66, 55, 62, 70, 58, 71, 65, 72, 60)(73, 75, 80, 92, 88, 77, 83, 74, 81, 91, 87, 78)(76, 82, 93, 89, 79, 84, 94, 85, 95, 90, 96, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.208 Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.208 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 6, 12, 12}) Quotient :: loop^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, R * Y1 * R * Y2, (Y2, Y1), Y2^-5 * Y1^-1, Y1^12, Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y2^-2 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76)(2, 26, 50, 74, 9, 33, 57, 81)(3, 27, 51, 75, 11, 35, 59, 83)(5, 29, 53, 77, 13, 37, 61, 85)(6, 30, 54, 78, 12, 36, 60, 84)(7, 31, 55, 79, 18, 42, 66, 90)(8, 32, 56, 80, 19, 43, 67, 91)(10, 34, 58, 82, 20, 44, 68, 92)(14, 38, 62, 86, 21, 45, 69, 93)(15, 39, 63, 87, 22, 46, 70, 94)(16, 40, 64, 88, 23, 47, 71, 95)(17, 41, 65, 89, 24, 48, 72, 96) L = (1, 26)(2, 31)(3, 32)(4, 35)(5, 25)(6, 34)(7, 40)(8, 41)(9, 43)(10, 27)(11, 42)(12, 28)(13, 44)(14, 29)(15, 30)(16, 39)(17, 38)(18, 48)(19, 47)(20, 33)(21, 36)(22, 37)(23, 45)(24, 46)(49, 75)(50, 80)(51, 79)(52, 81)(53, 82)(54, 73)(55, 89)(56, 88)(57, 90)(58, 74)(59, 91)(60, 92)(61, 76)(62, 78)(63, 77)(64, 86)(65, 87)(66, 95)(67, 96)(68, 83)(69, 85)(70, 84)(71, 94)(72, 93) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.207 Transitivity :: VT+ Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.209 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 6, 12, 12}) Quotient :: loop^2 Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1^-1), Y3^-1 * Y1 * Y3 * Y2^-1, Y3^2 * Y1^-1 * Y2^-1, Y2^2 * Y1^-2, (Y3 * Y1^-1)^2, Y1 * Y2 * Y3^-2, R * Y1 * R * Y2, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y2 * Y1)^3, Y1^-1 * Y3^-4 * Y2^-1, Y2^2 * Y1^10 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 9, 33, 57, 81, 23, 47, 71, 95, 16, 40, 64, 88, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 20, 44, 68, 92, 18, 42, 66, 90, 6, 30, 54, 78, 12, 36, 60, 84)(3, 27, 51, 75, 13, 37, 61, 85, 19, 43, 67, 91, 17, 41, 65, 89, 5, 29, 53, 77, 14, 38, 62, 86)(8, 32, 56, 80, 21, 45, 69, 93, 15, 39, 63, 87, 24, 48, 72, 96, 11, 35, 59, 83, 22, 46, 70, 94) L = (1, 26)(2, 32)(3, 33)(4, 37)(5, 25)(6, 35)(7, 38)(8, 43)(9, 44)(10, 47)(11, 27)(12, 28)(13, 45)(14, 46)(15, 29)(16, 30)(17, 48)(18, 31)(19, 40)(20, 39)(21, 42)(22, 34)(23, 41)(24, 36)(49, 75)(50, 81)(51, 80)(52, 82)(53, 83)(54, 73)(55, 84)(56, 92)(57, 91)(58, 93)(59, 74)(60, 94)(61, 95)(62, 76)(63, 78)(64, 77)(65, 79)(66, 96)(67, 87)(68, 88)(69, 89)(70, 85)(71, 90)(72, 86) 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 E15.206 Transitivity :: VT+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, (Y1 * Y2^-1)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3), (Y3^-1 * Y1^-1)^2, Y2^-4 * Y3^-1, Y1 * Y2 * Y3^-1 * Y1^-1 * Y2, (Y2^-1 * Y3)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 7, 31, 5, 29)(3, 27, 11, 35, 13, 37, 17, 41, 14, 38, 10, 34)(6, 30, 16, 40, 15, 39, 8, 32, 20, 44, 18, 42)(12, 36, 21, 45, 19, 43, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 60, 84, 68, 92, 55, 79, 62, 86, 72, 96, 63, 87, 52, 76, 61, 85, 67, 91, 54, 78)(50, 74, 56, 80, 69, 93, 65, 89, 53, 77, 64, 88, 71, 95, 59, 83, 57, 81, 66, 90, 70, 94, 58, 82) L = (1, 52)(2, 57)(3, 61)(4, 55)(5, 50)(6, 63)(7, 49)(8, 66)(9, 53)(10, 59)(11, 65)(12, 67)(13, 62)(14, 51)(15, 68)(16, 56)(17, 58)(18, 64)(19, 72)(20, 54)(21, 70)(22, 71)(23, 69)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.212 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-2, (Y1, Y3), (Y3 * Y1)^2, Y1^2 * Y3^2, (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y3^4, Y2 * Y1^2 * Y2^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 21, 45, 15, 39, 5, 29)(3, 27, 13, 37, 20, 44, 18, 42, 24, 48, 11, 35)(4, 28, 10, 34, 7, 31, 12, 36, 23, 47, 16, 40)(6, 30, 17, 41, 22, 46, 9, 33, 14, 38, 19, 43)(49, 73, 51, 75, 52, 76, 62, 86, 63, 87, 72, 96, 71, 95, 70, 94, 56, 80, 68, 92, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 66, 90, 53, 77, 65, 89, 64, 88, 61, 85, 69, 93, 67, 91, 60, 84, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 63)(5, 64)(6, 51)(7, 49)(8, 55)(9, 66)(10, 53)(11, 57)(12, 50)(13, 67)(14, 72)(15, 71)(16, 69)(17, 61)(18, 65)(19, 59)(20, 54)(21, 60)(22, 68)(23, 56)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 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 E15.213 Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 12^4, 24^2 ] E15.212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y3^-1 * Y1^4, Y1 * Y3 * Y2 * Y1 * Y2, (Y3 * Y2 * Y1^-1)^2, Y1^2 * Y2 * Y1^-2 * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-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, 25, 2, 26, 7, 31, 15, 39, 4, 28, 9, 33, 20, 44, 18, 42, 6, 30, 10, 34, 17, 41, 5, 29)(3, 27, 11, 35, 19, 43, 22, 46, 12, 36, 16, 40, 21, 45, 8, 32, 14, 38, 23, 47, 24, 48, 13, 37)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 60, 84)(53, 77, 64, 88)(54, 78, 62, 86)(55, 79, 67, 91)(57, 81, 61, 85)(58, 82, 70, 94)(59, 83, 66, 90)(63, 87, 71, 95)(65, 89, 72, 96)(68, 92, 69, 93) L = (1, 52)(2, 57)(3, 60)(4, 54)(5, 63)(6, 49)(7, 68)(8, 61)(9, 58)(10, 50)(11, 64)(12, 62)(13, 70)(14, 51)(15, 66)(16, 71)(17, 55)(18, 53)(19, 69)(20, 65)(21, 72)(22, 56)(23, 59)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.210 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 12, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3^2 * Y2 * Y1^-1, Y3^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 8, 32, 16, 40, 20, 44, 24, 48, 21, 45, 13, 37, 14, 38, 4, 28, 5, 29)(3, 27, 9, 33, 12, 36, 22, 46, 23, 47, 15, 39, 18, 42, 7, 31, 17, 41, 19, 43, 10, 34, 11, 35)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 63, 87)(54, 78, 60, 84)(56, 80, 67, 91)(57, 81, 69, 93)(59, 83, 68, 92)(61, 85, 65, 89)(62, 86, 70, 94)(64, 88, 71, 95)(66, 90, 72, 96) L = (1, 52)(2, 53)(3, 58)(4, 61)(5, 62)(6, 49)(7, 63)(8, 50)(9, 59)(10, 65)(11, 67)(12, 51)(13, 72)(14, 69)(15, 70)(16, 54)(17, 66)(18, 71)(19, 55)(20, 56)(21, 68)(22, 57)(23, 60)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E15.211 Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^8, (Y3 * Y2^-1)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28)(3, 27, 6, 30, 9, 33)(5, 29, 7, 31, 10, 34)(8, 32, 12, 36, 15, 39)(11, 35, 13, 37, 16, 40)(14, 38, 18, 42, 21, 45)(17, 41, 19, 43, 22, 46)(20, 44, 23, 47, 24, 48)(49, 73, 51, 75, 56, 80, 62, 86, 68, 92, 65, 89, 59, 83, 53, 77)(50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 67, 91, 61, 85, 55, 79)(52, 76, 57, 81, 63, 87, 69, 93, 72, 96, 70, 94, 64, 88, 58, 82) L = (1, 50)(2, 52)(3, 54)(4, 49)(5, 55)(6, 57)(7, 58)(8, 60)(9, 51)(10, 53)(11, 61)(12, 63)(13, 64)(14, 66)(15, 56)(16, 59)(17, 67)(18, 69)(19, 70)(20, 71)(21, 62)(22, 65)(23, 72)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 48, 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible Dual of E15.215 Graph:: bipartite v = 11 e = 48 f = 9 degree seq :: [ 6^8, 16^3 ] E15.215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y2^3, (Y3^-1, Y1^-1), (R * Y1)^2, R * Y2 * R * Y3^-1, (Y2^-1, Y1^-1), (Y3 * Y2^-1)^3, Y2 * Y1^8, (Y1^-1 * Y3^-1)^8 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 12, 36, 18, 42, 22, 46, 16, 40, 10, 34, 4, 28, 8, 32, 14, 38, 20, 44, 24, 48, 21, 45, 15, 39, 9, 33, 3, 27, 7, 31, 13, 37, 19, 43, 23, 47, 17, 41, 11, 35, 5, 29)(49, 73, 51, 75, 52, 76)(50, 74, 55, 79, 56, 80)(53, 77, 57, 81, 58, 82)(54, 78, 61, 85, 62, 86)(59, 83, 63, 87, 64, 88)(60, 84, 67, 91, 68, 92)(65, 89, 69, 93, 70, 94)(66, 90, 71, 95, 72, 96) L = (1, 52)(2, 56)(3, 49)(4, 51)(5, 58)(6, 62)(7, 50)(8, 55)(9, 53)(10, 57)(11, 64)(12, 68)(13, 54)(14, 61)(15, 59)(16, 63)(17, 70)(18, 72)(19, 60)(20, 67)(21, 65)(22, 69)(23, 66)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E15.214 Graph:: bipartite v = 9 e = 48 f = 11 degree seq :: [ 6^8, 48 ] E15.216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3 * Y1, (Y2, Y3^-1), (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3^4, Y3 * Y2 * Y3 * Y1 * Y3^2 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 17, 41)(12, 36, 18, 42)(13, 37, 19, 43)(14, 38, 20, 44)(15, 39, 21, 45)(16, 40, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 50, 74, 55, 79, 53, 77)(52, 76, 59, 83, 68, 92, 56, 80, 65, 89, 62, 86)(54, 78, 60, 84, 69, 93, 58, 82, 66, 90, 63, 87)(61, 85, 71, 95, 70, 94, 67, 91, 72, 96, 64, 88) L = (1, 52)(2, 56)(3, 59)(4, 61)(5, 62)(6, 49)(7, 65)(8, 67)(9, 68)(10, 50)(11, 71)(12, 51)(13, 60)(14, 64)(15, 53)(16, 54)(17, 72)(18, 55)(19, 66)(20, 70)(21, 57)(22, 58)(23, 69)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E15.219 Graph:: bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.217 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y1 * Y3)^2, (Y2, Y3), (R * Y2)^2, Y2^3 * Y3^-1 * Y2 * Y1^-1, Y2^2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 7, 31, 5, 29)(3, 27, 8, 32, 12, 36, 20, 44, 14, 38, 13, 37)(6, 30, 10, 34, 15, 39, 21, 45, 18, 42, 16, 40)(11, 35, 19, 43, 23, 47, 17, 41, 22, 46, 24, 48)(49, 73, 51, 75, 59, 83, 69, 93, 57, 81, 68, 92, 65, 89, 54, 78)(50, 74, 56, 80, 67, 91, 66, 90, 55, 79, 62, 86, 70, 94, 58, 82)(52, 76, 60, 84, 71, 95, 64, 88, 53, 77, 61, 85, 72, 96, 63, 87) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 50)(6, 63)(7, 49)(8, 68)(9, 53)(10, 69)(11, 71)(12, 62)(13, 56)(14, 51)(15, 66)(16, 58)(17, 72)(18, 54)(19, 65)(20, 61)(21, 64)(22, 59)(23, 70)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 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 E15.218 Graph:: bipartite v = 7 e = 48 f = 13 degree seq :: [ 12^4, 16^3 ] E15.218 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, Y2 * Y3^-1 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1), Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^-4, Y2 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1, Y1 * Y2 * 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, 25, 2, 26, 7, 31, 17, 41, 13, 37, 22, 46, 24, 48, 14, 38, 4, 28, 9, 33, 19, 43, 12, 36, 3, 27, 8, 32, 18, 42, 16, 40, 6, 30, 10, 34, 20, 44, 23, 47, 11, 35, 21, 45, 15, 39, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 66, 90)(57, 81, 69, 93)(58, 82, 70, 94)(62, 86, 71, 95)(63, 87, 67, 91)(64, 88, 65, 89)(68, 92, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 54)(5, 62)(6, 49)(7, 67)(8, 69)(9, 58)(10, 50)(11, 61)(12, 71)(13, 51)(14, 64)(15, 72)(16, 53)(17, 60)(18, 63)(19, 68)(20, 55)(21, 70)(22, 56)(23, 65)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E15.217 Graph:: bipartite v = 13 e = 48 f = 7 degree seq :: [ 4^12, 48 ] E15.219 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), (Y2, Y1), Y3 * Y2^2 * Y1^-1, Y2^-1 * Y1 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y3^-1)^2, Y3^-1 * Y1^2 * Y2 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-2, Y1 * Y3^-1 * Y2^22 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 14, 38, 24, 48, 16, 40, 5, 29)(3, 27, 9, 33, 20, 44, 15, 39, 4, 28, 10, 34, 21, 45, 13, 37)(6, 30, 11, 35, 22, 46, 18, 42, 7, 31, 12, 36, 23, 47, 17, 41)(49, 73, 51, 75, 60, 84, 72, 96, 58, 82, 70, 94, 56, 80, 68, 92, 65, 89, 53, 77, 61, 85, 55, 79, 62, 86, 52, 76, 59, 83, 50, 74, 57, 81, 71, 95, 64, 88, 69, 93, 66, 90, 67, 91, 63, 87, 54, 78) L = (1, 52)(2, 58)(3, 59)(4, 60)(5, 63)(6, 62)(7, 49)(8, 69)(9, 70)(10, 71)(11, 72)(12, 50)(13, 54)(14, 51)(15, 55)(16, 68)(17, 67)(18, 53)(19, 61)(20, 66)(21, 65)(22, 64)(23, 56)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E15.216 Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 16^3, 48 ] E15.220 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^-1 * Y3^-1, (R * Y1)^2, (Y3, Y2^-1), (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^4 * Y1, Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 8, 32)(5, 29, 9, 33)(6, 30, 10, 34)(11, 35, 16, 40)(12, 36, 17, 41)(13, 37, 18, 42)(14, 38, 19, 43)(15, 39, 20, 44)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 59, 83, 57, 81, 50, 74, 55, 79, 64, 88, 53, 77)(52, 76, 60, 84, 69, 93, 68, 92, 56, 80, 65, 89, 72, 96, 63, 87)(54, 78, 61, 85, 70, 94, 67, 91, 58, 82, 66, 90, 71, 95, 62, 86) L = (1, 52)(2, 56)(3, 60)(4, 62)(5, 63)(6, 49)(7, 65)(8, 67)(9, 68)(10, 50)(11, 69)(12, 54)(13, 51)(14, 53)(15, 71)(16, 72)(17, 58)(18, 55)(19, 57)(20, 70)(21, 61)(22, 59)(23, 64)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 48, 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible Dual of E15.221 Graph:: bipartite v = 15 e = 48 f = 5 degree seq :: [ 4^12, 16^3 ] E15.221 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 8, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, Y3^3, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y2, Y3), (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^4 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 7, 31, 5, 29)(3, 27, 8, 32, 12, 36, 19, 43, 14, 38, 13, 37)(6, 30, 10, 34, 15, 39, 20, 44, 18, 42, 16, 40)(11, 35, 17, 41, 21, 45, 24, 48, 23, 47, 22, 46)(49, 73, 51, 75, 59, 83, 64, 88, 53, 77, 61, 85, 70, 94, 66, 90, 55, 79, 62, 86, 71, 95, 68, 92, 57, 81, 67, 91, 72, 96, 63, 87, 52, 76, 60, 84, 69, 93, 58, 82, 50, 74, 56, 80, 65, 89, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 50)(6, 63)(7, 49)(8, 67)(9, 53)(10, 68)(11, 69)(12, 62)(13, 56)(14, 51)(15, 66)(16, 58)(17, 72)(18, 54)(19, 61)(20, 64)(21, 71)(22, 65)(23, 59)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 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 E15.220 Graph:: bipartite v = 5 e = 48 f = 15 degree seq :: [ 12^4, 48 ] E15.222 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y1, Y2^-1), (R * Y2 * Y3^-1)^2, Y1 * Y2^6, (Y3 * Y2^-1)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 7, 31, 13, 37, 10, 34)(5, 29, 8, 32, 14, 38, 11, 35)(9, 33, 15, 39, 21, 45, 18, 42)(12, 36, 16, 40, 22, 46, 19, 43)(17, 41, 20, 44, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 65, 89, 67, 91, 59, 83, 52, 76, 58, 82, 66, 90, 72, 96, 70, 94, 62, 86, 54, 78, 61, 85, 69, 93, 71, 95, 64, 88, 56, 80, 50, 74, 55, 79, 63, 87, 68, 92, 60, 84, 53, 77) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 52)(7, 61)(8, 62)(9, 63)(10, 51)(11, 53)(12, 64)(13, 58)(14, 59)(15, 69)(16, 70)(17, 68)(18, 57)(19, 60)(20, 71)(21, 66)(22, 67)(23, 72)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 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 E15.225 Graph:: bipartite v = 7 e = 48 f = 13 degree seq :: [ 8^6, 48 ] E15.223 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^6 * Y1^-1, (Y3 * Y2^-1)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 7, 31, 13, 37, 10, 34)(5, 29, 8, 32, 14, 38, 11, 35)(9, 33, 15, 39, 21, 45, 18, 42)(12, 36, 16, 40, 22, 46, 19, 43)(17, 41, 23, 47, 24, 48, 20, 44)(49, 73, 51, 75, 57, 81, 65, 89, 64, 88, 56, 80, 50, 74, 55, 79, 63, 87, 71, 95, 70, 94, 62, 86, 54, 78, 61, 85, 69, 93, 72, 96, 67, 91, 59, 83, 52, 76, 58, 82, 66, 90, 68, 92, 60, 84, 53, 77) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 52)(7, 61)(8, 62)(9, 63)(10, 51)(11, 53)(12, 64)(13, 58)(14, 59)(15, 69)(16, 70)(17, 71)(18, 57)(19, 60)(20, 65)(21, 66)(22, 67)(23, 72)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 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 E15.224 Graph:: bipartite v = 7 e = 48 f = 13 degree seq :: [ 8^6, 48 ] E15.224 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, (Y1, Y3), (R * Y3)^2, (R * Y2)^2, Y1^-3 * Y3^-1 * Y1^-3, Y1 * Y3 * Y1^5, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 22, 46, 14, 38, 6, 30, 10, 34, 18, 42, 24, 48, 19, 43, 11, 35, 3, 27, 8, 32, 16, 40, 23, 47, 20, 44, 12, 36, 4, 28, 9, 33, 17, 41, 21, 45, 13, 37, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 54, 78)(53, 77, 59, 83)(55, 79, 64, 88)(57, 81, 58, 82)(60, 84, 62, 86)(61, 85, 67, 91)(63, 87, 71, 95)(65, 89, 66, 90)(68, 92, 70, 94)(69, 93, 72, 96) L = (1, 52)(2, 57)(3, 54)(4, 51)(5, 60)(6, 49)(7, 65)(8, 58)(9, 56)(10, 50)(11, 62)(12, 59)(13, 68)(14, 53)(15, 69)(16, 66)(17, 64)(18, 55)(19, 70)(20, 67)(21, 71)(22, 61)(23, 72)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E15.223 Graph:: bipartite v = 13 e = 48 f = 7 degree seq :: [ 4^12, 48 ] E15.225 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (R * Y2)^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, Y1^-3 * Y3 * Y1^-3, Y1^-2 * Y3 * Y1^-4, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 20, 44, 12, 36, 4, 28, 9, 33, 17, 41, 24, 48, 19, 43, 11, 35, 3, 27, 8, 32, 16, 40, 23, 47, 22, 46, 14, 38, 6, 30, 10, 34, 18, 42, 21, 45, 13, 37, 5, 29)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 54, 78)(53, 77, 59, 83)(55, 79, 64, 88)(57, 81, 58, 82)(60, 84, 62, 86)(61, 85, 67, 91)(63, 87, 71, 95)(65, 89, 66, 90)(68, 92, 70, 94)(69, 93, 72, 96) L = (1, 52)(2, 57)(3, 54)(4, 51)(5, 60)(6, 49)(7, 65)(8, 58)(9, 56)(10, 50)(11, 62)(12, 59)(13, 68)(14, 53)(15, 72)(16, 66)(17, 64)(18, 55)(19, 70)(20, 67)(21, 63)(22, 61)(23, 69)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E15.222 Graph:: bipartite v = 13 e = 48 f = 7 degree seq :: [ 4^12, 48 ] E15.226 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 4}) Quotient :: edge^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1^2 * Y3^2, Y3^4, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1^2 * Y3^-1, Y2^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 3, 31, 6, 34, 5, 33)(2, 30, 7, 35, 4, 32, 8, 36)(9, 37, 13, 41, 10, 38, 14, 42)(11, 39, 15, 43, 12, 40, 16, 44)(17, 45, 21, 49, 18, 46, 22, 50)(19, 47, 23, 51, 20, 48, 24, 52)(25, 53, 27, 55, 26, 54, 28, 56)(57, 58, 62, 60)(59, 65, 61, 66)(63, 67, 64, 68)(69, 73, 70, 74)(71, 75, 72, 76)(77, 81, 78, 82)(79, 83, 80, 84)(85, 86, 90, 88)(87, 93, 89, 94)(91, 95, 92, 96)(97, 101, 98, 102)(99, 103, 100, 104)(105, 109, 106, 110)(107, 111, 108, 112) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.228 Graph:: bipartite v = 21 e = 56 f = 7 degree seq :: [ 4^14, 8^7 ] E15.227 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 4}) Quotient :: edge^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y1^-2 * Y3^2, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1^-2 * Y3^-1, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 3, 31, 6, 34, 5, 33)(2, 30, 7, 35, 4, 32, 8, 36)(9, 37, 13, 41, 10, 38, 14, 42)(11, 39, 15, 43, 12, 40, 16, 44)(17, 45, 21, 49, 18, 46, 22, 50)(19, 47, 23, 51, 20, 48, 24, 52)(25, 53, 28, 56, 26, 54, 27, 55)(57, 58, 62, 60)(59, 65, 61, 66)(63, 67, 64, 68)(69, 73, 70, 74)(71, 75, 72, 76)(77, 81, 78, 82)(79, 83, 80, 84)(85, 86, 90, 88)(87, 93, 89, 94)(91, 95, 92, 96)(97, 101, 98, 102)(99, 103, 100, 104)(105, 109, 106, 110)(107, 111, 108, 112) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.229 Graph:: bipartite v = 21 e = 56 f = 7 degree seq :: [ 4^14, 8^7 ] E15.228 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 4}) Quotient :: loop^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1^2 * Y3^2, Y3^4, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1^2 * Y3^-1, Y2^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 57, 85, 3, 31, 59, 87, 6, 34, 62, 90, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 4, 32, 60, 88, 8, 36, 64, 92)(9, 37, 65, 93, 13, 41, 69, 97, 10, 38, 66, 94, 14, 42, 70, 98)(11, 39, 67, 95, 15, 43, 71, 99, 12, 40, 68, 96, 16, 44, 72, 100)(17, 45, 73, 101, 21, 49, 77, 105, 18, 46, 74, 102, 22, 50, 78, 106)(19, 47, 75, 103, 23, 51, 79, 107, 20, 48, 76, 104, 24, 52, 80, 108)(25, 53, 81, 109, 27, 55, 83, 111, 26, 54, 82, 110, 28, 56, 84, 112) L = (1, 30)(2, 34)(3, 37)(4, 29)(5, 38)(6, 32)(7, 39)(8, 40)(9, 33)(10, 31)(11, 36)(12, 35)(13, 45)(14, 46)(15, 47)(16, 48)(17, 42)(18, 41)(19, 44)(20, 43)(21, 53)(22, 54)(23, 55)(24, 56)(25, 50)(26, 49)(27, 52)(28, 51)(57, 86)(58, 90)(59, 93)(60, 85)(61, 94)(62, 88)(63, 95)(64, 96)(65, 89)(66, 87)(67, 92)(68, 91)(69, 101)(70, 102)(71, 103)(72, 104)(73, 98)(74, 97)(75, 100)(76, 99)(77, 109)(78, 110)(79, 111)(80, 112)(81, 106)(82, 105)(83, 108)(84, 107) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.226 Transitivity :: VT+ Graph:: v = 7 e = 56 f = 21 degree seq :: [ 16^7 ] E15.229 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 4}) Quotient :: loop^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y1^-2 * Y3^2, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1^-2 * Y3^-1, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 57, 85, 3, 31, 59, 87, 6, 34, 62, 90, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 4, 32, 60, 88, 8, 36, 64, 92)(9, 37, 65, 93, 13, 41, 69, 97, 10, 38, 66, 94, 14, 42, 70, 98)(11, 39, 67, 95, 15, 43, 71, 99, 12, 40, 68, 96, 16, 44, 72, 100)(17, 45, 73, 101, 21, 49, 77, 105, 18, 46, 74, 102, 22, 50, 78, 106)(19, 47, 75, 103, 23, 51, 79, 107, 20, 48, 76, 104, 24, 52, 80, 108)(25, 53, 81, 109, 28, 56, 84, 112, 26, 54, 82, 110, 27, 55, 83, 111) L = (1, 30)(2, 34)(3, 37)(4, 29)(5, 38)(6, 32)(7, 39)(8, 40)(9, 33)(10, 31)(11, 36)(12, 35)(13, 45)(14, 46)(15, 47)(16, 48)(17, 42)(18, 41)(19, 44)(20, 43)(21, 53)(22, 54)(23, 55)(24, 56)(25, 50)(26, 49)(27, 52)(28, 51)(57, 86)(58, 90)(59, 93)(60, 85)(61, 94)(62, 88)(63, 95)(64, 96)(65, 89)(66, 87)(67, 92)(68, 91)(69, 101)(70, 102)(71, 103)(72, 104)(73, 98)(74, 97)(75, 100)(76, 99)(77, 109)(78, 110)(79, 111)(80, 112)(81, 106)(82, 105)(83, 108)(84, 107) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.227 Transitivity :: VT+ Graph:: v = 7 e = 56 f = 21 degree seq :: [ 16^7 ] E15.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3 * Y2^-1 * Y3, (Y3 * Y2)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 12, 42)(5, 35, 9, 39)(6, 36, 13, 43)(8, 38, 15, 45)(10, 40, 16, 46)(11, 41, 17, 47)(14, 44, 21, 51)(18, 48, 25, 55)(19, 49, 26, 56)(20, 50, 27, 57)(22, 52, 28, 58)(23, 53, 29, 59)(24, 54, 30, 60)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 69, 99)(64, 94, 71, 101, 66, 96)(68, 98, 74, 104, 70, 100)(72, 102, 77, 107, 73, 103)(75, 105, 81, 111, 76, 106)(78, 108, 80, 110, 79, 109)(82, 112, 84, 114, 83, 113)(85, 115, 87, 117, 86, 116)(88, 118, 90, 120, 89, 119) L = (1, 64)(2, 68)(3, 71)(4, 63)(5, 66)(6, 61)(7, 74)(8, 67)(9, 70)(10, 62)(11, 65)(12, 78)(13, 79)(14, 69)(15, 82)(16, 83)(17, 80)(18, 77)(19, 72)(20, 73)(21, 84)(22, 81)(23, 75)(24, 76)(25, 89)(26, 90)(27, 88)(28, 86)(29, 87)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 30, 12, 30 ), ( 12, 30, 12, 30, 12, 30 ) } Outer automorphisms :: reflexible Dual of E15.233 Graph:: simple bipartite v = 25 e = 60 f = 7 degree seq :: [ 4^15, 6^10 ] E15.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2 * Y1 * Y2, Y1^3, (Y2^-1 * Y1)^2, (R * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2^-1 * R * Y3 * Y2^-1 * Y3^-1, Y3 * Y2 * R * Y2 * R * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 6, 36, 9, 39)(4, 34, 8, 38, 7, 37)(10, 40, 14, 44, 11, 41)(12, 42, 13, 43, 15, 45)(16, 46, 17, 47, 18, 48)(19, 49, 21, 51, 20, 50)(22, 52, 24, 54, 23, 53)(25, 55, 26, 56, 27, 57)(28, 58, 29, 59, 30, 60)(61, 91, 63, 93, 65, 95, 69, 99, 62, 92, 66, 96)(64, 94, 72, 102, 67, 97, 75, 105, 68, 98, 73, 103)(70, 100, 76, 106, 71, 101, 78, 108, 74, 104, 77, 107)(79, 109, 85, 115, 80, 110, 87, 117, 81, 111, 86, 116)(82, 112, 88, 118, 83, 113, 90, 120, 84, 114, 89, 119) L = (1, 64)(2, 68)(3, 70)(4, 62)(5, 67)(6, 74)(7, 61)(8, 65)(9, 71)(10, 66)(11, 63)(12, 79)(13, 81)(14, 69)(15, 80)(16, 82)(17, 84)(18, 83)(19, 73)(20, 72)(21, 75)(22, 77)(23, 76)(24, 78)(25, 89)(26, 90)(27, 88)(28, 85)(29, 86)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E15.232 Graph:: bipartite v = 15 e = 60 f = 17 degree seq :: [ 6^10, 12^5 ] E15.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y1^3 * Y3^-1 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 17, 47, 24, 54, 13, 43, 22, 52, 29, 59, 30, 60, 25, 55, 12, 42, 21, 51, 28, 58, 16, 46, 5, 35)(3, 33, 11, 41, 23, 53, 19, 49, 8, 38, 6, 36, 15, 45, 27, 57, 18, 48, 10, 40, 4, 34, 14, 44, 26, 56, 20, 50, 9, 39)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 72, 102)(65, 95, 74, 104)(66, 96, 73, 103)(67, 97, 78, 108)(69, 99, 81, 111)(70, 100, 82, 112)(71, 101, 84, 114)(75, 105, 85, 115)(76, 106, 87, 117)(77, 107, 86, 116)(79, 109, 88, 118)(80, 110, 89, 119)(83, 113, 90, 120) L = (1, 64)(2, 69)(3, 72)(4, 73)(5, 75)(6, 61)(7, 79)(8, 81)(9, 82)(10, 62)(11, 65)(12, 66)(13, 63)(14, 85)(15, 84)(16, 83)(17, 87)(18, 88)(19, 89)(20, 67)(21, 70)(22, 68)(23, 77)(24, 74)(25, 71)(26, 76)(27, 90)(28, 80)(29, 78)(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, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E15.231 Graph:: bipartite v = 17 e = 60 f = 15 degree seq :: [ 4^15, 30^2 ] E15.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2^-1 * Y1^-3 * Y2^-1, Y2 * Y1 * Y2 * Y1^-3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^-1 * Y1^2 * Y2^-4 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 16, 46, 12, 42, 4, 34)(3, 33, 9, 39, 17, 47, 13, 43, 21, 51, 8, 38)(5, 35, 11, 41, 18, 48, 7, 37, 19, 49, 14, 44)(10, 40, 24, 54, 29, 59, 22, 52, 28, 58, 23, 53)(15, 45, 27, 57, 25, 55, 26, 56, 30, 60, 20, 50)(61, 91, 63, 93, 70, 100, 85, 115, 78, 108, 66, 96, 77, 107, 89, 119, 90, 120, 79, 109, 72, 102, 81, 111, 88, 118, 75, 105, 65, 95)(62, 92, 67, 97, 80, 110, 83, 113, 69, 99, 76, 106, 74, 104, 87, 117, 84, 114, 73, 103, 64, 94, 71, 101, 86, 116, 82, 112, 68, 98) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 71)(6, 76)(7, 79)(8, 63)(9, 77)(10, 84)(11, 78)(12, 64)(13, 81)(14, 65)(15, 87)(16, 72)(17, 73)(18, 67)(19, 74)(20, 75)(21, 68)(22, 88)(23, 70)(24, 89)(25, 86)(26, 90)(27, 85)(28, 83)(29, 82)(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) :: { ( 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 E15.230 Graph:: bipartite v = 7 e = 60 f = 25 degree seq :: [ 12^5, 30^2 ] E15.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3^-2 * Y1 * Y2^-1 * Y3, Y2^-1 * Y1 * Y2^2 * Y1 * Y3, (Y3 * Y2^-1)^3, Y2^6, Y2^-1 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 9, 39)(5, 35, 11, 41)(6, 36, 13, 43)(8, 38, 12, 42)(10, 40, 14, 44)(15, 45, 23, 53)(16, 46, 25, 55)(17, 47, 24, 54)(18, 48, 26, 56)(19, 49, 27, 57)(20, 50, 29, 59)(21, 51, 28, 58)(22, 52, 30, 60)(61, 91, 63, 93, 68, 98, 77, 107, 70, 100, 64, 94)(62, 92, 65, 95, 72, 102, 81, 111, 74, 104, 66, 96)(67, 97, 75, 105, 84, 114, 78, 108, 69, 99, 76, 106)(71, 101, 79, 109, 88, 118, 82, 112, 73, 103, 80, 110)(83, 113, 89, 119, 86, 116, 87, 117, 85, 115, 90, 120) L = (1, 64)(2, 66)(3, 61)(4, 70)(5, 62)(6, 74)(7, 76)(8, 63)(9, 78)(10, 77)(11, 80)(12, 65)(13, 82)(14, 81)(15, 67)(16, 69)(17, 68)(18, 84)(19, 71)(20, 73)(21, 72)(22, 88)(23, 90)(24, 75)(25, 87)(26, 89)(27, 86)(28, 79)(29, 83)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 30, 6, 30 ), ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E15.235 Graph:: bipartite v = 20 e = 60 f = 12 degree seq :: [ 4^15, 12^5 ] E15.235 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 15}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^-2 * Y1, (Y1^-1, Y2), (Y2 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, R * Y2 * Y1 * R * Y2^-1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2, Y1 * Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 13, 43)(4, 34, 9, 39, 7, 37)(6, 36, 10, 40, 17, 47)(11, 41, 21, 51, 25, 55)(12, 42, 16, 46, 14, 44)(15, 45, 18, 48, 20, 50)(19, 49, 22, 52, 23, 53)(24, 54, 27, 57, 26, 56)(28, 58, 29, 59, 30, 60)(61, 91, 63, 93, 71, 101, 83, 113, 77, 107, 65, 95, 73, 103, 85, 115, 82, 112, 70, 100, 62, 92, 68, 98, 81, 111, 79, 109, 66, 96)(64, 94, 75, 105, 88, 118, 87, 117, 72, 102, 67, 97, 80, 110, 90, 120, 84, 114, 74, 104, 69, 99, 78, 108, 89, 119, 86, 116, 76, 106) L = (1, 64)(2, 69)(3, 72)(4, 62)(5, 67)(6, 78)(7, 61)(8, 76)(9, 65)(10, 80)(11, 84)(12, 68)(13, 74)(14, 63)(15, 66)(16, 73)(17, 75)(18, 70)(19, 90)(20, 77)(21, 87)(22, 88)(23, 89)(24, 81)(25, 86)(26, 71)(27, 85)(28, 83)(29, 79)(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) :: { ( 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 E15.234 Graph:: bipartite v = 12 e = 60 f = 20 degree seq :: [ 6^10, 30^2 ] E15.236 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^-5 * Y2^-1, (Y2^-1 * Y3)^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 8, 38)(5, 35, 9, 39)(6, 36, 10, 40)(11, 41, 17, 47)(12, 42, 18, 48)(13, 43, 19, 49)(14, 44, 20, 50)(15, 45, 21, 51)(16, 46, 22, 52)(23, 53, 27, 57)(24, 54, 28, 58)(25, 55, 29, 59)(26, 56, 30, 60)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 69, 99)(64, 94, 71, 101, 74, 104)(66, 96, 72, 102, 75, 105)(68, 98, 77, 107, 80, 110)(70, 100, 78, 108, 81, 111)(73, 103, 83, 113, 86, 116)(76, 106, 84, 114, 85, 115)(79, 109, 87, 117, 90, 120)(82, 112, 88, 118, 89, 119) L = (1, 64)(2, 68)(3, 71)(4, 73)(5, 74)(6, 61)(7, 77)(8, 79)(9, 80)(10, 62)(11, 83)(12, 63)(13, 85)(14, 86)(15, 65)(16, 66)(17, 87)(18, 67)(19, 89)(20, 90)(21, 69)(22, 70)(23, 76)(24, 72)(25, 75)(26, 84)(27, 82)(28, 78)(29, 81)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 10, 60, 10, 60 ), ( 10, 60, 10, 60, 10, 60 ) } Outer automorphisms :: reflexible Dual of E15.239 Graph:: simple bipartite v = 25 e = 60 f = 7 degree seq :: [ 4^15, 6^10 ] E15.237 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (Y2, Y3), (Y3^-1 * Y1^-1)^2, Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 13, 43)(4, 34, 9, 39, 7, 37)(6, 36, 10, 40, 16, 46)(11, 41, 19, 49, 24, 54)(12, 42, 20, 50, 14, 44)(15, 45, 21, 51, 18, 48)(17, 47, 22, 52, 27, 57)(23, 53, 29, 59, 25, 55)(26, 56, 30, 60, 28, 58)(61, 91, 63, 93, 71, 101, 77, 107, 66, 96)(62, 92, 68, 98, 79, 109, 82, 112, 70, 100)(64, 94, 72, 102, 83, 113, 86, 116, 75, 105)(65, 95, 73, 103, 84, 114, 87, 117, 76, 106)(67, 97, 74, 104, 85, 115, 88, 118, 78, 108)(69, 99, 80, 110, 89, 119, 90, 120, 81, 111) L = (1, 64)(2, 69)(3, 72)(4, 62)(5, 67)(6, 75)(7, 61)(8, 80)(9, 65)(10, 81)(11, 83)(12, 68)(13, 74)(14, 63)(15, 70)(16, 78)(17, 86)(18, 66)(19, 89)(20, 73)(21, 76)(22, 90)(23, 79)(24, 85)(25, 71)(26, 82)(27, 88)(28, 77)(29, 84)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 60, 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E15.238 Graph:: simple bipartite v = 16 e = 60 f = 16 degree seq :: [ 6^10, 10^6 ] E15.238 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (Y1, Y3^-1), (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y3 * Y1^-4, Y3 * Y2 * Y1^-2 * Y2 * Y3^-1 * Y1^2, (Y1^-1 * Y3^-1)^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 17, 47, 14, 44, 4, 34, 9, 39, 19, 49, 28, 58, 25, 55, 13, 43, 22, 52, 30, 60, 24, 54, 12, 42, 3, 33, 8, 38, 18, 48, 27, 57, 23, 53, 11, 41, 21, 51, 29, 59, 26, 56, 16, 46, 6, 36, 10, 40, 20, 50, 15, 45, 5, 35)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 71, 101)(65, 95, 72, 102)(66, 96, 73, 103)(67, 97, 78, 108)(69, 99, 81, 111)(70, 100, 82, 112)(74, 104, 83, 113)(75, 105, 84, 114)(76, 106, 85, 115)(77, 107, 87, 117)(79, 109, 89, 119)(80, 110, 90, 120)(86, 116, 88, 118) L = (1, 64)(2, 69)(3, 71)(4, 73)(5, 74)(6, 61)(7, 79)(8, 81)(9, 82)(10, 62)(11, 66)(12, 83)(13, 63)(14, 85)(15, 77)(16, 65)(17, 88)(18, 89)(19, 90)(20, 67)(21, 70)(22, 68)(23, 76)(24, 87)(25, 72)(26, 75)(27, 86)(28, 84)(29, 80)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 10, 6, 10 ), ( 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 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 E15.237 Graph:: bipartite v = 16 e = 60 f = 16 degree seq :: [ 4^15, 60 ] E15.239 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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^-2, (R * Y2)^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (Y1^-1, Y2), Y3^-3 * Y1^2, Y1^5, Y3 * Y1^2 * Y2^26 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 5, 35)(3, 33, 9, 39, 23, 53, 22, 52, 15, 45)(4, 34, 10, 40, 24, 54, 21, 51, 17, 47)(6, 36, 11, 41, 14, 44, 26, 56, 19, 49)(7, 37, 12, 42, 13, 43, 25, 55, 20, 50)(16, 46, 27, 57, 28, 58, 30, 60, 29, 59)(61, 91, 63, 93, 73, 103, 88, 118, 84, 114, 79, 109, 65, 95, 75, 105, 72, 102, 87, 117, 70, 100, 86, 116, 78, 108, 82, 112, 67, 97, 76, 106, 64, 94, 74, 104, 68, 98, 83, 113, 80, 110, 89, 119, 77, 107, 71, 101, 62, 92, 69, 99, 85, 115, 90, 120, 81, 111, 66, 96) L = (1, 64)(2, 70)(3, 74)(4, 73)(5, 77)(6, 76)(7, 61)(8, 84)(9, 86)(10, 85)(11, 87)(12, 62)(13, 68)(14, 88)(15, 71)(16, 63)(17, 72)(18, 81)(19, 89)(20, 65)(21, 67)(22, 66)(23, 79)(24, 80)(25, 78)(26, 90)(27, 69)(28, 83)(29, 75)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E15.236 Graph:: bipartite v = 7 e = 60 f = 25 degree seq :: [ 10^6, 60 ] E15.240 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3^3 * Y2^2, Y2^5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 8, 38)(5, 35, 9, 39)(6, 36, 10, 40)(11, 41, 19, 49)(12, 42, 20, 50)(13, 43, 21, 51)(14, 44, 22, 52)(15, 45, 23, 53)(16, 46, 24, 54)(17, 47, 25, 55)(18, 48, 26, 56)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 71, 101, 76, 106, 65, 95)(62, 92, 67, 97, 79, 109, 84, 114, 69, 99)(64, 94, 72, 102, 78, 108, 88, 118, 75, 105)(66, 96, 73, 103, 87, 117, 74, 104, 77, 107)(68, 98, 80, 110, 86, 116, 90, 120, 83, 113)(70, 100, 81, 111, 89, 119, 82, 112, 85, 115) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 75)(6, 61)(7, 80)(8, 82)(9, 83)(10, 62)(11, 78)(12, 77)(13, 63)(14, 76)(15, 87)(16, 88)(17, 65)(18, 66)(19, 86)(20, 85)(21, 67)(22, 84)(23, 89)(24, 90)(25, 69)(26, 70)(27, 71)(28, 73)(29, 79)(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, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible Dual of E15.241 Graph:: simple bipartite v = 21 e = 60 f = 11 degree seq :: [ 4^15, 10^6 ] E15.241 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 5, 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^-2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3), (R * Y2)^2, (Y2, Y1^-1), (Y3^-1 * Y1^-1)^2, Y2^3 * Y3 * Y2^2, Y2^-1 * Y1^-1 * Y2^3 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y2^-1 * Y3)^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 13, 43)(4, 34, 9, 39, 7, 37)(6, 36, 10, 40, 16, 46)(11, 41, 19, 49, 25, 55)(12, 42, 20, 50, 14, 44)(15, 45, 21, 51, 18, 48)(17, 47, 22, 52, 28, 58)(23, 53, 27, 57, 30, 60)(24, 54, 29, 59, 26, 56)(61, 91, 63, 93, 71, 101, 83, 113, 78, 108, 67, 97, 74, 104, 86, 116, 88, 118, 76, 106, 65, 95, 73, 103, 85, 115, 90, 120, 81, 111, 69, 99, 80, 110, 89, 119, 82, 112, 70, 100, 62, 92, 68, 98, 79, 109, 87, 117, 75, 105, 64, 94, 72, 102, 84, 114, 77, 107, 66, 96) L = (1, 64)(2, 69)(3, 72)(4, 62)(5, 67)(6, 75)(7, 61)(8, 80)(9, 65)(10, 81)(11, 84)(12, 68)(13, 74)(14, 63)(15, 70)(16, 78)(17, 87)(18, 66)(19, 89)(20, 73)(21, 76)(22, 90)(23, 77)(24, 79)(25, 86)(26, 71)(27, 82)(28, 83)(29, 85)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 10, 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E15.240 Graph:: bipartite v = 11 e = 60 f = 21 degree seq :: [ 6^10, 60 ] E15.242 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^15 * Y1, (Y3 * Y2^-1)^30 ] Map:: R = (1, 31, 2, 32)(3, 33, 5, 35)(4, 34, 6, 36)(7, 37, 9, 39)(8, 38, 10, 40)(11, 41, 13, 43)(12, 42, 14, 44)(15, 45, 17, 47)(16, 46, 18, 48)(19, 49, 21, 51)(20, 50, 22, 52)(23, 53, 25, 55)(24, 54, 26, 56)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 67, 97, 71, 101, 75, 105, 79, 109, 83, 113, 87, 117, 90, 120, 86, 116, 82, 112, 78, 108, 74, 104, 70, 100, 66, 96, 62, 92, 65, 95, 69, 99, 73, 103, 77, 107, 81, 111, 85, 115, 89, 119, 88, 118, 84, 114, 80, 110, 76, 106, 72, 102, 68, 98, 64, 94) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 16 e = 60 f = 16 degree seq :: [ 4^15, 60 ] E15.243 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T1)^2, (F * T2)^2, T1 * T2^15, (T2^-1 * T1^-1)^31 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 30, 29, 25, 21, 17, 13, 9, 5)(32, 33, 34, 37, 38, 41, 42, 45, 46, 49, 50, 53, 54, 57, 58, 61, 62, 60, 59, 56, 55, 52, 51, 48, 47, 44, 43, 40, 39, 36, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.260 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.244 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T1 * T2^-15 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 30, 26, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 28, 31, 29, 25, 21, 17, 13, 9, 5)(32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, 60, 61, 62, 58, 59, 54, 55, 50, 51, 46, 47, 42, 43, 38, 39, 34, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.257 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.245 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^10, (T2^-1 * T1^-1)^31 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 31, 26, 20, 14, 8, 2, 7, 13, 19, 25, 29, 23, 17, 11, 5)(32, 33, 37, 34, 38, 43, 40, 44, 49, 46, 50, 55, 52, 56, 61, 58, 60, 62, 59, 54, 57, 53, 48, 51, 47, 42, 45, 41, 36, 39, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.262 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.246 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T1 * T2^-10 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 29, 23, 17, 11, 5)(32, 33, 37, 36, 39, 43, 42, 45, 49, 48, 51, 55, 54, 57, 61, 60, 58, 62, 59, 52, 56, 53, 46, 50, 47, 40, 44, 41, 34, 38, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.258 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.247 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^2 * T2^-1 * T1^2, T2^7 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-4 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 24, 16, 8, 2, 7, 15, 23, 31, 27, 19, 11, 6, 14, 22, 30, 28, 20, 12, 4, 10, 18, 26, 29, 21, 13, 5)(32, 33, 37, 41, 34, 38, 45, 49, 40, 46, 53, 57, 48, 54, 61, 60, 56, 62, 59, 52, 55, 58, 51, 44, 47, 50, 43, 36, 39, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.264 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.248 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-3 * T2^-1 * T1^-1, T2 * T1 * T2^7, T1 * T2^-3 * T1 * T2^-2 * T1 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 28, 20, 12, 4, 10, 18, 26, 30, 22, 14, 6, 11, 19, 27, 31, 24, 16, 8, 2, 7, 15, 23, 29, 21, 13, 5)(32, 33, 37, 43, 36, 39, 45, 51, 44, 47, 53, 59, 52, 55, 61, 56, 60, 62, 57, 48, 54, 58, 49, 40, 46, 50, 41, 34, 38, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.259 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.249 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T2 * T1 * T2^5, (T1^-1 * T2^-1)^31 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 12, 4, 10, 20, 28, 29, 21, 11, 14, 24, 30, 31, 26, 16, 6, 15, 25, 27, 18, 8, 2, 7, 17, 23, 13, 5)(32, 33, 37, 45, 41, 34, 38, 46, 55, 51, 40, 48, 56, 61, 59, 50, 54, 58, 62, 60, 53, 44, 49, 57, 52, 43, 36, 39, 47, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.263 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.250 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1^-5, T2^-6 * 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 * T1^2 * T2^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 27, 26, 16, 6, 15, 25, 31, 30, 24, 14, 11, 21, 28, 29, 22, 12, 4, 10, 20, 23, 13, 5)(32, 33, 37, 45, 43, 36, 39, 47, 55, 53, 44, 49, 57, 61, 60, 54, 50, 58, 62, 59, 51, 40, 48, 56, 52, 41, 34, 38, 46, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.261 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.251 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-2 * T2^-4 * T1^-1, T1^-1 * T2 * T1^-6 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 27, 14, 25, 13, 5)(32, 33, 37, 45, 57, 52, 41, 34, 38, 46, 56, 60, 62, 51, 40, 48, 55, 44, 49, 59, 61, 50, 54, 43, 36, 39, 47, 58, 53, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.266 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.252 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1^-1 * T2^4 * T1^-2, T1^2 * T2^-1 * T1 * T2^-3, T1^-2 * T2^-1 * T1^-5, T1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-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 * T1^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 31, 24, 12, 4, 10, 20, 16, 6, 15, 28, 30, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 22, 25, 13, 5)(32, 33, 37, 45, 57, 54, 43, 36, 39, 47, 50, 60, 61, 55, 44, 49, 51, 40, 48, 59, 62, 56, 52, 41, 34, 38, 46, 58, 53, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.265 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.253 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^4 * T2 * T1 * T2 * T1^4, (T1^-1 * T2^-1)^31 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 29, 31, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 30, 23, 25, 18, 11, 13, 5)(32, 33, 37, 45, 51, 57, 62, 56, 50, 44, 41, 34, 38, 46, 52, 58, 61, 55, 49, 43, 36, 39, 40, 47, 53, 59, 60, 54, 48, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.269 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.254 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2), T1 * T2 * T1 * T2^2, T1^-7 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-1, T1^-1 * T2^14 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 30, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 27, 20, 22, 15, 6, 13, 5)(32, 33, 37, 45, 51, 57, 60, 54, 48, 40, 43, 36, 39, 46, 52, 58, 61, 55, 49, 41, 34, 38, 44, 47, 53, 59, 62, 56, 50, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.267 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.255 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2^-1 * T1^-1 * T2^-4, T2^2 * T1^-1 * T2 * T1^-4, 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, 28, 14, 27, 30, 18, 8, 2, 7, 17, 24, 12, 4, 10, 20, 26, 31, 22, 29, 16, 6, 15, 25, 13, 5)(32, 33, 37, 45, 57, 50, 55, 44, 49, 60, 52, 41, 34, 38, 46, 58, 62, 54, 43, 36, 39, 47, 59, 51, 40, 48, 56, 61, 53, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.270 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.256 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {31, 31, 31}) Quotient :: edge Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, (T2, T1), T2^-1 * T1 * T2^-4 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T1^2 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 29, 22, 31, 26, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 30, 28, 14, 27, 23, 11, 21, 25, 13, 5)(32, 33, 37, 45, 57, 56, 51, 40, 48, 60, 54, 43, 36, 39, 47, 59, 62, 52, 41, 34, 38, 46, 58, 55, 44, 49, 50, 61, 53, 42, 35) L = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.268 Transitivity :: ET+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.257 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1, (F * T2)^2, (F * T1)^2, T1^31, T2^31, (T2^-1 * T1^-1)^31 ] Map:: non-degenerate R = (1, 32, 2, 33, 6, 37, 14, 45, 20, 51, 26, 57, 31, 62, 25, 56, 19, 50, 13, 44, 10, 41, 3, 34, 7, 38, 15, 46, 21, 52, 27, 58, 30, 61, 24, 55, 18, 49, 12, 43, 5, 36, 8, 39, 9, 40, 16, 47, 22, 53, 28, 59, 29, 60, 23, 54, 17, 48, 11, 42, 4, 35) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 40)(9, 47)(10, 34)(11, 35)(12, 36)(13, 41)(14, 51)(15, 52)(16, 53)(17, 42)(18, 43)(19, 44)(20, 57)(21, 58)(22, 59)(23, 48)(24, 49)(25, 50)(26, 62)(27, 61)(28, 60)(29, 54)(30, 55)(31, 56) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.244 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.258 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T1)^2, (F * T2)^2, T1 * T2^15, (T2^-1 * T1^-1)^31 ] Map:: non-degenerate R = (1, 32, 3, 34, 7, 38, 11, 42, 15, 46, 19, 50, 23, 54, 27, 58, 31, 62, 28, 59, 24, 55, 20, 51, 16, 47, 12, 43, 8, 39, 4, 35, 2, 33, 6, 37, 10, 41, 14, 45, 18, 49, 22, 53, 26, 57, 30, 61, 29, 60, 25, 56, 21, 52, 17, 48, 13, 44, 9, 40, 5, 36) L = (1, 33)(2, 34)(3, 37)(4, 32)(5, 35)(6, 38)(7, 41)(8, 36)(9, 39)(10, 42)(11, 45)(12, 40)(13, 43)(14, 46)(15, 49)(16, 44)(17, 47)(18, 50)(19, 53)(20, 48)(21, 51)(22, 54)(23, 57)(24, 52)(25, 55)(26, 58)(27, 61)(28, 56)(29, 59)(30, 62)(31, 60) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.246 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.259 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^10, (T2^-1 * T1^-1)^31 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 15, 46, 21, 52, 27, 58, 28, 59, 22, 53, 16, 47, 10, 41, 4, 35, 6, 37, 12, 43, 18, 49, 24, 55, 30, 61, 31, 62, 26, 57, 20, 51, 14, 45, 8, 39, 2, 33, 7, 38, 13, 44, 19, 50, 25, 56, 29, 60, 23, 54, 17, 48, 11, 42, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 34)(7, 43)(8, 35)(9, 44)(10, 36)(11, 45)(12, 40)(13, 49)(14, 41)(15, 50)(16, 42)(17, 51)(18, 46)(19, 55)(20, 47)(21, 56)(22, 48)(23, 57)(24, 52)(25, 61)(26, 53)(27, 60)(28, 54)(29, 62)(30, 58)(31, 59) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.248 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.260 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T1 * T2^-10 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 15, 46, 21, 52, 27, 58, 26, 57, 20, 51, 14, 45, 8, 39, 2, 33, 7, 38, 13, 44, 19, 50, 25, 56, 31, 62, 30, 61, 24, 55, 18, 49, 12, 43, 6, 37, 4, 35, 10, 41, 16, 47, 22, 53, 28, 59, 29, 60, 23, 54, 17, 48, 11, 42, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 36)(7, 35)(8, 43)(9, 44)(10, 34)(11, 45)(12, 42)(13, 41)(14, 49)(15, 50)(16, 40)(17, 51)(18, 48)(19, 47)(20, 55)(21, 56)(22, 46)(23, 57)(24, 54)(25, 53)(26, 61)(27, 62)(28, 52)(29, 58)(30, 60)(31, 59) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.243 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.261 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^2 * T2^-1 * T1^2, T2^7 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-4 * T1^-1 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 17, 48, 25, 56, 24, 55, 16, 47, 8, 39, 2, 33, 7, 38, 15, 46, 23, 54, 31, 62, 27, 58, 19, 50, 11, 42, 6, 37, 14, 45, 22, 53, 30, 61, 28, 59, 20, 51, 12, 43, 4, 35, 10, 41, 18, 49, 26, 57, 29, 60, 21, 52, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 41)(7, 45)(8, 42)(9, 46)(10, 34)(11, 35)(12, 36)(13, 47)(14, 49)(15, 53)(16, 50)(17, 54)(18, 40)(19, 43)(20, 44)(21, 55)(22, 57)(23, 61)(24, 58)(25, 62)(26, 48)(27, 51)(28, 52)(29, 56)(30, 60)(31, 59) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.250 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.262 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-3 * T2^-1 * T1^-1, T2 * T1 * T2^7, T1 * T2^-3 * T1 * T2^-2 * T1 * T2^-2 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 17, 48, 25, 56, 28, 59, 20, 51, 12, 43, 4, 35, 10, 41, 18, 49, 26, 57, 30, 61, 22, 53, 14, 45, 6, 37, 11, 42, 19, 50, 27, 58, 31, 62, 24, 55, 16, 47, 8, 39, 2, 33, 7, 38, 15, 46, 23, 54, 29, 60, 21, 52, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 43)(7, 42)(8, 45)(9, 46)(10, 34)(11, 35)(12, 36)(13, 47)(14, 51)(15, 50)(16, 53)(17, 54)(18, 40)(19, 41)(20, 44)(21, 55)(22, 59)(23, 58)(24, 61)(25, 60)(26, 48)(27, 49)(28, 52)(29, 62)(30, 56)(31, 57) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.245 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.263 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T2 * T1 * T2^5, (T1^-1 * T2^-1)^31 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 19, 50, 22, 53, 12, 43, 4, 35, 10, 41, 20, 51, 28, 59, 29, 60, 21, 52, 11, 42, 14, 45, 24, 55, 30, 61, 31, 62, 26, 57, 16, 47, 6, 37, 15, 46, 25, 56, 27, 58, 18, 49, 8, 39, 2, 33, 7, 38, 17, 48, 23, 54, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 47)(9, 48)(10, 34)(11, 35)(12, 36)(13, 49)(14, 41)(15, 55)(16, 42)(17, 56)(18, 57)(19, 54)(20, 40)(21, 43)(22, 44)(23, 58)(24, 51)(25, 61)(26, 52)(27, 62)(28, 50)(29, 53)(30, 59)(31, 60) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.249 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.264 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1^-5, T2^-6 * 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 * T1^2 * T2^-4 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 19, 50, 18, 49, 8, 39, 2, 33, 7, 38, 17, 48, 27, 58, 26, 57, 16, 47, 6, 37, 15, 46, 25, 56, 31, 62, 30, 61, 24, 55, 14, 45, 11, 42, 21, 52, 28, 59, 29, 60, 22, 53, 12, 43, 4, 35, 10, 41, 20, 51, 23, 54, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 47)(9, 48)(10, 34)(11, 35)(12, 36)(13, 49)(14, 43)(15, 42)(16, 55)(17, 56)(18, 57)(19, 58)(20, 40)(21, 41)(22, 44)(23, 50)(24, 53)(25, 52)(26, 61)(27, 62)(28, 51)(29, 54)(30, 60)(31, 59) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.247 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.265 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-1 * T2^-4, T2^-1 * T1^6, 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 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 19, 50, 12, 43, 4, 35, 10, 41, 20, 51, 27, 58, 23, 54, 11, 42, 21, 52, 28, 59, 31, 62, 29, 60, 22, 53, 14, 45, 24, 55, 30, 61, 26, 57, 16, 47, 6, 37, 15, 46, 25, 56, 18, 49, 8, 39, 2, 33, 7, 38, 17, 48, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 47)(9, 48)(10, 34)(11, 35)(12, 36)(13, 49)(14, 52)(15, 55)(16, 53)(17, 56)(18, 57)(19, 44)(20, 40)(21, 41)(22, 42)(23, 43)(24, 59)(25, 61)(26, 60)(27, 50)(28, 51)(29, 54)(30, 62)(31, 58) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.252 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.266 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-2 * T1^-1 * T2^-2, T1^-7 * T2^-1 * T1^-1, T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1, T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-4 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 12, 43, 4, 35, 10, 41, 18, 49, 21, 52, 11, 42, 19, 50, 26, 57, 29, 60, 20, 51, 27, 58, 30, 61, 22, 53, 28, 59, 31, 62, 24, 55, 14, 45, 23, 54, 25, 56, 16, 47, 6, 37, 15, 46, 17, 48, 8, 39, 2, 33, 7, 38, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 47)(9, 44)(10, 34)(11, 35)(12, 36)(13, 48)(14, 53)(15, 54)(16, 55)(17, 56)(18, 40)(19, 41)(20, 42)(21, 43)(22, 60)(23, 59)(24, 61)(25, 62)(26, 49)(27, 50)(28, 51)(29, 52)(30, 57)(31, 58) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.251 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.267 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T1^-10 * T2 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 4, 35, 10, 41, 15, 46, 11, 42, 16, 47, 21, 52, 17, 48, 22, 53, 27, 58, 23, 54, 28, 59, 31, 62, 29, 60, 24, 55, 30, 61, 26, 57, 18, 49, 25, 56, 20, 51, 12, 43, 19, 50, 14, 45, 6, 37, 13, 44, 8, 39, 2, 33, 7, 38, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 43)(7, 44)(8, 45)(9, 36)(10, 34)(11, 35)(12, 49)(13, 50)(14, 51)(15, 40)(16, 41)(17, 42)(18, 55)(19, 56)(20, 57)(21, 46)(22, 47)(23, 48)(24, 59)(25, 61)(26, 60)(27, 52)(28, 53)(29, 54)(30, 62)(31, 58) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.254 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.268 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^4 * T2 * T1 * T2 * T1^4, (T1^-1 * T2^-1)^31 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 6, 37, 15, 46, 22, 53, 20, 51, 27, 58, 29, 60, 31, 62, 24, 55, 17, 48, 19, 50, 12, 43, 4, 35, 10, 41, 8, 39, 2, 33, 7, 38, 16, 47, 14, 45, 21, 52, 28, 59, 26, 57, 30, 61, 23, 54, 25, 56, 18, 49, 11, 42, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 40)(9, 47)(10, 34)(11, 35)(12, 36)(13, 41)(14, 51)(15, 52)(16, 53)(17, 42)(18, 43)(19, 44)(20, 57)(21, 58)(22, 59)(23, 48)(24, 49)(25, 50)(26, 62)(27, 61)(28, 60)(29, 54)(30, 55)(31, 56) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.256 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.269 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, (T2, T1), T2^-1 * T1 * T2^-4 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T1^2 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 19, 50, 16, 47, 6, 37, 15, 46, 29, 60, 22, 53, 31, 62, 26, 57, 24, 55, 12, 43, 4, 35, 10, 41, 20, 51, 18, 49, 8, 39, 2, 33, 7, 38, 17, 48, 30, 61, 28, 59, 14, 45, 27, 58, 23, 54, 11, 42, 21, 52, 25, 56, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 47)(9, 48)(10, 34)(11, 35)(12, 36)(13, 49)(14, 57)(15, 58)(16, 59)(17, 60)(18, 50)(19, 61)(20, 40)(21, 41)(22, 42)(23, 43)(24, 44)(25, 51)(26, 56)(27, 55)(28, 62)(29, 54)(30, 53)(31, 52) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.253 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.270 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {31, 31, 31}) Quotient :: loop Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1^-1), T1 * T2^-1 * T1^4 * T2^-1, T2^-1 * T1^-2 * T2^-4 * T1^-1, T2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2 * T1 * T2^-1 * T1, T2^19 * T1^-1 ] Map:: non-degenerate R = (1, 32, 3, 34, 9, 40, 19, 50, 30, 61, 22, 53, 16, 47, 6, 37, 15, 46, 27, 58, 24, 55, 12, 43, 4, 35, 10, 41, 20, 51, 31, 62, 29, 60, 18, 49, 8, 39, 2, 33, 7, 38, 17, 48, 28, 59, 23, 54, 11, 42, 21, 52, 14, 45, 26, 57, 25, 56, 13, 44, 5, 36) L = (1, 33)(2, 37)(3, 38)(4, 32)(5, 39)(6, 45)(7, 46)(8, 47)(9, 48)(10, 34)(11, 35)(12, 36)(13, 49)(14, 51)(15, 57)(16, 52)(17, 58)(18, 53)(19, 59)(20, 40)(21, 41)(22, 42)(23, 43)(24, 44)(25, 60)(26, 62)(27, 56)(28, 55)(29, 61)(30, 54)(31, 50) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.255 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^15 * Y2, Y2 * Y1^-15 ] Map:: R = (1, 32, 2, 33, 6, 37, 10, 41, 14, 45, 18, 49, 22, 53, 26, 57, 30, 61, 28, 59, 24, 55, 20, 51, 16, 47, 12, 43, 8, 39, 3, 34, 5, 36, 7, 38, 11, 42, 15, 46, 19, 50, 23, 54, 27, 58, 31, 62, 29, 60, 25, 56, 21, 52, 17, 48, 13, 44, 9, 40, 4, 35)(63, 94, 65, 96, 66, 97, 70, 101, 71, 102, 74, 105, 75, 106, 78, 109, 79, 110, 82, 113, 83, 114, 86, 117, 87, 118, 90, 121, 91, 122, 92, 123, 93, 124, 88, 119, 89, 120, 84, 115, 85, 116, 80, 111, 81, 112, 76, 107, 77, 108, 72, 103, 73, 104, 68, 99, 69, 100, 64, 95, 67, 98) L = (1, 66)(2, 63)(3, 70)(4, 71)(5, 65)(6, 64)(7, 67)(8, 74)(9, 75)(10, 68)(11, 69)(12, 78)(13, 79)(14, 72)(15, 73)(16, 82)(17, 83)(18, 76)(19, 77)(20, 86)(21, 87)(22, 80)(23, 81)(24, 90)(25, 91)(26, 84)(27, 85)(28, 92)(29, 93)(30, 88)(31, 89)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.285 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y2^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y3^7 * Y2^-1 * Y3 * Y1^-7, Y2 * Y1^15, 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 * Y1^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 10, 41, 14, 45, 18, 49, 22, 53, 26, 57, 30, 61, 29, 60, 25, 56, 21, 52, 17, 48, 13, 44, 9, 40, 5, 36, 3, 34, 7, 38, 11, 42, 15, 46, 19, 50, 23, 54, 27, 58, 31, 62, 28, 59, 24, 55, 20, 51, 16, 47, 12, 43, 8, 39, 4, 35)(63, 94, 65, 96, 64, 95, 69, 100, 68, 99, 73, 104, 72, 103, 77, 108, 76, 107, 81, 112, 80, 111, 85, 116, 84, 115, 89, 120, 88, 119, 93, 124, 92, 123, 90, 121, 91, 122, 86, 117, 87, 118, 82, 113, 83, 114, 78, 109, 79, 110, 74, 105, 75, 106, 70, 101, 71, 102, 66, 97, 67, 98) L = (1, 66)(2, 63)(3, 67)(4, 70)(5, 71)(6, 64)(7, 65)(8, 74)(9, 75)(10, 68)(11, 69)(12, 78)(13, 79)(14, 72)(15, 73)(16, 82)(17, 83)(18, 76)(19, 77)(20, 86)(21, 87)(22, 80)(23, 81)(24, 90)(25, 91)(26, 84)(27, 85)(28, 93)(29, 92)(30, 88)(31, 89)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.294 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.273 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y2^-3, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^5 * Y2^-1 * Y3^-4 * Y1, Y2 * Y3^10 ] Map:: R = (1, 32, 2, 33, 6, 37, 12, 43, 18, 49, 24, 55, 28, 59, 22, 53, 16, 47, 10, 41, 3, 34, 7, 38, 13, 44, 19, 50, 25, 56, 30, 61, 31, 62, 27, 58, 21, 52, 15, 46, 9, 40, 5, 36, 8, 39, 14, 45, 20, 51, 26, 57, 29, 60, 23, 54, 17, 48, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 66, 97, 72, 103, 77, 108, 73, 104, 78, 109, 83, 114, 79, 110, 84, 115, 89, 120, 85, 116, 90, 121, 93, 124, 91, 122, 86, 117, 92, 123, 88, 119, 80, 111, 87, 118, 82, 113, 74, 105, 81, 112, 76, 107, 68, 99, 75, 106, 70, 101, 64, 95, 69, 100, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 71)(6, 64)(7, 65)(8, 67)(9, 77)(10, 78)(11, 79)(12, 68)(13, 69)(14, 70)(15, 83)(16, 84)(17, 85)(18, 74)(19, 75)(20, 76)(21, 89)(22, 90)(23, 91)(24, 80)(25, 81)(26, 82)(27, 93)(28, 86)(29, 88)(30, 87)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.298 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.274 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2 * Y1^10, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 12, 43, 18, 49, 24, 55, 29, 60, 23, 54, 17, 48, 11, 42, 5, 36, 8, 39, 14, 45, 20, 51, 26, 57, 30, 61, 31, 62, 27, 58, 21, 52, 15, 46, 9, 40, 3, 34, 7, 38, 13, 44, 19, 50, 25, 56, 28, 59, 22, 53, 16, 47, 10, 41, 4, 35)(63, 94, 65, 96, 70, 101, 64, 95, 69, 100, 76, 107, 68, 99, 75, 106, 82, 113, 74, 105, 81, 112, 88, 119, 80, 111, 87, 118, 92, 123, 86, 117, 90, 121, 93, 124, 91, 122, 84, 115, 89, 120, 85, 116, 78, 109, 83, 114, 79, 110, 72, 103, 77, 108, 73, 104, 66, 97, 71, 102, 67, 98) L = (1, 66)(2, 63)(3, 71)(4, 72)(5, 73)(6, 64)(7, 65)(8, 67)(9, 77)(10, 78)(11, 79)(12, 68)(13, 69)(14, 70)(15, 83)(16, 84)(17, 85)(18, 74)(19, 75)(20, 76)(21, 89)(22, 90)(23, 91)(24, 80)(25, 81)(26, 82)(27, 93)(28, 87)(29, 86)(30, 88)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.291 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.275 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y2, Y1^-1), (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y2^4 * Y1, Y3 * Y1^-5 * Y3 * Y2^-1 * Y3, Y2 * Y3 * Y2 * Y3^2 * Y2 * Y1^-4, Y1^-3 * Y3^2 * Y2^-1 * Y3^3 * Y2^-1 * Y3^3 * Y2^-1 * Y3^3 * Y2 * Y3^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 22, 53, 29, 60, 21, 52, 12, 43, 5, 36, 8, 39, 16, 47, 24, 55, 30, 61, 26, 57, 18, 49, 9, 40, 13, 44, 17, 48, 25, 56, 31, 62, 27, 58, 19, 50, 10, 41, 3, 34, 7, 38, 15, 46, 23, 54, 28, 59, 20, 51, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 74, 105, 66, 97, 72, 103, 80, 111, 83, 114, 73, 104, 81, 112, 88, 119, 91, 122, 82, 113, 89, 120, 92, 123, 84, 115, 90, 121, 93, 124, 86, 117, 76, 107, 85, 116, 87, 118, 78, 109, 68, 99, 77, 108, 79, 110, 70, 101, 64, 95, 69, 100, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 80)(10, 81)(11, 82)(12, 83)(13, 71)(14, 68)(15, 69)(16, 70)(17, 75)(18, 88)(19, 89)(20, 90)(21, 91)(22, 76)(23, 77)(24, 78)(25, 79)(26, 92)(27, 93)(28, 85)(29, 84)(30, 86)(31, 87)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.293 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.276 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2), (R * Y2)^2, (Y3^-1, Y2^-1), Y2^-4 * Y1, Y1 * Y3^-1 * Y2^-1 * Y3^2 * Y2, Y3^4 * Y2 * Y1^-4, Y3 * Y2 * Y3^2 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 22, 53, 26, 57, 18, 49, 10, 41, 3, 34, 7, 38, 15, 46, 23, 54, 30, 61, 29, 60, 21, 52, 13, 44, 9, 40, 17, 48, 25, 56, 31, 62, 28, 59, 20, 51, 12, 43, 5, 36, 8, 39, 16, 47, 24, 55, 27, 58, 19, 50, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 70, 101, 64, 95, 69, 100, 79, 110, 78, 109, 68, 99, 77, 108, 87, 118, 86, 117, 76, 107, 85, 116, 93, 124, 89, 120, 84, 115, 92, 123, 90, 121, 81, 112, 88, 119, 91, 122, 82, 113, 73, 104, 80, 111, 83, 114, 74, 105, 66, 97, 72, 103, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 75)(10, 80)(11, 81)(12, 82)(13, 83)(14, 68)(15, 69)(16, 70)(17, 71)(18, 88)(19, 89)(20, 90)(21, 91)(22, 76)(23, 77)(24, 78)(25, 79)(26, 84)(27, 86)(28, 93)(29, 92)(30, 85)(31, 87)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.290 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.277 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2^-1 * Y3 * Y2^-4, Y3 * Y2 * Y3^5, Y1 * Y2^-1 * Y1^2 * Y3^-3, Y1^4 * Y2^-1 * Y3^-2, Y2^-1 * Y1 * Y3^-2 * Y2 * Y3^-3 * Y2^-1, Y2^-1 * Y3^2 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^2 * Y3^2 * Y2^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 21, 52, 10, 41, 3, 34, 7, 38, 15, 46, 24, 55, 28, 59, 20, 51, 9, 40, 17, 48, 25, 56, 30, 61, 31, 62, 27, 58, 19, 50, 13, 44, 18, 49, 26, 57, 29, 60, 23, 54, 12, 43, 5, 36, 8, 39, 16, 47, 22, 53, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 81, 112, 74, 105, 66, 97, 72, 103, 82, 113, 89, 120, 85, 116, 73, 104, 83, 114, 90, 121, 93, 124, 91, 122, 84, 115, 76, 107, 86, 117, 92, 123, 88, 119, 78, 109, 68, 99, 77, 108, 87, 118, 80, 111, 70, 101, 64, 95, 69, 100, 79, 110, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 82)(10, 83)(11, 84)(12, 85)(13, 81)(14, 68)(15, 69)(16, 70)(17, 71)(18, 75)(19, 89)(20, 90)(21, 76)(22, 78)(23, 91)(24, 77)(25, 79)(26, 80)(27, 93)(28, 86)(29, 88)(30, 87)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.292 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.278 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1, (Y3^-1, Y2^-1), (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y2^3 * Y1^-1 * Y2^2, Y1 * Y2 * Y3^-5, Y1^2 * Y2 * Y1^2 * Y3^-2, Y3^-2 * Y1 * Y3^2 * Y2^-1 * Y3 * 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 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 22, 53, 12, 43, 5, 36, 8, 39, 16, 47, 24, 55, 29, 60, 23, 54, 13, 44, 18, 49, 26, 57, 30, 61, 31, 62, 27, 58, 19, 50, 9, 40, 17, 48, 25, 56, 28, 59, 20, 51, 10, 41, 3, 34, 7, 38, 15, 46, 21, 52, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 80, 111, 70, 101, 64, 95, 69, 100, 79, 110, 88, 119, 78, 109, 68, 99, 77, 108, 87, 118, 92, 123, 86, 117, 76, 107, 83, 114, 90, 121, 93, 124, 91, 122, 84, 115, 73, 104, 82, 113, 89, 120, 85, 116, 74, 105, 66, 97, 72, 103, 81, 112, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 68)(15, 69)(16, 70)(17, 71)(18, 75)(19, 89)(20, 90)(21, 77)(22, 76)(23, 91)(24, 78)(25, 79)(26, 80)(27, 93)(28, 87)(29, 86)(30, 88)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.289 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.279 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y1^2 * Y2^-1 * Y1 * Y2^-2 * Y3^-1, Y2^-1 * Y3 * Y2^-6, Y2 * Y1 * Y2 * Y1 * Y2^2 * 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^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^2 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 19, 50, 28, 59, 30, 61, 23, 54, 12, 43, 5, 36, 8, 39, 16, 47, 20, 51, 9, 40, 17, 48, 27, 58, 31, 62, 24, 55, 13, 44, 18, 49, 21, 52, 10, 41, 3, 34, 7, 38, 15, 46, 26, 57, 29, 60, 25, 56, 22, 53, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 81, 112, 91, 122, 86, 117, 74, 105, 66, 97, 72, 103, 82, 113, 76, 107, 88, 119, 93, 124, 85, 116, 73, 104, 83, 114, 78, 109, 68, 99, 77, 108, 89, 120, 92, 123, 84, 115, 80, 111, 70, 101, 64, 95, 69, 100, 79, 110, 90, 121, 87, 118, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 82)(10, 83)(11, 84)(12, 85)(13, 86)(14, 68)(15, 69)(16, 70)(17, 71)(18, 75)(19, 76)(20, 78)(21, 80)(22, 87)(23, 92)(24, 93)(25, 91)(26, 77)(27, 79)(28, 81)(29, 88)(30, 90)(31, 89)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.288 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.280 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-2, Y2^6 * Y1^-1 * Y2, Y3^-2 * Y1 * Y2^-2 * Y3^-2 * Y2^-2, Y2^-2 * Y3 * Y2^-5 * Y1^2 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 25, 56, 28, 59, 31, 62, 21, 52, 10, 41, 3, 34, 7, 38, 15, 46, 24, 55, 13, 44, 18, 49, 27, 58, 30, 61, 20, 51, 9, 40, 17, 48, 23, 54, 12, 43, 5, 36, 8, 39, 16, 47, 26, 57, 29, 60, 19, 50, 22, 53, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 81, 112, 90, 121, 80, 111, 70, 101, 64, 95, 69, 100, 79, 110, 84, 115, 93, 124, 89, 120, 78, 109, 68, 99, 77, 108, 85, 116, 73, 104, 83, 114, 92, 123, 88, 119, 76, 107, 86, 117, 74, 105, 66, 97, 72, 103, 82, 113, 91, 122, 87, 118, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 82)(10, 83)(11, 84)(12, 85)(13, 86)(14, 68)(15, 69)(16, 70)(17, 71)(18, 75)(19, 91)(20, 92)(21, 93)(22, 81)(23, 79)(24, 77)(25, 76)(26, 78)(27, 80)(28, 87)(29, 88)(30, 89)(31, 90)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.287 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.281 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^-9 * Y1^2, Y1^31, 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, Y2^133 * Y3 * Y1^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 13, 44, 15, 46, 20, 51, 25, 56, 27, 58, 28, 59, 30, 61, 23, 54, 16, 47, 18, 49, 10, 41, 3, 34, 7, 38, 12, 43, 5, 36, 8, 39, 14, 45, 19, 50, 21, 52, 26, 57, 31, 62, 29, 60, 22, 53, 24, 55, 17, 48, 9, 40, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 78, 109, 84, 115, 90, 121, 88, 119, 82, 113, 76, 107, 68, 99, 74, 105, 66, 97, 72, 103, 79, 110, 85, 116, 91, 122, 89, 120, 83, 114, 77, 108, 70, 101, 64, 95, 69, 100, 73, 104, 80, 111, 86, 117, 92, 123, 93, 124, 87, 118, 81, 112, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 79)(10, 80)(11, 71)(12, 69)(13, 68)(14, 70)(15, 75)(16, 85)(17, 86)(18, 78)(19, 76)(20, 77)(21, 81)(22, 91)(23, 92)(24, 84)(25, 82)(26, 83)(27, 87)(28, 89)(29, 93)(30, 90)(31, 88)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.286 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.282 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), Y2^-1 * Y1^2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1 * Y2^8 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 9, 40, 15, 46, 20, 51, 22, 53, 27, 58, 31, 62, 29, 60, 24, 55, 19, 50, 17, 48, 12, 43, 5, 36, 8, 39, 10, 41, 3, 34, 7, 38, 14, 45, 16, 47, 21, 52, 26, 57, 28, 59, 30, 61, 25, 56, 23, 54, 18, 49, 13, 44, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 78, 109, 84, 115, 90, 121, 91, 122, 85, 116, 79, 110, 73, 104, 70, 101, 64, 95, 69, 100, 77, 108, 83, 114, 89, 120, 92, 123, 86, 117, 80, 111, 74, 105, 66, 97, 72, 103, 68, 99, 76, 107, 82, 113, 88, 119, 93, 124, 87, 118, 81, 112, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 68)(10, 70)(11, 75)(12, 79)(13, 80)(14, 69)(15, 71)(16, 76)(17, 81)(18, 85)(19, 86)(20, 77)(21, 78)(22, 82)(23, 87)(24, 91)(25, 92)(26, 83)(27, 84)(28, 88)(29, 93)(30, 90)(31, 89)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.296 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.283 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y3, Y1 * Y3, Y3 * Y2 * Y1 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-3, Y1^4 * Y2^-2 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-3 * Y1^-1, Y3 * Y1 * Y2^-1 * Y1 * Y3^14, Y2 * Y1 * Y2^3 * Y3 * Y2^2 * Y3 * Y2^2 * Y3 * Y2^2 * Y3 * Y2^2 * Y3 * Y2^2, Y2 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^2 * Y3 * Y1^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 20, 51, 9, 40, 17, 48, 27, 58, 25, 56, 29, 60, 30, 61, 23, 54, 12, 43, 5, 36, 8, 39, 16, 47, 21, 52, 10, 41, 3, 34, 7, 38, 15, 46, 26, 57, 31, 62, 19, 50, 28, 59, 24, 55, 13, 44, 18, 49, 22, 53, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 81, 112, 92, 123, 84, 115, 78, 109, 68, 99, 77, 108, 89, 120, 86, 117, 74, 105, 66, 97, 72, 103, 82, 113, 93, 124, 91, 122, 80, 111, 70, 101, 64, 95, 69, 100, 79, 110, 90, 121, 85, 116, 73, 104, 83, 114, 76, 107, 88, 119, 87, 118, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 82)(10, 83)(11, 84)(12, 85)(13, 86)(14, 68)(15, 69)(16, 70)(17, 71)(18, 75)(19, 93)(20, 76)(21, 78)(22, 80)(23, 92)(24, 90)(25, 89)(26, 77)(27, 79)(28, 81)(29, 87)(30, 91)(31, 88)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.297 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.284 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3 * Y2^-1 * Y1, Y1^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y1^3 * Y2 * Y1 * Y2 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y3^-3, Y3 * Y2^3 * Y1^-1 * Y2 * Y3 * Y2, Y3 * Y2^-3 * Y3 * Y2^-4, Y2^-1 * Y1 * Y2^-3 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 32, 2, 33, 6, 37, 14, 45, 24, 55, 13, 44, 18, 49, 27, 58, 19, 50, 28, 59, 30, 61, 21, 52, 10, 41, 3, 34, 7, 38, 15, 46, 23, 54, 12, 43, 5, 36, 8, 39, 16, 47, 26, 57, 31, 62, 25, 56, 29, 60, 20, 51, 9, 40, 17, 48, 22, 53, 11, 42, 4, 35)(63, 94, 65, 96, 71, 102, 81, 112, 88, 119, 76, 107, 85, 116, 73, 104, 83, 114, 91, 122, 80, 111, 70, 101, 64, 95, 69, 100, 79, 110, 90, 121, 93, 124, 86, 117, 74, 105, 66, 97, 72, 103, 82, 113, 89, 120, 78, 109, 68, 99, 77, 108, 84, 115, 92, 123, 87, 118, 75, 106, 67, 98) L = (1, 66)(2, 63)(3, 72)(4, 73)(5, 74)(6, 64)(7, 65)(8, 67)(9, 82)(10, 83)(11, 84)(12, 85)(13, 86)(14, 68)(15, 69)(16, 70)(17, 71)(18, 75)(19, 89)(20, 91)(21, 92)(22, 79)(23, 77)(24, 76)(25, 93)(26, 78)(27, 80)(28, 81)(29, 87)(30, 90)(31, 88)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.295 Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.285 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2^31, (Y3^-1 * Y1^-1)^31, (Y3 * Y2^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 66, 97, 68, 99, 70, 101, 72, 103, 74, 105, 80, 111, 78, 109, 76, 107, 77, 108, 79, 110, 81, 112, 82, 113, 83, 114, 84, 115, 90, 121, 88, 119, 86, 117, 87, 118, 89, 120, 91, 122, 92, 123, 93, 124, 85, 116, 75, 106, 73, 104, 71, 102, 69, 100, 67, 98, 65, 96) L = (1, 65)(2, 63)(3, 67)(4, 64)(5, 69)(6, 66)(7, 71)(8, 68)(9, 73)(10, 70)(11, 75)(12, 72)(13, 85)(14, 78)(15, 76)(16, 80)(17, 77)(18, 74)(19, 79)(20, 81)(21, 82)(22, 83)(23, 93)(24, 88)(25, 86)(26, 90)(27, 87)(28, 84)(29, 89)(30, 91)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.271 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.286 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^-15, (Y3 * Y2^-1)^31, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 67, 98, 68, 99, 71, 102, 72, 103, 75, 106, 76, 107, 79, 110, 80, 111, 83, 114, 84, 115, 87, 118, 88, 119, 91, 122, 92, 123, 93, 124, 89, 120, 90, 121, 85, 116, 86, 117, 81, 112, 82, 113, 77, 108, 78, 109, 73, 104, 74, 105, 69, 100, 70, 101, 65, 96, 66, 97) L = (1, 65)(2, 66)(3, 69)(4, 70)(5, 63)(6, 64)(7, 73)(8, 74)(9, 67)(10, 68)(11, 77)(12, 78)(13, 71)(14, 72)(15, 81)(16, 82)(17, 75)(18, 76)(19, 85)(20, 86)(21, 79)(22, 80)(23, 89)(24, 90)(25, 83)(26, 84)(27, 92)(28, 93)(29, 87)(30, 88)(31, 91)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.281 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.287 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3^-10, (Y3^-1 * Y1^-1)^31, (Y3 * Y2^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 67, 98, 70, 101, 74, 105, 73, 104, 76, 107, 80, 111, 79, 110, 82, 113, 86, 117, 85, 116, 88, 119, 92, 123, 91, 122, 89, 120, 93, 124, 90, 121, 83, 114, 87, 118, 84, 115, 77, 108, 81, 112, 78, 109, 71, 102, 75, 106, 72, 103, 65, 96, 69, 100, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 66)(7, 75)(8, 64)(9, 77)(10, 78)(11, 67)(12, 68)(13, 81)(14, 70)(15, 83)(16, 84)(17, 73)(18, 74)(19, 87)(20, 76)(21, 89)(22, 90)(23, 79)(24, 80)(25, 93)(26, 82)(27, 88)(28, 91)(29, 85)(30, 86)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.280 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.288 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2^4, Y3^-7 * Y2^-1 * Y3^-1, Y3^2 * Y2^-1 * Y3^4 * Y2^-2 * Y3, (Y2^-1 * Y3)^31, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 74, 105, 67, 98, 70, 101, 76, 107, 82, 113, 75, 106, 78, 109, 84, 115, 90, 121, 83, 114, 86, 117, 92, 123, 87, 118, 91, 122, 93, 124, 88, 119, 79, 110, 85, 116, 89, 120, 80, 111, 71, 102, 77, 108, 81, 112, 72, 103, 65, 96, 69, 100, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 73)(7, 77)(8, 64)(9, 79)(10, 80)(11, 81)(12, 66)(13, 67)(14, 68)(15, 85)(16, 70)(17, 87)(18, 88)(19, 89)(20, 74)(21, 75)(22, 76)(23, 91)(24, 78)(25, 90)(26, 92)(27, 93)(28, 82)(29, 83)(30, 84)(31, 86)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.279 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.289 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2^2 * Y3^-1 * Y2^-2, Y3^-1 * Y2^-5, Y3^-1 * Y2 * Y3^-5, (Y2^-1 * Y3)^31, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 74, 105, 67, 98, 70, 101, 78, 109, 86, 117, 84, 115, 75, 106, 80, 111, 88, 119, 92, 123, 91, 122, 85, 116, 81, 112, 89, 120, 93, 124, 90, 121, 82, 113, 71, 102, 79, 110, 87, 118, 83, 114, 72, 103, 65, 96, 69, 100, 77, 108, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 79)(8, 64)(9, 81)(10, 82)(11, 83)(12, 66)(13, 67)(14, 73)(15, 87)(16, 68)(17, 89)(18, 70)(19, 80)(20, 85)(21, 90)(22, 74)(23, 75)(24, 76)(25, 93)(26, 78)(27, 88)(28, 91)(29, 84)(30, 86)(31, 92)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.278 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.290 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^3 * Y2^-1 * Y3^2, Y2^2 * Y3 * Y2^4, Y3 * Y2^3 * Y3^-1 * Y2^3 * Y3, Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-2 * Y2^-1, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 84, 115, 74, 105, 67, 98, 70, 101, 78, 109, 86, 117, 91, 122, 85, 116, 75, 106, 80, 111, 88, 119, 92, 123, 93, 124, 89, 120, 81, 112, 71, 102, 79, 110, 87, 118, 90, 121, 82, 113, 72, 103, 65, 96, 69, 100, 77, 108, 83, 114, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 79)(8, 64)(9, 80)(10, 81)(11, 82)(12, 66)(13, 67)(14, 83)(15, 87)(16, 68)(17, 88)(18, 70)(19, 75)(20, 89)(21, 90)(22, 73)(23, 74)(24, 76)(25, 92)(26, 78)(27, 85)(28, 93)(29, 84)(30, 86)(31, 91)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.276 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.291 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3^4 * Y2^-2, Y2^2 * Y3^-1 * Y2 * Y3^-3, Y2^-5 * Y3^-1 * Y2^-2, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 88, 119, 85, 116, 74, 105, 67, 98, 70, 101, 78, 109, 81, 112, 91, 122, 92, 123, 86, 117, 75, 106, 80, 111, 82, 113, 71, 102, 79, 110, 90, 121, 93, 124, 87, 118, 83, 114, 72, 103, 65, 96, 69, 100, 77, 108, 89, 120, 84, 115, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 79)(8, 64)(9, 81)(10, 82)(11, 83)(12, 66)(13, 67)(14, 89)(15, 90)(16, 68)(17, 91)(18, 70)(19, 76)(20, 78)(21, 80)(22, 87)(23, 73)(24, 74)(25, 75)(26, 84)(27, 93)(28, 92)(29, 88)(30, 85)(31, 86)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.274 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.292 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^-3 * Y2^-1 * Y3^-1, Y2 * Y3 * Y2^7, Y2^-3 * Y3^2 * Y2^-4 * Y3, (Y2^-1 * Y3)^31, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 84, 115, 91, 122, 83, 114, 74, 105, 67, 98, 70, 101, 78, 109, 86, 117, 92, 123, 88, 119, 80, 111, 71, 102, 75, 106, 79, 110, 87, 118, 93, 124, 89, 120, 81, 112, 72, 103, 65, 96, 69, 100, 77, 108, 85, 116, 90, 121, 82, 113, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 75)(8, 64)(9, 74)(10, 80)(11, 81)(12, 66)(13, 67)(14, 85)(15, 79)(16, 68)(17, 70)(18, 83)(19, 88)(20, 89)(21, 73)(22, 90)(23, 87)(24, 76)(25, 78)(26, 91)(27, 92)(28, 93)(29, 82)(30, 84)(31, 86)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.277 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.293 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y3^-1), Y2^3 * Y3^-1 * Y2 * Y3^-2, Y3^6 * Y2 * Y3, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 81, 112, 90, 121, 92, 123, 85, 116, 74, 105, 67, 98, 70, 101, 78, 109, 82, 113, 71, 102, 79, 110, 89, 120, 93, 124, 86, 117, 75, 106, 80, 111, 83, 114, 72, 103, 65, 96, 69, 100, 77, 108, 88, 119, 91, 122, 87, 118, 84, 115, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 79)(8, 64)(9, 81)(10, 82)(11, 83)(12, 66)(13, 67)(14, 88)(15, 89)(16, 68)(17, 90)(18, 70)(19, 91)(20, 76)(21, 78)(22, 80)(23, 73)(24, 74)(25, 75)(26, 93)(27, 92)(28, 87)(29, 86)(30, 84)(31, 85)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.275 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.294 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-3 * Y2, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^4 * Y3 * Y2^6, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 74, 105, 80, 111, 86, 117, 91, 122, 85, 116, 79, 110, 73, 104, 67, 98, 70, 101, 76, 107, 82, 113, 88, 119, 92, 123, 93, 124, 89, 120, 83, 114, 77, 108, 71, 102, 65, 96, 69, 100, 75, 106, 81, 112, 87, 118, 90, 121, 84, 115, 78, 109, 72, 103, 66, 97) L = (1, 65)(2, 69)(3, 70)(4, 71)(5, 63)(6, 75)(7, 76)(8, 64)(9, 67)(10, 77)(11, 66)(12, 81)(13, 82)(14, 68)(15, 73)(16, 83)(17, 72)(18, 87)(19, 88)(20, 74)(21, 79)(22, 89)(23, 78)(24, 90)(25, 92)(26, 80)(27, 85)(28, 93)(29, 84)(30, 86)(31, 91)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.272 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2 * Y3^2 * Y2, Y2^8 * Y3^-1 * Y2 * Y3^-1, (Y2^-1 * Y3)^31, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 82, 113, 88, 119, 91, 122, 85, 116, 79, 110, 71, 102, 74, 105, 67, 98, 70, 101, 77, 108, 83, 114, 89, 120, 92, 123, 86, 117, 80, 111, 72, 103, 65, 96, 69, 100, 75, 106, 78, 109, 84, 115, 90, 121, 93, 124, 87, 118, 81, 112, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 75)(7, 74)(8, 64)(9, 73)(10, 79)(11, 80)(12, 66)(13, 67)(14, 78)(15, 68)(16, 70)(17, 81)(18, 85)(19, 86)(20, 84)(21, 76)(22, 77)(23, 87)(24, 91)(25, 92)(26, 90)(27, 82)(28, 83)(29, 93)(30, 88)(31, 89)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.284 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3^-4 * Y2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-4 * Y3^-1, 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)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 88, 119, 87, 118, 82, 113, 71, 102, 79, 110, 91, 122, 85, 116, 74, 105, 67, 98, 70, 101, 78, 109, 90, 121, 93, 124, 83, 114, 72, 103, 65, 96, 69, 100, 77, 108, 89, 120, 86, 117, 75, 106, 80, 111, 81, 112, 92, 123, 84, 115, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 79)(8, 64)(9, 81)(10, 82)(11, 83)(12, 66)(13, 67)(14, 89)(15, 91)(16, 68)(17, 92)(18, 70)(19, 78)(20, 80)(21, 87)(22, 93)(23, 73)(24, 74)(25, 75)(26, 86)(27, 85)(28, 76)(29, 84)(30, 90)(31, 88)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.282 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.297 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2 * Y3^-1 * Y2^4 * Y3^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-4 * Y2^-1, Y2 * Y3^3 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^3, Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 76, 107, 82, 113, 71, 102, 79, 110, 89, 120, 87, 118, 91, 122, 92, 123, 85, 116, 74, 105, 67, 98, 70, 101, 78, 109, 83, 114, 72, 103, 65, 96, 69, 100, 77, 108, 88, 119, 93, 124, 81, 112, 90, 121, 86, 117, 75, 106, 80, 111, 84, 115, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 77)(7, 79)(8, 64)(9, 81)(10, 82)(11, 83)(12, 66)(13, 67)(14, 88)(15, 89)(16, 68)(17, 90)(18, 70)(19, 92)(20, 93)(21, 76)(22, 78)(23, 73)(24, 74)(25, 75)(26, 87)(27, 86)(28, 85)(29, 80)(30, 84)(31, 91)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.283 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.298 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {31, 31, 31}) Quotient :: dipole Aut^+ = C31 (small group id <31, 1>) Aut = D62 (small group id <62, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2^2 * Y3^-1 * Y2 * Y3^-1, Y3^8 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^31 ] Map:: R = (1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)(63, 94, 64, 95, 68, 99, 71, 102, 77, 108, 82, 113, 84, 115, 89, 120, 93, 124, 91, 122, 86, 117, 81, 112, 79, 110, 74, 105, 67, 98, 70, 101, 72, 103, 65, 96, 69, 100, 76, 107, 78, 109, 83, 114, 88, 119, 90, 121, 92, 123, 87, 118, 85, 116, 80, 111, 75, 106, 73, 104, 66, 97) L = (1, 65)(2, 69)(3, 71)(4, 72)(5, 63)(6, 76)(7, 77)(8, 64)(9, 78)(10, 68)(11, 70)(12, 66)(13, 67)(14, 82)(15, 83)(16, 84)(17, 73)(18, 74)(19, 75)(20, 88)(21, 89)(22, 90)(23, 79)(24, 80)(25, 81)(26, 93)(27, 92)(28, 91)(29, 85)(30, 86)(31, 87)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.273 Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.299 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ Y1^2, R^2, R * Y2 * R * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^4, (Y2 * Y1)^2, Y2^4, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1, Y2^-2 * Y3^-1 * Y2 * Y3^-2 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 12, 44)(10, 42, 13, 45)(11, 43, 19, 51)(15, 47, 27, 59)(16, 48, 21, 53)(17, 49, 29, 61)(20, 52, 23, 55)(22, 54, 24, 56)(25, 57, 30, 62)(26, 58, 28, 60)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 79, 111, 87, 119, 76, 108)(70, 102, 81, 113, 88, 120, 77, 109)(72, 104, 84, 116, 91, 123, 78, 110)(74, 106, 86, 118, 93, 125, 82, 114)(80, 112, 89, 121, 95, 127, 92, 124)(85, 117, 90, 122, 96, 128, 94, 126) L = (1, 68)(2, 72)(3, 76)(4, 80)(5, 79)(6, 65)(7, 78)(8, 85)(9, 84)(10, 66)(11, 87)(12, 89)(13, 67)(14, 90)(15, 92)(16, 70)(17, 69)(18, 71)(19, 91)(20, 94)(21, 74)(22, 73)(23, 95)(24, 75)(25, 77)(26, 82)(27, 96)(28, 81)(29, 83)(30, 86)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.334 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.300 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ Y1^2, R^2, R * Y2 * R * Y2^-1, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y2^-1 * Y1)^2, Y2^4, Y1 * Y3 * Y2 * Y1 * Y3^-1, (Y2 * Y3^-2)^4 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 15, 47)(10, 42, 17, 49)(11, 43, 19, 51)(12, 44, 25, 57)(13, 45, 27, 59)(16, 48, 22, 54)(20, 52, 23, 55)(21, 53, 24, 56)(26, 58, 28, 60)(29, 61, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 79, 111, 87, 119, 76, 108)(70, 102, 81, 113, 88, 120, 77, 109)(72, 104, 78, 110, 89, 121, 84, 116)(74, 106, 82, 114, 91, 123, 85, 117)(80, 112, 90, 122, 95, 127, 93, 125)(86, 118, 94, 126, 96, 128, 92, 124) L = (1, 68)(2, 72)(3, 76)(4, 80)(5, 79)(6, 65)(7, 84)(8, 86)(9, 78)(10, 66)(11, 87)(12, 90)(13, 67)(14, 92)(15, 93)(16, 70)(17, 69)(18, 73)(19, 89)(20, 94)(21, 71)(22, 74)(23, 95)(24, 75)(25, 96)(26, 77)(27, 83)(28, 82)(29, 81)(30, 85)(31, 88)(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 ) } Outer automorphisms :: reflexible Dual of E15.331 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.301 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ Y1^2, R^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^4, (Y2 * Y1)^2, Y2^4, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 13, 45)(10, 42, 12, 44)(11, 43, 19, 51)(15, 47, 26, 58)(16, 48, 21, 53)(17, 49, 29, 61)(20, 52, 24, 56)(22, 54, 23, 55)(25, 57, 30, 62)(27, 59, 28, 60)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 79, 111, 87, 119, 76, 108)(70, 102, 81, 113, 88, 120, 77, 109)(72, 104, 84, 116, 93, 125, 82, 114)(74, 106, 86, 118, 90, 122, 78, 110)(80, 112, 89, 121, 95, 127, 92, 124)(85, 117, 91, 123, 96, 128, 94, 126) L = (1, 68)(2, 72)(3, 76)(4, 80)(5, 79)(6, 65)(7, 82)(8, 85)(9, 84)(10, 66)(11, 87)(12, 89)(13, 67)(14, 71)(15, 92)(16, 70)(17, 69)(18, 91)(19, 93)(20, 94)(21, 74)(22, 73)(23, 95)(24, 75)(25, 77)(26, 83)(27, 78)(28, 81)(29, 96)(30, 86)(31, 88)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.333 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.302 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ Y1^2, R^2, R * Y2 * R * Y2^-1, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2^4, (Y2^-1 * Y1)^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 17, 49)(10, 42, 15, 47)(11, 43, 19, 51)(12, 44, 25, 57)(13, 45, 27, 59)(16, 48, 22, 54)(20, 52, 24, 56)(21, 53, 23, 55)(26, 58, 28, 60)(29, 61, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 79, 111, 87, 119, 76, 108)(70, 102, 81, 113, 88, 120, 77, 109)(72, 104, 82, 114, 91, 123, 84, 116)(74, 106, 78, 110, 89, 121, 85, 117)(80, 112, 90, 122, 95, 127, 93, 125)(86, 118, 94, 126, 96, 128, 92, 124) L = (1, 68)(2, 72)(3, 76)(4, 80)(5, 79)(6, 65)(7, 84)(8, 86)(9, 82)(10, 66)(11, 87)(12, 90)(13, 67)(14, 73)(15, 93)(16, 70)(17, 69)(18, 92)(19, 91)(20, 94)(21, 71)(22, 74)(23, 95)(24, 75)(25, 83)(26, 77)(27, 96)(28, 78)(29, 81)(30, 85)(31, 88)(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 ) } Outer automorphisms :: reflexible Dual of E15.332 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.303 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 14, 46)(10, 42, 15, 47)(11, 43, 13, 45)(12, 44, 18, 50)(16, 48, 17, 49)(19, 51, 21, 53)(20, 52, 24, 56)(22, 54, 23, 55)(25, 57, 27, 59)(26, 58, 28, 60)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 75, 107, 71, 103, 77, 109)(70, 102, 80, 112, 72, 104, 81, 113)(73, 105, 83, 115, 78, 110, 85, 117)(74, 106, 86, 118, 79, 111, 87, 119)(76, 108, 88, 120, 82, 114, 84, 116)(89, 121, 93, 125, 91, 123, 95, 127)(90, 122, 96, 128, 92, 124, 94, 126) L = (1, 68)(2, 71)(3, 73)(4, 76)(5, 78)(6, 65)(7, 82)(8, 66)(9, 84)(10, 67)(11, 89)(12, 72)(13, 91)(14, 88)(15, 69)(16, 92)(17, 90)(18, 70)(19, 93)(20, 79)(21, 95)(22, 96)(23, 94)(24, 74)(25, 80)(26, 75)(27, 81)(28, 77)(29, 86)(30, 83)(31, 87)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.338 Graph:: bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.304 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2, Y3 * Y1 * Y2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y3^-2 * Y2^-1 ] 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, 22, 54)(12, 44, 19, 51)(13, 45, 14, 46)(15, 47, 23, 55)(16, 48, 18, 50)(17, 49, 20, 52)(21, 53, 24, 56)(25, 57, 29, 61)(26, 58, 27, 59)(28, 60, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 78, 110, 89, 121, 80, 112)(70, 102, 83, 115, 90, 122, 84, 116)(72, 104, 77, 109, 93, 125, 82, 114)(74, 106, 76, 108, 91, 123, 81, 113)(79, 111, 94, 126, 85, 117, 92, 124)(87, 119, 95, 127, 88, 120, 96, 128) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 83)(8, 87)(9, 84)(10, 66)(11, 89)(12, 92)(13, 67)(14, 71)(15, 90)(16, 73)(17, 94)(18, 69)(19, 96)(20, 95)(21, 70)(22, 93)(23, 91)(24, 74)(25, 85)(26, 75)(27, 86)(28, 82)(29, 88)(30, 77)(31, 78)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.336 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.305 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y2 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y3^-2 * Y2^-1 ] 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, 22, 54)(12, 44, 20, 52)(13, 45, 16, 48)(14, 46, 18, 50)(15, 47, 23, 55)(17, 49, 19, 51)(21, 53, 24, 56)(25, 57, 29, 61)(26, 58, 28, 60)(27, 59, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 78, 110, 89, 121, 80, 112)(70, 102, 83, 115, 90, 122, 84, 116)(72, 104, 82, 114, 93, 125, 77, 109)(74, 106, 81, 113, 92, 124, 76, 108)(79, 111, 94, 126, 85, 117, 91, 123)(87, 119, 96, 128, 88, 120, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 84)(8, 87)(9, 83)(10, 66)(11, 89)(12, 91)(13, 67)(14, 73)(15, 90)(16, 71)(17, 94)(18, 69)(19, 96)(20, 95)(21, 70)(22, 93)(23, 92)(24, 74)(25, 85)(26, 75)(27, 82)(28, 86)(29, 88)(30, 77)(31, 78)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.340 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.306 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |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, Y3^4 * Y1, Y3 * Y1 * Y2 * Y3 * Y2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2 ] 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, 22, 54)(12, 44, 20, 52)(13, 45, 16, 48)(14, 46, 18, 50)(15, 47, 21, 53)(17, 49, 19, 51)(23, 55, 27, 59)(24, 56, 26, 58)(25, 57, 28, 60)(29, 61, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 78, 110, 87, 119, 80, 112)(70, 102, 83, 115, 88, 120, 84, 116)(72, 104, 82, 114, 91, 123, 77, 109)(74, 106, 81, 113, 90, 122, 76, 108)(79, 111, 92, 124, 95, 127, 94, 126)(85, 117, 89, 121, 96, 128, 93, 125) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 84)(8, 85)(9, 83)(10, 66)(11, 87)(12, 89)(13, 67)(14, 73)(15, 74)(16, 71)(17, 93)(18, 69)(19, 94)(20, 92)(21, 70)(22, 91)(23, 95)(24, 75)(25, 80)(26, 86)(27, 96)(28, 77)(29, 78)(30, 82)(31, 90)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.337 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |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, Y3 * Y1 * Y2^-1 * Y3 * Y2, Y3 * Y1 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3^-3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: polytopal 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, 22, 54)(12, 44, 19, 51)(13, 45, 14, 46)(15, 47, 23, 55)(16, 48, 18, 50)(17, 49, 20, 52)(21, 53, 24, 56)(25, 57, 29, 61)(26, 58, 27, 59)(28, 60, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 78, 110, 89, 121, 80, 112)(70, 102, 83, 115, 90, 122, 84, 116)(72, 104, 77, 109, 93, 125, 82, 114)(74, 106, 76, 108, 91, 123, 81, 113)(79, 111, 94, 126, 88, 120, 96, 128)(85, 117, 92, 124, 87, 119, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 83)(8, 87)(9, 84)(10, 66)(11, 89)(12, 92)(13, 67)(14, 71)(15, 91)(16, 73)(17, 95)(18, 69)(19, 96)(20, 94)(21, 70)(22, 93)(23, 90)(24, 74)(25, 88)(26, 75)(27, 86)(28, 80)(29, 85)(30, 77)(31, 78)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.335 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.308 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y2^-2, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-3 * Y2^-1, Y2 * Y3^-2 * Y2^-1 * Y3^-2, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 14, 46)(10, 42, 15, 47)(11, 43, 13, 45)(12, 44, 19, 51)(16, 48, 17, 49)(18, 50, 20, 52)(21, 53, 23, 55)(22, 54, 28, 60)(24, 56, 25, 57)(26, 58, 29, 61)(27, 59, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 75, 107, 71, 103, 77, 109)(70, 102, 80, 112, 72, 104, 81, 113)(73, 105, 85, 117, 78, 110, 87, 119)(74, 106, 88, 120, 79, 111, 89, 121)(76, 108, 90, 122, 83, 115, 93, 125)(82, 114, 86, 118, 84, 116, 92, 124)(91, 123, 95, 127, 94, 126, 96, 128) L = (1, 68)(2, 71)(3, 73)(4, 76)(5, 78)(6, 65)(7, 83)(8, 66)(9, 86)(10, 67)(11, 91)(12, 85)(13, 94)(14, 92)(15, 69)(16, 93)(17, 90)(18, 70)(19, 87)(20, 72)(21, 95)(22, 77)(23, 96)(24, 82)(25, 84)(26, 74)(27, 80)(28, 75)(29, 79)(30, 81)(31, 88)(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 ) } Outer automorphisms :: reflexible Dual of E15.339 Graph:: bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3 * Y1 * Y3^-1 * Y1, Y3^4 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2 ] 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, 18, 50)(12, 44, 19, 51)(13, 45, 20, 52)(14, 46, 17, 49)(15, 47, 21, 53)(16, 48, 22, 54)(23, 55, 29, 61)(24, 56, 30, 62)(25, 57, 26, 58)(27, 59, 28, 60)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 82, 114, 73, 105)(68, 100, 77, 109, 87, 119, 79, 111)(70, 102, 76, 108, 88, 120, 80, 112)(72, 104, 84, 116, 93, 125, 85, 117)(74, 106, 83, 115, 94, 126, 86, 118)(78, 110, 90, 122, 95, 127, 91, 123)(81, 113, 89, 121, 96, 128, 92, 124) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 80)(6, 65)(7, 83)(8, 81)(9, 86)(10, 66)(11, 87)(12, 89)(13, 67)(14, 74)(15, 69)(16, 92)(17, 70)(18, 93)(19, 90)(20, 71)(21, 73)(22, 91)(23, 95)(24, 75)(25, 84)(26, 77)(27, 79)(28, 85)(29, 96)(30, 82)(31, 94)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.341 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.310 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 13, 45)(10, 42, 12, 44)(11, 43, 15, 47)(14, 46, 16, 48)(17, 49, 21, 53)(18, 50, 20, 52)(19, 51, 23, 55)(22, 54, 24, 56)(25, 57, 29, 61)(26, 58, 28, 60)(27, 59, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 74, 106, 71, 103, 76, 108)(70, 102, 73, 105, 72, 104, 77, 109)(75, 107, 82, 114, 79, 111, 84, 116)(78, 110, 81, 113, 80, 112, 85, 117)(83, 115, 90, 122, 87, 119, 92, 124)(86, 118, 89, 121, 88, 120, 93, 125)(91, 123, 95, 127, 94, 126, 96, 128) L = (1, 68)(2, 71)(3, 73)(4, 75)(5, 77)(6, 65)(7, 79)(8, 66)(9, 81)(10, 67)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 89)(18, 74)(19, 91)(20, 76)(21, 93)(22, 78)(23, 94)(24, 80)(25, 95)(26, 82)(27, 86)(28, 84)(29, 96)(30, 88)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.342 Graph:: bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.311 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y1 * Y2^-1 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3 * Y1 * Y3^3, Y3^2 * Y1 * Y2 * Y3^-2 * Y2, Y2^-1 * Y1 * Y2^-1 * Y3^-4 ] 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, 18, 50)(12, 44, 19, 51)(13, 45, 20, 52)(14, 46, 21, 53)(15, 47, 22, 54)(16, 48, 23, 55)(17, 49, 24, 56)(25, 57, 32, 64)(26, 58, 29, 61)(27, 59, 30, 62)(28, 60, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 82, 114, 73, 105)(68, 100, 77, 109, 89, 121, 79, 111)(70, 102, 76, 108, 90, 122, 80, 112)(72, 104, 84, 116, 96, 128, 86, 118)(74, 106, 83, 115, 93, 125, 87, 119)(78, 110, 92, 124, 88, 120, 94, 126)(81, 113, 91, 123, 85, 117, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 80)(6, 65)(7, 83)(8, 85)(9, 87)(10, 66)(11, 89)(12, 91)(13, 67)(14, 93)(15, 69)(16, 95)(17, 70)(18, 96)(19, 94)(20, 71)(21, 90)(22, 73)(23, 92)(24, 74)(25, 88)(26, 75)(27, 86)(28, 77)(29, 82)(30, 79)(31, 84)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.343 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.312 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |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, Y3^4 * Y1, Y2^-1 * Y1 * Y3^-1 * Y2 * Y3^-1, (Y1 * Y2^-2)^2, (R * Y2 * Y3^-1)^2 ] 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, 22, 54)(12, 44, 19, 51)(13, 45, 14, 46)(15, 47, 21, 53)(16, 48, 18, 50)(17, 49, 20, 52)(23, 55, 27, 59)(24, 56, 25, 57)(26, 58, 28, 60)(29, 61, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 78, 110, 87, 119, 80, 112)(70, 102, 83, 115, 88, 120, 84, 116)(72, 104, 77, 109, 91, 123, 82, 114)(74, 106, 76, 108, 89, 121, 81, 113)(79, 111, 92, 124, 95, 127, 93, 125)(85, 117, 90, 122, 96, 128, 94, 126) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 83)(8, 85)(9, 84)(10, 66)(11, 87)(12, 90)(13, 67)(14, 71)(15, 74)(16, 73)(17, 94)(18, 69)(19, 92)(20, 93)(21, 70)(22, 91)(23, 95)(24, 75)(25, 86)(26, 78)(27, 96)(28, 77)(29, 82)(30, 80)(31, 89)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.344 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.313 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2^-1 * Y3 * Y2 * Y3^-1, Y2 * Y3^-2 * Y2^-1 * Y3^-2, (Y2^-1 * Y3^-1 * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 14, 46)(10, 42, 15, 47)(11, 43, 13, 45)(12, 44, 19, 51)(16, 48, 17, 49)(18, 50, 20, 52)(21, 53, 23, 55)(22, 54, 30, 62)(24, 56, 25, 57)(26, 58, 28, 60)(27, 59, 29, 61)(31, 63, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 75, 107, 71, 103, 77, 109)(70, 102, 80, 112, 72, 104, 81, 113)(73, 105, 85, 117, 78, 110, 87, 119)(74, 106, 88, 120, 79, 111, 89, 121)(76, 108, 90, 122, 83, 115, 92, 124)(82, 114, 86, 118, 84, 116, 94, 126)(91, 123, 95, 127, 93, 125, 96, 128) L = (1, 68)(2, 71)(3, 73)(4, 76)(5, 78)(6, 65)(7, 83)(8, 66)(9, 86)(10, 67)(11, 91)(12, 87)(13, 93)(14, 94)(15, 69)(16, 90)(17, 92)(18, 70)(19, 85)(20, 72)(21, 95)(22, 75)(23, 96)(24, 84)(25, 82)(26, 74)(27, 80)(28, 79)(29, 81)(30, 77)(31, 88)(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 ) } Outer automorphisms :: reflexible Dual of E15.346 Graph:: bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.314 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y3 * Y1 * Y2 * Y3 * Y2, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-3 * Y2^-1 ] 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, 22, 54)(12, 44, 20, 52)(13, 45, 16, 48)(14, 46, 18, 50)(15, 47, 23, 55)(17, 49, 19, 51)(21, 53, 24, 56)(25, 57, 29, 61)(26, 58, 28, 60)(27, 59, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 78, 110, 89, 121, 80, 112)(70, 102, 83, 115, 90, 122, 84, 116)(72, 104, 82, 114, 93, 125, 77, 109)(74, 106, 81, 113, 92, 124, 76, 108)(79, 111, 94, 126, 88, 120, 95, 127)(85, 117, 91, 123, 87, 119, 96, 128) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 84)(8, 87)(9, 83)(10, 66)(11, 89)(12, 91)(13, 67)(14, 73)(15, 92)(16, 71)(17, 96)(18, 69)(19, 94)(20, 95)(21, 70)(22, 93)(23, 90)(24, 74)(25, 88)(26, 75)(27, 78)(28, 86)(29, 85)(30, 77)(31, 82)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.345 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.315 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, (Y3 * Y1^-1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2^-1)^2, Y2^4, (Y3 * Y1^-1)^2, Y1^4, Y2 * Y1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 20, 52, 14, 46)(4, 36, 16, 48, 21, 53, 12, 44)(6, 38, 9, 41, 22, 54, 18, 50)(7, 39, 19, 51, 23, 55, 10, 42)(13, 45, 24, 56, 30, 62, 27, 59)(15, 47, 28, 60, 31, 63, 26, 58)(17, 49, 29, 61, 32, 64, 25, 57)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 71, 103, 79, 111, 81, 113)(69, 101, 82, 114, 91, 123, 78, 110)(72, 104, 84, 116, 94, 126, 86, 118)(74, 106, 76, 108, 89, 121, 90, 122)(80, 112, 93, 125, 92, 124, 83, 115)(85, 117, 87, 119, 95, 127, 96, 128) L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 83)(6, 81)(7, 65)(8, 85)(9, 76)(10, 75)(11, 90)(12, 66)(13, 79)(14, 92)(15, 67)(16, 69)(17, 77)(18, 80)(19, 78)(20, 87)(21, 86)(22, 96)(23, 72)(24, 89)(25, 73)(26, 88)(27, 93)(28, 91)(29, 82)(30, 95)(31, 84)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.325 Graph:: simple bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.316 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y3 * Y1)^2, (R * Y1)^2, Y2^4, (Y1^-1 * Y3)^2, (R * Y2)^2, Y1^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 20, 52, 15, 47)(4, 36, 16, 48, 21, 53, 12, 44)(6, 38, 9, 41, 22, 54, 17, 49)(7, 39, 18, 50, 23, 55, 10, 42)(13, 45, 24, 56, 30, 62, 27, 59)(14, 46, 28, 60, 31, 63, 26, 58)(19, 51, 29, 61, 32, 64, 25, 57)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 78, 110, 83, 115, 71, 103)(69, 101, 81, 113, 91, 123, 79, 111)(72, 104, 84, 116, 94, 126, 86, 118)(74, 106, 89, 121, 90, 122, 76, 108)(80, 112, 82, 114, 93, 125, 92, 124)(85, 117, 95, 127, 96, 128, 87, 119) L = (1, 68)(2, 74)(3, 78)(4, 67)(5, 82)(6, 71)(7, 65)(8, 85)(9, 89)(10, 73)(11, 76)(12, 66)(13, 83)(14, 77)(15, 80)(16, 69)(17, 93)(18, 81)(19, 70)(20, 95)(21, 84)(22, 87)(23, 72)(24, 90)(25, 88)(26, 75)(27, 92)(28, 79)(29, 91)(30, 96)(31, 94)(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, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.326 Graph:: simple bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.317 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (Y3^-1, Y2^-1), (Y3^-1 * Y1^-1)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, Y1^4, Y2^4, Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3^-1, Y1^-2 * Y3^2 * Y2, Y2^-1 * Y1^2 * Y3^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 23, 55, 15, 47)(4, 36, 17, 49, 22, 54, 12, 44)(6, 38, 9, 41, 18, 50, 20, 52)(7, 39, 21, 53, 14, 46, 10, 42)(13, 45, 24, 56, 31, 63, 28, 60)(16, 48, 30, 62, 27, 59, 26, 58)(19, 51, 32, 64, 29, 61, 25, 57)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 78, 110, 91, 123, 83, 115)(69, 101, 84, 116, 92, 124, 79, 111)(71, 103, 80, 112, 93, 125, 86, 118)(72, 104, 87, 119, 95, 127, 82, 114)(74, 106, 81, 113, 96, 128, 90, 122)(76, 108, 89, 121, 94, 126, 85, 117) L = (1, 68)(2, 74)(3, 78)(4, 82)(5, 85)(6, 83)(7, 65)(8, 86)(9, 81)(10, 79)(11, 90)(12, 66)(13, 91)(14, 72)(15, 94)(16, 67)(17, 69)(18, 93)(19, 95)(20, 76)(21, 75)(22, 70)(23, 71)(24, 96)(25, 73)(26, 92)(27, 87)(28, 89)(29, 77)(30, 88)(31, 80)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.323 Graph:: simple bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.318 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, (Y1 * Y3^-1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (Y3, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y2)^2, Y2^4, Y2^-1 * Y1^2 * Y3^2, Y3 * Y1^-1 * Y3^-1 * Y2 * Y1, Y3^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 18, 50, 15, 47)(4, 36, 17, 49, 16, 48, 12, 44)(6, 38, 9, 41, 23, 55, 20, 52)(7, 39, 21, 53, 19, 51, 10, 42)(13, 45, 24, 56, 31, 63, 28, 60)(14, 46, 30, 62, 29, 61, 26, 58)(22, 54, 32, 64, 27, 59, 25, 57)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 78, 110, 91, 123, 83, 115)(69, 101, 84, 116, 92, 124, 79, 111)(71, 103, 80, 112, 93, 125, 86, 118)(72, 104, 82, 114, 95, 127, 87, 119)(74, 106, 89, 121, 94, 126, 81, 113)(76, 108, 85, 117, 96, 128, 90, 122) L = (1, 68)(2, 74)(3, 78)(4, 82)(5, 85)(6, 83)(7, 65)(8, 80)(9, 89)(10, 84)(11, 81)(12, 66)(13, 91)(14, 95)(15, 76)(16, 67)(17, 69)(18, 93)(19, 72)(20, 96)(21, 73)(22, 70)(23, 71)(24, 94)(25, 92)(26, 75)(27, 87)(28, 90)(29, 77)(30, 79)(31, 86)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.324 Graph:: simple bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.319 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y1)^2, Y2^4, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^2 * Y1^-1 * Y2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 16, 48, 11, 43)(5, 37, 14, 46, 17, 49, 15, 47)(7, 39, 18, 50, 12, 44, 20, 52)(8, 40, 21, 53, 13, 45, 22, 54)(10, 42, 19, 51, 28, 60, 25, 57)(23, 55, 30, 62, 26, 58, 32, 64)(24, 56, 29, 61, 27, 59, 31, 63)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 71, 103, 83, 115, 72, 104)(68, 100, 76, 108, 89, 121, 77, 109)(70, 102, 80, 112, 92, 124, 81, 113)(73, 105, 87, 119, 78, 110, 88, 120)(75, 107, 90, 122, 79, 111, 91, 123)(82, 114, 93, 125, 85, 117, 94, 126)(84, 116, 95, 127, 86, 118, 96, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 83)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 92)(20, 71)(21, 77)(22, 72)(23, 94)(24, 93)(25, 74)(26, 96)(27, 95)(28, 89)(29, 91)(30, 90)(31, 88)(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, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.329 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.320 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-2, Y3^-2 * Y1^2, (Y1^-1, Y3), Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y1^-1 * Y2^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y3 * Y1^-1)^2, Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y2, Y2^-1 * R * Y3^-1 * Y1^-1 * R * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-2 * Y2^-1 * Y3^2 * 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, 13, 45, 19, 51, 15, 47)(4, 36, 10, 42, 7, 39, 12, 44)(6, 38, 16, 48, 20, 52, 14, 46)(9, 41, 21, 53, 18, 50, 23, 55)(11, 43, 24, 56, 17, 49, 22, 54)(25, 57, 30, 62, 28, 60, 31, 63)(26, 58, 29, 61, 27, 59, 32, 64)(65, 97, 67, 99, 74, 106, 70, 102)(66, 98, 73, 105, 71, 103, 75, 107)(68, 100, 81, 113, 69, 101, 82, 114)(72, 104, 83, 115, 76, 108, 84, 116)(77, 109, 89, 121, 80, 112, 90, 122)(78, 110, 91, 123, 79, 111, 92, 124)(85, 117, 93, 125, 88, 120, 94, 126)(86, 118, 95, 127, 87, 119, 96, 128) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 79)(7, 65)(8, 71)(9, 86)(10, 69)(11, 87)(12, 66)(13, 70)(14, 83)(15, 84)(16, 67)(17, 85)(18, 88)(19, 80)(20, 77)(21, 75)(22, 82)(23, 81)(24, 73)(25, 96)(26, 95)(27, 94)(28, 93)(29, 89)(30, 90)(31, 91)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.327 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.321 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, Y1^4, Y2^4, (Y3^-1, Y1^-1), Y3 * Y2^-2 * Y1^-1, Y1^-1 * Y2^2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * R * Y1 * Y3^-1 * R * Y2^-1, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y1 * Y2)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 19, 51, 15, 47)(4, 36, 10, 42, 7, 39, 12, 44)(6, 38, 14, 46, 20, 52, 16, 48)(9, 41, 21, 53, 17, 49, 23, 55)(11, 43, 22, 54, 18, 50, 24, 56)(25, 57, 30, 62, 27, 59, 32, 64)(26, 58, 29, 61, 28, 60, 31, 63)(65, 97, 67, 99, 76, 108, 70, 102)(66, 98, 73, 105, 68, 100, 75, 107)(69, 101, 81, 113, 71, 103, 82, 114)(72, 104, 83, 115, 74, 106, 84, 116)(77, 109, 89, 121, 78, 110, 90, 122)(79, 111, 91, 123, 80, 112, 92, 124)(85, 117, 93, 125, 86, 118, 94, 126)(87, 119, 95, 127, 88, 120, 96, 128) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 77)(7, 65)(8, 71)(9, 86)(10, 69)(11, 85)(12, 66)(13, 84)(14, 83)(15, 70)(16, 67)(17, 88)(18, 87)(19, 80)(20, 79)(21, 82)(22, 81)(23, 75)(24, 73)(25, 93)(26, 94)(27, 95)(28, 96)(29, 91)(30, 92)(31, 89)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.328 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.322 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1 * Y3^-1, Y1^-2 * Y3^-1 * Y1^-1, (R * Y1)^2, Y2^4, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 16, 48, 11, 43)(5, 37, 14, 46, 17, 49, 15, 47)(7, 39, 18, 50, 12, 44, 20, 52)(8, 40, 21, 53, 13, 45, 22, 54)(10, 42, 19, 51, 28, 60, 25, 57)(23, 55, 32, 64, 26, 58, 30, 62)(24, 56, 31, 63, 27, 59, 29, 61)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 71, 103, 83, 115, 72, 104)(68, 100, 76, 108, 89, 121, 77, 109)(70, 102, 80, 112, 92, 124, 81, 113)(73, 105, 87, 119, 78, 110, 88, 120)(75, 107, 90, 122, 79, 111, 91, 123)(82, 114, 93, 125, 85, 117, 94, 126)(84, 116, 95, 127, 86, 118, 96, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 83)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 92)(20, 71)(21, 77)(22, 72)(23, 96)(24, 95)(25, 74)(26, 94)(27, 93)(28, 89)(29, 88)(30, 87)(31, 91)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.330 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.323 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y1^-1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, (R * Y2 * Y3)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y3 * Y2)^4, Y1^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 16, 48, 28, 60, 24, 56, 15, 47, 5, 37)(3, 35, 9, 41, 23, 55, 29, 61, 22, 54, 8, 40, 17, 49, 11, 43)(4, 36, 7, 39, 19, 51, 14, 46, 25, 57, 32, 64, 18, 50, 13, 45)(10, 42, 20, 52, 30, 62, 27, 59, 12, 44, 21, 53, 31, 63, 26, 58)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 76, 108)(69, 101, 78, 110)(70, 102, 81, 113)(72, 104, 85, 117)(73, 105, 84, 116)(74, 106, 89, 121)(75, 107, 91, 123)(77, 109, 80, 112)(79, 111, 87, 119)(82, 114, 95, 127)(83, 115, 94, 126)(86, 118, 92, 124)(88, 120, 96, 128)(90, 122, 93, 125) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 75)(6, 82)(7, 84)(8, 66)(9, 88)(10, 67)(11, 69)(12, 86)(13, 91)(14, 90)(15, 83)(16, 93)(17, 94)(18, 70)(19, 79)(20, 71)(21, 96)(22, 76)(23, 95)(24, 73)(25, 92)(26, 78)(27, 77)(28, 89)(29, 80)(30, 81)(31, 87)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.317 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.324 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, (R * Y2 * Y3)^2, (Y2 * Y1^-2)^2, (Y1 * Y2)^4, (Y3 * Y2)^4, Y1^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 16, 48, 28, 60, 25, 57, 15, 47, 5, 37)(3, 35, 8, 40, 21, 53, 14, 46, 26, 58, 31, 63, 17, 49, 10, 42)(4, 36, 11, 43, 24, 56, 29, 61, 20, 52, 7, 39, 18, 50, 13, 45)(9, 41, 19, 51, 30, 62, 27, 59, 12, 44, 22, 54, 32, 64, 23, 55)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 76, 108)(69, 101, 77, 109)(70, 102, 81, 113)(72, 104, 86, 118)(73, 105, 84, 116)(74, 106, 87, 119)(75, 107, 89, 121)(78, 110, 91, 123)(79, 111, 85, 117)(80, 112, 93, 125)(82, 114, 96, 128)(83, 115, 95, 127)(88, 120, 94, 126)(90, 122, 92, 124) L = (1, 68)(2, 72)(3, 73)(4, 65)(5, 78)(6, 82)(7, 83)(8, 66)(9, 67)(10, 80)(11, 86)(12, 90)(13, 87)(14, 69)(15, 88)(16, 74)(17, 94)(18, 70)(19, 71)(20, 92)(21, 96)(22, 75)(23, 77)(24, 79)(25, 95)(26, 76)(27, 93)(28, 84)(29, 91)(30, 81)(31, 89)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.318 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.325 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-2 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^4 * Y3 * Y1^-2, (Y2 * Y1^2 * Y3)^2, (Y2 * Y1 * Y3 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 22, 54, 10, 42, 5, 37)(3, 35, 9, 41, 19, 51, 28, 60, 15, 47, 12, 44, 4, 36, 11, 43)(7, 39, 16, 48, 13, 45, 25, 57, 27, 59, 18, 50, 8, 40, 17, 49)(20, 52, 29, 61, 23, 55, 31, 63, 24, 56, 32, 64, 21, 53, 30, 62)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 70, 102)(69, 101, 77, 109)(72, 104, 78, 110)(73, 105, 84, 116)(74, 106, 83, 115)(75, 107, 87, 119)(76, 108, 88, 120)(79, 111, 90, 122)(80, 112, 93, 125)(81, 113, 95, 127)(82, 114, 96, 128)(85, 117, 92, 124)(86, 118, 91, 123)(89, 121, 94, 126) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 71)(6, 79)(7, 69)(8, 66)(9, 85)(10, 67)(11, 84)(12, 87)(13, 86)(14, 91)(15, 70)(16, 94)(17, 93)(18, 95)(19, 90)(20, 75)(21, 73)(22, 77)(23, 76)(24, 92)(25, 96)(26, 83)(27, 78)(28, 88)(29, 81)(30, 80)(31, 82)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.315 Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.326 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^8, Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y2 * Y3)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 24, 56, 12, 44, 5, 37)(3, 35, 9, 41, 4, 36, 11, 43, 22, 54, 28, 60, 15, 47, 10, 42)(7, 39, 16, 48, 8, 40, 18, 50, 13, 45, 25, 57, 27, 59, 17, 49)(19, 51, 29, 61, 20, 52, 30, 62, 21, 53, 31, 63, 23, 55, 32, 64)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 76, 108)(69, 101, 72, 104)(70, 102, 79, 111)(73, 105, 83, 115)(74, 106, 84, 116)(75, 107, 87, 119)(77, 109, 88, 120)(78, 110, 91, 123)(80, 112, 93, 125)(81, 113, 94, 126)(82, 114, 96, 128)(85, 117, 92, 124)(86, 118, 90, 122)(89, 121, 95, 127) L = (1, 68)(2, 72)(3, 70)(4, 65)(5, 77)(6, 67)(7, 78)(8, 66)(9, 84)(10, 85)(11, 83)(12, 86)(13, 69)(14, 71)(15, 90)(16, 94)(17, 95)(18, 93)(19, 75)(20, 73)(21, 74)(22, 76)(23, 92)(24, 91)(25, 96)(26, 79)(27, 88)(28, 87)(29, 82)(30, 80)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.316 Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.327 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (Y3 * R)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y2)^2, (R * Y1)^2, Y1^-4 * Y2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 11, 43, 3, 35, 8, 40, 15, 47, 5, 37)(4, 36, 12, 44, 20, 52, 18, 50, 6, 38, 17, 49, 19, 51, 13, 45)(9, 41, 21, 53, 14, 46, 24, 56, 10, 42, 23, 55, 16, 48, 22, 54)(25, 57, 29, 61, 27, 59, 31, 63, 26, 58, 30, 62, 28, 60, 32, 64)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 70, 102)(69, 101, 75, 107)(71, 103, 79, 111)(73, 105, 74, 106)(76, 108, 81, 113)(77, 109, 82, 114)(78, 110, 80, 112)(83, 115, 84, 116)(85, 117, 87, 119)(86, 118, 88, 120)(89, 121, 90, 122)(91, 123, 92, 124)(93, 125, 94, 126)(95, 127, 96, 128) L = (1, 68)(2, 73)(3, 70)(4, 67)(5, 78)(6, 65)(7, 83)(8, 74)(9, 72)(10, 66)(11, 80)(12, 89)(13, 91)(14, 75)(15, 84)(16, 69)(17, 90)(18, 92)(19, 79)(20, 71)(21, 93)(22, 95)(23, 94)(24, 96)(25, 81)(26, 76)(27, 82)(28, 77)(29, 87)(30, 85)(31, 88)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.320 Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.328 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, Y1^-1 * Y2 * Y1 * Y2, Y1 * Y2 * Y3^-1 * Y1 * Y3, Y1^-2 * Y3^2 * Y1^-2, Y3^-1 * Y1^2 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 22, 54, 15, 47, 26, 58, 18, 50, 5, 37)(3, 35, 8, 40, 23, 55, 31, 63, 29, 61, 32, 64, 30, 62, 12, 44)(4, 36, 14, 46, 25, 57, 21, 53, 6, 38, 20, 52, 24, 56, 16, 48)(9, 41, 11, 43, 17, 49, 28, 60, 10, 42, 13, 45, 19, 51, 27, 59)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 87, 119)(73, 105, 80, 112)(74, 106, 85, 117)(78, 110, 81, 113)(79, 111, 93, 125)(82, 114, 94, 126)(83, 115, 84, 116)(86, 118, 95, 127)(88, 120, 91, 123)(89, 121, 92, 124)(90, 122, 96, 128) L = (1, 68)(2, 73)(3, 75)(4, 79)(5, 81)(6, 65)(7, 88)(8, 80)(9, 90)(10, 66)(11, 93)(12, 78)(13, 67)(14, 95)(15, 70)(16, 96)(17, 86)(18, 89)(19, 69)(20, 76)(21, 72)(22, 83)(23, 91)(24, 82)(25, 71)(26, 74)(27, 94)(28, 87)(29, 77)(30, 92)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.321 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.329 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y1^-1 * Y2 * Y1 * Y2, Y1 * Y2 * Y3 * Y1 * Y3, Y1 * Y2 * Y3^-1 * Y1 * Y3^-1, Y3^-2 * Y1^-4 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 22, 54, 15, 47, 26, 58, 18, 50, 5, 37)(3, 35, 8, 40, 23, 55, 31, 63, 29, 61, 32, 64, 30, 62, 12, 44)(4, 36, 14, 46, 25, 57, 21, 53, 6, 38, 20, 52, 24, 56, 16, 48)(9, 41, 13, 45, 17, 49, 28, 60, 10, 42, 11, 43, 19, 51, 27, 59)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 87, 119)(73, 105, 85, 117)(74, 106, 80, 112)(78, 110, 83, 115)(79, 111, 93, 125)(81, 113, 84, 116)(82, 114, 94, 126)(86, 118, 95, 127)(88, 120, 92, 124)(89, 121, 91, 123)(90, 122, 96, 128) L = (1, 68)(2, 73)(3, 75)(4, 79)(5, 81)(6, 65)(7, 88)(8, 85)(9, 90)(10, 66)(11, 93)(12, 84)(13, 67)(14, 76)(15, 70)(16, 72)(17, 86)(18, 89)(19, 69)(20, 95)(21, 96)(22, 83)(23, 92)(24, 82)(25, 71)(26, 74)(27, 87)(28, 94)(29, 77)(30, 91)(31, 78)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.319 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.330 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y2 * Y1 * Y2 * Y1^-1, (Y3 * R)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y1^3 * Y3 * Y1^-1 * Y3^-1, (Y3^-1 * Y1)^4, (Y3 * Y1 * Y3^-1 * Y1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 19, 51, 31, 63, 30, 62, 15, 47, 5, 37)(3, 35, 8, 40, 20, 52, 28, 60, 32, 64, 29, 61, 27, 59, 11, 43)(4, 36, 12, 44, 24, 56, 9, 41, 23, 55, 14, 46, 21, 53, 13, 45)(6, 38, 17, 49, 26, 58, 10, 42, 25, 57, 16, 48, 22, 54, 18, 50)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 70, 102)(69, 101, 75, 107)(71, 103, 84, 116)(73, 105, 74, 106)(76, 108, 81, 113)(77, 109, 82, 114)(78, 110, 80, 112)(79, 111, 91, 123)(83, 115, 92, 124)(85, 117, 86, 118)(87, 119, 89, 121)(88, 120, 90, 122)(93, 125, 94, 126)(95, 127, 96, 128) L = (1, 68)(2, 73)(3, 70)(4, 67)(5, 78)(6, 65)(7, 85)(8, 74)(9, 72)(10, 66)(11, 80)(12, 92)(13, 93)(14, 75)(15, 88)(16, 69)(17, 83)(18, 94)(19, 76)(20, 86)(21, 84)(22, 71)(23, 96)(24, 91)(25, 95)(26, 79)(27, 90)(28, 81)(29, 82)(30, 77)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.322 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, (Y1^-1 * Y2)^2, Y3^2 * Y1^2, (Y2^-1 * Y3^-1)^2, (R * Y1)^2, Y3 * Y2^2 * Y1^-1, Y3 * Y1^-2 * Y3, (Y3 * Y2^-1)^2, Y1^4, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1)^4, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 19, 51, 11, 43)(4, 36, 17, 49, 7, 39, 14, 46)(6, 38, 18, 50, 20, 52, 9, 41)(10, 42, 24, 56, 12, 44, 21, 53)(15, 47, 28, 60, 16, 48, 25, 57)(22, 54, 32, 64, 23, 55, 29, 61)(26, 58, 30, 62, 27, 59, 31, 63)(65, 97, 67, 99, 78, 110, 89, 121, 95, 127, 86, 118, 76, 108, 70, 102)(66, 98, 73, 105, 85, 117, 93, 125, 90, 122, 80, 112, 68, 100, 75, 107)(69, 101, 82, 114, 88, 120, 96, 128, 91, 123, 79, 111, 71, 103, 77, 109)(72, 104, 83, 115, 81, 113, 92, 124, 94, 126, 87, 119, 74, 106, 84, 116) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 77)(7, 65)(8, 71)(9, 86)(10, 69)(11, 70)(12, 66)(13, 84)(14, 90)(15, 83)(16, 67)(17, 91)(18, 87)(19, 80)(20, 75)(21, 94)(22, 82)(23, 73)(24, 95)(25, 96)(26, 81)(27, 78)(28, 93)(29, 89)(30, 88)(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) :: { ( 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 E15.300 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.332 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, (Y1^-1 * Y2^-1)^2, Y2 * Y1 * Y2^-1 * Y3^-1, Y1 * Y3^2 * Y1, Y3^-1 * Y2^2 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, (Y3 * Y2^-1)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, R * Y3^-1 * Y1 * Y2^-1 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 19, 51, 11, 43)(4, 36, 14, 46, 7, 39, 17, 49)(6, 38, 18, 50, 20, 52, 9, 41)(10, 42, 21, 53, 12, 44, 24, 56)(15, 47, 25, 57, 16, 48, 28, 60)(22, 54, 29, 61, 23, 55, 32, 64)(26, 58, 30, 62, 27, 59, 31, 63)(65, 97, 67, 99, 78, 110, 89, 121, 94, 126, 87, 119, 74, 106, 70, 102)(66, 98, 73, 105, 85, 117, 93, 125, 91, 123, 79, 111, 71, 103, 75, 107)(68, 100, 77, 109, 69, 101, 82, 114, 88, 120, 96, 128, 90, 122, 80, 112)(72, 104, 83, 115, 81, 113, 92, 124, 95, 127, 86, 118, 76, 108, 84, 116) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 75)(7, 65)(8, 71)(9, 86)(10, 69)(11, 84)(12, 66)(13, 70)(14, 90)(15, 83)(16, 67)(17, 91)(18, 87)(19, 80)(20, 77)(21, 94)(22, 82)(23, 73)(24, 95)(25, 93)(26, 81)(27, 78)(28, 96)(29, 92)(30, 88)(31, 85)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.302 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.333 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2 * Y1^-1)^2, (Y2^-1 * Y3^-1)^2, (Y1^-1 * Y2^-1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y2^6 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 19, 51, 11, 43)(4, 36, 15, 47, 7, 39, 17, 49)(6, 38, 14, 46, 20, 52, 9, 41)(10, 42, 21, 53, 12, 44, 23, 55)(16, 48, 28, 60, 18, 50, 26, 58)(22, 54, 32, 64, 24, 56, 30, 62)(25, 57, 29, 61, 27, 59, 31, 63)(65, 97, 67, 99, 74, 106, 86, 118, 93, 125, 90, 122, 79, 111, 70, 102)(66, 98, 73, 105, 71, 103, 82, 114, 91, 123, 94, 126, 85, 117, 75, 107)(68, 100, 80, 112, 89, 121, 96, 128, 87, 119, 77, 109, 69, 101, 78, 110)(72, 104, 83, 115, 76, 108, 88, 120, 95, 127, 92, 124, 81, 113, 84, 116) L = (1, 68)(2, 74)(3, 73)(4, 72)(5, 76)(6, 82)(7, 65)(8, 71)(9, 83)(10, 69)(11, 88)(12, 66)(13, 86)(14, 67)(15, 89)(16, 70)(17, 91)(18, 84)(19, 78)(20, 80)(21, 93)(22, 75)(23, 95)(24, 77)(25, 81)(26, 94)(27, 79)(28, 96)(29, 87)(30, 92)(31, 85)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.301 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.334 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2 * Y1, Y2^-2 * Y1 * Y3^-1, Y1 * Y2 * Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y1 * Y2^2 * Y3^-1, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^2 * Y2^-1 * Y1^-1 * Y3^-1, (Y1^-1 * Y3)^4, (Y3^-1 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 19, 51, 11, 43)(4, 36, 15, 47, 7, 39, 17, 49)(6, 38, 14, 46, 20, 52, 9, 41)(10, 42, 21, 53, 12, 44, 23, 55)(16, 48, 28, 60, 18, 50, 26, 58)(22, 54, 32, 64, 24, 56, 30, 62)(25, 57, 29, 61, 27, 59, 31, 63)(65, 97, 67, 99, 76, 108, 88, 120, 93, 125, 92, 124, 81, 113, 70, 102)(66, 98, 73, 105, 68, 100, 80, 112, 91, 123, 96, 128, 87, 119, 75, 107)(69, 101, 78, 110, 71, 103, 82, 114, 89, 121, 94, 126, 85, 117, 77, 109)(72, 104, 83, 115, 74, 106, 86, 118, 95, 127, 90, 122, 79, 111, 84, 116) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 82)(7, 65)(8, 71)(9, 67)(10, 69)(11, 88)(12, 66)(13, 86)(14, 83)(15, 89)(16, 70)(17, 91)(18, 84)(19, 73)(20, 80)(21, 93)(22, 75)(23, 95)(24, 77)(25, 81)(26, 96)(27, 79)(28, 94)(29, 87)(30, 90)(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) :: { ( 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 E15.299 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.335 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y3 * Y1, (Y2^-1 * Y3)^2, Y1 * Y3^-1 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y2^-1, Y3^-1), Y1^4, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2 * Y1^-2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1, Y2 * Y1^-1 * Y3^-1 * Y2^-2 * Y1^-1, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 22, 54, 15, 47)(4, 36, 11, 43, 23, 55, 17, 49)(6, 38, 10, 42, 24, 56, 19, 51)(7, 39, 9, 41, 25, 57, 18, 50)(13, 45, 29, 61, 20, 52, 26, 58)(14, 46, 30, 62, 21, 53, 27, 59)(16, 48, 28, 60, 32, 64, 31, 63)(65, 97, 67, 99, 77, 109, 88, 120, 72, 104, 86, 118, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 81, 113, 69, 101, 82, 114, 93, 125, 75, 107)(68, 100, 78, 110, 89, 121, 96, 128, 87, 119, 85, 117, 71, 103, 80, 112)(74, 106, 91, 123, 79, 111, 95, 127, 83, 115, 94, 126, 76, 108, 92, 124) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 89)(14, 88)(15, 69)(16, 67)(17, 95)(18, 94)(19, 93)(20, 71)(21, 70)(22, 85)(23, 84)(24, 96)(25, 72)(26, 79)(27, 81)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.307 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.336 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^2 * Y3^-1, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1 * Y2^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^4, Y3 * Y1^-1 * Y2 * Y1, (Y2^-1, Y3^-1), (R * Y1)^2, Y1^-2 * Y3 * Y2^3, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2, Y2 * Y1^-1 * Y3^-2 * Y2^-1 * Y1^-1, Y2 * Y3^2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2^-3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 22, 54, 15, 47)(4, 36, 11, 43, 23, 55, 17, 49)(6, 38, 10, 42, 24, 56, 19, 51)(7, 39, 9, 41, 25, 57, 18, 50)(13, 45, 29, 61, 21, 53, 27, 59)(14, 46, 30, 62, 20, 52, 26, 58)(16, 48, 28, 60, 32, 64, 31, 63)(65, 97, 67, 99, 77, 109, 89, 121, 96, 128, 87, 119, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 79, 111, 95, 127, 83, 115, 93, 125, 75, 107)(68, 100, 78, 110, 88, 120, 72, 104, 86, 118, 85, 117, 71, 103, 80, 112)(69, 101, 82, 114, 94, 126, 76, 108, 92, 124, 74, 106, 91, 123, 81, 113) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 88)(14, 89)(15, 69)(16, 67)(17, 95)(18, 93)(19, 94)(20, 71)(21, 70)(22, 84)(23, 85)(24, 96)(25, 72)(26, 81)(27, 79)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.304 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.337 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y1^-2 * Y2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2)^2, (Y3, Y2^-1), Y1 * Y3^-1 * Y2 * Y1, (R * Y3)^2, Y2 * Y3 * Y2^2, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 4, 36, 16, 48)(6, 38, 17, 49, 7, 39, 18, 50)(9, 41, 19, 51, 10, 42, 22, 54)(11, 43, 23, 55, 12, 44, 24, 56)(14, 46, 21, 53, 15, 47, 20, 52)(25, 57, 29, 61, 26, 58, 30, 62)(27, 59, 32, 64, 28, 60, 31, 63)(65, 97, 67, 99, 78, 110, 71, 103, 72, 104, 68, 100, 79, 111, 70, 102)(66, 98, 73, 105, 84, 116, 76, 108, 69, 101, 74, 106, 85, 117, 75, 107)(77, 109, 89, 121, 81, 113, 92, 124, 80, 112, 90, 122, 82, 114, 91, 123)(83, 115, 93, 125, 87, 119, 96, 128, 86, 118, 94, 126, 88, 120, 95, 127) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 73)(6, 72)(7, 65)(8, 67)(9, 85)(10, 84)(11, 69)(12, 66)(13, 90)(14, 70)(15, 71)(16, 89)(17, 91)(18, 92)(19, 94)(20, 75)(21, 76)(22, 93)(23, 95)(24, 96)(25, 82)(26, 81)(27, 80)(28, 77)(29, 88)(30, 87)(31, 86)(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) :: { ( 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 E15.306 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.338 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-3, (Y3, Y2^-1), Y3^2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y3 * Y1^-1 * Y2 * Y1^-1, Y1^4, (Y3 * Y2^-1)^2, Y3^2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 20, 52, 12, 44)(4, 36, 17, 49, 21, 53, 11, 43)(6, 38, 19, 51, 22, 54, 10, 42)(7, 39, 18, 50, 23, 55, 9, 41)(14, 46, 25, 57, 30, 62, 29, 61)(15, 47, 24, 56, 31, 63, 28, 60)(16, 48, 26, 58, 32, 64, 27, 59)(65, 97, 67, 99, 78, 110, 71, 103, 80, 112, 68, 100, 79, 111, 70, 102)(66, 98, 73, 105, 88, 120, 76, 108, 90, 122, 74, 106, 89, 121, 75, 107)(69, 101, 82, 114, 92, 124, 77, 109, 91, 123, 83, 115, 93, 125, 81, 113)(72, 104, 84, 116, 94, 126, 87, 119, 96, 128, 85, 117, 95, 127, 86, 118) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 83)(6, 80)(7, 65)(8, 85)(9, 89)(10, 88)(11, 90)(12, 66)(13, 69)(14, 70)(15, 71)(16, 67)(17, 91)(18, 93)(19, 92)(20, 95)(21, 94)(22, 96)(23, 72)(24, 75)(25, 76)(26, 73)(27, 82)(28, 81)(29, 77)(30, 86)(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) :: { ( 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 E15.303 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.339 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^2 * Y3^-1, (Y2^-1 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3), Y3 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y1^4, Y1^-1 * Y3^-2 * Y2^-2 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y1^-2, Y2^3 * Y1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 22, 54, 12, 44)(4, 36, 17, 49, 23, 55, 11, 43)(6, 38, 19, 51, 24, 56, 10, 42)(7, 39, 18, 50, 25, 57, 9, 41)(14, 46, 29, 61, 20, 52, 26, 58)(15, 47, 30, 62, 21, 53, 27, 59)(16, 48, 28, 60, 32, 64, 31, 63)(65, 97, 67, 99, 78, 110, 88, 120, 72, 104, 86, 118, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 81, 113, 69, 101, 82, 114, 93, 125, 75, 107)(68, 100, 79, 111, 89, 121, 96, 128, 87, 119, 85, 117, 71, 103, 80, 112)(74, 106, 91, 123, 77, 109, 95, 127, 83, 115, 94, 126, 76, 108, 92, 124) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 69)(14, 89)(15, 88)(16, 67)(17, 95)(18, 94)(19, 93)(20, 71)(21, 70)(22, 85)(23, 84)(24, 96)(25, 72)(26, 77)(27, 81)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.308 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.340 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = Q8 : C4 (small group id <32, 10>) Aut = (C2 x D16) : C2 (small group id <64, 130>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y1^-1 * Y2 * Y3^-1 * Y1^-1, (R * Y1)^2, (Y3^-1 * Y2)^2, Y1^-2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y2)^2, Y3 * Y1^2 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y2^2 * Y1^-1 * Y2 * Y3 * Y1^-1, Y2^3 * Y1^-1 * Y3^-1 * Y1, (Y1^-1 * Y3 * Y1 * Y2)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 4, 36, 16, 48)(6, 38, 17, 49, 7, 39, 18, 50)(9, 41, 21, 53, 10, 42, 24, 56)(11, 43, 25, 57, 12, 44, 26, 58)(14, 46, 27, 59, 15, 47, 28, 60)(19, 51, 22, 54, 20, 52, 23, 55)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 78, 110, 85, 117, 95, 127, 89, 121, 83, 115, 70, 102)(66, 98, 73, 105, 86, 118, 80, 112, 94, 126, 82, 114, 91, 123, 75, 107)(68, 100, 79, 111, 88, 120, 96, 128, 90, 122, 84, 116, 71, 103, 72, 104)(69, 101, 74, 106, 87, 119, 77, 109, 93, 125, 81, 113, 92, 124, 76, 108) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 73)(6, 72)(7, 65)(8, 67)(9, 87)(10, 86)(11, 69)(12, 66)(13, 94)(14, 88)(15, 85)(16, 93)(17, 91)(18, 92)(19, 71)(20, 70)(21, 96)(22, 77)(23, 80)(24, 95)(25, 84)(26, 83)(27, 76)(28, 75)(29, 82)(30, 81)(31, 90)(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) :: { ( 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 E15.305 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.341 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^-1 * Y2^-1, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^4, Y3 * Y1 * Y3 * Y1^-1, (Y3 * Y2^-1)^2, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 20, 52, 15, 47)(4, 36, 12, 44, 21, 53, 17, 49)(6, 38, 9, 41, 22, 54, 18, 50)(7, 39, 10, 42, 23, 55, 19, 51)(13, 45, 25, 57, 30, 62, 27, 59)(14, 46, 24, 56, 31, 63, 28, 60)(16, 48, 26, 58, 32, 64, 29, 61)(65, 97, 67, 99, 77, 109, 71, 103, 80, 112, 68, 100, 78, 110, 70, 102)(66, 98, 73, 105, 88, 120, 76, 108, 90, 122, 74, 106, 89, 121, 75, 107)(69, 101, 82, 114, 92, 124, 81, 113, 93, 125, 83, 115, 91, 123, 79, 111)(72, 104, 84, 116, 94, 126, 87, 119, 96, 128, 85, 117, 95, 127, 86, 118) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 83)(6, 80)(7, 65)(8, 85)(9, 89)(10, 88)(11, 90)(12, 66)(13, 70)(14, 71)(15, 93)(16, 67)(17, 69)(18, 91)(19, 92)(20, 95)(21, 94)(22, 96)(23, 72)(24, 75)(25, 76)(26, 73)(27, 81)(28, 79)(29, 82)(30, 86)(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) :: { ( 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 E15.309 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.342 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1^2, Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y1^-2, (Y3, Y2^-1), Y3^-2 * Y2^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^8, Y3^-4 * Y1 * Y2^-4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 4, 36, 12, 44)(6, 38, 9, 41, 7, 39, 10, 42)(13, 45, 19, 51, 14, 46, 20, 52)(15, 47, 17, 49, 16, 48, 18, 50)(21, 53, 27, 59, 22, 54, 28, 60)(23, 55, 25, 57, 24, 56, 26, 58)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 77, 109, 85, 117, 93, 125, 87, 119, 79, 111, 70, 102)(66, 98, 73, 105, 81, 113, 89, 121, 95, 127, 91, 123, 83, 115, 75, 107)(68, 100, 78, 110, 86, 118, 94, 126, 88, 120, 80, 112, 71, 103, 72, 104)(69, 101, 74, 106, 82, 114, 90, 122, 96, 128, 92, 124, 84, 116, 76, 108) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 73)(6, 72)(7, 65)(8, 67)(9, 82)(10, 81)(11, 69)(12, 66)(13, 86)(14, 85)(15, 71)(16, 70)(17, 90)(18, 89)(19, 76)(20, 75)(21, 94)(22, 93)(23, 80)(24, 79)(25, 96)(26, 95)(27, 84)(28, 83)(29, 88)(30, 87)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.310 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.343 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 14>) Aut = (C8 x C2 x C2) : C2 (small group id <64, 147>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y2^-1, Y3^-1), (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y3 * Y2^3 * Y1^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 22, 54, 15, 47)(4, 36, 12, 44, 23, 55, 17, 49)(6, 38, 9, 41, 24, 56, 18, 50)(7, 39, 10, 42, 25, 57, 19, 51)(13, 45, 29, 61, 21, 53, 27, 59)(14, 46, 30, 62, 20, 52, 26, 58)(16, 48, 28, 60, 32, 64, 31, 63)(65, 97, 67, 99, 77, 109, 89, 121, 96, 128, 87, 119, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 81, 113, 95, 127, 83, 115, 93, 125, 75, 107)(68, 100, 78, 110, 88, 120, 72, 104, 86, 118, 85, 117, 71, 103, 80, 112)(69, 101, 82, 114, 94, 126, 76, 108, 92, 124, 74, 106, 91, 123, 79, 111) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 88)(14, 89)(15, 95)(16, 67)(17, 69)(18, 93)(19, 94)(20, 71)(21, 70)(22, 84)(23, 85)(24, 96)(25, 72)(26, 79)(27, 81)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.311 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.344 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^-1 * Y2^-3, Y3 * Y1 * Y2 * Y1^-1, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y3^-1, Y3 * Y2 * Y1 * Y2^-2 * Y1^-1, (Y1^-1 * Y2)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 20, 52, 15, 47)(4, 36, 11, 43, 21, 53, 17, 49)(6, 38, 10, 42, 22, 54, 19, 51)(7, 39, 9, 41, 23, 55, 18, 50)(13, 45, 25, 57, 30, 62, 27, 59)(14, 46, 24, 56, 31, 63, 28, 60)(16, 48, 26, 58, 32, 64, 29, 61)(65, 97, 67, 99, 77, 109, 71, 103, 80, 112, 68, 100, 78, 110, 70, 102)(66, 98, 73, 105, 88, 120, 76, 108, 90, 122, 74, 106, 89, 121, 75, 107)(69, 101, 82, 114, 92, 124, 79, 111, 93, 125, 83, 115, 91, 123, 81, 113)(72, 104, 84, 116, 94, 126, 87, 119, 96, 128, 85, 117, 95, 127, 86, 118) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 83)(6, 80)(7, 65)(8, 85)(9, 89)(10, 88)(11, 90)(12, 66)(13, 70)(14, 71)(15, 69)(16, 67)(17, 93)(18, 91)(19, 92)(20, 95)(21, 94)(22, 96)(23, 72)(24, 75)(25, 76)(26, 73)(27, 79)(28, 81)(29, 82)(30, 86)(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) :: { ( 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 E15.312 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.345 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^2 * Y3^-1, Y1^4, Y1^2 * Y3 * Y2^-1, (Y3^-1 * Y2)^2, (R * Y2)^2, Y1 * Y2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^2 * Y3^-1, Y3 * Y1^2 * Y2^-1, Y2 * Y3^2 * Y1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y3 * Y2^2, Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2^8, Y2^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 4, 36, 16, 48)(6, 38, 17, 49, 7, 39, 18, 50)(9, 41, 21, 53, 10, 42, 24, 56)(11, 43, 25, 57, 12, 44, 26, 58)(14, 46, 27, 59, 15, 47, 28, 60)(19, 51, 22, 54, 20, 52, 23, 55)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 78, 110, 88, 120, 96, 128, 90, 122, 83, 115, 70, 102)(66, 98, 73, 105, 86, 118, 77, 109, 93, 125, 81, 113, 91, 123, 75, 107)(68, 100, 79, 111, 85, 117, 95, 127, 89, 121, 84, 116, 71, 103, 72, 104)(69, 101, 74, 106, 87, 119, 80, 112, 94, 126, 82, 114, 92, 124, 76, 108) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 73)(6, 72)(7, 65)(8, 67)(9, 87)(10, 86)(11, 69)(12, 66)(13, 94)(14, 85)(15, 88)(16, 93)(17, 92)(18, 91)(19, 71)(20, 70)(21, 96)(22, 80)(23, 77)(24, 95)(25, 83)(26, 84)(27, 76)(28, 75)(29, 82)(30, 81)(31, 90)(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) :: { ( 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 E15.314 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.346 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C8 : C4 (small group id <32, 13>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 150>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y2)^2, (R * Y2)^2, (R * Y1)^2, Y2^-2 * Y3^2, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2^-1, Y2^2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2^6 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 22, 54, 12, 44)(4, 36, 17, 49, 23, 55, 11, 43)(6, 38, 19, 51, 24, 56, 10, 42)(7, 39, 18, 50, 25, 57, 9, 41)(14, 46, 29, 61, 21, 53, 27, 59)(15, 47, 30, 62, 20, 52, 26, 58)(16, 48, 28, 60, 32, 64, 31, 63)(65, 97, 67, 99, 78, 110, 89, 121, 96, 128, 87, 119, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 77, 109, 95, 127, 83, 115, 93, 125, 75, 107)(68, 100, 79, 111, 88, 120, 72, 104, 86, 118, 85, 117, 71, 103, 80, 112)(69, 101, 82, 114, 94, 126, 76, 108, 92, 124, 74, 106, 91, 123, 81, 113) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 69)(14, 88)(15, 89)(16, 67)(17, 95)(18, 93)(19, 94)(20, 71)(21, 70)(22, 84)(23, 85)(24, 96)(25, 72)(26, 81)(27, 77)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.313 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.347 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^4, Y2^4, (Y2^-1 * Y1)^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 12, 44)(10, 42, 17, 49)(11, 43, 19, 51)(13, 45, 26, 58)(15, 47, 29, 61)(16, 48, 27, 59)(20, 52, 24, 56)(21, 53, 32, 64)(22, 54, 23, 55)(25, 57, 28, 60)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 76, 108, 87, 119, 80, 112)(70, 102, 77, 109, 88, 120, 81, 113)(72, 104, 78, 110, 91, 123, 86, 118)(74, 106, 84, 116, 90, 122, 82, 114)(79, 111, 89, 121, 96, 128, 94, 126)(85, 117, 92, 124, 93, 125, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 80)(6, 65)(7, 78)(8, 85)(9, 86)(10, 66)(11, 87)(12, 89)(13, 67)(14, 92)(15, 70)(16, 94)(17, 69)(18, 73)(19, 91)(20, 71)(21, 74)(22, 95)(23, 96)(24, 75)(25, 77)(26, 83)(27, 93)(28, 84)(29, 90)(30, 81)(31, 82)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.375 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.348 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^4, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 14, 46)(5, 37, 9, 41)(6, 38, 18, 50)(8, 40, 17, 49)(10, 42, 12, 44)(11, 43, 19, 51)(13, 45, 26, 58)(15, 47, 29, 61)(16, 48, 27, 59)(20, 52, 23, 55)(21, 53, 32, 64)(22, 54, 24, 56)(25, 57, 28, 60)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 76, 108, 87, 119, 80, 112)(70, 102, 77, 109, 88, 120, 81, 113)(72, 104, 82, 114, 90, 122, 86, 118)(74, 106, 84, 116, 91, 123, 78, 110)(79, 111, 89, 121, 96, 128, 94, 126)(85, 117, 95, 127, 93, 125, 92, 124) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 80)(6, 65)(7, 82)(8, 85)(9, 86)(10, 66)(11, 87)(12, 89)(13, 67)(14, 73)(15, 70)(16, 94)(17, 69)(18, 95)(19, 90)(20, 71)(21, 74)(22, 92)(23, 96)(24, 75)(25, 77)(26, 93)(27, 83)(28, 78)(29, 91)(30, 81)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.376 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.349 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y2)^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y3^4, Y2^4, (Y2^-1 * Y1)^2, Y1 * Y2^-1 * Y3 * Y1 * Y3^-1, Y1 * Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 16, 48)(10, 42, 13, 45)(11, 43, 19, 51)(12, 44, 25, 57)(15, 47, 28, 60)(17, 49, 30, 62)(20, 52, 23, 55)(21, 53, 32, 64)(22, 54, 24, 56)(26, 58, 31, 63)(27, 59, 29, 61)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 76, 108, 87, 119, 80, 112)(70, 102, 77, 109, 88, 120, 81, 113)(72, 104, 84, 116, 89, 121, 78, 110)(74, 106, 82, 114, 94, 126, 86, 118)(79, 111, 90, 122, 96, 128, 93, 125)(85, 117, 95, 127, 92, 124, 91, 123) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 80)(6, 65)(7, 84)(8, 85)(9, 78)(10, 66)(11, 87)(12, 90)(13, 67)(14, 91)(15, 70)(16, 93)(17, 69)(18, 71)(19, 89)(20, 95)(21, 74)(22, 73)(23, 96)(24, 75)(25, 92)(26, 77)(27, 86)(28, 94)(29, 81)(30, 83)(31, 82)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.373 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.350 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y2)^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y3^4, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 14, 46)(5, 37, 9, 41)(6, 38, 18, 50)(8, 40, 13, 45)(10, 42, 16, 48)(11, 43, 19, 51)(12, 44, 25, 57)(15, 47, 28, 60)(17, 49, 30, 62)(20, 52, 24, 56)(21, 53, 32, 64)(22, 54, 23, 55)(26, 58, 31, 63)(27, 59, 29, 61)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 76, 108, 87, 119, 80, 112)(70, 102, 77, 109, 88, 120, 81, 113)(72, 104, 84, 116, 94, 126, 82, 114)(74, 106, 78, 110, 89, 121, 86, 118)(79, 111, 90, 122, 96, 128, 93, 125)(85, 117, 91, 123, 92, 124, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 80)(6, 65)(7, 84)(8, 85)(9, 82)(10, 66)(11, 87)(12, 90)(13, 67)(14, 71)(15, 70)(16, 93)(17, 69)(18, 95)(19, 94)(20, 91)(21, 74)(22, 73)(23, 96)(24, 75)(25, 83)(26, 77)(27, 78)(28, 89)(29, 81)(30, 92)(31, 86)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.374 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.351 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1 * Y3^-1, Y3^4, Y2^4 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 8, 40)(4, 36, 7, 39)(5, 37, 10, 42)(6, 38, 9, 41)(11, 43, 20, 52)(12, 44, 18, 50)(13, 45, 21, 53)(14, 46, 17, 49)(15, 47, 19, 51)(16, 48, 22, 54)(23, 55, 29, 61)(24, 56, 30, 62)(25, 57, 27, 59)(26, 58, 28, 60)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 81, 113, 73, 105)(68, 100, 76, 108, 87, 119, 79, 111)(70, 102, 77, 109, 88, 120, 80, 112)(72, 104, 82, 114, 91, 123, 85, 117)(74, 106, 83, 115, 92, 124, 86, 118)(78, 110, 89, 121, 95, 127, 90, 122)(84, 116, 93, 125, 96, 128, 94, 126) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 82)(8, 84)(9, 85)(10, 66)(11, 87)(12, 89)(13, 67)(14, 70)(15, 90)(16, 69)(17, 91)(18, 93)(19, 71)(20, 74)(21, 94)(22, 73)(23, 95)(24, 75)(25, 77)(26, 80)(27, 96)(28, 81)(29, 83)(30, 86)(31, 88)(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 ) } Outer automorphisms :: reflexible Dual of E15.372 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.352 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1, Y2^4, Y3^4 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 10, 42)(4, 36, 9, 41)(5, 37, 8, 40)(6, 38, 7, 39)(11, 43, 20, 52)(12, 44, 22, 54)(13, 45, 19, 51)(14, 46, 17, 49)(15, 47, 21, 53)(16, 48, 18, 50)(23, 55, 30, 62)(24, 56, 29, 61)(25, 57, 28, 60)(26, 58, 27, 59)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 81, 113, 73, 105)(68, 100, 76, 108, 87, 119, 79, 111)(70, 102, 77, 109, 88, 120, 80, 112)(72, 104, 82, 114, 91, 123, 85, 117)(74, 106, 83, 115, 92, 124, 86, 118)(78, 110, 89, 121, 95, 127, 90, 122)(84, 116, 93, 125, 96, 128, 94, 126) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 82)(8, 84)(9, 85)(10, 66)(11, 87)(12, 89)(13, 67)(14, 70)(15, 90)(16, 69)(17, 91)(18, 93)(19, 71)(20, 74)(21, 94)(22, 73)(23, 95)(24, 75)(25, 77)(26, 80)(27, 96)(28, 81)(29, 83)(30, 86)(31, 88)(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 ) } Outer automorphisms :: reflexible Dual of E15.369 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.353 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, Y2^4, (R * Y2)^2, Y3^4, (R * Y3)^2, Y3^-2 * Y1 * Y2^-2 * Y1, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1, Y2 * Y3 * Y2 * Y1 * Y2 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3^-1, Y1 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 15, 47)(5, 37, 18, 50)(6, 38, 20, 52)(7, 39, 21, 53)(8, 40, 25, 57)(9, 41, 28, 60)(10, 42, 30, 62)(12, 44, 26, 58)(13, 45, 23, 55)(14, 46, 27, 59)(16, 48, 22, 54)(17, 49, 24, 56)(19, 51, 29, 61)(31, 63, 32, 64)(65, 97, 67, 99, 76, 108, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 77, 109, 92, 124, 81, 113)(70, 102, 78, 110, 85, 117, 83, 115)(72, 104, 87, 119, 82, 114, 91, 123)(74, 106, 88, 120, 75, 107, 93, 125)(79, 111, 90, 122, 84, 116, 95, 127)(80, 112, 94, 126, 96, 128, 89, 121) L = (1, 68)(2, 72)(3, 77)(4, 80)(5, 81)(6, 65)(7, 87)(8, 90)(9, 91)(10, 66)(11, 86)(12, 92)(13, 94)(14, 67)(15, 93)(16, 70)(17, 89)(18, 95)(19, 69)(20, 88)(21, 76)(22, 82)(23, 84)(24, 71)(25, 83)(26, 74)(27, 79)(28, 96)(29, 73)(30, 78)(31, 75)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.371 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.354 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y2^4, Y3 * Y1 * Y3^2 * Y2^-1 * Y1, Y3 * Y1 * Y3 * Y1 * Y2^-1 * Y3, Y2^-1 * Y1 * Y3 * Y2^-2 * Y1, Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3, Y2^-2 * Y1 * Y3^-2 * Y1 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 15, 47)(5, 37, 18, 50)(6, 38, 20, 52)(7, 39, 21, 53)(8, 40, 25, 57)(9, 41, 28, 60)(10, 42, 30, 62)(12, 44, 26, 58)(13, 45, 29, 61)(14, 46, 24, 56)(16, 48, 22, 54)(17, 49, 27, 59)(19, 51, 23, 55)(31, 63, 32, 64)(65, 97, 67, 99, 76, 108, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105)(68, 100, 77, 109, 85, 117, 81, 113)(70, 102, 78, 110, 92, 124, 83, 115)(72, 104, 87, 119, 75, 107, 91, 123)(74, 106, 88, 120, 82, 114, 93, 125)(79, 111, 95, 127, 84, 116, 90, 122)(80, 112, 89, 121, 96, 128, 94, 126) L = (1, 68)(2, 72)(3, 77)(4, 80)(5, 81)(6, 65)(7, 87)(8, 90)(9, 91)(10, 66)(11, 95)(12, 85)(13, 89)(14, 67)(15, 88)(16, 70)(17, 94)(18, 86)(19, 69)(20, 93)(21, 96)(22, 75)(23, 79)(24, 71)(25, 78)(26, 74)(27, 84)(28, 76)(29, 73)(30, 83)(31, 82)(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 ) } Outer automorphisms :: reflexible Dual of E15.370 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.355 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y3^4 * Y1, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2 * R * Y1 * Y2^2 * R * Y2 ] 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, 20, 52)(12, 44, 21, 53)(13, 45, 16, 48)(14, 46, 22, 54)(15, 47, 19, 51)(17, 49, 18, 50)(23, 55, 28, 60)(24, 56, 26, 58)(25, 57, 27, 59)(29, 61, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 84, 116, 73, 105)(68, 100, 78, 110, 92, 124, 80, 112)(70, 102, 82, 114, 90, 122, 76, 108)(72, 104, 86, 118, 87, 119, 77, 109)(74, 106, 81, 113, 88, 120, 85, 117)(79, 111, 89, 121, 95, 127, 94, 126)(83, 115, 91, 123, 96, 128, 93, 125) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 85)(8, 83)(9, 82)(10, 66)(11, 87)(12, 89)(13, 67)(14, 69)(15, 74)(16, 71)(17, 94)(18, 93)(19, 70)(20, 92)(21, 91)(22, 73)(23, 95)(24, 75)(25, 80)(26, 84)(27, 77)(28, 96)(29, 78)(30, 86)(31, 90)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.377 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.356 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1 * Y3^-1)^2, (Y3^-1 * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 14, 46)(10, 42, 15, 47)(11, 43, 13, 45)(12, 44, 18, 50)(16, 48, 17, 49)(19, 51, 21, 53)(20, 52, 24, 56)(22, 54, 23, 55)(25, 57, 27, 59)(26, 58, 28, 60)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 75, 107, 71, 103, 77, 109)(70, 102, 80, 112, 72, 104, 81, 113)(73, 105, 83, 115, 78, 110, 85, 117)(74, 106, 86, 118, 79, 111, 87, 119)(76, 108, 84, 116, 82, 114, 88, 120)(89, 121, 95, 127, 91, 123, 93, 125)(90, 122, 96, 128, 92, 124, 94, 126) L = (1, 68)(2, 71)(3, 73)(4, 76)(5, 78)(6, 65)(7, 82)(8, 66)(9, 84)(10, 67)(11, 89)(12, 72)(13, 91)(14, 88)(15, 69)(16, 90)(17, 92)(18, 70)(19, 93)(20, 79)(21, 95)(22, 94)(23, 96)(24, 74)(25, 81)(26, 75)(27, 80)(28, 77)(29, 87)(30, 83)(31, 86)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.378 Graph:: bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.357 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2^2 * Y3^-4 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 20, 52)(8, 40, 25, 57)(10, 42, 27, 59)(11, 43, 24, 56)(12, 44, 21, 53)(13, 45, 17, 49)(15, 47, 19, 51)(16, 48, 26, 58)(18, 50, 22, 54)(23, 55, 28, 60)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 88, 120, 73, 105)(68, 100, 79, 111, 89, 121, 81, 113)(70, 102, 85, 117, 91, 123, 86, 118)(72, 104, 83, 115, 78, 110, 77, 109)(74, 106, 76, 108, 84, 116, 82, 114)(80, 112, 93, 125, 87, 119, 94, 126)(90, 122, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 72)(3, 76)(4, 80)(5, 82)(6, 65)(7, 85)(8, 90)(9, 86)(10, 66)(11, 89)(12, 93)(13, 67)(14, 92)(15, 73)(16, 91)(17, 71)(18, 94)(19, 69)(20, 88)(21, 95)(22, 96)(23, 70)(24, 78)(25, 87)(26, 84)(27, 75)(28, 74)(29, 83)(30, 77)(31, 79)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.379 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.358 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2^4, Y2 * Y1 * Y3 * Y2^-1 * Y3, Y2^-1 * Y1 * Y3 * Y2 * Y3, Y3 * Y1 * Y3 * Y1 * Y3^2, Y3^2 * Y1 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 20, 52)(8, 40, 25, 57)(10, 42, 27, 59)(11, 43, 24, 56)(12, 44, 22, 54)(13, 45, 15, 47)(16, 48, 26, 58)(17, 49, 19, 51)(18, 50, 21, 53)(23, 55, 28, 60)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 88, 120, 73, 105)(68, 100, 79, 111, 89, 121, 81, 113)(70, 102, 85, 117, 91, 123, 86, 118)(72, 104, 77, 109, 78, 110, 83, 115)(74, 106, 82, 114, 84, 116, 76, 108)(80, 112, 93, 125, 87, 119, 94, 126)(90, 122, 96, 128, 92, 124, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 80)(5, 82)(6, 65)(7, 86)(8, 90)(9, 85)(10, 66)(11, 89)(12, 93)(13, 67)(14, 92)(15, 71)(16, 91)(17, 73)(18, 94)(19, 69)(20, 88)(21, 95)(22, 96)(23, 70)(24, 78)(25, 87)(26, 84)(27, 75)(28, 74)(29, 83)(30, 77)(31, 79)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.380 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.359 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, (Y1, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y3 * Y1)^2, Y1^4, Y2^-1 * Y3 * Y2^-2 * Y3, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 22, 54, 14, 46)(4, 36, 16, 48, 31, 63, 17, 49)(6, 38, 11, 43, 24, 56, 20, 52)(7, 39, 21, 53, 28, 60, 10, 42)(12, 44, 15, 47, 30, 62, 23, 55)(13, 45, 26, 58, 32, 64, 29, 61)(18, 50, 19, 51, 25, 57, 27, 59)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 90, 122, 75, 107)(68, 100, 71, 103, 79, 111, 82, 114)(69, 101, 78, 110, 93, 125, 84, 116)(72, 104, 86, 118, 96, 128, 88, 120)(74, 106, 76, 108, 91, 123, 81, 113)(80, 112, 85, 117, 94, 126, 83, 115)(87, 119, 89, 121, 95, 127, 92, 124) L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 83)(6, 82)(7, 65)(8, 87)(9, 76)(10, 75)(11, 81)(12, 66)(13, 79)(14, 80)(15, 67)(16, 69)(17, 90)(18, 77)(19, 84)(20, 94)(21, 78)(22, 89)(23, 88)(24, 92)(25, 72)(26, 91)(27, 73)(28, 96)(29, 85)(30, 93)(31, 86)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.367 Graph:: simple bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.360 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2, (Y2^-1, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^2, Y2^4, Y1^4, Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 22, 54, 15, 47)(4, 36, 16, 48, 31, 63, 17, 49)(6, 38, 11, 43, 24, 56, 19, 51)(7, 39, 21, 53, 27, 59, 10, 42)(12, 44, 20, 52, 30, 62, 23, 55)(13, 45, 26, 58, 32, 64, 29, 61)(14, 46, 18, 50, 25, 57, 28, 60)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 90, 122, 75, 107)(68, 100, 78, 110, 84, 116, 71, 103)(69, 101, 79, 111, 93, 125, 83, 115)(72, 104, 86, 118, 96, 128, 88, 120)(74, 106, 81, 113, 92, 124, 76, 108)(80, 112, 82, 114, 94, 126, 85, 117)(87, 119, 91, 123, 95, 127, 89, 121) L = (1, 68)(2, 74)(3, 78)(4, 67)(5, 82)(6, 71)(7, 65)(8, 87)(9, 81)(10, 73)(11, 76)(12, 66)(13, 84)(14, 77)(15, 94)(16, 69)(17, 90)(18, 79)(19, 80)(20, 70)(21, 83)(22, 91)(23, 86)(24, 89)(25, 72)(26, 92)(27, 96)(28, 75)(29, 85)(30, 93)(31, 88)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.368 Graph:: simple bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.361 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y3 * Y1 * Y2, (Y3 * Y1^-1)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1 * Y2 * Y3 * Y1^-1 * Y2 * Y1, Y2 * Y3 * Y2^-1 * Y3 * Y2 * 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 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 18, 50, 14, 46)(4, 36, 12, 44, 19, 51, 9, 41)(6, 38, 17, 49, 20, 52, 13, 45)(8, 40, 21, 53, 15, 47, 23, 55)(10, 42, 24, 56, 16, 48, 22, 54)(25, 57, 29, 61, 27, 59, 31, 63)(26, 58, 32, 64, 28, 60, 30, 62)(65, 97, 67, 99, 76, 108, 70, 102)(66, 98, 72, 104, 68, 100, 74, 106)(69, 101, 79, 111, 83, 115, 80, 112)(71, 103, 82, 114, 73, 105, 84, 116)(75, 107, 89, 121, 77, 109, 90, 122)(78, 110, 91, 123, 81, 113, 92, 124)(85, 117, 93, 125, 86, 118, 94, 126)(87, 119, 95, 127, 88, 120, 96, 128) L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 76)(6, 78)(7, 83)(8, 86)(9, 66)(10, 87)(11, 84)(12, 69)(13, 67)(14, 70)(15, 88)(16, 85)(17, 82)(18, 81)(19, 71)(20, 75)(21, 80)(22, 72)(23, 74)(24, 79)(25, 94)(26, 95)(27, 96)(28, 93)(29, 92)(30, 89)(31, 90)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.366 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.362 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1^-1 * Y3)^2, Y1^4, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y3)^2, Y2^-2 * Y3 * Y1^-1, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^-1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1, (Y1^-1 * Y2)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 18, 50, 13, 45)(4, 36, 14, 46, 19, 51, 9, 41)(6, 38, 12, 44, 20, 52, 17, 49)(8, 40, 21, 53, 16, 48, 23, 55)(10, 42, 22, 54, 15, 47, 24, 56)(25, 57, 29, 61, 28, 60, 32, 64)(26, 58, 31, 63, 27, 59, 30, 62)(65, 97, 67, 99, 73, 105, 70, 102)(66, 98, 72, 104, 83, 115, 74, 106)(68, 100, 79, 111, 69, 101, 80, 112)(71, 103, 82, 114, 78, 110, 84, 116)(75, 107, 89, 121, 81, 113, 90, 122)(76, 108, 91, 123, 77, 109, 92, 124)(85, 117, 93, 125, 88, 120, 94, 126)(86, 118, 95, 127, 87, 119, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 75)(7, 83)(8, 86)(9, 66)(10, 85)(11, 70)(12, 67)(13, 84)(14, 69)(15, 87)(16, 88)(17, 82)(18, 81)(19, 71)(20, 77)(21, 74)(22, 72)(23, 79)(24, 80)(25, 95)(26, 93)(27, 96)(28, 94)(29, 90)(30, 92)(31, 89)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.365 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.363 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, (R * Y3)^2, Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^4, Y2 * Y1^-2 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 16, 48, 11, 43)(5, 37, 14, 46, 17, 49, 15, 47)(7, 39, 18, 50, 12, 44, 20, 52)(8, 40, 21, 53, 13, 45, 22, 54)(10, 42, 25, 57, 28, 60, 19, 51)(23, 55, 29, 61, 26, 58, 31, 63)(24, 56, 32, 64, 27, 59, 30, 62)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 71, 103, 83, 115, 72, 104)(68, 100, 76, 108, 89, 121, 77, 109)(70, 102, 80, 112, 92, 124, 81, 113)(73, 105, 87, 119, 79, 111, 88, 120)(75, 107, 90, 122, 78, 110, 91, 123)(82, 114, 93, 125, 86, 118, 94, 126)(84, 116, 95, 127, 85, 117, 96, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 89)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 74)(20, 71)(21, 77)(22, 72)(23, 93)(24, 96)(25, 92)(26, 95)(27, 94)(28, 83)(29, 90)(30, 88)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.364 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.364 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3^4, Y2 * Y1^4, Y1 * Y2 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 12, 44, 3, 35, 8, 40, 17, 49, 5, 37)(4, 36, 14, 46, 20, 52, 22, 54, 11, 43, 18, 50, 24, 56, 10, 42)(6, 38, 16, 48, 21, 53, 9, 41, 13, 45, 26, 58, 30, 62, 19, 51)(15, 47, 28, 60, 31, 63, 29, 61, 25, 57, 23, 55, 32, 64, 27, 59)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 81, 113)(73, 105, 83, 115)(74, 106, 86, 118)(78, 110, 82, 114)(79, 111, 89, 121)(80, 112, 90, 122)(84, 116, 88, 120)(85, 117, 94, 126)(87, 119, 92, 124)(91, 123, 93, 125)(95, 127, 96, 128) L = (1, 68)(2, 73)(3, 75)(4, 79)(5, 80)(6, 65)(7, 84)(8, 83)(9, 87)(10, 66)(11, 89)(12, 90)(13, 67)(14, 76)(15, 70)(16, 93)(17, 88)(18, 69)(19, 92)(20, 95)(21, 71)(22, 72)(23, 74)(24, 96)(25, 77)(26, 91)(27, 78)(28, 86)(29, 82)(30, 81)(31, 85)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.363 Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.365 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1 * Y3 * Y2, (Y1^-1 * R * Y2)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y2, Y3 * Y1^2 * Y3 * Y1^-2, (Y1 * Y2 * Y1^-1 * Y2)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 31, 63, 25, 57, 17, 49, 5, 37)(3, 35, 9, 41, 19, 51, 15, 47, 23, 55, 7, 39, 21, 53, 11, 43)(4, 36, 12, 44, 20, 52, 22, 54, 27, 59, 28, 60, 30, 62, 14, 46)(8, 40, 10, 42, 26, 58, 32, 64, 29, 61, 13, 45, 16, 48, 24, 56)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 77, 109)(69, 101, 79, 111)(70, 102, 83, 115)(72, 104, 78, 110)(73, 105, 89, 121)(74, 106, 91, 123)(75, 107, 82, 114)(76, 108, 90, 122)(80, 112, 92, 124)(81, 113, 85, 117)(84, 116, 88, 120)(86, 118, 93, 125)(87, 119, 95, 127)(94, 126, 96, 128) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 80)(6, 84)(7, 86)(8, 66)(9, 78)(10, 67)(11, 92)(12, 79)(13, 87)(14, 73)(15, 76)(16, 69)(17, 94)(18, 90)(19, 96)(20, 70)(21, 88)(22, 71)(23, 77)(24, 85)(25, 93)(26, 82)(27, 95)(28, 75)(29, 89)(30, 81)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.362 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.366 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y3 * Y1 * Y3, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, (Y1^-1 * Y2 * Y1 * Y2)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 31, 63, 25, 57, 17, 49, 5, 37)(3, 35, 9, 41, 19, 51, 15, 47, 22, 54, 7, 39, 21, 53, 11, 43)(4, 36, 12, 44, 20, 52, 23, 55, 26, 58, 30, 62, 29, 61, 14, 46)(8, 40, 13, 45, 28, 60, 32, 64, 27, 59, 10, 42, 16, 48, 24, 56)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 77, 109)(69, 101, 79, 111)(70, 102, 83, 115)(72, 104, 87, 119)(73, 105, 89, 121)(74, 106, 90, 122)(75, 107, 82, 114)(76, 108, 80, 112)(78, 110, 91, 123)(81, 113, 85, 117)(84, 116, 96, 128)(86, 118, 95, 127)(88, 120, 93, 125)(92, 124, 94, 126) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 80)(6, 84)(7, 78)(8, 66)(9, 87)(10, 67)(11, 76)(12, 75)(13, 86)(14, 71)(15, 94)(16, 69)(17, 93)(18, 92)(19, 88)(20, 70)(21, 96)(22, 77)(23, 73)(24, 83)(25, 91)(26, 95)(27, 89)(28, 82)(29, 81)(30, 79)(31, 90)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.361 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.367 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, Y1^2 * Y3^-1 * Y2, Y3 * Y2 * Y1^-2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1^-3 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 18, 50, 15, 47, 23, 55, 13, 45, 5, 37)(3, 35, 11, 43, 4, 36, 14, 46, 19, 51, 17, 49, 6, 38, 12, 44)(8, 40, 20, 52, 9, 41, 22, 54, 16, 48, 24, 56, 10, 42, 21, 53)(25, 57, 32, 64, 26, 58, 31, 63, 28, 60, 29, 61, 27, 59, 30, 62)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 71, 103)(69, 101, 74, 106)(70, 102, 77, 109)(73, 105, 82, 114)(75, 107, 89, 121)(76, 108, 91, 123)(78, 110, 90, 122)(79, 111, 83, 115)(80, 112, 87, 119)(81, 113, 92, 124)(84, 116, 93, 125)(85, 117, 95, 127)(86, 118, 94, 126)(88, 120, 96, 128) L = (1, 68)(2, 73)(3, 71)(4, 79)(5, 72)(6, 65)(7, 83)(8, 82)(9, 87)(10, 66)(11, 90)(12, 89)(13, 67)(14, 92)(15, 70)(16, 69)(17, 91)(18, 80)(19, 77)(20, 94)(21, 93)(22, 96)(23, 74)(24, 95)(25, 78)(26, 81)(27, 75)(28, 76)(29, 86)(30, 88)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.359 Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.368 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, Y1^-2 * Y3^-1 * Y2, (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, (R * Y1)^2, Y3^4, Y3 * Y2 * Y1^-1 * Y3^-2 * Y1^-1, Y1^4 * Y3^-2, (Y2 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 18, 50, 14, 46, 22, 54, 12, 44, 5, 37)(3, 35, 11, 43, 6, 38, 17, 49, 19, 51, 15, 47, 4, 36, 13, 45)(8, 40, 20, 52, 10, 42, 24, 56, 16, 48, 23, 55, 9, 41, 21, 53)(25, 57, 32, 64, 27, 59, 30, 62, 28, 60, 29, 61, 26, 58, 31, 63)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 76, 108)(69, 101, 73, 105)(70, 102, 71, 103)(74, 106, 82, 114)(75, 107, 89, 121)(77, 109, 90, 122)(78, 110, 83, 115)(79, 111, 92, 124)(80, 112, 86, 118)(81, 113, 91, 123)(84, 116, 93, 125)(85, 117, 94, 126)(87, 119, 96, 128)(88, 120, 95, 127) L = (1, 68)(2, 73)(3, 76)(4, 78)(5, 80)(6, 65)(7, 67)(8, 69)(9, 86)(10, 66)(11, 90)(12, 83)(13, 92)(14, 70)(15, 91)(16, 82)(17, 89)(18, 72)(19, 71)(20, 94)(21, 96)(22, 74)(23, 95)(24, 93)(25, 77)(26, 79)(27, 75)(28, 81)(29, 85)(30, 87)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.360 Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.369 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, Y1^4, Y3^4, (Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 6, 38, 10, 42, 13, 45)(4, 36, 9, 41, 22, 54, 17, 49)(7, 39, 11, 43, 23, 55, 18, 50)(12, 44, 19, 51, 21, 53, 26, 58)(14, 46, 20, 52, 25, 57, 15, 47)(16, 48, 24, 56, 32, 64, 30, 62)(27, 59, 31, 63, 29, 61, 28, 60)(65, 97, 67, 99, 69, 101, 77, 109, 72, 104, 74, 106, 66, 98, 70, 102)(68, 100, 79, 111, 81, 113, 89, 121, 86, 118, 84, 116, 73, 105, 78, 110)(71, 103, 83, 115, 82, 114, 76, 108, 87, 119, 90, 122, 75, 107, 85, 117)(80, 112, 93, 125, 94, 126, 95, 127, 96, 128, 91, 123, 88, 120, 92, 124) L = (1, 68)(2, 73)(3, 76)(4, 80)(5, 81)(6, 83)(7, 65)(8, 86)(9, 88)(10, 85)(11, 66)(12, 91)(13, 90)(14, 67)(15, 77)(16, 71)(17, 94)(18, 69)(19, 95)(20, 70)(21, 93)(22, 96)(23, 72)(24, 75)(25, 74)(26, 92)(27, 78)(28, 79)(29, 89)(30, 82)(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) :: { ( 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 E15.352 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.370 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2, (Y3 * Y2^-1)^2, (Y3^-1, Y1), Y1^4, (R * Y1)^2, (R * Y3)^2, Y3^4, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 17, 49, 6, 38)(4, 36, 10, 42, 22, 54, 16, 48)(7, 39, 11, 43, 23, 55, 18, 50)(12, 44, 24, 56, 21, 53, 19, 51)(13, 45, 14, 46, 25, 57, 20, 52)(15, 47, 26, 58, 32, 64, 30, 62)(27, 59, 28, 60, 29, 61, 31, 63)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 81, 113, 69, 101, 70, 102)(68, 100, 78, 110, 74, 106, 89, 121, 86, 118, 84, 116, 80, 112, 77, 109)(71, 103, 83, 115, 75, 107, 76, 108, 87, 119, 88, 120, 82, 114, 85, 117)(79, 111, 93, 125, 90, 122, 95, 127, 96, 128, 91, 123, 94, 126, 92, 124) L = (1, 68)(2, 74)(3, 76)(4, 79)(5, 80)(6, 83)(7, 65)(8, 86)(9, 88)(10, 90)(11, 66)(12, 91)(13, 67)(14, 73)(15, 71)(16, 94)(17, 85)(18, 69)(19, 95)(20, 70)(21, 93)(22, 96)(23, 72)(24, 92)(25, 81)(26, 75)(27, 77)(28, 78)(29, 89)(30, 82)(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) :: { ( 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 E15.354 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.371 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, (Y2 * Y3^-1)^2, (R * Y3)^2, Y3^4, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y1^4, (Y3^-1, Y1^-1), Y2 * Y3^-2 * Y2 * Y1^-1, Y3 * Y1 * Y2^2 * Y3, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 26, 58, 9, 41)(4, 36, 10, 42, 27, 59, 19, 51)(6, 38, 20, 52, 28, 60, 11, 43)(7, 39, 12, 44, 29, 61, 21, 53)(14, 46, 18, 50, 23, 55, 31, 63)(15, 47, 24, 56, 25, 57, 17, 49)(16, 48, 22, 54, 32, 64, 30, 62)(65, 97, 67, 99, 78, 110, 92, 124, 72, 104, 90, 122, 87, 119, 70, 102)(66, 98, 73, 105, 82, 114, 84, 116, 69, 101, 77, 109, 95, 127, 75, 107)(68, 100, 81, 113, 85, 117, 96, 128, 91, 123, 88, 120, 76, 108, 80, 112)(71, 103, 86, 118, 83, 115, 79, 111, 93, 125, 94, 126, 74, 106, 89, 121) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 83)(6, 86)(7, 65)(8, 91)(9, 81)(10, 87)(11, 80)(12, 66)(13, 88)(14, 85)(15, 75)(16, 67)(17, 92)(18, 71)(19, 78)(20, 96)(21, 69)(22, 77)(23, 76)(24, 70)(25, 84)(26, 89)(27, 95)(28, 94)(29, 72)(30, 73)(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) :: { ( 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 E15.353 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.372 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y3^4, Y1^4, (Y3 * Y2^-1)^2, R * Y2 * Y1 * R * Y2, Y2 * Y1^-1 * Y3^-2 * Y2, Y3 * Y1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y2^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2, Y2 * Y1 * Y3 * Y2^-1 * Y3^-1, Y2^8 ] Map:: polytopal non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 26, 58, 9, 41)(4, 36, 10, 42, 27, 59, 19, 51)(6, 38, 20, 52, 28, 60, 11, 43)(7, 39, 12, 44, 29, 61, 21, 53)(14, 46, 30, 62, 23, 55, 18, 50)(15, 47, 17, 49, 25, 57, 24, 56)(16, 48, 32, 64, 31, 63, 22, 54)(65, 97, 67, 99, 78, 110, 92, 124, 72, 104, 90, 122, 87, 119, 70, 102)(66, 98, 73, 105, 94, 126, 84, 116, 69, 101, 77, 109, 82, 114, 75, 107)(68, 100, 81, 113, 76, 108, 95, 127, 91, 123, 88, 120, 85, 117, 80, 112)(71, 103, 86, 118, 74, 106, 79, 111, 93, 125, 96, 128, 83, 115, 89, 121) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 83)(6, 86)(7, 65)(8, 91)(9, 88)(10, 78)(11, 95)(12, 66)(13, 81)(14, 76)(15, 84)(16, 67)(17, 92)(18, 71)(19, 87)(20, 80)(21, 69)(22, 73)(23, 85)(24, 70)(25, 75)(26, 89)(27, 94)(28, 96)(29, 72)(30, 93)(31, 90)(32, 77)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.351 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.373 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y1^-1)^2, Y1^-1 * Y3 * Y2^-2, Y1^4, Y3 * Y1^-1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y3 * Y2^-1, Y3^4, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3 * Y2^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 27, 59, 16, 48)(4, 36, 10, 42, 21, 53, 14, 46)(6, 38, 19, 51, 24, 56, 9, 41)(7, 39, 12, 44, 23, 55, 18, 50)(11, 43, 26, 58, 30, 62, 20, 52)(15, 47, 22, 54, 32, 64, 28, 60)(17, 49, 25, 57, 31, 63, 29, 61)(65, 97, 67, 99, 78, 110, 92, 124, 95, 127, 90, 122, 76, 108, 70, 102)(66, 98, 73, 105, 68, 100, 80, 112, 93, 125, 96, 128, 87, 119, 75, 107)(69, 101, 79, 111, 85, 117, 94, 126, 89, 121, 83, 115, 71, 103, 77, 109)(72, 104, 84, 116, 74, 106, 88, 120, 81, 113, 91, 123, 82, 114, 86, 118) L = (1, 68)(2, 74)(3, 79)(4, 81)(5, 78)(6, 77)(7, 65)(8, 85)(9, 67)(10, 89)(11, 70)(12, 66)(13, 86)(14, 93)(15, 84)(16, 92)(17, 71)(18, 69)(19, 91)(20, 73)(21, 95)(22, 75)(23, 72)(24, 80)(25, 76)(26, 83)(27, 96)(28, 94)(29, 82)(30, 88)(31, 87)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.349 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.374 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y2^-2, (Y3 * Y2^-1)^2, Y2^2 * Y3^-1 * Y1^-1, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, Y3 * Y2 * Y1^-1 * Y2^-1, Y1^4, Y3^4, Y3^-2 * Y2^-2 * Y3^-1 * Y1, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 26, 58, 11, 43)(4, 36, 10, 42, 21, 53, 16, 48)(6, 38, 14, 46, 27, 59, 19, 51)(7, 39, 12, 44, 23, 55, 18, 50)(9, 41, 24, 56, 32, 64, 22, 54)(15, 47, 25, 57, 31, 63, 28, 60)(17, 49, 20, 52, 30, 62, 29, 61)(65, 97, 67, 99, 74, 106, 88, 120, 95, 127, 93, 125, 82, 114, 70, 102)(66, 98, 73, 105, 85, 117, 94, 126, 92, 124, 83, 115, 71, 103, 75, 107)(68, 100, 77, 109, 89, 121, 96, 128, 87, 119, 81, 113, 69, 101, 78, 110)(72, 104, 84, 116, 80, 112, 91, 123, 79, 111, 90, 122, 76, 108, 86, 118) L = (1, 68)(2, 74)(3, 73)(4, 79)(5, 80)(6, 75)(7, 65)(8, 85)(9, 84)(10, 89)(11, 86)(12, 66)(13, 88)(14, 67)(15, 71)(16, 92)(17, 70)(18, 69)(19, 90)(20, 78)(21, 95)(22, 81)(23, 72)(24, 94)(25, 76)(26, 96)(27, 77)(28, 82)(29, 83)(30, 91)(31, 87)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.350 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.375 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y3 * Y2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^4, Y3^4, (Y2^-1 * Y1^-1)^2, Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-2, Y3^-2 * Y2 * Y1^2 * Y2^-1, Y2^-1 * Y1^2 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 28, 60, 15, 47)(4, 36, 10, 42, 23, 55, 18, 50)(6, 38, 14, 46, 27, 59, 9, 41)(7, 39, 12, 44, 25, 57, 20, 52)(11, 43, 26, 58, 21, 53, 22, 54)(16, 48, 30, 62, 19, 51, 24, 56)(17, 49, 29, 61, 32, 64, 31, 63)(65, 97, 67, 99, 76, 108, 94, 126, 96, 128, 90, 122, 82, 114, 70, 102)(66, 98, 73, 105, 89, 121, 79, 111, 95, 127, 80, 112, 68, 100, 75, 107)(69, 101, 83, 115, 71, 103, 85, 117, 93, 125, 78, 110, 87, 119, 77, 109)(72, 104, 86, 118, 84, 116, 91, 123, 81, 113, 92, 124, 74, 106, 88, 120) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 85)(7, 65)(8, 87)(9, 90)(10, 93)(11, 94)(12, 66)(13, 91)(14, 86)(15, 70)(16, 67)(17, 71)(18, 95)(19, 92)(20, 69)(21, 88)(22, 80)(23, 96)(24, 79)(25, 72)(26, 83)(27, 75)(28, 73)(29, 76)(30, 77)(31, 84)(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) :: { ( 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 E15.347 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.376 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-2 * Y1^-1, Y1^4, (Y3^-1 * Y2)^2, (Y3, Y1), (R * Y1)^2, Y3^4, (Y2 * Y1^-1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1, Y3 * Y2^-1 * Y1 * Y2 * Y1^-2, Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y1^-2, Y2^-1 * Y1 * Y3^2 * Y2^-1 * Y1^-1, (Y2 * Y1 * Y2^-1 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 27, 59, 11, 43)(4, 36, 10, 42, 23, 55, 19, 51)(6, 38, 20, 52, 30, 62, 15, 47)(7, 39, 12, 44, 25, 57, 14, 46)(9, 41, 26, 58, 16, 48, 24, 56)(17, 49, 22, 54, 21, 53, 28, 60)(18, 50, 29, 61, 32, 64, 31, 63)(65, 97, 67, 99, 78, 110, 90, 122, 96, 128, 92, 124, 74, 106, 70, 102)(66, 98, 73, 105, 71, 103, 85, 117, 95, 127, 79, 111, 87, 119, 75, 107)(68, 100, 81, 113, 69, 101, 84, 116, 89, 121, 77, 109, 93, 125, 80, 112)(72, 104, 86, 118, 76, 108, 94, 126, 82, 114, 91, 123, 83, 115, 88, 120) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 83)(6, 85)(7, 65)(8, 87)(9, 91)(10, 93)(11, 94)(12, 66)(13, 70)(14, 69)(15, 86)(16, 67)(17, 90)(18, 71)(19, 95)(20, 92)(21, 88)(22, 80)(23, 96)(24, 77)(25, 72)(26, 75)(27, 84)(28, 73)(29, 76)(30, 81)(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) :: { ( 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 E15.348 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.377 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y2^-1, Y3^-1 * Y1^-2 * Y2, Y2 * Y1^2 * Y3^-1, (Y3^-1 * Y2)^2, Y1 * Y2^-1 * Y3 * Y1, (R * Y2)^2, Y2^-2 * Y3^-1 * Y2^-1, Y1^-2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1 * Y2^-1)^2, (Y3^-1 * Y2^-1 * Y1^-1)^2, (Y2^-1 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 4, 36, 16, 48)(6, 38, 17, 49, 7, 39, 18, 50)(9, 41, 19, 51, 10, 42, 22, 54)(11, 43, 23, 55, 12, 44, 24, 56)(14, 46, 20, 52, 15, 47, 21, 53)(25, 57, 30, 62, 26, 58, 29, 61)(27, 59, 32, 64, 28, 60, 31, 63)(65, 97, 67, 99, 78, 110, 71, 103, 72, 104, 68, 100, 79, 111, 70, 102)(66, 98, 73, 105, 84, 116, 76, 108, 69, 101, 74, 106, 85, 117, 75, 107)(77, 109, 89, 121, 82, 114, 92, 124, 80, 112, 90, 122, 81, 113, 91, 123)(83, 115, 93, 125, 88, 120, 96, 128, 86, 118, 94, 126, 87, 119, 95, 127) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 73)(6, 72)(7, 65)(8, 67)(9, 85)(10, 84)(11, 69)(12, 66)(13, 90)(14, 70)(15, 71)(16, 89)(17, 92)(18, 91)(19, 94)(20, 75)(21, 76)(22, 93)(23, 96)(24, 95)(25, 81)(26, 82)(27, 80)(28, 77)(29, 87)(30, 88)(31, 86)(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) :: { ( 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 E15.355 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.378 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^2, Y3^-1 * Y2^-3, (Y3, Y2^-1), (R * Y1)^2, Y1^4, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, (Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 17, 49, 20, 52, 12, 44)(6, 38, 18, 50, 23, 55, 10, 42)(7, 39, 19, 51, 22, 54, 9, 41)(14, 46, 24, 56, 30, 62, 28, 60)(15, 47, 25, 57, 31, 63, 29, 61)(16, 48, 26, 58, 32, 64, 27, 59)(65, 97, 67, 99, 78, 110, 71, 103, 80, 112, 68, 100, 79, 111, 70, 102)(66, 98, 73, 105, 88, 120, 76, 108, 90, 122, 74, 106, 89, 121, 75, 107)(69, 101, 82, 114, 92, 124, 77, 109, 91, 123, 83, 115, 93, 125, 81, 113)(72, 104, 84, 116, 94, 126, 87, 119, 96, 128, 85, 117, 95, 127, 86, 118) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 83)(6, 80)(7, 65)(8, 85)(9, 89)(10, 88)(11, 90)(12, 66)(13, 69)(14, 70)(15, 71)(16, 67)(17, 91)(18, 93)(19, 92)(20, 95)(21, 94)(22, 96)(23, 72)(24, 75)(25, 76)(26, 73)(27, 82)(28, 81)(29, 77)(30, 86)(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) :: { ( 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 E15.356 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.379 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y1^-1)^2, Y2 * Y3^-1 * Y1^2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y2, (Y1^-1 * Y3)^2, Y2^-2 * Y3^-2, (R * Y1)^2, Y1 * Y2^-1 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, (Y3 * Y1)^4, Y3^-2 * Y2^6 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 29, 61, 16, 48)(4, 36, 11, 43, 27, 59, 12, 44)(6, 38, 19, 51, 7, 39, 9, 41)(10, 42, 21, 53, 31, 63, 22, 54)(14, 46, 23, 55, 17, 49, 25, 57)(15, 47, 24, 56, 18, 50, 26, 58)(20, 52, 28, 60, 32, 64, 30, 62)(65, 97, 67, 99, 78, 110, 86, 118, 96, 128, 91, 123, 82, 114, 70, 102)(66, 98, 73, 105, 87, 119, 80, 112, 94, 126, 95, 127, 90, 122, 75, 107)(68, 100, 81, 113, 71, 103, 84, 116, 93, 125, 79, 111, 85, 117, 72, 104)(69, 101, 74, 106, 89, 121, 76, 108, 92, 124, 83, 115, 88, 120, 77, 109) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 73)(6, 84)(7, 65)(8, 67)(9, 88)(10, 90)(11, 92)(12, 66)(13, 94)(14, 71)(15, 70)(16, 69)(17, 86)(18, 85)(19, 87)(20, 91)(21, 96)(22, 72)(23, 76)(24, 75)(25, 80)(26, 77)(27, 81)(28, 95)(29, 78)(30, 83)(31, 89)(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, 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 E15.357 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.380 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y1^-2, Y2^-1 * Y3 * Y1^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y2 * Y1 * Y3 * Y1^-1, Y2^-2 * Y3^-2, (R * Y1)^2, Y3 * Y2^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-2 * Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y1^-1 * Y3 * Y2 * Y3^-2 * Y1^-1, Y3^-3 * Y1^2 * Y2^3 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 4, 36, 15, 47)(6, 38, 10, 42, 25, 57, 9, 41)(7, 39, 20, 52, 29, 61, 19, 51)(11, 43, 22, 54, 31, 63, 21, 53)(13, 45, 23, 55, 14, 46, 24, 56)(16, 48, 26, 58, 32, 64, 30, 62)(17, 49, 27, 59, 18, 50, 28, 60)(65, 97, 67, 99, 77, 109, 93, 125, 96, 128, 86, 118, 82, 114, 70, 102)(66, 98, 73, 105, 87, 119, 79, 111, 94, 126, 84, 116, 92, 124, 75, 107)(68, 100, 81, 113, 71, 103, 72, 104, 85, 117, 78, 110, 89, 121, 80, 112)(69, 101, 83, 115, 88, 120, 95, 127, 90, 122, 74, 106, 91, 123, 76, 108) L = (1, 68)(2, 74)(3, 78)(4, 82)(5, 84)(6, 72)(7, 65)(8, 86)(9, 88)(10, 92)(11, 69)(12, 66)(13, 71)(14, 70)(15, 90)(16, 67)(17, 93)(18, 89)(19, 87)(20, 91)(21, 77)(22, 81)(23, 76)(24, 75)(25, 96)(26, 73)(27, 79)(28, 95)(29, 80)(30, 83)(31, 94)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.358 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.381 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x Q16 (small group id <32, 41>) Aut = C2 x ((C8 x C2) : C2) (small group id <64, 253>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2 ] 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, 18, 50)(12, 44, 19, 51)(13, 45, 20, 52)(14, 46, 21, 53)(15, 47, 22, 54)(16, 48, 23, 55)(17, 49, 24, 56)(25, 57, 29, 61)(26, 58, 30, 62)(27, 59, 31, 63)(28, 60, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 82, 114, 73, 105)(68, 100, 77, 109, 89, 121, 79, 111)(70, 102, 76, 108, 90, 122, 80, 112)(72, 104, 84, 116, 93, 125, 86, 118)(74, 106, 83, 115, 94, 126, 87, 119)(78, 110, 92, 124, 81, 113, 91, 123)(85, 117, 96, 128, 88, 120, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 80)(6, 65)(7, 83)(8, 85)(9, 87)(10, 66)(11, 89)(12, 91)(13, 67)(14, 90)(15, 69)(16, 92)(17, 70)(18, 93)(19, 95)(20, 71)(21, 94)(22, 73)(23, 96)(24, 74)(25, 81)(26, 75)(27, 79)(28, 77)(29, 88)(30, 82)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.392 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.382 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x QD16 (small group id <32, 40>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-2 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-2 * Y2^2, (R * Y3)^2, (Y2^-1 * Y1)^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 15, 47)(8, 40, 19, 51)(10, 42, 20, 52)(11, 43, 16, 48)(12, 44, 21, 53)(13, 45, 22, 54)(17, 49, 25, 57)(18, 50, 26, 58)(23, 55, 28, 60)(24, 56, 27, 59)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 80, 112, 73, 105)(68, 100, 77, 109, 70, 102, 76, 108)(72, 104, 82, 114, 74, 106, 81, 113)(78, 110, 85, 117, 79, 111, 86, 118)(83, 115, 89, 121, 84, 116, 90, 122)(87, 119, 94, 126, 88, 120, 93, 125)(91, 123, 96, 128, 92, 124, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 75)(5, 77)(6, 65)(7, 81)(8, 80)(9, 82)(10, 66)(11, 70)(12, 69)(13, 67)(14, 87)(15, 88)(16, 74)(17, 73)(18, 71)(19, 91)(20, 92)(21, 93)(22, 94)(23, 79)(24, 78)(25, 95)(26, 96)(27, 84)(28, 83)(29, 86)(30, 85)(31, 90)(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 ) } Outer automorphisms :: reflexible Dual of E15.393 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.383 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x QD16 (small group id <32, 40>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, Y3 * Y2^-2 * Y3, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, R * Y2 * R * Y2^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 15, 47)(5, 37, 16, 48)(6, 38, 17, 49)(7, 39, 18, 50)(8, 40, 22, 54)(9, 41, 23, 55)(10, 42, 24, 56)(12, 44, 19, 51)(13, 45, 21, 53)(14, 46, 20, 52)(25, 57, 31, 63)(26, 58, 30, 62)(27, 59, 29, 61)(28, 60, 32, 64)(65, 97, 67, 99, 76, 108, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 78, 110, 70, 102, 77, 109)(72, 104, 85, 117, 74, 106, 84, 116)(75, 107, 89, 121, 80, 112, 91, 123)(79, 111, 90, 122, 81, 113, 92, 124)(82, 114, 93, 125, 87, 119, 95, 127)(86, 118, 94, 126, 88, 120, 96, 128) L = (1, 68)(2, 72)(3, 77)(4, 76)(5, 78)(6, 65)(7, 84)(8, 83)(9, 85)(10, 66)(11, 90)(12, 70)(13, 69)(14, 67)(15, 91)(16, 92)(17, 89)(18, 94)(19, 74)(20, 73)(21, 71)(22, 95)(23, 96)(24, 93)(25, 79)(26, 80)(27, 81)(28, 75)(29, 86)(30, 87)(31, 88)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.394 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.384 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2 * Y2^-2, Y2^-2 * Y3^-2, Y3^-1 * Y2^2 * Y3^-1, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y3)^2, Y2^4, R * Y2 * R * Y2^-1, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3^-1 * Y1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 15, 47)(5, 37, 16, 48)(6, 38, 17, 49)(7, 39, 18, 50)(8, 40, 22, 54)(9, 41, 23, 55)(10, 42, 24, 56)(12, 44, 19, 51)(13, 45, 20, 52)(14, 46, 21, 53)(25, 57, 31, 63)(26, 58, 32, 64)(27, 59, 29, 61)(28, 60, 30, 62)(65, 97, 67, 99, 76, 108, 69, 101)(66, 98, 71, 103, 83, 115, 73, 105)(68, 100, 78, 110, 70, 102, 77, 109)(72, 104, 85, 117, 74, 106, 84, 116)(75, 107, 89, 121, 80, 112, 91, 123)(79, 111, 92, 124, 81, 113, 90, 122)(82, 114, 93, 125, 87, 119, 95, 127)(86, 118, 96, 128, 88, 120, 94, 126) L = (1, 68)(2, 72)(3, 77)(4, 76)(5, 78)(6, 65)(7, 84)(8, 83)(9, 85)(10, 66)(11, 90)(12, 70)(13, 69)(14, 67)(15, 89)(16, 92)(17, 91)(18, 94)(19, 74)(20, 73)(21, 71)(22, 93)(23, 96)(24, 95)(25, 81)(26, 80)(27, 79)(28, 75)(29, 88)(30, 87)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.395 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.385 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y2 * Y1 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, Y2^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2^2 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-3 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 14, 46)(5, 37, 9, 41)(6, 38, 18, 50)(8, 40, 23, 55)(10, 42, 27, 59)(11, 43, 20, 52)(12, 44, 26, 58)(13, 45, 25, 57)(15, 47, 24, 56)(16, 48, 22, 54)(17, 49, 21, 53)(19, 51, 28, 60)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 84, 116, 73, 105)(68, 100, 77, 109, 87, 119, 80, 112)(70, 102, 76, 108, 91, 123, 81, 113)(72, 104, 86, 118, 78, 110, 89, 121)(74, 106, 85, 117, 82, 114, 90, 122)(79, 111, 94, 126, 83, 115, 93, 125)(88, 120, 96, 128, 92, 124, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 85)(8, 88)(9, 90)(10, 66)(11, 87)(12, 93)(13, 67)(14, 92)(15, 91)(16, 69)(17, 94)(18, 84)(19, 70)(20, 78)(21, 95)(22, 71)(23, 83)(24, 82)(25, 73)(26, 96)(27, 75)(28, 74)(29, 80)(30, 77)(31, 89)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.396 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.386 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y1^4, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y2^4, R * Y2 * R * Y2^-1, Y1^-1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y3)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^4 * 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, 12, 44)(7, 39, 18, 50, 22, 54, 10, 42)(13, 45, 27, 59, 16, 48, 24, 56)(14, 46, 25, 57, 19, 51, 23, 55)(17, 49, 28, 60, 20, 52, 26, 58)(29, 61, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 80, 112, 85, 117, 77, 109)(71, 103, 83, 115, 86, 118, 78, 110)(74, 106, 89, 121, 82, 114, 87, 119)(76, 108, 91, 123, 79, 111, 88, 120)(81, 113, 93, 125, 84, 116, 94, 126)(90, 122, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 81)(5, 82)(6, 80)(7, 65)(8, 85)(9, 87)(10, 90)(11, 89)(12, 66)(13, 93)(14, 67)(15, 69)(16, 94)(17, 86)(18, 92)(19, 70)(20, 71)(21, 84)(22, 72)(23, 95)(24, 73)(25, 96)(26, 79)(27, 75)(28, 76)(29, 83)(30, 78)(31, 91)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.389 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.387 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x QD16 (small group id <32, 40>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, Y2^-2 * Y1^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, Y2^4, Y2^-1 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3, Y3^3 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 6, 38, 9, 41)(4, 36, 15, 47, 21, 53, 12, 44)(7, 39, 18, 50, 22, 54, 10, 42)(13, 45, 24, 56, 17, 49, 27, 59)(14, 46, 23, 55, 19, 51, 26, 58)(16, 48, 28, 60, 20, 52, 25, 57)(29, 61, 31, 63, 30, 62, 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, 82, 114, 90, 122)(76, 108, 88, 120, 79, 111, 91, 123)(80, 112, 93, 125, 84, 116, 94, 126)(89, 121, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 80)(5, 82)(6, 81)(7, 65)(8, 85)(9, 87)(10, 89)(11, 90)(12, 66)(13, 93)(14, 67)(15, 69)(16, 86)(17, 94)(18, 92)(19, 70)(20, 71)(21, 84)(22, 72)(23, 95)(24, 73)(25, 79)(26, 96)(27, 75)(28, 76)(29, 83)(30, 78)(31, 91)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.390 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.388 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2 * Y3 * Y2, Y1^4, Y2^-1 * Y1 * Y2 * Y1, Y2^4, (R * Y3)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y2^2 * Y1, (R * Y1)^2, R * Y2 * R * Y2^-1, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y3)^2, Y2^2 * Y3^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 6, 38, 9, 41)(4, 36, 15, 47, 21, 53, 12, 44)(7, 39, 18, 50, 22, 54, 10, 42)(13, 45, 24, 56, 16, 48, 27, 59)(14, 46, 23, 55, 19, 51, 25, 57)(17, 49, 28, 60, 20, 52, 26, 58)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 80, 112, 85, 117, 77, 109)(71, 103, 83, 115, 86, 118, 78, 110)(74, 106, 89, 121, 82, 114, 87, 119)(76, 108, 91, 123, 79, 111, 88, 120)(81, 113, 93, 125, 84, 116, 94, 126)(90, 122, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 81)(5, 82)(6, 80)(7, 65)(8, 85)(9, 87)(10, 90)(11, 89)(12, 66)(13, 93)(14, 67)(15, 69)(16, 94)(17, 86)(18, 92)(19, 70)(20, 71)(21, 84)(22, 72)(23, 95)(24, 73)(25, 96)(26, 79)(27, 75)(28, 76)(29, 83)(30, 78)(31, 91)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.391 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.389 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1^3 * Y3 * Y1^-1, (R * Y2 * Y3)^2, (Y3 * Y1^-2)^2, Y1^8, (Y3 * Y1)^4, (Y3 * Y2)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 16, 48, 28, 60, 27, 59, 15, 47, 5, 37)(3, 35, 9, 41, 23, 55, 32, 64, 26, 58, 29, 61, 17, 49, 7, 39)(4, 36, 11, 43, 22, 54, 8, 40, 20, 52, 14, 46, 18, 50, 13, 45)(10, 42, 21, 53, 30, 62, 24, 56, 12, 44, 19, 51, 31, 63, 25, 57)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 76, 108)(69, 101, 73, 105)(70, 102, 81, 113)(72, 104, 85, 117)(74, 106, 84, 116)(75, 107, 88, 120)(77, 109, 83, 115)(78, 110, 89, 121)(79, 111, 87, 119)(80, 112, 93, 125)(82, 114, 95, 127)(86, 118, 94, 126)(90, 122, 92, 124)(91, 123, 96, 128) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 78)(6, 82)(7, 83)(8, 66)(9, 88)(10, 67)(11, 80)(12, 90)(13, 91)(14, 69)(15, 86)(16, 75)(17, 94)(18, 70)(19, 71)(20, 92)(21, 96)(22, 79)(23, 95)(24, 73)(25, 93)(26, 76)(27, 77)(28, 84)(29, 89)(30, 81)(31, 87)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.386 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.390 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x QD16 (small group id <32, 40>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y2 * Y1^-1 * R * Y2 * R * Y1^-1, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^-3, Y3 * Y1 * Y3 * Y1^-3, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 30, 62, 29, 61, 17, 49, 5, 37)(3, 35, 9, 41, 23, 55, 7, 39, 21, 53, 15, 47, 19, 51, 11, 43)(4, 36, 12, 44, 26, 58, 8, 40, 24, 56, 16, 48, 20, 52, 14, 46)(10, 42, 22, 54, 31, 63, 27, 59, 13, 45, 25, 57, 32, 64, 28, 60)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 77, 109)(69, 101, 79, 111)(70, 102, 83, 115)(72, 104, 89, 121)(73, 105, 82, 114)(74, 106, 88, 120)(75, 107, 93, 125)(76, 108, 92, 124)(78, 110, 86, 118)(80, 112, 91, 123)(81, 113, 87, 119)(84, 116, 96, 128)(85, 117, 94, 126)(90, 122, 95, 127) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 80)(6, 84)(7, 86)(8, 66)(9, 91)(10, 67)(11, 89)(12, 82)(13, 85)(14, 93)(15, 92)(16, 69)(17, 90)(18, 76)(19, 95)(20, 70)(21, 77)(22, 71)(23, 96)(24, 94)(25, 75)(26, 81)(27, 73)(28, 79)(29, 78)(30, 88)(31, 83)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.387 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.391 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^4, (Y2 * Y1^2)^2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, Y1^-1 * Y2 * Y1 * Y2 * Y1^-2, Y1^-2 * Y3^-2 * Y1^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 20, 52, 16, 48, 28, 60, 18, 50, 5, 37)(3, 35, 11, 43, 26, 58, 8, 40, 24, 56, 17, 49, 21, 53, 13, 45)(4, 36, 15, 47, 23, 55, 10, 42, 6, 38, 19, 51, 22, 54, 9, 41)(12, 44, 27, 59, 31, 63, 30, 62, 14, 46, 25, 57, 32, 64, 29, 61)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 76, 108)(69, 101, 81, 113)(70, 102, 78, 110)(71, 103, 85, 117)(73, 105, 89, 121)(74, 106, 91, 123)(75, 107, 84, 116)(77, 109, 92, 124)(79, 111, 94, 126)(80, 112, 88, 120)(82, 114, 90, 122)(83, 115, 93, 125)(86, 118, 95, 127)(87, 119, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 80)(5, 79)(6, 65)(7, 86)(8, 89)(9, 92)(10, 66)(11, 93)(12, 88)(13, 91)(14, 67)(15, 84)(16, 70)(17, 94)(18, 87)(19, 69)(20, 83)(21, 95)(22, 82)(23, 71)(24, 78)(25, 77)(26, 96)(27, 72)(28, 74)(29, 81)(30, 75)(31, 90)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.388 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.392 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x Q16 (small group id <32, 41>) Aut = C2 x ((C8 x C2) : C2) (small group id <64, 253>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y3)^2, Y3^-2 * Y2^2, Y3 * Y1^-1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, (Y2^-1, Y3^-1), Y1^4, Y3 * Y2 * Y3 * Y2 * Y1^-2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 22, 54, 15, 47)(4, 36, 12, 44, 23, 55, 17, 49)(6, 38, 9, 41, 24, 56, 18, 50)(7, 39, 10, 42, 25, 57, 19, 51)(13, 45, 29, 61, 20, 52, 26, 58)(14, 46, 30, 62, 21, 53, 27, 59)(16, 48, 28, 60, 32, 64, 31, 63)(65, 97, 67, 99, 77, 109, 88, 120, 72, 104, 86, 118, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 79, 111, 69, 101, 82, 114, 93, 125, 75, 107)(68, 100, 78, 110, 89, 121, 96, 128, 87, 119, 85, 117, 71, 103, 80, 112)(74, 106, 91, 123, 81, 113, 95, 127, 83, 115, 94, 126, 76, 108, 92, 124) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 89)(14, 88)(15, 95)(16, 67)(17, 69)(18, 94)(19, 93)(20, 71)(21, 70)(22, 85)(23, 84)(24, 96)(25, 72)(26, 81)(27, 79)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.381 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.393 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x QD16 (small group id <32, 40>) Aut = C2 x ((C2 x D8) : C2) (small group id <64, 254>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y3 * Y1^-1, Y3^4, Y1^4, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1 * Y3^2 * Y1, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, Y3^-2 * Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-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, 28, 60, 20, 52, 23, 55)(15, 47, 27, 59, 16, 48, 26, 58)(17, 49, 25, 57, 19, 51, 24, 56)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 78, 110, 86, 118, 72, 104, 85, 117, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 77, 109, 69, 101, 82, 114, 92, 124, 75, 107)(68, 100, 81, 113, 94, 126, 79, 111, 71, 103, 83, 115, 93, 125, 80, 112)(74, 106, 90, 122, 96, 128, 88, 120, 76, 108, 91, 123, 95, 127, 89, 121) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 83)(7, 65)(8, 71)(9, 88)(10, 69)(11, 91)(12, 66)(13, 90)(14, 93)(15, 85)(16, 67)(17, 70)(18, 89)(19, 86)(20, 94)(21, 80)(22, 81)(23, 95)(24, 82)(25, 73)(26, 75)(27, 77)(28, 96)(29, 84)(30, 78)(31, 92)(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, 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 E15.382 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.394 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = C2 x QD16 (small group id <32, 40>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y1^-1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y2^-1, Y1), (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (Y2^-1 * Y3^-1)^2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y2 * Y3 * Y1^-1 * Y2, Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-2, Y2^2 * R * Y2 * R * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 15, 47)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 11, 43, 22, 54, 18, 50)(13, 45, 23, 55, 20, 52, 28, 60)(14, 46, 25, 57, 16, 48, 24, 56)(17, 49, 27, 59, 19, 51, 26, 58)(29, 61, 32, 64, 30, 62, 31, 63)(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, 79, 111, 92, 124, 75, 107)(68, 100, 81, 113, 94, 126, 78, 110, 71, 103, 83, 115, 93, 125, 80, 112)(74, 106, 90, 122, 96, 128, 88, 120, 76, 108, 91, 123, 95, 127, 89, 121) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 83)(7, 65)(8, 71)(9, 88)(10, 69)(11, 91)(12, 66)(13, 93)(14, 85)(15, 89)(16, 67)(17, 70)(18, 90)(19, 86)(20, 94)(21, 80)(22, 81)(23, 95)(24, 79)(25, 73)(26, 75)(27, 82)(28, 96)(29, 84)(30, 77)(31, 92)(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, 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 E15.383 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.395 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y1^4, (Y2^-1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 9, 41)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 18, 50, 22, 54, 11, 43)(14, 46, 23, 55, 20, 52, 28, 60)(15, 47, 24, 56, 16, 48, 25, 57)(17, 49, 26, 58, 19, 51, 27, 59)(29, 61, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 78, 110, 86, 118, 72, 104, 85, 117, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 82, 114, 69, 101, 77, 109, 92, 124, 75, 107)(68, 100, 81, 113, 94, 126, 79, 111, 71, 103, 83, 115, 93, 125, 80, 112)(74, 106, 90, 122, 96, 128, 88, 120, 76, 108, 91, 123, 95, 127, 89, 121) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 83)(7, 65)(8, 71)(9, 88)(10, 69)(11, 91)(12, 66)(13, 89)(14, 93)(15, 85)(16, 67)(17, 70)(18, 90)(19, 86)(20, 94)(21, 80)(22, 81)(23, 95)(24, 77)(25, 73)(26, 75)(27, 82)(28, 96)(29, 84)(30, 78)(31, 92)(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, 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 E15.384 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.396 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x QD16) : C2 (small group id <64, 258>) |r| :: 2 Presentation :: [ R^2, Y1^4, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y3)^2, Y1^4, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-1, Y3^-2 * Y2^-2, Y3^-2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y2^-2 * Y1^2 * Y3^2, Y2^-1 * Y3^-1 * Y2 * Y3 * Y1^-2, (Y2^-1 * Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1 * Y1^-1)^2, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 23, 55, 15, 47)(4, 36, 12, 44, 24, 56, 19, 51)(6, 38, 9, 41, 25, 57, 20, 52)(7, 39, 10, 42, 26, 58, 21, 53)(13, 45, 31, 63, 18, 50, 27, 59)(14, 46, 28, 60, 17, 49, 30, 62)(16, 48, 32, 64, 22, 54, 29, 61)(65, 97, 67, 99, 77, 109, 89, 121, 72, 104, 87, 119, 82, 114, 70, 102)(66, 98, 73, 105, 91, 123, 79, 111, 69, 101, 84, 116, 95, 127, 75, 107)(68, 100, 81, 113, 71, 103, 86, 118, 88, 120, 78, 110, 90, 122, 80, 112)(74, 106, 94, 126, 76, 108, 96, 128, 85, 117, 92, 124, 83, 115, 93, 125) L = (1, 68)(2, 74)(3, 78)(4, 82)(5, 85)(6, 86)(7, 65)(8, 88)(9, 92)(10, 95)(11, 96)(12, 66)(13, 71)(14, 70)(15, 93)(16, 67)(17, 89)(18, 90)(19, 69)(20, 94)(21, 91)(22, 87)(23, 81)(24, 77)(25, 80)(26, 72)(27, 76)(28, 75)(29, 73)(30, 79)(31, 83)(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, 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 E15.385 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.397 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 256>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3^-1 * Y2, Y3^-2 * Y2^-2, (R * Y1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4, (R * Y3)^2, R * Y2 * R * Y2^-1, Y2 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 14, 46)(5, 37, 9, 41)(6, 38, 15, 47)(8, 40, 19, 51)(10, 42, 20, 52)(11, 43, 16, 48)(12, 44, 21, 53)(13, 45, 22, 54)(17, 49, 25, 57)(18, 50, 26, 58)(23, 55, 28, 60)(24, 56, 27, 59)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 80, 112, 73, 105)(68, 100, 77, 109, 70, 102, 76, 108)(72, 104, 82, 114, 74, 106, 81, 113)(78, 110, 86, 118, 79, 111, 85, 117)(83, 115, 90, 122, 84, 116, 89, 121)(87, 119, 93, 125, 88, 120, 94, 126)(91, 123, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 72)(3, 76)(4, 75)(5, 77)(6, 65)(7, 81)(8, 80)(9, 82)(10, 66)(11, 70)(12, 69)(13, 67)(14, 87)(15, 88)(16, 74)(17, 73)(18, 71)(19, 91)(20, 92)(21, 93)(22, 94)(23, 79)(24, 78)(25, 95)(26, 96)(27, 84)(28, 83)(29, 86)(30, 85)(31, 90)(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 ) } Outer automorphisms :: reflexible Dual of E15.408 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.398 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 256>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y3 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^-1 * Y1 * Y3 * Y1, Y3^-1 * Y2^-2 * Y1 * Y3 * Y1, Y2^-1 * Y3^-4 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 14, 46)(5, 37, 7, 39)(6, 38, 18, 50)(8, 40, 23, 55)(10, 42, 27, 59)(11, 43, 20, 52)(12, 44, 21, 53)(13, 45, 22, 54)(15, 47, 24, 56)(16, 48, 25, 57)(17, 49, 26, 58)(19, 51, 28, 60)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 84, 116, 73, 105)(68, 100, 77, 109, 87, 119, 80, 112)(70, 102, 76, 108, 91, 123, 81, 113)(72, 104, 86, 118, 78, 110, 89, 121)(74, 106, 85, 117, 82, 114, 90, 122)(79, 111, 94, 126, 83, 115, 93, 125)(88, 120, 96, 128, 92, 124, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 79)(5, 81)(6, 65)(7, 85)(8, 88)(9, 90)(10, 66)(11, 87)(12, 93)(13, 67)(14, 92)(15, 91)(16, 69)(17, 94)(18, 84)(19, 70)(20, 78)(21, 95)(22, 71)(23, 83)(24, 82)(25, 73)(26, 96)(27, 75)(28, 74)(29, 80)(30, 77)(31, 89)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.409 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.399 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2 * Y1 * Y3 * Y1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 11, 43)(5, 37, 8, 40)(7, 39, 15, 47)(9, 41, 13, 45)(10, 42, 18, 50)(12, 44, 20, 52)(14, 46, 22, 54)(16, 48, 24, 56)(17, 49, 25, 57)(19, 51, 27, 59)(21, 53, 29, 61)(23, 55, 31, 63)(26, 58, 32, 64)(28, 60, 30, 62)(65, 97, 67, 99, 73, 105, 69, 101)(66, 98, 70, 102, 77, 109, 72, 104)(68, 100, 74, 106, 81, 113, 76, 108)(71, 103, 78, 110, 85, 117, 80, 112)(75, 107, 82, 114, 89, 121, 84, 116)(79, 111, 86, 118, 93, 125, 88, 120)(83, 115, 90, 122, 95, 127, 92, 124)(87, 119, 94, 126, 91, 123, 96, 128) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 76)(6, 78)(7, 66)(8, 80)(9, 81)(10, 67)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 73)(18, 90)(19, 75)(20, 92)(21, 77)(22, 94)(23, 79)(24, 96)(25, 95)(26, 82)(27, 93)(28, 84)(29, 91)(30, 86)(31, 89)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.411 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.400 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 8, 40)(4, 36, 11, 43)(5, 37, 6, 38)(7, 39, 15, 47)(9, 41, 13, 45)(10, 42, 18, 50)(12, 44, 19, 51)(14, 46, 22, 54)(16, 48, 23, 55)(17, 49, 25, 57)(20, 52, 28, 60)(21, 53, 29, 61)(24, 56, 32, 64)(26, 58, 30, 62)(27, 59, 31, 63)(65, 97, 67, 99, 73, 105, 69, 101)(66, 98, 70, 102, 77, 109, 72, 104)(68, 100, 74, 106, 81, 113, 76, 108)(71, 103, 78, 110, 85, 117, 80, 112)(75, 107, 83, 115, 89, 121, 82, 114)(79, 111, 87, 119, 93, 125, 86, 118)(84, 116, 91, 123, 96, 128, 90, 122)(88, 120, 95, 127, 92, 124, 94, 126) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 76)(6, 78)(7, 66)(8, 80)(9, 81)(10, 67)(11, 84)(12, 69)(13, 85)(14, 70)(15, 88)(16, 72)(17, 73)(18, 90)(19, 91)(20, 75)(21, 77)(22, 94)(23, 95)(24, 79)(25, 96)(26, 82)(27, 83)(28, 93)(29, 92)(30, 86)(31, 87)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.413 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.401 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |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 * Y2 * Y1 * Y3 * Y2^-1 * Y1, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 12, 44)(5, 37, 14, 46)(6, 38, 15, 47)(7, 39, 18, 50)(8, 40, 20, 52)(10, 42, 16, 48)(11, 43, 17, 49)(13, 45, 19, 51)(21, 53, 28, 60)(22, 54, 30, 62)(23, 55, 26, 58)(24, 56, 31, 63)(25, 57, 27, 59)(29, 61, 32, 64)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 70, 102, 80, 112, 72, 104)(68, 100, 75, 107, 88, 120, 77, 109)(71, 103, 81, 113, 93, 125, 83, 115)(73, 105, 85, 117, 78, 110, 87, 119)(76, 108, 86, 118, 95, 127, 89, 121)(79, 111, 90, 122, 84, 116, 92, 124)(82, 114, 91, 123, 96, 128, 94, 126) L = (1, 68)(2, 71)(3, 75)(4, 65)(5, 77)(6, 81)(7, 66)(8, 83)(9, 86)(10, 88)(11, 67)(12, 87)(13, 69)(14, 89)(15, 91)(16, 93)(17, 70)(18, 92)(19, 72)(20, 94)(21, 95)(22, 73)(23, 76)(24, 74)(25, 78)(26, 96)(27, 79)(28, 82)(29, 80)(30, 84)(31, 85)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.410 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.402 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 12, 44)(5, 37, 14, 46)(6, 38, 15, 47)(7, 39, 18, 50)(8, 40, 20, 52)(10, 42, 16, 48)(11, 43, 19, 51)(13, 45, 17, 49)(21, 53, 28, 60)(22, 54, 27, 59)(23, 55, 26, 58)(24, 56, 31, 63)(25, 57, 30, 62)(29, 61, 32, 64)(65, 97, 67, 99, 74, 106, 69, 101)(66, 98, 70, 102, 80, 112, 72, 104)(68, 100, 75, 107, 88, 120, 77, 109)(71, 103, 81, 113, 93, 125, 83, 115)(73, 105, 85, 117, 78, 110, 87, 119)(76, 108, 89, 121, 95, 127, 86, 118)(79, 111, 90, 122, 84, 116, 92, 124)(82, 114, 94, 126, 96, 128, 91, 123) L = (1, 68)(2, 71)(3, 75)(4, 65)(5, 77)(6, 81)(7, 66)(8, 83)(9, 86)(10, 88)(11, 67)(12, 85)(13, 69)(14, 89)(15, 91)(16, 93)(17, 70)(18, 90)(19, 72)(20, 94)(21, 76)(22, 73)(23, 95)(24, 74)(25, 78)(26, 82)(27, 79)(28, 96)(29, 80)(30, 84)(31, 87)(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 ) } Outer automorphisms :: reflexible Dual of E15.412 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.403 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-1 * Y3 * Y2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (Y2 * Y1)^2, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2 * Y1)^2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 8, 40)(5, 37, 7, 39)(6, 38, 10, 42)(11, 43, 18, 50)(12, 44, 23, 55)(13, 45, 22, 54)(14, 46, 21, 53)(15, 47, 20, 52)(16, 48, 19, 51)(17, 49, 24, 56)(25, 57, 29, 61)(26, 58, 30, 62)(27, 59, 32, 64)(28, 60, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 82, 114, 73, 105)(68, 100, 77, 109, 89, 121, 79, 111)(70, 102, 76, 108, 90, 122, 80, 112)(72, 104, 84, 116, 93, 125, 86, 118)(74, 106, 83, 115, 94, 126, 87, 119)(78, 110, 92, 124, 81, 113, 91, 123)(85, 117, 96, 128, 88, 120, 95, 127) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 80)(6, 65)(7, 83)(8, 85)(9, 87)(10, 66)(11, 89)(12, 91)(13, 67)(14, 90)(15, 69)(16, 92)(17, 70)(18, 93)(19, 95)(20, 71)(21, 94)(22, 73)(23, 96)(24, 74)(25, 81)(26, 75)(27, 79)(28, 77)(29, 88)(30, 82)(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) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.414 Graph:: simple bipartite v = 24 e = 64 f = 12 degree seq :: [ 4^16, 8^8 ] E15.404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 256>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2^-2 * Y1, Y2^4, Y1^4, (R * Y1)^2, (Y1^-1 * Y3)^2, Y1 * Y2^2 * Y1, (R * Y3)^2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-1, (Y2^-2 * Y3)^2, (R * Y2 * Y3)^2, Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3, Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 6, 38, 13, 45)(4, 36, 14, 46, 18, 50, 9, 41)(8, 40, 19, 51, 10, 42, 21, 53)(12, 44, 23, 55, 17, 49, 22, 54)(15, 47, 24, 56, 16, 48, 20, 52)(25, 57, 30, 62, 26, 58, 29, 61)(27, 59, 31, 63, 28, 60, 32, 64)(65, 97, 67, 99, 71, 103, 70, 102)(66, 98, 72, 104, 69, 101, 74, 106)(68, 100, 79, 111, 82, 114, 80, 112)(73, 105, 86, 118, 78, 110, 87, 119)(75, 107, 89, 121, 77, 109, 90, 122)(76, 108, 91, 123, 81, 113, 92, 124)(83, 115, 93, 125, 85, 117, 94, 126)(84, 116, 95, 127, 88, 120, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 81)(7, 82)(8, 84)(9, 66)(10, 88)(11, 86)(12, 67)(13, 87)(14, 69)(15, 85)(16, 83)(17, 70)(18, 71)(19, 80)(20, 72)(21, 79)(22, 75)(23, 77)(24, 74)(25, 96)(26, 95)(27, 93)(28, 94)(29, 91)(30, 92)(31, 90)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.406 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, (Y2 * Y1)^2, Y2^-2 * Y1^-2, (R * Y3)^2, Y1^-1 * Y2^2 * Y1^-1, (Y3^-1, Y2), Y2^4, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, Y3^3 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-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, 12, 44)(7, 39, 18, 50, 22, 54, 10, 42)(13, 45, 27, 59, 17, 49, 24, 56)(14, 46, 26, 58, 19, 51, 23, 55)(16, 48, 28, 60, 20, 52, 25, 57)(29, 61, 32, 64, 30, 62, 31, 63)(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, 82, 114, 90, 122)(76, 108, 88, 120, 79, 111, 91, 123)(80, 112, 93, 125, 84, 116, 94, 126)(89, 121, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 80)(5, 82)(6, 81)(7, 65)(8, 85)(9, 87)(10, 89)(11, 90)(12, 66)(13, 93)(14, 67)(15, 69)(16, 86)(17, 94)(18, 92)(19, 70)(20, 71)(21, 84)(22, 72)(23, 95)(24, 73)(25, 79)(26, 96)(27, 75)(28, 76)(29, 83)(30, 78)(31, 91)(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) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.407 Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 256>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y3 * Y1^-3, Y3 * Y1 * Y2 * Y3 * Y2 * Y1, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y1^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, (Y1^-1 * R * Y2)^2, (Y2 * Y1 * Y2 * Y1^-1)^2, (Y3 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 30, 62, 27, 59, 17, 49, 5, 37)(3, 35, 9, 41, 19, 51, 15, 47, 23, 55, 7, 39, 21, 53, 11, 43)(4, 36, 12, 44, 26, 58, 8, 40, 24, 56, 16, 48, 20, 52, 14, 46)(10, 42, 28, 60, 32, 64, 25, 57, 13, 45, 29, 61, 31, 63, 22, 54)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 77, 109)(69, 101, 79, 111)(70, 102, 83, 115)(72, 104, 89, 121)(73, 105, 91, 123)(74, 106, 88, 120)(75, 107, 82, 114)(76, 108, 92, 124)(78, 110, 86, 118)(80, 112, 93, 125)(81, 113, 85, 117)(84, 116, 96, 128)(87, 119, 94, 126)(90, 122, 95, 127) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 80)(6, 84)(7, 86)(8, 66)(9, 89)(10, 67)(11, 93)(12, 82)(13, 87)(14, 91)(15, 92)(16, 69)(17, 90)(18, 76)(19, 95)(20, 70)(21, 96)(22, 71)(23, 77)(24, 94)(25, 73)(26, 81)(27, 78)(28, 79)(29, 75)(30, 88)(31, 83)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.404 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y3^4, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, (Y2 * Y1^-1)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 18, 50, 15, 47, 24, 56, 16, 48, 5, 37)(3, 35, 11, 43, 25, 57, 32, 64, 28, 60, 29, 61, 19, 51, 8, 40)(4, 36, 14, 46, 21, 53, 10, 42, 6, 38, 17, 49, 20, 52, 9, 41)(12, 44, 22, 54, 30, 62, 27, 59, 13, 45, 23, 55, 31, 63, 26, 58)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 76, 108)(69, 101, 75, 107)(70, 102, 77, 109)(71, 103, 83, 115)(73, 105, 86, 118)(74, 106, 87, 119)(78, 110, 90, 122)(79, 111, 92, 124)(80, 112, 89, 121)(81, 113, 91, 123)(82, 114, 93, 125)(84, 116, 94, 126)(85, 117, 95, 127)(88, 120, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 78)(6, 65)(7, 84)(8, 86)(9, 88)(10, 66)(11, 90)(12, 92)(13, 67)(14, 82)(15, 70)(16, 85)(17, 69)(18, 81)(19, 94)(20, 80)(21, 71)(22, 96)(23, 72)(24, 74)(25, 95)(26, 93)(27, 75)(28, 77)(29, 91)(30, 89)(31, 83)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.405 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.408 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 256>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2^-1)^2, (Y2^-1 * Y3^-1)^2, Y1^4, Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1 ] 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, 28, 60, 20, 52, 23, 55)(14, 46, 26, 58, 16, 48, 27, 59)(17, 49, 24, 56, 19, 51, 25, 57)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 77, 109, 86, 118, 72, 104, 85, 117, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 79, 111, 69, 101, 82, 114, 92, 124, 75, 107)(68, 100, 81, 113, 94, 126, 78, 110, 71, 103, 83, 115, 93, 125, 80, 112)(74, 106, 90, 122, 96, 128, 88, 120, 76, 108, 91, 123, 95, 127, 89, 121) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 83)(7, 65)(8, 71)(9, 88)(10, 69)(11, 91)(12, 66)(13, 93)(14, 85)(15, 90)(16, 67)(17, 70)(18, 89)(19, 86)(20, 94)(21, 80)(22, 81)(23, 95)(24, 82)(25, 73)(26, 75)(27, 79)(28, 96)(29, 84)(30, 77)(31, 92)(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, 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 E15.397 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.409 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x Q8) : C2 (small group id <32, 44>) Aut = (C2 x (C8 : C2)) : C2 (small group id <64, 256>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-1, Y3^-4 * Y1^-2, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y3^-2 * Y1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-4 * Y1^-1, Y2^-2 * Y1 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 23, 55, 11, 43)(4, 36, 12, 44, 24, 56, 19, 51)(6, 38, 20, 52, 25, 57, 9, 41)(7, 39, 10, 42, 26, 58, 21, 53)(14, 46, 31, 63, 18, 50, 27, 59)(15, 47, 30, 62, 17, 49, 28, 60)(16, 48, 29, 61, 22, 54, 32, 64)(65, 97, 67, 99, 78, 110, 89, 121, 72, 104, 87, 119, 82, 114, 70, 102)(66, 98, 73, 105, 91, 123, 77, 109, 69, 101, 84, 116, 95, 127, 75, 107)(68, 100, 81, 113, 71, 103, 86, 118, 88, 120, 79, 111, 90, 122, 80, 112)(74, 106, 94, 126, 76, 108, 96, 128, 85, 117, 92, 124, 83, 115, 93, 125) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 85)(6, 86)(7, 65)(8, 88)(9, 92)(10, 95)(11, 96)(12, 66)(13, 93)(14, 71)(15, 70)(16, 67)(17, 89)(18, 90)(19, 69)(20, 94)(21, 91)(22, 87)(23, 81)(24, 78)(25, 80)(26, 72)(27, 76)(28, 75)(29, 73)(30, 77)(31, 83)(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, 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 E15.398 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.410 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (Y2^-1 * Y3)^2, (R * Y3)^2, Y1^4, (Y2^-1, Y1), Y2^4 * Y1^2, Y2^2 * Y1^-1 * Y3 * Y2^-2 * Y3 * 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, 15, 47)(6, 38, 10, 42, 20, 52, 16, 48)(11, 43, 21, 53, 17, 49, 24, 56)(12, 44, 22, 54, 29, 61, 26, 58)(14, 46, 23, 55, 30, 62, 28, 60)(25, 57, 31, 63, 27, 59, 32, 64)(65, 97, 67, 99, 75, 107, 84, 116, 71, 103, 82, 114, 81, 113, 70, 102)(66, 98, 72, 104, 85, 117, 80, 112, 69, 101, 77, 109, 88, 120, 74, 106)(68, 100, 78, 110, 91, 123, 93, 125, 83, 115, 94, 126, 89, 121, 76, 108)(73, 105, 87, 119, 96, 128, 90, 122, 79, 111, 92, 124, 95, 127, 86, 118) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 79)(6, 78)(7, 83)(8, 86)(9, 66)(10, 87)(11, 89)(12, 67)(13, 90)(14, 70)(15, 69)(16, 92)(17, 91)(18, 93)(19, 71)(20, 94)(21, 95)(22, 72)(23, 74)(24, 96)(25, 75)(26, 77)(27, 81)(28, 80)(29, 82)(30, 84)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.401 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.411 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y1 * Y3 * Y1^-1 * Y3, (Y2^-1 * Y3)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^4, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 10, 42, 18, 50, 13, 45)(4, 36, 9, 41, 19, 51, 15, 47)(6, 38, 8, 40, 20, 52, 16, 48)(11, 43, 24, 56, 17, 49, 21, 53)(12, 44, 23, 55, 29, 61, 26, 58)(14, 46, 22, 54, 30, 62, 28, 60)(25, 57, 32, 64, 27, 59, 31, 63)(65, 97, 67, 99, 75, 107, 84, 116, 71, 103, 82, 114, 81, 113, 70, 102)(66, 98, 72, 104, 85, 117, 77, 109, 69, 101, 80, 112, 88, 120, 74, 106)(68, 100, 78, 110, 91, 123, 93, 125, 83, 115, 94, 126, 89, 121, 76, 108)(73, 105, 87, 119, 96, 128, 92, 124, 79, 111, 90, 122, 95, 127, 86, 118) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 79)(6, 78)(7, 83)(8, 86)(9, 66)(10, 87)(11, 89)(12, 67)(13, 90)(14, 70)(15, 69)(16, 92)(17, 91)(18, 93)(19, 71)(20, 94)(21, 95)(22, 72)(23, 74)(24, 96)(25, 75)(26, 77)(27, 81)(28, 80)(29, 82)(30, 84)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.399 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.412 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^4, R * Y2 * R * Y2^-1, (Y2^-1 * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1 * Y3)^2, Y1^-1 * Y2^4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 18, 50, 8, 40)(4, 36, 9, 41, 19, 51, 15, 47)(6, 38, 16, 48, 20, 52, 10, 42)(12, 44, 21, 53, 17, 49, 24, 56)(13, 45, 25, 57, 29, 61, 22, 54)(14, 46, 27, 59, 30, 62, 23, 55)(26, 58, 31, 63, 28, 60, 32, 64)(65, 97, 67, 99, 76, 108, 84, 116, 71, 103, 82, 114, 81, 113, 70, 102)(66, 98, 72, 104, 85, 117, 80, 112, 69, 101, 75, 107, 88, 120, 74, 106)(68, 100, 78, 110, 92, 124, 93, 125, 83, 115, 94, 126, 90, 122, 77, 109)(73, 105, 87, 119, 96, 128, 89, 121, 79, 111, 91, 123, 95, 127, 86, 118) L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 79)(6, 78)(7, 83)(8, 86)(9, 66)(10, 87)(11, 89)(12, 90)(13, 67)(14, 70)(15, 69)(16, 91)(17, 92)(18, 93)(19, 71)(20, 94)(21, 95)(22, 72)(23, 74)(24, 96)(25, 75)(26, 76)(27, 80)(28, 81)(29, 82)(30, 84)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.402 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.413 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C2 x D8) : C2 (small group id <32, 43>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2^-1 * Y1^-1)^2, R * Y2 * R * Y2^-1, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y1^4, Y1^-2 * Y2^4, Y2 * Y1 * Y2^-3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 18, 50, 10, 42)(4, 36, 9, 41, 19, 51, 15, 47)(6, 38, 16, 48, 20, 52, 8, 40)(12, 44, 24, 56, 17, 49, 21, 53)(13, 45, 25, 57, 29, 61, 23, 55)(14, 46, 27, 59, 30, 62, 22, 54)(26, 58, 32, 64, 28, 60, 31, 63)(65, 97, 67, 99, 76, 108, 84, 116, 71, 103, 82, 114, 81, 113, 70, 102)(66, 98, 72, 104, 85, 117, 75, 107, 69, 101, 80, 112, 88, 120, 74, 106)(68, 100, 78, 110, 92, 124, 93, 125, 83, 115, 94, 126, 90, 122, 77, 109)(73, 105, 87, 119, 96, 128, 91, 123, 79, 111, 89, 121, 95, 127, 86, 118) L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 79)(6, 78)(7, 83)(8, 86)(9, 66)(10, 87)(11, 89)(12, 90)(13, 67)(14, 70)(15, 69)(16, 91)(17, 92)(18, 93)(19, 71)(20, 94)(21, 95)(22, 72)(23, 74)(24, 96)(25, 75)(26, 76)(27, 80)(28, 81)(29, 82)(30, 84)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E15.400 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.414 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 42>) Aut = (C2 x D16) : C2 (small group id <64, 257>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2^-1)^2, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1, Y1^4, (Y1^-1 * Y2^-1)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2^2 * Y1^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 22, 54, 11, 43)(4, 36, 12, 44, 23, 55, 17, 49)(6, 38, 18, 50, 24, 56, 9, 41)(7, 39, 10, 42, 25, 57, 19, 51)(14, 46, 29, 61, 20, 52, 26, 58)(15, 47, 27, 59, 21, 53, 30, 62)(16, 48, 31, 63, 32, 64, 28, 60)(65, 97, 67, 99, 78, 110, 88, 120, 72, 104, 86, 118, 84, 116, 70, 102)(66, 98, 73, 105, 90, 122, 77, 109, 69, 101, 82, 114, 93, 125, 75, 107)(68, 100, 79, 111, 89, 121, 96, 128, 87, 119, 85, 117, 71, 103, 80, 112)(74, 106, 91, 123, 81, 113, 95, 127, 83, 115, 94, 126, 76, 108, 92, 124) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 83)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 95)(14, 89)(15, 88)(16, 67)(17, 69)(18, 94)(19, 93)(20, 71)(21, 70)(22, 85)(23, 84)(24, 96)(25, 72)(26, 81)(27, 77)(28, 73)(29, 76)(30, 75)(31, 82)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.403 Graph:: bipartite v = 12 e = 64 f = 24 degree seq :: [ 8^8, 16^4 ] E15.415 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, Y1^-1 * Y3 * Y1^-1 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y1^16 ] Map:: R = (1, 34, 2, 37, 5, 41, 9, 45, 13, 49, 17, 53, 21, 57, 25, 61, 29, 60, 28, 56, 24, 52, 20, 48, 16, 44, 12, 40, 8, 36, 4, 33)(3, 39, 7, 43, 11, 47, 15, 51, 19, 55, 23, 59, 27, 63, 31, 64, 32, 62, 30, 58, 26, 54, 22, 50, 18, 46, 14, 42, 10, 38, 6, 35) 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, 32)(33, 35)(34, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 50)(48, 51)(49, 54)(52, 55)(53, 58)(56, 59)(57, 62)(60, 63)(61, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.416 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y2 * Y1^-2, (Y3 * Y2)^4, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 44, 12, 50, 18, 56, 24, 62, 30, 61, 29, 64, 32, 59, 27, 52, 20, 42, 10, 49, 17, 45, 13, 37, 5, 33)(3, 41, 9, 51, 19, 57, 25, 53, 21, 60, 28, 63, 31, 58, 26, 54, 22, 55, 23, 48, 16, 40, 8, 36, 4, 43, 11, 47, 15, 39, 7, 35) 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, 29)(23, 30)(26, 32)(27, 31)(33, 36)(34, 40)(35, 42)(37, 43)(38, 48)(39, 49)(41, 52)(44, 54)(45, 47)(46, 55)(50, 58)(51, 59)(53, 61)(56, 63)(57, 64)(60, 62) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.418 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.417 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (Y3 * Y2)^2, Y1^-2 * Y2 * Y1 * Y3 * Y1^-5 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 45, 13, 53, 21, 61, 29, 58, 26, 50, 18, 42, 10, 48, 16, 56, 24, 64, 32, 60, 28, 52, 20, 44, 12, 37, 5, 33)(3, 41, 9, 49, 17, 57, 25, 63, 31, 55, 23, 47, 15, 40, 8, 36, 4, 43, 11, 51, 19, 59, 27, 62, 30, 54, 22, 46, 14, 39, 7, 35) 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, 29)(28, 31)(33, 36)(34, 40)(35, 42)(37, 43)(38, 47)(39, 48)(41, 50)(44, 51)(45, 55)(46, 56)(49, 58)(52, 59)(53, 63)(54, 64)(57, 61)(60, 62) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.418 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y1 * Y3 * Y1^-3, (Y2 * Y3)^4, (Y2 * Y1^-2 * Y3)^8 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 42, 10, 49, 17, 56, 24, 62, 30, 59, 27, 64, 32, 60, 28, 53, 21, 44, 12, 50, 18, 45, 13, 37, 5, 33)(3, 41, 9, 48, 16, 40, 8, 36, 4, 43, 11, 52, 20, 58, 26, 54, 22, 61, 29, 63, 31, 57, 25, 51, 19, 55, 23, 47, 15, 39, 7, 35) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 19)(11, 21)(13, 16)(14, 23)(17, 25)(20, 28)(22, 27)(24, 31)(26, 32)(29, 30)(33, 36)(34, 40)(35, 42)(37, 43)(38, 48)(39, 49)(41, 46)(44, 54)(45, 52)(47, 56)(50, 58)(51, 59)(53, 61)(55, 62)(57, 64)(60, 63) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.416 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.419 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^16 ] Map:: R = (1, 33, 3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 28, 60, 24, 56, 20, 52, 16, 48, 12, 44, 8, 40, 4, 36)(2, 34, 5, 37, 9, 41, 13, 45, 17, 49, 21, 53, 25, 57, 29, 61, 32, 64, 30, 62, 26, 58, 22, 54, 18, 50, 14, 46, 10, 42, 6, 38)(65, 66)(67, 70)(68, 69)(71, 74)(72, 73)(75, 78)(76, 77)(79, 82)(80, 81)(83, 86)(84, 85)(87, 90)(88, 89)(91, 94)(92, 93)(95, 96)(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, 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, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.426 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.420 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^-3 * Y2 * Y3 * Y1, (Y2 * Y1)^4, Y1 * Y3^2 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 ] Map:: R = (1, 33, 4, 36, 12, 44, 21, 53, 9, 41, 20, 52, 29, 61, 31, 63, 23, 55, 30, 62, 26, 58, 16, 48, 6, 38, 15, 47, 13, 45, 5, 37)(2, 34, 7, 39, 17, 49, 25, 57, 14, 46, 24, 56, 32, 64, 28, 60, 19, 51, 27, 59, 22, 54, 11, 43, 3, 35, 10, 42, 18, 50, 8, 40)(65, 66)(67, 73)(68, 72)(69, 71)(70, 78)(74, 85)(75, 84)(76, 82)(77, 81)(79, 89)(80, 88)(83, 87)(86, 93)(90, 96)(91, 95)(92, 94)(97, 99)(98, 102)(100, 107)(101, 106)(103, 112)(104, 111)(105, 115)(108, 118)(109, 114)(110, 119)(113, 122)(116, 124)(117, 123)(120, 127)(121, 126)(125, 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, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.429 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.421 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1, Y3^3 * Y2 * Y3^-5 * 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 ] Map:: 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)(67, 70)(68, 72)(69, 71)(73, 78)(74, 77)(75, 80)(76, 79)(81, 86)(82, 85)(83, 88)(84, 87)(89, 94)(90, 93)(91, 96)(92, 95)(97, 99)(98, 102)(100, 106)(101, 105)(103, 110)(104, 109)(107, 114)(108, 113)(111, 118)(112, 117)(115, 122)(116, 121)(119, 126)(120, 125)(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, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.428 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.422 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y2 * Y3^-4 * Y1, (Y2 * Y1)^4, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 33, 4, 36, 12, 44, 16, 48, 6, 38, 15, 47, 26, 58, 31, 63, 23, 55, 30, 62, 29, 61, 21, 53, 9, 41, 20, 52, 13, 45, 5, 37)(2, 34, 7, 39, 17, 49, 11, 43, 3, 35, 10, 42, 22, 54, 28, 60, 19, 51, 27, 59, 32, 64, 25, 57, 14, 46, 24, 56, 18, 50, 8, 40)(65, 66)(67, 73)(68, 72)(69, 71)(70, 78)(74, 85)(75, 84)(76, 82)(77, 81)(79, 89)(80, 88)(83, 87)(86, 93)(90, 96)(91, 95)(92, 94)(97, 99)(98, 102)(100, 107)(101, 106)(103, 112)(104, 111)(105, 115)(108, 113)(109, 118)(110, 119)(114, 122)(116, 124)(117, 123)(120, 127)(121, 126)(125, 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, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.427 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.423 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = C2 x (C16 : C2) (small group id <64, 184>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-2 * Y3 * Y2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y1^4 * Y2^2 * Y3 * Y2, Y2^2 * Y3 * Y2 * Y3 * Y1^-5, Y3 * Y2^4 * Y1^-1 * Y3 * Y1^-3, Y2^16 ] Map:: non-degenerate R = (1, 33, 4, 36)(2, 34, 6, 38)(3, 35, 8, 40)(5, 37, 12, 44)(7, 39, 16, 48)(9, 41, 18, 50)(10, 42, 19, 51)(11, 43, 21, 53)(13, 45, 23, 55)(14, 46, 24, 56)(15, 47, 26, 58)(17, 49, 28, 60)(20, 52, 30, 62)(22, 54, 32, 64)(25, 57, 31, 63)(27, 59, 29, 61)(65, 66, 69, 75, 84, 93, 92, 83, 88, 82, 87, 96, 89, 79, 71, 67)(68, 73, 76, 86, 94, 90, 81, 72, 78, 70, 77, 85, 95, 91, 80, 74)(97, 99, 103, 111, 121, 128, 119, 114, 120, 115, 124, 125, 116, 107, 101, 98)(100, 106, 112, 123, 127, 117, 109, 102, 110, 104, 113, 122, 126, 118, 108, 105) 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.430 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.424 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^16, Y2^16 ] Map:: non-degenerate R = (1, 33, 4, 36)(2, 34, 6, 38)(3, 35, 8, 40)(5, 37, 10, 42)(7, 39, 12, 44)(9, 41, 14, 46)(11, 43, 16, 48)(13, 45, 18, 50)(15, 47, 20, 52)(17, 49, 22, 54)(19, 51, 24, 56)(21, 53, 26, 58)(23, 55, 28, 60)(25, 57, 30, 62)(27, 59, 31, 63)(29, 61, 32, 64)(65, 66, 69, 73, 77, 81, 85, 89, 93, 91, 87, 83, 79, 75, 71, 67)(68, 72, 76, 80, 84, 88, 92, 95, 96, 94, 90, 86, 82, 78, 74, 70)(97, 99, 103, 107, 111, 115, 119, 123, 125, 121, 117, 113, 109, 105, 101, 98)(100, 102, 106, 110, 114, 118, 122, 126, 128, 127, 124, 120, 116, 112, 108, 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.431 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.425 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = C2 x QD32 (small group id <64, 187>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2 * Y1, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1 * Y3 * Y2^-1)^2, Y2^4 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, Y1^16, Y2^16 ] Map:: non-degenerate R = (1, 33, 4, 36)(2, 34, 6, 38)(3, 35, 8, 40)(5, 37, 12, 44)(7, 39, 16, 48)(9, 41, 18, 50)(10, 42, 19, 51)(11, 43, 21, 53)(13, 45, 23, 55)(14, 46, 24, 56)(15, 47, 26, 58)(17, 49, 28, 60)(20, 52, 30, 62)(22, 54, 32, 64)(25, 57, 31, 63)(27, 59, 29, 61)(65, 66, 69, 75, 84, 93, 92, 82, 87, 83, 88, 96, 89, 79, 71, 67)(68, 73, 80, 91, 95, 85, 78, 70, 77, 72, 81, 90, 94, 86, 76, 74)(97, 99, 103, 111, 121, 128, 120, 115, 119, 114, 124, 125, 116, 107, 101, 98)(100, 106, 108, 118, 126, 122, 113, 104, 109, 102, 110, 117, 127, 123, 112, 105) 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.432 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.426 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^16 ] Map:: R = (1, 33, 65, 97, 3, 35, 67, 99, 7, 39, 71, 103, 11, 43, 75, 107, 15, 47, 79, 111, 19, 51, 83, 115, 23, 55, 87, 119, 27, 59, 91, 123, 31, 63, 95, 127, 28, 60, 92, 124, 24, 56, 88, 120, 20, 52, 84, 116, 16, 48, 80, 112, 12, 44, 76, 108, 8, 40, 72, 104, 4, 36, 68, 100)(2, 34, 66, 98, 5, 37, 69, 101, 9, 41, 73, 105, 13, 45, 77, 109, 17, 49, 81, 113, 21, 53, 85, 117, 25, 57, 89, 121, 29, 61, 93, 125, 32, 64, 96, 128, 30, 62, 94, 126, 26, 58, 90, 122, 22, 54, 86, 118, 18, 50, 82, 114, 14, 46, 78, 110, 10, 42, 74, 106, 6, 38, 70, 102) L = (1, 34)(2, 33)(3, 38)(4, 37)(5, 36)(6, 35)(7, 42)(8, 41)(9, 40)(10, 39)(11, 46)(12, 45)(13, 44)(14, 43)(15, 50)(16, 49)(17, 48)(18, 47)(19, 54)(20, 53)(21, 52)(22, 51)(23, 58)(24, 57)(25, 56)(26, 55)(27, 62)(28, 61)(29, 60)(30, 59)(31, 64)(32, 63)(65, 98)(66, 97)(67, 102)(68, 101)(69, 100)(70, 99)(71, 106)(72, 105)(73, 104)(74, 103)(75, 110)(76, 109)(77, 108)(78, 107)(79, 114)(80, 113)(81, 112)(82, 111)(83, 118)(84, 117)(85, 116)(86, 115)(87, 122)(88, 121)(89, 120)(90, 119)(91, 126)(92, 125)(93, 124)(94, 123)(95, 128)(96, 127) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.419 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.427 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^-3 * Y2 * Y3 * Y1, (Y2 * Y1)^4, Y1 * Y3^2 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 21, 53, 85, 117, 9, 41, 73, 105, 20, 52, 84, 116, 29, 61, 93, 125, 31, 63, 95, 127, 23, 55, 87, 119, 30, 62, 94, 126, 26, 58, 90, 122, 16, 48, 80, 112, 6, 38, 70, 102, 15, 47, 79, 111, 13, 45, 77, 109, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 17, 49, 81, 113, 25, 57, 89, 121, 14, 46, 78, 110, 24, 56, 88, 120, 32, 64, 96, 128, 28, 60, 92, 124, 19, 51, 83, 115, 27, 59, 91, 123, 22, 54, 86, 118, 11, 43, 75, 107, 3, 35, 67, 99, 10, 42, 74, 106, 18, 50, 82, 114, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 46)(7, 37)(8, 36)(9, 35)(10, 53)(11, 52)(12, 50)(13, 49)(14, 38)(15, 57)(16, 56)(17, 45)(18, 44)(19, 55)(20, 43)(21, 42)(22, 61)(23, 51)(24, 48)(25, 47)(26, 64)(27, 63)(28, 62)(29, 54)(30, 60)(31, 59)(32, 58)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 112)(72, 111)(73, 115)(74, 101)(75, 100)(76, 118)(77, 114)(78, 119)(79, 104)(80, 103)(81, 122)(82, 109)(83, 105)(84, 124)(85, 123)(86, 108)(87, 110)(88, 127)(89, 126)(90, 113)(91, 117)(92, 116)(93, 128)(94, 121)(95, 120)(96, 125) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.422 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.428 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1, Y3^3 * Y2 * Y3^-5 * 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 ] Map:: 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, 33)(3, 38)(4, 40)(5, 39)(6, 35)(7, 37)(8, 36)(9, 46)(10, 45)(11, 48)(12, 47)(13, 42)(14, 41)(15, 44)(16, 43)(17, 54)(18, 53)(19, 56)(20, 55)(21, 50)(22, 49)(23, 52)(24, 51)(25, 62)(26, 61)(27, 64)(28, 63)(29, 58)(30, 57)(31, 60)(32, 59)(65, 99)(66, 102)(67, 97)(68, 106)(69, 105)(70, 98)(71, 110)(72, 109)(73, 101)(74, 100)(75, 114)(76, 113)(77, 104)(78, 103)(79, 118)(80, 117)(81, 108)(82, 107)(83, 122)(84, 121)(85, 112)(86, 111)(87, 126)(88, 125)(89, 116)(90, 115)(91, 127)(92, 128)(93, 120)(94, 119)(95, 123)(96, 124) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.421 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.429 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y2 * Y3^-4 * Y1, (Y2 * Y1)^4, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 16, 48, 80, 112, 6, 38, 70, 102, 15, 47, 79, 111, 26, 58, 90, 122, 31, 63, 95, 127, 23, 55, 87, 119, 30, 62, 94, 126, 29, 61, 93, 125, 21, 53, 85, 117, 9, 41, 73, 105, 20, 52, 84, 116, 13, 45, 77, 109, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 17, 49, 81, 113, 11, 43, 75, 107, 3, 35, 67, 99, 10, 42, 74, 106, 22, 54, 86, 118, 28, 60, 92, 124, 19, 51, 83, 115, 27, 59, 91, 123, 32, 64, 96, 128, 25, 57, 89, 121, 14, 46, 78, 110, 24, 56, 88, 120, 18, 50, 82, 114, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 46)(7, 37)(8, 36)(9, 35)(10, 53)(11, 52)(12, 50)(13, 49)(14, 38)(15, 57)(16, 56)(17, 45)(18, 44)(19, 55)(20, 43)(21, 42)(22, 61)(23, 51)(24, 48)(25, 47)(26, 64)(27, 63)(28, 62)(29, 54)(30, 60)(31, 59)(32, 58)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 112)(72, 111)(73, 115)(74, 101)(75, 100)(76, 113)(77, 118)(78, 119)(79, 104)(80, 103)(81, 108)(82, 122)(83, 105)(84, 124)(85, 123)(86, 109)(87, 110)(88, 127)(89, 126)(90, 114)(91, 117)(92, 116)(93, 128)(94, 121)(95, 120)(96, 125) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.420 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.430 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = C2 x (C16 : C2) (small group id <64, 184>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-2 * Y3 * Y2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y1^4 * Y2^2 * Y3 * Y2, Y2^2 * Y3 * Y2 * Y3 * Y1^-5, Y3 * Y2^4 * Y1^-1 * Y3 * Y1^-3, Y2^16 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100)(2, 34, 66, 98, 6, 38, 70, 102)(3, 35, 67, 99, 8, 40, 72, 104)(5, 37, 69, 101, 12, 44, 76, 108)(7, 39, 71, 103, 16, 48, 80, 112)(9, 41, 73, 105, 18, 50, 82, 114)(10, 42, 74, 106, 19, 51, 83, 115)(11, 43, 75, 107, 21, 53, 85, 117)(13, 45, 77, 109, 23, 55, 87, 119)(14, 46, 78, 110, 24, 56, 88, 120)(15, 47, 79, 111, 26, 58, 90, 122)(17, 49, 81, 113, 28, 60, 92, 124)(20, 52, 84, 116, 30, 62, 94, 126)(22, 54, 86, 118, 32, 64, 96, 128)(25, 57, 89, 121, 31, 63, 95, 127)(27, 59, 91, 123, 29, 61, 93, 125) L = (1, 34)(2, 37)(3, 33)(4, 41)(5, 43)(6, 45)(7, 35)(8, 46)(9, 44)(10, 36)(11, 52)(12, 54)(13, 53)(14, 38)(15, 39)(16, 42)(17, 40)(18, 55)(19, 56)(20, 61)(21, 63)(22, 62)(23, 64)(24, 50)(25, 47)(26, 49)(27, 48)(28, 51)(29, 60)(30, 58)(31, 59)(32, 57)(65, 99)(66, 97)(67, 103)(68, 106)(69, 98)(70, 110)(71, 111)(72, 113)(73, 100)(74, 112)(75, 101)(76, 105)(77, 102)(78, 104)(79, 121)(80, 123)(81, 122)(82, 120)(83, 124)(84, 107)(85, 109)(86, 108)(87, 114)(88, 115)(89, 128)(90, 126)(91, 127)(92, 125)(93, 116)(94, 118)(95, 117)(96, 119) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.423 Transitivity :: VT+ Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.431 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^16, Y2^16 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100)(2, 34, 66, 98, 6, 38, 70, 102)(3, 35, 67, 99, 8, 40, 72, 104)(5, 37, 69, 101, 10, 42, 74, 106)(7, 39, 71, 103, 12, 44, 76, 108)(9, 41, 73, 105, 14, 46, 78, 110)(11, 43, 75, 107, 16, 48, 80, 112)(13, 45, 77, 109, 18, 50, 82, 114)(15, 47, 79, 111, 20, 52, 84, 116)(17, 49, 81, 113, 22, 54, 86, 118)(19, 51, 83, 115, 24, 56, 88, 120)(21, 53, 85, 117, 26, 58, 90, 122)(23, 55, 87, 119, 28, 60, 92, 124)(25, 57, 89, 121, 30, 62, 94, 126)(27, 59, 91, 123, 31, 63, 95, 127)(29, 61, 93, 125, 32, 64, 96, 128) L = (1, 34)(2, 37)(3, 33)(4, 40)(5, 41)(6, 36)(7, 35)(8, 44)(9, 45)(10, 38)(11, 39)(12, 48)(13, 49)(14, 42)(15, 43)(16, 52)(17, 53)(18, 46)(19, 47)(20, 56)(21, 57)(22, 50)(23, 51)(24, 60)(25, 61)(26, 54)(27, 55)(28, 63)(29, 59)(30, 58)(31, 64)(32, 62)(65, 99)(66, 97)(67, 103)(68, 102)(69, 98)(70, 106)(71, 107)(72, 100)(73, 101)(74, 110)(75, 111)(76, 104)(77, 105)(78, 114)(79, 115)(80, 108)(81, 109)(82, 118)(83, 119)(84, 112)(85, 113)(86, 122)(87, 123)(88, 116)(89, 117)(90, 126)(91, 125)(92, 120)(93, 121)(94, 128)(95, 124)(96, 127) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.424 Transitivity :: VT+ Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.432 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = C2 x QD32 (small group id <64, 187>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2 * Y1, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1 * Y3 * Y2^-1)^2, Y2^4 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, Y1^16, Y2^16 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100)(2, 34, 66, 98, 6, 38, 70, 102)(3, 35, 67, 99, 8, 40, 72, 104)(5, 37, 69, 101, 12, 44, 76, 108)(7, 39, 71, 103, 16, 48, 80, 112)(9, 41, 73, 105, 18, 50, 82, 114)(10, 42, 74, 106, 19, 51, 83, 115)(11, 43, 75, 107, 21, 53, 85, 117)(13, 45, 77, 109, 23, 55, 87, 119)(14, 46, 78, 110, 24, 56, 88, 120)(15, 47, 79, 111, 26, 58, 90, 122)(17, 49, 81, 113, 28, 60, 92, 124)(20, 52, 84, 116, 30, 62, 94, 126)(22, 54, 86, 118, 32, 64, 96, 128)(25, 57, 89, 121, 31, 63, 95, 127)(27, 59, 91, 123, 29, 61, 93, 125) L = (1, 34)(2, 37)(3, 33)(4, 41)(5, 43)(6, 45)(7, 35)(8, 49)(9, 48)(10, 36)(11, 52)(12, 42)(13, 40)(14, 38)(15, 39)(16, 59)(17, 58)(18, 55)(19, 56)(20, 61)(21, 46)(22, 44)(23, 51)(24, 64)(25, 47)(26, 62)(27, 63)(28, 50)(29, 60)(30, 54)(31, 53)(32, 57)(65, 99)(66, 97)(67, 103)(68, 106)(69, 98)(70, 110)(71, 111)(72, 109)(73, 100)(74, 108)(75, 101)(76, 118)(77, 102)(78, 117)(79, 121)(80, 105)(81, 104)(82, 124)(83, 119)(84, 107)(85, 127)(86, 126)(87, 114)(88, 115)(89, 128)(90, 113)(91, 112)(92, 125)(93, 116)(94, 122)(95, 123)(96, 120) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.425 Transitivity :: VT+ Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.433 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^16, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 6, 38)(7, 39, 9, 41)(8, 40, 10, 42)(11, 43, 13, 45)(12, 44, 14, 46)(15, 47, 17, 49)(16, 48, 18, 50)(19, 51, 21, 53)(20, 52, 22, 54)(23, 55, 25, 57)(24, 56, 26, 58)(27, 59, 29, 61)(28, 60, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 71, 103, 75, 107, 79, 111, 83, 115, 87, 119, 91, 123, 95, 127, 92, 124, 88, 120, 84, 116, 80, 112, 76, 108, 72, 104, 68, 100)(66, 98, 69, 101, 73, 105, 77, 109, 81, 113, 85, 117, 89, 121, 93, 125, 96, 128, 94, 126, 90, 122, 86, 118, 82, 114, 78, 110, 74, 106, 70, 102) 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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.434 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) 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, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^16, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 5, 37)(7, 39, 10, 42)(8, 40, 9, 41)(11, 43, 14, 46)(12, 44, 13, 45)(15, 47, 18, 50)(16, 48, 17, 49)(19, 51, 22, 54)(20, 52, 21, 53)(23, 55, 26, 58)(24, 56, 25, 57)(27, 59, 30, 62)(28, 60, 29, 61)(31, 63, 32, 64)(65, 97, 67, 99, 71, 103, 75, 107, 79, 111, 83, 115, 87, 119, 91, 123, 95, 127, 92, 124, 88, 120, 84, 116, 80, 112, 76, 108, 72, 104, 68, 100)(66, 98, 69, 101, 73, 105, 77, 109, 81, 113, 85, 117, 89, 121, 93, 125, 96, 128, 94, 126, 90, 122, 86, 118, 82, 114, 78, 110, 74, 106, 70, 102) 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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.435 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, (Y3 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y2^8 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 7, 39)(5, 37, 8, 40)(9, 41, 13, 45)(10, 42, 14, 46)(11, 43, 15, 47)(12, 44, 16, 48)(17, 49, 21, 53)(18, 50, 22, 54)(19, 51, 23, 55)(20, 52, 24, 56)(25, 57, 28, 60)(26, 58, 29, 61)(27, 59, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 88, 120, 80, 112, 72, 104, 66, 98, 70, 102, 77, 109, 85, 117, 92, 124, 84, 116, 76, 108, 69, 101)(68, 100, 74, 106, 82, 114, 90, 122, 95, 127, 94, 126, 87, 119, 79, 111, 71, 103, 78, 110, 86, 118, 93, 125, 96, 128, 91, 123, 83, 115, 75, 107) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 75)(6, 78)(7, 66)(8, 79)(9, 82)(10, 67)(11, 69)(12, 83)(13, 86)(14, 70)(15, 72)(16, 87)(17, 90)(18, 73)(19, 76)(20, 91)(21, 93)(22, 77)(23, 80)(24, 94)(25, 95)(26, 81)(27, 84)(28, 96)(29, 85)(30, 88)(31, 89)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.436 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.436 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, Y2^6 * Y3 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 7, 39)(5, 37, 8, 40)(9, 41, 13, 45)(10, 42, 14, 46)(11, 43, 15, 47)(12, 44, 16, 48)(17, 49, 21, 53)(18, 50, 22, 54)(19, 51, 23, 55)(20, 52, 24, 56)(25, 57, 29, 61)(26, 58, 30, 62)(27, 59, 31, 63)(28, 60, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 95, 127, 87, 119, 79, 111, 71, 103, 78, 110, 86, 118, 94, 126, 92, 124, 84, 116, 76, 108, 69, 101)(66, 98, 70, 102, 77, 109, 85, 117, 93, 125, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 75)(6, 78)(7, 66)(8, 79)(9, 82)(10, 67)(11, 69)(12, 83)(13, 86)(14, 70)(15, 72)(16, 87)(17, 90)(18, 73)(19, 76)(20, 91)(21, 94)(22, 77)(23, 80)(24, 95)(25, 96)(26, 81)(27, 84)(28, 93)(29, 92)(30, 85)(31, 88)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.435 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.437 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, Y2 * Y1 * Y2^-1 * Y1, Y2^8 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 7, 39)(5, 37, 8, 40)(9, 41, 13, 45)(10, 42, 14, 46)(11, 43, 15, 47)(12, 44, 16, 48)(17, 49, 21, 53)(18, 50, 22, 54)(19, 51, 23, 55)(20, 52, 24, 56)(25, 57, 29, 61)(26, 58, 30, 62)(27, 59, 31, 63)(28, 60, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 92, 124, 84, 116, 76, 108, 69, 101)(66, 98, 70, 102, 77, 109, 85, 117, 93, 125, 95, 127, 87, 119, 79, 111, 71, 103, 78, 110, 86, 118, 94, 126, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 75)(6, 78)(7, 66)(8, 79)(9, 82)(10, 67)(11, 69)(12, 83)(13, 86)(14, 70)(15, 72)(16, 87)(17, 90)(18, 73)(19, 76)(20, 91)(21, 94)(22, 77)(23, 80)(24, 95)(25, 92)(26, 81)(27, 84)(28, 89)(29, 96)(30, 85)(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, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.438 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, (Y2 * Y1)^2, Y2^8 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 8, 40)(4, 36, 7, 39)(5, 37, 6, 38)(9, 41, 16, 48)(10, 42, 15, 47)(11, 43, 14, 46)(12, 44, 13, 45)(17, 49, 24, 56)(18, 50, 23, 55)(19, 51, 22, 54)(20, 52, 21, 53)(25, 57, 32, 64)(26, 58, 31, 63)(27, 59, 30, 62)(28, 60, 29, 61)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 92, 124, 84, 116, 76, 108, 69, 101)(66, 98, 70, 102, 77, 109, 85, 117, 93, 125, 95, 127, 87, 119, 79, 111, 71, 103, 78, 110, 86, 118, 94, 126, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 75)(6, 78)(7, 66)(8, 79)(9, 82)(10, 67)(11, 69)(12, 83)(13, 86)(14, 70)(15, 72)(16, 87)(17, 90)(18, 73)(19, 76)(20, 91)(21, 94)(22, 77)(23, 80)(24, 95)(25, 92)(26, 81)(27, 84)(28, 89)(29, 96)(30, 85)(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, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.439 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, (Y2 * Y1)^2, Y3^4, Y3 * 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 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 23, 55)(12, 44, 24, 56)(13, 45, 22, 54)(14, 46, 21, 53)(15, 47, 20, 52)(16, 48, 18, 50)(17, 49, 19, 51)(25, 57, 32, 64)(26, 58, 31, 63)(27, 59, 30, 62)(28, 60, 29, 61)(65, 97, 67, 99, 75, 107, 81, 113, 70, 102, 77, 109, 89, 121, 91, 123, 78, 110, 90, 122, 92, 124, 79, 111, 68, 100, 76, 108, 80, 112, 69, 101)(66, 98, 71, 103, 82, 114, 88, 120, 74, 106, 84, 116, 93, 125, 95, 127, 85, 117, 94, 126, 96, 128, 86, 118, 72, 104, 83, 115, 87, 119, 73, 105) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 83)(8, 85)(9, 86)(10, 66)(11, 80)(12, 90)(13, 67)(14, 70)(15, 91)(16, 92)(17, 69)(18, 87)(19, 94)(20, 71)(21, 74)(22, 95)(23, 96)(24, 73)(25, 75)(26, 77)(27, 81)(28, 89)(29, 82)(30, 84)(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, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.440 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.440 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (Y2 * Y1)^2, (R * Y2)^2, Y3^4, Y3^-1 * Y2^4 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 23, 55)(12, 44, 24, 56)(13, 45, 22, 54)(14, 46, 21, 53)(15, 47, 20, 52)(16, 48, 18, 50)(17, 49, 19, 51)(25, 57, 32, 64)(26, 58, 31, 63)(27, 59, 30, 62)(28, 60, 29, 61)(65, 97, 67, 99, 75, 107, 79, 111, 68, 100, 76, 108, 89, 121, 91, 123, 78, 110, 90, 122, 92, 124, 81, 113, 70, 102, 77, 109, 80, 112, 69, 101)(66, 98, 71, 103, 82, 114, 86, 118, 72, 104, 83, 115, 93, 125, 95, 127, 85, 117, 94, 126, 96, 128, 88, 120, 74, 106, 84, 116, 87, 119, 73, 105) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 83)(8, 85)(9, 86)(10, 66)(11, 89)(12, 90)(13, 67)(14, 70)(15, 91)(16, 75)(17, 69)(18, 93)(19, 94)(20, 71)(21, 74)(22, 95)(23, 82)(24, 73)(25, 92)(26, 77)(27, 81)(28, 80)(29, 96)(30, 84)(31, 88)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.439 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.441 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1)^2, Y3^8, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 17, 49)(12, 44, 18, 50)(13, 45, 15, 47)(14, 46, 16, 48)(19, 51, 25, 57)(20, 52, 26, 58)(21, 53, 23, 55)(22, 54, 24, 56)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 70, 102, 75, 107, 78, 110, 83, 115, 86, 118, 91, 123, 92, 124, 93, 125, 84, 116, 85, 117, 76, 108, 77, 109, 68, 100, 69, 101)(66, 98, 71, 103, 74, 106, 79, 111, 82, 114, 87, 119, 90, 122, 94, 126, 95, 127, 96, 128, 88, 120, 89, 121, 80, 112, 81, 113, 72, 104, 73, 105) L = (1, 68)(2, 72)(3, 69)(4, 76)(5, 77)(6, 65)(7, 73)(8, 80)(9, 81)(10, 66)(11, 67)(12, 84)(13, 85)(14, 70)(15, 71)(16, 88)(17, 89)(18, 74)(19, 75)(20, 92)(21, 93)(22, 78)(23, 79)(24, 95)(25, 96)(26, 82)(27, 83)(28, 86)(29, 91)(30, 87)(31, 90)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.444 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.442 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y3^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 17, 49)(12, 44, 18, 50)(13, 45, 15, 47)(14, 46, 16, 48)(19, 51, 25, 57)(20, 52, 26, 58)(21, 53, 23, 55)(22, 54, 24, 56)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 68, 100, 75, 107, 76, 108, 83, 115, 84, 116, 91, 123, 92, 124, 93, 125, 86, 118, 85, 117, 78, 110, 77, 109, 70, 102, 69, 101)(66, 98, 71, 103, 72, 104, 79, 111, 80, 112, 87, 119, 88, 120, 94, 126, 95, 127, 96, 128, 90, 122, 89, 121, 82, 114, 81, 113, 74, 106, 73, 105) L = (1, 68)(2, 72)(3, 75)(4, 76)(5, 67)(6, 65)(7, 79)(8, 80)(9, 71)(10, 66)(11, 83)(12, 84)(13, 69)(14, 70)(15, 87)(16, 88)(17, 73)(18, 74)(19, 91)(20, 92)(21, 77)(22, 78)(23, 94)(24, 95)(25, 81)(26, 82)(27, 93)(28, 86)(29, 85)(30, 96)(31, 90)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.443 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y3^3 * Y2^2, Y2^4 * Y3^-2, Y3^2 * Y2^-4, (Y2^-2 * Y3)^2, Y2^16 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 24, 56)(12, 44, 25, 57)(13, 45, 23, 55)(14, 46, 26, 58)(15, 47, 21, 53)(16, 48, 19, 51)(17, 49, 20, 52)(18, 50, 22, 54)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 75, 107, 91, 123, 78, 110, 81, 113, 70, 102, 77, 109, 92, 124, 79, 111, 68, 100, 76, 108, 82, 114, 93, 125, 80, 112, 69, 101)(66, 98, 71, 103, 83, 115, 94, 126, 86, 118, 89, 121, 74, 106, 85, 117, 95, 127, 87, 119, 72, 104, 84, 116, 90, 122, 96, 128, 88, 120, 73, 105) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 84)(8, 86)(9, 87)(10, 66)(11, 82)(12, 81)(13, 67)(14, 80)(15, 91)(16, 92)(17, 69)(18, 70)(19, 90)(20, 89)(21, 71)(22, 88)(23, 94)(24, 95)(25, 73)(26, 74)(27, 93)(28, 75)(29, 77)(30, 96)(31, 83)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.444 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^2, Y2^-1 * Y3^-1 * Y2^-3 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 24, 56)(12, 44, 25, 57)(13, 45, 23, 55)(14, 46, 26, 58)(15, 47, 21, 53)(16, 48, 19, 51)(17, 49, 20, 52)(18, 50, 22, 54)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 75, 107, 91, 123, 82, 114, 79, 111, 68, 100, 76, 108, 92, 124, 81, 113, 70, 102, 77, 109, 78, 110, 93, 125, 80, 112, 69, 101)(66, 98, 71, 103, 83, 115, 94, 126, 90, 122, 87, 119, 72, 104, 84, 116, 95, 127, 89, 121, 74, 106, 85, 117, 86, 118, 96, 128, 88, 120, 73, 105) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 84)(8, 86)(9, 87)(10, 66)(11, 92)(12, 93)(13, 67)(14, 75)(15, 77)(16, 82)(17, 69)(18, 70)(19, 95)(20, 96)(21, 71)(22, 83)(23, 85)(24, 90)(25, 73)(26, 74)(27, 81)(28, 80)(29, 91)(30, 89)(31, 88)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.441 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.445 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, R * Y3 * R * Y2, Y3 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y1 * Y3, (R * Y1)^2, Y1^-1 * Y3 * Y1^-3 * Y3 * Y1^-4 ] Map:: R = (1, 34, 2, 38, 6, 45, 13, 53, 21, 61, 29, 57, 25, 49, 17, 41, 9, 48, 16, 56, 24, 64, 32, 60, 28, 52, 20, 44, 12, 37, 5, 33)(3, 40, 8, 46, 14, 55, 23, 62, 30, 59, 27, 51, 19, 43, 11, 36, 4, 39, 7, 47, 15, 54, 22, 63, 31, 58, 26, 50, 18, 42, 10, 35) L = (1, 3)(2, 7)(4, 9)(5, 11)(6, 14)(8, 16)(10, 17)(12, 18)(13, 22)(15, 24)(19, 25)(20, 27)(21, 30)(23, 32)(26, 29)(28, 31)(33, 36)(34, 40)(35, 41)(37, 42)(38, 47)(39, 48)(43, 49)(44, 51)(45, 55)(46, 56)(50, 57)(52, 58)(53, 63)(54, 64)(59, 61)(60, 62) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.446 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y1^-1 * Y3 * Y1, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, (Y3 * Y1^-2)^2, (Y2 * Y1^2)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^2, Y1^-1 * Y2 * Y3 * Y1^-5, Y2 * Y3 * Y2 * Y3 * Y1^4 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 48, 16, 60, 28, 58, 26, 42, 10, 52, 20, 62, 30, 59, 27, 44, 12, 53, 21, 63, 31, 56, 24, 47, 15, 37, 5, 33)(3, 41, 9, 55, 23, 64, 32, 50, 18, 45, 13, 36, 4, 39, 7, 51, 19, 46, 14, 57, 25, 61, 29, 54, 22, 40, 8, 49, 17, 43, 11, 35) L = (1, 3)(2, 7)(4, 12)(5, 14)(6, 17)(8, 21)(9, 20)(10, 25)(11, 27)(13, 16)(15, 23)(18, 31)(19, 30)(22, 28)(24, 29)(26, 32)(33, 36)(34, 40)(35, 42)(37, 43)(38, 50)(39, 52)(41, 56)(44, 54)(45, 59)(46, 58)(47, 51)(48, 61)(49, 62)(53, 64)(55, 60)(57, 63) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.448 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.447 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y1 * Y3 * Y1^-1, (R * Y1)^2, R * Y3 * R * Y2, Y2 * Y1^-1 * Y3 * Y1^-3, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1, Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-2, (Y3 * Y1^-1)^4 ] Map:: R = (1, 34, 2, 38, 6, 48, 16, 60, 28, 59, 27, 44, 12, 54, 22, 64, 32, 55, 23, 41, 9, 51, 19, 62, 30, 57, 25, 47, 15, 37, 5, 33)(3, 40, 8, 53, 21, 46, 14, 58, 26, 61, 29, 52, 20, 39, 7, 50, 18, 45, 13, 36, 4, 43, 11, 56, 24, 63, 31, 49, 17, 42, 10, 35) L = (1, 3)(2, 7)(4, 12)(5, 13)(6, 17)(8, 22)(9, 20)(10, 23)(11, 25)(14, 27)(15, 21)(16, 29)(18, 32)(19, 31)(24, 28)(26, 30)(33, 36)(34, 40)(35, 41)(37, 46)(38, 50)(39, 51)(42, 48)(43, 54)(44, 58)(45, 55)(47, 56)(49, 62)(52, 60)(53, 64)(57, 61)(59, 63) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.448 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-3 * Y2 * Y1 * Y3 * Y1^-2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 58, 26, 53, 21, 62, 30, 52, 20, 61, 29, 55, 23, 63, 31, 56, 24, 64, 32, 54, 22, 42, 10, 37, 5, 33)(3, 41, 9, 51, 19, 59, 27, 50, 18, 40, 8, 49, 17, 39, 7, 48, 16, 45, 13, 57, 25, 60, 28, 47, 15, 44, 12, 36, 4, 43, 11, 35) L = (1, 3)(2, 7)(4, 6)(5, 13)(8, 14)(9, 20)(10, 19)(11, 23)(12, 24)(15, 26)(16, 29)(17, 31)(18, 32)(21, 27)(22, 28)(25, 30)(33, 36)(34, 40)(35, 42)(37, 39)(38, 47)(41, 53)(43, 52)(44, 55)(45, 54)(46, 59)(48, 62)(49, 61)(50, 63)(51, 64)(56, 60)(57, 58) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.446 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.449 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 16, 16}) Quotient :: halfedge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-2 * Y2 * Y3, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3, Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1 * Y3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 46, 14, 58, 26, 55, 23, 64, 32, 51, 19, 61, 29, 52, 20, 62, 30, 53, 21, 63, 31, 56, 24, 44, 12, 37, 5, 33)(3, 41, 9, 36, 4, 43, 11, 54, 22, 59, 27, 49, 17, 39, 7, 48, 16, 40, 8, 50, 18, 45, 13, 57, 25, 60, 28, 47, 15, 42, 10, 35) L = (1, 3)(2, 7)(4, 12)(5, 8)(6, 15)(9, 19)(10, 20)(11, 23)(13, 24)(14, 27)(16, 29)(17, 30)(18, 32)(21, 28)(22, 31)(25, 26)(33, 36)(34, 40)(35, 38)(37, 45)(39, 46)(41, 52)(42, 53)(43, 51)(44, 54)(47, 58)(48, 62)(49, 63)(50, 61)(55, 59)(56, 60)(57, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.450 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3 * Y2, Y3 * Y1 * Y3^7 * Y1 ] Map:: 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)(67, 70)(68, 73)(69, 74)(71, 77)(72, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 89)(84, 90)(87, 93)(88, 94)(91, 95)(92, 96)(97, 99)(98, 102)(100, 103)(101, 104)(105, 109)(106, 110)(107, 113)(108, 114)(111, 117)(112, 118)(115, 119)(116, 120)(121, 125)(122, 126)(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, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.457 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.451 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y3^-1 * Y2 * Y3 * Y1, Y2 * Y3 * Y1 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3 * Y2 * Y3^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y3^2 * Y2, Y3^16 ] Map:: R = (1, 33, 4, 36, 13, 45, 26, 58, 32, 64, 18, 50, 6, 38, 17, 49, 30, 62, 21, 53, 9, 41, 24, 56, 28, 60, 19, 51, 15, 47, 5, 37)(2, 34, 7, 39, 20, 52, 31, 63, 27, 59, 11, 43, 3, 35, 10, 42, 25, 57, 14, 46, 16, 48, 29, 61, 23, 55, 12, 44, 22, 54, 8, 40)(65, 66)(67, 73)(68, 74)(69, 78)(70, 80)(71, 81)(72, 85)(75, 90)(76, 88)(77, 86)(79, 84)(82, 95)(83, 93)(87, 96)(89, 94)(91, 92)(97, 99)(98, 102)(100, 108)(101, 104)(103, 115)(105, 119)(106, 113)(107, 117)(109, 123)(110, 114)(111, 121)(112, 124)(116, 128)(118, 126)(120, 127)(122, 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) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.458 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.452 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y1 * Y3 * Y2 * Y3^-1, Y3 * Y2 * Y3^-1 * Y1, Y3 * Y2 * Y3^-1 * Y1, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-2 * Y2)^2, Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y3, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y2 ] Map:: R = (1, 33, 4, 36, 13, 45, 21, 53, 28, 60, 24, 56, 9, 41, 19, 51, 32, 64, 18, 50, 6, 38, 17, 49, 31, 63, 25, 57, 15, 47, 5, 37)(2, 34, 7, 39, 20, 52, 14, 46, 23, 55, 29, 61, 16, 48, 12, 44, 27, 59, 11, 43, 3, 35, 10, 42, 26, 58, 30, 62, 22, 54, 8, 40)(65, 66)(67, 73)(68, 76)(69, 75)(70, 80)(71, 83)(72, 82)(74, 89)(77, 86)(78, 88)(79, 84)(81, 94)(85, 93)(87, 95)(90, 92)(91, 96)(97, 99)(98, 102)(100, 103)(101, 110)(104, 117)(105, 119)(106, 115)(107, 114)(108, 113)(109, 123)(111, 122)(112, 124)(116, 128)(118, 127)(120, 126)(121, 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) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.461 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.453 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y3^2 * Y1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y1, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y1 * Y2)^8 ] Map:: R = (1, 33, 4, 36, 9, 41, 20, 52, 31, 63, 17, 49, 30, 62, 16, 48, 29, 61, 18, 50, 32, 64, 21, 53, 26, 58, 15, 47, 6, 38, 5, 37)(2, 34, 7, 39, 14, 46, 27, 59, 24, 56, 12, 44, 23, 55, 11, 43, 22, 54, 13, 45, 25, 57, 28, 60, 19, 51, 10, 42, 3, 35, 8, 40)(65, 66)(67, 73)(68, 75)(69, 77)(70, 78)(71, 80)(72, 82)(74, 85)(76, 84)(79, 92)(81, 91)(83, 95)(86, 93)(87, 96)(88, 90)(89, 94)(97, 99)(98, 102)(100, 108)(101, 107)(103, 113)(104, 112)(105, 115)(106, 114)(109, 111)(110, 122)(116, 123)(117, 124)(118, 126)(119, 125)(120, 128)(121, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.460 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.454 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-2 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y3^7 * Y1 * Y3 * Y2, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 ] Map:: R = (1, 33, 4, 36, 6, 38, 15, 47, 26, 58, 21, 53, 30, 62, 16, 48, 29, 61, 17, 49, 31, 63, 18, 50, 32, 64, 20, 52, 9, 41, 5, 37)(2, 34, 7, 39, 3, 35, 10, 42, 19, 51, 28, 60, 23, 55, 11, 43, 22, 54, 12, 44, 24, 56, 13, 45, 25, 57, 27, 59, 14, 46, 8, 40)(65, 66)(67, 73)(68, 75)(69, 76)(70, 78)(71, 80)(72, 81)(74, 85)(77, 84)(79, 92)(82, 91)(83, 96)(86, 93)(87, 95)(88, 94)(89, 90)(97, 99)(98, 102)(100, 108)(101, 109)(103, 113)(104, 114)(105, 115)(106, 112)(107, 111)(110, 122)(116, 123)(117, 124)(118, 127)(119, 128)(120, 125)(121, 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, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.459 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.455 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 16, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, (Y2^-1, Y1^-1), (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y1)^2, R * Y1 * R * Y2, (Y3 * Y2^-1)^2, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 4, 36)(2, 34, 9, 41)(3, 35, 12, 44)(5, 37, 14, 46)(6, 38, 15, 47)(7, 39, 17, 49)(8, 40, 19, 51)(10, 42, 20, 52)(11, 43, 22, 54)(13, 45, 24, 56)(16, 48, 26, 58)(18, 50, 28, 60)(21, 53, 29, 61)(23, 55, 30, 62)(25, 57, 31, 63)(27, 59, 32, 64)(65, 66, 71, 80, 89, 85, 77, 67, 72, 70, 74, 82, 91, 87, 75, 69)(68, 78, 86, 94, 96, 92, 84, 79, 83, 76, 88, 93, 95, 90, 81, 73)(97, 99, 107, 117, 123, 112, 106, 98, 104, 101, 109, 119, 121, 114, 103, 102)(100, 111, 113, 124, 127, 126, 120, 110, 115, 105, 116, 122, 128, 125, 118, 108) 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.462 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.456 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 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, Y3^2, (Y2^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^2 * Y1^2, R * Y1 * R * Y2, Y1^-1 * Y3 * Y2 * Y3, (Y3 * Y2^-2)^2, Y1^-6 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 4, 36)(2, 34, 9, 41)(3, 35, 12, 44)(5, 37, 15, 47)(6, 38, 14, 46)(7, 39, 17, 49)(8, 40, 19, 51)(10, 42, 20, 52)(11, 43, 22, 54)(13, 45, 24, 56)(16, 48, 26, 58)(18, 50, 28, 60)(21, 53, 29, 61)(23, 55, 30, 62)(25, 57, 31, 63)(27, 59, 32, 64)(65, 66, 71, 80, 89, 85, 77, 67, 72, 70, 74, 82, 91, 87, 75, 69)(68, 76, 86, 93, 96, 90, 84, 73, 83, 79, 88, 94, 95, 92, 81, 78)(97, 99, 107, 117, 123, 112, 106, 98, 104, 101, 109, 119, 121, 114, 103, 102)(100, 105, 113, 122, 127, 125, 120, 108, 115, 110, 116, 124, 128, 126, 118, 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.463 Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.457 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3 * Y2, Y3 * Y1 * Y3^7 * Y1 ] Map:: 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, 33)(3, 38)(4, 41)(5, 42)(6, 35)(7, 45)(8, 46)(9, 36)(10, 37)(11, 47)(12, 48)(13, 39)(14, 40)(15, 43)(16, 44)(17, 53)(18, 54)(19, 57)(20, 58)(21, 49)(22, 50)(23, 61)(24, 62)(25, 51)(26, 52)(27, 63)(28, 64)(29, 55)(30, 56)(31, 59)(32, 60)(65, 99)(66, 102)(67, 97)(68, 103)(69, 104)(70, 98)(71, 100)(72, 101)(73, 109)(74, 110)(75, 113)(76, 114)(77, 105)(78, 106)(79, 117)(80, 118)(81, 107)(82, 108)(83, 119)(84, 120)(85, 111)(86, 112)(87, 115)(88, 116)(89, 125)(90, 126)(91, 128)(92, 127)(93, 121)(94, 122)(95, 124)(96, 123) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.450 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.458 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y3^-1 * Y2 * Y3 * Y1, Y2 * Y3 * Y1 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3 * Y2 * Y3^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y3^2 * Y2, Y3^16 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 13, 45, 77, 109, 26, 58, 90, 122, 32, 64, 96, 128, 18, 50, 82, 114, 6, 38, 70, 102, 17, 49, 81, 113, 30, 62, 94, 126, 21, 53, 85, 117, 9, 41, 73, 105, 24, 56, 88, 120, 28, 60, 92, 124, 19, 51, 83, 115, 15, 47, 79, 111, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 20, 52, 84, 116, 31, 63, 95, 127, 27, 59, 91, 123, 11, 43, 75, 107, 3, 35, 67, 99, 10, 42, 74, 106, 25, 57, 89, 121, 14, 46, 78, 110, 16, 48, 80, 112, 29, 61, 93, 125, 23, 55, 87, 119, 12, 44, 76, 108, 22, 54, 86, 118, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 42)(5, 46)(6, 48)(7, 49)(8, 53)(9, 35)(10, 36)(11, 58)(12, 56)(13, 54)(14, 37)(15, 52)(16, 38)(17, 39)(18, 63)(19, 61)(20, 47)(21, 40)(22, 45)(23, 64)(24, 44)(25, 62)(26, 43)(27, 60)(28, 59)(29, 51)(30, 57)(31, 50)(32, 55)(65, 99)(66, 102)(67, 97)(68, 108)(69, 104)(70, 98)(71, 115)(72, 101)(73, 119)(74, 113)(75, 117)(76, 100)(77, 123)(78, 114)(79, 121)(80, 124)(81, 106)(82, 110)(83, 103)(84, 128)(85, 107)(86, 126)(87, 105)(88, 127)(89, 111)(90, 125)(91, 109)(92, 112)(93, 122)(94, 118)(95, 120)(96, 116) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.451 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.459 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y1 * Y3 * Y2 * Y3^-1, Y3 * Y2 * Y3^-1 * Y1, Y3 * Y2 * Y3^-1 * Y1, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-2 * Y2)^2, Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y3, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y2 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 13, 45, 77, 109, 21, 53, 85, 117, 28, 60, 92, 124, 24, 56, 88, 120, 9, 41, 73, 105, 19, 51, 83, 115, 32, 64, 96, 128, 18, 50, 82, 114, 6, 38, 70, 102, 17, 49, 81, 113, 31, 63, 95, 127, 25, 57, 89, 121, 15, 47, 79, 111, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 20, 52, 84, 116, 14, 46, 78, 110, 23, 55, 87, 119, 29, 61, 93, 125, 16, 48, 80, 112, 12, 44, 76, 108, 27, 59, 91, 123, 11, 43, 75, 107, 3, 35, 67, 99, 10, 42, 74, 106, 26, 58, 90, 122, 30, 62, 94, 126, 22, 54, 86, 118, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 44)(5, 43)(6, 48)(7, 51)(8, 50)(9, 35)(10, 57)(11, 37)(12, 36)(13, 54)(14, 56)(15, 52)(16, 38)(17, 62)(18, 40)(19, 39)(20, 47)(21, 61)(22, 45)(23, 63)(24, 46)(25, 42)(26, 60)(27, 64)(28, 58)(29, 53)(30, 49)(31, 55)(32, 59)(65, 99)(66, 102)(67, 97)(68, 103)(69, 110)(70, 98)(71, 100)(72, 117)(73, 119)(74, 115)(75, 114)(76, 113)(77, 123)(78, 101)(79, 122)(80, 124)(81, 108)(82, 107)(83, 106)(84, 128)(85, 104)(86, 127)(87, 105)(88, 126)(89, 125)(90, 111)(91, 109)(92, 112)(93, 121)(94, 120)(95, 118)(96, 116) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.454 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.460 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, Y3^2 * Y1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y1, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y1 * Y2)^8 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 9, 41, 73, 105, 20, 52, 84, 116, 31, 63, 95, 127, 17, 49, 81, 113, 30, 62, 94, 126, 16, 48, 80, 112, 29, 61, 93, 125, 18, 50, 82, 114, 32, 64, 96, 128, 21, 53, 85, 117, 26, 58, 90, 122, 15, 47, 79, 111, 6, 38, 70, 102, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 14, 46, 78, 110, 27, 59, 91, 123, 24, 56, 88, 120, 12, 44, 76, 108, 23, 55, 87, 119, 11, 43, 75, 107, 22, 54, 86, 118, 13, 45, 77, 109, 25, 57, 89, 121, 28, 60, 92, 124, 19, 51, 83, 115, 10, 42, 74, 106, 3, 35, 67, 99, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 43)(5, 45)(6, 46)(7, 48)(8, 50)(9, 35)(10, 53)(11, 36)(12, 52)(13, 37)(14, 38)(15, 60)(16, 39)(17, 59)(18, 40)(19, 63)(20, 44)(21, 42)(22, 61)(23, 64)(24, 58)(25, 62)(26, 56)(27, 49)(28, 47)(29, 54)(30, 57)(31, 51)(32, 55)(65, 99)(66, 102)(67, 97)(68, 108)(69, 107)(70, 98)(71, 113)(72, 112)(73, 115)(74, 114)(75, 101)(76, 100)(77, 111)(78, 122)(79, 109)(80, 104)(81, 103)(82, 106)(83, 105)(84, 123)(85, 124)(86, 126)(87, 125)(88, 128)(89, 127)(90, 110)(91, 116)(92, 117)(93, 119)(94, 118)(95, 121)(96, 120) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.453 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.461 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-2 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y3^7 * Y1 * Y3 * Y2, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 6, 38, 70, 102, 15, 47, 79, 111, 26, 58, 90, 122, 21, 53, 85, 117, 30, 62, 94, 126, 16, 48, 80, 112, 29, 61, 93, 125, 17, 49, 81, 113, 31, 63, 95, 127, 18, 50, 82, 114, 32, 64, 96, 128, 20, 52, 84, 116, 9, 41, 73, 105, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 3, 35, 67, 99, 10, 42, 74, 106, 19, 51, 83, 115, 28, 60, 92, 124, 23, 55, 87, 119, 11, 43, 75, 107, 22, 54, 86, 118, 12, 44, 76, 108, 24, 56, 88, 120, 13, 45, 77, 109, 25, 57, 89, 121, 27, 59, 91, 123, 14, 46, 78, 110, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 43)(5, 44)(6, 46)(7, 48)(8, 49)(9, 35)(10, 53)(11, 36)(12, 37)(13, 52)(14, 38)(15, 60)(16, 39)(17, 40)(18, 59)(19, 64)(20, 45)(21, 42)(22, 61)(23, 63)(24, 62)(25, 58)(26, 57)(27, 50)(28, 47)(29, 54)(30, 56)(31, 55)(32, 51)(65, 99)(66, 102)(67, 97)(68, 108)(69, 109)(70, 98)(71, 113)(72, 114)(73, 115)(74, 112)(75, 111)(76, 100)(77, 101)(78, 122)(79, 107)(80, 106)(81, 103)(82, 104)(83, 105)(84, 123)(85, 124)(86, 127)(87, 128)(88, 125)(89, 126)(90, 110)(91, 116)(92, 117)(93, 120)(94, 121)(95, 118)(96, 119) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.452 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.462 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 16, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, (Y2^-1, Y1^-1), (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y1)^2, R * Y1 * R * Y2, (Y3 * Y2^-1)^2, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100)(2, 34, 66, 98, 9, 41, 73, 105)(3, 35, 67, 99, 12, 44, 76, 108)(5, 37, 69, 101, 14, 46, 78, 110)(6, 38, 70, 102, 15, 47, 79, 111)(7, 39, 71, 103, 17, 49, 81, 113)(8, 40, 72, 104, 19, 51, 83, 115)(10, 42, 74, 106, 20, 52, 84, 116)(11, 43, 75, 107, 22, 54, 86, 118)(13, 45, 77, 109, 24, 56, 88, 120)(16, 48, 80, 112, 26, 58, 90, 122)(18, 50, 82, 114, 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, 39)(3, 40)(4, 46)(5, 33)(6, 42)(7, 48)(8, 38)(9, 36)(10, 50)(11, 37)(12, 56)(13, 35)(14, 54)(15, 51)(16, 57)(17, 41)(18, 59)(19, 44)(20, 47)(21, 45)(22, 62)(23, 43)(24, 61)(25, 53)(26, 49)(27, 55)(28, 52)(29, 63)(30, 64)(31, 58)(32, 60)(65, 99)(66, 104)(67, 107)(68, 111)(69, 109)(70, 97)(71, 102)(72, 101)(73, 116)(74, 98)(75, 117)(76, 100)(77, 119)(78, 115)(79, 113)(80, 106)(81, 124)(82, 103)(83, 105)(84, 122)(85, 123)(86, 108)(87, 121)(88, 110)(89, 114)(90, 128)(91, 112)(92, 127)(93, 118)(94, 120)(95, 126)(96, 125) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.455 Transitivity :: VT+ Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.463 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 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, Y3^2, (Y2^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^2 * Y1^2, R * Y1 * R * Y2, Y1^-1 * Y3 * Y2 * Y3, (Y3 * Y2^-2)^2, Y1^-6 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100)(2, 34, 66, 98, 9, 41, 73, 105)(3, 35, 67, 99, 12, 44, 76, 108)(5, 37, 69, 101, 15, 47, 79, 111)(6, 38, 70, 102, 14, 46, 78, 110)(7, 39, 71, 103, 17, 49, 81, 113)(8, 40, 72, 104, 19, 51, 83, 115)(10, 42, 74, 106, 20, 52, 84, 116)(11, 43, 75, 107, 22, 54, 86, 118)(13, 45, 77, 109, 24, 56, 88, 120)(16, 48, 80, 112, 26, 58, 90, 122)(18, 50, 82, 114, 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, 39)(3, 40)(4, 44)(5, 33)(6, 42)(7, 48)(8, 38)(9, 51)(10, 50)(11, 37)(12, 54)(13, 35)(14, 36)(15, 56)(16, 57)(17, 46)(18, 59)(19, 47)(20, 41)(21, 45)(22, 61)(23, 43)(24, 62)(25, 53)(26, 52)(27, 55)(28, 49)(29, 64)(30, 63)(31, 60)(32, 58)(65, 99)(66, 104)(67, 107)(68, 105)(69, 109)(70, 97)(71, 102)(72, 101)(73, 113)(74, 98)(75, 117)(76, 115)(77, 119)(78, 116)(79, 100)(80, 106)(81, 122)(82, 103)(83, 110)(84, 124)(85, 123)(86, 111)(87, 121)(88, 108)(89, 114)(90, 127)(91, 112)(92, 128)(93, 120)(94, 118)(95, 125)(96, 126) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.456 Transitivity :: VT+ Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.464 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * Y1 * Y2 * Y1)^2, Y2^7 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 11, 43)(6, 38, 13, 45)(8, 40, 12, 44)(10, 42, 14, 46)(15, 47, 20, 52)(16, 48, 21, 53)(17, 49, 25, 57)(18, 50, 23, 55)(19, 51, 27, 59)(22, 54, 29, 61)(24, 56, 31, 63)(26, 58, 30, 62)(28, 60, 32, 64)(65, 97, 67, 99, 72, 104, 81, 113, 90, 122, 95, 127, 87, 119, 77, 109, 85, 117, 75, 107, 84, 116, 93, 125, 92, 124, 83, 115, 74, 106, 68, 100)(66, 98, 69, 101, 76, 108, 86, 118, 94, 126, 91, 123, 82, 114, 73, 105, 80, 112, 71, 103, 79, 111, 89, 121, 96, 128, 88, 120, 78, 110, 70, 102) 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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.465 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2 * Y1)^4, Y2^7 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 11, 43)(6, 38, 13, 45)(8, 40, 14, 46)(10, 42, 12, 44)(15, 47, 20, 52)(16, 48, 23, 55)(17, 49, 25, 57)(18, 50, 21, 53)(19, 51, 27, 59)(22, 54, 29, 61)(24, 56, 31, 63)(26, 58, 32, 64)(28, 60, 30, 62)(65, 97, 67, 99, 72, 104, 81, 113, 90, 122, 93, 125, 85, 117, 75, 107, 84, 116, 77, 109, 87, 119, 95, 127, 92, 124, 83, 115, 74, 106, 68, 100)(66, 98, 69, 101, 76, 108, 86, 118, 94, 126, 89, 121, 80, 112, 71, 103, 79, 111, 73, 105, 82, 114, 91, 123, 96, 128, 88, 120, 78, 110, 70, 102) 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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.466 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y3 * Y1 * Y2^-1, Y3 * Y2^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 7, 39)(5, 37, 13, 45)(6, 38, 11, 43)(8, 40, 12, 44)(10, 42, 15, 47)(14, 46, 16, 48)(17, 49, 19, 51)(18, 50, 25, 57)(20, 52, 21, 53)(22, 54, 29, 61)(23, 55, 27, 59)(24, 56, 28, 60)(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, 69, 101)(66, 98, 70, 102, 79, 111, 87, 119, 95, 127, 93, 125, 85, 117, 77, 109, 71, 103, 73, 105, 81, 113, 89, 121, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 71)(3, 75)(4, 65)(5, 76)(6, 73)(7, 66)(8, 77)(9, 70)(10, 83)(11, 67)(12, 69)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.467 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y3 * Y2^-1 * Y3 * Y2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y3 * Y2, Y3 * Y2^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 7, 39)(5, 37, 13, 45)(6, 38, 12, 44)(8, 40, 11, 43)(10, 42, 16, 48)(14, 46, 15, 47)(17, 49, 19, 51)(18, 50, 25, 57)(20, 52, 21, 53)(22, 54, 29, 61)(23, 55, 28, 60)(24, 56, 27, 59)(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, 69, 101)(66, 98, 70, 102, 79, 111, 87, 119, 95, 127, 89, 121, 81, 113, 73, 105, 71, 103, 77, 109, 85, 117, 93, 125, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 71)(3, 75)(4, 65)(5, 76)(6, 77)(7, 66)(8, 73)(9, 72)(10, 83)(11, 67)(12, 69)(13, 70)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.468 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y2 * Y1 * Y3, R * Y2 * Y1 * R * Y2, Y2^8 * Y1, Y1 * Y3 * Y2^3 * Y3 * Y2^-3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 7, 39)(5, 37, 8, 40)(9, 41, 15, 47)(10, 42, 11, 43)(12, 44, 13, 45)(14, 46, 16, 48)(17, 49, 23, 55)(18, 50, 19, 51)(20, 52, 21, 53)(22, 54, 24, 56)(25, 57, 30, 62)(26, 58, 27, 59)(28, 60, 29, 61)(31, 63, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 88, 120, 80, 112, 72, 104, 66, 98, 70, 102, 79, 111, 87, 119, 94, 126, 86, 118, 78, 110, 69, 101)(68, 100, 75, 107, 82, 114, 91, 123, 95, 127, 93, 125, 85, 117, 77, 109, 71, 103, 74, 106, 83, 115, 90, 122, 96, 128, 92, 124, 84, 116, 76, 108) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 77)(6, 75)(7, 66)(8, 76)(9, 82)(10, 67)(11, 70)(12, 72)(13, 69)(14, 84)(15, 83)(16, 85)(17, 90)(18, 73)(19, 79)(20, 78)(21, 80)(22, 93)(23, 91)(24, 92)(25, 95)(26, 81)(27, 87)(28, 88)(29, 86)(30, 96)(31, 89)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.469 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.469 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 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 :: [ Y1^2, R^2, Y3^2, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y1, (Y3 * Y1)^2, Y2^-1 * Y3 * Y2 * Y1, (R * Y3)^2, (R * Y2 * Y3)^2, Y3 * Y2^7 * Y3 * Y2, (Y2^-1 * Y1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 7, 39)(5, 37, 11, 43)(6, 38, 13, 45)(8, 40, 15, 47)(10, 42, 14, 46)(12, 44, 16, 48)(17, 49, 21, 53)(18, 50, 25, 57)(19, 51, 23, 55)(20, 52, 27, 59)(22, 54, 29, 61)(24, 56, 31, 63)(26, 58, 30, 62)(28, 60, 32, 64)(65, 97, 67, 99, 74, 106, 82, 114, 90, 122, 95, 127, 87, 119, 79, 111, 71, 103, 77, 109, 85, 117, 93, 125, 92, 124, 84, 116, 76, 108, 69, 101)(66, 98, 70, 102, 78, 110, 86, 118, 94, 126, 91, 123, 83, 115, 75, 107, 68, 100, 73, 105, 81, 113, 89, 121, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 71)(3, 70)(4, 65)(5, 72)(6, 67)(7, 66)(8, 69)(9, 77)(10, 81)(11, 79)(12, 83)(13, 73)(14, 85)(15, 75)(16, 87)(17, 74)(18, 86)(19, 76)(20, 88)(21, 78)(22, 82)(23, 80)(24, 84)(25, 93)(26, 96)(27, 95)(28, 94)(29, 89)(30, 92)(31, 91)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.468 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.470 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (Y3 * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^4, Y2^4 * Y3, (Y1 * Y2^-2)^2, Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y3 * 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 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 10, 42)(5, 37, 17, 49)(6, 38, 8, 40)(7, 39, 20, 52)(9, 41, 26, 58)(12, 44, 27, 59)(13, 45, 25, 57)(14, 46, 28, 60)(15, 47, 24, 56)(16, 48, 22, 54)(18, 50, 21, 53)(19, 51, 23, 55)(29, 61, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 76, 108, 83, 115, 70, 102, 78, 110, 94, 126, 84, 116, 79, 111, 90, 122, 95, 127, 80, 112, 68, 100, 77, 109, 82, 114, 69, 101)(66, 98, 71, 103, 85, 117, 92, 124, 74, 106, 87, 119, 93, 125, 75, 107, 88, 120, 81, 113, 96, 128, 89, 121, 72, 104, 86, 118, 91, 123, 73, 105) L = (1, 68)(2, 72)(3, 77)(4, 79)(5, 80)(6, 65)(7, 86)(8, 88)(9, 89)(10, 66)(11, 92)(12, 82)(13, 90)(14, 67)(15, 70)(16, 84)(17, 87)(18, 95)(19, 69)(20, 83)(21, 91)(22, 81)(23, 71)(24, 74)(25, 75)(26, 78)(27, 96)(28, 73)(29, 85)(30, 76)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.471 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.471 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y1 * Y3^-1)^2, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^4, Y3^-1 * Y2^4, Y3^-1 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1, (Y2^2 * Y1)^2, Y2 * Y3 * Y2^2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 10, 42)(5, 37, 17, 49)(6, 38, 8, 40)(7, 39, 20, 52)(9, 41, 26, 58)(12, 44, 27, 59)(13, 45, 25, 57)(14, 46, 28, 60)(15, 47, 24, 56)(16, 48, 22, 54)(18, 50, 21, 53)(19, 51, 23, 55)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 76, 108, 80, 112, 68, 100, 77, 109, 94, 126, 84, 116, 79, 111, 90, 122, 96, 128, 83, 115, 70, 102, 78, 110, 82, 114, 69, 101)(66, 98, 71, 103, 85, 117, 89, 121, 72, 104, 86, 118, 93, 125, 75, 107, 88, 120, 81, 113, 95, 127, 92, 124, 74, 106, 87, 119, 91, 123, 73, 105) L = (1, 68)(2, 72)(3, 77)(4, 79)(5, 80)(6, 65)(7, 86)(8, 88)(9, 89)(10, 66)(11, 92)(12, 94)(13, 90)(14, 67)(15, 70)(16, 84)(17, 87)(18, 76)(19, 69)(20, 83)(21, 93)(22, 81)(23, 71)(24, 74)(25, 75)(26, 78)(27, 85)(28, 73)(29, 95)(30, 96)(31, 91)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.470 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.472 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3 * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y1 * Y2^-1 * Y3^2 * Y1, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3, Y3^8, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 10, 42)(5, 37, 15, 47)(6, 38, 8, 40)(7, 39, 17, 49)(9, 41, 21, 53)(12, 44, 24, 56)(13, 45, 22, 54)(14, 46, 29, 61)(16, 48, 19, 51)(18, 50, 26, 58)(20, 52, 28, 60)(23, 55, 32, 64)(25, 57, 27, 59)(30, 62, 31, 63)(65, 97, 67, 99, 70, 102, 76, 108, 80, 112, 90, 122, 95, 127, 81, 113, 96, 128, 85, 117, 91, 123, 92, 124, 77, 109, 78, 110, 68, 100, 69, 101)(66, 98, 71, 103, 74, 106, 82, 114, 86, 118, 88, 120, 89, 121, 75, 107, 87, 119, 79, 111, 94, 126, 93, 125, 83, 115, 84, 116, 72, 104, 73, 105) L = (1, 68)(2, 72)(3, 69)(4, 77)(5, 78)(6, 65)(7, 73)(8, 83)(9, 84)(10, 66)(11, 88)(12, 67)(13, 91)(14, 92)(15, 75)(16, 70)(17, 90)(18, 71)(19, 94)(20, 93)(21, 81)(22, 74)(23, 89)(24, 82)(25, 86)(26, 76)(27, 96)(28, 85)(29, 79)(30, 87)(31, 80)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.475 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.473 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y3, Y1 * Y2 * Y3^3 * Y1 * Y2^-1, Y3^8 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 10, 42)(5, 37, 14, 46)(6, 38, 8, 40)(7, 39, 17, 49)(9, 41, 20, 52)(12, 44, 25, 57)(13, 45, 22, 54)(15, 47, 29, 61)(16, 48, 19, 51)(18, 50, 26, 58)(21, 53, 30, 62)(23, 55, 32, 64)(24, 56, 31, 63)(27, 59, 28, 60)(65, 97, 67, 99, 68, 100, 76, 108, 77, 109, 90, 122, 91, 123, 81, 113, 96, 128, 84, 116, 95, 127, 94, 126, 80, 112, 79, 111, 70, 102, 69, 101)(66, 98, 71, 103, 72, 104, 82, 114, 83, 115, 89, 121, 88, 120, 75, 107, 87, 119, 78, 110, 92, 124, 93, 125, 86, 118, 85, 117, 74, 106, 73, 105) L = (1, 68)(2, 72)(3, 76)(4, 77)(5, 67)(6, 65)(7, 82)(8, 83)(9, 71)(10, 66)(11, 78)(12, 90)(13, 91)(14, 93)(15, 69)(16, 70)(17, 84)(18, 89)(19, 88)(20, 94)(21, 73)(22, 74)(23, 92)(24, 87)(25, 75)(26, 81)(27, 96)(28, 86)(29, 85)(30, 79)(31, 80)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.474 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^3 * Y2^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y2, Y3^2 * Y2^-4, Y2^4 * Y3^-2, (Y2^-1 * Y3 * Y2^-1)^2, (Y2^2 * Y1)^2, Y2^4 * Y3^-2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 10, 42)(5, 37, 17, 49)(6, 38, 8, 40)(7, 39, 14, 46)(9, 41, 16, 48)(12, 44, 24, 56)(13, 45, 28, 60)(15, 47, 26, 58)(18, 50, 21, 53)(19, 51, 32, 64)(20, 52, 23, 55)(22, 54, 31, 63)(25, 57, 29, 61)(27, 59, 30, 62)(65, 97, 67, 99, 76, 108, 93, 125, 79, 111, 83, 115, 70, 102, 78, 110, 94, 126, 80, 112, 68, 100, 77, 109, 84, 116, 95, 127, 82, 114, 69, 101)(66, 98, 71, 103, 85, 117, 96, 128, 87, 119, 89, 121, 74, 106, 75, 107, 91, 123, 81, 113, 72, 104, 86, 118, 90, 122, 92, 124, 88, 120, 73, 105) L = (1, 68)(2, 72)(3, 77)(4, 79)(5, 80)(6, 65)(7, 86)(8, 87)(9, 81)(10, 66)(11, 71)(12, 84)(13, 83)(14, 67)(15, 82)(16, 93)(17, 96)(18, 94)(19, 69)(20, 70)(21, 90)(22, 89)(23, 88)(24, 91)(25, 73)(26, 74)(27, 85)(28, 75)(29, 95)(30, 76)(31, 78)(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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.475 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^2 * Y3^-2, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1, Y3^-2 * Y2^-4, (Y2^-1 * Y3^-1 * Y2^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 11, 43)(4, 36, 10, 42)(5, 37, 17, 49)(6, 38, 8, 40)(7, 39, 13, 45)(9, 41, 19, 51)(12, 44, 25, 57)(14, 46, 28, 60)(15, 47, 26, 58)(16, 48, 32, 64)(18, 50, 21, 53)(20, 52, 23, 55)(22, 54, 31, 63)(24, 56, 29, 61)(27, 59, 30, 62)(65, 97, 67, 99, 76, 108, 93, 125, 84, 116, 80, 112, 68, 100, 77, 109, 94, 126, 83, 115, 70, 102, 78, 110, 79, 111, 95, 127, 82, 114, 69, 101)(66, 98, 71, 103, 85, 117, 96, 128, 90, 122, 88, 120, 72, 104, 75, 107, 91, 123, 81, 113, 74, 106, 86, 118, 87, 119, 92, 124, 89, 121, 73, 105) L = (1, 68)(2, 72)(3, 77)(4, 79)(5, 80)(6, 65)(7, 75)(8, 87)(9, 88)(10, 66)(11, 92)(12, 94)(13, 95)(14, 67)(15, 76)(16, 78)(17, 73)(18, 84)(19, 69)(20, 70)(21, 91)(22, 71)(23, 85)(24, 86)(25, 90)(26, 74)(27, 89)(28, 96)(29, 83)(30, 82)(31, 93)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 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 E15.472 Graph:: bipartite v = 18 e = 64 f = 18 degree seq :: [ 4^16, 32^2 ] E15.476 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^16 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 30, 31, 26, 27, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(33, 34, 38, 42, 46, 50, 54, 58, 62, 61, 57, 53, 49, 45, 41, 36)(35, 37, 39, 43, 47, 51, 55, 59, 63, 64, 60, 56, 52, 48, 44, 40) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.487 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.477 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^16, (T2^-1 * T1^-1)^32 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 19, 18, 23, 22, 27, 26, 31, 30, 32, 28, 29, 24, 25, 20, 21, 16, 17, 12, 13, 8, 9, 4, 5)(33, 34, 38, 42, 46, 50, 54, 58, 62, 60, 56, 52, 48, 44, 40, 36)(35, 39, 43, 47, 51, 55, 59, 63, 64, 61, 57, 53, 49, 45, 41, 37) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.489 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.478 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T1 * T2^-10 ] Map:: non-degenerate R = (1, 3, 9, 16, 22, 28, 27, 21, 15, 8, 2, 7, 11, 18, 24, 30, 32, 26, 20, 14, 6, 12, 4, 10, 17, 23, 29, 31, 25, 19, 13, 5)(33, 34, 38, 45, 47, 52, 57, 59, 64, 61, 54, 56, 49, 41, 43, 36)(35, 39, 44, 37, 40, 46, 51, 53, 58, 63, 60, 62, 55, 48, 50, 42) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.488 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.479 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^9, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 3, 9, 16, 22, 28, 30, 24, 18, 12, 4, 10, 6, 14, 20, 26, 32, 29, 23, 17, 11, 8, 2, 7, 15, 21, 27, 31, 25, 19, 13, 5)(33, 34, 38, 41, 47, 52, 54, 59, 64, 62, 57, 55, 50, 45, 43, 36)(35, 39, 46, 48, 53, 58, 60, 63, 61, 56, 51, 49, 44, 37, 40, 42) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.491 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.480 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2 * T1, T2^-6 * T1, T1 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-2 * T1, (T2^-1 * T1^-1 * T2^-1)^12 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 28, 27, 16, 6, 15, 22, 30, 32, 26, 14, 23, 11, 21, 29, 31, 24, 12, 4, 10, 20, 25, 13, 5)(33, 34, 38, 46, 56, 45, 50, 59, 64, 61, 52, 41, 49, 54, 43, 36)(35, 39, 47, 55, 44, 37, 40, 48, 58, 63, 57, 51, 60, 62, 53, 42) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.490 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.481 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^5, T1^3 * T2^-1 * T1 * T2^-1 * T1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 12, 4, 10, 20, 29, 31, 23, 11, 21, 14, 26, 32, 30, 22, 16, 6, 15, 27, 28, 18, 8, 2, 7, 17, 25, 13, 5)(33, 34, 38, 46, 52, 41, 49, 59, 64, 63, 56, 45, 50, 54, 43, 36)(35, 39, 47, 58, 61, 51, 57, 60, 62, 55, 44, 37, 40, 48, 53, 42) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.493 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.482 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-3 * T1, T1^2 * T2 * T1 * T2 * T1^4, T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^4 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 31, 23, 29, 20, 27, 22, 12, 4, 10, 18, 8, 2, 7, 17, 25, 14, 24, 28, 32, 30, 21, 11, 19, 13, 5)(33, 34, 38, 46, 55, 62, 54, 45, 50, 41, 49, 58, 60, 52, 43, 36)(35, 39, 47, 56, 61, 53, 44, 37, 40, 48, 57, 63, 64, 59, 51, 42) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.492 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.483 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-3 * T1^-1, T1^6 * T2^-1 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 32, 30, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 23, 31, 26, 16, 6, 15, 13, 5)(33, 34, 38, 46, 55, 60, 52, 41, 49, 45, 50, 58, 62, 54, 43, 36)(35, 39, 47, 56, 63, 64, 59, 51, 44, 37, 40, 48, 57, 61, 53, 42) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^16 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.494 Transitivity :: ET+ Graph:: bipartite v = 3 e = 32 f = 1 degree seq :: [ 16^2, 32 ] E15.484 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T2 * T1^3, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-10, (T2^5 * T1^-1)^2 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 29, 23, 17, 11, 5)(33, 34, 38, 37, 40, 44, 43, 46, 50, 49, 52, 56, 55, 58, 62, 61, 64, 59, 63, 60, 53, 57, 54, 47, 51, 48, 41, 45, 42, 35, 39, 36) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.495 Transitivity :: ET+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.485 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T1^-1 * T2 * T1^-4, T1 * T2 * T1 * T2^5, T2 * 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^-2 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 21, 11, 14, 24, 31, 28, 18, 8, 2, 7, 17, 27, 22, 12, 4, 10, 20, 30, 32, 26, 16, 6, 15, 25, 23, 13, 5)(33, 34, 38, 46, 42, 35, 39, 47, 56, 52, 41, 49, 57, 63, 62, 51, 59, 55, 60, 64, 61, 54, 45, 50, 58, 53, 44, 37, 40, 48, 43, 36) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.496 Transitivity :: ET+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.486 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {16, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2^2 * T1^-2 * T2, T2^-1 * T1^-1 * T2^-4 * T1^-2, T2^4 * T1^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 26, 22, 32, 18, 8, 2, 7, 17, 31, 23, 11, 21, 30, 16, 6, 15, 29, 24, 12, 4, 10, 20, 28, 14, 27, 25, 13, 5)(33, 34, 38, 46, 58, 55, 44, 37, 40, 48, 60, 51, 63, 56, 45, 50, 62, 52, 41, 49, 61, 57, 64, 53, 42, 35, 39, 47, 59, 54, 43, 36) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.497 Transitivity :: ET+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.487 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^16 ] Map:: non-degenerate R = (1, 33, 3, 35, 4, 36, 8, 40, 9, 41, 12, 44, 13, 45, 16, 48, 17, 49, 20, 52, 21, 53, 24, 56, 25, 57, 28, 60, 29, 61, 32, 64, 30, 62, 31, 63, 26, 58, 27, 59, 22, 54, 23, 55, 18, 50, 19, 51, 14, 46, 15, 47, 10, 42, 11, 43, 6, 38, 7, 39, 2, 34, 5, 37) L = (1, 34)(2, 38)(3, 37)(4, 33)(5, 39)(6, 42)(7, 43)(8, 35)(9, 36)(10, 46)(11, 47)(12, 40)(13, 41)(14, 50)(15, 51)(16, 44)(17, 45)(18, 54)(19, 55)(20, 48)(21, 49)(22, 58)(23, 59)(24, 52)(25, 53)(26, 62)(27, 63)(28, 56)(29, 57)(30, 61)(31, 64)(32, 60) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.476 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.488 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^16, (T2^-1 * T1^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 2, 34, 7, 39, 6, 38, 11, 43, 10, 42, 15, 47, 14, 46, 19, 51, 18, 50, 23, 55, 22, 54, 27, 59, 26, 58, 31, 63, 30, 62, 32, 64, 28, 60, 29, 61, 24, 56, 25, 57, 20, 52, 21, 53, 16, 48, 17, 49, 12, 44, 13, 45, 8, 40, 9, 41, 4, 36, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 35)(6, 42)(7, 43)(8, 36)(9, 37)(10, 46)(11, 47)(12, 40)(13, 41)(14, 50)(15, 51)(16, 44)(17, 45)(18, 54)(19, 55)(20, 48)(21, 49)(22, 58)(23, 59)(24, 52)(25, 53)(26, 62)(27, 63)(28, 56)(29, 57)(30, 60)(31, 64)(32, 61) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.478 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.489 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T1 * T2^-10 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 16, 48, 22, 54, 28, 60, 27, 59, 21, 53, 15, 47, 8, 40, 2, 34, 7, 39, 11, 43, 18, 50, 24, 56, 30, 62, 32, 64, 26, 58, 20, 52, 14, 46, 6, 38, 12, 44, 4, 36, 10, 42, 17, 49, 23, 55, 29, 61, 31, 63, 25, 57, 19, 51, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 45)(7, 44)(8, 46)(9, 43)(10, 35)(11, 36)(12, 37)(13, 47)(14, 51)(15, 52)(16, 50)(17, 41)(18, 42)(19, 53)(20, 57)(21, 58)(22, 56)(23, 48)(24, 49)(25, 59)(26, 63)(27, 64)(28, 62)(29, 54)(30, 55)(31, 60)(32, 61) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.477 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.490 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^9, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 16, 48, 22, 54, 28, 60, 30, 62, 24, 56, 18, 50, 12, 44, 4, 36, 10, 42, 6, 38, 14, 46, 20, 52, 26, 58, 32, 64, 29, 61, 23, 55, 17, 49, 11, 43, 8, 40, 2, 34, 7, 39, 15, 47, 21, 53, 27, 59, 31, 63, 25, 57, 19, 51, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 41)(7, 46)(8, 42)(9, 47)(10, 35)(11, 36)(12, 37)(13, 43)(14, 48)(15, 52)(16, 53)(17, 44)(18, 45)(19, 49)(20, 54)(21, 58)(22, 59)(23, 50)(24, 51)(25, 55)(26, 60)(27, 64)(28, 63)(29, 56)(30, 57)(31, 61)(32, 62) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.480 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.491 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2 * T1, T2^-6 * T1, T1 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-2 * T1, (T2^-1 * T1^-1 * T2^-1)^12 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 18, 50, 8, 40, 2, 34, 7, 39, 17, 49, 28, 60, 27, 59, 16, 48, 6, 38, 15, 47, 22, 54, 30, 62, 32, 64, 26, 58, 14, 46, 23, 55, 11, 43, 21, 53, 29, 61, 31, 63, 24, 56, 12, 44, 4, 36, 10, 42, 20, 52, 25, 57, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 56)(15, 55)(16, 58)(17, 54)(18, 59)(19, 60)(20, 41)(21, 42)(22, 43)(23, 44)(24, 45)(25, 51)(26, 63)(27, 64)(28, 62)(29, 52)(30, 53)(31, 57)(32, 61) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.479 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.492 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^5, T1^3 * T2^-1 * T1 * T2^-1 * T1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 24, 56, 12, 44, 4, 36, 10, 42, 20, 52, 29, 61, 31, 63, 23, 55, 11, 43, 21, 53, 14, 46, 26, 58, 32, 64, 30, 62, 22, 54, 16, 48, 6, 38, 15, 47, 27, 59, 28, 60, 18, 50, 8, 40, 2, 34, 7, 39, 17, 49, 25, 57, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 52)(15, 58)(16, 53)(17, 59)(18, 54)(19, 57)(20, 41)(21, 42)(22, 43)(23, 44)(24, 45)(25, 60)(26, 61)(27, 64)(28, 62)(29, 51)(30, 55)(31, 56)(32, 63) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.482 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.493 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-3 * T1, T1^2 * T2 * T1 * T2 * T1^4, T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^4 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 16, 48, 6, 38, 15, 47, 26, 58, 31, 63, 23, 55, 29, 61, 20, 52, 27, 59, 22, 54, 12, 44, 4, 36, 10, 42, 18, 50, 8, 40, 2, 34, 7, 39, 17, 49, 25, 57, 14, 46, 24, 56, 28, 60, 32, 64, 30, 62, 21, 53, 11, 43, 19, 51, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 55)(15, 56)(16, 57)(17, 58)(18, 41)(19, 42)(20, 43)(21, 44)(22, 45)(23, 62)(24, 61)(25, 63)(26, 60)(27, 51)(28, 52)(29, 53)(30, 54)(31, 64)(32, 59) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.481 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.494 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-3 * T1^-1, T1^6 * T2^-1 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 11, 43, 21, 53, 28, 60, 32, 64, 30, 62, 25, 57, 14, 46, 24, 56, 18, 50, 8, 40, 2, 34, 7, 39, 17, 49, 12, 44, 4, 36, 10, 42, 20, 52, 27, 59, 22, 54, 29, 61, 23, 55, 31, 63, 26, 58, 16, 48, 6, 38, 15, 47, 13, 45, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 55)(15, 56)(16, 57)(17, 45)(18, 58)(19, 44)(20, 41)(21, 42)(22, 43)(23, 60)(24, 63)(25, 61)(26, 62)(27, 51)(28, 52)(29, 53)(30, 54)(31, 64)(32, 59) local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E15.483 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 3 degree seq :: [ 64 ] E15.495 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2, (F * T2)^2, (F * T1)^2, T2^16, (T2^-1 * T1^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 29, 61, 25, 57, 21, 53, 17, 49, 13, 45, 9, 41, 5, 37)(2, 34, 6, 38, 10, 42, 14, 46, 18, 50, 22, 54, 26, 58, 30, 62, 32, 64, 28, 60, 24, 56, 20, 52, 16, 48, 12, 44, 8, 40, 4, 36) L = (1, 34)(2, 35)(3, 38)(4, 33)(5, 36)(6, 39)(7, 42)(8, 37)(9, 40)(10, 43)(11, 46)(12, 41)(13, 44)(14, 47)(15, 50)(16, 45)(17, 48)(18, 51)(19, 54)(20, 49)(21, 52)(22, 55)(23, 58)(24, 53)(25, 56)(26, 59)(27, 62)(28, 57)(29, 60)(30, 63)(31, 64)(32, 61) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.484 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.496 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-5 * T1^2, T2^-1 * T1^-6, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 16, 48, 6, 38, 15, 47, 27, 59, 32, 64, 30, 62, 23, 55, 11, 43, 21, 53, 25, 57, 13, 45, 5, 37)(2, 34, 7, 39, 17, 49, 28, 60, 26, 58, 14, 46, 22, 54, 29, 61, 31, 63, 24, 56, 12, 44, 4, 36, 10, 42, 20, 52, 18, 50, 8, 40) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 55)(15, 54)(16, 58)(17, 59)(18, 51)(19, 60)(20, 41)(21, 42)(22, 43)(23, 44)(24, 45)(25, 52)(26, 62)(27, 61)(28, 64)(29, 53)(30, 56)(31, 57)(32, 63) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.485 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.497 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {16, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^6, T2 * T1 * T2 * T1 * T2^3, (T1^-1 * T2^-1 * T1^-1)^4 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 19, 51, 23, 55, 11, 43, 21, 53, 30, 62, 32, 64, 27, 59, 16, 48, 6, 38, 15, 47, 25, 57, 13, 45, 5, 37)(2, 34, 7, 39, 17, 49, 24, 56, 12, 44, 4, 36, 10, 42, 20, 52, 29, 61, 31, 63, 22, 54, 14, 46, 26, 58, 28, 60, 18, 50, 8, 40) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 46)(7, 47)(8, 48)(9, 49)(10, 35)(11, 36)(12, 37)(13, 50)(14, 53)(15, 58)(16, 54)(17, 57)(18, 59)(19, 56)(20, 41)(21, 42)(22, 43)(23, 44)(24, 45)(25, 60)(26, 62)(27, 63)(28, 64)(29, 51)(30, 52)(31, 55)(32, 61) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible Dual of E15.486 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.498 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-7 * Y1^2 * Y3^-7, 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:: R = (1, 33, 2, 34, 6, 38, 10, 42, 14, 46, 18, 50, 22, 54, 26, 58, 30, 62, 28, 60, 24, 56, 20, 52, 16, 48, 12, 44, 8, 40, 4, 36)(3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 32, 64, 29, 61, 25, 57, 21, 53, 17, 49, 13, 45, 9, 41, 5, 37)(65, 97, 67, 99, 66, 98, 71, 103, 70, 102, 75, 107, 74, 106, 79, 111, 78, 110, 83, 115, 82, 114, 87, 119, 86, 118, 91, 123, 90, 122, 95, 127, 94, 126, 96, 128, 92, 124, 93, 125, 88, 120, 89, 121, 84, 116, 85, 117, 80, 112, 81, 113, 76, 108, 77, 109, 72, 104, 73, 105, 68, 100, 69, 101) L = (1, 68)(2, 65)(3, 69)(4, 72)(5, 73)(6, 66)(7, 67)(8, 76)(9, 77)(10, 70)(11, 71)(12, 80)(13, 81)(14, 74)(15, 75)(16, 84)(17, 85)(18, 78)(19, 79)(20, 88)(21, 89)(22, 82)(23, 83)(24, 92)(25, 93)(26, 86)(27, 87)(28, 94)(29, 96)(30, 90)(31, 91)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 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 E15.514 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.499 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^16, Y1^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 10, 42, 14, 46, 18, 50, 22, 54, 26, 58, 30, 62, 29, 61, 25, 57, 21, 53, 17, 49, 13, 45, 9, 41, 4, 36)(3, 35, 5, 37, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 32, 64, 28, 60, 24, 56, 20, 52, 16, 48, 12, 44, 8, 40)(65, 97, 67, 99, 68, 100, 72, 104, 73, 105, 76, 108, 77, 109, 80, 112, 81, 113, 84, 116, 85, 117, 88, 120, 89, 121, 92, 124, 93, 125, 96, 128, 94, 126, 95, 127, 90, 122, 91, 123, 86, 118, 87, 119, 82, 114, 83, 115, 78, 110, 79, 111, 74, 106, 75, 107, 70, 102, 71, 103, 66, 98, 69, 101) L = (1, 68)(2, 65)(3, 72)(4, 73)(5, 67)(6, 66)(7, 69)(8, 76)(9, 77)(10, 70)(11, 71)(12, 80)(13, 81)(14, 74)(15, 75)(16, 84)(17, 85)(18, 78)(19, 79)(20, 88)(21, 89)(22, 82)(23, 83)(24, 92)(25, 93)(26, 86)(27, 87)(28, 96)(29, 94)(30, 90)(31, 91)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 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 E15.512 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.500 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2 * Y1 * Y2 * Y1 * Y3^-3, Y1^3 * Y2 * Y1 * Y2 * Y3^-1, Y2^-6 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * 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 * Y3^2 * Y2 * Y3 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 24, 56, 13, 45, 18, 50, 27, 59, 32, 64, 29, 61, 20, 52, 9, 41, 17, 49, 22, 54, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 26, 58, 31, 63, 25, 57, 19, 51, 28, 60, 30, 62, 21, 53, 10, 42)(65, 97, 67, 99, 73, 105, 83, 115, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 92, 124, 91, 123, 80, 112, 70, 102, 79, 111, 86, 118, 94, 126, 96, 128, 90, 122, 78, 110, 87, 119, 75, 107, 85, 117, 93, 125, 95, 127, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 89, 121, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 84)(10, 85)(11, 86)(12, 87)(13, 88)(14, 70)(15, 71)(16, 72)(17, 73)(18, 77)(19, 89)(20, 93)(21, 94)(22, 81)(23, 79)(24, 78)(25, 95)(26, 80)(27, 82)(28, 83)(29, 96)(30, 92)(31, 90)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E15.515 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.501 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1 * Y2^-1 * Y1^2 * Y3^-2 * Y2^-1, Y2^4 * Y3^-1 * Y2^2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-3, Y1^4 * Y2^-2 * Y3^-1, Y2 * Y3 * Y2^3 * Y3 * Y2^2 * Y3 * Y2^2 * Y3, 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 * Y2^3 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 20, 52, 9, 41, 17, 49, 27, 59, 32, 64, 31, 63, 24, 56, 13, 45, 18, 50, 22, 54, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 26, 58, 29, 61, 19, 51, 25, 57, 28, 60, 30, 62, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 21, 53, 10, 42)(65, 97, 67, 99, 73, 105, 83, 115, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 93, 125, 95, 127, 87, 119, 75, 107, 85, 117, 78, 110, 90, 122, 96, 128, 94, 126, 86, 118, 80, 112, 70, 102, 79, 111, 91, 123, 92, 124, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 89, 121, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 84)(10, 85)(11, 86)(12, 87)(13, 88)(14, 70)(15, 71)(16, 72)(17, 73)(18, 77)(19, 93)(20, 78)(21, 80)(22, 82)(23, 94)(24, 95)(25, 83)(26, 79)(27, 81)(28, 89)(29, 90)(30, 92)(31, 96)(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) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E15.518 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.502 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y1^-1), Y3^-3 * Y2^2, Y3 * Y2^10, Y1^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 13, 45, 15, 47, 20, 52, 25, 57, 27, 59, 32, 64, 29, 61, 22, 54, 24, 56, 17, 49, 9, 41, 11, 43, 4, 36)(3, 35, 7, 39, 12, 44, 5, 37, 8, 40, 14, 46, 19, 51, 21, 53, 26, 58, 31, 63, 28, 60, 30, 62, 23, 55, 16, 48, 18, 50, 10, 42)(65, 97, 67, 99, 73, 105, 80, 112, 86, 118, 92, 124, 91, 123, 85, 117, 79, 111, 72, 104, 66, 98, 71, 103, 75, 107, 82, 114, 88, 120, 94, 126, 96, 128, 90, 122, 84, 116, 78, 110, 70, 102, 76, 108, 68, 100, 74, 106, 81, 113, 87, 119, 93, 125, 95, 127, 89, 121, 83, 115, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 81)(10, 82)(11, 73)(12, 71)(13, 70)(14, 72)(15, 77)(16, 87)(17, 88)(18, 80)(19, 78)(20, 79)(21, 83)(22, 93)(23, 94)(24, 86)(25, 84)(26, 85)(27, 89)(28, 95)(29, 96)(30, 92)(31, 90)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E15.513 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.503 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^-1 * Y2 * Y1^-2 * Y2, Y3 * Y2 * Y3 * Y2 * Y3, Y2^10 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 9, 41, 15, 47, 20, 52, 22, 54, 27, 59, 32, 64, 30, 62, 25, 57, 23, 55, 18, 50, 13, 45, 11, 43, 4, 36)(3, 35, 7, 39, 14, 46, 16, 48, 21, 53, 26, 58, 28, 60, 31, 63, 29, 61, 24, 56, 19, 51, 17, 49, 12, 44, 5, 37, 8, 40, 10, 42)(65, 97, 67, 99, 73, 105, 80, 112, 86, 118, 92, 124, 94, 126, 88, 120, 82, 114, 76, 108, 68, 100, 74, 106, 70, 102, 78, 110, 84, 116, 90, 122, 96, 128, 93, 125, 87, 119, 81, 113, 75, 107, 72, 104, 66, 98, 71, 103, 79, 111, 85, 117, 91, 123, 95, 127, 89, 121, 83, 115, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 70)(10, 72)(11, 77)(12, 81)(13, 82)(14, 71)(15, 73)(16, 78)(17, 83)(18, 87)(19, 88)(20, 79)(21, 80)(22, 84)(23, 89)(24, 93)(25, 94)(26, 85)(27, 86)(28, 90)(29, 95)(30, 96)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) } Outer automorphisms :: reflexible Dual of E15.516 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.504 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y3^-1, Y2), (R * Y3)^2, (Y1^-1, Y2), (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2^-3 * Y3, Y3^-1 * Y1^4 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y2^-1 * Y1^3 * Y3^-3 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-4, Y1^-3 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y2^-2 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 23, 55, 28, 60, 20, 52, 9, 41, 17, 49, 13, 45, 18, 50, 26, 58, 30, 62, 22, 54, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 24, 56, 31, 63, 32, 64, 27, 59, 19, 51, 12, 44, 5, 37, 8, 40, 16, 48, 25, 57, 29, 61, 21, 53, 10, 42)(65, 97, 67, 99, 73, 105, 83, 115, 75, 107, 85, 117, 92, 124, 96, 128, 94, 126, 89, 121, 78, 110, 88, 120, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 76, 108, 68, 100, 74, 106, 84, 116, 91, 123, 86, 118, 93, 125, 87, 119, 95, 127, 90, 122, 80, 112, 70, 102, 79, 111, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 84)(10, 85)(11, 86)(12, 83)(13, 81)(14, 70)(15, 71)(16, 72)(17, 73)(18, 77)(19, 91)(20, 92)(21, 93)(22, 94)(23, 78)(24, 79)(25, 80)(26, 82)(27, 96)(28, 87)(29, 89)(30, 90)(31, 88)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 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 E15.519 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.505 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y1^-1, Y2^-1), Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-4 * Y1^2, Y1 * Y2 * Y1^2 * Y2 * Y1^2 * Y3^-2, Y3^16, Y1^16, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 23, 55, 30, 62, 22, 54, 13, 45, 18, 50, 9, 41, 17, 49, 26, 58, 28, 60, 20, 52, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 24, 56, 29, 61, 21, 53, 12, 44, 5, 37, 8, 40, 16, 48, 25, 57, 31, 63, 32, 64, 27, 59, 19, 51, 10, 42)(65, 97, 67, 99, 73, 105, 80, 112, 70, 102, 79, 111, 90, 122, 95, 127, 87, 119, 93, 125, 84, 116, 91, 123, 86, 118, 76, 108, 68, 100, 74, 106, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 89, 121, 78, 110, 88, 120, 92, 124, 96, 128, 94, 126, 85, 117, 75, 107, 83, 115, 77, 109, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 75)(5, 76)(6, 66)(7, 67)(8, 69)(9, 82)(10, 83)(11, 84)(12, 85)(13, 86)(14, 70)(15, 71)(16, 72)(17, 73)(18, 77)(19, 91)(20, 92)(21, 93)(22, 94)(23, 78)(24, 79)(25, 80)(26, 81)(27, 96)(28, 90)(29, 88)(30, 87)(31, 89)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 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 E15.517 Graph:: bipartite v = 3 e = 64 f = 33 degree seq :: [ 32^2, 64 ] E15.506 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^-1 * Y1^-1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^-1 * Y1^-11, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 12, 44, 18, 50, 24, 56, 30, 62, 27, 59, 21, 53, 15, 47, 9, 41, 5, 37, 8, 40, 14, 46, 20, 52, 26, 58, 32, 64, 28, 60, 22, 54, 16, 48, 10, 42, 3, 35, 7, 39, 13, 45, 19, 51, 25, 57, 31, 63, 29, 61, 23, 55, 17, 49, 11, 43, 4, 36)(65, 97, 67, 99, 73, 105, 68, 100, 74, 106, 79, 111, 75, 107, 80, 112, 85, 117, 81, 113, 86, 118, 91, 123, 87, 119, 92, 124, 94, 126, 93, 125, 96, 128, 88, 120, 95, 127, 90, 122, 82, 114, 89, 121, 84, 116, 76, 108, 83, 115, 78, 110, 70, 102, 77, 109, 72, 104, 66, 98, 71, 103, 69, 101) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 77)(7, 69)(8, 66)(9, 68)(10, 79)(11, 80)(12, 83)(13, 72)(14, 70)(15, 75)(16, 85)(17, 86)(18, 89)(19, 78)(20, 76)(21, 81)(22, 91)(23, 92)(24, 95)(25, 84)(26, 82)(27, 87)(28, 94)(29, 96)(30, 93)(31, 90)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.509 Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.507 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1), Y2^-2 * Y1 * Y2^-3, Y2^-2 * Y1^-2 * Y2^2 * Y1^2, Y1 * Y2 * Y1^5 * Y2, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 24, 56, 23, 55, 13, 45, 18, 50, 28, 60, 32, 64, 30, 62, 20, 52, 10, 42, 3, 35, 7, 39, 15, 47, 25, 57, 22, 54, 12, 44, 5, 37, 8, 40, 16, 48, 26, 58, 31, 63, 29, 61, 19, 51, 9, 41, 17, 49, 27, 59, 21, 53, 11, 43, 4, 36)(65, 97, 67, 99, 73, 105, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 92, 124, 80, 112, 70, 102, 79, 111, 91, 123, 96, 128, 90, 122, 78, 110, 89, 121, 85, 117, 94, 126, 95, 127, 88, 120, 86, 118, 75, 107, 84, 116, 93, 125, 87, 119, 76, 108, 68, 100, 74, 106, 83, 115, 77, 109, 69, 101) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 82)(10, 83)(11, 84)(12, 68)(13, 69)(14, 89)(15, 91)(16, 70)(17, 92)(18, 72)(19, 77)(20, 93)(21, 94)(22, 75)(23, 76)(24, 86)(25, 85)(26, 78)(27, 96)(28, 80)(29, 87)(30, 95)(31, 88)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.511 Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.508 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2, Y1), (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), Y1^-3 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y2^3 * Y1^-1 * Y2 * Y1^-3, Y2^-2 * Y1^2 * Y2^2 * Y1^-2, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 25, 57, 32, 64, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 27, 59, 24, 56, 13, 45, 18, 50, 30, 62, 20, 52, 9, 41, 17, 49, 29, 61, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 28, 60, 19, 51, 31, 63, 22, 54, 11, 43, 4, 36)(65, 97, 67, 99, 73, 105, 83, 115, 90, 122, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 92, 124, 78, 110, 91, 123, 87, 119, 75, 107, 85, 117, 94, 126, 80, 112, 70, 102, 79, 111, 93, 125, 86, 118, 96, 128, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 95, 127, 89, 121, 77, 109, 69, 101) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 91)(15, 93)(16, 70)(17, 95)(18, 72)(19, 90)(20, 92)(21, 94)(22, 96)(23, 75)(24, 76)(25, 77)(26, 88)(27, 87)(28, 78)(29, 86)(30, 80)(31, 89)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.510 Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.509 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^16, (Y3^-1 * Y1^-1)^32, (Y3 * Y2^-1)^32 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 74, 106, 78, 110, 82, 114, 86, 118, 90, 122, 94, 126, 93, 125, 89, 121, 85, 117, 81, 113, 77, 109, 73, 105, 68, 100)(67, 99, 69, 101, 71, 103, 75, 107, 79, 111, 83, 115, 87, 119, 91, 123, 95, 127, 96, 128, 92, 124, 88, 120, 84, 116, 80, 112, 76, 108, 72, 104) L = (1, 67)(2, 69)(3, 68)(4, 72)(5, 65)(6, 71)(7, 66)(8, 73)(9, 76)(10, 75)(11, 70)(12, 77)(13, 80)(14, 79)(15, 74)(16, 81)(17, 84)(18, 83)(19, 78)(20, 85)(21, 88)(22, 87)(23, 82)(24, 89)(25, 92)(26, 91)(27, 86)(28, 93)(29, 96)(30, 95)(31, 90)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.506 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.510 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y3 * Y2 * Y3 * Y2^2, Y3^-1 * Y2 * Y3^-9, (Y2^-1 * Y3)^32, (Y3^-1 * Y1^-1)^32 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 77, 109, 79, 111, 84, 116, 89, 121, 91, 123, 96, 128, 93, 125, 86, 118, 88, 120, 81, 113, 73, 105, 75, 107, 68, 100)(67, 99, 71, 103, 76, 108, 69, 101, 72, 104, 78, 110, 83, 115, 85, 117, 90, 122, 95, 127, 92, 124, 94, 126, 87, 119, 80, 112, 82, 114, 74, 106) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 76)(7, 75)(8, 66)(9, 80)(10, 81)(11, 82)(12, 68)(13, 69)(14, 70)(15, 72)(16, 86)(17, 87)(18, 88)(19, 77)(20, 78)(21, 79)(22, 92)(23, 93)(24, 94)(25, 83)(26, 84)(27, 85)(28, 91)(29, 95)(30, 96)(31, 89)(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) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.508 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.511 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^2 * Y2^-1 * Y3^4, Y2^3 * Y3 * Y2 * Y3 * Y2, Y2^-1 * Y3^-3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^32 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 78, 110, 88, 120, 77, 109, 82, 114, 91, 123, 96, 128, 93, 125, 84, 116, 73, 105, 81, 113, 86, 118, 75, 107, 68, 100)(67, 99, 71, 103, 79, 111, 87, 119, 76, 108, 69, 101, 72, 104, 80, 112, 90, 122, 95, 127, 89, 121, 83, 115, 92, 124, 94, 126, 85, 117, 74, 106) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 87)(15, 86)(16, 70)(17, 92)(18, 72)(19, 82)(20, 89)(21, 93)(22, 94)(23, 75)(24, 76)(25, 77)(26, 78)(27, 80)(28, 91)(29, 95)(30, 96)(31, 88)(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) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.507 Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.512 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^16, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34, 5, 37, 6, 38, 9, 41, 10, 42, 13, 45, 14, 46, 17, 49, 18, 50, 21, 53, 22, 54, 25, 57, 26, 58, 29, 61, 30, 62, 31, 63, 32, 64, 27, 59, 28, 60, 23, 55, 24, 56, 19, 51, 20, 52, 15, 47, 16, 48, 11, 43, 12, 44, 7, 39, 8, 40, 3, 35, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 68)(3, 71)(4, 72)(5, 65)(6, 66)(7, 75)(8, 76)(9, 69)(10, 70)(11, 79)(12, 80)(13, 73)(14, 74)(15, 83)(16, 84)(17, 77)(18, 78)(19, 87)(20, 88)(21, 81)(22, 82)(23, 91)(24, 92)(25, 85)(26, 86)(27, 95)(28, 96)(29, 89)(30, 90)(31, 93)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 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 E15.499 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.513 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^16, (Y3 * Y2^-1)^16, (Y3^-1 * Y1^-1)^32 ] Map:: R = (1, 33, 2, 34, 3, 35, 6, 38, 7, 39, 10, 42, 11, 43, 14, 46, 15, 47, 18, 50, 19, 51, 22, 54, 23, 55, 26, 58, 27, 59, 30, 62, 31, 63, 32, 64, 29, 61, 28, 60, 25, 57, 24, 56, 21, 53, 20, 52, 17, 49, 16, 48, 13, 45, 12, 44, 9, 41, 8, 40, 5, 37, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 70)(3, 71)(4, 66)(5, 65)(6, 74)(7, 75)(8, 68)(9, 69)(10, 78)(11, 79)(12, 72)(13, 73)(14, 82)(15, 83)(16, 76)(17, 77)(18, 86)(19, 87)(20, 80)(21, 81)(22, 90)(23, 91)(24, 84)(25, 85)(26, 94)(27, 95)(28, 88)(29, 89)(30, 96)(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) :: { ( 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 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 E15.502 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.514 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^3 * Y1^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-10, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 20, 52, 26, 58, 30, 62, 24, 56, 18, 50, 10, 42, 3, 35, 7, 39, 13, 45, 16, 48, 22, 54, 28, 60, 32, 64, 29, 61, 23, 55, 17, 49, 9, 41, 12, 44, 5, 37, 8, 40, 15, 47, 21, 53, 27, 59, 31, 63, 25, 57, 19, 51, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 77)(7, 76)(8, 66)(9, 75)(10, 81)(11, 82)(12, 68)(13, 69)(14, 80)(15, 70)(16, 72)(17, 83)(18, 87)(19, 88)(20, 86)(21, 78)(22, 79)(23, 89)(24, 93)(25, 94)(26, 92)(27, 84)(28, 85)(29, 95)(30, 96)(31, 90)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 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 E15.498 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.515 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y1 * Y3^-1 * Y1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^7, (Y3 * Y2^-1)^16, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 20, 52, 26, 58, 30, 62, 24, 56, 18, 50, 12, 44, 5, 37, 8, 40, 9, 41, 16, 48, 22, 54, 28, 60, 32, 64, 31, 63, 25, 57, 19, 51, 13, 45, 10, 42, 3, 35, 7, 39, 15, 47, 21, 53, 27, 59, 29, 61, 23, 55, 17, 49, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 80)(8, 66)(9, 70)(10, 72)(11, 77)(12, 68)(13, 69)(14, 85)(15, 86)(16, 78)(17, 83)(18, 75)(19, 76)(20, 91)(21, 92)(22, 84)(23, 89)(24, 81)(25, 82)(26, 93)(27, 96)(28, 90)(29, 95)(30, 87)(31, 88)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 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 E15.500 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.516 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^3 * Y1, Y1 * Y3^-1 * Y1^5, (Y3 * Y2^-1)^16, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-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:: R = (1, 33, 2, 34, 6, 38, 14, 46, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 26, 58, 30, 62, 20, 52, 9, 41, 17, 49, 25, 57, 28, 60, 32, 64, 29, 61, 19, 51, 24, 56, 13, 45, 18, 50, 27, 59, 31, 63, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 22, 54, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 90)(15, 89)(16, 70)(17, 88)(18, 72)(19, 87)(20, 93)(21, 94)(22, 78)(23, 75)(24, 76)(25, 77)(26, 92)(27, 80)(28, 82)(29, 95)(30, 96)(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) :: { ( 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 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 E15.503 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.517 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-3, Y1^2 * Y3 * Y1^4, (Y3 * Y2^-1)^16, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^3 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 26, 58, 30, 62, 24, 56, 13, 45, 18, 50, 19, 51, 28, 60, 32, 64, 31, 63, 25, 57, 20, 52, 9, 41, 17, 49, 27, 59, 29, 61, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 22, 54, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 86)(15, 91)(16, 70)(17, 92)(18, 72)(19, 80)(20, 82)(21, 89)(22, 93)(23, 75)(24, 76)(25, 77)(26, 78)(27, 96)(28, 90)(29, 95)(30, 87)(31, 88)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 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 E15.505 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.518 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1^-3 * Y3, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^6 * Y1, (Y3 * Y2^-1)^16, Y1^-1 * Y3^3 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^4 * Y1^-1 * Y3^3 * Y1^-2 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 9, 41, 17, 49, 24, 56, 31, 63, 27, 59, 29, 61, 22, 54, 26, 58, 20, 52, 12, 44, 5, 37, 8, 40, 16, 48, 10, 42, 3, 35, 7, 39, 15, 47, 23, 55, 19, 51, 25, 57, 30, 62, 32, 64, 28, 60, 21, 53, 13, 45, 18, 50, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 78)(11, 80)(12, 68)(13, 69)(14, 87)(15, 88)(16, 70)(17, 89)(18, 72)(19, 91)(20, 75)(21, 76)(22, 77)(23, 95)(24, 94)(25, 93)(26, 82)(27, 92)(28, 84)(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 ) } Outer automorphisms :: reflexible Dual of E15.501 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.519 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y3^-2 * Y1^-4, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^-7 * Y1^2, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 13, 45, 18, 50, 24, 56, 31, 63, 30, 62, 28, 60, 19, 51, 25, 57, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 12, 44, 5, 37, 8, 40, 16, 48, 23, 55, 22, 54, 26, 58, 27, 59, 32, 64, 29, 61, 20, 52, 9, 41, 17, 49, 11, 43, 4, 36)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 76)(15, 75)(16, 70)(17, 89)(18, 72)(19, 91)(20, 92)(21, 93)(22, 77)(23, 78)(24, 80)(25, 96)(26, 82)(27, 88)(28, 90)(29, 94)(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 ) } Outer automorphisms :: reflexible Dual of E15.504 Graph:: bipartite v = 33 e = 64 f = 3 degree seq :: [ 2^32, 64 ] E15.520 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^-3 * T1^3, T2^3 * T1^8, T1^-22, T2^33 ] Map:: non-degenerate R = (1, 3, 9, 14, 23, 30, 31, 27, 20, 11, 18, 8, 2, 7, 17, 22, 29, 32, 25, 21, 12, 4, 10, 16, 6, 15, 24, 28, 33, 26, 19, 13, 5)(34, 35, 39, 47, 55, 61, 64, 58, 52, 44, 37)(36, 40, 48, 56, 62, 66, 60, 54, 46, 51, 43)(38, 41, 49, 42, 50, 57, 63, 65, 59, 53, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.535 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.521 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2^-1 * T1 * T2^-5, T2^2 * T1 * T2 * T1^4, T1^3 * T2^-1 * T1^3 * T2^-2, 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 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 31, 30, 16, 6, 15, 29, 22, 33, 28, 14, 27, 23, 11, 21, 32, 26, 24, 12, 4, 10, 20, 25, 13, 5)(34, 35, 39, 47, 59, 58, 52, 64, 55, 44, 37)(36, 40, 48, 60, 57, 46, 51, 63, 66, 54, 43)(38, 41, 49, 61, 65, 53, 42, 50, 62, 56, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.540 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.522 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^5, T2^-1 * T1 * T2^-2 * T1^4, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 12, 4, 10, 20, 26, 33, 23, 11, 21, 28, 14, 27, 32, 22, 30, 16, 6, 15, 29, 31, 18, 8, 2, 7, 17, 25, 13, 5)(34, 35, 39, 47, 59, 52, 58, 64, 55, 44, 37)(36, 40, 48, 60, 66, 57, 46, 51, 63, 54, 43)(38, 41, 49, 61, 53, 42, 50, 62, 65, 56, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.533 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.523 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^11, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 3, 8, 2, 7, 14, 6, 13, 20, 12, 19, 26, 18, 25, 31, 24, 30, 33, 28, 32, 29, 22, 27, 23, 16, 21, 17, 10, 15, 11, 4, 9, 5)(34, 35, 39, 45, 51, 57, 61, 55, 49, 43, 37)(36, 40, 46, 52, 58, 63, 65, 60, 54, 48, 42)(38, 41, 47, 53, 59, 64, 66, 62, 56, 50, 44) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.539 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.524 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^11 ] Map:: non-degenerate R = (1, 3, 9, 4, 10, 15, 11, 16, 21, 17, 22, 27, 23, 28, 32, 29, 33, 31, 24, 30, 26, 18, 25, 20, 12, 19, 14, 6, 13, 8, 2, 7, 5)(34, 35, 39, 45, 51, 57, 62, 56, 50, 44, 37)(36, 40, 46, 52, 58, 63, 66, 61, 55, 49, 43)(38, 41, 47, 53, 59, 64, 65, 60, 54, 48, 42) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.541 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.525 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T1^3 * T2^-1 * T1 * T2^-2, T1^-1 * T2^-1 * T1^-1 * T2^-5 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 30, 22, 18, 8, 2, 7, 17, 28, 31, 23, 11, 21, 16, 6, 15, 27, 32, 24, 12, 4, 10, 20, 14, 26, 33, 25, 13, 5)(34, 35, 39, 47, 52, 61, 65, 58, 55, 44, 37)(36, 40, 48, 59, 62, 64, 57, 46, 51, 54, 43)(38, 41, 49, 53, 42, 50, 60, 66, 63, 56, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.538 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.526 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2^2, T2^-6 * T1^3, T1 * T2^-1 * T1 * T2^-5 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 26, 14, 24, 12, 4, 10, 20, 30, 27, 16, 6, 15, 23, 11, 21, 31, 28, 18, 8, 2, 7, 17, 22, 32, 33, 25, 13, 5)(34, 35, 39, 47, 58, 61, 63, 52, 55, 44, 37)(36, 40, 48, 57, 46, 51, 60, 62, 65, 54, 43)(38, 41, 49, 59, 66, 64, 53, 42, 50, 56, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.536 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.527 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^11, T1^11, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 33, 29, 31, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 32, 30, 23, 25, 18, 11, 13, 5)(34, 35, 39, 47, 53, 59, 62, 56, 50, 44, 37)(36, 40, 48, 54, 60, 65, 64, 58, 52, 46, 43)(38, 41, 42, 49, 55, 61, 66, 63, 57, 51, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.534 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.528 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^11, T1^-11, T1^11 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 30, 32, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 33, 27, 20, 22, 15, 6, 13, 5)(34, 35, 39, 47, 53, 59, 64, 58, 52, 44, 37)(36, 40, 46, 49, 55, 61, 66, 63, 57, 51, 43)(38, 41, 48, 54, 60, 65, 62, 56, 50, 42, 45) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 66^11 ), ( 66^33 ) } Outer automorphisms :: reflexible Dual of E15.537 Transitivity :: ET+ Graph:: bipartite v = 4 e = 33 f = 1 degree seq :: [ 11^3, 33 ] E15.529 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^16, (T2^-1 * T1^-1)^11 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 32, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 30, 33, 29, 25, 21, 17, 13, 9, 5)(34, 35, 36, 39, 40, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 63, 64, 66, 65, 62, 61, 58, 57, 54, 53, 50, 49, 46, 45, 42, 41, 38, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 22^33 ) } Outer automorphisms :: reflexible Dual of E15.544 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 3 degree seq :: [ 33^2 ] E15.530 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2, T2^-8 * T1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 24, 16, 8, 2, 7, 15, 23, 31, 30, 22, 14, 6, 11, 19, 27, 32, 33, 28, 20, 12, 4, 10, 18, 26, 29, 21, 13, 5)(34, 35, 39, 45, 38, 41, 47, 53, 46, 49, 55, 61, 54, 57, 63, 66, 62, 58, 64, 65, 59, 50, 56, 60, 51, 42, 48, 52, 43, 36, 40, 44, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 22^33 ) } Outer automorphisms :: reflexible Dual of E15.543 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 3 degree seq :: [ 33^2 ] E15.531 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2^-1 * T1, T1^3 * T2^-1 * T1^2, T1^2 * T2 * T1 * T2^5, T2^-3 * T1 * T2^-4 * T1, (T1^-1 * T2^-1)^11 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 26, 16, 6, 15, 25, 32, 22, 12, 4, 10, 20, 30, 28, 18, 8, 2, 7, 17, 27, 31, 21, 11, 14, 24, 33, 23, 13, 5)(34, 35, 39, 47, 43, 36, 40, 48, 57, 53, 42, 50, 58, 66, 63, 52, 60, 65, 56, 61, 62, 64, 55, 46, 51, 59, 54, 45, 38, 41, 49, 44, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 22^33 ) } Outer automorphisms :: reflexible Dual of E15.542 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 3 degree seq :: [ 33^2 ] E15.532 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 33, 33}) Quotient :: edge Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^-2 * T2^-1 * T1^-5, T1 * T2^-1 * T1^3 * T2^-3 * T1, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-3 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 23, 11, 21, 32, 28, 14, 27, 30, 18, 8, 2, 7, 17, 24, 12, 4, 10, 20, 31, 26, 22, 33, 29, 16, 6, 15, 25, 13, 5)(34, 35, 39, 47, 59, 56, 45, 38, 41, 49, 61, 64, 52, 57, 46, 51, 62, 65, 53, 42, 50, 58, 63, 66, 54, 43, 36, 40, 48, 60, 55, 44, 37) L = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66) local type(s) :: { ( 22^33 ) } Outer automorphisms :: reflexible Dual of E15.545 Transitivity :: ET+ Graph:: bipartite v = 2 e = 33 f = 3 degree seq :: [ 33^2 ] E15.533 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^-3 * T1^3, T2^3 * T1^8, T1^-22, T2^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 14, 47, 23, 56, 30, 63, 31, 64, 27, 60, 20, 53, 11, 44, 18, 51, 8, 41, 2, 35, 7, 40, 17, 50, 22, 55, 29, 62, 32, 65, 25, 58, 21, 54, 12, 45, 4, 37, 10, 43, 16, 49, 6, 39, 15, 48, 24, 57, 28, 61, 33, 66, 26, 59, 19, 52, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 55)(15, 56)(16, 42)(17, 57)(18, 43)(19, 44)(20, 45)(21, 46)(22, 61)(23, 62)(24, 63)(25, 52)(26, 53)(27, 54)(28, 64)(29, 66)(30, 65)(31, 58)(32, 59)(33, 60) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.522 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.534 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2^-1 * T1 * T2^-5, T2^2 * T1 * T2 * T1^4, T1^3 * T2^-1 * T1^3 * T2^-2, 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 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 19, 52, 18, 51, 8, 41, 2, 35, 7, 40, 17, 50, 31, 64, 30, 63, 16, 49, 6, 39, 15, 48, 29, 62, 22, 55, 33, 66, 28, 61, 14, 47, 27, 60, 23, 56, 11, 44, 21, 54, 32, 65, 26, 59, 24, 57, 12, 45, 4, 37, 10, 43, 20, 53, 25, 58, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 42)(21, 43)(22, 44)(23, 45)(24, 46)(25, 52)(26, 58)(27, 57)(28, 65)(29, 56)(30, 66)(31, 55)(32, 53)(33, 54) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.527 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.535 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^5, T2^-1 * T1 * T2^-2 * T1^4, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 19, 52, 24, 57, 12, 45, 4, 37, 10, 43, 20, 53, 26, 59, 33, 66, 23, 56, 11, 44, 21, 54, 28, 61, 14, 47, 27, 60, 32, 65, 22, 55, 30, 63, 16, 49, 6, 39, 15, 48, 29, 62, 31, 64, 18, 51, 8, 41, 2, 35, 7, 40, 17, 50, 25, 58, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 58)(20, 42)(21, 43)(22, 44)(23, 45)(24, 46)(25, 64)(26, 52)(27, 66)(28, 53)(29, 65)(30, 54)(31, 55)(32, 56)(33, 57) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.520 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.536 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^11, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 8, 41, 2, 35, 7, 40, 14, 47, 6, 39, 13, 46, 20, 53, 12, 45, 19, 52, 26, 59, 18, 51, 25, 58, 31, 64, 24, 57, 30, 63, 33, 66, 28, 61, 32, 65, 29, 62, 22, 55, 27, 60, 23, 56, 16, 49, 21, 54, 17, 50, 10, 43, 15, 48, 11, 44, 4, 37, 9, 42, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 45)(7, 46)(8, 47)(9, 36)(10, 37)(11, 38)(12, 51)(13, 52)(14, 53)(15, 42)(16, 43)(17, 44)(18, 57)(19, 58)(20, 59)(21, 48)(22, 49)(23, 50)(24, 61)(25, 63)(26, 64)(27, 54)(28, 55)(29, 56)(30, 65)(31, 66)(32, 60)(33, 62) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.526 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.537 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^11 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 4, 37, 10, 43, 15, 48, 11, 44, 16, 49, 21, 54, 17, 50, 22, 55, 27, 60, 23, 56, 28, 61, 32, 65, 29, 62, 33, 66, 31, 64, 24, 57, 30, 63, 26, 59, 18, 51, 25, 58, 20, 53, 12, 45, 19, 52, 14, 47, 6, 39, 13, 46, 8, 41, 2, 35, 7, 40, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 45)(7, 46)(8, 47)(9, 38)(10, 36)(11, 37)(12, 51)(13, 52)(14, 53)(15, 42)(16, 43)(17, 44)(18, 57)(19, 58)(20, 59)(21, 48)(22, 49)(23, 50)(24, 62)(25, 63)(26, 64)(27, 54)(28, 55)(29, 56)(30, 66)(31, 65)(32, 60)(33, 61) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.528 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.538 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T1^3 * T2^-1 * T1 * T2^-2, T1^-1 * T2^-1 * T1^-1 * T2^-5 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 19, 52, 29, 62, 30, 63, 22, 55, 18, 51, 8, 41, 2, 35, 7, 40, 17, 50, 28, 61, 31, 64, 23, 56, 11, 44, 21, 54, 16, 49, 6, 39, 15, 48, 27, 60, 32, 65, 24, 57, 12, 45, 4, 37, 10, 43, 20, 53, 14, 47, 26, 59, 33, 66, 25, 58, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 52)(15, 59)(16, 53)(17, 60)(18, 54)(19, 61)(20, 42)(21, 43)(22, 44)(23, 45)(24, 46)(25, 55)(26, 62)(27, 66)(28, 65)(29, 64)(30, 56)(31, 57)(32, 58)(33, 63) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.525 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.539 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2^2, T2^-6 * T1^3, T1 * T2^-1 * T1 * T2^-5 * T1 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 19, 52, 29, 62, 26, 59, 14, 47, 24, 57, 12, 45, 4, 37, 10, 43, 20, 53, 30, 63, 27, 60, 16, 49, 6, 39, 15, 48, 23, 56, 11, 44, 21, 54, 31, 64, 28, 61, 18, 51, 8, 41, 2, 35, 7, 40, 17, 50, 22, 55, 32, 65, 33, 66, 25, 58, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 58)(15, 57)(16, 59)(17, 56)(18, 60)(19, 55)(20, 42)(21, 43)(22, 44)(23, 45)(24, 46)(25, 61)(26, 66)(27, 62)(28, 63)(29, 65)(30, 52)(31, 53)(32, 54)(33, 64) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.523 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.540 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^11, T1^11, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 6, 39, 15, 48, 22, 55, 20, 53, 27, 60, 33, 66, 29, 62, 31, 64, 24, 57, 17, 50, 19, 52, 12, 45, 4, 37, 10, 43, 8, 41, 2, 35, 7, 40, 16, 49, 14, 47, 21, 54, 28, 61, 26, 59, 32, 65, 30, 63, 23, 56, 25, 58, 18, 51, 11, 44, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 42)(9, 49)(10, 36)(11, 37)(12, 38)(13, 43)(14, 53)(15, 54)(16, 55)(17, 44)(18, 45)(19, 46)(20, 59)(21, 60)(22, 61)(23, 50)(24, 51)(25, 52)(26, 62)(27, 65)(28, 66)(29, 56)(30, 57)(31, 58)(32, 64)(33, 63) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.521 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.541 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^11, T1^-11, T1^11 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 11, 44, 18, 51, 23, 56, 25, 58, 30, 63, 32, 65, 26, 59, 28, 61, 21, 54, 14, 47, 16, 49, 8, 41, 2, 35, 7, 40, 12, 45, 4, 37, 10, 43, 17, 50, 19, 52, 24, 57, 29, 62, 31, 64, 33, 66, 27, 60, 20, 53, 22, 55, 15, 48, 6, 39, 13, 46, 5, 38) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 46)(8, 48)(9, 45)(10, 36)(11, 37)(12, 38)(13, 49)(14, 53)(15, 54)(16, 55)(17, 42)(18, 43)(19, 44)(20, 59)(21, 60)(22, 61)(23, 50)(24, 51)(25, 52)(26, 64)(27, 65)(28, 66)(29, 56)(30, 57)(31, 58)(32, 62)(33, 63) local type(s) :: { ( 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33, 11, 33 ) } Outer automorphisms :: reflexible Dual of E15.524 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 33 f = 4 degree seq :: [ 66 ] E15.542 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^3 * T1^-3, T1^-9 * T2^-2, T1^4 * T2 * T1 * T2 * T1^4, T2^11, 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^-2 * T1^4 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 14, 47, 23, 56, 30, 63, 33, 66, 26, 59, 19, 52, 13, 46, 5, 38)(2, 35, 7, 40, 17, 50, 22, 55, 29, 62, 31, 64, 27, 60, 20, 53, 11, 44, 18, 51, 8, 41)(4, 37, 10, 43, 16, 49, 6, 39, 15, 48, 24, 57, 28, 61, 32, 65, 25, 58, 21, 54, 12, 45) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 55)(15, 56)(16, 42)(17, 57)(18, 43)(19, 44)(20, 45)(21, 46)(22, 61)(23, 62)(24, 63)(25, 52)(26, 53)(27, 54)(28, 66)(29, 65)(30, 64)(31, 58)(32, 59)(33, 60) local type(s) :: { ( 33^22 ) } Outer automorphisms :: reflexible Dual of E15.531 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 33 f = 2 degree seq :: [ 22^3 ] E15.543 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2), T1^2 * T2 * T1 * T2^3, T1^-6 * T2^3, T2^2 * T1^-1 * T2 * T1^-5 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 19, 52, 22, 55, 32, 65, 27, 60, 14, 47, 25, 58, 13, 46, 5, 38)(2, 35, 7, 40, 17, 50, 23, 56, 11, 44, 21, 54, 31, 64, 26, 59, 29, 62, 18, 51, 8, 41)(4, 37, 10, 43, 20, 53, 30, 63, 33, 66, 28, 61, 16, 49, 6, 39, 15, 48, 24, 57, 12, 45) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 47)(7, 48)(8, 49)(9, 50)(10, 36)(11, 37)(12, 38)(13, 51)(14, 59)(15, 58)(16, 60)(17, 57)(18, 61)(19, 56)(20, 42)(21, 43)(22, 44)(23, 45)(24, 46)(25, 62)(26, 63)(27, 64)(28, 65)(29, 66)(30, 52)(31, 53)(32, 54)(33, 55) local type(s) :: { ( 33^22 ) } Outer automorphisms :: reflexible Dual of E15.530 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 33 f = 2 degree seq :: [ 22^3 ] E15.544 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^11 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 15, 48, 21, 54, 27, 60, 29, 62, 23, 56, 17, 50, 11, 44, 5, 38)(2, 35, 7, 40, 13, 46, 19, 52, 25, 58, 31, 64, 32, 65, 26, 59, 20, 53, 14, 47, 8, 41)(4, 37, 10, 43, 16, 49, 22, 55, 28, 61, 33, 66, 30, 63, 24, 57, 18, 51, 12, 45, 6, 39) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 38)(7, 37)(8, 45)(9, 46)(10, 36)(11, 47)(12, 44)(13, 43)(14, 51)(15, 52)(16, 42)(17, 53)(18, 50)(19, 49)(20, 57)(21, 58)(22, 48)(23, 59)(24, 56)(25, 55)(26, 63)(27, 64)(28, 54)(29, 65)(30, 62)(31, 61)(32, 66)(33, 60) local type(s) :: { ( 33^22 ) } Outer automorphisms :: reflexible Dual of E15.529 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 33 f = 2 degree seq :: [ 22^3 ] E15.545 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 33, 33}) Quotient :: loop Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-2 * T1^3, T2^-11, T2^11, T2^-1 * T1^-1 * T2^-3 * T1^-1 * T2^-5 * T1^-1, (T1^-1 * T2^-1)^33 ] Map:: non-degenerate R = (1, 34, 3, 36, 9, 42, 16, 49, 22, 55, 28, 61, 31, 64, 25, 58, 19, 52, 13, 46, 5, 38)(2, 35, 7, 40, 15, 48, 21, 54, 27, 60, 33, 66, 29, 62, 23, 56, 17, 50, 11, 44, 8, 41)(4, 37, 10, 43, 6, 39, 14, 47, 20, 53, 26, 59, 32, 65, 30, 63, 24, 57, 18, 51, 12, 45) L = (1, 35)(2, 39)(3, 40)(4, 34)(5, 41)(6, 42)(7, 47)(8, 43)(9, 48)(10, 36)(11, 37)(12, 38)(13, 44)(14, 49)(15, 53)(16, 54)(17, 45)(18, 46)(19, 50)(20, 55)(21, 59)(22, 60)(23, 51)(24, 52)(25, 56)(26, 61)(27, 65)(28, 66)(29, 57)(30, 58)(31, 62)(32, 64)(33, 63) local type(s) :: { ( 33^22 ) } Outer automorphisms :: reflexible Dual of E15.532 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 33 f = 2 degree seq :: [ 22^3 ] E15.546 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2 * Y3 * Y2^-1 * Y1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^3 * Y1^-2, Y2^-9 * Y1^-2, Y2^3 * Y1^8, Y1^2 * Y2 * Y3^-2 * Y2^2 * Y3^-4, (Y2^-1 * Y1^-1)^33 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 22, 55, 28, 61, 31, 64, 25, 58, 19, 52, 11, 44, 4, 37)(3, 36, 7, 40, 15, 48, 23, 56, 29, 62, 33, 66, 27, 60, 21, 54, 13, 46, 18, 51, 10, 43)(5, 38, 8, 41, 16, 49, 9, 42, 17, 50, 24, 57, 30, 63, 32, 65, 26, 59, 20, 53, 12, 45)(67, 100, 69, 102, 75, 108, 80, 113, 89, 122, 96, 129, 97, 130, 93, 126, 86, 119, 77, 110, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 88, 121, 95, 128, 98, 131, 91, 124, 87, 120, 78, 111, 70, 103, 76, 109, 82, 115, 72, 105, 81, 114, 90, 123, 94, 127, 99, 132, 92, 125, 85, 118, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 82)(10, 84)(11, 85)(12, 86)(13, 87)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 91)(20, 92)(21, 93)(22, 80)(23, 81)(24, 83)(25, 97)(26, 98)(27, 99)(28, 88)(29, 89)(30, 90)(31, 94)(32, 96)(33, 95)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.565 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.547 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y1^-1, Y2), (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, (Y3^-1, Y2^-1), Y3 * Y1^-2 * Y2^3 * Y3, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-5 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 34, 2, 35, 6, 39, 14, 47, 19, 52, 28, 61, 32, 65, 25, 58, 22, 55, 11, 44, 4, 37)(3, 36, 7, 40, 15, 48, 26, 59, 29, 62, 31, 64, 24, 57, 13, 46, 18, 51, 21, 54, 10, 43)(5, 38, 8, 41, 16, 49, 20, 53, 9, 42, 17, 50, 27, 60, 33, 66, 30, 63, 23, 56, 12, 45)(67, 100, 69, 102, 75, 108, 85, 118, 95, 128, 96, 129, 88, 121, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 94, 127, 97, 130, 89, 122, 77, 110, 87, 120, 82, 115, 72, 105, 81, 114, 93, 126, 98, 131, 90, 123, 78, 111, 70, 103, 76, 109, 86, 119, 80, 113, 92, 125, 99, 132, 91, 124, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 86)(10, 87)(11, 88)(12, 89)(13, 90)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 80)(20, 82)(21, 84)(22, 91)(23, 96)(24, 97)(25, 98)(26, 81)(27, 83)(28, 85)(29, 92)(30, 99)(31, 95)(32, 94)(33, 93)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.568 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.548 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^-1 * Y1^-1, Y3 * Y1, Y1 * Y3, Y3^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2, Y2^2 * Y1 * Y2 * Y1 * Y3^-2, Y1^2 * Y2^-1 * Y1 * Y2^-5, Y2^-1 * Y3 * Y1^-1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 * Y2 * Y1^2 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 25, 58, 28, 61, 30, 63, 19, 52, 22, 55, 11, 44, 4, 37)(3, 36, 7, 40, 15, 48, 24, 57, 13, 46, 18, 51, 27, 60, 29, 62, 32, 65, 21, 54, 10, 43)(5, 38, 8, 41, 16, 49, 26, 59, 33, 66, 31, 64, 20, 53, 9, 42, 17, 50, 23, 56, 12, 45)(67, 100, 69, 102, 75, 108, 85, 118, 95, 128, 92, 125, 80, 113, 90, 123, 78, 111, 70, 103, 76, 109, 86, 119, 96, 129, 93, 126, 82, 115, 72, 105, 81, 114, 89, 122, 77, 110, 87, 120, 97, 130, 94, 127, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 88, 121, 98, 131, 99, 132, 91, 124, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 86)(10, 87)(11, 88)(12, 89)(13, 90)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 96)(20, 97)(21, 98)(22, 85)(23, 83)(24, 81)(25, 80)(26, 82)(27, 84)(28, 91)(29, 93)(30, 94)(31, 99)(32, 95)(33, 92)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.566 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.549 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y2^-3, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y1^11, Y3^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 12, 45, 18, 51, 24, 57, 29, 62, 23, 56, 17, 50, 11, 44, 4, 37)(3, 36, 7, 40, 13, 46, 19, 52, 25, 58, 30, 63, 33, 66, 28, 61, 22, 55, 16, 49, 10, 43)(5, 38, 8, 41, 14, 47, 20, 53, 26, 59, 31, 64, 32, 65, 27, 60, 21, 54, 15, 48, 9, 42)(67, 100, 69, 102, 75, 108, 70, 103, 76, 109, 81, 114, 77, 110, 82, 115, 87, 120, 83, 116, 88, 121, 93, 126, 89, 122, 94, 127, 98, 131, 95, 128, 99, 132, 97, 130, 90, 123, 96, 129, 92, 125, 84, 117, 91, 124, 86, 119, 78, 111, 85, 118, 80, 113, 72, 105, 79, 112, 74, 107, 68, 101, 73, 106, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 75)(6, 68)(7, 69)(8, 71)(9, 81)(10, 82)(11, 83)(12, 72)(13, 73)(14, 74)(15, 87)(16, 88)(17, 89)(18, 78)(19, 79)(20, 80)(21, 93)(22, 94)(23, 95)(24, 84)(25, 85)(26, 86)(27, 98)(28, 99)(29, 90)(30, 91)(31, 92)(32, 97)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.571 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.550 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y1^11, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 34, 2, 35, 6, 39, 12, 45, 18, 51, 24, 57, 28, 61, 22, 55, 16, 49, 10, 43, 4, 37)(3, 36, 7, 40, 13, 46, 19, 52, 25, 58, 30, 63, 32, 65, 27, 60, 21, 54, 15, 48, 9, 42)(5, 38, 8, 41, 14, 47, 20, 53, 26, 59, 31, 64, 33, 66, 29, 62, 23, 56, 17, 50, 11, 44)(67, 100, 69, 102, 74, 107, 68, 101, 73, 106, 80, 113, 72, 105, 79, 112, 86, 119, 78, 111, 85, 118, 92, 125, 84, 117, 91, 124, 97, 130, 90, 123, 96, 129, 99, 132, 94, 127, 98, 131, 95, 128, 88, 121, 93, 126, 89, 122, 82, 115, 87, 120, 83, 116, 76, 109, 81, 114, 77, 110, 70, 103, 75, 108, 71, 104) L = (1, 70)(2, 67)(3, 75)(4, 76)(5, 77)(6, 68)(7, 69)(8, 71)(9, 81)(10, 82)(11, 83)(12, 72)(13, 73)(14, 74)(15, 87)(16, 88)(17, 89)(18, 78)(19, 79)(20, 80)(21, 93)(22, 94)(23, 95)(24, 84)(25, 85)(26, 86)(27, 98)(28, 90)(29, 99)(30, 91)(31, 92)(32, 96)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.569 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.551 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, (Y3^-1, Y2^-1), Y1 * Y2^-1 * Y1 * Y2^-2, Y3^11, Y3^5 * Y1^-6, Y2^-33 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 20, 53, 26, 59, 29, 62, 23, 56, 17, 50, 11, 44, 4, 37)(3, 36, 7, 40, 15, 48, 21, 54, 27, 60, 32, 65, 31, 64, 25, 58, 19, 52, 13, 46, 10, 43)(5, 38, 8, 41, 9, 42, 16, 49, 22, 55, 28, 61, 33, 66, 30, 63, 24, 57, 18, 51, 12, 45)(67, 100, 69, 102, 75, 108, 72, 105, 81, 114, 88, 121, 86, 119, 93, 126, 99, 132, 95, 128, 97, 130, 90, 123, 83, 116, 85, 118, 78, 111, 70, 103, 76, 109, 74, 107, 68, 101, 73, 106, 82, 115, 80, 113, 87, 120, 94, 127, 92, 125, 98, 131, 96, 129, 89, 122, 91, 124, 84, 117, 77, 110, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 74)(10, 79)(11, 83)(12, 84)(13, 85)(14, 72)(15, 73)(16, 75)(17, 89)(18, 90)(19, 91)(20, 80)(21, 81)(22, 82)(23, 95)(24, 96)(25, 97)(26, 86)(27, 87)(28, 88)(29, 92)(30, 99)(31, 98)(32, 93)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.564 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.552 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y3^-2 * Y2^3, Y2 * Y1 * Y2^2 * Y1, Y3^11, Y1^11, Y3 * Y2 * Y3^3 * Y2^2 * Y1^-5, Y3^22 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 20, 53, 26, 59, 31, 64, 25, 58, 19, 52, 11, 44, 4, 37)(3, 36, 7, 40, 13, 46, 16, 49, 22, 55, 28, 61, 33, 66, 30, 63, 24, 57, 18, 51, 10, 43)(5, 38, 8, 41, 15, 48, 21, 54, 27, 60, 32, 65, 29, 62, 23, 56, 17, 50, 9, 42, 12, 45)(67, 100, 69, 102, 75, 108, 77, 110, 84, 117, 89, 122, 91, 124, 96, 129, 98, 131, 92, 125, 94, 127, 87, 120, 80, 113, 82, 115, 74, 107, 68, 101, 73, 106, 78, 111, 70, 103, 76, 109, 83, 116, 85, 118, 90, 123, 95, 128, 97, 130, 99, 132, 93, 126, 86, 119, 88, 121, 81, 114, 72, 105, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 83)(10, 84)(11, 85)(12, 75)(13, 73)(14, 72)(15, 74)(16, 79)(17, 89)(18, 90)(19, 91)(20, 80)(21, 81)(22, 82)(23, 95)(24, 96)(25, 97)(26, 86)(27, 87)(28, 88)(29, 98)(30, 99)(31, 92)(32, 93)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.567 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.553 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), (R * Y1)^2, Y1 * Y2^-6, Y1^-1 * Y2^6, Y3^-3 * Y1 * Y3^-1 * Y2^3, Y3 * Y2^-1 * Y3^2 * Y2^-2 * Y1^-2, Y1^-3 * Y2^-1 * Y3^-3 * Y2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-3, Y2^-3 * Y1^-5, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-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:: R = (1, 34, 2, 35, 6, 39, 14, 47, 26, 59, 25, 58, 19, 52, 31, 64, 22, 55, 11, 44, 4, 37)(3, 36, 7, 40, 15, 48, 27, 60, 24, 57, 13, 46, 18, 51, 30, 63, 33, 66, 21, 54, 10, 43)(5, 38, 8, 41, 16, 49, 28, 61, 32, 65, 20, 53, 9, 42, 17, 50, 29, 62, 23, 56, 12, 45)(67, 100, 69, 102, 75, 108, 85, 118, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 97, 130, 96, 129, 82, 115, 72, 105, 81, 114, 95, 128, 88, 121, 99, 132, 94, 127, 80, 113, 93, 126, 89, 122, 77, 110, 87, 120, 98, 131, 92, 125, 90, 123, 78, 111, 70, 103, 76, 109, 86, 119, 91, 124, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 86)(10, 87)(11, 88)(12, 89)(13, 90)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 91)(20, 98)(21, 99)(22, 97)(23, 95)(24, 93)(25, 92)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 94)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.570 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.554 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y3^-1), Y2^2 * Y1 * Y2^4, Y3 * Y2^3 * Y1^-4, Y1 * Y2^-1 * Y1 * Y2^-2 * Y3^-3, Y2^3 * Y1^6, (Y2^-1 * Y3)^33 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 26, 59, 19, 52, 25, 58, 31, 64, 22, 55, 11, 44, 4, 37)(3, 36, 7, 40, 15, 48, 27, 60, 33, 66, 24, 57, 13, 46, 18, 51, 30, 63, 21, 54, 10, 43)(5, 38, 8, 41, 16, 49, 28, 61, 20, 53, 9, 42, 17, 50, 29, 62, 32, 65, 23, 56, 12, 45)(67, 100, 69, 102, 75, 108, 85, 118, 90, 123, 78, 111, 70, 103, 76, 109, 86, 119, 92, 125, 99, 132, 89, 122, 77, 110, 87, 120, 94, 127, 80, 113, 93, 126, 98, 131, 88, 121, 96, 129, 82, 115, 72, 105, 81, 114, 95, 128, 97, 130, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 91, 124, 79, 112, 71, 104) L = (1, 70)(2, 67)(3, 76)(4, 77)(5, 78)(6, 68)(7, 69)(8, 71)(9, 86)(10, 87)(11, 88)(12, 89)(13, 90)(14, 72)(15, 73)(16, 74)(17, 75)(18, 79)(19, 92)(20, 94)(21, 96)(22, 97)(23, 98)(24, 99)(25, 85)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 91)(32, 95)(33, 93)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.563 Graph:: bipartite v = 4 e = 66 f = 34 degree seq :: [ 22^3, 66 ] E15.555 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y1^14 * Y2 * Y1^2, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 10, 43, 14, 47, 18, 51, 22, 55, 26, 59, 30, 63, 33, 66, 29, 62, 25, 58, 21, 54, 17, 50, 13, 46, 9, 42, 5, 38, 3, 36, 7, 40, 11, 44, 15, 48, 19, 52, 23, 56, 27, 60, 31, 64, 32, 65, 28, 61, 24, 57, 20, 53, 16, 49, 12, 45, 8, 41, 4, 37)(67, 100, 69, 102, 68, 101, 73, 106, 72, 105, 77, 110, 76, 109, 81, 114, 80, 113, 85, 118, 84, 117, 89, 122, 88, 121, 93, 126, 92, 125, 97, 130, 96, 129, 98, 131, 99, 132, 94, 127, 95, 128, 90, 123, 91, 124, 86, 119, 87, 120, 82, 115, 83, 116, 78, 111, 79, 112, 74, 107, 75, 108, 70, 103, 71, 104) L = (1, 69)(2, 73)(3, 68)(4, 71)(5, 67)(6, 77)(7, 72)(8, 75)(9, 70)(10, 81)(11, 76)(12, 79)(13, 74)(14, 85)(15, 80)(16, 83)(17, 78)(18, 89)(19, 84)(20, 87)(21, 82)(22, 93)(23, 88)(24, 91)(25, 86)(26, 97)(27, 92)(28, 95)(29, 90)(30, 98)(31, 96)(32, 99)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E15.561 Graph:: bipartite v = 2 e = 66 f = 36 degree seq :: [ 66^2 ] E15.556 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y2^3, Y1^-1 * Y2 * Y1^-7, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 22, 55, 27, 60, 19, 52, 10, 43, 3, 36, 7, 40, 15, 48, 23, 56, 30, 63, 32, 65, 26, 59, 18, 51, 9, 42, 13, 46, 17, 50, 25, 58, 31, 64, 33, 66, 29, 62, 21, 54, 12, 45, 5, 38, 8, 41, 16, 49, 24, 57, 28, 61, 20, 53, 11, 44, 4, 37)(67, 100, 69, 102, 75, 108, 78, 111, 70, 103, 76, 109, 84, 117, 87, 120, 77, 110, 85, 118, 92, 125, 95, 128, 86, 119, 93, 126, 98, 131, 99, 132, 94, 127, 88, 121, 96, 129, 97, 130, 90, 123, 80, 113, 89, 122, 91, 124, 82, 115, 72, 105, 81, 114, 83, 116, 74, 107, 68, 101, 73, 106, 79, 112, 71, 104) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 79)(8, 68)(9, 78)(10, 84)(11, 85)(12, 70)(13, 71)(14, 89)(15, 83)(16, 72)(17, 74)(18, 87)(19, 92)(20, 93)(21, 77)(22, 96)(23, 91)(24, 80)(25, 82)(26, 95)(27, 98)(28, 88)(29, 86)(30, 97)(31, 90)(32, 99)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E15.562 Graph:: bipartite v = 2 e = 66 f = 36 degree seq :: [ 66^2 ] E15.557 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y1, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y2^-5 * Y1, Y2 * Y1 * Y2 * Y1^5 * Y2, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 24, 57, 29, 62, 19, 52, 9, 42, 17, 50, 27, 60, 32, 65, 22, 55, 12, 45, 5, 38, 8, 41, 16, 49, 26, 59, 30, 63, 20, 53, 10, 43, 3, 36, 7, 40, 15, 48, 25, 58, 33, 66, 23, 56, 13, 46, 18, 51, 28, 61, 31, 64, 21, 54, 11, 44, 4, 37)(67, 100, 69, 102, 75, 108, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 94, 127, 82, 115, 72, 105, 81, 114, 93, 126, 97, 130, 92, 125, 80, 113, 91, 124, 98, 131, 87, 120, 96, 129, 90, 123, 99, 132, 88, 121, 77, 110, 86, 119, 95, 128, 89, 122, 78, 111, 70, 103, 76, 109, 85, 118, 79, 112, 71, 104) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 84)(10, 85)(11, 86)(12, 70)(13, 71)(14, 91)(15, 93)(16, 72)(17, 94)(18, 74)(19, 79)(20, 95)(21, 96)(22, 77)(23, 78)(24, 99)(25, 98)(26, 80)(27, 97)(28, 82)(29, 89)(30, 90)(31, 92)(32, 87)(33, 88)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E15.559 Graph:: bipartite v = 2 e = 66 f = 36 degree seq :: [ 66^2 ] E15.558 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1 * Y2 * Y1^4 * Y2, Y2^-1 * Y1^-1 * Y2^-6, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 24, 57, 13, 46, 18, 51, 27, 60, 31, 64, 19, 52, 28, 61, 33, 66, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 26, 59, 30, 63, 25, 58, 29, 62, 32, 65, 20, 53, 9, 42, 17, 50, 22, 55, 11, 44, 4, 37)(67, 100, 69, 102, 75, 108, 85, 118, 96, 129, 90, 123, 78, 111, 70, 103, 76, 109, 86, 119, 97, 130, 92, 125, 80, 113, 89, 122, 77, 110, 87, 120, 98, 131, 93, 126, 82, 115, 72, 105, 81, 114, 88, 121, 99, 132, 95, 128, 84, 117, 74, 107, 68, 101, 73, 106, 83, 116, 94, 127, 91, 124, 79, 112, 71, 104) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 89)(15, 88)(16, 72)(17, 94)(18, 74)(19, 96)(20, 97)(21, 98)(22, 99)(23, 77)(24, 78)(25, 79)(26, 80)(27, 82)(28, 91)(29, 84)(30, 90)(31, 92)(32, 93)(33, 95)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E15.560 Graph:: bipartite v = 2 e = 66 f = 36 degree seq :: [ 66^2 ] E15.559 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3), Y2^-3 * Y3^-3, Y3^-9 * Y2^2, Y2^4 * Y3^-1 * Y2 * Y3^-5, Y2^11, (Y2^-1 * Y3)^33, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 80, 113, 88, 121, 94, 127, 99, 132, 92, 125, 85, 118, 77, 110, 70, 103)(69, 102, 73, 106, 81, 114, 79, 112, 84, 117, 90, 123, 96, 129, 98, 131, 91, 124, 87, 120, 76, 109)(71, 104, 74, 107, 82, 115, 89, 122, 95, 128, 97, 130, 93, 126, 86, 119, 75, 108, 83, 116, 78, 111) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 79)(15, 78)(16, 72)(17, 77)(18, 74)(19, 91)(20, 92)(21, 93)(22, 84)(23, 80)(24, 82)(25, 97)(26, 98)(27, 99)(28, 90)(29, 88)(30, 89)(31, 94)(32, 95)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^22 ) } Outer automorphisms :: reflexible Dual of E15.557 Graph:: simple bipartite v = 36 e = 66 f = 2 degree seq :: [ 2^33, 22^3 ] E15.560 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y3 * Y2 * Y3^5, Y3^-1 * Y2 * Y3^-2 * Y2^4, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 80, 113, 92, 125, 85, 118, 91, 124, 97, 130, 88, 121, 77, 110, 70, 103)(69, 102, 73, 106, 81, 114, 93, 126, 99, 132, 90, 123, 79, 112, 84, 117, 96, 129, 87, 120, 76, 109)(71, 104, 74, 107, 82, 115, 94, 127, 86, 119, 75, 108, 83, 116, 95, 128, 98, 131, 89, 122, 78, 111) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 93)(15, 95)(16, 72)(17, 91)(18, 74)(19, 90)(20, 92)(21, 94)(22, 96)(23, 77)(24, 78)(25, 79)(26, 99)(27, 98)(28, 80)(29, 97)(30, 82)(31, 84)(32, 88)(33, 89)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^22 ) } Outer automorphisms :: reflexible Dual of E15.558 Graph:: simple bipartite v = 36 e = 66 f = 2 degree seq :: [ 2^33, 22^3 ] E15.561 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^11, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 78, 111, 84, 117, 90, 123, 94, 127, 88, 121, 82, 115, 76, 109, 70, 103)(69, 102, 73, 106, 79, 112, 85, 118, 91, 124, 96, 129, 98, 131, 93, 126, 87, 120, 81, 114, 75, 108)(71, 104, 74, 107, 80, 113, 86, 119, 92, 125, 97, 130, 99, 132, 95, 128, 89, 122, 83, 116, 77, 110) L = (1, 69)(2, 73)(3, 74)(4, 75)(5, 67)(6, 79)(7, 80)(8, 68)(9, 71)(10, 81)(11, 70)(12, 85)(13, 86)(14, 72)(15, 77)(16, 87)(17, 76)(18, 91)(19, 92)(20, 78)(21, 83)(22, 93)(23, 82)(24, 96)(25, 97)(26, 84)(27, 89)(28, 98)(29, 88)(30, 99)(31, 90)(32, 95)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^22 ) } Outer automorphisms :: reflexible Dual of E15.555 Graph:: simple bipartite v = 36 e = 66 f = 2 degree seq :: [ 2^33, 22^3 ] E15.562 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^11, (Y3 * Y2^-1)^33, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11, 44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31, 64)(32, 65)(33, 66)(67, 100, 68, 101, 72, 105, 78, 111, 84, 117, 90, 123, 95, 128, 89, 122, 83, 116, 77, 110, 70, 103)(69, 102, 73, 106, 79, 112, 85, 118, 91, 124, 96, 129, 99, 132, 94, 127, 88, 121, 82, 115, 76, 109)(71, 104, 74, 107, 80, 113, 86, 119, 92, 125, 97, 130, 98, 131, 93, 126, 87, 120, 81, 114, 75, 108) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 79)(7, 71)(8, 68)(9, 70)(10, 81)(11, 82)(12, 85)(13, 74)(14, 72)(15, 77)(16, 87)(17, 88)(18, 91)(19, 80)(20, 78)(21, 83)(22, 93)(23, 94)(24, 96)(25, 86)(26, 84)(27, 89)(28, 98)(29, 99)(30, 92)(31, 90)(32, 95)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^22 ) } Outer automorphisms :: reflexible Dual of E15.556 Graph:: simple bipartite v = 36 e = 66 f = 2 degree seq :: [ 2^33, 22^3 ] E15.563 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1^-1 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^5 * Y3 * Y1 * Y3 * Y1^3, (Y3 * Y2^-1)^11, (Y1^-1 * Y3^-1)^33 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 22, 55, 28, 61, 33, 66, 27, 60, 21, 54, 13, 46, 18, 51, 10, 43, 3, 36, 7, 40, 15, 48, 23, 56, 29, 62, 32, 65, 26, 59, 20, 53, 12, 45, 5, 38, 8, 41, 16, 49, 9, 42, 17, 50, 24, 57, 30, 63, 31, 64, 25, 58, 19, 52, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 80)(10, 82)(11, 84)(12, 70)(13, 71)(14, 89)(15, 90)(16, 72)(17, 88)(18, 74)(19, 79)(20, 77)(21, 78)(22, 95)(23, 96)(24, 94)(25, 87)(26, 85)(27, 86)(28, 98)(29, 97)(30, 99)(31, 93)(32, 91)(33, 92)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.554 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.564 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^5, Y1 * Y3 * Y1 * Y3^4 * Y1, (Y3 * Y2^-1)^11, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 26, 59, 33, 66, 20, 53, 9, 42, 17, 50, 27, 60, 25, 58, 30, 63, 32, 65, 19, 52, 29, 62, 24, 57, 13, 46, 18, 51, 28, 61, 31, 64, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 22, 55, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 92)(15, 93)(16, 72)(17, 95)(18, 74)(19, 97)(20, 98)(21, 99)(22, 80)(23, 77)(24, 78)(25, 79)(26, 91)(27, 90)(28, 82)(29, 89)(30, 84)(31, 88)(32, 94)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.551 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.565 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^3, Y1 * Y3^-1 * Y1 * Y3^-4 * Y1, (Y3 * Y2^-1)^11, (Y1^-1 * Y3^-1)^33 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 26, 59, 32, 65, 24, 57, 13, 46, 18, 51, 28, 61, 19, 52, 29, 62, 33, 66, 25, 58, 30, 63, 20, 53, 9, 42, 17, 50, 27, 60, 31, 64, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 22, 55, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 88)(15, 93)(16, 72)(17, 95)(18, 74)(19, 92)(20, 94)(21, 96)(22, 97)(23, 77)(24, 78)(25, 79)(26, 80)(27, 99)(28, 82)(29, 98)(30, 84)(31, 91)(32, 89)(33, 90)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.546 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.566 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^-3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^11, (Y3 * Y2^-1)^11, (Y3^-1 * Y1^-1)^33 ] Map:: R = (1, 34, 2, 35, 6, 39, 3, 36, 7, 40, 12, 45, 9, 42, 13, 46, 18, 51, 15, 48, 19, 52, 24, 57, 21, 54, 25, 58, 30, 63, 27, 60, 31, 64, 33, 66, 29, 62, 32, 65, 28, 61, 23, 56, 26, 59, 22, 55, 17, 50, 20, 53, 16, 49, 11, 44, 14, 47, 10, 43, 5, 38, 8, 41, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 72)(5, 67)(6, 78)(7, 79)(8, 68)(9, 81)(10, 70)(11, 71)(12, 84)(13, 85)(14, 74)(15, 87)(16, 76)(17, 77)(18, 90)(19, 91)(20, 80)(21, 93)(22, 82)(23, 83)(24, 96)(25, 97)(26, 86)(27, 95)(28, 88)(29, 89)(30, 99)(31, 98)(32, 92)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.548 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.567 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-2 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^11, (Y3 * Y2^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 5, 38, 8, 41, 12, 45, 11, 44, 14, 47, 18, 51, 17, 50, 20, 53, 24, 57, 23, 56, 26, 59, 30, 63, 29, 62, 32, 65, 33, 66, 27, 60, 31, 64, 28, 61, 21, 54, 25, 58, 22, 55, 15, 48, 19, 52, 16, 49, 9, 42, 13, 46, 10, 43, 3, 36, 7, 40, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 70)(7, 79)(8, 68)(9, 81)(10, 82)(11, 71)(12, 72)(13, 85)(14, 74)(15, 87)(16, 88)(17, 77)(18, 78)(19, 91)(20, 80)(21, 93)(22, 94)(23, 83)(24, 84)(25, 97)(26, 86)(27, 95)(28, 99)(29, 89)(30, 90)(31, 98)(32, 92)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.552 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.568 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-3 * Y1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-5 * Y3^-1, (Y3 * Y2^-1)^11, (Y1^-1 * Y3^-1)^33 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 26, 59, 33, 66, 25, 58, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 27, 60, 32, 65, 24, 57, 13, 46, 18, 51, 20, 53, 9, 42, 17, 50, 28, 61, 31, 64, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 19, 52, 29, 62, 30, 63, 22, 55, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 93)(15, 94)(16, 72)(17, 95)(18, 74)(19, 80)(20, 82)(21, 84)(22, 91)(23, 77)(24, 78)(25, 79)(26, 98)(27, 97)(28, 96)(29, 92)(30, 99)(31, 88)(32, 89)(33, 90)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.547 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.569 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y1^-1, Y3), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3^4, Y3^3 * Y1^-6, Y1^-6 * Y3^3, (Y3 * Y2^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 14, 47, 26, 59, 30, 63, 19, 52, 23, 56, 12, 45, 5, 38, 8, 41, 16, 49, 27, 60, 31, 64, 20, 53, 9, 42, 17, 50, 24, 57, 13, 46, 18, 51, 28, 61, 32, 65, 21, 54, 10, 43, 3, 36, 7, 40, 15, 48, 25, 58, 29, 62, 33, 66, 22, 55, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 81)(7, 83)(8, 68)(9, 85)(10, 86)(11, 87)(12, 70)(13, 71)(14, 91)(15, 90)(16, 72)(17, 89)(18, 74)(19, 88)(20, 96)(21, 97)(22, 98)(23, 77)(24, 78)(25, 79)(26, 95)(27, 80)(28, 82)(29, 84)(30, 99)(31, 92)(32, 93)(33, 94)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.550 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.570 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^-2 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^-11, Y3^-11, Y3^22, (Y3 * Y2^-1)^11, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 34, 2, 35, 6, 39, 9, 42, 15, 48, 20, 53, 22, 55, 27, 60, 32, 65, 31, 64, 29, 62, 24, 57, 19, 52, 17, 50, 12, 45, 5, 38, 8, 41, 10, 43, 3, 36, 7, 40, 14, 47, 16, 49, 21, 54, 26, 59, 28, 61, 33, 66, 30, 63, 25, 58, 23, 56, 18, 51, 13, 46, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 80)(7, 81)(8, 68)(9, 82)(10, 72)(11, 74)(12, 70)(13, 71)(14, 86)(15, 87)(16, 88)(17, 77)(18, 78)(19, 79)(20, 92)(21, 93)(22, 94)(23, 83)(24, 84)(25, 85)(26, 98)(27, 99)(28, 97)(29, 89)(30, 90)(31, 91)(32, 96)(33, 95)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.553 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.571 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 33, 33}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3^2 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^11, Y3^11, Y3^3 * Y1^-1 * Y3^5 * Y1^-2 * Y3, (Y3 * Y2^-1)^11 ] Map:: R = (1, 34, 2, 35, 6, 39, 13, 46, 15, 48, 20, 53, 25, 58, 27, 60, 32, 65, 28, 61, 30, 63, 23, 56, 16, 49, 18, 51, 10, 43, 3, 36, 7, 40, 12, 45, 5, 38, 8, 41, 14, 47, 19, 52, 21, 54, 26, 59, 31, 64, 33, 66, 29, 62, 22, 55, 24, 57, 17, 50, 9, 42, 11, 44, 4, 37)(67, 100)(68, 101)(69, 102)(70, 103)(71, 104)(72, 105)(73, 106)(74, 107)(75, 108)(76, 109)(77, 110)(78, 111)(79, 112)(80, 113)(81, 114)(82, 115)(83, 116)(84, 117)(85, 118)(86, 119)(87, 120)(88, 121)(89, 122)(90, 123)(91, 124)(92, 125)(93, 126)(94, 127)(95, 128)(96, 129)(97, 130)(98, 131)(99, 132) L = (1, 69)(2, 73)(3, 75)(4, 76)(5, 67)(6, 78)(7, 77)(8, 68)(9, 82)(10, 83)(11, 84)(12, 70)(13, 71)(14, 72)(15, 74)(16, 88)(17, 89)(18, 90)(19, 79)(20, 80)(21, 81)(22, 94)(23, 95)(24, 96)(25, 85)(26, 86)(27, 87)(28, 97)(29, 98)(30, 99)(31, 91)(32, 92)(33, 93)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 22, 66 ), ( 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66, 22, 66 ) } Outer automorphisms :: reflexible Dual of E15.549 Graph:: bipartite v = 34 e = 66 f = 4 degree seq :: [ 2^33, 66 ] E15.572 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5 * T1^2, T1^7, T2^3 * T1^-2 * T2^2 * T1^-3 ] Map:: non-degenerate R = (1, 3, 9, 19, 23, 11, 21, 31, 34, 27, 14, 26, 29, 18, 8, 2, 7, 17, 24, 12, 4, 10, 20, 30, 33, 22, 32, 35, 28, 16, 6, 15, 25, 13, 5)(36, 37, 41, 49, 57, 46, 39)(38, 42, 50, 61, 67, 56, 45)(40, 43, 51, 62, 68, 58, 47)(44, 52, 60, 64, 70, 66, 55)(48, 53, 63, 69, 65, 54, 59) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^7 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E15.581 Transitivity :: ET+ Graph:: bipartite v = 6 e = 35 f = 1 degree seq :: [ 7^5, 35 ] E15.573 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-7, T1^7, T2^5 * T1^-3, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 14, 26, 35, 24, 12, 4, 10, 20, 29, 16, 6, 15, 28, 34, 23, 11, 21, 31, 18, 8, 2, 7, 17, 30, 33, 22, 32, 25, 13, 5)(36, 37, 41, 49, 57, 46, 39)(38, 42, 50, 61, 67, 56, 45)(40, 43, 51, 62, 68, 58, 47)(44, 52, 63, 70, 60, 66, 55)(48, 53, 64, 54, 65, 69, 59) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^7 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E15.583 Transitivity :: ET+ Graph:: bipartite v = 6 e = 35 f = 1 degree seq :: [ 7^5, 35 ] E15.574 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^7, T2^-5 * T1^-3, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1, T2^2 * 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^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 32, 22, 35, 31, 18, 8, 2, 7, 17, 30, 23, 11, 21, 34, 29, 16, 6, 15, 28, 24, 12, 4, 10, 20, 33, 27, 14, 26, 25, 13, 5)(36, 37, 41, 49, 57, 46, 39)(38, 42, 50, 61, 70, 56, 45)(40, 43, 51, 62, 67, 58, 47)(44, 52, 63, 60, 66, 69, 55)(48, 53, 64, 68, 54, 65, 59) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^7 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E15.579 Transitivity :: ET+ Graph:: bipartite v = 6 e = 35 f = 1 degree seq :: [ 7^5, 35 ] E15.575 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5 * T1^-1, T1^7, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 3, 9, 18, 8, 2, 7, 17, 27, 16, 6, 15, 26, 33, 25, 14, 24, 32, 35, 30, 21, 29, 34, 31, 22, 11, 20, 28, 23, 12, 4, 10, 19, 13, 5)(36, 37, 41, 49, 56, 46, 39)(38, 42, 50, 59, 64, 55, 45)(40, 43, 51, 60, 65, 57, 47)(44, 52, 61, 67, 69, 63, 54)(48, 53, 62, 68, 70, 66, 58) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^7 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E15.582 Transitivity :: ET+ Graph:: bipartite v = 6 e = 35 f = 1 degree seq :: [ 7^5, 35 ] E15.576 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2^-5, T1^7, T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 12, 4, 10, 20, 28, 23, 11, 21, 29, 34, 31, 22, 30, 35, 33, 25, 14, 24, 32, 27, 16, 6, 15, 26, 18, 8, 2, 7, 17, 13, 5)(36, 37, 41, 49, 57, 46, 39)(38, 42, 50, 59, 65, 56, 45)(40, 43, 51, 60, 66, 58, 47)(44, 52, 61, 67, 70, 64, 55)(48, 53, 62, 68, 69, 63, 54) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^7 ), ( 70^35 ) } Outer automorphisms :: reflexible Dual of E15.580 Transitivity :: ET+ Graph:: bipartite v = 6 e = 35 f = 1 degree seq :: [ 7^5, 35 ] E15.577 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^2 * T2^-1 * T1^2, T2^8 * T1^-1 * T2, (T1^-1 * T2^-1)^7 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 32, 24, 16, 8, 2, 7, 15, 23, 31, 34, 27, 19, 11, 6, 14, 22, 30, 35, 28, 20, 12, 4, 10, 18, 26, 33, 29, 21, 13, 5)(36, 37, 41, 45, 38, 42, 49, 53, 44, 50, 57, 61, 52, 58, 65, 68, 60, 66, 70, 64, 67, 69, 63, 56, 59, 62, 55, 48, 51, 54, 47, 40, 43, 46, 39) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 14^35 ) } Outer automorphisms :: reflexible Dual of E15.585 Transitivity :: ET+ Graph:: bipartite v = 2 e = 35 f = 5 degree seq :: [ 35^2 ] E15.578 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 35, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^-3 * T2^-1 * T1^-8, (T1^-1 * T2^-1)^7 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 34, 32, 29, 31, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 33, 35, 30, 23, 25, 18, 11, 13, 5)(36, 37, 41, 49, 55, 61, 67, 65, 59, 53, 47, 40, 43, 44, 51, 57, 63, 69, 70, 66, 60, 54, 48, 45, 38, 42, 50, 56, 62, 68, 64, 58, 52, 46, 39) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 14^35 ) } Outer automorphisms :: reflexible Dual of E15.584 Transitivity :: ET+ Graph:: bipartite v = 2 e = 35 f = 5 degree seq :: [ 35^2 ] E15.579 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5 * T1^2, T1^7, T2^3 * T1^-2 * T2^2 * T1^-3 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 23, 58, 11, 46, 21, 56, 31, 66, 34, 69, 27, 62, 14, 49, 26, 61, 29, 64, 18, 53, 8, 43, 2, 37, 7, 42, 17, 52, 24, 59, 12, 47, 4, 39, 10, 45, 20, 55, 30, 65, 33, 68, 22, 57, 32, 67, 35, 70, 28, 63, 16, 51, 6, 41, 15, 50, 25, 60, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 57)(15, 61)(16, 62)(17, 60)(18, 63)(19, 59)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 64)(26, 67)(27, 68)(28, 69)(29, 70)(30, 54)(31, 55)(32, 56)(33, 58)(34, 65)(35, 66) local type(s) :: { ( 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35 ) } Outer automorphisms :: reflexible Dual of E15.574 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 6 degree seq :: [ 70 ] E15.580 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-7, T1^7, T2^5 * T1^-3, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 27, 62, 14, 49, 26, 61, 35, 70, 24, 59, 12, 47, 4, 39, 10, 45, 20, 55, 29, 64, 16, 51, 6, 41, 15, 50, 28, 63, 34, 69, 23, 58, 11, 46, 21, 56, 31, 66, 18, 53, 8, 43, 2, 37, 7, 42, 17, 52, 30, 65, 33, 68, 22, 57, 32, 67, 25, 60, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 57)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 66)(26, 67)(27, 68)(28, 70)(29, 54)(30, 69)(31, 55)(32, 56)(33, 58)(34, 59)(35, 60) local type(s) :: { ( 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35 ) } Outer automorphisms :: reflexible Dual of E15.576 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 6 degree seq :: [ 70 ] E15.581 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^7, T2^-5 * T1^-3, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1, T2^2 * 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^-4 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 32, 67, 22, 57, 35, 70, 31, 66, 18, 53, 8, 43, 2, 37, 7, 42, 17, 52, 30, 65, 23, 58, 11, 46, 21, 56, 34, 69, 29, 64, 16, 51, 6, 41, 15, 50, 28, 63, 24, 59, 12, 47, 4, 39, 10, 45, 20, 55, 33, 68, 27, 62, 14, 49, 26, 61, 25, 60, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 57)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 66)(26, 70)(27, 67)(28, 60)(29, 68)(30, 59)(31, 69)(32, 58)(33, 54)(34, 55)(35, 56) local type(s) :: { ( 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35 ) } Outer automorphisms :: reflexible Dual of E15.572 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 6 degree seq :: [ 70 ] E15.582 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5 * T1^-1, T1^7, (T1^-1 * T2^-1)^35 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 18, 53, 8, 43, 2, 37, 7, 42, 17, 52, 27, 62, 16, 51, 6, 41, 15, 50, 26, 61, 33, 68, 25, 60, 14, 49, 24, 59, 32, 67, 35, 70, 30, 65, 21, 56, 29, 64, 34, 69, 31, 66, 22, 57, 11, 46, 20, 55, 28, 63, 23, 58, 12, 47, 4, 39, 10, 45, 19, 54, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 56)(15, 59)(16, 60)(17, 61)(18, 62)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 64)(25, 65)(26, 67)(27, 68)(28, 54)(29, 55)(30, 57)(31, 58)(32, 69)(33, 70)(34, 63)(35, 66) local type(s) :: { ( 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35 ) } Outer automorphisms :: reflexible Dual of E15.575 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 6 degree seq :: [ 70 ] E15.583 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2^-5, T1^7, T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^2 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 12, 47, 4, 39, 10, 45, 20, 55, 28, 63, 23, 58, 11, 46, 21, 56, 29, 64, 34, 69, 31, 66, 22, 57, 30, 65, 35, 70, 33, 68, 25, 60, 14, 49, 24, 59, 32, 67, 27, 62, 16, 51, 6, 41, 15, 50, 26, 61, 18, 53, 8, 43, 2, 37, 7, 42, 17, 52, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 57)(15, 59)(16, 60)(17, 61)(18, 62)(19, 48)(20, 44)(21, 45)(22, 46)(23, 47)(24, 65)(25, 66)(26, 67)(27, 68)(28, 54)(29, 55)(30, 56)(31, 58)(32, 70)(33, 69)(34, 63)(35, 64) local type(s) :: { ( 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35, 7, 35 ) } Outer automorphisms :: reflexible Dual of E15.573 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 6 degree seq :: [ 70 ] E15.584 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^5, T2^7, T2^2 * T1^-1 * T2 * T1^-1 * T2^2 * T1^-3 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 25, 60, 13, 48, 5, 40)(2, 37, 7, 42, 17, 52, 28, 63, 29, 64, 18, 53, 8, 43)(4, 39, 10, 45, 20, 55, 30, 65, 33, 68, 24, 59, 12, 47)(6, 41, 15, 50, 22, 57, 32, 67, 35, 70, 27, 62, 16, 51)(11, 46, 21, 56, 31, 66, 34, 69, 26, 61, 14, 49, 23, 58) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 59)(15, 58)(16, 61)(17, 57)(18, 62)(19, 63)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 64)(26, 68)(27, 69)(28, 67)(29, 70)(30, 54)(31, 55)(32, 56)(33, 60)(34, 65)(35, 66) local type(s) :: { ( 35^14 ) } Outer automorphisms :: reflexible Dual of E15.578 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 35 f = 2 degree seq :: [ 14^5 ] E15.585 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 35, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-5, T2^7, 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 * T1^2 * T2^3 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 23, 58, 13, 48, 5, 40)(2, 37, 7, 42, 17, 52, 27, 62, 28, 63, 18, 53, 8, 43)(4, 39, 10, 45, 20, 55, 29, 64, 31, 66, 22, 57, 12, 47)(6, 41, 15, 50, 25, 60, 33, 68, 34, 69, 26, 61, 16, 51)(11, 46, 21, 56, 30, 65, 35, 70, 32, 67, 24, 59, 14, 49) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 47)(15, 46)(16, 59)(17, 60)(18, 61)(19, 62)(20, 44)(21, 45)(22, 48)(23, 63)(24, 57)(25, 56)(26, 67)(27, 68)(28, 69)(29, 54)(30, 55)(31, 58)(32, 66)(33, 65)(34, 70)(35, 64) local type(s) :: { ( 35^14 ) } Outer automorphisms :: reflexible Dual of E15.577 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 35 f = 2 degree seq :: [ 14^5 ] E15.586 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^3 * Y1^-3 * Y3, Y2^5 * Y1^2, Y1^7, Y2^2 * Y3 * Y2^3 * Y3^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 26, 61, 32, 67, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 27, 62, 33, 68, 23, 58, 12, 47)(9, 44, 17, 52, 25, 60, 29, 64, 35, 70, 31, 66, 20, 55)(13, 48, 18, 53, 28, 63, 34, 69, 30, 65, 19, 54, 24, 59)(71, 106, 73, 108, 79, 114, 89, 124, 93, 128, 81, 116, 91, 126, 101, 136, 104, 139, 97, 132, 84, 119, 96, 131, 99, 134, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 94, 129, 82, 117, 74, 109, 80, 115, 90, 125, 100, 135, 103, 138, 92, 127, 102, 137, 105, 140, 98, 133, 86, 121, 76, 111, 85, 120, 95, 130, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 76)(15, 77)(16, 78)(17, 79)(18, 83)(19, 100)(20, 101)(21, 102)(22, 84)(23, 103)(24, 89)(25, 87)(26, 85)(27, 86)(28, 88)(29, 95)(30, 104)(31, 105)(32, 96)(33, 97)(34, 98)(35, 99)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E15.597 Graph:: bipartite v = 6 e = 70 f = 36 degree seq :: [ 14^5, 70 ] E15.587 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^5 * Y1^-1, Y1^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 21, 56, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 24, 59, 29, 64, 20, 55, 10, 45)(5, 40, 8, 43, 16, 51, 25, 60, 30, 65, 22, 57, 12, 47)(9, 44, 17, 52, 26, 61, 32, 67, 34, 69, 28, 63, 19, 54)(13, 48, 18, 53, 27, 62, 33, 68, 35, 70, 31, 66, 23, 58)(71, 106, 73, 108, 79, 114, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 97, 132, 86, 121, 76, 111, 85, 120, 96, 131, 103, 138, 95, 130, 84, 119, 94, 129, 102, 137, 105, 140, 100, 135, 91, 126, 99, 134, 104, 139, 101, 136, 92, 127, 81, 116, 90, 125, 98, 133, 93, 128, 82, 117, 74, 109, 80, 115, 89, 124, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 76)(15, 77)(16, 78)(17, 79)(18, 83)(19, 98)(20, 99)(21, 84)(22, 100)(23, 101)(24, 85)(25, 86)(26, 87)(27, 88)(28, 104)(29, 94)(30, 95)(31, 105)(32, 96)(33, 97)(34, 102)(35, 103)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E15.598 Graph:: bipartite v = 6 e = 70 f = 36 degree seq :: [ 14^5, 70 ] E15.588 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (Y3^-1, Y2^-1), Y3 * Y2^-5, Y3^7, Y1^7, Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^4 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 24, 59, 30, 65, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 25, 60, 31, 66, 23, 58, 12, 47)(9, 44, 17, 52, 26, 61, 32, 67, 35, 70, 29, 64, 20, 55)(13, 48, 18, 53, 27, 62, 33, 68, 34, 69, 28, 63, 19, 54)(71, 106, 73, 108, 79, 114, 89, 124, 82, 117, 74, 109, 80, 115, 90, 125, 98, 133, 93, 128, 81, 116, 91, 126, 99, 134, 104, 139, 101, 136, 92, 127, 100, 135, 105, 140, 103, 138, 95, 130, 84, 119, 94, 129, 102, 137, 97, 132, 86, 121, 76, 111, 85, 120, 96, 131, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 90)(10, 91)(11, 92)(12, 93)(13, 89)(14, 76)(15, 77)(16, 78)(17, 79)(18, 83)(19, 98)(20, 99)(21, 100)(22, 84)(23, 101)(24, 85)(25, 86)(26, 87)(27, 88)(28, 104)(29, 105)(30, 94)(31, 95)(32, 96)(33, 97)(34, 103)(35, 102)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E15.596 Graph:: bipartite v = 6 e = 70 f = 36 degree seq :: [ 14^5, 70 ] E15.589 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y1, Y1 * Y3, Y2 * Y3 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^7, Y1^5 * Y3^-2, Y2^3 * Y1^-1 * Y2 * Y3 * Y2 * Y3, Y2^-35 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 26, 61, 32, 67, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 27, 62, 33, 68, 23, 58, 12, 47)(9, 44, 17, 52, 28, 63, 35, 70, 25, 60, 31, 66, 20, 55)(13, 48, 18, 53, 29, 64, 19, 54, 30, 65, 34, 69, 24, 59)(71, 106, 73, 108, 79, 114, 89, 124, 97, 132, 84, 119, 96, 131, 105, 140, 94, 129, 82, 117, 74, 109, 80, 115, 90, 125, 99, 134, 86, 121, 76, 111, 85, 120, 98, 133, 104, 139, 93, 128, 81, 116, 91, 126, 101, 136, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 100, 135, 103, 138, 92, 127, 102, 137, 95, 130, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 76)(15, 77)(16, 78)(17, 79)(18, 83)(19, 99)(20, 101)(21, 102)(22, 84)(23, 103)(24, 104)(25, 105)(26, 85)(27, 86)(28, 87)(29, 88)(30, 89)(31, 95)(32, 96)(33, 97)(34, 100)(35, 98)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E15.599 Graph:: bipartite v = 6 e = 70 f = 36 degree seq :: [ 14^5, 70 ] E15.590 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y3^-1, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y1^7, Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-3, Y2^-1 * Y3 * Y2^-4 * Y1^-2, Y1 * Y2^-1 * Y1 * Y2^-2 * Y3^-2 * Y2^-2, Y1^2 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-3, Y1^-2 * Y3 * Y2^30, 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 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 26, 61, 35, 70, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 27, 62, 32, 67, 23, 58, 12, 47)(9, 44, 17, 52, 28, 63, 25, 60, 31, 66, 34, 69, 20, 55)(13, 48, 18, 53, 29, 64, 33, 68, 19, 54, 30, 65, 24, 59)(71, 106, 73, 108, 79, 114, 89, 124, 102, 137, 92, 127, 105, 140, 101, 136, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 100, 135, 93, 128, 81, 116, 91, 126, 104, 139, 99, 134, 86, 121, 76, 111, 85, 120, 98, 133, 94, 129, 82, 117, 74, 109, 80, 115, 90, 125, 103, 138, 97, 132, 84, 119, 96, 131, 95, 130, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 76)(15, 77)(16, 78)(17, 79)(18, 83)(19, 103)(20, 104)(21, 105)(22, 84)(23, 102)(24, 100)(25, 98)(26, 85)(27, 86)(28, 87)(29, 88)(30, 89)(31, 95)(32, 97)(33, 99)(34, 101)(35, 96)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E15.595 Graph:: bipartite v = 6 e = 70 f = 36 degree seq :: [ 14^5, 70 ] E15.591 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^-1 * Y2, Y1^7 * Y2^-1 * Y1^2, (Y3^-1 * Y1^-1)^7 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 30, 65, 26, 61, 18, 53, 10, 45, 3, 38, 7, 42, 15, 50, 23, 58, 31, 66, 35, 70, 29, 64, 21, 56, 13, 48, 9, 44, 17, 52, 25, 60, 33, 68, 34, 69, 28, 63, 20, 55, 12, 47, 5, 40, 8, 43, 16, 51, 24, 59, 32, 67, 27, 62, 19, 54, 11, 46, 4, 39)(71, 106, 73, 108, 79, 114, 78, 113, 72, 107, 77, 112, 87, 122, 86, 121, 76, 111, 85, 120, 95, 130, 94, 129, 84, 119, 93, 128, 103, 138, 102, 137, 92, 127, 101, 136, 104, 139, 97, 132, 100, 135, 105, 140, 98, 133, 89, 124, 96, 131, 99, 134, 90, 125, 81, 116, 88, 123, 91, 126, 82, 117, 74, 109, 80, 115, 83, 118, 75, 110) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 78)(10, 83)(11, 88)(12, 74)(13, 75)(14, 93)(15, 95)(16, 76)(17, 86)(18, 91)(19, 96)(20, 81)(21, 82)(22, 101)(23, 103)(24, 84)(25, 94)(26, 99)(27, 100)(28, 89)(29, 90)(30, 105)(31, 104)(32, 92)(33, 102)(34, 97)(35, 98)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.594 Graph:: bipartite v = 2 e = 70 f = 40 degree seq :: [ 70^2 ] E15.592 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^9 * Y1 * Y2^2, (Y3^-1 * Y1^-1)^7 ] Map:: R = (1, 36, 2, 37, 6, 41, 9, 44, 15, 50, 20, 55, 22, 57, 27, 62, 32, 67, 34, 69, 31, 66, 29, 64, 24, 59, 19, 54, 17, 52, 12, 47, 5, 40, 8, 43, 10, 45, 3, 38, 7, 42, 14, 49, 16, 51, 21, 56, 26, 61, 28, 63, 33, 68, 35, 70, 30, 65, 25, 60, 23, 58, 18, 53, 13, 48, 11, 46, 4, 39)(71, 106, 73, 108, 79, 114, 86, 121, 92, 127, 98, 133, 104, 139, 100, 135, 94, 129, 88, 123, 82, 117, 74, 109, 80, 115, 76, 111, 84, 119, 90, 125, 96, 131, 102, 137, 105, 140, 99, 134, 93, 128, 87, 122, 81, 116, 78, 113, 72, 107, 77, 112, 85, 120, 91, 126, 97, 132, 103, 138, 101, 136, 95, 130, 89, 124, 83, 118, 75, 110) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 84)(7, 85)(8, 72)(9, 86)(10, 76)(11, 78)(12, 74)(13, 75)(14, 90)(15, 91)(16, 92)(17, 81)(18, 82)(19, 83)(20, 96)(21, 97)(22, 98)(23, 87)(24, 88)(25, 89)(26, 102)(27, 103)(28, 104)(29, 93)(30, 94)(31, 95)(32, 105)(33, 101)(34, 100)(35, 99)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.593 Graph:: bipartite v = 2 e = 70 f = 40 degree seq :: [ 70^2 ] E15.593 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^5 * Y2^-2, Y2^7, Y2^-2 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3 * Y2^-3 * Y3^-1, (Y3^-1 * Y1^-1)^35 ] Map:: R = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70)(71, 106, 72, 107, 76, 111, 84, 119, 92, 127, 81, 116, 74, 109)(73, 108, 77, 112, 85, 120, 96, 131, 100, 135, 91, 126, 80, 115)(75, 110, 78, 113, 86, 121, 97, 132, 101, 136, 93, 128, 82, 117)(79, 114, 87, 122, 98, 133, 104, 139, 103, 138, 95, 130, 90, 125)(83, 118, 88, 123, 89, 124, 99, 134, 105, 140, 102, 137, 94, 129) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 96)(15, 98)(16, 76)(17, 99)(18, 78)(19, 86)(20, 88)(21, 95)(22, 100)(23, 81)(24, 82)(25, 83)(26, 104)(27, 84)(28, 105)(29, 97)(30, 103)(31, 92)(32, 93)(33, 94)(34, 102)(35, 101)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 70, 70 ), ( 70^14 ) } Outer automorphisms :: reflexible Dual of E15.592 Graph:: simple bipartite v = 40 e = 70 f = 2 degree seq :: [ 2^35, 14^5 ] E15.594 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y2^7, Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^2, Y3^-5 * Y2^-3, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-3, Y3^-1 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-2, (Y3^-1 * Y1^-1)^35 ] Map:: R = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70)(71, 106, 72, 107, 76, 111, 84, 119, 92, 127, 81, 116, 74, 109)(73, 108, 77, 112, 85, 120, 96, 131, 105, 140, 91, 126, 80, 115)(75, 110, 78, 113, 86, 121, 97, 132, 102, 137, 93, 128, 82, 117)(79, 114, 87, 122, 98, 133, 95, 130, 101, 136, 104, 139, 90, 125)(83, 118, 88, 123, 99, 134, 103, 138, 89, 124, 100, 135, 94, 129) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 96)(15, 98)(16, 76)(17, 100)(18, 78)(19, 102)(20, 103)(21, 104)(22, 105)(23, 81)(24, 82)(25, 83)(26, 95)(27, 84)(28, 94)(29, 86)(30, 93)(31, 88)(32, 92)(33, 97)(34, 99)(35, 101)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 70, 70 ), ( 70^14 ) } Outer automorphisms :: reflexible Dual of E15.591 Graph:: simple bipartite v = 40 e = 70 f = 2 degree seq :: [ 2^35, 14^5 ] E15.595 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^7, Y3^2 * Y1^5, (Y3 * Y2^-1)^7, Y3^-2 * Y1^3 * Y3^-2 * Y1^3 * Y3^-2 * Y1^3 * Y3^-2 * Y1^3 * Y3^-2 * Y1^3 * Y3^-2 * Y1^-1 * Y3^-3 * Y1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 24, 59, 13, 48, 18, 53, 27, 62, 34, 69, 30, 65, 19, 54, 28, 63, 32, 67, 21, 56, 10, 45, 3, 38, 7, 42, 15, 50, 23, 58, 12, 47, 5, 40, 8, 43, 16, 51, 26, 61, 33, 68, 25, 60, 29, 64, 35, 70, 31, 66, 20, 55, 9, 44, 17, 52, 22, 57, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 93)(15, 92)(16, 76)(17, 98)(18, 78)(19, 95)(20, 100)(21, 101)(22, 102)(23, 81)(24, 82)(25, 83)(26, 84)(27, 86)(28, 99)(29, 88)(30, 103)(31, 104)(32, 105)(33, 94)(34, 96)(35, 97)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) } Outer automorphisms :: reflexible Dual of E15.590 Graph:: bipartite v = 36 e = 70 f = 6 degree seq :: [ 2^35, 70 ] E15.596 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^2 * Y1^-4 * Y3, Y1 * Y3 * Y1^2 * Y3^3 * Y1^2, (Y3 * Y2^-1)^7, Y3^2 * Y1^30 * Y3, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 26, 61, 19, 54, 31, 66, 33, 68, 23, 58, 12, 47, 5, 40, 8, 43, 16, 51, 28, 63, 20, 55, 9, 44, 17, 52, 29, 64, 34, 69, 24, 59, 13, 48, 18, 53, 30, 65, 21, 56, 10, 45, 3, 38, 7, 42, 15, 50, 27, 62, 35, 70, 25, 60, 32, 67, 22, 57, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 97)(15, 99)(16, 76)(17, 101)(18, 78)(19, 95)(20, 96)(21, 98)(22, 100)(23, 81)(24, 82)(25, 83)(26, 105)(27, 104)(28, 84)(29, 103)(30, 86)(31, 102)(32, 88)(33, 92)(34, 93)(35, 94)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) } Outer automorphisms :: reflexible Dual of E15.588 Graph:: bipartite v = 36 e = 70 f = 6 degree seq :: [ 2^35, 70 ] E15.597 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-7, Y3^-3 * Y1^-5, (Y3 * Y2^-1)^7, Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3^-1 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 26, 61, 25, 60, 32, 67, 35, 70, 21, 56, 10, 45, 3, 38, 7, 42, 15, 50, 27, 62, 24, 59, 13, 48, 18, 53, 30, 65, 34, 69, 20, 55, 9, 44, 17, 52, 29, 64, 23, 58, 12, 47, 5, 40, 8, 43, 16, 51, 28, 63, 33, 68, 19, 54, 31, 66, 22, 57, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 97)(15, 99)(16, 76)(17, 101)(18, 78)(19, 95)(20, 103)(21, 104)(22, 105)(23, 81)(24, 82)(25, 83)(26, 94)(27, 93)(28, 84)(29, 92)(30, 86)(31, 102)(32, 88)(33, 96)(34, 98)(35, 100)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) } Outer automorphisms :: reflexible Dual of E15.586 Graph:: bipartite v = 36 e = 70 f = 6 degree seq :: [ 2^35, 70 ] E15.598 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3 * Y1^-5, (R * Y2 * Y3^-1)^2, Y3^7, (Y3 * Y2^-1)^7, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^3 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 10, 45, 3, 38, 7, 42, 15, 50, 24, 59, 20, 55, 9, 44, 17, 52, 25, 60, 32, 67, 29, 64, 19, 54, 27, 62, 33, 68, 35, 70, 31, 66, 23, 58, 28, 63, 34, 69, 30, 65, 22, 57, 13, 48, 18, 53, 26, 61, 21, 56, 12, 47, 5, 40, 8, 43, 16, 51, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 84)(12, 74)(13, 75)(14, 94)(15, 95)(16, 76)(17, 97)(18, 78)(19, 93)(20, 99)(21, 81)(22, 82)(23, 83)(24, 102)(25, 103)(26, 86)(27, 98)(28, 88)(29, 101)(30, 91)(31, 92)(32, 105)(33, 104)(34, 96)(35, 100)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) } Outer automorphisms :: reflexible Dual of E15.587 Graph:: bipartite v = 36 e = 70 f = 6 degree seq :: [ 2^35, 70 ] E15.599 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 35, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-5, Y3^-1 * Y1^-1 * Y3^-4 * Y1 * Y3^-2, (Y3 * Y2^-1)^7, Y3^21 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 12, 47, 5, 40, 8, 43, 16, 51, 24, 59, 22, 57, 13, 48, 18, 53, 26, 61, 32, 67, 31, 66, 23, 58, 28, 63, 34, 69, 35, 70, 29, 64, 19, 54, 27, 62, 33, 68, 30, 65, 20, 55, 9, 44, 17, 52, 25, 60, 21, 56, 10, 45, 3, 38, 7, 42, 15, 50, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 81)(15, 95)(16, 76)(17, 97)(18, 78)(19, 93)(20, 99)(21, 100)(22, 82)(23, 83)(24, 84)(25, 103)(26, 86)(27, 98)(28, 88)(29, 101)(30, 105)(31, 92)(32, 94)(33, 104)(34, 96)(35, 102)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) } Outer automorphisms :: reflexible Dual of E15.589 Graph:: bipartite v = 36 e = 70 f = 6 degree seq :: [ 2^35, 70 ] E15.600 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 9, 9}) Quotient :: halfedge^2 Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1^-1, Y1 * Y3 * Y2 * Y1^-1 * Y3, Y1^9 ] Map:: R = (1, 38, 2, 42, 6, 51, 15, 59, 23, 66, 30, 58, 22, 50, 14, 41, 5, 37)(3, 44, 8, 54, 18, 60, 24, 68, 32, 70, 34, 63, 27, 55, 19, 46, 10, 39)(4, 47, 11, 52, 16, 61, 25, 69, 33, 71, 35, 64, 28, 56, 20, 48, 12, 40)(7, 53, 17, 62, 26, 67, 31, 72, 36, 65, 29, 57, 21, 49, 13, 45, 9, 43) L = (1, 3)(2, 7)(4, 9)(5, 12)(6, 16)(8, 11)(10, 13)(14, 21)(15, 24)(17, 18)(19, 20)(22, 27)(23, 31)(25, 26)(28, 29)(30, 35)(32, 33)(34, 36)(37, 40)(38, 44)(39, 45)(41, 49)(42, 53)(43, 47)(46, 48)(50, 55)(51, 61)(52, 54)(56, 57)(58, 64)(59, 68)(60, 62)(63, 65)(66, 72)(67, 69)(70, 71) local type(s) :: { ( 18^18 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: v = 4 e = 36 f = 4 degree seq :: [ 18^4 ] E15.601 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 9}) Quotient :: edge^2 Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, Y3^-1 * Y2 * Y3 * Y1, Y3^-1 * Y2 * Y1 * Y3 * Y2, Y3^9 ] Map:: R = (1, 37, 4, 40, 12, 48, 20, 56, 28, 64, 30, 66, 22, 58, 14, 50, 5, 41)(2, 38, 7, 43, 15, 51, 23, 59, 31, 67, 32, 68, 24, 60, 16, 52, 8, 44)(3, 39, 9, 45, 17, 53, 25, 61, 33, 69, 34, 70, 26, 62, 18, 54, 10, 46)(6, 42, 11, 47, 19, 55, 27, 63, 35, 71, 36, 72, 29, 65, 21, 57, 13, 49)(73, 74)(75, 78)(76, 81)(77, 85)(79, 83)(80, 82)(84, 91)(86, 90)(87, 89)(88, 93)(92, 95)(94, 96)(97, 99)(98, 101)(100, 105)(102, 108)(103, 107)(104, 106)(109, 111)(110, 114)(112, 119)(113, 116)(115, 117)(118, 121)(120, 123)(122, 129)(124, 126)(125, 127)(128, 133)(130, 134)(131, 135)(132, 137)(136, 143)(138, 140)(139, 141)(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, 36 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E15.603 Graph:: simple bipartite v = 40 e = 72 f = 4 degree seq :: [ 2^36, 18^4 ] E15.602 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 9, 9}) Quotient :: edge^2 Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = C2 x ((C2 x C2) : C9) (small group id <72, 16>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3, Y2 * Y3 * Y2 * Y3 * Y2^-2 * Y3, Y1^2 * Y3 * Y2 * Y3 * Y1^-1 * Y3, Y2^2 * Y3 * Y1 * Y3 * Y2^-1 * Y3, Y2^9, Y1^9 ] Map:: non-degenerate R = (1, 37, 4, 40)(2, 38, 6, 42)(3, 39, 8, 44)(5, 41, 12, 48)(7, 43, 16, 52)(9, 45, 20, 56)(10, 46, 22, 58)(11, 47, 24, 60)(13, 49, 19, 55)(14, 50, 17, 53)(15, 51, 28, 64)(18, 54, 21, 57)(23, 59, 31, 67)(25, 61, 26, 62)(27, 63, 34, 70)(29, 65, 30, 66)(32, 68, 33, 69)(35, 71, 36, 72)(73, 74, 77, 83, 95, 99, 87, 79, 75)(76, 81, 91, 96, 104, 107, 100, 93, 82)(78, 85, 98, 103, 108, 101, 88, 94, 86)(80, 89, 92, 84, 97, 105, 106, 102, 90)(109, 111, 115, 123, 135, 131, 119, 113, 110)(112, 118, 129, 136, 143, 140, 132, 127, 117)(114, 122, 130, 124, 137, 144, 139, 134, 121)(116, 126, 138, 142, 141, 133, 120, 128, 125) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8^4 ), ( 8^9 ) } Outer automorphisms :: reflexible Dual of E15.604 Graph:: simple bipartite v = 26 e = 72 f = 18 degree seq :: [ 4^18, 9^8 ] E15.603 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 9}) Quotient :: loop^2 Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, Y3^-1 * Y2 * Y3 * Y1, Y3^-1 * Y2 * Y1 * Y3 * Y2, Y3^9 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 20, 56, 92, 128, 28, 64, 100, 136, 30, 66, 102, 138, 22, 58, 94, 130, 14, 50, 86, 122, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 15, 51, 87, 123, 23, 59, 95, 131, 31, 67, 103, 139, 32, 68, 104, 140, 24, 60, 96, 132, 16, 52, 88, 124, 8, 44, 80, 116)(3, 39, 75, 111, 9, 45, 81, 117, 17, 53, 89, 125, 25, 61, 97, 133, 33, 69, 105, 141, 34, 70, 106, 142, 26, 62, 98, 134, 18, 54, 90, 126, 10, 46, 82, 118)(6, 42, 78, 114, 11, 47, 83, 119, 19, 55, 91, 127, 27, 63, 99, 135, 35, 71, 107, 143, 36, 72, 108, 144, 29, 65, 101, 137, 21, 57, 93, 129, 13, 49, 85, 121) L = (1, 38)(2, 37)(3, 42)(4, 45)(5, 49)(6, 39)(7, 47)(8, 46)(9, 40)(10, 44)(11, 43)(12, 55)(13, 41)(14, 54)(15, 53)(16, 57)(17, 51)(18, 50)(19, 48)(20, 59)(21, 52)(22, 60)(23, 56)(24, 58)(25, 63)(26, 65)(27, 61)(28, 69)(29, 62)(30, 72)(31, 71)(32, 70)(33, 64)(34, 68)(35, 67)(36, 66)(73, 111)(74, 114)(75, 109)(76, 119)(77, 116)(78, 110)(79, 117)(80, 113)(81, 115)(82, 121)(83, 112)(84, 123)(85, 118)(86, 129)(87, 120)(88, 126)(89, 127)(90, 124)(91, 125)(92, 133)(93, 122)(94, 134)(95, 135)(96, 137)(97, 128)(98, 130)(99, 131)(100, 143)(101, 132)(102, 140)(103, 141)(104, 138)(105, 139)(106, 144)(107, 136)(108, 142) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E15.601 Transitivity :: VT+ Graph:: v = 4 e = 72 f = 40 degree seq :: [ 36^4 ] E15.604 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 9, 9}) Quotient :: loop^2 Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = C2 x ((C2 x C2) : C9) (small group id <72, 16>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3, Y2 * Y3 * Y2 * Y3 * Y2^-2 * Y3, Y1^2 * Y3 * Y2 * Y3 * Y1^-1 * Y3, Y2^2 * Y3 * Y1 * Y3 * Y2^-1 * Y3, Y2^9, Y1^9 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112)(2, 38, 74, 110, 6, 42, 78, 114)(3, 39, 75, 111, 8, 44, 80, 116)(5, 41, 77, 113, 12, 48, 84, 120)(7, 43, 79, 115, 16, 52, 88, 124)(9, 45, 81, 117, 20, 56, 92, 128)(10, 46, 82, 118, 22, 58, 94, 130)(11, 47, 83, 119, 24, 60, 96, 132)(13, 49, 85, 121, 19, 55, 91, 127)(14, 50, 86, 122, 17, 53, 89, 125)(15, 51, 87, 123, 28, 64, 100, 136)(18, 54, 90, 126, 21, 57, 93, 129)(23, 59, 95, 131, 31, 67, 103, 139)(25, 61, 97, 133, 26, 62, 98, 134)(27, 63, 99, 135, 34, 70, 106, 142)(29, 65, 101, 137, 30, 66, 102, 138)(32, 68, 104, 140, 33, 69, 105, 141)(35, 71, 107, 143, 36, 72, 108, 144) L = (1, 38)(2, 41)(3, 37)(4, 45)(5, 47)(6, 49)(7, 39)(8, 53)(9, 55)(10, 40)(11, 59)(12, 61)(13, 62)(14, 42)(15, 43)(16, 58)(17, 56)(18, 44)(19, 60)(20, 48)(21, 46)(22, 50)(23, 63)(24, 68)(25, 69)(26, 67)(27, 51)(28, 57)(29, 52)(30, 54)(31, 72)(32, 71)(33, 70)(34, 66)(35, 64)(36, 65)(73, 111)(74, 109)(75, 115)(76, 118)(77, 110)(78, 122)(79, 123)(80, 126)(81, 112)(82, 129)(83, 113)(84, 128)(85, 114)(86, 130)(87, 135)(88, 137)(89, 116)(90, 138)(91, 117)(92, 125)(93, 136)(94, 124)(95, 119)(96, 127)(97, 120)(98, 121)(99, 131)(100, 143)(101, 144)(102, 142)(103, 134)(104, 132)(105, 133)(106, 141)(107, 140)(108, 139) local type(s) :: { ( 4, 9, 4, 9, 4, 9, 4, 9 ) } Outer automorphisms :: reflexible Dual of E15.602 Transitivity :: VT+ Graph:: v = 18 e = 72 f = 26 degree seq :: [ 8^18 ] E15.605 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 9, 9}) Quotient :: dipole Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-2, Y2^9, (Y3 * Y2^-1)^9 ] Map:: R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 11, 47)(6, 42, 13, 49)(8, 44, 17, 53)(10, 46, 21, 57)(12, 48, 15, 51)(14, 50, 20, 56)(16, 52, 19, 55)(18, 54, 23, 59)(22, 58, 24, 60)(25, 61, 26, 62)(27, 63, 33, 69)(28, 64, 29, 65)(30, 66, 35, 71)(31, 67, 34, 70)(32, 68, 36, 72)(73, 109, 75, 111, 80, 116, 90, 126, 99, 135, 102, 138, 94, 130, 82, 118, 76, 112)(74, 110, 77, 113, 84, 120, 95, 131, 103, 139, 104, 140, 96, 132, 86, 122, 78, 114)(79, 115, 87, 123, 97, 133, 105, 141, 108, 144, 101, 137, 93, 129, 85, 121, 88, 124)(81, 117, 91, 127, 83, 119, 89, 125, 98, 134, 106, 142, 107, 143, 100, 136, 92, 128) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 selfdual Graph:: bipartite v = 22 e = 72 f = 22 degree seq :: [ 4^18, 18^4 ] E15.606 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y1 * Y3 * Y1^-3, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 46, 10, 53, 17, 60, 24, 67, 31, 63, 27, 69, 33, 66, 30, 70, 34, 64, 28, 57, 21, 48, 12, 54, 18, 49, 13, 41, 5, 37)(3, 45, 9, 52, 16, 44, 8, 40, 4, 47, 11, 56, 20, 62, 26, 58, 22, 65, 29, 71, 35, 72, 36, 68, 32, 61, 25, 55, 19, 59, 23, 51, 15, 43, 7, 39) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 19)(11, 21)(13, 16)(14, 23)(17, 25)(20, 28)(22, 30)(24, 32)(26, 34)(27, 35)(29, 33)(31, 36)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 53)(45, 50)(48, 58)(49, 56)(51, 60)(54, 62)(55, 63)(57, 65)(59, 67)(61, 69)(64, 71)(66, 68)(70, 72) local type(s) :: { ( 12^36 ) } Outer automorphisms :: reflexible Dual of E15.607 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 36 f = 6 degree seq :: [ 36^2 ] E15.607 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1)^2, Y1^6, Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 49, 13, 41, 5, 37)(3, 45, 9, 55, 19, 61, 25, 51, 15, 43, 7, 39)(4, 47, 11, 58, 22, 62, 26, 52, 16, 44, 8, 40)(10, 53, 17, 63, 27, 70, 34, 67, 31, 56, 20, 46)(12, 54, 18, 64, 28, 71, 35, 68, 32, 59, 23, 48)(21, 66, 30, 60, 24, 69, 33, 72, 36, 65, 29, 57) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 25)(16, 28)(17, 29)(20, 30)(22, 32)(24, 31)(26, 35)(27, 36)(33, 34)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 53)(45, 56)(48, 60)(49, 58)(50, 62)(51, 63)(54, 66)(55, 67)(57, 64)(59, 69)(61, 70)(65, 71)(68, 72) local type(s) :: { ( 36^12 ) } Outer automorphisms :: reflexible Dual of E15.606 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 36 f = 2 degree seq :: [ 12^6 ] E15.608 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^6, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y1 * Y3^-1 * Y2)^18 ] Map:: R = (1, 37, 4, 40, 12, 48, 24, 60, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 30, 66, 18, 54, 8, 44)(3, 39, 10, 46, 22, 58, 33, 69, 23, 59, 11, 47)(6, 42, 15, 51, 28, 64, 36, 72, 29, 65, 16, 52)(9, 45, 20, 56, 25, 61, 34, 70, 32, 68, 21, 57)(14, 50, 26, 62, 19, 55, 31, 67, 35, 71, 27, 63)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 93)(83, 92)(84, 90)(85, 89)(87, 99)(88, 98)(91, 101)(94, 104)(95, 97)(96, 102)(100, 107)(103, 108)(105, 106)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 127)(120, 131)(121, 130)(122, 133)(125, 137)(126, 136)(128, 134)(129, 139)(132, 141)(135, 142)(138, 144)(140, 143) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 72, 72 ), ( 72^12 ) } Outer automorphisms :: reflexible Dual of E15.611 Graph:: simple bipartite v = 42 e = 72 f = 2 degree seq :: [ 2^36, 12^6 ] E15.609 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y2, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: R = (1, 37, 4, 40, 12, 48, 21, 57, 9, 45, 20, 56, 30, 66, 35, 71, 27, 63, 33, 69, 23, 59, 32, 68, 26, 62, 16, 52, 6, 42, 15, 51, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 25, 61, 14, 50, 24, 60, 34, 70, 36, 72, 31, 67, 29, 65, 19, 55, 28, 64, 22, 58, 11, 47, 3, 39, 10, 46, 18, 54, 8, 44)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 93)(83, 92)(84, 90)(85, 89)(87, 97)(88, 96)(91, 99)(94, 102)(95, 103)(98, 106)(100, 107)(101, 105)(104, 108)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 127)(120, 130)(121, 126)(122, 131)(125, 134)(128, 137)(129, 136)(132, 141)(133, 140)(135, 142)(138, 139)(143, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24, 24 ), ( 24^36 ) } Outer automorphisms :: reflexible Dual of E15.610 Graph:: simple bipartite v = 38 e = 72 f = 6 degree seq :: [ 2^36, 36^2 ] E15.610 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^6, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y1 * Y3^-1 * Y2)^18 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 24, 60, 96, 132, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 30, 66, 102, 138, 18, 54, 90, 126, 8, 44, 80, 116)(3, 39, 75, 111, 10, 46, 82, 118, 22, 58, 94, 130, 33, 69, 105, 141, 23, 59, 95, 131, 11, 47, 83, 119)(6, 42, 78, 114, 15, 51, 87, 123, 28, 64, 100, 136, 36, 72, 108, 144, 29, 65, 101, 137, 16, 52, 88, 124)(9, 45, 81, 117, 20, 56, 92, 128, 25, 61, 97, 133, 34, 70, 106, 142, 32, 68, 104, 140, 21, 57, 93, 129)(14, 50, 86, 122, 26, 62, 98, 134, 19, 55, 91, 127, 31, 67, 103, 139, 35, 71, 107, 143, 27, 63, 99, 135) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 57)(11, 56)(12, 54)(13, 53)(14, 42)(15, 63)(16, 62)(17, 49)(18, 48)(19, 65)(20, 47)(21, 46)(22, 68)(23, 61)(24, 66)(25, 59)(26, 52)(27, 51)(28, 71)(29, 55)(30, 60)(31, 72)(32, 58)(33, 70)(34, 69)(35, 64)(36, 67)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 127)(82, 113)(83, 112)(84, 131)(85, 130)(86, 133)(87, 116)(88, 115)(89, 137)(90, 136)(91, 117)(92, 134)(93, 139)(94, 121)(95, 120)(96, 141)(97, 122)(98, 128)(99, 142)(100, 126)(101, 125)(102, 144)(103, 129)(104, 143)(105, 132)(106, 135)(107, 140)(108, 138) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E15.609 Transitivity :: VT+ Graph:: bipartite v = 6 e = 72 f = 38 degree seq :: [ 24^6 ] E15.611 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y2, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 21, 57, 93, 129, 9, 45, 81, 117, 20, 56, 92, 128, 30, 66, 102, 138, 35, 71, 107, 143, 27, 63, 99, 135, 33, 69, 105, 141, 23, 59, 95, 131, 32, 68, 104, 140, 26, 62, 98, 134, 16, 52, 88, 124, 6, 42, 78, 114, 15, 51, 87, 123, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 25, 61, 97, 133, 14, 50, 86, 122, 24, 60, 96, 132, 34, 70, 106, 142, 36, 72, 108, 144, 31, 67, 103, 139, 29, 65, 101, 137, 19, 55, 91, 127, 28, 64, 100, 136, 22, 58, 94, 130, 11, 47, 83, 119, 3, 39, 75, 111, 10, 46, 82, 118, 18, 54, 90, 126, 8, 44, 80, 116) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 57)(11, 56)(12, 54)(13, 53)(14, 42)(15, 61)(16, 60)(17, 49)(18, 48)(19, 63)(20, 47)(21, 46)(22, 66)(23, 67)(24, 52)(25, 51)(26, 70)(27, 55)(28, 71)(29, 69)(30, 58)(31, 59)(32, 72)(33, 65)(34, 62)(35, 64)(36, 68)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 127)(82, 113)(83, 112)(84, 130)(85, 126)(86, 131)(87, 116)(88, 115)(89, 134)(90, 121)(91, 117)(92, 137)(93, 136)(94, 120)(95, 122)(96, 141)(97, 140)(98, 125)(99, 142)(100, 129)(101, 128)(102, 139)(103, 138)(104, 133)(105, 132)(106, 135)(107, 144)(108, 143) 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 ) } Outer automorphisms :: reflexible Dual of E15.608 Transitivity :: VT+ Graph:: bipartite v = 2 e = 72 f = 42 degree seq :: [ 72^2 ] E15.612 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2), (R * Y2)^2, (Y2^-1 * Y1)^2, Y3^3 * Y2^2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 24, 60)(12, 48, 25, 61)(13, 49, 23, 59)(14, 50, 26, 62)(15, 51, 21, 57)(16, 52, 19, 55)(17, 53, 20, 56)(18, 54, 22, 58)(27, 63, 32, 68)(28, 64, 36, 72)(29, 65, 35, 71)(30, 66, 34, 70)(31, 67, 33, 69)(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) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E15.615 Graph:: simple bipartite v = 24 e = 72 f = 20 degree seq :: [ 4^18, 12^6 ] E15.613 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y3, Y2), (R * Y3)^2, (Y2^-1 * Y1)^2, Y3^-3 * Y2^2, Y2^6, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 24, 60)(12, 48, 25, 61)(13, 49, 23, 59)(14, 50, 26, 62)(15, 51, 21, 57)(16, 52, 19, 55)(17, 53, 20, 56)(18, 54, 22, 58)(27, 63, 32, 68)(28, 64, 35, 71)(29, 65, 36, 72)(30, 66, 33, 69)(31, 67, 34, 70)(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) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E15.614 Graph:: simple bipartite v = 24 e = 72 f = 20 degree seq :: [ 4^18, 12^6 ] E15.614 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^2 * Y3^-1, (R * Y1)^2, (Y1 * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^9, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 4, 40, 8, 44, 12, 48, 16, 52, 20, 56, 24, 60, 28, 64, 32, 68, 30, 66, 29, 65, 22, 58, 21, 57, 14, 50, 13, 49, 6, 42, 5, 41)(3, 39, 9, 45, 10, 46, 17, 53, 18, 54, 25, 61, 26, 62, 33, 69, 34, 70, 36, 72, 35, 71, 31, 67, 27, 63, 23, 59, 19, 55, 15, 51, 11, 47, 7, 43)(73, 109, 75, 111)(74, 110, 79, 115)(76, 112, 83, 119)(77, 113, 81, 117)(78, 114, 82, 118)(80, 116, 87, 123)(84, 120, 91, 127)(85, 121, 89, 125)(86, 122, 90, 126)(88, 124, 95, 131)(92, 128, 99, 135)(93, 129, 97, 133)(94, 130, 98, 134)(96, 132, 103, 139)(100, 136, 107, 143)(101, 137, 105, 141)(102, 138, 106, 142)(104, 140, 108, 144) L = (1, 76)(2, 80)(3, 82)(4, 84)(5, 74)(6, 73)(7, 81)(8, 88)(9, 89)(10, 90)(11, 75)(12, 92)(13, 77)(14, 78)(15, 79)(16, 96)(17, 97)(18, 98)(19, 83)(20, 100)(21, 85)(22, 86)(23, 87)(24, 104)(25, 105)(26, 106)(27, 91)(28, 102)(29, 93)(30, 94)(31, 95)(32, 101)(33, 108)(34, 107)(35, 99)(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, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.613 Graph:: bipartite v = 20 e = 72 f = 24 degree seq :: [ 4^18, 36^2 ] E15.615 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y1 * Y3 * Y1^3, (R * Y2 * Y3^-1)^2, Y1 * Y3^-3 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 6, 42, 10, 46, 20, 56, 31, 67, 18, 54, 24, 60, 14, 50, 23, 59, 30, 66, 15, 51, 4, 40, 9, 45, 16, 52, 5, 41)(3, 39, 11, 47, 25, 61, 22, 58, 13, 49, 27, 63, 35, 71, 34, 70, 29, 65, 33, 69, 28, 64, 36, 72, 32, 68, 21, 57, 12, 48, 26, 62, 19, 55, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 91, 127)(81, 117, 94, 130)(82, 118, 93, 129)(86, 122, 101, 137)(87, 123, 99, 135)(88, 124, 97, 133)(89, 125, 98, 134)(90, 126, 100, 136)(92, 128, 104, 140)(95, 131, 106, 142)(96, 132, 105, 141)(102, 138, 107, 143)(103, 139, 108, 144) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 88)(8, 93)(9, 95)(10, 74)(11, 98)(12, 100)(13, 75)(14, 92)(15, 96)(16, 102)(17, 77)(18, 78)(19, 104)(20, 79)(21, 105)(22, 80)(23, 103)(24, 82)(25, 91)(26, 108)(27, 83)(28, 107)(29, 85)(30, 90)(31, 89)(32, 101)(33, 99)(34, 94)(35, 97)(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, 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 E15.612 Graph:: bipartite v = 20 e = 72 f = 24 degree seq :: [ 4^18, 36^2 ] E15.616 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 12, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^3, T1^9, T1^-27 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 35, 31, 22, 25, 13, 5)(2, 7, 17, 29, 26, 34, 32, 23, 11, 21, 18, 8)(4, 10, 20, 16, 6, 15, 28, 36, 30, 33, 24, 12)(37, 38, 42, 50, 62, 66, 58, 47, 40)(39, 43, 51, 63, 70, 69, 61, 57, 46)(41, 44, 52, 55, 65, 72, 67, 59, 48)(45, 53, 64, 71, 68, 60, 49, 54, 56) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^9 ), ( 72^12 ) } Outer automorphisms :: reflexible Dual of E15.625 Transitivity :: ET+ Graph:: bipartite v = 7 e = 36 f = 1 degree seq :: [ 9^4, 12^3 ] E15.617 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 12, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^3, T1^9 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 32, 35, 27, 14, 25, 13, 5)(2, 7, 17, 23, 11, 21, 31, 34, 26, 29, 18, 8)(4, 10, 20, 30, 33, 36, 28, 16, 6, 15, 24, 12)(37, 38, 42, 50, 62, 69, 58, 47, 40)(39, 43, 51, 61, 65, 72, 68, 57, 46)(41, 44, 52, 63, 70, 66, 55, 59, 48)(45, 53, 60, 49, 54, 64, 71, 67, 56) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^9 ), ( 72^12 ) } Outer automorphisms :: reflexible Dual of E15.624 Transitivity :: ET+ Graph:: bipartite v = 7 e = 36 f = 1 degree seq :: [ 9^4, 12^3 ] E15.618 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 12, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^12, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 3, 8, 2, 7, 14, 6, 13, 20, 12, 19, 26, 18, 25, 32, 24, 31, 36, 30, 35, 34, 28, 33, 29, 22, 27, 23, 16, 21, 17, 10, 15, 11, 4, 9, 5)(37, 38, 42, 48, 54, 60, 66, 64, 58, 52, 46, 40)(39, 43, 49, 55, 61, 67, 71, 69, 63, 57, 51, 45)(41, 44, 50, 56, 62, 68, 72, 70, 65, 59, 53, 47) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^12 ), ( 18^36 ) } Outer automorphisms :: reflexible Dual of E15.627 Transitivity :: ET+ Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.619 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 12, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^2 * T1^-4, T2 * T1^-1 * T2^2 * T1^-4, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-4, T2^2 * T1^7 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 23, 11, 21, 28, 14, 27, 36, 32, 18, 8, 2, 7, 17, 31, 24, 12, 4, 10, 20, 26, 35, 34, 22, 30, 16, 6, 15, 29, 25, 13, 5)(37, 38, 42, 50, 62, 55, 67, 61, 68, 58, 47, 40)(39, 43, 51, 63, 71, 69, 60, 49, 54, 66, 57, 46)(41, 44, 52, 64, 56, 45, 53, 65, 72, 70, 59, 48) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^12 ), ( 18^36 ) } Outer automorphisms :: reflexible Dual of E15.626 Transitivity :: ET+ Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 12^3, 36 ] E15.620 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 12, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-4 * T2^2, T2^9, T2^9, 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 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 30, 22, 13, 5)(2, 7, 17, 25, 33, 34, 26, 18, 8)(4, 10, 14, 23, 31, 36, 29, 21, 12)(6, 15, 24, 32, 35, 28, 20, 11, 16)(37, 38, 42, 50, 45, 53, 60, 67, 63, 69, 71, 65, 58, 62, 56, 48, 41, 44, 52, 46, 39, 43, 51, 59, 55, 61, 68, 72, 66, 70, 64, 57, 49, 54, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 24^9 ), ( 24^36 ) } Outer automorphisms :: reflexible Dual of E15.622 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 9^4, 36 ] E15.621 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 12, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^4, T2^9, T1 * T2^-3 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 29, 21, 13, 5)(2, 7, 15, 23, 31, 32, 24, 16, 8)(4, 10, 18, 26, 33, 35, 28, 20, 12)(6, 11, 19, 27, 34, 36, 30, 22, 14)(37, 38, 42, 48, 41, 44, 50, 56, 49, 52, 58, 64, 57, 60, 66, 71, 65, 68, 72, 69, 61, 67, 70, 62, 53, 59, 63, 54, 45, 51, 55, 46, 39, 43, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 24^9 ), ( 24^36 ) } Outer automorphisms :: reflexible Dual of E15.623 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 3 degree seq :: [ 9^4, 36 ] E15.622 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 12, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^3, T1^9, T1^-27 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 14, 50, 27, 63, 35, 71, 31, 67, 22, 58, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 29, 65, 26, 62, 34, 70, 32, 68, 23, 59, 11, 47, 21, 57, 18, 54, 8, 44)(4, 40, 10, 46, 20, 56, 16, 52, 6, 42, 15, 51, 28, 64, 36, 72, 30, 66, 33, 69, 24, 60, 12, 48) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 63)(16, 55)(17, 64)(18, 56)(19, 65)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 57)(26, 66)(27, 70)(28, 71)(29, 72)(30, 58)(31, 59)(32, 60)(33, 61)(34, 69)(35, 68)(36, 67) local type(s) :: { ( 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36 ) } Outer automorphisms :: reflexible Dual of E15.620 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 36 f = 5 degree seq :: [ 24^3 ] E15.623 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 12, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^3, T1^9 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 22, 58, 32, 68, 35, 71, 27, 63, 14, 50, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 23, 59, 11, 47, 21, 57, 31, 67, 34, 70, 26, 62, 29, 65, 18, 54, 8, 44)(4, 40, 10, 46, 20, 56, 30, 66, 33, 69, 36, 72, 28, 64, 16, 52, 6, 42, 15, 51, 24, 60, 12, 48) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 61)(16, 63)(17, 60)(18, 64)(19, 59)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 65)(26, 69)(27, 70)(28, 71)(29, 72)(30, 55)(31, 56)(32, 57)(33, 58)(34, 66)(35, 67)(36, 68) local type(s) :: { ( 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36, 9, 36 ) } Outer automorphisms :: reflexible Dual of E15.621 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 36 f = 5 degree seq :: [ 24^3 ] E15.624 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 12, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^12, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 37, 3, 39, 8, 44, 2, 38, 7, 43, 14, 50, 6, 42, 13, 49, 20, 56, 12, 48, 19, 55, 26, 62, 18, 54, 25, 61, 32, 68, 24, 60, 31, 67, 36, 72, 30, 66, 35, 71, 34, 70, 28, 64, 33, 69, 29, 65, 22, 58, 27, 63, 23, 59, 16, 52, 21, 57, 17, 53, 10, 46, 15, 51, 11, 47, 4, 40, 9, 45, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 48)(7, 49)(8, 50)(9, 39)(10, 40)(11, 41)(12, 54)(13, 55)(14, 56)(15, 45)(16, 46)(17, 47)(18, 60)(19, 61)(20, 62)(21, 51)(22, 52)(23, 53)(24, 66)(25, 67)(26, 68)(27, 57)(28, 58)(29, 59)(30, 64)(31, 71)(32, 72)(33, 63)(34, 65)(35, 69)(36, 70) local type(s) :: { ( 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12 ) } Outer automorphisms :: reflexible Dual of E15.617 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 7 degree seq :: [ 72 ] E15.625 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 12, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^2 * T1^-4, T2 * T1^-1 * T2^2 * T1^-4, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-4, T2^2 * T1^7 * T2 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 33, 69, 23, 59, 11, 47, 21, 57, 28, 64, 14, 50, 27, 63, 36, 72, 32, 68, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 31, 67, 24, 60, 12, 48, 4, 40, 10, 46, 20, 56, 26, 62, 35, 71, 34, 70, 22, 58, 30, 66, 16, 52, 6, 42, 15, 51, 29, 65, 25, 61, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 68)(26, 55)(27, 71)(28, 56)(29, 72)(30, 57)(31, 61)(32, 58)(33, 60)(34, 59)(35, 69)(36, 70) local type(s) :: { ( 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12, 9, 12 ) } Outer automorphisms :: reflexible Dual of E15.616 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 7 degree seq :: [ 72 ] E15.626 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 12, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-4 * T2^2, T2^9, T2^9, 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 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 27, 63, 30, 66, 22, 58, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 25, 61, 33, 69, 34, 70, 26, 62, 18, 54, 8, 44)(4, 40, 10, 46, 14, 50, 23, 59, 31, 67, 36, 72, 29, 65, 21, 57, 12, 48)(6, 42, 15, 51, 24, 60, 32, 68, 35, 71, 28, 64, 20, 56, 11, 47, 16, 52) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 45)(15, 59)(16, 46)(17, 60)(18, 47)(19, 61)(20, 48)(21, 49)(22, 62)(23, 55)(24, 67)(25, 68)(26, 56)(27, 69)(28, 57)(29, 58)(30, 70)(31, 63)(32, 72)(33, 71)(34, 64)(35, 65)(36, 66) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E15.619 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 18^4 ] E15.627 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 12, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^4, T2^9, T1 * T2^-3 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 17, 53, 25, 61, 29, 65, 21, 57, 13, 49, 5, 41)(2, 38, 7, 43, 15, 51, 23, 59, 31, 67, 32, 68, 24, 60, 16, 52, 8, 44)(4, 40, 10, 46, 18, 54, 26, 62, 33, 69, 35, 71, 28, 64, 20, 56, 12, 48)(6, 42, 11, 47, 19, 55, 27, 63, 34, 70, 36, 72, 30, 66, 22, 58, 14, 50) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 48)(7, 47)(8, 50)(9, 51)(10, 39)(11, 40)(12, 41)(13, 52)(14, 56)(15, 55)(16, 58)(17, 59)(18, 45)(19, 46)(20, 49)(21, 60)(22, 64)(23, 63)(24, 66)(25, 67)(26, 53)(27, 54)(28, 57)(29, 68)(30, 71)(31, 70)(32, 72)(33, 61)(34, 62)(35, 65)(36, 69) local type(s) :: { ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) } Outer automorphisms :: reflexible Dual of E15.618 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 36 f = 4 degree seq :: [ 18^4 ] E15.628 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y2, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2^2 * Y1 * Y2^2 * Y1 * Y3^-1, Y2^2 * Y1^2 * Y2 * Y3^-1 * Y2, Y1^9, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 33, 69, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 29, 65, 36, 72, 32, 68, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 27, 63, 34, 70, 30, 66, 19, 55, 23, 59, 12, 48)(9, 45, 17, 53, 24, 60, 13, 49, 18, 54, 28, 64, 35, 71, 31, 67, 20, 56)(73, 109, 75, 111, 81, 117, 91, 127, 94, 130, 104, 140, 107, 143, 99, 135, 86, 122, 97, 133, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 95, 131, 83, 119, 93, 129, 103, 139, 106, 142, 98, 134, 101, 137, 90, 126, 80, 116)(76, 112, 82, 118, 92, 128, 102, 138, 105, 141, 108, 144, 100, 136, 88, 124, 78, 114, 87, 123, 96, 132, 84, 120) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 94)(12, 95)(13, 96)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 102)(20, 103)(21, 104)(22, 105)(23, 91)(24, 89)(25, 87)(26, 86)(27, 88)(28, 90)(29, 97)(30, 106)(31, 107)(32, 108)(33, 98)(34, 99)(35, 100)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E15.635 Graph:: bipartite v = 7 e = 72 f = 37 degree seq :: [ 18^4, 24^3 ] E15.629 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1, Y1^9, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 30, 66, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 34, 70, 33, 69, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 19, 55, 29, 65, 36, 72, 31, 67, 23, 59, 12, 48)(9, 45, 17, 53, 28, 64, 35, 71, 32, 68, 24, 60, 13, 49, 18, 54, 20, 56)(73, 109, 75, 111, 81, 117, 91, 127, 86, 122, 99, 135, 107, 143, 103, 139, 94, 130, 97, 133, 85, 121, 77, 113)(74, 110, 79, 115, 89, 125, 101, 137, 98, 134, 106, 142, 104, 140, 95, 131, 83, 119, 93, 129, 90, 126, 80, 116)(76, 112, 82, 118, 92, 128, 88, 124, 78, 114, 87, 123, 100, 136, 108, 144, 102, 138, 105, 141, 96, 132, 84, 120) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 94)(12, 95)(13, 96)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 88)(20, 90)(21, 97)(22, 102)(23, 103)(24, 104)(25, 105)(26, 86)(27, 87)(28, 89)(29, 91)(30, 98)(31, 108)(32, 107)(33, 106)(34, 99)(35, 100)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E15.634 Graph:: bipartite v = 7 e = 72 f = 37 degree seq :: [ 18^4, 24^3 ] E15.630 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^12, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 28, 64, 22, 58, 16, 52, 10, 46, 4, 40)(3, 39, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67, 35, 71, 33, 69, 27, 63, 21, 57, 15, 51, 9, 45)(5, 41, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 36, 72, 34, 70, 29, 65, 23, 59, 17, 53, 11, 47)(73, 109, 75, 111, 80, 116, 74, 110, 79, 115, 86, 122, 78, 114, 85, 121, 92, 128, 84, 120, 91, 127, 98, 134, 90, 126, 97, 133, 104, 140, 96, 132, 103, 139, 108, 144, 102, 138, 107, 143, 106, 142, 100, 136, 105, 141, 101, 137, 94, 130, 99, 135, 95, 131, 88, 124, 93, 129, 89, 125, 82, 118, 87, 123, 83, 119, 76, 112, 81, 117, 77, 113) L = (1, 75)(2, 79)(3, 80)(4, 81)(5, 73)(6, 85)(7, 86)(8, 74)(9, 77)(10, 87)(11, 76)(12, 91)(13, 92)(14, 78)(15, 83)(16, 93)(17, 82)(18, 97)(19, 98)(20, 84)(21, 89)(22, 99)(23, 88)(24, 103)(25, 104)(26, 90)(27, 95)(28, 105)(29, 94)(30, 107)(31, 108)(32, 96)(33, 101)(34, 100)(35, 106)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E15.633 Graph:: bipartite v = 4 e = 72 f = 40 degree seq :: [ 24^3, 72 ] E15.631 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^-1 * Y1^-1 * Y2^-5, Y2^2 * Y1^-1 * Y2 * Y1^-4, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 19, 55, 31, 67, 25, 61, 32, 68, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 35, 71, 33, 69, 24, 60, 13, 49, 18, 54, 30, 66, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 28, 64, 20, 56, 9, 45, 17, 53, 29, 65, 36, 72, 34, 70, 23, 59, 12, 48)(73, 109, 75, 111, 81, 117, 91, 127, 105, 141, 95, 131, 83, 119, 93, 129, 100, 136, 86, 122, 99, 135, 108, 144, 104, 140, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 103, 139, 96, 132, 84, 120, 76, 112, 82, 118, 92, 128, 98, 134, 107, 143, 106, 142, 94, 130, 102, 138, 88, 124, 78, 114, 87, 123, 101, 137, 97, 133, 85, 121, 77, 113) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 98)(21, 100)(22, 102)(23, 83)(24, 84)(25, 85)(26, 107)(27, 108)(28, 86)(29, 97)(30, 88)(31, 96)(32, 90)(33, 95)(34, 94)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E15.632 Graph:: bipartite v = 4 e = 72 f = 40 degree seq :: [ 24^3, 72 ] E15.632 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y2^-2 * Y3^-4, Y2^-9, Y2^9, (Y2^-1 * Y3)^12, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 86, 122, 95, 131, 102, 138, 94, 130, 83, 119, 76, 112)(75, 111, 79, 115, 87, 123, 96, 132, 103, 139, 108, 144, 101, 137, 93, 129, 82, 118)(77, 113, 80, 116, 88, 124, 97, 133, 104, 140, 106, 142, 99, 135, 91, 127, 84, 120)(81, 117, 89, 125, 85, 121, 90, 126, 98, 134, 105, 141, 107, 143, 100, 136, 92, 128) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 96)(15, 85)(16, 78)(17, 84)(18, 80)(19, 83)(20, 99)(21, 100)(22, 101)(23, 103)(24, 90)(25, 86)(26, 88)(27, 94)(28, 106)(29, 107)(30, 108)(31, 98)(32, 95)(33, 97)(34, 102)(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) :: { ( 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) } Outer automorphisms :: reflexible Dual of E15.631 Graph:: simple bipartite v = 40 e = 72 f = 4 degree seq :: [ 2^36, 18^4 ] E15.633 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3^-4 * Y2, Y2^9, Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-3 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 86, 122, 94, 130, 99, 135, 91, 127, 83, 119, 76, 112)(75, 111, 79, 115, 87, 123, 95, 131, 102, 138, 105, 141, 98, 134, 90, 126, 82, 118)(77, 113, 80, 116, 88, 124, 96, 132, 103, 139, 106, 142, 100, 136, 92, 128, 84, 120)(81, 117, 89, 125, 97, 133, 104, 140, 108, 144, 107, 143, 101, 137, 93, 129, 85, 121) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 80)(10, 85)(11, 90)(12, 76)(13, 77)(14, 95)(15, 97)(16, 78)(17, 88)(18, 93)(19, 98)(20, 83)(21, 84)(22, 102)(23, 104)(24, 86)(25, 96)(26, 101)(27, 105)(28, 91)(29, 92)(30, 108)(31, 94)(32, 103)(33, 107)(34, 99)(35, 100)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) } Outer automorphisms :: reflexible Dual of E15.630 Graph:: simple bipartite v = 40 e = 72 f = 4 degree seq :: [ 2^36, 18^4 ] E15.634 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y1^-4 * Y3^2, (R * Y2 * Y3^-1)^2, Y3^18, (Y3 * Y2^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 9, 45, 17, 53, 24, 60, 31, 67, 27, 63, 33, 69, 35, 71, 29, 65, 22, 58, 26, 62, 20, 56, 12, 48, 5, 41, 8, 44, 16, 52, 10, 46, 3, 39, 7, 43, 15, 51, 23, 59, 19, 55, 25, 61, 32, 68, 36, 72, 30, 66, 34, 70, 28, 64, 21, 57, 13, 49, 18, 54, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 86)(11, 88)(12, 76)(13, 77)(14, 95)(15, 96)(16, 78)(17, 97)(18, 80)(19, 99)(20, 83)(21, 84)(22, 85)(23, 103)(24, 104)(25, 105)(26, 90)(27, 102)(28, 92)(29, 93)(30, 94)(31, 108)(32, 107)(33, 106)(34, 98)(35, 100)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) } Outer automorphisms :: reflexible Dual of E15.629 Graph:: bipartite v = 37 e = 72 f = 7 degree seq :: [ 2^36, 72 ] E15.635 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^9, (Y1 * Y3^-2)^4, (Y3 * Y2^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 12, 48, 5, 41, 8, 44, 14, 50, 20, 56, 13, 49, 16, 52, 22, 58, 28, 64, 21, 57, 24, 60, 30, 66, 35, 71, 29, 65, 32, 68, 36, 72, 33, 69, 25, 61, 31, 67, 34, 70, 26, 62, 17, 53, 23, 59, 27, 63, 18, 54, 9, 45, 15, 51, 19, 55, 10, 46, 3, 39, 7, 43, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 83)(7, 87)(8, 74)(9, 89)(10, 90)(11, 91)(12, 76)(13, 77)(14, 78)(15, 95)(16, 80)(17, 97)(18, 98)(19, 99)(20, 84)(21, 85)(22, 86)(23, 103)(24, 88)(25, 101)(26, 105)(27, 106)(28, 92)(29, 93)(30, 94)(31, 104)(32, 96)(33, 107)(34, 108)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) } Outer automorphisms :: reflexible Dual of E15.628 Graph:: bipartite v = 37 e = 72 f = 7 degree seq :: [ 2^36, 72 ] E15.636 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y2^-4 * Y1^2, Y1^9, Y3^18, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 23, 59, 28, 64, 20, 56, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 24, 60, 31, 67, 34, 70, 27, 63, 19, 55, 10, 46)(5, 41, 8, 44, 16, 52, 25, 61, 32, 68, 35, 71, 29, 65, 21, 57, 12, 48)(9, 45, 17, 53, 26, 62, 33, 69, 36, 72, 30, 66, 22, 58, 13, 49, 18, 54)(73, 109, 75, 111, 81, 117, 88, 124, 78, 114, 87, 123, 98, 134, 104, 140, 95, 131, 103, 139, 108, 144, 101, 137, 92, 128, 99, 135, 94, 130, 84, 120, 76, 112, 82, 118, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 97, 133, 86, 122, 96, 132, 105, 141, 107, 143, 100, 136, 106, 142, 102, 138, 93, 129, 83, 119, 91, 127, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 99)(20, 100)(21, 101)(22, 102)(23, 86)(24, 87)(25, 88)(26, 89)(27, 106)(28, 95)(29, 107)(30, 108)(31, 96)(32, 97)(33, 98)(34, 103)(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) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E15.639 Graph:: bipartite v = 5 e = 72 f = 39 degree seq :: [ 18^4, 72 ] E15.637 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, Y2^2 * Y3^-1 * Y2^2, Y1^9, (Y2 * Y3^2)^4 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 22, 58, 28, 64, 20, 56, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 23, 59, 30, 66, 34, 70, 27, 63, 19, 55, 10, 46)(5, 41, 8, 44, 16, 52, 24, 60, 31, 67, 35, 71, 29, 65, 21, 57, 12, 48)(9, 45, 13, 49, 17, 53, 25, 61, 32, 68, 36, 72, 33, 69, 26, 62, 18, 54)(73, 109, 75, 111, 81, 117, 84, 120, 76, 112, 82, 118, 90, 126, 93, 129, 83, 119, 91, 127, 98, 134, 101, 137, 92, 128, 99, 135, 105, 141, 107, 143, 100, 136, 106, 142, 108, 144, 103, 139, 94, 130, 102, 138, 104, 140, 96, 132, 86, 122, 95, 131, 97, 133, 88, 124, 78, 114, 87, 123, 89, 125, 80, 116, 74, 110, 79, 115, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 90)(10, 91)(11, 92)(12, 93)(13, 81)(14, 78)(15, 79)(16, 80)(17, 85)(18, 98)(19, 99)(20, 100)(21, 101)(22, 86)(23, 87)(24, 88)(25, 89)(26, 105)(27, 106)(28, 94)(29, 107)(30, 95)(31, 96)(32, 97)(33, 108)(34, 102)(35, 103)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E15.638 Graph:: bipartite v = 5 e = 72 f = 39 degree seq :: [ 18^4, 72 ] E15.638 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-1 * Y3^3, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^12, (Y1^-1 * Y3^-1)^9, (Y3 * Y2^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 28, 64, 22, 58, 16, 52, 10, 46, 4, 40)(3, 39, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67, 35, 71, 33, 69, 27, 63, 21, 57, 15, 51, 9, 45)(5, 41, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 36, 72, 34, 70, 29, 65, 23, 59, 17, 53, 11, 47)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 80)(4, 81)(5, 73)(6, 85)(7, 86)(8, 74)(9, 77)(10, 87)(11, 76)(12, 91)(13, 92)(14, 78)(15, 83)(16, 93)(17, 82)(18, 97)(19, 98)(20, 84)(21, 89)(22, 99)(23, 88)(24, 103)(25, 104)(26, 90)(27, 95)(28, 105)(29, 94)(30, 107)(31, 108)(32, 96)(33, 101)(34, 100)(35, 106)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) } Outer automorphisms :: reflexible Dual of E15.637 Graph:: simple bipartite v = 39 e = 72 f = 5 degree seq :: [ 2^36, 24^3 ] E15.639 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 12, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^2 * Y1^-4 * Y3, Y3^-2 * Y1^-1 * Y3^-4 * Y1^-1, Y3^2 * Y1^7 * Y3, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, (Y3 * Y2^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 19, 55, 31, 67, 25, 61, 32, 68, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 35, 71, 33, 69, 24, 60, 13, 49, 18, 54, 30, 66, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 28, 64, 20, 56, 9, 45, 17, 53, 29, 65, 36, 72, 34, 70, 23, 59, 12, 48)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 98)(21, 100)(22, 102)(23, 83)(24, 84)(25, 85)(26, 107)(27, 108)(28, 86)(29, 97)(30, 88)(31, 96)(32, 90)(33, 95)(34, 94)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) } Outer automorphisms :: reflexible Dual of E15.636 Graph:: simple bipartite v = 39 e = 72 f = 5 degree seq :: [ 2^36, 24^3 ] E15.640 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^6 * T1^-1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 29, 28, 16, 6, 15, 27, 35, 34, 26, 14, 25, 33, 36, 31, 22, 11, 21, 30, 32, 23, 12, 4, 10, 20, 24, 13, 5)(37, 38, 42, 50, 47, 40)(39, 43, 51, 61, 57, 46)(41, 44, 52, 62, 58, 48)(45, 53, 63, 69, 66, 56)(49, 54, 64, 70, 67, 59)(55, 65, 71, 72, 68, 60) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^6 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E15.644 Transitivity :: ET+ Graph:: bipartite v = 7 e = 36 f = 1 degree seq :: [ 6^6, 36 ] E15.641 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^6 * T1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 3, 9, 19, 23, 12, 4, 10, 20, 30, 32, 22, 11, 21, 31, 36, 34, 26, 14, 25, 33, 35, 28, 16, 6, 15, 27, 29, 18, 8, 2, 7, 17, 24, 13, 5)(37, 38, 42, 50, 47, 40)(39, 43, 51, 61, 57, 46)(41, 44, 52, 62, 58, 48)(45, 53, 63, 69, 67, 56)(49, 54, 64, 70, 68, 59)(55, 60, 65, 71, 72, 66) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^6 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E15.643 Transitivity :: ET+ Graph:: bipartite v = 7 e = 36 f = 1 degree seq :: [ 6^6, 36 ] E15.642 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-4, T2 * T1 * T2^6, (T1^-1 * T2^-1)^6 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 22, 12, 4, 10, 20, 30, 35, 31, 21, 11, 14, 24, 32, 36, 34, 26, 16, 6, 15, 25, 33, 28, 18, 8, 2, 7, 17, 27, 23, 13, 5)(37, 38, 42, 50, 46, 39, 43, 51, 60, 56, 45, 53, 61, 68, 66, 55, 63, 69, 72, 71, 65, 59, 64, 70, 67, 58, 49, 54, 62, 57, 48, 41, 44, 52, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12^36 ) } Outer automorphisms :: reflexible Dual of E15.645 Transitivity :: ET+ Graph:: bipartite v = 2 e = 36 f = 6 degree seq :: [ 36^2 ] E15.643 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^6 * T1^-1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 29, 65, 28, 64, 16, 52, 6, 42, 15, 51, 27, 63, 35, 71, 34, 70, 26, 62, 14, 50, 25, 61, 33, 69, 36, 72, 31, 67, 22, 58, 11, 47, 21, 57, 30, 66, 32, 68, 23, 59, 12, 48, 4, 40, 10, 46, 20, 56, 24, 60, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 47)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 45)(21, 46)(22, 48)(23, 49)(24, 55)(25, 57)(26, 58)(27, 69)(28, 70)(29, 71)(30, 56)(31, 59)(32, 60)(33, 66)(34, 67)(35, 72)(36, 68) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E15.641 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 7 degree seq :: [ 72 ] E15.644 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^6 * T1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 23, 59, 12, 48, 4, 40, 10, 46, 20, 56, 30, 66, 32, 68, 22, 58, 11, 47, 21, 57, 31, 67, 36, 72, 34, 70, 26, 62, 14, 50, 25, 61, 33, 69, 35, 71, 28, 64, 16, 52, 6, 42, 15, 51, 27, 63, 29, 65, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 24, 60, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 47)(15, 61)(16, 62)(17, 63)(18, 64)(19, 60)(20, 45)(21, 46)(22, 48)(23, 49)(24, 65)(25, 57)(26, 58)(27, 69)(28, 70)(29, 71)(30, 55)(31, 56)(32, 59)(33, 67)(34, 68)(35, 72)(36, 66) local type(s) :: { ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E15.640 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 7 degree seq :: [ 72 ] E15.645 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6, T2^-1 * T1^6, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 28, 64, 18, 54, 8, 44)(4, 40, 10, 46, 20, 56, 29, 65, 24, 60, 12, 48)(6, 42, 15, 51, 26, 62, 34, 70, 27, 63, 16, 52)(11, 47, 21, 57, 30, 66, 35, 71, 32, 68, 23, 59)(14, 50, 25, 61, 33, 69, 36, 72, 31, 67, 22, 58) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 57)(15, 61)(16, 58)(17, 62)(18, 63)(19, 64)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 66)(26, 69)(27, 67)(28, 70)(29, 55)(30, 56)(31, 59)(32, 60)(33, 71)(34, 72)(35, 65)(36, 68) local type(s) :: { ( 36^12 ) } Outer automorphisms :: reflexible Dual of E15.642 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 36 f = 2 degree seq :: [ 12^6 ] E15.646 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^6, Y1^6, 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 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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, 37, 2, 38, 6, 42, 14, 50, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 12, 48)(9, 45, 17, 53, 27, 63, 33, 69, 31, 67, 20, 56)(13, 49, 18, 54, 28, 64, 34, 70, 32, 68, 23, 59)(19, 55, 24, 60, 29, 65, 35, 71, 36, 72, 30, 66)(73, 109, 75, 111, 81, 117, 91, 127, 95, 131, 84, 120, 76, 112, 82, 118, 92, 128, 102, 138, 104, 140, 94, 130, 83, 119, 93, 129, 103, 139, 108, 144, 106, 142, 98, 134, 86, 122, 97, 133, 105, 141, 107, 143, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 101, 137, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 96, 132, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 86)(12, 94)(13, 95)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 102)(20, 103)(21, 97)(22, 98)(23, 104)(24, 91)(25, 87)(26, 88)(27, 89)(28, 90)(29, 96)(30, 108)(31, 105)(32, 106)(33, 99)(34, 100)(35, 101)(36, 107)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E15.650 Graph:: bipartite v = 7 e = 72 f = 37 degree seq :: [ 12^6, 72 ] E15.647 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y1^6, Y3^6, Y1^3 * Y3^-3, 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 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 12, 48)(9, 45, 17, 53, 27, 63, 33, 69, 30, 66, 20, 56)(13, 49, 18, 54, 28, 64, 34, 70, 31, 67, 23, 59)(19, 55, 29, 65, 35, 71, 36, 72, 32, 68, 24, 60)(73, 109, 75, 111, 81, 117, 91, 127, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 101, 137, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 107, 143, 106, 142, 98, 134, 86, 122, 97, 133, 105, 141, 108, 144, 103, 139, 94, 130, 83, 119, 93, 129, 102, 138, 104, 140, 95, 131, 84, 120, 76, 112, 82, 118, 92, 128, 96, 132, 85, 121, 77, 113) L = (1, 76)(2, 73)(3, 82)(4, 83)(5, 84)(6, 74)(7, 75)(8, 77)(9, 92)(10, 93)(11, 86)(12, 94)(13, 95)(14, 78)(15, 79)(16, 80)(17, 81)(18, 85)(19, 96)(20, 102)(21, 97)(22, 98)(23, 103)(24, 104)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 105)(31, 106)(32, 108)(33, 99)(34, 100)(35, 101)(36, 107)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) } Outer automorphisms :: reflexible Dual of E15.651 Graph:: bipartite v = 7 e = 72 f = 37 degree seq :: [ 12^6, 72 ] E15.648 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^-1 * Y2, Y1^-1 * Y2^-1 * Y1^-6, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 24, 60, 22, 58, 12, 48, 5, 41, 8, 44, 16, 52, 26, 62, 32, 68, 31, 67, 23, 59, 13, 49, 18, 54, 28, 64, 34, 70, 36, 72, 35, 71, 29, 65, 19, 55, 9, 45, 17, 53, 27, 63, 33, 69, 30, 66, 20, 56, 10, 46, 3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 11, 47, 4, 40)(73, 109, 75, 111, 81, 117, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 106, 142, 98, 134, 86, 122, 97, 133, 105, 141, 108, 144, 104, 140, 96, 132, 93, 129, 102, 138, 107, 143, 103, 139, 94, 130, 83, 119, 92, 128, 101, 137, 95, 131, 84, 120, 76, 112, 82, 118, 91, 127, 85, 121, 77, 113) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 90)(10, 91)(11, 92)(12, 76)(13, 77)(14, 97)(15, 99)(16, 78)(17, 100)(18, 80)(19, 85)(20, 101)(21, 102)(22, 83)(23, 84)(24, 93)(25, 105)(26, 86)(27, 106)(28, 88)(29, 95)(30, 107)(31, 94)(32, 96)(33, 108)(34, 98)(35, 103)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 2, 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 E15.649 Graph:: bipartite v = 2 e = 72 f = 42 degree seq :: [ 72^2 ] E15.649 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2^6, Y3^6 * Y2^-1, (Y2^-1 * Y3)^36, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 86, 122, 83, 119, 76, 112)(75, 111, 79, 115, 87, 123, 97, 133, 93, 129, 82, 118)(77, 113, 80, 116, 88, 124, 98, 134, 94, 130, 84, 120)(81, 117, 89, 125, 99, 135, 105, 141, 102, 138, 92, 128)(85, 121, 90, 126, 100, 136, 106, 142, 103, 139, 95, 131)(91, 127, 101, 137, 107, 143, 108, 144, 104, 140, 96, 132) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 97)(15, 99)(16, 78)(17, 101)(18, 80)(19, 90)(20, 96)(21, 102)(22, 83)(23, 84)(24, 85)(25, 105)(26, 86)(27, 107)(28, 88)(29, 100)(30, 104)(31, 94)(32, 95)(33, 108)(34, 98)(35, 106)(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) :: { ( 72, 72 ), ( 72^12 ) } Outer automorphisms :: reflexible Dual of E15.648 Graph:: simple bipartite v = 42 e = 72 f = 2 degree seq :: [ 2^36, 12^6 ] E15.650 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^6, Y3^-1 * Y1^6, (Y3 * Y2^-1)^6, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 25, 61, 30, 66, 20, 56, 9, 45, 17, 53, 26, 62, 33, 69, 35, 71, 29, 65, 19, 55, 28, 64, 34, 70, 36, 72, 32, 68, 24, 60, 13, 49, 18, 54, 27, 63, 31, 67, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 22, 58, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 97)(15, 98)(16, 78)(17, 100)(18, 80)(19, 85)(20, 101)(21, 102)(22, 86)(23, 83)(24, 84)(25, 105)(26, 106)(27, 88)(28, 90)(29, 96)(30, 107)(31, 94)(32, 95)(33, 108)(34, 99)(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) :: { ( 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) } Outer automorphisms :: reflexible Dual of E15.646 Graph:: bipartite v = 37 e = 72 f = 7 degree seq :: [ 2^36, 72 ] E15.651 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^6, Y3 * Y1^6, Y1^2 * Y3^-2 * Y1^-2 * Y3^2, (Y3 * Y2^-1)^6, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^2 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 23, 59, 12, 48, 5, 41, 8, 44, 16, 52, 25, 61, 32, 68, 24, 60, 13, 49, 18, 54, 27, 63, 33, 69, 35, 71, 29, 65, 19, 55, 28, 64, 34, 70, 36, 72, 30, 66, 20, 56, 9, 45, 17, 53, 26, 62, 31, 67, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 22, 58, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 94)(15, 98)(16, 78)(17, 100)(18, 80)(19, 85)(20, 101)(21, 102)(22, 103)(23, 83)(24, 84)(25, 86)(26, 106)(27, 88)(28, 90)(29, 96)(30, 107)(31, 108)(32, 95)(33, 97)(34, 99)(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) :: { ( 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) } Outer automorphisms :: reflexible Dual of E15.647 Graph:: bipartite v = 37 e = 72 f = 7 degree seq :: [ 2^36, 72 ] E15.652 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3, 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 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 6, 46)(4, 44, 9, 49)(5, 45, 10, 50)(7, 47, 11, 51)(8, 48, 12, 52)(13, 53, 17, 57)(14, 54, 18, 58)(15, 55, 19, 59)(16, 56, 20, 60)(21, 61, 25, 65)(22, 62, 26, 66)(23, 63, 27, 67)(24, 64, 28, 68)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(81, 121, 83, 123)(82, 122, 86, 126)(84, 124, 85, 125)(87, 127, 88, 128)(89, 129, 90, 130)(91, 131, 92, 132)(93, 133, 94, 134)(95, 135, 96, 136)(97, 137, 98, 138)(99, 139, 100, 140)(101, 141, 102, 142)(103, 143, 104, 144)(105, 145, 106, 146)(107, 147, 108, 148)(109, 149, 110, 150)(111, 151, 112, 152)(113, 153, 114, 154)(115, 155, 116, 156)(117, 157, 118, 158)(119, 159, 120, 160) L = (1, 84)(2, 87)(3, 85)(4, 83)(5, 81)(6, 88)(7, 86)(8, 82)(9, 93)(10, 94)(11, 95)(12, 96)(13, 90)(14, 89)(15, 92)(16, 91)(17, 101)(18, 102)(19, 103)(20, 104)(21, 98)(22, 97)(23, 100)(24, 99)(25, 109)(26, 110)(27, 111)(28, 112)(29, 106)(30, 105)(31, 108)(32, 107)(33, 117)(34, 118)(35, 119)(36, 120)(37, 114)(38, 113)(39, 116)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E15.661 Graph:: simple bipartite v = 40 e = 80 f = 12 degree seq :: [ 4^40 ] E15.653 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (R * Y3)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y2^4, Y3^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 10, 50)(5, 45, 9, 49)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 20, 60)(13, 53, 19, 59)(14, 54, 24, 64)(15, 55, 23, 63)(16, 56, 22, 62)(17, 57, 21, 61)(25, 65, 32, 72)(26, 66, 31, 71)(27, 67, 34, 74)(28, 68, 33, 73)(29, 69, 36, 76)(30, 70, 35, 75)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 98, 138, 89, 129)(84, 124, 92, 132, 105, 145, 95, 135)(86, 126, 93, 133, 106, 146, 96, 136)(88, 128, 99, 139, 111, 151, 102, 142)(90, 130, 100, 140, 112, 152, 103, 143)(94, 134, 107, 147, 117, 157, 109, 149)(97, 137, 108, 148, 118, 158, 110, 150)(101, 141, 113, 153, 119, 159, 115, 155)(104, 144, 114, 154, 120, 160, 116, 156) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 97)(15, 109)(16, 85)(17, 86)(18, 111)(19, 113)(20, 87)(21, 104)(22, 115)(23, 89)(24, 90)(25, 117)(26, 91)(27, 108)(28, 93)(29, 110)(30, 96)(31, 119)(32, 98)(33, 114)(34, 100)(35, 116)(36, 103)(37, 118)(38, 106)(39, 120)(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, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.659 Graph:: simple bipartite v = 30 e = 80 f = 22 degree seq :: [ 4^20, 8^10 ] E15.654 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y2^4, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-5 * Y2^2 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 10, 50)(5, 45, 9, 49)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 20, 60)(13, 53, 19, 59)(14, 54, 24, 64)(15, 55, 23, 63)(16, 56, 22, 62)(17, 57, 21, 61)(25, 65, 34, 74)(26, 66, 33, 73)(27, 67, 36, 76)(28, 68, 35, 75)(29, 69, 40, 80)(30, 70, 39, 79)(31, 71, 38, 78)(32, 72, 37, 77)(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, 112, 152, 110, 150)(97, 137, 108, 148, 109, 149, 111, 151)(101, 141, 115, 155, 120, 160, 118, 158)(104, 144, 116, 156, 117, 157, 119, 159) 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, 117)(22, 118)(23, 89)(24, 90)(25, 112)(26, 91)(27, 111)(28, 93)(29, 106)(30, 108)(31, 96)(32, 97)(33, 120)(34, 98)(35, 119)(36, 100)(37, 114)(38, 116)(39, 103)(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 ) } Outer automorphisms :: reflexible Dual of E15.660 Graph:: simple bipartite v = 30 e = 80 f = 22 degree seq :: [ 4^20, 8^10 ] E15.655 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, R^2, Y2 * Y1 * Y2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 5, 45)(4, 44, 6, 46)(7, 47, 10, 50)(8, 48, 9, 49)(11, 51, 12, 52)(13, 53, 14, 54)(15, 55, 16, 56)(17, 57, 18, 58)(19, 59, 20, 60)(21, 61, 22, 62)(23, 63, 24, 64)(25, 65, 26, 66)(27, 67, 28, 68)(29, 69, 30, 70)(31, 71, 32, 72)(33, 73, 34, 74)(35, 75, 36, 76)(37, 77, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 82, 122, 85, 125)(84, 124, 88, 128, 86, 126, 89, 129)(87, 127, 91, 131, 90, 130, 92, 132)(93, 133, 97, 137, 94, 134, 98, 138)(95, 135, 99, 139, 96, 136, 100, 140)(101, 141, 105, 145, 102, 142, 106, 146)(103, 143, 107, 147, 104, 144, 108, 148)(109, 149, 113, 153, 110, 150, 114, 154)(111, 151, 115, 155, 112, 152, 116, 156)(117, 157, 119, 159, 118, 158, 120, 160) L = (1, 84)(2, 86)(3, 87)(4, 81)(5, 90)(6, 82)(7, 83)(8, 93)(9, 94)(10, 85)(11, 95)(12, 96)(13, 88)(14, 89)(15, 91)(16, 92)(17, 101)(18, 102)(19, 103)(20, 104)(21, 97)(22, 98)(23, 99)(24, 100)(25, 109)(26, 110)(27, 111)(28, 112)(29, 105)(30, 106)(31, 107)(32, 108)(33, 117)(34, 118)(35, 119)(36, 120)(37, 113)(38, 114)(39, 115)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.658 Graph:: bipartite v = 30 e = 80 f = 22 degree seq :: [ 4^20, 8^10 ] E15.656 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, R^2, Y2^4, (Y3 * Y1)^2, (R * Y3)^2, Y2^2 * Y3 * Y1, (R * Y1)^2, (R * Y2 * Y3)^2, Y2^-1 * R * Y1 * Y3 * R * 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 * Y1, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 7, 47)(5, 45, 10, 50)(6, 46, 11, 51)(8, 48, 12, 52)(13, 53, 17, 57)(14, 54, 18, 58)(15, 55, 19, 59)(16, 56, 20, 60)(21, 61, 25, 65)(22, 62, 26, 66)(23, 63, 27, 67)(24, 64, 28, 68)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(81, 121, 83, 123, 87, 127, 85, 125)(82, 122, 86, 126, 84, 124, 88, 128)(89, 129, 93, 133, 90, 130, 94, 134)(91, 131, 95, 135, 92, 132, 96, 136)(97, 137, 101, 141, 98, 138, 102, 142)(99, 139, 103, 143, 100, 140, 104, 144)(105, 145, 109, 149, 106, 146, 110, 150)(107, 147, 111, 151, 108, 148, 112, 152)(113, 153, 117, 157, 114, 154, 118, 158)(115, 155, 119, 159, 116, 156, 120, 160) L = (1, 84)(2, 87)(3, 90)(4, 81)(5, 89)(6, 92)(7, 82)(8, 91)(9, 85)(10, 83)(11, 88)(12, 86)(13, 98)(14, 97)(15, 100)(16, 99)(17, 94)(18, 93)(19, 96)(20, 95)(21, 106)(22, 105)(23, 108)(24, 107)(25, 102)(26, 101)(27, 104)(28, 103)(29, 114)(30, 113)(31, 116)(32, 115)(33, 110)(34, 109)(35, 112)(36, 111)(37, 120)(38, 119)(39, 118)(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, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.657 Graph:: bipartite v = 30 e = 80 f = 22 degree seq :: [ 4^20, 8^10 ] E15.657 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (Y3 * Y2)^2, Y3 * Y2 * Y1 * Y3 * Y1, Y2 * Y1^10, Y3 * Y1^5 * Y3 * Y1^-5 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 15, 55, 23, 63, 31, 71, 35, 75, 27, 67, 19, 59, 10, 50, 3, 43, 7, 47, 16, 56, 24, 64, 32, 72, 38, 78, 30, 70, 22, 62, 14, 54, 5, 45)(4, 44, 11, 51, 20, 60, 28, 68, 36, 76, 39, 79, 34, 74, 25, 65, 18, 58, 8, 48, 9, 49, 13, 53, 21, 61, 29, 69, 37, 77, 40, 80, 33, 73, 26, 66, 17, 57, 12, 52)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 89, 129)(85, 125, 90, 130)(86, 126, 96, 136)(88, 128, 92, 132)(91, 131, 93, 133)(94, 134, 99, 139)(95, 135, 104, 144)(97, 137, 98, 138)(100, 140, 101, 141)(102, 142, 107, 147)(103, 143, 112, 152)(105, 145, 106, 146)(108, 148, 109, 149)(110, 150, 115, 155)(111, 151, 118, 158)(113, 153, 114, 154)(116, 156, 117, 157)(119, 159, 120, 160) L = (1, 84)(2, 88)(3, 89)(4, 81)(5, 93)(6, 97)(7, 92)(8, 82)(9, 83)(10, 91)(11, 90)(12, 87)(13, 85)(14, 100)(15, 105)(16, 98)(17, 86)(18, 96)(19, 101)(20, 94)(21, 99)(22, 109)(23, 113)(24, 106)(25, 95)(26, 104)(27, 108)(28, 107)(29, 102)(30, 116)(31, 119)(32, 114)(33, 103)(34, 112)(35, 117)(36, 110)(37, 115)(38, 120)(39, 111)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.656 Graph:: bipartite v = 22 e = 80 f = 30 degree seq :: [ 4^20, 40^2 ] E15.658 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (R * Y2)^2, Y1^-1 * Y3 * Y1^-1 * Y2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^10, Y1^-1 * Y3 * Y1^4 * Y2 * Y1^-5 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 13, 53, 21, 61, 29, 69, 37, 77, 34, 74, 26, 66, 18, 58, 10, 50, 16, 56, 24, 64, 32, 72, 40, 80, 36, 76, 28, 68, 20, 60, 12, 52, 5, 45)(3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 38, 78, 31, 71, 22, 62, 15, 55, 7, 47, 4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 39, 79, 30, 70, 23, 63, 14, 54, 8, 48)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 90, 130)(85, 125, 91, 131)(86, 126, 94, 134)(88, 128, 96, 136)(89, 129, 98, 138)(92, 132, 97, 137)(93, 133, 102, 142)(95, 135, 104, 144)(99, 139, 106, 146)(100, 140, 107, 147)(101, 141, 110, 150)(103, 143, 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, 84)(2, 88)(3, 90)(4, 81)(5, 89)(6, 95)(7, 96)(8, 82)(9, 85)(10, 83)(11, 98)(12, 99)(13, 103)(14, 104)(15, 86)(16, 87)(17, 106)(18, 91)(19, 92)(20, 105)(21, 111)(22, 112)(23, 93)(24, 94)(25, 100)(26, 97)(27, 114)(28, 115)(29, 119)(30, 120)(31, 101)(32, 102)(33, 117)(34, 107)(35, 108)(36, 118)(37, 113)(38, 116)(39, 109)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.655 Graph:: bipartite v = 22 e = 80 f = 30 degree seq :: [ 4^20, 40^2 ] E15.659 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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), (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^4, Y3^5, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y1^-1 * Y2, (Y1^2 * Y2)^2, Y1 * Y3^-1 * Y2 * R * Y1 * Y2 * R, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 16, 56, 4, 44, 9, 49, 22, 62, 35, 75, 15, 55, 27, 67, 39, 79, 32, 72, 20, 60, 28, 68, 37, 77, 19, 59, 6, 46, 10, 50, 18, 58, 5, 45)(3, 43, 11, 51, 29, 69, 31, 71, 12, 52, 26, 66, 40, 80, 36, 76, 25, 65, 8, 48, 23, 63, 17, 57, 34, 74, 24, 64, 38, 78, 33, 73, 14, 54, 30, 70, 21, 61, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 94, 134)(85, 125, 97, 137)(86, 126, 92, 132)(87, 127, 101, 141)(89, 129, 106, 146)(90, 130, 104, 144)(91, 131, 107, 147)(93, 133, 112, 152)(95, 135, 114, 154)(96, 136, 116, 156)(98, 138, 109, 149)(99, 139, 113, 153)(100, 140, 105, 145)(102, 142, 118, 158)(103, 143, 119, 159)(108, 148, 110, 150)(111, 151, 115, 155)(117, 157, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 102)(8, 104)(9, 107)(10, 82)(11, 106)(12, 105)(13, 111)(14, 83)(15, 100)(16, 115)(17, 113)(18, 87)(19, 85)(20, 86)(21, 109)(22, 119)(23, 118)(24, 110)(25, 114)(26, 88)(27, 108)(28, 90)(29, 120)(30, 91)(31, 116)(32, 99)(33, 93)(34, 94)(35, 112)(36, 97)(37, 98)(38, 101)(39, 117)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.653 Graph:: bipartite v = 22 e = 80 f = 30 degree seq :: [ 4^20, 40^2 ] E15.660 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y1^-1 * Y2, (Y2 * Y1^-2)^2, Y1^3 * Y3 * Y1^3, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 21, 61, 37, 77, 19, 59, 6, 46, 10, 50, 15, 55, 28, 68, 39, 79, 32, 72, 20, 60, 16, 56, 4, 44, 9, 49, 23, 63, 36, 76, 18, 58, 5, 45)(3, 43, 11, 51, 29, 69, 25, 65, 38, 78, 33, 73, 14, 54, 30, 70, 26, 66, 8, 48, 24, 64, 17, 57, 34, 74, 31, 71, 12, 52, 27, 67, 40, 80, 35, 75, 22, 62, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 94, 134)(85, 125, 97, 137)(86, 126, 92, 132)(87, 127, 102, 142)(89, 129, 107, 147)(90, 130, 105, 145)(91, 131, 108, 148)(93, 133, 112, 152)(95, 135, 114, 154)(96, 136, 115, 155)(98, 138, 109, 149)(99, 139, 113, 153)(100, 140, 106, 146)(101, 141, 110, 150)(103, 143, 118, 158)(104, 144, 119, 159)(111, 151, 116, 156)(117, 157, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 103)(8, 105)(9, 108)(10, 82)(11, 107)(12, 106)(13, 111)(14, 83)(15, 87)(16, 90)(17, 113)(18, 100)(19, 85)(20, 86)(21, 116)(22, 114)(23, 119)(24, 118)(25, 115)(26, 109)(27, 88)(28, 101)(29, 120)(30, 91)(31, 110)(32, 99)(33, 93)(34, 94)(35, 97)(36, 112)(37, 98)(38, 102)(39, 117)(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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.654 Graph:: bipartite v = 22 e = 80 f = 30 degree seq :: [ 4^20, 40^2 ] E15.661 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-10 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 8, 48)(5, 45, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 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, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129, 84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 120, 160, 112, 152, 104, 144, 96, 136, 88, 128) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 91)(6, 84)(7, 85)(8, 83)(9, 93)(10, 96)(11, 94)(12, 95)(13, 88)(14, 87)(15, 102)(16, 101)(17, 90)(18, 105)(19, 92)(20, 107)(21, 97)(22, 99)(23, 100)(24, 98)(25, 109)(26, 112)(27, 110)(28, 111)(29, 104)(30, 103)(31, 118)(32, 117)(33, 106)(34, 119)(35, 108)(36, 120)(37, 113)(38, 115)(39, 116)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^40 ) } Outer automorphisms :: reflexible Dual of E15.652 Graph:: bipartite v = 12 e = 80 f = 40 degree seq :: [ 8^10, 40^2 ] E15.662 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 20}) Quotient :: halfedge^2 Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y2 * Y1^-2, (Y3 * Y2)^5, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 42, 2, 46, 6, 54, 14, 52, 12, 58, 18, 64, 24, 71, 31, 70, 30, 74, 34, 79, 39, 76, 36, 69, 29, 73, 33, 67, 27, 60, 20, 50, 10, 57, 17, 53, 13, 45, 5, 41)(3, 49, 9, 59, 19, 65, 25, 61, 21, 68, 28, 75, 35, 80, 40, 77, 37, 78, 38, 72, 32, 66, 26, 62, 22, 63, 23, 56, 16, 48, 8, 44, 4, 51, 11, 55, 15, 47, 7, 43) 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, 39)(33, 40)(36, 38)(41, 44)(42, 48)(43, 50)(45, 51)(46, 56)(47, 57)(49, 60)(52, 62)(53, 55)(54, 63)(58, 66)(59, 67)(61, 69)(64, 72)(65, 73)(68, 76)(70, 77)(71, 78)(74, 80)(75, 79) local type(s) :: { ( 8^40 ) } Outer automorphisms :: reflexible Dual of E15.663 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 40 f = 10 degree seq :: [ 40^2 ] E15.663 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 20}) Quotient :: halfedge^2 Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, Y1^4, (Y3 * Y1^-1)^2, (Y3 * Y2)^5, 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 ] Map:: non-degenerate R = (1, 42, 2, 46, 6, 45, 5, 41)(3, 49, 9, 53, 13, 47, 7, 43)(4, 51, 11, 54, 14, 48, 8, 44)(10, 55, 15, 61, 21, 57, 17, 50)(12, 56, 16, 62, 22, 59, 19, 52)(18, 65, 25, 69, 29, 63, 23, 58)(20, 67, 27, 70, 30, 64, 24, 60)(26, 71, 31, 76, 36, 73, 33, 66)(28, 72, 32, 77, 37, 75, 35, 68)(34, 79, 39, 80, 40, 78, 38, 74) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 13)(8, 16)(10, 18)(11, 19)(14, 22)(15, 23)(17, 25)(20, 28)(21, 29)(24, 32)(26, 34)(27, 35)(30, 37)(31, 38)(33, 39)(36, 40)(41, 44)(42, 48)(43, 50)(45, 51)(46, 54)(47, 55)(49, 57)(52, 60)(53, 61)(56, 64)(58, 66)(59, 67)(62, 70)(63, 71)(65, 73)(68, 74)(69, 76)(72, 78)(75, 79)(77, 80) local type(s) :: { ( 40^8 ) } Outer automorphisms :: reflexible Dual of E15.662 Transitivity :: VT+ AT Graph:: bipartite v = 10 e = 40 f = 2 degree seq :: [ 8^10 ] E15.664 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 20}) Quotient :: edge^2 Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, Y3^4, (Y2 * Y1)^5, (Y3 * Y1 * Y2)^20 ] Map:: R = (1, 41, 4, 44, 12, 52, 5, 45)(2, 42, 7, 47, 16, 56, 8, 48)(3, 43, 10, 50, 20, 60, 11, 51)(6, 46, 14, 54, 24, 64, 15, 55)(9, 49, 18, 58, 28, 68, 19, 59)(13, 53, 22, 62, 32, 72, 23, 63)(17, 57, 26, 66, 35, 75, 27, 67)(21, 61, 30, 70, 38, 78, 31, 71)(25, 65, 33, 73, 39, 79, 34, 74)(29, 69, 36, 76, 40, 80, 37, 77)(81, 82)(83, 89)(84, 88)(85, 87)(86, 93)(90, 99)(91, 98)(92, 96)(94, 103)(95, 102)(97, 105)(100, 108)(101, 109)(104, 112)(106, 114)(107, 113)(110, 117)(111, 116)(115, 119)(118, 120)(121, 123)(122, 126)(124, 131)(125, 130)(127, 135)(128, 134)(129, 137)(132, 140)(133, 141)(136, 144)(138, 147)(139, 146)(142, 151)(143, 150)(145, 149)(148, 155)(152, 158)(153, 157)(154, 156)(159, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^8 ) } Outer automorphisms :: reflexible Dual of E15.667 Graph:: simple bipartite v = 50 e = 80 f = 2 degree seq :: [ 2^40, 8^10 ] E15.665 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 20}) Quotient :: edge^2 Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-3 * Y1 * Y3 * Y2, (Y1 * Y2)^5, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 41, 4, 44, 12, 52, 16, 56, 6, 46, 15, 55, 26, 66, 33, 73, 23, 63, 32, 72, 40, 80, 36, 76, 27, 67, 35, 75, 30, 70, 21, 61, 9, 49, 20, 60, 13, 53, 5, 45)(2, 42, 7, 47, 17, 57, 11, 51, 3, 43, 10, 50, 22, 62, 29, 69, 19, 59, 28, 68, 37, 77, 39, 79, 31, 71, 38, 78, 34, 74, 25, 65, 14, 54, 24, 64, 18, 58, 8, 48)(81, 82)(83, 89)(84, 88)(85, 87)(86, 94)(90, 101)(91, 100)(92, 98)(93, 97)(95, 105)(96, 104)(99, 107)(102, 110)(103, 111)(106, 114)(108, 116)(109, 115)(112, 119)(113, 118)(117, 120)(121, 123)(122, 126)(124, 131)(125, 130)(127, 136)(128, 135)(129, 139)(132, 137)(133, 142)(134, 143)(138, 146)(140, 149)(141, 148)(144, 153)(145, 152)(147, 151)(150, 157)(154, 160)(155, 159)(156, 158) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 16 ), ( 16^40 ) } Outer automorphisms :: reflexible Dual of E15.666 Graph:: simple bipartite v = 42 e = 80 f = 10 degree seq :: [ 2^40, 40^2 ] E15.666 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 20}) Quotient :: loop^2 Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, Y3^4, (Y2 * Y1)^5, (Y3 * Y1 * Y2)^20 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 10, 50, 90, 130, 20, 60, 100, 140, 11, 51, 91, 131)(6, 46, 86, 126, 14, 54, 94, 134, 24, 64, 104, 144, 15, 55, 95, 135)(9, 49, 89, 129, 18, 58, 98, 138, 28, 68, 108, 148, 19, 59, 99, 139)(13, 53, 93, 133, 22, 62, 102, 142, 32, 72, 112, 152, 23, 63, 103, 143)(17, 57, 97, 137, 26, 66, 106, 146, 35, 75, 115, 155, 27, 67, 107, 147)(21, 61, 101, 141, 30, 70, 110, 150, 38, 78, 118, 158, 31, 71, 111, 151)(25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154)(29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157) L = (1, 42)(2, 41)(3, 49)(4, 48)(5, 47)(6, 53)(7, 45)(8, 44)(9, 43)(10, 59)(11, 58)(12, 56)(13, 46)(14, 63)(15, 62)(16, 52)(17, 65)(18, 51)(19, 50)(20, 68)(21, 69)(22, 55)(23, 54)(24, 72)(25, 57)(26, 74)(27, 73)(28, 60)(29, 61)(30, 77)(31, 76)(32, 64)(33, 67)(34, 66)(35, 79)(36, 71)(37, 70)(38, 80)(39, 75)(40, 78)(81, 123)(82, 126)(83, 121)(84, 131)(85, 130)(86, 122)(87, 135)(88, 134)(89, 137)(90, 125)(91, 124)(92, 140)(93, 141)(94, 128)(95, 127)(96, 144)(97, 129)(98, 147)(99, 146)(100, 132)(101, 133)(102, 151)(103, 150)(104, 136)(105, 149)(106, 139)(107, 138)(108, 155)(109, 145)(110, 143)(111, 142)(112, 158)(113, 157)(114, 156)(115, 148)(116, 154)(117, 153)(118, 152)(119, 160)(120, 159) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E15.665 Transitivity :: VT+ Graph:: bipartite v = 10 e = 80 f = 42 degree seq :: [ 16^10 ] E15.667 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 20}) Quotient :: loop^2 Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-3 * Y1 * Y3 * Y2, (Y1 * Y2)^5, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 16, 56, 96, 136, 6, 46, 86, 126, 15, 55, 95, 135, 26, 66, 106, 146, 33, 73, 113, 153, 23, 63, 103, 143, 32, 72, 112, 152, 40, 80, 120, 160, 36, 76, 116, 156, 27, 67, 107, 147, 35, 75, 115, 155, 30, 70, 110, 150, 21, 61, 101, 141, 9, 49, 89, 129, 20, 60, 100, 140, 13, 53, 93, 133, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 17, 57, 97, 137, 11, 51, 91, 131, 3, 43, 83, 123, 10, 50, 90, 130, 22, 62, 102, 142, 29, 69, 109, 149, 19, 59, 99, 139, 28, 68, 108, 148, 37, 77, 117, 157, 39, 79, 119, 159, 31, 71, 111, 151, 38, 78, 118, 158, 34, 74, 114, 154, 25, 65, 105, 145, 14, 54, 94, 134, 24, 64, 104, 144, 18, 58, 98, 138, 8, 48, 88, 128) L = (1, 42)(2, 41)(3, 49)(4, 48)(5, 47)(6, 54)(7, 45)(8, 44)(9, 43)(10, 61)(11, 60)(12, 58)(13, 57)(14, 46)(15, 65)(16, 64)(17, 53)(18, 52)(19, 67)(20, 51)(21, 50)(22, 70)(23, 71)(24, 56)(25, 55)(26, 74)(27, 59)(28, 76)(29, 75)(30, 62)(31, 63)(32, 79)(33, 78)(34, 66)(35, 69)(36, 68)(37, 80)(38, 73)(39, 72)(40, 77)(81, 123)(82, 126)(83, 121)(84, 131)(85, 130)(86, 122)(87, 136)(88, 135)(89, 139)(90, 125)(91, 124)(92, 137)(93, 142)(94, 143)(95, 128)(96, 127)(97, 132)(98, 146)(99, 129)(100, 149)(101, 148)(102, 133)(103, 134)(104, 153)(105, 152)(106, 138)(107, 151)(108, 141)(109, 140)(110, 157)(111, 147)(112, 145)(113, 144)(114, 160)(115, 159)(116, 158)(117, 150)(118, 156)(119, 155)(120, 154) 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 ) } Outer automorphisms :: reflexible Dual of E15.664 Transitivity :: VT+ Graph:: bipartite v = 2 e = 80 f = 50 degree seq :: [ 80^2 ] E15.668 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y2^4, Y3^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 23, 63)(13, 53, 22, 62)(14, 54, 24, 64)(15, 55, 20, 60)(16, 56, 19, 59)(17, 57, 21, 61)(25, 65, 32, 72)(26, 66, 31, 71)(27, 67, 36, 76)(28, 68, 35, 75)(29, 69, 34, 74)(30, 70, 33, 73)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 98, 138, 89, 129)(84, 124, 92, 132, 105, 145, 95, 135)(86, 126, 93, 133, 106, 146, 96, 136)(88, 128, 99, 139, 111, 151, 102, 142)(90, 130, 100, 140, 112, 152, 103, 143)(94, 134, 107, 147, 117, 157, 109, 149)(97, 137, 108, 148, 118, 158, 110, 150)(101, 141, 113, 153, 119, 159, 115, 155)(104, 144, 114, 154, 120, 160, 116, 156) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 97)(15, 109)(16, 85)(17, 86)(18, 111)(19, 113)(20, 87)(21, 104)(22, 115)(23, 89)(24, 90)(25, 117)(26, 91)(27, 108)(28, 93)(29, 110)(30, 96)(31, 119)(32, 98)(33, 114)(34, 100)(35, 116)(36, 103)(37, 118)(38, 106)(39, 120)(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, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.670 Graph:: simple bipartite v = 30 e = 80 f = 22 degree seq :: [ 4^20, 8^10 ] E15.669 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y3^-5 * Y2^2 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 23, 63)(13, 53, 22, 62)(14, 54, 24, 64)(15, 55, 20, 60)(16, 56, 19, 59)(17, 57, 21, 61)(25, 65, 34, 74)(26, 66, 33, 73)(27, 67, 39, 79)(28, 68, 38, 78)(29, 69, 40, 80)(30, 70, 36, 76)(31, 71, 35, 75)(32, 72, 37, 77)(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, 112, 152, 110, 150)(97, 137, 108, 148, 109, 149, 111, 151)(101, 141, 115, 155, 120, 160, 118, 158)(104, 144, 116, 156, 117, 157, 119, 159) 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, 117)(22, 118)(23, 89)(24, 90)(25, 112)(26, 91)(27, 111)(28, 93)(29, 106)(30, 108)(31, 96)(32, 97)(33, 120)(34, 98)(35, 119)(36, 100)(37, 114)(38, 116)(39, 103)(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 ) } Outer automorphisms :: reflexible Dual of E15.671 Graph:: simple bipartite v = 30 e = 80 f = 22 degree seq :: [ 4^20, 8^10 ] E15.670 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |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^-1 * Y1^4, Y3^5, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 15, 55, 4, 44, 9, 49, 20, 60, 30, 70, 14, 54, 23, 63, 34, 74, 32, 72, 18, 58, 24, 64, 31, 71, 17, 57, 6, 46, 10, 50, 16, 56, 5, 45)(3, 43, 11, 51, 25, 65, 21, 61, 12, 52, 26, 66, 37, 77, 35, 75, 28, 68, 38, 78, 40, 80, 36, 76, 29, 69, 39, 79, 33, 73, 22, 62, 13, 53, 27, 67, 19, 59, 8, 48)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 99, 139)(89, 129, 102, 142)(90, 130, 101, 141)(94, 134, 109, 149)(95, 135, 107, 147)(96, 136, 105, 145)(97, 137, 106, 146)(98, 138, 108, 148)(100, 140, 113, 153)(103, 143, 116, 156)(104, 144, 115, 155)(110, 150, 119, 159)(111, 151, 117, 157)(112, 152, 118, 158)(114, 154, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 101)(9, 103)(10, 82)(11, 106)(12, 108)(13, 83)(14, 98)(15, 110)(16, 87)(17, 85)(18, 86)(19, 105)(20, 114)(21, 115)(22, 88)(23, 104)(24, 90)(25, 117)(26, 118)(27, 91)(28, 109)(29, 93)(30, 112)(31, 96)(32, 97)(33, 99)(34, 111)(35, 116)(36, 102)(37, 120)(38, 119)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.668 Graph:: bipartite v = 22 e = 80 f = 30 degree seq :: [ 4^20, 40^2 ] E15.671 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 20}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-1 * Y1 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^3, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 19, 59, 31, 71, 17, 57, 6, 46, 10, 50, 14, 54, 24, 64, 35, 75, 32, 72, 18, 58, 15, 55, 4, 44, 9, 49, 21, 61, 30, 70, 16, 56, 5, 45)(3, 43, 11, 51, 25, 65, 37, 77, 34, 74, 23, 63, 13, 53, 27, 67, 28, 68, 39, 79, 40, 80, 36, 76, 29, 69, 22, 62, 12, 52, 26, 66, 38, 78, 33, 73, 20, 60, 8, 48)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 102, 142)(94, 134, 109, 149)(95, 135, 107, 147)(96, 136, 105, 145)(97, 137, 106, 146)(98, 138, 108, 148)(99, 139, 113, 153)(101, 141, 114, 154)(104, 144, 116, 156)(110, 150, 117, 157)(111, 151, 118, 158)(112, 152, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 94)(5, 95)(6, 81)(7, 101)(8, 102)(9, 104)(10, 82)(11, 106)(12, 108)(13, 83)(14, 87)(15, 90)(16, 98)(17, 85)(18, 86)(19, 110)(20, 109)(21, 115)(22, 107)(23, 88)(24, 99)(25, 118)(26, 119)(27, 91)(28, 105)(29, 93)(30, 112)(31, 96)(32, 97)(33, 116)(34, 100)(35, 111)(36, 103)(37, 113)(38, 120)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.669 Graph:: bipartite v = 22 e = 80 f = 30 degree seq :: [ 4^20, 40^2 ] E15.672 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 8, 20}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-3 * T2 * T1^-1, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1^2 * T2^4, (T2 * T1 * T2 * T1^-1)^2 ] Map:: non-degenerate R = (1, 3, 10, 29, 21, 13, 24, 39, 38, 23, 36, 25, 40, 37, 20, 6, 19, 35, 17, 5)(2, 7, 22, 30, 14, 4, 12, 32, 28, 9, 27, 15, 33, 31, 11, 18, 16, 34, 26, 8)(41, 42, 46, 58, 76, 67, 53, 44)(43, 49, 59, 54, 65, 48, 64, 51)(45, 55, 60, 52, 63, 47, 61, 56)(50, 66, 75, 71, 80, 68, 79, 70)(57, 62, 77, 74, 78, 73, 69, 72) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^8 ), ( 16^20 ) } Outer automorphisms :: reflexible Dual of E15.674 Transitivity :: ET+ Graph:: bipartite v = 7 e = 40 f = 5 degree seq :: [ 8^5, 20^2 ] E15.673 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 8, 20}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2 * T1^2, T2 * T1^-3 * T2 * T1^-1, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^2 * T2^-1 * T1^-2, T2^-2 * T1 * T2^2 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 10, 29, 20, 6, 19, 37, 39, 23, 36, 25, 40, 38, 21, 13, 24, 35, 17, 5)(2, 7, 22, 31, 11, 18, 16, 34, 28, 9, 27, 15, 33, 30, 14, 4, 12, 32, 26, 8)(41, 42, 46, 58, 76, 67, 53, 44)(43, 49, 59, 54, 65, 48, 64, 51)(45, 55, 60, 52, 63, 47, 61, 56)(50, 66, 77, 71, 80, 68, 75, 70)(57, 62, 69, 74, 79, 73, 78, 72) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^8 ), ( 16^20 ) } Outer automorphisms :: reflexible Dual of E15.675 Transitivity :: ET+ Graph:: bipartite v = 7 e = 40 f = 5 degree seq :: [ 8^5, 20^2 ] E15.674 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 8, 20}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^-2, (F * T1)^2, (F * T2)^2, T1^2 * T2^6, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^20 ] Map:: non-degenerate R = (1, 41, 3, 43, 6, 46, 15, 55, 26, 66, 23, 63, 11, 51, 5, 45)(2, 42, 7, 47, 14, 54, 27, 67, 22, 62, 12, 52, 4, 44, 8, 48)(9, 49, 19, 59, 28, 68, 25, 65, 13, 53, 21, 61, 10, 50, 20, 60)(16, 56, 29, 69, 24, 64, 32, 72, 18, 58, 31, 71, 17, 57, 30, 70)(33, 73, 37, 77, 36, 76, 40, 80, 35, 75, 39, 79, 34, 74, 38, 78) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 50)(6, 54)(7, 56)(8, 57)(9, 55)(10, 43)(11, 44)(12, 58)(13, 45)(14, 66)(15, 68)(16, 67)(17, 47)(18, 48)(19, 73)(20, 74)(21, 75)(22, 51)(23, 53)(24, 52)(25, 76)(26, 62)(27, 64)(28, 63)(29, 77)(30, 78)(31, 79)(32, 80)(33, 65)(34, 59)(35, 60)(36, 61)(37, 72)(38, 69)(39, 70)(40, 71) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E15.672 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 40 f = 7 degree seq :: [ 16^5 ] E15.675 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 8, 20}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^-2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-1, T1^8, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 41, 3, 43, 6, 46, 15, 55, 26, 66, 23, 63, 11, 51, 5, 45)(2, 42, 7, 47, 14, 54, 27, 67, 22, 62, 12, 52, 4, 44, 8, 48)(9, 49, 19, 59, 28, 68, 25, 65, 13, 53, 21, 61, 10, 50, 20, 60)(16, 56, 29, 69, 24, 64, 32, 72, 18, 58, 31, 71, 17, 57, 30, 70)(33, 73, 39, 79, 36, 76, 38, 78, 35, 75, 37, 77, 34, 74, 40, 80) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 50)(6, 54)(7, 56)(8, 57)(9, 55)(10, 43)(11, 44)(12, 58)(13, 45)(14, 66)(15, 68)(16, 67)(17, 47)(18, 48)(19, 73)(20, 74)(21, 75)(22, 51)(23, 53)(24, 52)(25, 76)(26, 62)(27, 64)(28, 63)(29, 77)(30, 78)(31, 79)(32, 80)(33, 65)(34, 59)(35, 60)(36, 61)(37, 72)(38, 69)(39, 70)(40, 71) local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E15.673 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 40 f = 7 degree seq :: [ 16^5 ] E15.676 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 20}) Quotient :: dipole Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2 * Y1^2 * Y2^4, (Y2 * Y1 * Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 41, 2, 42, 6, 46, 18, 58, 36, 76, 27, 67, 13, 53, 4, 44)(3, 43, 9, 49, 19, 59, 14, 54, 25, 65, 8, 48, 24, 64, 11, 51)(5, 45, 15, 55, 20, 60, 12, 52, 23, 63, 7, 47, 21, 61, 16, 56)(10, 50, 26, 66, 35, 75, 31, 71, 40, 80, 28, 68, 39, 79, 30, 70)(17, 57, 22, 62, 37, 77, 34, 74, 38, 78, 33, 73, 29, 69, 32, 72)(81, 121, 83, 123, 90, 130, 109, 149, 101, 141, 93, 133, 104, 144, 119, 159, 118, 158, 103, 143, 116, 156, 105, 145, 120, 160, 117, 157, 100, 140, 86, 126, 99, 139, 115, 155, 97, 137, 85, 125)(82, 122, 87, 127, 102, 142, 110, 150, 94, 134, 84, 124, 92, 132, 112, 152, 108, 148, 89, 129, 107, 147, 95, 135, 113, 153, 111, 151, 91, 131, 98, 138, 96, 136, 114, 154, 106, 146, 88, 128) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 109)(11, 98)(12, 112)(13, 104)(14, 84)(15, 113)(16, 114)(17, 85)(18, 96)(19, 115)(20, 86)(21, 93)(22, 110)(23, 116)(24, 119)(25, 120)(26, 88)(27, 95)(28, 89)(29, 101)(30, 94)(31, 91)(32, 108)(33, 111)(34, 106)(35, 97)(36, 105)(37, 100)(38, 103)(39, 118)(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) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E15.679 Graph:: bipartite v = 7 e = 80 f = 45 degree seq :: [ 16^5, 40^2 ] E15.677 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 20}) Quotient :: dipole Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y1^2, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^-2 * Y1^2 * Y2^-3, Y1^8, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 41, 2, 42, 6, 46, 18, 58, 36, 76, 27, 67, 13, 53, 4, 44)(3, 43, 9, 49, 19, 59, 14, 54, 25, 65, 8, 48, 24, 64, 11, 51)(5, 45, 15, 55, 20, 60, 12, 52, 23, 63, 7, 47, 21, 61, 16, 56)(10, 50, 26, 66, 37, 77, 31, 71, 40, 80, 28, 68, 35, 75, 30, 70)(17, 57, 22, 62, 29, 69, 34, 74, 39, 79, 33, 73, 38, 78, 32, 72)(81, 121, 83, 123, 90, 130, 109, 149, 100, 140, 86, 126, 99, 139, 117, 157, 119, 159, 103, 143, 116, 156, 105, 145, 120, 160, 118, 158, 101, 141, 93, 133, 104, 144, 115, 155, 97, 137, 85, 125)(82, 122, 87, 127, 102, 142, 111, 151, 91, 131, 98, 138, 96, 136, 114, 154, 108, 148, 89, 129, 107, 147, 95, 135, 113, 153, 110, 150, 94, 134, 84, 124, 92, 132, 112, 152, 106, 146, 88, 128) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 109)(11, 98)(12, 112)(13, 104)(14, 84)(15, 113)(16, 114)(17, 85)(18, 96)(19, 117)(20, 86)(21, 93)(22, 111)(23, 116)(24, 115)(25, 120)(26, 88)(27, 95)(28, 89)(29, 100)(30, 94)(31, 91)(32, 106)(33, 110)(34, 108)(35, 97)(36, 105)(37, 119)(38, 101)(39, 103)(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) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E15.678 Graph:: bipartite v = 7 e = 80 f = 45 degree seq :: [ 16^5, 40^2 ] E15.678 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 20}) Quotient :: dipole Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-3, Y3^2 * Y2 * Y3^2 * Y2^-1, Y2^-2 * Y3^-5, (Y3 * Y2 * Y3 * Y2^-1)^2, (Y3^-1 * Y1^-1)^20 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 98, 138, 116, 156, 107, 147, 93, 133, 84, 124)(83, 123, 89, 129, 99, 139, 94, 134, 105, 145, 88, 128, 104, 144, 91, 131)(85, 125, 95, 135, 100, 140, 92, 132, 103, 143, 87, 127, 101, 141, 96, 136)(90, 130, 106, 146, 115, 155, 111, 151, 120, 160, 108, 148, 119, 159, 110, 150)(97, 137, 102, 142, 117, 157, 114, 154, 118, 158, 113, 153, 109, 149, 112, 152) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 109)(11, 98)(12, 112)(13, 104)(14, 84)(15, 113)(16, 114)(17, 85)(18, 96)(19, 115)(20, 86)(21, 93)(22, 110)(23, 116)(24, 119)(25, 120)(26, 88)(27, 95)(28, 89)(29, 101)(30, 94)(31, 91)(32, 108)(33, 111)(34, 106)(35, 97)(36, 105)(37, 100)(38, 103)(39, 118)(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) :: { ( 16, 40 ), ( 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40 ) } Outer automorphisms :: reflexible Dual of E15.677 Graph:: simple bipartite v = 45 e = 80 f = 7 degree seq :: [ 2^40, 16^5 ] E15.679 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 20}) Quotient :: dipole Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-3, Y3^2 * Y2 * Y3^2 * Y2^-1, Y3^-2 * Y2^2 * Y3^-3, Y3^-1 * Y2^-1 * Y3^-1 * Y2^5, (Y3^-1 * Y1^-1)^20 ] Map:: R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 121, 82, 122, 86, 126, 98, 138, 116, 156, 107, 147, 93, 133, 84, 124)(83, 123, 89, 129, 99, 139, 94, 134, 105, 145, 88, 128, 104, 144, 91, 131)(85, 125, 95, 135, 100, 140, 92, 132, 103, 143, 87, 127, 101, 141, 96, 136)(90, 130, 106, 146, 117, 157, 111, 151, 120, 160, 108, 148, 115, 155, 110, 150)(97, 137, 102, 142, 109, 149, 114, 154, 119, 159, 113, 153, 118, 158, 112, 152) L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 109)(11, 98)(12, 112)(13, 104)(14, 84)(15, 113)(16, 114)(17, 85)(18, 96)(19, 117)(20, 86)(21, 93)(22, 111)(23, 116)(24, 115)(25, 120)(26, 88)(27, 95)(28, 89)(29, 100)(30, 94)(31, 91)(32, 106)(33, 110)(34, 108)(35, 97)(36, 105)(37, 119)(38, 101)(39, 103)(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) :: { ( 16, 40 ), ( 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40 ) } Outer automorphisms :: reflexible Dual of E15.676 Graph:: simple bipartite v = 45 e = 80 f = 7 degree seq :: [ 2^40, 16^5 ] E15.680 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 40, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^10 * T1^-1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 38, 30, 22, 14, 6, 13, 21, 29, 37, 40, 35, 27, 19, 11, 4, 10, 18, 26, 34, 36, 28, 20, 12, 5)(41, 42, 46, 44)(43, 47, 53, 50)(45, 48, 54, 51)(49, 55, 61, 58)(52, 56, 62, 59)(57, 63, 69, 66)(60, 64, 70, 67)(65, 71, 77, 74)(68, 72, 78, 75)(73, 79, 80, 76) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^4 ), ( 80^40 ) } Outer automorphisms :: reflexible Dual of E15.682 Transitivity :: ET+ Graph:: bipartite v = 11 e = 40 f = 1 degree seq :: [ 4^10, 40 ] E15.681 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 40, 40}) Quotient :: edge Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^10 * T1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 35, 27, 19, 11, 4, 10, 18, 26, 34, 40, 38, 30, 22, 14, 6, 13, 21, 29, 37, 39, 32, 24, 16, 8, 2, 7, 15, 23, 31, 36, 28, 20, 12, 5)(41, 42, 46, 44)(43, 47, 53, 50)(45, 48, 54, 51)(49, 55, 61, 58)(52, 56, 62, 59)(57, 63, 69, 66)(60, 64, 70, 67)(65, 71, 77, 74)(68, 72, 78, 75)(73, 76, 79, 80) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 80^4 ), ( 80^40 ) } Outer automorphisms :: reflexible Dual of E15.683 Transitivity :: ET+ Graph:: bipartite v = 11 e = 40 f = 1 degree seq :: [ 4^10, 40 ] E15.682 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 40, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^10 * T1^-1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 32, 72, 24, 64, 16, 56, 8, 48, 2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 39, 79, 38, 78, 30, 70, 22, 62, 14, 54, 6, 46, 13, 53, 21, 61, 29, 69, 37, 77, 40, 80, 35, 75, 27, 67, 19, 59, 11, 51, 4, 44, 10, 50, 18, 58, 26, 66, 34, 74, 36, 76, 28, 68, 20, 60, 12, 52, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 44)(7, 53)(8, 54)(9, 55)(10, 43)(11, 45)(12, 56)(13, 50)(14, 51)(15, 61)(16, 62)(17, 63)(18, 49)(19, 52)(20, 64)(21, 58)(22, 59)(23, 69)(24, 70)(25, 71)(26, 57)(27, 60)(28, 72)(29, 66)(30, 67)(31, 77)(32, 78)(33, 79)(34, 65)(35, 68)(36, 73)(37, 74)(38, 75)(39, 80)(40, 76) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.680 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 11 degree seq :: [ 80 ] E15.683 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 40, 40}) Quotient :: loop Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^10 * T1, (T1^-1 * T2^-1)^40 ] Map:: non-degenerate R = (1, 41, 3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 35, 75, 27, 67, 19, 59, 11, 51, 4, 44, 10, 50, 18, 58, 26, 66, 34, 74, 40, 80, 38, 78, 30, 70, 22, 62, 14, 54, 6, 46, 13, 53, 21, 61, 29, 69, 37, 77, 39, 79, 32, 72, 24, 64, 16, 56, 8, 48, 2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 36, 76, 28, 68, 20, 60, 12, 52, 5, 45) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 44)(7, 53)(8, 54)(9, 55)(10, 43)(11, 45)(12, 56)(13, 50)(14, 51)(15, 61)(16, 62)(17, 63)(18, 49)(19, 52)(20, 64)(21, 58)(22, 59)(23, 69)(24, 70)(25, 71)(26, 57)(27, 60)(28, 72)(29, 66)(30, 67)(31, 77)(32, 78)(33, 76)(34, 65)(35, 68)(36, 79)(37, 74)(38, 75)(39, 80)(40, 73) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.681 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 40 f = 11 degree seq :: [ 80 ] E15.684 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^10 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 7, 47, 13, 53, 10, 50)(5, 45, 8, 48, 14, 54, 11, 51)(9, 49, 15, 55, 21, 61, 18, 58)(12, 52, 16, 56, 22, 62, 19, 59)(17, 57, 23, 63, 29, 69, 26, 66)(20, 60, 24, 64, 30, 70, 27, 67)(25, 65, 31, 71, 37, 77, 34, 74)(28, 68, 32, 72, 38, 78, 35, 75)(33, 73, 36, 76, 39, 79, 40, 80)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 115, 155, 107, 147, 99, 139, 91, 131, 84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 120, 160, 118, 158, 110, 150, 102, 142, 94, 134, 86, 126, 93, 133, 101, 141, 109, 149, 117, 157, 119, 159, 112, 152, 104, 144, 96, 136, 88, 128, 82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 116, 156, 108, 148, 100, 140, 92, 132, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 86)(5, 91)(6, 82)(7, 83)(8, 85)(9, 98)(10, 93)(11, 94)(12, 99)(13, 87)(14, 88)(15, 89)(16, 92)(17, 106)(18, 101)(19, 102)(20, 107)(21, 95)(22, 96)(23, 97)(24, 100)(25, 114)(26, 109)(27, 110)(28, 115)(29, 103)(30, 104)(31, 105)(32, 108)(33, 120)(34, 117)(35, 118)(36, 113)(37, 111)(38, 112)(39, 116)(40, 119)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 2, 80, 2, 80, 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E15.687 Graph:: bipartite v = 11 e = 80 f = 41 degree seq :: [ 8^10, 80 ] E15.685 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^4, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^10, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 7, 47, 13, 53, 10, 50)(5, 45, 8, 48, 14, 54, 11, 51)(9, 49, 15, 55, 21, 61, 18, 58)(12, 52, 16, 56, 22, 62, 19, 59)(17, 57, 23, 63, 29, 69, 26, 66)(20, 60, 24, 64, 30, 70, 27, 67)(25, 65, 31, 71, 37, 77, 34, 74)(28, 68, 32, 72, 38, 78, 35, 75)(33, 73, 39, 79, 40, 80, 36, 76)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 112, 152, 104, 144, 96, 136, 88, 128, 82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 119, 159, 118, 158, 110, 150, 102, 142, 94, 134, 86, 126, 93, 133, 101, 141, 109, 149, 117, 157, 120, 160, 115, 155, 107, 147, 99, 139, 91, 131, 84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 116, 156, 108, 148, 100, 140, 92, 132, 85, 125) L = (1, 84)(2, 81)(3, 90)(4, 86)(5, 91)(6, 82)(7, 83)(8, 85)(9, 98)(10, 93)(11, 94)(12, 99)(13, 87)(14, 88)(15, 89)(16, 92)(17, 106)(18, 101)(19, 102)(20, 107)(21, 95)(22, 96)(23, 97)(24, 100)(25, 114)(26, 109)(27, 110)(28, 115)(29, 103)(30, 104)(31, 105)(32, 108)(33, 116)(34, 117)(35, 118)(36, 120)(37, 111)(38, 112)(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) :: { ( 2, 80, 2, 80, 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E15.686 Graph:: bipartite v = 11 e = 80 f = 41 degree seq :: [ 8^10, 80 ] E15.686 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3^-1 * Y1^10, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 13, 53, 21, 61, 29, 69, 34, 74, 26, 66, 18, 58, 10, 50, 3, 43, 7, 47, 14, 54, 22, 62, 30, 70, 37, 77, 39, 79, 33, 73, 25, 65, 17, 57, 9, 49, 16, 56, 24, 64, 32, 72, 38, 78, 40, 80, 36, 76, 28, 68, 20, 60, 12, 52, 5, 45, 8, 48, 15, 55, 23, 63, 31, 71, 35, 75, 27, 67, 19, 59, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 94)(7, 96)(8, 82)(9, 85)(10, 97)(11, 98)(12, 84)(13, 102)(14, 104)(15, 86)(16, 88)(17, 92)(18, 105)(19, 106)(20, 91)(21, 110)(22, 112)(23, 93)(24, 95)(25, 100)(26, 113)(27, 114)(28, 99)(29, 117)(30, 118)(31, 101)(32, 103)(33, 108)(34, 119)(35, 109)(36, 107)(37, 120)(38, 111)(39, 116)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 80 ), ( 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80 ) } Outer automorphisms :: reflexible Dual of E15.685 Graph:: bipartite v = 41 e = 80 f = 11 degree seq :: [ 2^40, 80 ] E15.687 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3 * Y1^10, Y1^4 * Y3^-2 * Y1^-4 * Y3^-2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 41, 2, 42, 6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 28, 68, 20, 60, 12, 52, 5, 45, 8, 48, 15, 55, 23, 63, 31, 71, 37, 77, 39, 79, 33, 73, 25, 65, 17, 57, 9, 49, 16, 56, 24, 64, 32, 72, 38, 78, 40, 80, 34, 74, 26, 66, 18, 58, 10, 50, 3, 43, 7, 47, 14, 54, 22, 62, 30, 70, 35, 75, 27, 67, 19, 59, 11, 51, 4, 44)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 90)(5, 81)(6, 94)(7, 96)(8, 82)(9, 85)(10, 97)(11, 98)(12, 84)(13, 102)(14, 104)(15, 86)(16, 88)(17, 92)(18, 105)(19, 106)(20, 91)(21, 110)(22, 112)(23, 93)(24, 95)(25, 100)(26, 113)(27, 114)(28, 99)(29, 115)(30, 118)(31, 101)(32, 103)(33, 108)(34, 119)(35, 120)(36, 107)(37, 109)(38, 111)(39, 116)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 80 ), ( 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80, 8, 80 ) } Outer automorphisms :: reflexible Dual of E15.684 Graph:: bipartite v = 41 e = 80 f = 11 degree seq :: [ 2^40, 80 ] E15.688 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^6, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^3 * Y1^-3, Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-2 * Y3 * Y1^-2, Y3 * Y2^2 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-3 ] Map:: non-degenerate R = (1, 43, 4, 46)(2, 44, 6, 48)(3, 45, 8, 50)(5, 47, 12, 54)(7, 49, 15, 57)(9, 51, 17, 59)(10, 52, 13, 55)(11, 53, 20, 62)(14, 56, 21, 63)(16, 58, 26, 68)(18, 60, 30, 72)(19, 61, 31, 73)(22, 64, 32, 74)(23, 65, 37, 79)(24, 66, 38, 80)(25, 67, 33, 75)(27, 69, 36, 78)(28, 70, 35, 77)(29, 71, 39, 81)(34, 76, 42, 84)(40, 82, 41, 83)(85, 86, 89, 95, 91, 87)(88, 93, 102, 113, 103, 94)(90, 97, 107, 120, 108, 98)(92, 100, 111, 124, 112, 101)(96, 105, 118, 114, 119, 106)(99, 109, 123, 126, 122, 110)(104, 116, 125, 121, 115, 117)(127, 129, 133, 137, 131, 128)(130, 136, 145, 155, 144, 135)(132, 140, 150, 162, 149, 139)(134, 143, 154, 166, 153, 142)(138, 148, 161, 156, 160, 147)(141, 152, 164, 168, 165, 151)(146, 159, 157, 163, 167, 158) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 8^4 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E15.691 Graph:: simple bipartite v = 35 e = 84 f = 21 degree seq :: [ 4^21, 6^14 ] E15.689 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y3, Y2^-3 * Y1^3, Y2^6, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-2 * Y3 * Y1 * Y2^-1, Y3 * Y2^2 * Y3 * Y1^-2 * Y2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 43, 4, 46)(2, 44, 6, 48)(3, 45, 8, 50)(5, 47, 12, 54)(7, 49, 15, 57)(9, 51, 17, 59)(10, 52, 13, 55)(11, 53, 20, 62)(14, 56, 21, 63)(16, 58, 26, 68)(18, 60, 30, 72)(19, 61, 31, 73)(22, 64, 32, 74)(23, 65, 37, 79)(24, 66, 38, 80)(25, 67, 33, 75)(27, 69, 34, 76)(28, 70, 40, 82)(29, 71, 35, 77)(36, 78, 41, 83)(39, 81, 42, 84)(85, 86, 89, 95, 91, 87)(88, 93, 102, 113, 103, 94)(90, 97, 107, 120, 108, 98)(92, 100, 111, 122, 112, 101)(96, 105, 118, 126, 119, 106)(99, 109, 121, 115, 123, 110)(104, 116, 114, 124, 125, 117)(127, 129, 133, 137, 131, 128)(130, 136, 145, 155, 144, 135)(132, 140, 150, 162, 149, 139)(134, 143, 154, 164, 153, 142)(138, 148, 161, 168, 160, 147)(141, 152, 165, 157, 163, 151)(146, 159, 167, 166, 156, 158) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 8^4 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E15.690 Graph:: simple bipartite v = 35 e = 84 f = 21 degree seq :: [ 4^21, 6^14 ] E15.690 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^6, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^3 * Y1^-3, Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-2 * Y3 * Y1^-2, Y3 * Y2^2 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-3 ] Map:: non-degenerate R = (1, 43, 85, 127, 4, 46, 88, 130)(2, 44, 86, 128, 6, 48, 90, 132)(3, 45, 87, 129, 8, 50, 92, 134)(5, 47, 89, 131, 12, 54, 96, 138)(7, 49, 91, 133, 15, 57, 99, 141)(9, 51, 93, 135, 17, 59, 101, 143)(10, 52, 94, 136, 13, 55, 97, 139)(11, 53, 95, 137, 20, 62, 104, 146)(14, 56, 98, 140, 21, 63, 105, 147)(16, 58, 100, 142, 26, 68, 110, 152)(18, 60, 102, 144, 30, 72, 114, 156)(19, 61, 103, 145, 31, 73, 115, 157)(22, 64, 106, 148, 32, 74, 116, 158)(23, 65, 107, 149, 37, 79, 121, 163)(24, 66, 108, 150, 38, 80, 122, 164)(25, 67, 109, 151, 33, 75, 117, 159)(27, 69, 111, 153, 36, 78, 120, 162)(28, 70, 112, 154, 35, 77, 119, 161)(29, 71, 113, 155, 39, 81, 123, 165)(34, 76, 118, 160, 42, 84, 126, 168)(40, 82, 124, 166, 41, 83, 125, 167) L = (1, 44)(2, 47)(3, 43)(4, 51)(5, 53)(6, 55)(7, 45)(8, 58)(9, 60)(10, 46)(11, 49)(12, 63)(13, 65)(14, 48)(15, 67)(16, 69)(17, 50)(18, 71)(19, 52)(20, 74)(21, 76)(22, 54)(23, 78)(24, 56)(25, 81)(26, 57)(27, 82)(28, 59)(29, 61)(30, 77)(31, 75)(32, 83)(33, 62)(34, 72)(35, 64)(36, 66)(37, 73)(38, 68)(39, 84)(40, 70)(41, 79)(42, 80)(85, 129)(86, 127)(87, 133)(88, 136)(89, 128)(90, 140)(91, 137)(92, 143)(93, 130)(94, 145)(95, 131)(96, 148)(97, 132)(98, 150)(99, 152)(100, 134)(101, 154)(102, 135)(103, 155)(104, 159)(105, 138)(106, 161)(107, 139)(108, 162)(109, 141)(110, 164)(111, 142)(112, 166)(113, 144)(114, 160)(115, 163)(116, 146)(117, 157)(118, 147)(119, 156)(120, 149)(121, 167)(122, 168)(123, 151)(124, 153)(125, 158)(126, 165) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.689 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 35 degree seq :: [ 8^21 ] E15.691 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y3, Y2^-3 * Y1^3, Y2^6, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-2 * Y3 * Y1 * Y2^-1, Y3 * Y2^2 * Y3 * Y1^-2 * Y2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 43, 85, 127, 4, 46, 88, 130)(2, 44, 86, 128, 6, 48, 90, 132)(3, 45, 87, 129, 8, 50, 92, 134)(5, 47, 89, 131, 12, 54, 96, 138)(7, 49, 91, 133, 15, 57, 99, 141)(9, 51, 93, 135, 17, 59, 101, 143)(10, 52, 94, 136, 13, 55, 97, 139)(11, 53, 95, 137, 20, 62, 104, 146)(14, 56, 98, 140, 21, 63, 105, 147)(16, 58, 100, 142, 26, 68, 110, 152)(18, 60, 102, 144, 30, 72, 114, 156)(19, 61, 103, 145, 31, 73, 115, 157)(22, 64, 106, 148, 32, 74, 116, 158)(23, 65, 107, 149, 37, 79, 121, 163)(24, 66, 108, 150, 38, 80, 122, 164)(25, 67, 109, 151, 33, 75, 117, 159)(27, 69, 111, 153, 34, 76, 118, 160)(28, 70, 112, 154, 40, 82, 124, 166)(29, 71, 113, 155, 35, 77, 119, 161)(36, 78, 120, 162, 41, 83, 125, 167)(39, 81, 123, 165, 42, 84, 126, 168) L = (1, 44)(2, 47)(3, 43)(4, 51)(5, 53)(6, 55)(7, 45)(8, 58)(9, 60)(10, 46)(11, 49)(12, 63)(13, 65)(14, 48)(15, 67)(16, 69)(17, 50)(18, 71)(19, 52)(20, 74)(21, 76)(22, 54)(23, 78)(24, 56)(25, 79)(26, 57)(27, 80)(28, 59)(29, 61)(30, 82)(31, 81)(32, 72)(33, 62)(34, 84)(35, 64)(36, 66)(37, 73)(38, 70)(39, 68)(40, 83)(41, 75)(42, 77)(85, 129)(86, 127)(87, 133)(88, 136)(89, 128)(90, 140)(91, 137)(92, 143)(93, 130)(94, 145)(95, 131)(96, 148)(97, 132)(98, 150)(99, 152)(100, 134)(101, 154)(102, 135)(103, 155)(104, 159)(105, 138)(106, 161)(107, 139)(108, 162)(109, 141)(110, 165)(111, 142)(112, 164)(113, 144)(114, 158)(115, 163)(116, 146)(117, 167)(118, 147)(119, 168)(120, 149)(121, 151)(122, 153)(123, 157)(124, 156)(125, 166)(126, 160) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.688 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 35 degree seq :: [ 8^21 ] E15.692 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 6 Presentation :: [ Y1^2, Y2^2, Y3^3, R^2 * Y3^-1, Y1 * R * Y2 * R^-1, Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3 * Y1 * Y2 * Y1 * Y3^-1, Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3, (Y2 * Y1 * Y3)^3 ] Map:: polytopal non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 12, 54)(5, 47, 14, 56)(6, 48, 16, 58)(7, 49, 19, 61)(8, 50, 21, 63)(10, 52, 17, 59)(11, 53, 26, 68)(13, 55, 29, 71)(15, 57, 22, 64)(18, 60, 37, 79)(20, 62, 38, 80)(23, 65, 41, 83)(24, 66, 35, 77)(25, 67, 33, 75)(27, 69, 30, 72)(28, 70, 32, 74)(31, 73, 40, 82)(34, 76, 39, 81)(36, 78, 42, 84)(85, 127, 87, 129)(86, 128, 90, 132)(88, 130, 97, 139)(89, 131, 99, 141)(91, 133, 104, 146)(92, 134, 106, 148)(93, 135, 107, 149)(94, 136, 109, 151)(95, 137, 111, 153)(96, 138, 103, 145)(98, 140, 116, 158)(100, 142, 120, 162)(101, 143, 119, 161)(102, 144, 112, 154)(105, 147, 114, 156)(108, 150, 122, 164)(110, 152, 121, 163)(113, 155, 117, 159)(115, 157, 123, 165)(118, 160, 125, 167)(124, 166, 126, 168) L = (1, 88)(2, 91)(3, 94)(4, 89)(5, 85)(6, 101)(7, 92)(8, 86)(9, 108)(10, 95)(11, 87)(12, 112)(13, 114)(14, 100)(15, 118)(16, 117)(17, 102)(18, 90)(19, 111)(20, 116)(21, 93)(22, 124)(23, 96)(24, 105)(25, 106)(26, 125)(27, 120)(28, 107)(29, 110)(30, 115)(31, 97)(32, 123)(33, 98)(34, 119)(35, 99)(36, 103)(37, 126)(38, 121)(39, 104)(40, 109)(41, 113)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 12^4 ) } Outer automorphisms :: reflexible Dual of E15.693 Transitivity :: VT Graph:: simple bipartite v = 42 e = 84 f = 14 degree seq :: [ 4^42 ] E15.693 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 6 Presentation :: [ R^2 * Y3^-1, Y3^3, Y2 * R^-1 * Y1 * R, (Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y3^-1 * Y1^-2 * Y2^2, Y2^-3 * Y3 * Y1, Y1 * Y2 * Y1^-1 * Y3 * Y2, Y1 * Y2 * Y1^2 * Y3^-1, Y1^-1 * R * Y1 * R^-1 * Y2^-1 * Y1^-1, Y1^6, (Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 43, 2, 44, 8, 50, 32, 74, 23, 65, 5, 47)(3, 45, 13, 55, 22, 64, 35, 77, 33, 75, 16, 58)(4, 46, 18, 60, 40, 82, 29, 71, 9, 51, 20, 62)(6, 48, 25, 67, 17, 59, 37, 79, 31, 73, 27, 69)(7, 49, 30, 72, 38, 80, 15, 57, 28, 70, 10, 52)(11, 53, 36, 78, 21, 63, 41, 83, 39, 81, 19, 61)(12, 54, 24, 66, 42, 84, 34, 76, 26, 68, 14, 56)(85, 127, 87, 129, 98, 140, 102, 144, 112, 154, 90, 132)(86, 128, 93, 135, 115, 157, 91, 133, 110, 152, 95, 137)(88, 130, 103, 145, 97, 139, 114, 156, 107, 149, 101, 143)(89, 131, 105, 147, 94, 136, 119, 161, 104, 146, 108, 150)(92, 134, 99, 141, 123, 165, 96, 138, 121, 163, 117, 159)(100, 142, 120, 162, 109, 151, 126, 168, 122, 164, 113, 155)(106, 148, 111, 153, 125, 167, 124, 166, 116, 158, 118, 160) L = (1, 88)(2, 94)(3, 99)(4, 91)(5, 106)(6, 110)(7, 85)(8, 98)(9, 118)(10, 96)(11, 121)(12, 86)(13, 109)(14, 111)(15, 101)(16, 108)(17, 87)(18, 89)(19, 116)(20, 120)(21, 93)(22, 102)(23, 123)(24, 112)(25, 124)(26, 113)(27, 92)(28, 100)(29, 90)(30, 104)(31, 103)(32, 115)(33, 125)(34, 105)(35, 107)(36, 114)(37, 122)(38, 95)(39, 119)(40, 97)(41, 126)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.692 Transitivity :: VT Graph:: bipartite v = 14 e = 84 f = 42 degree seq :: [ 12^14 ] E15.694 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 6}) Quotient :: halfedge^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^6, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 ] Map:: R = (1, 44, 2, 47, 5, 53, 11, 52, 10, 46, 4, 43)(3, 49, 7, 54, 12, 62, 20, 59, 17, 50, 8, 45)(6, 55, 13, 61, 19, 60, 18, 51, 9, 56, 14, 48)(15, 65, 23, 69, 27, 67, 25, 58, 16, 66, 24, 57)(21, 70, 28, 68, 26, 72, 30, 64, 22, 71, 29, 63)(31, 79, 37, 75, 33, 81, 39, 74, 32, 80, 38, 73)(34, 82, 40, 78, 36, 84, 42, 77, 35, 83, 41, 76) 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, 42)(38, 40)(39, 41)(43, 45)(44, 48)(46, 51)(47, 54)(49, 57)(50, 58)(52, 59)(53, 61)(55, 63)(56, 64)(60, 68)(62, 69)(65, 73)(66, 74)(67, 75)(70, 76)(71, 77)(72, 78)(79, 84)(80, 82)(81, 83) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: v = 7 e = 42 f = 7 degree seq :: [ 12^7 ] E15.695 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^6, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: R = (1, 43, 3, 45, 8, 50, 17, 59, 10, 52, 4, 46)(2, 44, 5, 47, 12, 54, 21, 63, 14, 56, 6, 48)(7, 49, 15, 57, 24, 66, 18, 60, 9, 51, 16, 58)(11, 53, 19, 61, 28, 70, 22, 64, 13, 55, 20, 62)(23, 65, 31, 73, 26, 68, 33, 75, 25, 67, 32, 74)(27, 69, 34, 76, 30, 72, 36, 78, 29, 71, 35, 77)(37, 79, 41, 83, 39, 81, 40, 82, 38, 80, 42, 84)(85, 86)(87, 91)(88, 93)(89, 95)(90, 97)(92, 96)(94, 98)(99, 107)(100, 109)(101, 108)(102, 110)(103, 111)(104, 113)(105, 112)(106, 114)(115, 121)(116, 122)(117, 123)(118, 124)(119, 125)(120, 126)(127, 128)(129, 133)(130, 135)(131, 137)(132, 139)(134, 138)(136, 140)(141, 149)(142, 151)(143, 150)(144, 152)(145, 153)(146, 155)(147, 154)(148, 156)(157, 163)(158, 164)(159, 165)(160, 166)(161, 167)(162, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 24, 24 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.697 Graph:: simple bipartite v = 49 e = 84 f = 7 degree seq :: [ 2^42, 12^7 ] E15.696 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = C6 x D14 (small group id <84, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y1^6, Y3 * Y2^2 * Y3 * Y2^-2, Y3 * Y1^2 * Y3 * Y1^-2, Y2^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 43, 4, 46)(2, 44, 6, 48)(3, 45, 8, 50)(5, 47, 12, 54)(7, 49, 15, 57)(9, 51, 17, 59)(10, 52, 18, 60)(11, 53, 19, 61)(13, 55, 21, 63)(14, 56, 22, 64)(16, 58, 23, 65)(20, 62, 27, 69)(24, 66, 31, 73)(25, 67, 32, 74)(26, 68, 33, 75)(28, 70, 34, 76)(29, 71, 35, 77)(30, 72, 36, 78)(37, 79, 42, 84)(38, 80, 40, 82)(39, 81, 41, 83)(85, 86, 89, 95, 91, 87)(88, 93, 96, 104, 99, 94)(90, 97, 103, 100, 92, 98)(101, 108, 111, 110, 102, 109)(105, 112, 107, 114, 106, 113)(115, 121, 117, 123, 116, 122)(118, 124, 120, 126, 119, 125)(127, 129, 133, 137, 131, 128)(130, 136, 141, 146, 138, 135)(132, 140, 134, 142, 145, 139)(143, 151, 144, 152, 153, 150)(147, 155, 148, 156, 149, 154)(157, 164, 158, 165, 159, 163)(160, 167, 161, 168, 162, 166) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 8^4 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E15.698 Graph:: simple bipartite v = 35 e = 84 f = 21 degree seq :: [ 4^21, 6^14 ] E15.697 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^6, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: R = (1, 43, 85, 127, 3, 45, 87, 129, 8, 50, 92, 134, 17, 59, 101, 143, 10, 52, 94, 136, 4, 46, 88, 130)(2, 44, 86, 128, 5, 47, 89, 131, 12, 54, 96, 138, 21, 63, 105, 147, 14, 56, 98, 140, 6, 48, 90, 132)(7, 49, 91, 133, 15, 57, 99, 141, 24, 66, 108, 150, 18, 60, 102, 144, 9, 51, 93, 135, 16, 58, 100, 142)(11, 53, 95, 137, 19, 61, 103, 145, 28, 70, 112, 154, 22, 64, 106, 148, 13, 55, 97, 139, 20, 62, 104, 146)(23, 65, 107, 149, 31, 73, 115, 157, 26, 68, 110, 152, 33, 75, 117, 159, 25, 67, 109, 151, 32, 74, 116, 158)(27, 69, 111, 153, 34, 76, 118, 160, 30, 72, 114, 156, 36, 78, 120, 162, 29, 71, 113, 155, 35, 77, 119, 161)(37, 79, 121, 163, 41, 83, 125, 167, 39, 81, 123, 165, 40, 82, 124, 166, 38, 80, 122, 164, 42, 84, 126, 168) L = (1, 44)(2, 43)(3, 49)(4, 51)(5, 53)(6, 55)(7, 45)(8, 54)(9, 46)(10, 56)(11, 47)(12, 50)(13, 48)(14, 52)(15, 65)(16, 67)(17, 66)(18, 68)(19, 69)(20, 71)(21, 70)(22, 72)(23, 57)(24, 59)(25, 58)(26, 60)(27, 61)(28, 63)(29, 62)(30, 64)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 73)(38, 74)(39, 75)(40, 76)(41, 77)(42, 78)(85, 128)(86, 127)(87, 133)(88, 135)(89, 137)(90, 139)(91, 129)(92, 138)(93, 130)(94, 140)(95, 131)(96, 134)(97, 132)(98, 136)(99, 149)(100, 151)(101, 150)(102, 152)(103, 153)(104, 155)(105, 154)(106, 156)(107, 141)(108, 143)(109, 142)(110, 144)(111, 145)(112, 147)(113, 146)(114, 148)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 157)(122, 158)(123, 159)(124, 160)(125, 161)(126, 162) 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 E15.695 Transitivity :: VT+ Graph:: v = 7 e = 84 f = 49 degree seq :: [ 24^7 ] E15.698 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = C6 x D14 (small group id <84, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y1^6, Y3 * Y2^2 * Y3 * Y2^-2, Y3 * Y1^2 * Y3 * Y1^-2, Y2^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 43, 85, 127, 4, 46, 88, 130)(2, 44, 86, 128, 6, 48, 90, 132)(3, 45, 87, 129, 8, 50, 92, 134)(5, 47, 89, 131, 12, 54, 96, 138)(7, 49, 91, 133, 15, 57, 99, 141)(9, 51, 93, 135, 17, 59, 101, 143)(10, 52, 94, 136, 18, 60, 102, 144)(11, 53, 95, 137, 19, 61, 103, 145)(13, 55, 97, 139, 21, 63, 105, 147)(14, 56, 98, 140, 22, 64, 106, 148)(16, 58, 100, 142, 23, 65, 107, 149)(20, 62, 104, 146, 27, 69, 111, 153)(24, 66, 108, 150, 31, 73, 115, 157)(25, 67, 109, 151, 32, 74, 116, 158)(26, 68, 110, 152, 33, 75, 117, 159)(28, 70, 112, 154, 34, 76, 118, 160)(29, 71, 113, 155, 35, 77, 119, 161)(30, 72, 114, 156, 36, 78, 120, 162)(37, 79, 121, 163, 42, 84, 126, 168)(38, 80, 122, 164, 40, 82, 124, 166)(39, 81, 123, 165, 41, 83, 125, 167) L = (1, 44)(2, 47)(3, 43)(4, 51)(5, 53)(6, 55)(7, 45)(8, 56)(9, 54)(10, 46)(11, 49)(12, 62)(13, 61)(14, 48)(15, 52)(16, 50)(17, 66)(18, 67)(19, 58)(20, 57)(21, 70)(22, 71)(23, 72)(24, 69)(25, 59)(26, 60)(27, 68)(28, 65)(29, 63)(30, 64)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 75)(38, 73)(39, 74)(40, 78)(41, 76)(42, 77)(85, 129)(86, 127)(87, 133)(88, 136)(89, 128)(90, 140)(91, 137)(92, 142)(93, 130)(94, 141)(95, 131)(96, 135)(97, 132)(98, 134)(99, 146)(100, 145)(101, 151)(102, 152)(103, 139)(104, 138)(105, 155)(106, 156)(107, 154)(108, 143)(109, 144)(110, 153)(111, 150)(112, 147)(113, 148)(114, 149)(115, 164)(116, 165)(117, 163)(118, 167)(119, 168)(120, 166)(121, 157)(122, 158)(123, 159)(124, 160)(125, 161)(126, 162) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.696 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 35 degree seq :: [ 8^21 ] E15.699 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ 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, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2^6, (Y3 * Y2^-1)^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 ] Map:: R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 9, 51)(5, 47, 11, 53)(6, 48, 13, 55)(8, 50, 12, 54)(10, 52, 14, 56)(15, 57, 23, 65)(16, 58, 25, 67)(17, 59, 24, 66)(18, 60, 26, 68)(19, 61, 27, 69)(20, 62, 29, 71)(21, 63, 28, 70)(22, 64, 30, 72)(31, 73, 37, 79)(32, 74, 38, 80)(33, 75, 39, 81)(34, 76, 40, 82)(35, 77, 41, 83)(36, 78, 42, 84)(85, 127, 87, 129, 92, 134, 101, 143, 94, 136, 88, 130)(86, 128, 89, 131, 96, 138, 105, 147, 98, 140, 90, 132)(91, 133, 99, 141, 108, 150, 102, 144, 93, 135, 100, 142)(95, 137, 103, 145, 112, 154, 106, 148, 97, 139, 104, 146)(107, 149, 115, 157, 110, 152, 117, 159, 109, 151, 116, 158)(111, 153, 118, 160, 114, 156, 120, 162, 113, 155, 119, 161)(121, 163, 125, 167, 123, 165, 124, 166, 122, 164, 126, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 28 e = 84 f = 28 degree seq :: [ 4^21, 12^7 ] E15.700 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-1 * Y1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^7, Y3^3 * Y1 * Y2 * Y3^2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 10, 52)(5, 47, 17, 59)(6, 48, 8, 50)(7, 49, 21, 63)(9, 51, 24, 66)(12, 54, 16, 58)(13, 55, 27, 69)(14, 56, 19, 61)(15, 57, 26, 68)(18, 60, 30, 72)(20, 62, 23, 65)(22, 64, 33, 75)(25, 67, 36, 78)(28, 70, 39, 81)(29, 71, 38, 80)(31, 73, 41, 83)(32, 74, 35, 77)(34, 76, 40, 82)(37, 79, 42, 84)(85, 127, 87, 129, 96, 138, 92, 134, 103, 145, 89, 131)(86, 128, 91, 133, 100, 142, 88, 130, 98, 140, 93, 135)(90, 132, 97, 139, 101, 143, 107, 149, 95, 137, 102, 144)(94, 136, 106, 148, 108, 150, 99, 141, 105, 147, 109, 151)(104, 146, 112, 154, 114, 156, 119, 161, 111, 153, 115, 157)(110, 152, 118, 160, 120, 162, 113, 155, 117, 159, 121, 163)(116, 158, 124, 166, 125, 167, 122, 164, 123, 165, 126, 168) L = (1, 88)(2, 92)(3, 97)(4, 99)(5, 102)(6, 85)(7, 106)(8, 107)(9, 109)(10, 86)(11, 103)(12, 93)(13, 112)(14, 87)(15, 113)(16, 89)(17, 96)(18, 115)(19, 91)(20, 90)(21, 98)(22, 118)(23, 119)(24, 100)(25, 121)(26, 94)(27, 95)(28, 124)(29, 116)(30, 101)(31, 126)(32, 104)(33, 105)(34, 123)(35, 122)(36, 108)(37, 125)(38, 110)(39, 111)(40, 117)(41, 114)(42, 120)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 28 e = 84 f = 28 degree seq :: [ 4^21, 12^7 ] E15.701 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 7, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 13, 5)(2, 7, 17, 29, 30, 18, 8)(4, 10, 20, 31, 34, 23, 12)(6, 15, 27, 37, 38, 28, 16)(11, 21, 32, 39, 40, 33, 22)(14, 25, 35, 41, 42, 36, 26)(43, 44, 48, 56, 53, 46)(45, 49, 57, 67, 63, 52)(47, 50, 58, 68, 64, 54)(51, 59, 69, 77, 74, 62)(55, 60, 70, 78, 75, 65)(61, 71, 79, 83, 81, 73)(66, 72, 80, 84, 82, 76) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 84^6 ), ( 84^7 ) } Outer automorphisms :: reflexible Dual of E15.705 Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 42 f = 1 degree seq :: [ 6^7, 7^6 ] E15.702 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 7, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6 * T1^-1, T1^7, (T1^-1 * T2^-1)^6 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 30, 29, 16, 6, 15, 28, 38, 37, 27, 14, 26, 36, 42, 40, 33, 22, 32, 39, 41, 34, 23, 11, 21, 31, 35, 24, 12, 4, 10, 20, 25, 13, 5)(43, 44, 48, 56, 64, 53, 46)(45, 49, 57, 68, 74, 63, 52)(47, 50, 58, 69, 75, 65, 54)(51, 59, 70, 78, 81, 73, 62)(55, 60, 71, 79, 82, 76, 66)(61, 72, 80, 84, 83, 77, 67) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 12^7 ), ( 12^42 ) } Outer automorphisms :: reflexible Dual of E15.706 Transitivity :: ET+ Graph:: bipartite v = 7 e = 42 f = 7 degree seq :: [ 7^6, 42 ] E15.703 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 7, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6, T2^-1 * T1^3 * T2 * T1^-3, T2^-1 * T1^-7, T1 * T2^-1 * T1^2 * T2^-1 * T1^3 * T2^-1 * T1 * T2^-2, (T1^-1 * T2^-1)^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 13, 5)(2, 7, 17, 30, 18, 8)(4, 10, 20, 31, 24, 12)(6, 15, 28, 38, 29, 16)(11, 21, 32, 39, 34, 23)(14, 26, 36, 42, 37, 27)(22, 33, 40, 41, 35, 25)(43, 44, 48, 56, 67, 65, 54, 47, 50, 58, 69, 77, 76, 66, 55, 60, 71, 79, 83, 81, 73, 61, 72, 80, 84, 82, 74, 62, 51, 59, 70, 78, 75, 63, 52, 45, 49, 57, 68, 64, 53, 46) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14^6 ), ( 14^42 ) } Outer automorphisms :: reflexible Dual of E15.704 Transitivity :: ET+ Graph:: bipartite v = 8 e = 42 f = 6 degree seq :: [ 6^7, 42 ] E15.704 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 7, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^7 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 24, 66, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 29, 71, 30, 72, 18, 60, 8, 50)(4, 46, 10, 52, 20, 62, 31, 73, 34, 76, 23, 65, 12, 54)(6, 48, 15, 57, 27, 69, 37, 79, 38, 80, 28, 70, 16, 58)(11, 53, 21, 63, 32, 74, 39, 81, 40, 82, 33, 75, 22, 64)(14, 56, 25, 67, 35, 77, 41, 83, 42, 84, 36, 78, 26, 68) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 53)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 51)(21, 52)(22, 54)(23, 55)(24, 72)(25, 63)(26, 64)(27, 77)(28, 78)(29, 79)(30, 80)(31, 61)(32, 62)(33, 65)(34, 66)(35, 74)(36, 75)(37, 83)(38, 84)(39, 73)(40, 76)(41, 81)(42, 82) local type(s) :: { ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E15.703 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 42 f = 8 degree seq :: [ 14^6 ] E15.705 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 7, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6 * T1^-1, T1^7, (T1^-1 * T2^-1)^6 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 18, 60, 8, 50, 2, 44, 7, 49, 17, 59, 30, 72, 29, 71, 16, 58, 6, 48, 15, 57, 28, 70, 38, 80, 37, 79, 27, 69, 14, 56, 26, 68, 36, 78, 42, 84, 40, 82, 33, 75, 22, 64, 32, 74, 39, 81, 41, 83, 34, 76, 23, 65, 11, 53, 21, 63, 31, 73, 35, 77, 24, 66, 12, 54, 4, 46, 10, 52, 20, 62, 25, 67, 13, 55, 5, 47) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 64)(15, 68)(16, 69)(17, 70)(18, 71)(19, 72)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 61)(26, 74)(27, 75)(28, 78)(29, 79)(30, 80)(31, 62)(32, 63)(33, 65)(34, 66)(35, 67)(36, 81)(37, 82)(38, 84)(39, 73)(40, 76)(41, 77)(42, 83) local type(s) :: { ( 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7 ) } Outer automorphisms :: reflexible Dual of E15.701 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 13 degree seq :: [ 84 ] E15.706 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 7, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^6, T2^-1 * T1^3 * T2 * T1^-3, T2^-1 * T1^-7, T1 * T2^-1 * T1^2 * T2^-1 * T1^3 * T2^-1 * T1 * T2^-2, (T1^-1 * T2^-1)^7 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 30, 72, 18, 60, 8, 50)(4, 46, 10, 52, 20, 62, 31, 73, 24, 66, 12, 54)(6, 48, 15, 57, 28, 70, 38, 80, 29, 71, 16, 58)(11, 53, 21, 63, 32, 74, 39, 81, 34, 76, 23, 65)(14, 56, 26, 68, 36, 78, 42, 84, 37, 79, 27, 69)(22, 64, 33, 75, 40, 82, 41, 83, 35, 77, 25, 67) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 56)(7, 57)(8, 58)(9, 59)(10, 45)(11, 46)(12, 47)(13, 60)(14, 67)(15, 68)(16, 69)(17, 70)(18, 71)(19, 72)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 65)(26, 64)(27, 77)(28, 78)(29, 79)(30, 80)(31, 61)(32, 62)(33, 63)(34, 66)(35, 76)(36, 75)(37, 83)(38, 84)(39, 73)(40, 74)(41, 81)(42, 82) local type(s) :: { ( 7, 42, 7, 42, 7, 42, 7, 42, 7, 42, 7, 42 ) } Outer automorphisms :: reflexible Dual of E15.702 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 42 f = 7 degree seq :: [ 12^7 ] E15.707 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 7, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y1^6, Y2^7, Y3^42 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 25, 67, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 26, 68, 22, 64, 12, 54)(9, 51, 17, 59, 27, 69, 35, 77, 32, 74, 20, 62)(13, 55, 18, 60, 28, 70, 36, 78, 33, 75, 23, 65)(19, 61, 29, 71, 37, 79, 41, 83, 39, 81, 31, 73)(24, 66, 30, 72, 38, 80, 42, 84, 40, 82, 34, 76)(85, 127, 87, 129, 93, 135, 103, 145, 108, 150, 97, 139, 89, 131)(86, 128, 91, 133, 101, 143, 113, 155, 114, 156, 102, 144, 92, 134)(88, 130, 94, 136, 104, 146, 115, 157, 118, 160, 107, 149, 96, 138)(90, 132, 99, 141, 111, 153, 121, 163, 122, 164, 112, 154, 100, 142)(95, 137, 105, 147, 116, 158, 123, 165, 124, 166, 117, 159, 106, 148)(98, 140, 109, 151, 119, 161, 125, 167, 126, 168, 120, 162, 110, 152) L = (1, 88)(2, 85)(3, 94)(4, 95)(5, 96)(6, 86)(7, 87)(8, 89)(9, 104)(10, 105)(11, 98)(12, 106)(13, 107)(14, 90)(15, 91)(16, 92)(17, 93)(18, 97)(19, 115)(20, 116)(21, 109)(22, 110)(23, 117)(24, 118)(25, 99)(26, 100)(27, 101)(28, 102)(29, 103)(30, 108)(31, 123)(32, 119)(33, 120)(34, 124)(35, 111)(36, 112)(37, 113)(38, 114)(39, 125)(40, 126)(41, 121)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84 ), ( 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84 ) } Outer automorphisms :: reflexible Dual of E15.710 Graph:: bipartite v = 13 e = 84 f = 43 degree seq :: [ 12^7, 14^6 ] E15.708 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 7, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^6 * Y1^-1, Y1^7, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 22, 64, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 26, 68, 32, 74, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 27, 69, 33, 75, 23, 65, 12, 54)(9, 51, 17, 59, 28, 70, 36, 78, 39, 81, 31, 73, 20, 62)(13, 55, 18, 60, 29, 71, 37, 79, 40, 82, 34, 76, 24, 66)(19, 61, 30, 72, 38, 80, 42, 84, 41, 83, 35, 77, 25, 67)(85, 127, 87, 129, 93, 135, 103, 145, 102, 144, 92, 134, 86, 128, 91, 133, 101, 143, 114, 156, 113, 155, 100, 142, 90, 132, 99, 141, 112, 154, 122, 164, 121, 163, 111, 153, 98, 140, 110, 152, 120, 162, 126, 168, 124, 166, 117, 159, 106, 148, 116, 158, 123, 165, 125, 167, 118, 160, 107, 149, 95, 137, 105, 147, 115, 157, 119, 161, 108, 150, 96, 138, 88, 130, 94, 136, 104, 146, 109, 151, 97, 139, 89, 131) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 110)(15, 112)(16, 90)(17, 114)(18, 92)(19, 102)(20, 109)(21, 115)(22, 116)(23, 95)(24, 96)(25, 97)(26, 120)(27, 98)(28, 122)(29, 100)(30, 113)(31, 119)(32, 123)(33, 106)(34, 107)(35, 108)(36, 126)(37, 111)(38, 121)(39, 125)(40, 117)(41, 118)(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) :: { ( 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 E15.709 Graph:: bipartite v = 7 e = 84 f = 49 degree seq :: [ 14^6, 84 ] E15.709 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 7, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y2^6, Y3^7 * Y2^-1, (Y2^-1 * Y3)^7, (Y3^-1 * Y1^-1)^42 ] Map:: R = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(85, 127, 86, 128, 90, 132, 98, 140, 95, 137, 88, 130)(87, 129, 91, 133, 99, 141, 109, 151, 105, 147, 94, 136)(89, 131, 92, 134, 100, 142, 110, 152, 106, 148, 96, 138)(93, 135, 101, 143, 111, 153, 119, 161, 116, 158, 104, 146)(97, 139, 102, 144, 112, 154, 120, 162, 117, 159, 107, 149)(103, 145, 113, 155, 121, 163, 125, 167, 123, 165, 115, 157)(108, 150, 114, 156, 122, 164, 126, 168, 124, 166, 118, 160) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 109)(15, 111)(16, 90)(17, 113)(18, 92)(19, 114)(20, 115)(21, 116)(22, 95)(23, 96)(24, 97)(25, 119)(26, 98)(27, 121)(28, 100)(29, 122)(30, 102)(31, 108)(32, 123)(33, 106)(34, 107)(35, 125)(36, 110)(37, 126)(38, 112)(39, 118)(40, 117)(41, 124)(42, 120)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 14, 84 ), ( 14, 84, 14, 84, 14, 84, 14, 84, 14, 84, 14, 84 ) } Outer automorphisms :: reflexible Dual of E15.708 Graph:: simple bipartite v = 49 e = 84 f = 7 degree seq :: [ 2^42, 12^7 ] E15.710 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 7, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-7, Y1^4 * Y3^2 * Y1^3 * Y3^-1, Y1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^2, Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1 * Y3^-3, (Y3 * Y2^-1)^6 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 25, 67, 23, 65, 12, 54, 5, 47, 8, 50, 16, 58, 27, 69, 35, 77, 34, 76, 24, 66, 13, 55, 18, 60, 29, 71, 37, 79, 41, 83, 39, 81, 31, 73, 19, 61, 30, 72, 38, 80, 42, 84, 40, 82, 32, 74, 20, 62, 9, 51, 17, 59, 28, 70, 36, 78, 33, 75, 21, 63, 10, 52, 3, 45, 7, 49, 15, 57, 26, 68, 22, 64, 11, 53, 4, 46)(85, 127)(86, 128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95, 137)(96, 138)(97, 139)(98, 140)(99, 141)(100, 142)(101, 143)(102, 144)(103, 145)(104, 146)(105, 147)(106, 148)(107, 149)(108, 150)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 157)(116, 158)(117, 159)(118, 160)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 110)(15, 112)(16, 90)(17, 114)(18, 92)(19, 97)(20, 115)(21, 116)(22, 117)(23, 95)(24, 96)(25, 106)(26, 120)(27, 98)(28, 122)(29, 100)(30, 102)(31, 108)(32, 123)(33, 124)(34, 107)(35, 109)(36, 126)(37, 111)(38, 113)(39, 118)(40, 125)(41, 119)(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) :: { ( 12, 14 ), ( 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14 ) } Outer automorphisms :: reflexible Dual of E15.707 Graph:: bipartite v = 43 e = 84 f = 13 degree seq :: [ 2^42, 84 ] E15.711 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 7, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^6, Y1^6, Y3 * Y2^-7, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^2 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 25, 67, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 26, 68, 22, 64, 12, 54)(9, 51, 17, 59, 27, 69, 35, 77, 33, 75, 20, 62)(13, 55, 18, 60, 28, 70, 36, 78, 34, 76, 23, 65)(19, 61, 29, 71, 37, 79, 41, 83, 40, 82, 32, 74)(24, 66, 30, 72, 38, 80, 42, 84, 39, 81, 31, 73)(85, 127, 87, 129, 93, 135, 103, 145, 115, 157, 107, 149, 96, 138, 88, 130, 94, 136, 104, 146, 116, 158, 123, 165, 118, 160, 106, 148, 95, 137, 105, 147, 117, 159, 124, 166, 126, 168, 120, 162, 110, 152, 98, 140, 109, 151, 119, 161, 125, 167, 122, 164, 112, 154, 100, 142, 90, 132, 99, 141, 111, 153, 121, 163, 114, 156, 102, 144, 92, 134, 86, 128, 91, 133, 101, 143, 113, 155, 108, 150, 97, 139, 89, 131) L = (1, 88)(2, 85)(3, 94)(4, 95)(5, 96)(6, 86)(7, 87)(8, 89)(9, 104)(10, 105)(11, 98)(12, 106)(13, 107)(14, 90)(15, 91)(16, 92)(17, 93)(18, 97)(19, 116)(20, 117)(21, 109)(22, 110)(23, 118)(24, 115)(25, 99)(26, 100)(27, 101)(28, 102)(29, 103)(30, 108)(31, 123)(32, 124)(33, 119)(34, 120)(35, 111)(36, 112)(37, 113)(38, 114)(39, 126)(40, 125)(41, 121)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.712 Graph:: bipartite v = 8 e = 84 f = 48 degree seq :: [ 12^7, 84 ] E15.712 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 7, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^6, Y1^7, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^42 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 22, 64, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 26, 68, 32, 74, 21, 63, 10, 52)(5, 47, 8, 50, 16, 58, 27, 69, 33, 75, 23, 65, 12, 54)(9, 51, 17, 59, 28, 70, 36, 78, 39, 81, 31, 73, 20, 62)(13, 55, 18, 60, 29, 71, 37, 79, 40, 82, 34, 76, 24, 66)(19, 61, 30, 72, 38, 80, 42, 84, 41, 83, 35, 77, 25, 67)(85, 127)(86, 128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95, 137)(96, 138)(97, 139)(98, 140)(99, 141)(100, 142)(101, 143)(102, 144)(103, 145)(104, 146)(105, 147)(106, 148)(107, 149)(108, 150)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 157)(116, 158)(117, 159)(118, 160)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 104)(11, 105)(12, 88)(13, 89)(14, 110)(15, 112)(16, 90)(17, 114)(18, 92)(19, 102)(20, 109)(21, 115)(22, 116)(23, 95)(24, 96)(25, 97)(26, 120)(27, 98)(28, 122)(29, 100)(30, 113)(31, 119)(32, 123)(33, 106)(34, 107)(35, 108)(36, 126)(37, 111)(38, 121)(39, 125)(40, 117)(41, 118)(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) :: { ( 12, 84 ), ( 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84 ) } Outer automorphisms :: reflexible Dual of E15.711 Graph:: simple bipartite v = 48 e = 84 f = 8 degree seq :: [ 2^42, 14^6 ] E15.713 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 11, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^11 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 40, 32, 24, 16, 8)(4, 10, 18, 26, 34, 41, 42, 35, 27, 19, 11)(6, 13, 21, 29, 37, 43, 44, 38, 30, 22, 14)(45, 46, 50, 48)(47, 51, 57, 54)(49, 52, 58, 55)(53, 59, 65, 62)(56, 60, 66, 63)(61, 67, 73, 70)(64, 68, 74, 71)(69, 75, 81, 78)(72, 76, 82, 79)(77, 83, 87, 85)(80, 84, 88, 86) L = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 88^4 ), ( 88^11 ) } Outer automorphisms :: reflexible Dual of E15.717 Transitivity :: ET+ Graph:: simple bipartite v = 15 e = 44 f = 1 degree seq :: [ 4^11, 11^4 ] E15.714 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 11, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^-4, (T1^-1 * T2^-1)^4, T2^-8 * T1^3, T1^3 * T2^-1 * T1^3 * T2^-3 * T1, T1^11, T2^44 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 41, 39, 28, 14, 27, 24, 12, 4, 10, 20, 34, 42, 40, 30, 16, 6, 15, 29, 23, 11, 21, 35, 43, 37, 32, 18, 8, 2, 7, 17, 31, 22, 36, 44, 38, 26, 25, 13, 5)(45, 46, 50, 58, 70, 81, 86, 77, 66, 55, 48)(47, 51, 59, 71, 69, 76, 84, 85, 80, 65, 54)(49, 52, 60, 72, 82, 87, 78, 63, 75, 67, 56)(53, 61, 73, 68, 57, 62, 74, 83, 88, 79, 64) L = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 8^11 ), ( 8^44 ) } Outer automorphisms :: reflexible Dual of E15.718 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 11 degree seq :: [ 11^4, 44 ] E15.715 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 11, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-11, (T1^-1 * T2^-1)^11 ] Map:: non-degenerate R = (1, 3, 9, 5)(2, 7, 16, 8)(4, 10, 17, 12)(6, 14, 24, 15)(11, 18, 25, 20)(13, 22, 32, 23)(19, 26, 33, 28)(21, 30, 40, 31)(27, 34, 41, 36)(29, 38, 44, 39)(35, 37, 43, 42)(45, 46, 50, 57, 65, 73, 81, 78, 70, 62, 54, 47, 51, 58, 66, 74, 82, 87, 85, 77, 69, 61, 53, 60, 68, 76, 84, 88, 86, 80, 72, 64, 56, 49, 52, 59, 67, 75, 83, 79, 71, 63, 55, 48) L = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88) local type(s) :: { ( 22^4 ), ( 22^44 ) } Outer automorphisms :: reflexible Dual of E15.716 Transitivity :: ET+ Graph:: bipartite v = 12 e = 44 f = 4 degree seq :: [ 4^11, 44 ] E15.716 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 11, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^11 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 17, 61, 25, 69, 33, 77, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49)(2, 46, 7, 51, 15, 59, 23, 67, 31, 75, 39, 83, 40, 84, 32, 76, 24, 68, 16, 60, 8, 52)(4, 48, 10, 54, 18, 62, 26, 70, 34, 78, 41, 85, 42, 86, 35, 79, 27, 71, 19, 63, 11, 55)(6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 43, 87, 44, 88, 38, 82, 30, 74, 22, 66, 14, 58) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 48)(7, 57)(8, 58)(9, 59)(10, 47)(11, 49)(12, 60)(13, 54)(14, 55)(15, 65)(16, 66)(17, 67)(18, 53)(19, 56)(20, 68)(21, 62)(22, 63)(23, 73)(24, 74)(25, 75)(26, 61)(27, 64)(28, 76)(29, 70)(30, 71)(31, 81)(32, 82)(33, 83)(34, 69)(35, 72)(36, 84)(37, 78)(38, 79)(39, 87)(40, 88)(41, 77)(42, 80)(43, 85)(44, 86) local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E15.715 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 44 f = 12 degree seq :: [ 22^4 ] E15.717 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 11, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^-4, (T1^-1 * T2^-1)^4, T2^-8 * T1^3, T1^3 * T2^-1 * T1^3 * T2^-3 * T1, T1^11, T2^44 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 41, 85, 39, 83, 28, 72, 14, 58, 27, 71, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 34, 78, 42, 86, 40, 84, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 23, 67, 11, 55, 21, 65, 35, 79, 43, 87, 37, 81, 32, 76, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 31, 75, 22, 66, 36, 80, 44, 88, 38, 82, 26, 70, 25, 69, 13, 57, 5, 49) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 58)(7, 59)(8, 60)(9, 61)(10, 47)(11, 48)(12, 49)(13, 62)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 76)(26, 81)(27, 69)(28, 82)(29, 68)(30, 83)(31, 67)(32, 84)(33, 66)(34, 63)(35, 64)(36, 65)(37, 86)(38, 87)(39, 88)(40, 85)(41, 80)(42, 77)(43, 78)(44, 79) local type(s) :: { ( 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11, 4, 11 ) } Outer automorphisms :: reflexible Dual of E15.713 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 15 degree seq :: [ 88 ] E15.718 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 11, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-11, (T1^-1 * T2^-1)^11 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 5, 49)(2, 46, 7, 51, 16, 60, 8, 52)(4, 48, 10, 54, 17, 61, 12, 56)(6, 50, 14, 58, 24, 68, 15, 59)(11, 55, 18, 62, 25, 69, 20, 64)(13, 57, 22, 66, 32, 76, 23, 67)(19, 63, 26, 70, 33, 77, 28, 72)(21, 65, 30, 74, 40, 84, 31, 75)(27, 71, 34, 78, 41, 85, 36, 80)(29, 73, 38, 82, 44, 88, 39, 83)(35, 79, 37, 81, 43, 87, 42, 86) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 57)(7, 58)(8, 59)(9, 60)(10, 47)(11, 48)(12, 49)(13, 65)(14, 66)(15, 67)(16, 68)(17, 53)(18, 54)(19, 55)(20, 56)(21, 73)(22, 74)(23, 75)(24, 76)(25, 61)(26, 62)(27, 63)(28, 64)(29, 81)(30, 82)(31, 83)(32, 84)(33, 69)(34, 70)(35, 71)(36, 72)(37, 78)(38, 87)(39, 79)(40, 88)(41, 77)(42, 80)(43, 85)(44, 86) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E15.714 Transitivity :: ET+ VT+ AT Graph:: v = 11 e = 44 f = 5 degree seq :: [ 8^11 ] E15.719 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 11, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^11, Y3^44 ] Map:: R = (1, 45, 2, 46, 6, 50, 4, 48)(3, 47, 7, 51, 13, 57, 10, 54)(5, 49, 8, 52, 14, 58, 11, 55)(9, 53, 15, 59, 21, 65, 18, 62)(12, 56, 16, 60, 22, 66, 19, 63)(17, 61, 23, 67, 29, 73, 26, 70)(20, 64, 24, 68, 30, 74, 27, 71)(25, 69, 31, 75, 37, 81, 34, 78)(28, 72, 32, 76, 38, 82, 35, 79)(33, 77, 39, 83, 43, 87, 41, 85)(36, 80, 40, 84, 44, 88, 42, 86)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137)(90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 128, 172, 120, 164, 112, 156, 104, 148, 96, 140)(92, 136, 98, 142, 106, 150, 114, 158, 122, 166, 129, 173, 130, 174, 123, 167, 115, 159, 107, 151, 99, 143)(94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 131, 175, 132, 176, 126, 170, 118, 162, 110, 154, 102, 146) L = (1, 92)(2, 89)(3, 98)(4, 94)(5, 99)(6, 90)(7, 91)(8, 93)(9, 106)(10, 101)(11, 102)(12, 107)(13, 95)(14, 96)(15, 97)(16, 100)(17, 114)(18, 109)(19, 110)(20, 115)(21, 103)(22, 104)(23, 105)(24, 108)(25, 122)(26, 117)(27, 118)(28, 123)(29, 111)(30, 112)(31, 113)(32, 116)(33, 129)(34, 125)(35, 126)(36, 130)(37, 119)(38, 120)(39, 121)(40, 124)(41, 131)(42, 132)(43, 127)(44, 128)(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) :: { ( 2, 88, 2, 88, 2, 88, 2, 88 ), ( 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88 ) } Outer automorphisms :: reflexible Dual of E15.722 Graph:: bipartite v = 15 e = 88 f = 45 degree seq :: [ 8^11, 22^4 ] E15.720 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 11, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^4, (Y3^-1 * Y1^-1)^4, Y2^8 * Y1^-3, Y1 * Y2^-1 * Y1 * Y2^-7 * Y1, Y1^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 37, 81, 42, 86, 33, 77, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 25, 69, 32, 76, 40, 84, 41, 85, 36, 80, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 28, 72, 38, 82, 43, 87, 34, 78, 19, 63, 31, 75, 23, 67, 12, 56)(9, 53, 17, 61, 29, 73, 24, 68, 13, 57, 18, 62, 30, 74, 39, 83, 44, 88, 35, 79, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 121, 165, 129, 173, 127, 171, 116, 160, 102, 146, 115, 159, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 122, 166, 130, 174, 128, 172, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 111, 155, 99, 143, 109, 153, 123, 167, 131, 175, 125, 169, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 110, 154, 124, 168, 132, 176, 126, 170, 114, 158, 113, 157, 101, 145, 93, 137) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 115)(15, 117)(16, 94)(17, 119)(18, 96)(19, 121)(20, 122)(21, 123)(22, 124)(23, 99)(24, 100)(25, 101)(26, 113)(27, 112)(28, 102)(29, 111)(30, 104)(31, 110)(32, 106)(33, 129)(34, 130)(35, 131)(36, 132)(37, 120)(38, 114)(39, 116)(40, 118)(41, 127)(42, 128)(43, 125)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.721 Graph:: bipartite v = 5 e = 88 f = 55 degree seq :: [ 22^4, 88 ] E15.721 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 11, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y3, Y2^-1), Y3^-11 * Y2^-1, (Y2^-1 * Y3)^11, (Y3^-1 * Y1^-1)^44 ] Map:: R = (1, 45)(2, 46)(3, 47)(4, 48)(5, 49)(6, 50)(7, 51)(8, 52)(9, 53)(10, 54)(11, 55)(12, 56)(13, 57)(14, 58)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 69)(26, 70)(27, 71)(28, 72)(29, 73)(30, 74)(31, 75)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 82)(39, 83)(40, 84)(41, 85)(42, 86)(43, 87)(44, 88)(89, 133, 90, 134, 94, 138, 92, 136)(91, 135, 95, 139, 101, 145, 98, 142)(93, 137, 96, 140, 102, 146, 99, 143)(97, 141, 103, 147, 109, 153, 106, 150)(100, 144, 104, 148, 110, 154, 107, 151)(105, 149, 111, 155, 117, 161, 114, 158)(108, 152, 112, 156, 118, 162, 115, 159)(113, 157, 119, 163, 125, 169, 122, 166)(116, 160, 120, 164, 126, 170, 123, 167)(121, 165, 127, 171, 131, 175, 130, 174)(124, 168, 128, 172, 132, 176, 129, 173) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 101)(7, 103)(8, 90)(9, 105)(10, 106)(11, 92)(12, 93)(13, 109)(14, 94)(15, 111)(16, 96)(17, 113)(18, 114)(19, 99)(20, 100)(21, 117)(22, 102)(23, 119)(24, 104)(25, 121)(26, 122)(27, 107)(28, 108)(29, 125)(30, 110)(31, 127)(32, 112)(33, 129)(34, 130)(35, 115)(36, 116)(37, 131)(38, 118)(39, 124)(40, 120)(41, 123)(42, 132)(43, 128)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E15.720 Graph:: simple bipartite v = 55 e = 88 f = 5 degree seq :: [ 2^44, 8^11 ] E15.722 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 11, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3 * Y1^-11, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 34, 78, 26, 70, 18, 62, 10, 54, 3, 47, 7, 51, 14, 58, 22, 66, 30, 74, 38, 82, 43, 87, 41, 85, 33, 77, 25, 69, 17, 61, 9, 53, 16, 60, 24, 68, 32, 76, 40, 84, 44, 88, 42, 86, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49, 8, 52, 15, 59, 23, 67, 31, 75, 39, 83, 35, 79, 27, 71, 19, 63, 11, 55, 4, 48)(89, 133)(90, 134)(91, 135)(92, 136)(93, 137)(94, 138)(95, 139)(96, 140)(97, 141)(98, 142)(99, 143)(100, 144)(101, 145)(102, 146)(103, 147)(104, 148)(105, 149)(106, 150)(107, 151)(108, 152)(109, 153)(110, 154)(111, 155)(112, 156)(113, 157)(114, 158)(115, 159)(116, 160)(117, 161)(118, 162)(119, 163)(120, 164)(121, 165)(122, 166)(123, 167)(124, 168)(125, 169)(126, 170)(127, 171)(128, 172)(129, 173)(130, 174)(131, 175)(132, 176) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 102)(7, 104)(8, 90)(9, 93)(10, 105)(11, 106)(12, 92)(13, 110)(14, 112)(15, 94)(16, 96)(17, 100)(18, 113)(19, 114)(20, 99)(21, 118)(22, 120)(23, 101)(24, 103)(25, 108)(26, 121)(27, 122)(28, 107)(29, 126)(30, 128)(31, 109)(32, 111)(33, 116)(34, 129)(35, 125)(36, 115)(37, 131)(38, 132)(39, 117)(40, 119)(41, 124)(42, 123)(43, 130)(44, 127)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 8, 22 ), ( 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22, 8, 22 ) } Outer automorphisms :: reflexible Dual of E15.719 Graph:: bipartite v = 45 e = 88 f = 15 degree seq :: [ 2^44, 88 ] E15.723 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 11, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^4, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y2^11 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 4, 48)(3, 47, 7, 51, 13, 57, 10, 54)(5, 49, 8, 52, 14, 58, 11, 55)(9, 53, 15, 59, 21, 65, 18, 62)(12, 56, 16, 60, 22, 66, 19, 63)(17, 61, 23, 67, 29, 73, 26, 70)(20, 64, 24, 68, 30, 74, 27, 71)(25, 69, 31, 75, 37, 81, 34, 78)(28, 72, 32, 76, 38, 82, 35, 79)(33, 77, 39, 83, 43, 87, 41, 85)(36, 80, 40, 84, 44, 88, 42, 86)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 128, 172, 120, 164, 112, 156, 104, 148, 96, 140, 90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 132, 176, 126, 170, 118, 162, 110, 154, 102, 146, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 131, 175, 130, 174, 123, 167, 115, 159, 107, 151, 99, 143, 92, 136, 98, 142, 106, 150, 114, 158, 122, 166, 129, 173, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 94)(5, 99)(6, 90)(7, 91)(8, 93)(9, 106)(10, 101)(11, 102)(12, 107)(13, 95)(14, 96)(15, 97)(16, 100)(17, 114)(18, 109)(19, 110)(20, 115)(21, 103)(22, 104)(23, 105)(24, 108)(25, 122)(26, 117)(27, 118)(28, 123)(29, 111)(30, 112)(31, 113)(32, 116)(33, 129)(34, 125)(35, 126)(36, 130)(37, 119)(38, 120)(39, 121)(40, 124)(41, 131)(42, 132)(43, 127)(44, 128)(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) :: { ( 2, 22, 2, 22, 2, 22, 2, 22 ), ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E15.724 Graph:: bipartite v = 12 e = 88 f = 48 degree seq :: [ 8^11, 88 ] E15.724 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 11, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-4 * Y1^-4, Y3^-8 * Y1^3, Y1^4 * Y3^-1 * Y1^3 * Y3^-3, Y1^11, (Y3 * Y2^-1)^44 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 37, 81, 42, 86, 33, 77, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 25, 69, 32, 76, 40, 84, 41, 85, 36, 80, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 28, 72, 38, 82, 43, 87, 34, 78, 19, 63, 31, 75, 23, 67, 12, 56)(9, 53, 17, 61, 29, 73, 24, 68, 13, 57, 18, 62, 30, 74, 39, 83, 44, 88, 35, 79, 20, 64)(89, 133)(90, 134)(91, 135)(92, 136)(93, 137)(94, 138)(95, 139)(96, 140)(97, 141)(98, 142)(99, 143)(100, 144)(101, 145)(102, 146)(103, 147)(104, 148)(105, 149)(106, 150)(107, 151)(108, 152)(109, 153)(110, 154)(111, 155)(112, 156)(113, 157)(114, 158)(115, 159)(116, 160)(117, 161)(118, 162)(119, 163)(120, 164)(121, 165)(122, 166)(123, 167)(124, 168)(125, 169)(126, 170)(127, 171)(128, 172)(129, 173)(130, 174)(131, 175)(132, 176) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 115)(15, 117)(16, 94)(17, 119)(18, 96)(19, 121)(20, 122)(21, 123)(22, 124)(23, 99)(24, 100)(25, 101)(26, 113)(27, 112)(28, 102)(29, 111)(30, 104)(31, 110)(32, 106)(33, 129)(34, 130)(35, 131)(36, 132)(37, 120)(38, 114)(39, 116)(40, 118)(41, 127)(42, 128)(43, 125)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 8, 88 ), ( 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88 ) } Outer automorphisms :: reflexible Dual of E15.723 Graph:: simple bipartite v = 48 e = 88 f = 12 degree seq :: [ 2^44, 22^4 ] E15.725 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-15 * T1^-1, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 45, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 41, 35, 29, 23, 17, 11, 5)(46, 47, 49)(48, 51, 54)(50, 52, 55)(53, 57, 60)(56, 58, 61)(59, 63, 66)(62, 64, 67)(65, 69, 72)(68, 70, 73)(71, 75, 78)(74, 76, 79)(77, 81, 84)(80, 82, 85)(83, 87, 90)(86, 88, 89) L = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90) local type(s) :: { ( 90^3 ), ( 90^45 ) } Outer automorphisms :: reflexible Dual of E15.729 Transitivity :: ET+ Graph:: bipartite v = 16 e = 45 f = 1 degree seq :: [ 3^15, 45 ] E15.726 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^15 * T1^-1, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 45, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 44, 41, 35, 29, 23, 17, 11, 5)(46, 47, 49)(48, 51, 54)(50, 52, 55)(53, 57, 60)(56, 58, 61)(59, 63, 66)(62, 64, 67)(65, 69, 72)(68, 70, 73)(71, 75, 78)(74, 76, 79)(77, 81, 84)(80, 82, 85)(83, 87, 89)(86, 88, 90) L = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90) local type(s) :: { ( 90^3 ), ( 90^45 ) } Outer automorphisms :: reflexible Dual of E15.728 Transitivity :: ET+ Graph:: bipartite v = 16 e = 45 f = 1 degree seq :: [ 3^15, 45 ] E15.727 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1 * T2^2, T1^12 * T2^-1 * T1^2, T2^9 * T1^-1 * T2 * T1^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 25, 31, 37, 43, 42, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 38, 44, 40, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 39, 45, 41, 34, 30, 23, 14, 13, 5)(46, 47, 51, 59, 67, 73, 79, 85, 88, 84, 77, 70, 66, 55, 48, 52, 60, 58, 63, 69, 75, 81, 87, 90, 83, 76, 72, 65, 54, 62, 57, 50, 53, 61, 68, 74, 80, 86, 89, 82, 78, 71, 64, 56, 49) L = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90) local type(s) :: { ( 6^45 ) } Outer automorphisms :: reflexible Dual of E15.730 Transitivity :: ET+ Graph:: bipartite v = 2 e = 45 f = 15 degree seq :: [ 45^2 ] E15.728 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-15 * T1^-1, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 46, 3, 48, 8, 53, 14, 59, 20, 65, 26, 71, 32, 77, 38, 83, 44, 89, 40, 85, 34, 79, 28, 73, 22, 67, 16, 61, 10, 55, 4, 49, 9, 54, 15, 60, 21, 66, 27, 72, 33, 78, 39, 84, 45, 90, 43, 88, 37, 82, 31, 76, 25, 70, 19, 64, 13, 58, 7, 52, 2, 47, 6, 51, 12, 57, 18, 63, 24, 69, 30, 75, 36, 81, 42, 87, 41, 86, 35, 80, 29, 74, 23, 68, 17, 62, 11, 56, 5, 50) L = (1, 47)(2, 49)(3, 51)(4, 46)(5, 52)(6, 54)(7, 55)(8, 57)(9, 48)(10, 50)(11, 58)(12, 60)(13, 61)(14, 63)(15, 53)(16, 56)(17, 64)(18, 66)(19, 67)(20, 69)(21, 59)(22, 62)(23, 70)(24, 72)(25, 73)(26, 75)(27, 65)(28, 68)(29, 76)(30, 78)(31, 79)(32, 81)(33, 71)(34, 74)(35, 82)(36, 84)(37, 85)(38, 87)(39, 77)(40, 80)(41, 88)(42, 90)(43, 89)(44, 86)(45, 83) local type(s) :: { ( 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45 ) } Outer automorphisms :: reflexible Dual of E15.726 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 45 f = 16 degree seq :: [ 90 ] E15.729 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^15 * T1^-1, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 46, 3, 48, 8, 53, 14, 59, 20, 65, 26, 71, 32, 77, 38, 83, 43, 88, 37, 82, 31, 76, 25, 70, 19, 64, 13, 58, 7, 52, 2, 47, 6, 51, 12, 57, 18, 63, 24, 69, 30, 75, 36, 81, 42, 87, 45, 90, 40, 85, 34, 79, 28, 73, 22, 67, 16, 61, 10, 55, 4, 49, 9, 54, 15, 60, 21, 66, 27, 72, 33, 78, 39, 84, 44, 89, 41, 86, 35, 80, 29, 74, 23, 68, 17, 62, 11, 56, 5, 50) L = (1, 47)(2, 49)(3, 51)(4, 46)(5, 52)(6, 54)(7, 55)(8, 57)(9, 48)(10, 50)(11, 58)(12, 60)(13, 61)(14, 63)(15, 53)(16, 56)(17, 64)(18, 66)(19, 67)(20, 69)(21, 59)(22, 62)(23, 70)(24, 72)(25, 73)(26, 75)(27, 65)(28, 68)(29, 76)(30, 78)(31, 79)(32, 81)(33, 71)(34, 74)(35, 82)(36, 84)(37, 85)(38, 87)(39, 77)(40, 80)(41, 88)(42, 89)(43, 90)(44, 83)(45, 86) local type(s) :: { ( 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45, 3, 45 ) } Outer automorphisms :: reflexible Dual of E15.725 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 45 f = 16 degree seq :: [ 90 ] E15.730 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-1 * T1^-15, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 46, 3, 48, 5, 50)(2, 47, 7, 52, 8, 53)(4, 49, 9, 54, 11, 56)(6, 51, 13, 58, 14, 59)(10, 55, 15, 60, 17, 62)(12, 57, 19, 64, 20, 65)(16, 61, 21, 66, 23, 68)(18, 63, 25, 70, 26, 71)(22, 67, 27, 72, 29, 74)(24, 69, 31, 76, 32, 77)(28, 73, 33, 78, 35, 80)(30, 75, 37, 82, 38, 83)(34, 79, 39, 84, 41, 86)(36, 81, 43, 88, 44, 89)(40, 85, 45, 90, 42, 87) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 57)(7, 58)(8, 59)(9, 48)(10, 49)(11, 50)(12, 63)(13, 64)(14, 65)(15, 54)(16, 55)(17, 56)(18, 69)(19, 70)(20, 71)(21, 60)(22, 61)(23, 62)(24, 75)(25, 76)(26, 77)(27, 66)(28, 67)(29, 68)(30, 81)(31, 82)(32, 83)(33, 72)(34, 73)(35, 74)(36, 87)(37, 88)(38, 89)(39, 78)(40, 79)(41, 80)(42, 86)(43, 85)(44, 90)(45, 84) local type(s) :: { ( 45^6 ) } Outer automorphisms :: reflexible Dual of E15.727 Transitivity :: ET+ VT+ AT Graph:: v = 15 e = 45 f = 2 degree seq :: [ 6^15 ] E15.731 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y2^15 * 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 ] Map:: R = (1, 46, 2, 47, 4, 49)(3, 48, 6, 51, 9, 54)(5, 50, 7, 52, 10, 55)(8, 53, 12, 57, 15, 60)(11, 56, 13, 58, 16, 61)(14, 59, 18, 63, 21, 66)(17, 62, 19, 64, 22, 67)(20, 65, 24, 69, 27, 72)(23, 68, 25, 70, 28, 73)(26, 71, 30, 75, 33, 78)(29, 74, 31, 76, 34, 79)(32, 77, 36, 81, 39, 84)(35, 80, 37, 82, 40, 85)(38, 83, 42, 87, 44, 89)(41, 86, 43, 88, 45, 90)(91, 136, 93, 138, 98, 143, 104, 149, 110, 155, 116, 161, 122, 167, 128, 173, 133, 178, 127, 172, 121, 166, 115, 160, 109, 154, 103, 148, 97, 142, 92, 137, 96, 141, 102, 147, 108, 153, 114, 159, 120, 165, 126, 171, 132, 177, 135, 180, 130, 175, 124, 169, 118, 163, 112, 157, 106, 151, 100, 145, 94, 139, 99, 144, 105, 150, 111, 156, 117, 162, 123, 168, 129, 174, 134, 179, 131, 176, 125, 170, 119, 164, 113, 158, 107, 152, 101, 146, 95, 140) L = (1, 94)(2, 91)(3, 99)(4, 92)(5, 100)(6, 93)(7, 95)(8, 105)(9, 96)(10, 97)(11, 106)(12, 98)(13, 101)(14, 111)(15, 102)(16, 103)(17, 112)(18, 104)(19, 107)(20, 117)(21, 108)(22, 109)(23, 118)(24, 110)(25, 113)(26, 123)(27, 114)(28, 115)(29, 124)(30, 116)(31, 119)(32, 129)(33, 120)(34, 121)(35, 130)(36, 122)(37, 125)(38, 134)(39, 126)(40, 127)(41, 135)(42, 128)(43, 131)(44, 132)(45, 133)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 2, 90, 2, 90, 2, 90 ), ( 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ) } Outer automorphisms :: reflexible Dual of E15.735 Graph:: bipartite v = 16 e = 90 f = 46 degree seq :: [ 6^15, 90 ] E15.732 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3^3, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * Y2^-15, Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 46, 2, 47, 4, 49)(3, 48, 6, 51, 9, 54)(5, 50, 7, 52, 10, 55)(8, 53, 12, 57, 15, 60)(11, 56, 13, 58, 16, 61)(14, 59, 18, 63, 21, 66)(17, 62, 19, 64, 22, 67)(20, 65, 24, 69, 27, 72)(23, 68, 25, 70, 28, 73)(26, 71, 30, 75, 33, 78)(29, 74, 31, 76, 34, 79)(32, 77, 36, 81, 39, 84)(35, 80, 37, 82, 40, 85)(38, 83, 42, 87, 45, 90)(41, 86, 43, 88, 44, 89)(91, 136, 93, 138, 98, 143, 104, 149, 110, 155, 116, 161, 122, 167, 128, 173, 134, 179, 130, 175, 124, 169, 118, 163, 112, 157, 106, 151, 100, 145, 94, 139, 99, 144, 105, 150, 111, 156, 117, 162, 123, 168, 129, 174, 135, 180, 133, 178, 127, 172, 121, 166, 115, 160, 109, 154, 103, 148, 97, 142, 92, 137, 96, 141, 102, 147, 108, 153, 114, 159, 120, 165, 126, 171, 132, 177, 131, 176, 125, 170, 119, 164, 113, 158, 107, 152, 101, 146, 95, 140) L = (1, 94)(2, 91)(3, 99)(4, 92)(5, 100)(6, 93)(7, 95)(8, 105)(9, 96)(10, 97)(11, 106)(12, 98)(13, 101)(14, 111)(15, 102)(16, 103)(17, 112)(18, 104)(19, 107)(20, 117)(21, 108)(22, 109)(23, 118)(24, 110)(25, 113)(26, 123)(27, 114)(28, 115)(29, 124)(30, 116)(31, 119)(32, 129)(33, 120)(34, 121)(35, 130)(36, 122)(37, 125)(38, 135)(39, 126)(40, 127)(41, 134)(42, 128)(43, 131)(44, 133)(45, 132)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 2, 90, 2, 90, 2, 90 ), ( 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ) } Outer automorphisms :: reflexible Dual of E15.736 Graph:: bipartite v = 16 e = 90 f = 46 degree seq :: [ 6^15, 90 ] E15.733 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^3, (Y3^-1 * Y1^-1)^3, Y2^-8 * Y1^7, Y2^5 * Y1^35, Y1^45, Y1^112 * Y2^7 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 22, 67, 28, 73, 34, 79, 40, 85, 45, 90, 38, 83, 31, 76, 27, 72, 20, 65, 9, 54, 17, 62, 12, 57, 5, 50, 8, 53, 16, 61, 23, 68, 29, 74, 35, 80, 41, 86, 43, 88, 39, 84, 32, 77, 25, 70, 21, 66, 10, 55, 3, 48, 7, 52, 15, 60, 13, 58, 18, 63, 24, 69, 30, 75, 36, 81, 42, 87, 44, 89, 37, 82, 33, 78, 26, 71, 19, 64, 11, 56, 4, 49)(91, 136, 93, 138, 99, 144, 109, 154, 115, 160, 121, 166, 127, 172, 133, 178, 130, 175, 126, 171, 119, 164, 112, 157, 108, 153, 98, 143, 92, 137, 97, 142, 107, 152, 101, 146, 111, 156, 117, 162, 123, 168, 129, 174, 135, 180, 132, 177, 125, 170, 118, 163, 114, 159, 106, 151, 96, 141, 105, 150, 102, 147, 94, 139, 100, 145, 110, 155, 116, 161, 122, 167, 128, 173, 134, 179, 131, 176, 124, 169, 120, 165, 113, 158, 104, 149, 103, 148, 95, 140) L = (1, 93)(2, 97)(3, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 109)(10, 110)(11, 111)(12, 94)(13, 95)(14, 103)(15, 102)(16, 96)(17, 101)(18, 98)(19, 115)(20, 116)(21, 117)(22, 108)(23, 104)(24, 106)(25, 121)(26, 122)(27, 123)(28, 114)(29, 112)(30, 113)(31, 127)(32, 128)(33, 129)(34, 120)(35, 118)(36, 119)(37, 133)(38, 134)(39, 135)(40, 126)(41, 124)(42, 125)(43, 130)(44, 131)(45, 132)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) 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 ) } Outer automorphisms :: reflexible Dual of E15.734 Graph:: bipartite v = 2 e = 90 f = 60 degree seq :: [ 90^2 ] E15.734 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y3^-15 * Y2^-1, (Y2^-1 * Y3)^45, (Y3^-1 * Y1^-1)^45 ] Map:: R = (1, 46)(2, 47)(3, 48)(4, 49)(5, 50)(6, 51)(7, 52)(8, 53)(9, 54)(10, 55)(11, 56)(12, 57)(13, 58)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(26, 71)(27, 72)(28, 73)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 89)(45, 90)(91, 136, 92, 137, 94, 139)(93, 138, 96, 141, 99, 144)(95, 140, 97, 142, 100, 145)(98, 143, 102, 147, 105, 150)(101, 146, 103, 148, 106, 151)(104, 149, 108, 153, 111, 156)(107, 152, 109, 154, 112, 157)(110, 155, 114, 159, 117, 162)(113, 158, 115, 160, 118, 163)(116, 161, 120, 165, 123, 168)(119, 164, 121, 166, 124, 169)(122, 167, 126, 171, 129, 174)(125, 170, 127, 172, 130, 175)(128, 173, 132, 177, 135, 180)(131, 176, 133, 178, 134, 179) L = (1, 93)(2, 96)(3, 98)(4, 99)(5, 91)(6, 102)(7, 92)(8, 104)(9, 105)(10, 94)(11, 95)(12, 108)(13, 97)(14, 110)(15, 111)(16, 100)(17, 101)(18, 114)(19, 103)(20, 116)(21, 117)(22, 106)(23, 107)(24, 120)(25, 109)(26, 122)(27, 123)(28, 112)(29, 113)(30, 126)(31, 115)(32, 128)(33, 129)(34, 118)(35, 119)(36, 132)(37, 121)(38, 134)(39, 135)(40, 124)(41, 125)(42, 131)(43, 127)(44, 130)(45, 133)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 90, 90 ), ( 90^6 ) } Outer automorphisms :: reflexible Dual of E15.733 Graph:: simple bipartite v = 60 e = 90 f = 2 degree seq :: [ 2^45, 6^15 ] E15.735 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^-15, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 46, 2, 47, 6, 51, 12, 57, 18, 63, 24, 69, 30, 75, 36, 81, 42, 87, 41, 86, 35, 80, 29, 74, 23, 68, 17, 62, 11, 56, 5, 50, 8, 53, 14, 59, 20, 65, 26, 71, 32, 77, 38, 83, 44, 89, 45, 90, 39, 84, 33, 78, 27, 72, 21, 66, 15, 60, 9, 54, 3, 48, 7, 52, 13, 58, 19, 64, 25, 70, 31, 76, 37, 82, 43, 88, 40, 85, 34, 79, 28, 73, 22, 67, 16, 61, 10, 55, 4, 49)(91, 136)(92, 137)(93, 138)(94, 139)(95, 140)(96, 141)(97, 142)(98, 143)(99, 144)(100, 145)(101, 146)(102, 147)(103, 148)(104, 149)(105, 150)(106, 151)(107, 152)(108, 153)(109, 154)(110, 155)(111, 156)(112, 157)(113, 158)(114, 159)(115, 160)(116, 161)(117, 162)(118, 163)(119, 164)(120, 165)(121, 166)(122, 167)(123, 168)(124, 169)(125, 170)(126, 171)(127, 172)(128, 173)(129, 174)(130, 175)(131, 176)(132, 177)(133, 178)(134, 179)(135, 180) L = (1, 93)(2, 97)(3, 95)(4, 99)(5, 91)(6, 103)(7, 98)(8, 92)(9, 101)(10, 105)(11, 94)(12, 109)(13, 104)(14, 96)(15, 107)(16, 111)(17, 100)(18, 115)(19, 110)(20, 102)(21, 113)(22, 117)(23, 106)(24, 121)(25, 116)(26, 108)(27, 119)(28, 123)(29, 112)(30, 127)(31, 122)(32, 114)(33, 125)(34, 129)(35, 118)(36, 133)(37, 128)(38, 120)(39, 131)(40, 135)(41, 124)(42, 130)(43, 134)(44, 126)(45, 132)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 6, 90 ), ( 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90 ) } Outer automorphisms :: reflexible Dual of E15.731 Graph:: bipartite v = 46 e = 90 f = 16 degree seq :: [ 2^45, 90 ] E15.736 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^-15, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 46, 2, 47, 6, 51, 12, 57, 18, 63, 24, 69, 30, 75, 36, 81, 42, 87, 39, 84, 33, 78, 27, 72, 21, 66, 15, 60, 9, 54, 3, 48, 7, 52, 13, 58, 19, 64, 25, 70, 31, 76, 37, 82, 43, 88, 45, 90, 41, 86, 35, 80, 29, 74, 23, 68, 17, 62, 11, 56, 5, 50, 8, 53, 14, 59, 20, 65, 26, 71, 32, 77, 38, 83, 44, 89, 40, 85, 34, 79, 28, 73, 22, 67, 16, 61, 10, 55, 4, 49)(91, 136)(92, 137)(93, 138)(94, 139)(95, 140)(96, 141)(97, 142)(98, 143)(99, 144)(100, 145)(101, 146)(102, 147)(103, 148)(104, 149)(105, 150)(106, 151)(107, 152)(108, 153)(109, 154)(110, 155)(111, 156)(112, 157)(113, 158)(114, 159)(115, 160)(116, 161)(117, 162)(118, 163)(119, 164)(120, 165)(121, 166)(122, 167)(123, 168)(124, 169)(125, 170)(126, 171)(127, 172)(128, 173)(129, 174)(130, 175)(131, 176)(132, 177)(133, 178)(134, 179)(135, 180) L = (1, 93)(2, 97)(3, 95)(4, 99)(5, 91)(6, 103)(7, 98)(8, 92)(9, 101)(10, 105)(11, 94)(12, 109)(13, 104)(14, 96)(15, 107)(16, 111)(17, 100)(18, 115)(19, 110)(20, 102)(21, 113)(22, 117)(23, 106)(24, 121)(25, 116)(26, 108)(27, 119)(28, 123)(29, 112)(30, 127)(31, 122)(32, 114)(33, 125)(34, 129)(35, 118)(36, 133)(37, 128)(38, 120)(39, 131)(40, 132)(41, 124)(42, 135)(43, 134)(44, 126)(45, 130)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 141)(52, 142)(53, 143)(54, 144)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 151)(62, 152)(63, 153)(64, 154)(65, 155)(66, 156)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 163)(74, 164)(75, 165)(76, 166)(77, 167)(78, 168)(79, 169)(80, 170)(81, 171)(82, 172)(83, 173)(84, 174)(85, 175)(86, 176)(87, 177)(88, 178)(89, 179)(90, 180) local type(s) :: { ( 6, 90 ), ( 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90, 6, 90 ) } Outer automorphisms :: reflexible Dual of E15.732 Graph:: bipartite v = 46 e = 90 f = 16 degree seq :: [ 2^45, 90 ] E15.737 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 3, 3, 4}) Quotient :: edge^2 Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 72>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y3^-2 * Y2 * Y3 * Y1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y1, Y2^-1 * Y3^-1 * Y1 * Y3 * Y1, Y1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1^-1)^3, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, (Y2 * Y1^-1)^3, (Y3 * Y2^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 49, 4, 52, 18, 66, 7, 55)(2, 50, 9, 57, 32, 80, 11, 59)(3, 51, 13, 61, 45, 93, 15, 63)(5, 53, 22, 70, 43, 91, 24, 72)(6, 54, 26, 74, 16, 64, 28, 76)(8, 56, 34, 82, 27, 75, 36, 84)(10, 58, 25, 73, 17, 65, 31, 79)(12, 60, 38, 86, 47, 95, 44, 92)(14, 62, 33, 81, 48, 96, 29, 77)(19, 67, 41, 89, 35, 83, 30, 78)(20, 68, 40, 88, 46, 94, 21, 69)(23, 71, 39, 87, 37, 85, 42, 90)(97, 98, 101)(99, 108, 110)(100, 112, 115)(102, 121, 123)(103, 125, 127)(104, 129, 131)(105, 113, 134)(106, 135, 136)(107, 137, 138)(109, 114, 142)(111, 130, 128)(116, 139, 132)(117, 126, 140)(118, 133, 144)(119, 122, 141)(120, 143, 124)(145, 147, 150)(146, 152, 154)(148, 161, 164)(149, 165, 167)(151, 174, 176)(153, 181, 157)(155, 156, 187)(158, 183, 163)(159, 184, 191)(160, 178, 166)(162, 168, 177)(169, 192, 188)(170, 182, 179)(171, 185, 190)(172, 186, 175)(173, 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) :: { ( 8^3 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E15.740 Graph:: simple bipartite v = 44 e = 96 f = 24 degree seq :: [ 3^32, 8^12 ] E15.738 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 3, 3, 4}) Quotient :: edge^2 Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 72>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3, Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3, Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1 * Y2, Y2 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y1, (Y3 * Y2^-1)^3, (Y2 * Y1^-1)^3, (Y1 * Y3)^3, Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 8, 56)(3, 51, 11, 59)(5, 53, 18, 66)(6, 54, 21, 69)(7, 55, 23, 71)(9, 57, 29, 77)(10, 58, 19, 67)(12, 60, 36, 84)(13, 61, 38, 86)(14, 62, 40, 88)(15, 63, 25, 73)(16, 64, 33, 81)(17, 65, 44, 92)(20, 68, 37, 85)(22, 70, 43, 91)(24, 72, 42, 90)(26, 74, 35, 83)(27, 75, 39, 87)(28, 76, 47, 95)(30, 78, 31, 79)(32, 80, 46, 94)(34, 82, 41, 89)(45, 93, 48, 96)(97, 98, 101)(99, 106, 108)(100, 109, 111)(102, 116, 118)(103, 117, 120)(104, 121, 122)(105, 124, 126)(107, 128, 130)(110, 115, 137)(112, 138, 139)(113, 125, 141)(114, 131, 134)(119, 129, 133)(123, 144, 127)(132, 136, 142)(135, 143, 140)(145, 147, 150)(146, 151, 153)(148, 158, 160)(149, 161, 163)(152, 166, 171)(154, 159, 175)(155, 177, 179)(156, 172, 181)(157, 167, 183)(162, 174, 190)(164, 178, 189)(165, 170, 184)(168, 185, 191)(169, 188, 176)(173, 182, 187)(180, 192, 186) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^3 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E15.739 Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 3^32, 4^24 ] E15.739 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 3, 3, 4}) Quotient :: loop^2 Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 72>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y3^-2 * Y2 * Y3 * Y1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y1, Y2^-1 * Y3^-1 * Y1 * Y3 * Y1, Y1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1^-1)^3, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, (Y2 * Y1^-1)^3, (Y3 * Y2^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148, 18, 66, 114, 162, 7, 55, 103, 151)(2, 50, 98, 146, 9, 57, 105, 153, 32, 80, 128, 176, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 45, 93, 141, 189, 15, 63, 111, 159)(5, 53, 101, 149, 22, 70, 118, 166, 43, 91, 139, 187, 24, 72, 120, 168)(6, 54, 102, 150, 26, 74, 122, 170, 16, 64, 112, 160, 28, 76, 124, 172)(8, 56, 104, 152, 34, 82, 130, 178, 27, 75, 123, 171, 36, 84, 132, 180)(10, 58, 106, 154, 25, 73, 121, 169, 17, 65, 113, 161, 31, 79, 127, 175)(12, 60, 108, 156, 38, 86, 134, 182, 47, 95, 143, 191, 44, 92, 140, 188)(14, 62, 110, 158, 33, 81, 129, 177, 48, 96, 144, 192, 29, 77, 125, 173)(19, 67, 115, 163, 41, 89, 137, 185, 35, 83, 131, 179, 30, 78, 126, 174)(20, 68, 116, 164, 40, 88, 136, 184, 46, 94, 142, 190, 21, 69, 117, 165)(23, 71, 119, 167, 39, 87, 135, 183, 37, 85, 133, 181, 42, 90, 138, 186) L = (1, 50)(2, 53)(3, 60)(4, 64)(5, 49)(6, 73)(7, 77)(8, 81)(9, 65)(10, 87)(11, 89)(12, 62)(13, 66)(14, 51)(15, 82)(16, 67)(17, 86)(18, 94)(19, 52)(20, 91)(21, 78)(22, 85)(23, 74)(24, 95)(25, 75)(26, 93)(27, 54)(28, 72)(29, 79)(30, 92)(31, 55)(32, 63)(33, 83)(34, 80)(35, 56)(36, 68)(37, 96)(38, 57)(39, 88)(40, 58)(41, 90)(42, 59)(43, 84)(44, 69)(45, 71)(46, 61)(47, 76)(48, 70)(97, 147)(98, 152)(99, 150)(100, 161)(101, 165)(102, 145)(103, 174)(104, 154)(105, 181)(106, 146)(107, 156)(108, 187)(109, 153)(110, 183)(111, 184)(112, 178)(113, 164)(114, 168)(115, 158)(116, 148)(117, 167)(118, 160)(119, 149)(120, 177)(121, 192)(122, 182)(123, 185)(124, 186)(125, 180)(126, 176)(127, 172)(128, 151)(129, 162)(130, 166)(131, 170)(132, 189)(133, 157)(134, 179)(135, 163)(136, 191)(137, 190)(138, 175)(139, 155)(140, 169)(141, 173)(142, 171)(143, 159)(144, 188) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E15.738 Transitivity :: VT+ Graph:: v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.740 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 3, 3, 4}) Quotient :: loop^2 Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 72>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3, Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3, Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1 * Y2, Y2 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y1, (Y3 * Y2^-1)^3, (Y2 * Y1^-1)^3, (Y1 * Y3)^3, Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 8, 56, 104, 152)(3, 51, 99, 147, 11, 59, 107, 155)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 21, 69, 117, 165)(7, 55, 103, 151, 23, 71, 119, 167)(9, 57, 105, 153, 29, 77, 125, 173)(10, 58, 106, 154, 19, 67, 115, 163)(12, 60, 108, 156, 36, 84, 132, 180)(13, 61, 109, 157, 38, 86, 134, 182)(14, 62, 110, 158, 40, 88, 136, 184)(15, 63, 111, 159, 25, 73, 121, 169)(16, 64, 112, 160, 33, 81, 129, 177)(17, 65, 113, 161, 44, 92, 140, 188)(20, 68, 116, 164, 37, 85, 133, 181)(22, 70, 118, 166, 43, 91, 139, 187)(24, 72, 120, 168, 42, 90, 138, 186)(26, 74, 122, 170, 35, 83, 131, 179)(27, 75, 123, 171, 39, 87, 135, 183)(28, 76, 124, 172, 47, 95, 143, 191)(30, 78, 126, 174, 31, 79, 127, 175)(32, 80, 128, 176, 46, 94, 142, 190)(34, 82, 130, 178, 41, 89, 137, 185)(45, 93, 141, 189, 48, 96, 144, 192) L = (1, 50)(2, 53)(3, 58)(4, 61)(5, 49)(6, 68)(7, 69)(8, 73)(9, 76)(10, 60)(11, 80)(12, 51)(13, 63)(14, 67)(15, 52)(16, 90)(17, 77)(18, 83)(19, 89)(20, 70)(21, 72)(22, 54)(23, 81)(24, 55)(25, 74)(26, 56)(27, 96)(28, 78)(29, 93)(30, 57)(31, 75)(32, 82)(33, 85)(34, 59)(35, 86)(36, 88)(37, 71)(38, 66)(39, 95)(40, 94)(41, 62)(42, 91)(43, 64)(44, 87)(45, 65)(46, 84)(47, 92)(48, 79)(97, 147)(98, 151)(99, 150)(100, 158)(101, 161)(102, 145)(103, 153)(104, 166)(105, 146)(106, 159)(107, 177)(108, 172)(109, 167)(110, 160)(111, 175)(112, 148)(113, 163)(114, 174)(115, 149)(116, 178)(117, 170)(118, 171)(119, 183)(120, 185)(121, 188)(122, 184)(123, 152)(124, 181)(125, 182)(126, 190)(127, 154)(128, 169)(129, 179)(130, 189)(131, 155)(132, 192)(133, 156)(134, 187)(135, 157)(136, 165)(137, 191)(138, 180)(139, 173)(140, 176)(141, 164)(142, 162)(143, 168)(144, 186) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E15.737 Transitivity :: VT+ Graph:: simple v = 24 e = 96 f = 44 degree seq :: [ 8^24 ] E15.741 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 4}) Quotient :: dipole Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 64>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3^-2, Y2^3, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^3, (Y2^-1 * Y3^-1)^3, (Y2^-1 * Y1)^3, (Y2 * Y3^-1)^3, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2 * R * Y2 * Y1 * Y2^-1 * R * Y2^-1 * Y1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 6, 54)(5, 53, 14, 62)(7, 55, 19, 67)(8, 56, 22, 70)(10, 58, 11, 59)(12, 60, 30, 78)(13, 61, 33, 81)(15, 63, 16, 64)(17, 65, 39, 87)(18, 66, 41, 89)(20, 68, 21, 69)(23, 71, 24, 72)(25, 73, 35, 83)(26, 74, 42, 90)(27, 75, 43, 91)(28, 76, 34, 82)(29, 77, 44, 92)(31, 79, 32, 80)(36, 84, 45, 93)(37, 85, 40, 88)(38, 86, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 104, 152)(100, 148, 108, 156, 109, 157)(102, 150, 113, 161, 114, 162)(105, 153, 118, 166, 121, 169)(106, 154, 122, 170, 123, 171)(107, 155, 124, 172, 125, 173)(110, 158, 131, 179, 115, 163)(111, 159, 132, 180, 133, 181)(112, 160, 134, 182, 127, 175)(116, 164, 130, 178, 139, 187)(117, 165, 138, 186, 140, 188)(119, 167, 141, 189, 128, 176)(120, 168, 142, 190, 136, 184)(126, 174, 137, 185, 143, 191)(129, 177, 144, 192, 135, 183) L = (1, 100)(2, 102)(3, 106)(4, 98)(5, 111)(6, 97)(7, 116)(8, 119)(9, 107)(10, 105)(11, 99)(12, 127)(13, 124)(14, 112)(15, 110)(16, 101)(17, 136)(18, 138)(19, 117)(20, 115)(21, 103)(22, 120)(23, 118)(24, 104)(25, 143)(26, 114)(27, 134)(28, 129)(29, 141)(30, 128)(31, 126)(32, 108)(33, 130)(34, 109)(35, 144)(36, 125)(37, 113)(38, 139)(39, 133)(40, 135)(41, 122)(42, 137)(43, 142)(44, 132)(45, 140)(46, 123)(47, 131)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.742 Graph:: simple bipartite v = 40 e = 96 f = 28 degree seq :: [ 4^24, 6^16 ] E15.742 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 4}) Quotient :: dipole Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 64>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y1^3, (R * Y1)^2, Y2^4, R * Y2 * R * Y3^-1, (Y3 * Y2^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1, (Y3^-1 * Y1^-1)^3, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 10, 58)(4, 52, 11, 59, 12, 60)(6, 54, 15, 63, 17, 65)(7, 55, 18, 66, 19, 67)(9, 57, 22, 70, 23, 71)(13, 61, 28, 76, 26, 74)(14, 62, 30, 78, 20, 68)(16, 64, 32, 80, 33, 81)(21, 69, 38, 86, 36, 84)(24, 72, 42, 90, 39, 87)(25, 73, 41, 89, 34, 82)(27, 75, 44, 92, 40, 88)(29, 77, 45, 93, 46, 94)(31, 79, 47, 95, 37, 85)(35, 83, 48, 96, 43, 91)(97, 145, 99, 147, 105, 153, 100, 148)(98, 146, 102, 150, 112, 160, 103, 151)(101, 149, 109, 157, 125, 173, 110, 158)(104, 152, 116, 164, 133, 181, 117, 165)(106, 154, 114, 162, 131, 179, 120, 168)(107, 155, 121, 169, 139, 187, 122, 170)(108, 156, 123, 171, 127, 175, 111, 159)(113, 161, 126, 174, 138, 186, 130, 178)(115, 163, 132, 180, 140, 188, 124, 172)(118, 166, 135, 183, 142, 190, 136, 184)(119, 167, 134, 182, 128, 176, 137, 185)(129, 177, 143, 191, 141, 189, 144, 192) L = (1, 100)(2, 103)(3, 97)(4, 105)(5, 110)(6, 98)(7, 112)(8, 117)(9, 99)(10, 120)(11, 122)(12, 111)(13, 101)(14, 125)(15, 127)(16, 102)(17, 130)(18, 106)(19, 124)(20, 104)(21, 133)(22, 136)(23, 137)(24, 131)(25, 107)(26, 139)(27, 108)(28, 140)(29, 109)(30, 113)(31, 123)(32, 134)(33, 144)(34, 138)(35, 114)(36, 115)(37, 116)(38, 119)(39, 118)(40, 142)(41, 128)(42, 126)(43, 121)(44, 132)(45, 143)(46, 135)(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, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.741 Graph:: bipartite v = 28 e = 96 f = 40 degree seq :: [ 6^16, 8^12 ] E15.743 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 4}) 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, Y2^3, (R * Y3)^2, (R * Y1)^2, Y3^4, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y3^-2 * Y2 * Y3^-2 * Y2^-1, (Y2^-1 * Y3)^3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * 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, 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, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 109, 157, 111, 159)(102, 150, 114, 162, 115, 163)(104, 152, 118, 166, 120, 168)(106, 154, 123, 171, 124, 172)(107, 155, 125, 173, 127, 175)(108, 156, 128, 176, 129, 177)(110, 158, 126, 174, 132, 180)(112, 160, 133, 181, 130, 178)(113, 161, 134, 182, 131, 179)(116, 164, 135, 183, 137, 185)(117, 165, 138, 186, 139, 187)(119, 167, 136, 184, 142, 190)(121, 169, 143, 191, 140, 188)(122, 170, 144, 192, 141, 189) L = (1, 100)(2, 104)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 119)(9, 121)(10, 98)(11, 126)(12, 99)(13, 130)(14, 102)(15, 128)(16, 132)(17, 101)(18, 131)(19, 125)(20, 136)(21, 103)(22, 140)(23, 106)(24, 138)(25, 142)(26, 105)(27, 141)(28, 135)(29, 111)(30, 108)(31, 134)(32, 115)(33, 133)(34, 114)(35, 109)(36, 113)(37, 127)(38, 129)(39, 120)(40, 117)(41, 144)(42, 124)(43, 143)(44, 123)(45, 118)(46, 122)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.744 Graph:: simple bipartite v = 40 e = 96 f = 28 degree seq :: [ 4^24, 6^16 ] E15.744 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 4}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3^-1 * Y2^-1)^2, (Y3, Y2^-1), Y3^-2 * Y2^2, (R * Y2)^2, Y2^-1 * Y3^-2 * Y2^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y1^-1, Y3^-2 * Y1 * Y2^-2 * Y1^-1, Y1 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 18, 66)(6, 54, 23, 71, 24, 72)(7, 55, 25, 73, 26, 74)(8, 56, 27, 75, 30, 78)(9, 57, 32, 80, 33, 81)(10, 58, 34, 82, 35, 83)(11, 59, 36, 84, 37, 85)(13, 61, 28, 76, 42, 90)(14, 62, 29, 77, 43, 91)(16, 64, 31, 79, 44, 92)(19, 67, 45, 93, 41, 89)(20, 68, 46, 94, 40, 88)(21, 69, 47, 95, 39, 87)(22, 70, 48, 96, 38, 86)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 124, 172, 106, 154)(100, 148, 110, 158, 103, 151, 112, 160)(101, 149, 115, 163, 138, 186, 117, 165)(105, 153, 125, 173, 107, 155, 127, 175)(108, 156, 134, 182, 119, 167, 136, 184)(111, 159, 128, 176, 120, 168, 132, 180)(113, 161, 135, 183, 121, 169, 137, 185)(114, 162, 123, 171, 122, 170, 130, 178)(116, 164, 139, 187, 118, 166, 140, 188)(126, 174, 142, 190, 131, 179, 144, 192)(129, 177, 141, 189, 133, 181, 143, 191) L = (1, 100)(2, 105)(3, 110)(4, 109)(5, 116)(6, 112)(7, 97)(8, 125)(9, 124)(10, 127)(11, 98)(12, 135)(13, 103)(14, 102)(15, 123)(16, 99)(17, 134)(18, 128)(19, 139)(20, 138)(21, 140)(22, 101)(23, 137)(24, 130)(25, 136)(26, 132)(27, 120)(28, 107)(29, 106)(30, 141)(31, 104)(32, 122)(33, 142)(34, 111)(35, 143)(36, 114)(37, 144)(38, 121)(39, 119)(40, 113)(41, 108)(42, 118)(43, 117)(44, 115)(45, 131)(46, 133)(47, 126)(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, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.743 Graph:: simple bipartite v = 28 e = 96 f = 40 degree seq :: [ 6^16, 8^12 ] E15.745 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 4}) 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^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3^-2 * Y2 * Y3^-2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 8, 56)(5, 53, 17, 65)(6, 54, 10, 58)(7, 55, 22, 70)(9, 57, 28, 76)(12, 60, 25, 73)(13, 61, 31, 79)(14, 62, 23, 71)(15, 63, 26, 74)(16, 64, 29, 77)(18, 66, 27, 75)(19, 67, 32, 80)(20, 68, 24, 72)(21, 69, 30, 78)(33, 81, 41, 89)(34, 82, 46, 94)(35, 83, 45, 93)(36, 84, 47, 95)(37, 85, 40, 88)(38, 86, 43, 91)(39, 87, 44, 92)(42, 90, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 110, 158, 112, 160)(102, 150, 116, 164, 117, 165)(104, 152, 121, 169, 123, 171)(106, 154, 127, 175, 128, 176)(107, 155, 126, 174, 129, 177)(108, 156, 124, 172, 131, 179)(109, 157, 132, 180, 133, 181)(111, 159, 130, 178, 135, 183)(113, 161, 136, 184, 119, 167)(114, 162, 137, 185, 134, 182)(115, 163, 138, 186, 118, 166)(120, 168, 140, 188, 141, 189)(122, 170, 139, 187, 143, 191)(125, 173, 144, 192, 142, 190) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 114)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 121)(12, 130)(13, 99)(14, 134)(15, 102)(16, 132)(17, 123)(18, 135)(19, 101)(20, 118)(21, 124)(22, 110)(23, 139)(24, 103)(25, 142)(26, 106)(27, 140)(28, 112)(29, 143)(30, 105)(31, 107)(32, 113)(33, 141)(34, 109)(35, 138)(36, 117)(37, 137)(38, 116)(39, 115)(40, 129)(41, 131)(42, 133)(43, 120)(44, 128)(45, 144)(46, 127)(47, 126)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.746 Graph:: simple bipartite v = 40 e = 96 f = 28 degree seq :: [ 4^24, 6^16 ] E15.746 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 4}) 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, Y3^2 * Y2^2, (Y3, Y2^-1), (Y2^-1, Y1^-1), (R * Y3)^2, Y2^4, (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 14, 62)(4, 52, 16, 64, 17, 65)(6, 54, 10, 58, 19, 67)(7, 55, 21, 69, 22, 70)(9, 57, 26, 74, 27, 75)(11, 59, 28, 76, 29, 77)(12, 60, 23, 71, 30, 78)(13, 61, 31, 79, 32, 80)(15, 63, 35, 83, 36, 84)(18, 66, 39, 87, 38, 86)(20, 68, 40, 88, 37, 85)(24, 72, 41, 89, 42, 90)(25, 73, 43, 91, 44, 92)(33, 81, 47, 95, 46, 94)(34, 82, 48, 96, 45, 93)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 119, 167, 106, 154)(100, 148, 109, 157, 103, 151, 111, 159)(101, 149, 110, 158, 126, 174, 115, 163)(105, 153, 120, 168, 107, 155, 121, 169)(112, 160, 127, 175, 117, 165, 131, 179)(113, 161, 128, 176, 118, 166, 132, 180)(114, 162, 129, 177, 116, 164, 130, 178)(122, 170, 137, 185, 124, 172, 139, 187)(123, 171, 138, 186, 125, 173, 140, 188)(133, 181, 141, 189, 134, 182, 142, 190)(135, 183, 143, 191, 136, 184, 144, 192) L = (1, 100)(2, 105)(3, 109)(4, 108)(5, 114)(6, 111)(7, 97)(8, 120)(9, 119)(10, 121)(11, 98)(12, 103)(13, 102)(14, 129)(15, 99)(16, 133)(17, 122)(18, 126)(19, 130)(20, 101)(21, 134)(22, 124)(23, 107)(24, 106)(25, 104)(26, 118)(27, 135)(28, 113)(29, 136)(30, 116)(31, 141)(32, 137)(33, 115)(34, 110)(35, 142)(36, 139)(37, 117)(38, 112)(39, 125)(40, 123)(41, 132)(42, 143)(43, 128)(44, 144)(45, 131)(46, 127)(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) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.745 Graph:: simple bipartite v = 28 e = 96 f = 40 degree seq :: [ 6^16, 8^12 ] E15.747 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^4, (R * Y1)^2, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y3, Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y3, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, (Y2^-1 * Y3^-1 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y2^-1 * Y3^-1)^3, (Y2 * Y3^-1 * Y1)^2, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y3 * Y1 * Y2 * Y3 * Y2 * Y1 * 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, 22, 70)(9, 57, 28, 76)(12, 60, 23, 71)(13, 61, 35, 83)(14, 62, 27, 75)(15, 63, 30, 78)(16, 64, 25, 73)(18, 66, 42, 90)(19, 67, 26, 74)(20, 68, 43, 91)(21, 69, 45, 93)(24, 72, 41, 89)(29, 77, 40, 88)(31, 79, 38, 86)(32, 80, 39, 87)(33, 81, 44, 92)(34, 82, 46, 94)(36, 84, 48, 96)(37, 85, 47, 95)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 119, 167, 105, 153)(100, 148, 111, 159, 132, 180, 112, 160)(102, 150, 116, 164, 133, 181, 117, 165)(104, 152, 122, 170, 143, 191, 123, 171)(106, 154, 127, 175, 144, 192, 128, 176)(107, 155, 129, 177, 113, 161, 130, 178)(109, 157, 134, 182, 114, 162, 135, 183)(110, 158, 136, 184, 115, 163, 137, 185)(118, 166, 142, 190, 124, 172, 140, 188)(120, 168, 139, 187, 125, 173, 141, 189)(121, 169, 138, 186, 126, 174, 131, 179) L = (1, 100)(2, 104)(3, 109)(4, 102)(5, 114)(6, 97)(7, 120)(8, 106)(9, 125)(10, 98)(11, 123)(12, 132)(13, 110)(14, 99)(15, 136)(16, 137)(17, 122)(18, 115)(19, 101)(20, 140)(21, 142)(22, 112)(23, 143)(24, 121)(25, 103)(26, 138)(27, 131)(28, 111)(29, 126)(30, 105)(31, 130)(32, 129)(33, 139)(34, 141)(35, 107)(36, 133)(37, 108)(38, 117)(39, 116)(40, 124)(41, 118)(42, 113)(43, 128)(44, 135)(45, 127)(46, 134)(47, 144)(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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.749 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.748 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y3^-1 * Y1)^2, Y3^3 * Y2^-2, Y2^-1 * Y3^-3 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, (Y2^-2 * Y1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y1, Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 18, 66)(6, 54, 8, 56)(7, 55, 24, 72)(9, 57, 31, 79)(12, 60, 25, 73)(13, 61, 39, 87)(14, 62, 30, 78)(15, 63, 33, 81)(16, 64, 36, 84)(17, 65, 27, 75)(19, 67, 44, 92)(20, 68, 28, 76)(21, 69, 45, 93)(22, 70, 47, 95)(23, 71, 29, 77)(26, 74, 42, 90)(32, 80, 43, 91)(34, 82, 41, 89)(35, 83, 40, 88)(37, 85, 48, 96)(38, 86, 46, 94)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 121, 169, 105, 153)(100, 148, 111, 159, 119, 167, 113, 161)(102, 150, 117, 165, 112, 160, 118, 166)(104, 152, 124, 172, 132, 180, 126, 174)(106, 154, 130, 178, 125, 173, 131, 179)(107, 155, 133, 181, 114, 162, 134, 182)(109, 157, 136, 184, 115, 163, 137, 185)(110, 158, 138, 186, 116, 164, 139, 187)(120, 168, 142, 190, 127, 175, 144, 192)(122, 170, 143, 191, 128, 176, 141, 189)(123, 171, 135, 183, 129, 177, 140, 188) L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 115)(6, 97)(7, 122)(8, 125)(9, 128)(10, 98)(11, 126)(12, 119)(13, 116)(14, 99)(15, 138)(16, 108)(17, 139)(18, 124)(19, 110)(20, 101)(21, 142)(22, 144)(23, 102)(24, 113)(25, 132)(26, 129)(27, 103)(28, 135)(29, 121)(30, 140)(31, 111)(32, 123)(33, 105)(34, 133)(35, 134)(36, 106)(37, 143)(38, 141)(39, 107)(40, 118)(41, 117)(42, 120)(43, 127)(44, 114)(45, 130)(46, 136)(47, 131)(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 ) } Outer automorphisms :: reflexible Dual of E15.750 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.749 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1^-2 * Y3, Y1^-2 * Y3 * Y1 * Y3, Y1 * Y2 * Y1 * Y2 * Y3 * Y1, Y1^2 * Y2 * Y1 * Y2 * Y3, (Y3 * Y2 * Y1^-1)^2, (Y3 * Y1^-1)^3, Y1^6, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 23, 71, 19, 67, 5, 53)(3, 51, 11, 59, 32, 80, 46, 94, 27, 75, 13, 61)(4, 52, 15, 63, 37, 85, 45, 93, 20, 68, 16, 64)(6, 54, 21, 69, 9, 57, 30, 78, 42, 90, 22, 70)(8, 56, 26, 74, 38, 86, 35, 83, 41, 89, 28, 76)(10, 58, 31, 79, 25, 73, 33, 81, 44, 92, 18, 66)(12, 60, 36, 84, 17, 65, 43, 91, 39, 87, 24, 72)(14, 62, 40, 88, 34, 82, 48, 96, 47, 95, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 120, 168)(105, 153, 125, 173)(106, 154, 123, 171)(107, 155, 129, 177)(109, 157, 133, 181)(111, 159, 137, 185)(112, 160, 128, 176)(114, 162, 136, 184)(115, 163, 131, 179)(116, 164, 122, 170)(117, 165, 134, 182)(118, 166, 130, 178)(119, 167, 142, 190)(121, 169, 143, 191)(124, 172, 138, 186)(126, 174, 139, 187)(127, 175, 132, 180)(135, 183, 140, 188)(141, 189, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 102)(5, 114)(6, 97)(7, 121)(8, 123)(9, 106)(10, 98)(11, 130)(12, 110)(13, 134)(14, 99)(15, 103)(16, 127)(17, 122)(18, 116)(19, 118)(20, 101)(21, 133)(22, 129)(23, 141)(24, 137)(25, 111)(26, 136)(27, 125)(28, 132)(29, 104)(30, 119)(31, 138)(32, 124)(33, 115)(34, 131)(35, 107)(36, 128)(37, 140)(38, 135)(39, 109)(40, 113)(41, 143)(42, 112)(43, 144)(44, 117)(45, 126)(46, 139)(47, 120)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.747 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.750 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y1^2 * Y3^-1 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-3 * Y3^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 25, 73, 20, 68, 5, 53)(3, 51, 11, 59, 33, 81, 46, 94, 37, 85, 13, 61)(4, 52, 15, 63, 41, 89, 24, 72, 21, 69, 17, 65)(6, 54, 22, 70, 9, 57, 16, 64, 42, 90, 23, 71)(8, 56, 28, 76, 48, 96, 45, 93, 44, 92, 29, 77)(10, 58, 32, 80, 27, 75, 31, 79, 43, 91, 19, 67)(12, 60, 35, 83, 26, 74, 40, 88, 38, 86, 18, 66)(14, 62, 39, 87, 34, 82, 36, 84, 47, 95, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 114, 162)(102, 150, 108, 156)(103, 151, 122, 170)(105, 153, 126, 174)(106, 154, 107, 155)(109, 157, 113, 161)(111, 159, 124, 172)(112, 160, 136, 184)(115, 163, 135, 183)(116, 164, 141, 189)(117, 165, 140, 188)(118, 166, 125, 173)(119, 167, 130, 178)(120, 168, 132, 180)(121, 169, 142, 190)(123, 171, 143, 191)(127, 175, 133, 181)(128, 176, 131, 179)(129, 177, 137, 185)(134, 182, 139, 187)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 123)(8, 107)(9, 127)(10, 98)(11, 130)(12, 132)(13, 125)(14, 99)(15, 103)(16, 121)(17, 139)(18, 140)(19, 111)(20, 119)(21, 101)(22, 113)(23, 106)(24, 102)(25, 120)(26, 124)(27, 117)(28, 135)(29, 131)(30, 104)(31, 116)(32, 118)(33, 144)(34, 141)(35, 129)(36, 142)(37, 126)(38, 109)(39, 114)(40, 110)(41, 128)(42, 137)(43, 138)(44, 143)(45, 133)(46, 136)(47, 122)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.748 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.751 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, (Y1 * Y2)^2, (Y3^-1 * Y1 * Y3^-1)^2, (Y3 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 13, 61)(7, 55, 16, 64)(8, 56, 18, 66)(9, 57, 19, 67)(10, 58, 21, 69)(12, 60, 17, 65)(14, 62, 24, 72)(15, 63, 26, 74)(20, 68, 25, 73)(22, 70, 31, 79)(23, 71, 32, 80)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(33, 81, 41, 89)(34, 82, 42, 90)(39, 87, 44, 92)(40, 88, 43, 91)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 106, 154)(103, 151, 110, 158)(104, 152, 111, 159)(107, 155, 115, 163)(108, 156, 116, 164)(109, 157, 117, 165)(112, 160, 120, 168)(113, 161, 121, 169)(114, 162, 122, 170)(118, 166, 125, 173)(119, 167, 126, 174)(123, 171, 129, 177)(124, 172, 130, 178)(127, 175, 133, 181)(128, 176, 134, 182)(131, 179, 137, 185)(132, 180, 138, 186)(135, 183, 141, 189)(136, 184, 142, 190)(139, 187, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 97)(6, 110)(7, 113)(8, 98)(9, 116)(10, 99)(11, 118)(12, 101)(13, 119)(14, 121)(15, 102)(16, 123)(17, 104)(18, 124)(19, 125)(20, 106)(21, 126)(22, 109)(23, 107)(24, 129)(25, 111)(26, 130)(27, 114)(28, 112)(29, 117)(30, 115)(31, 135)(32, 136)(33, 122)(34, 120)(35, 139)(36, 140)(37, 141)(38, 142)(39, 128)(40, 127)(41, 143)(42, 144)(43, 132)(44, 131)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.776 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.752 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y1 * Y3 * Y2)^2, (Y3 * Y2)^4, (Y3 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 8, 56)(6, 54, 11, 59)(7, 55, 13, 61)(9, 57, 15, 63)(10, 58, 18, 66)(12, 60, 20, 68)(14, 62, 23, 71)(16, 64, 27, 75)(17, 65, 22, 70)(19, 67, 28, 76)(21, 69, 32, 80)(24, 72, 34, 82)(25, 73, 30, 78)(26, 74, 35, 83)(29, 77, 38, 86)(31, 79, 39, 87)(33, 81, 41, 89)(36, 84, 40, 88)(37, 85, 44, 92)(42, 90, 45, 93)(43, 91, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 105, 153)(102, 150, 108, 156)(103, 151, 110, 158)(104, 152, 111, 159)(106, 154, 115, 163)(107, 155, 116, 164)(109, 157, 119, 167)(112, 160, 120, 168)(113, 161, 121, 169)(114, 162, 124, 172)(117, 165, 125, 173)(118, 166, 126, 174)(122, 170, 129, 177)(123, 171, 130, 178)(127, 175, 133, 181)(128, 176, 134, 182)(131, 179, 137, 185)(132, 180, 139, 187)(135, 183, 140, 188)(136, 184, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 102)(3, 103)(4, 97)(5, 106)(6, 98)(7, 99)(8, 112)(9, 113)(10, 101)(11, 117)(12, 118)(13, 120)(14, 121)(15, 122)(16, 104)(17, 105)(18, 125)(19, 126)(20, 127)(21, 107)(22, 108)(23, 129)(24, 109)(25, 110)(26, 111)(27, 132)(28, 133)(29, 114)(30, 115)(31, 116)(32, 136)(33, 119)(34, 138)(35, 139)(36, 123)(37, 124)(38, 141)(39, 142)(40, 128)(41, 143)(42, 130)(43, 131)(44, 144)(45, 134)(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) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.775 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.753 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2, (Y3 * Y2)^4, (Y3 * Y1)^6 ] Map:: polytopal 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, 16, 64)(10, 58, 19, 67)(12, 60, 21, 69)(14, 62, 24, 72)(15, 63, 20, 68)(17, 65, 26, 74)(18, 66, 27, 75)(22, 70, 30, 78)(23, 71, 31, 79)(25, 73, 33, 81)(28, 76, 36, 84)(29, 77, 37, 85)(32, 80, 40, 88)(34, 82, 42, 90)(35, 83, 39, 87)(38, 86, 45, 93)(41, 89, 46, 94)(43, 91, 44, 92)(47, 95, 48, 96)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 106, 154)(102, 150, 110, 158)(103, 151, 111, 159)(104, 152, 113, 161)(105, 153, 112, 160)(107, 155, 116, 164)(108, 156, 118, 166)(109, 157, 117, 165)(114, 162, 124, 172)(115, 163, 122, 170)(119, 167, 128, 176)(120, 168, 126, 174)(121, 169, 130, 178)(123, 171, 129, 177)(125, 173, 134, 182)(127, 175, 133, 181)(131, 179, 139, 187)(132, 180, 138, 186)(135, 183, 142, 190)(136, 184, 141, 189)(137, 185, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 102)(3, 104)(4, 97)(5, 108)(6, 98)(7, 110)(8, 99)(9, 114)(10, 107)(11, 106)(12, 101)(13, 119)(14, 103)(15, 118)(16, 121)(17, 116)(18, 105)(19, 124)(20, 113)(21, 125)(22, 111)(23, 109)(24, 128)(25, 112)(26, 130)(27, 131)(28, 115)(29, 117)(30, 134)(31, 135)(32, 120)(33, 137)(34, 122)(35, 123)(36, 139)(37, 140)(38, 126)(39, 127)(40, 142)(41, 129)(42, 143)(43, 132)(44, 133)(45, 144)(46, 136)(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) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.773 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.754 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^4, (Y3^-2 * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y3 * Y1)^6 ] Map:: polytopal 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, 17, 65)(11, 59, 16, 64)(13, 61, 19, 67)(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, 47, 95)(43, 91, 46, 94)(44, 92, 48, 96)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 106, 154)(101, 149, 107, 155)(103, 151, 112, 160)(104, 152, 113, 161)(105, 153, 117, 165)(108, 156, 119, 167)(109, 157, 120, 168)(110, 158, 118, 166)(111, 159, 122, 170)(114, 162, 124, 172)(115, 163, 125, 173)(116, 164, 123, 171)(121, 169, 129, 177)(126, 174, 134, 182)(127, 175, 137, 185)(128, 176, 139, 187)(130, 178, 138, 186)(131, 179, 140, 188)(132, 180, 141, 189)(133, 181, 143, 191)(135, 183, 142, 190)(136, 184, 144, 192) L = (1, 100)(2, 103)(3, 106)(4, 109)(5, 97)(6, 112)(7, 115)(8, 98)(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, 110)(22, 129)(23, 105)(24, 107)(25, 108)(26, 116)(27, 134)(28, 111)(29, 113)(30, 114)(31, 138)(32, 137)(33, 119)(34, 140)(35, 139)(36, 142)(37, 141)(38, 124)(39, 144)(40, 143)(41, 130)(42, 131)(43, 127)(44, 128)(45, 135)(46, 136)(47, 132)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.774 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.755 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = C2 x D24 (small group id <48, 36>) Aut = C2 x C2 x D24 (small group id <96, 207>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^4, Y3^-6 * Y2^2 ] Map:: polytopal 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, 18, 66)(12, 60, 23, 71)(13, 61, 22, 70)(14, 62, 24, 72)(15, 63, 20, 68)(16, 64, 19, 67)(17, 65, 21, 69)(25, 73, 34, 82)(26, 74, 33, 81)(27, 75, 39, 87)(28, 76, 38, 86)(29, 77, 40, 88)(30, 78, 36, 84)(31, 79, 35, 83)(32, 80, 37, 85)(41, 89, 46, 94)(42, 90, 45, 93)(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, 108, 156, 121, 169, 111, 159)(102, 150, 109, 157, 122, 170, 112, 160)(104, 152, 115, 163, 129, 177, 118, 166)(106, 154, 116, 164, 130, 178, 119, 167)(110, 158, 123, 171, 137, 185, 126, 174)(113, 161, 124, 172, 138, 186, 127, 175)(117, 165, 131, 179, 141, 189, 134, 182)(120, 168, 132, 180, 142, 190, 135, 183)(125, 173, 139, 187, 128, 176, 140, 188)(133, 181, 143, 191, 136, 184, 144, 192) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 126)(16, 101)(17, 102)(18, 129)(19, 131)(20, 103)(21, 133)(22, 134)(23, 105)(24, 106)(25, 137)(26, 107)(27, 139)(28, 109)(29, 138)(30, 140)(31, 112)(32, 113)(33, 141)(34, 114)(35, 143)(36, 116)(37, 142)(38, 144)(39, 119)(40, 120)(41, 128)(42, 122)(43, 127)(44, 124)(45, 136)(46, 130)(47, 135)(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, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.764 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.756 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1, Y2^4, Y3^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 10, 58)(5, 53, 9, 57)(6, 54, 8, 56)(11, 59, 18, 66)(12, 60, 20, 68)(13, 61, 19, 67)(14, 62, 23, 71)(15, 63, 24, 72)(16, 64, 21, 69)(17, 65, 22, 70)(25, 73, 33, 81)(26, 74, 32, 80)(27, 75, 35, 83)(28, 76, 34, 82)(29, 77, 38, 86)(30, 78, 37, 85)(31, 79, 36, 84)(39, 87, 44, 92)(40, 88, 43, 91)(41, 89, 45, 93)(42, 90, 46, 94)(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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.771 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.757 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y2^-1 * Y1)^2, Y2^4, Y3^6 ] Map:: polytopal 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, 18, 66)(12, 60, 23, 71)(13, 61, 21, 69)(14, 62, 20, 68)(15, 63, 24, 72)(16, 64, 19, 67)(17, 65, 22, 70)(25, 73, 33, 81)(26, 74, 32, 80)(27, 75, 38, 86)(28, 76, 36, 84)(29, 77, 35, 83)(30, 78, 37, 85)(31, 79, 34, 82)(39, 87, 44, 92)(40, 88, 43, 91)(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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.768 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.758 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y2^4, (Y3 * Y2^-2)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 16, 64)(12, 60, 17, 65)(13, 61, 18, 66)(19, 67, 24, 72)(20, 68, 25, 73)(21, 69, 26, 74)(22, 70, 27, 75)(23, 71, 28, 76)(29, 77, 33, 81)(30, 78, 34, 82)(31, 79, 35, 83)(32, 80, 36, 84)(37, 85, 41, 89)(38, 86, 42, 90)(39, 87, 43, 91)(40, 88, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 110, 158, 104, 152)(100, 148, 107, 155, 115, 163, 108, 156)(103, 151, 112, 160, 120, 168, 113, 161)(106, 154, 116, 164, 109, 157, 117, 165)(111, 159, 121, 169, 114, 162, 122, 170)(118, 166, 127, 175, 119, 167, 128, 176)(123, 171, 131, 179, 124, 172, 132, 180)(125, 173, 133, 181, 126, 174, 134, 182)(129, 177, 137, 185, 130, 178, 138, 186)(135, 183, 142, 190, 136, 184, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 111)(7, 98)(8, 114)(9, 115)(10, 99)(11, 118)(12, 119)(13, 101)(14, 120)(15, 102)(16, 123)(17, 124)(18, 104)(19, 105)(20, 125)(21, 126)(22, 107)(23, 108)(24, 110)(25, 129)(26, 130)(27, 112)(28, 113)(29, 116)(30, 117)(31, 135)(32, 136)(33, 121)(34, 122)(35, 139)(36, 140)(37, 141)(38, 142)(39, 127)(40, 128)(41, 143)(42, 144)(43, 131)(44, 132)(45, 133)(46, 134)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.769 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.759 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, Y2^4, (Y2 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y3 * Y2^-2)^2, Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1, (Y3 * Y2)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 8, 56)(4, 52, 7, 55)(5, 53, 6, 54)(9, 57, 14, 62)(10, 58, 18, 66)(11, 59, 17, 65)(12, 60, 16, 64)(13, 61, 15, 63)(19, 67, 24, 72)(20, 68, 25, 73)(21, 69, 26, 74)(22, 70, 28, 76)(23, 71, 27, 75)(29, 77, 33, 81)(30, 78, 34, 82)(31, 79, 35, 83)(32, 80, 36, 84)(37, 85, 42, 90)(38, 86, 41, 89)(39, 87, 43, 91)(40, 88, 44, 92)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 110, 158, 104, 152)(100, 148, 107, 155, 115, 163, 108, 156)(103, 151, 112, 160, 120, 168, 113, 161)(106, 154, 116, 164, 109, 157, 117, 165)(111, 159, 121, 169, 114, 162, 122, 170)(118, 166, 127, 175, 119, 167, 128, 176)(123, 171, 131, 179, 124, 172, 132, 180)(125, 173, 133, 181, 126, 174, 134, 182)(129, 177, 137, 185, 130, 178, 138, 186)(135, 183, 142, 190, 136, 184, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 111)(7, 98)(8, 114)(9, 115)(10, 99)(11, 118)(12, 119)(13, 101)(14, 120)(15, 102)(16, 123)(17, 124)(18, 104)(19, 105)(20, 125)(21, 126)(22, 107)(23, 108)(24, 110)(25, 129)(26, 130)(27, 112)(28, 113)(29, 116)(30, 117)(31, 135)(32, 136)(33, 121)(34, 122)(35, 139)(36, 140)(37, 141)(38, 142)(39, 127)(40, 128)(41, 143)(42, 144)(43, 131)(44, 132)(45, 133)(46, 134)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.767 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.760 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y2^4, (R * Y1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2 * Y3 * Y1)^2, (Y3 * Y2^-2)^2, (R * Y2 * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 16, 64)(8, 56, 21, 69)(10, 58, 17, 65)(11, 59, 20, 68)(12, 60, 22, 70)(13, 61, 18, 66)(15, 63, 19, 67)(23, 71, 33, 81)(24, 72, 35, 83)(25, 73, 30, 78)(26, 74, 36, 84)(27, 75, 34, 82)(28, 76, 37, 85)(29, 77, 39, 87)(31, 79, 40, 88)(32, 80, 38, 86)(41, 89, 45, 93)(42, 90, 46, 94)(43, 91, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 113, 161, 104, 152)(100, 148, 108, 156, 121, 169, 109, 157)(103, 151, 115, 163, 126, 174, 116, 164)(105, 153, 119, 167, 110, 158, 120, 168)(107, 155, 122, 170, 111, 159, 123, 171)(112, 160, 124, 172, 117, 165, 125, 173)(114, 162, 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, 100)(2, 103)(3, 107)(4, 97)(5, 111)(6, 114)(7, 98)(8, 118)(9, 116)(10, 121)(11, 99)(12, 117)(13, 112)(14, 115)(15, 101)(16, 109)(17, 126)(18, 102)(19, 110)(20, 105)(21, 108)(22, 104)(23, 130)(24, 132)(25, 106)(26, 131)(27, 129)(28, 134)(29, 136)(30, 113)(31, 135)(32, 133)(33, 123)(34, 119)(35, 122)(36, 120)(37, 128)(38, 124)(39, 127)(40, 125)(41, 144)(42, 143)(43, 142)(44, 141)(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 ) } Outer automorphisms :: reflexible Dual of E15.766 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.761 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, (R * Y2 * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 16, 64)(8, 56, 21, 69)(10, 58, 17, 65)(11, 59, 19, 67)(12, 60, 18, 66)(13, 61, 22, 70)(15, 63, 20, 68)(23, 71, 33, 81)(24, 72, 35, 83)(25, 73, 30, 78)(26, 74, 34, 82)(27, 75, 36, 84)(28, 76, 37, 85)(29, 77, 39, 87)(31, 79, 38, 86)(32, 80, 40, 88)(41, 89, 46, 94)(42, 90, 45, 93)(43, 91, 48, 96)(44, 92, 47, 95)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 113, 161, 104, 152)(100, 148, 108, 156, 121, 169, 109, 157)(103, 151, 115, 163, 126, 174, 116, 164)(105, 153, 119, 167, 110, 158, 120, 168)(107, 155, 122, 170, 111, 159, 123, 171)(112, 160, 124, 172, 117, 165, 125, 173)(114, 162, 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, 100)(2, 103)(3, 107)(4, 97)(5, 111)(6, 114)(7, 98)(8, 118)(9, 115)(10, 121)(11, 99)(12, 112)(13, 117)(14, 116)(15, 101)(16, 108)(17, 126)(18, 102)(19, 105)(20, 110)(21, 109)(22, 104)(23, 130)(24, 132)(25, 106)(26, 129)(27, 131)(28, 134)(29, 136)(30, 113)(31, 133)(32, 135)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 124)(39, 128)(40, 125)(41, 144)(42, 143)(43, 142)(44, 141)(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 ) } Outer automorphisms :: reflexible Dual of E15.765 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.762 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, Y3^-2 * Y2^-2, Y3^4, (R * Y1)^2, Y3^-1 * Y2^2 * Y3^-1, (R * Y3)^2, Y2^4, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal 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, 16, 64)(12, 60, 17, 65)(13, 61, 18, 66)(14, 62, 19, 67)(15, 63, 20, 68)(21, 69, 26, 74)(22, 70, 25, 73)(23, 71, 28, 76)(24, 72, 27, 75)(29, 77, 33, 81)(30, 78, 34, 82)(31, 79, 35, 83)(32, 80, 36, 84)(37, 85, 42, 90)(38, 86, 41, 89)(39, 87, 44, 92)(40, 88, 43, 91)(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, 110, 158, 102, 150, 111, 159)(104, 152, 115, 163, 106, 154, 116, 164)(108, 156, 117, 165, 109, 157, 118, 166)(113, 161, 121, 169, 114, 162, 122, 170)(119, 167, 127, 175, 120, 168, 128, 176)(123, 171, 131, 179, 124, 172, 132, 180)(125, 173, 133, 181, 126, 174, 134, 182)(129, 177, 137, 185, 130, 178, 138, 186)(135, 183, 141, 189, 136, 184, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192) 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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.770 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.763 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^4, Y3^6 * Y2^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 10, 58)(5, 53, 9, 57)(6, 54, 8, 56)(11, 59, 18, 66)(12, 60, 20, 68)(13, 61, 19, 67)(14, 62, 24, 72)(15, 63, 23, 71)(16, 64, 22, 70)(17, 65, 21, 69)(25, 73, 34, 82)(26, 74, 33, 81)(27, 75, 36, 84)(28, 76, 35, 83)(29, 77, 40, 88)(30, 78, 39, 87)(31, 79, 38, 86)(32, 80, 37, 85)(41, 89, 46, 94)(42, 90, 45, 93)(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, 108, 156, 121, 169, 111, 159)(102, 150, 109, 157, 122, 170, 112, 160)(104, 152, 115, 163, 129, 177, 118, 166)(106, 154, 116, 164, 130, 178, 119, 167)(110, 158, 123, 171, 137, 185, 126, 174)(113, 161, 124, 172, 138, 186, 127, 175)(117, 165, 131, 179, 141, 189, 134, 182)(120, 168, 132, 180, 142, 190, 135, 183)(125, 173, 139, 187, 128, 176, 140, 188)(133, 181, 143, 191, 136, 184, 144, 192) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 126)(16, 101)(17, 102)(18, 129)(19, 131)(20, 103)(21, 133)(22, 134)(23, 105)(24, 106)(25, 137)(26, 107)(27, 139)(28, 109)(29, 138)(30, 140)(31, 112)(32, 113)(33, 141)(34, 114)(35, 143)(36, 116)(37, 142)(38, 144)(39, 119)(40, 120)(41, 128)(42, 122)(43, 127)(44, 124)(45, 136)(46, 130)(47, 135)(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, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.772 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.764 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = C2 x D24 (small group id <48, 36>) Aut = C2 x C2 x D24 (small group id <96, 207>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^4 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 35, 83, 20, 68, 8, 56)(4, 52, 9, 57, 21, 69, 36, 84, 32, 80, 15, 63)(6, 54, 10, 58, 22, 70, 37, 85, 33, 81, 17, 65)(12, 60, 28, 76, 43, 91, 46, 94, 38, 86, 23, 71)(13, 61, 29, 77, 44, 92, 47, 95, 39, 87, 24, 72)(14, 62, 25, 73, 40, 88, 34, 82, 18, 66, 26, 74)(30, 78, 45, 93, 48, 96, 42, 90, 31, 79, 41, 89)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 116, 164)(105, 153, 120, 168)(106, 154, 119, 167)(110, 158, 127, 175)(111, 159, 125, 173)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 126, 174)(115, 163, 131, 179)(117, 165, 135, 183)(118, 166, 134, 182)(121, 169, 138, 186)(122, 170, 137, 185)(128, 176, 140, 188)(129, 177, 139, 187)(130, 178, 141, 189)(132, 180, 143, 191)(133, 181, 142, 190)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 111)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 124)(12, 126)(13, 99)(14, 118)(15, 122)(16, 128)(17, 101)(18, 102)(19, 132)(20, 134)(21, 136)(22, 103)(23, 137)(24, 104)(25, 133)(26, 106)(27, 139)(28, 141)(29, 107)(30, 140)(31, 109)(32, 114)(33, 112)(34, 113)(35, 142)(36, 130)(37, 115)(38, 127)(39, 116)(40, 129)(41, 125)(42, 120)(43, 144)(44, 123)(45, 143)(46, 138)(47, 131)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.755 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.765 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (Y1^-2 * Y3)^2, Y1^6, (Y3 * Y1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 14, 62, 5, 53)(3, 51, 7, 55, 16, 64, 29, 77, 24, 72, 10, 58)(4, 52, 11, 59, 25, 73, 32, 80, 17, 65, 12, 60)(8, 56, 19, 67, 13, 61, 28, 76, 30, 78, 20, 68)(9, 57, 21, 69, 37, 85, 43, 91, 31, 79, 22, 70)(18, 66, 33, 81, 23, 71, 40, 88, 42, 90, 34, 82)(26, 74, 35, 83, 27, 75, 36, 84, 44, 92, 41, 89)(38, 86, 45, 93, 39, 87, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 105, 153)(101, 149, 106, 154)(102, 150, 112, 160)(104, 152, 114, 162)(107, 155, 117, 165)(108, 156, 118, 166)(109, 157, 119, 167)(110, 158, 120, 168)(111, 159, 125, 173)(113, 161, 127, 175)(115, 163, 129, 177)(116, 164, 130, 178)(121, 169, 133, 181)(122, 170, 134, 182)(123, 171, 135, 183)(124, 172, 136, 184)(126, 174, 138, 186)(128, 176, 139, 187)(131, 179, 141, 189)(132, 180, 142, 190)(137, 185, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 109)(6, 113)(7, 114)(8, 98)(9, 99)(10, 119)(11, 122)(12, 123)(13, 101)(14, 121)(15, 126)(16, 127)(17, 102)(18, 103)(19, 131)(20, 132)(21, 134)(22, 135)(23, 106)(24, 133)(25, 110)(26, 107)(27, 108)(28, 137)(29, 138)(30, 111)(31, 112)(32, 140)(33, 141)(34, 142)(35, 115)(36, 116)(37, 120)(38, 117)(39, 118)(40, 143)(41, 124)(42, 125)(43, 144)(44, 128)(45, 129)(46, 130)(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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.761 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.766 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2 * Y1^-1)^2, (Y3 * Y1^-2)^2, Y1^6, Y2 * Y1^2 * Y2 * Y1^-2, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2, (Y1 * Y2 * Y1^-1 * Y2)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 16, 64, 5, 53)(3, 51, 9, 57, 18, 66, 36, 84, 30, 78, 11, 59)(4, 52, 12, 60, 31, 79, 38, 86, 19, 67, 13, 61)(7, 55, 20, 68, 34, 82, 32, 80, 14, 62, 22, 70)(8, 56, 23, 71, 15, 63, 33, 81, 35, 83, 24, 72)(10, 58, 27, 75, 43, 91, 46, 94, 37, 85, 21, 69)(25, 73, 39, 87, 47, 95, 44, 92, 28, 76, 41, 89)(26, 74, 42, 90, 29, 77, 45, 93, 48, 96, 40, 88)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 110, 158)(102, 150, 114, 162)(104, 152, 117, 165)(105, 153, 121, 169)(107, 155, 124, 172)(108, 156, 125, 173)(109, 157, 122, 170)(111, 159, 123, 171)(112, 160, 126, 174)(113, 161, 130, 178)(115, 163, 133, 181)(116, 164, 135, 183)(118, 166, 137, 185)(119, 167, 138, 186)(120, 168, 136, 184)(127, 175, 139, 187)(128, 176, 140, 188)(129, 177, 141, 189)(131, 179, 142, 190)(132, 180, 143, 191)(134, 182, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 111)(6, 115)(7, 117)(8, 98)(9, 122)(10, 99)(11, 125)(12, 124)(13, 121)(14, 123)(15, 101)(16, 127)(17, 131)(18, 133)(19, 102)(20, 136)(21, 103)(22, 138)(23, 137)(24, 135)(25, 109)(26, 105)(27, 110)(28, 108)(29, 107)(30, 139)(31, 112)(32, 141)(33, 140)(34, 142)(35, 113)(36, 144)(37, 114)(38, 143)(39, 120)(40, 116)(41, 119)(42, 118)(43, 126)(44, 129)(45, 128)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.760 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.767 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y1^-2 * Y3)^2, Y1^6, (Y3 * Y1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 14, 62, 5, 53)(3, 51, 9, 57, 21, 69, 29, 77, 16, 64, 7, 55)(4, 52, 11, 59, 25, 73, 32, 80, 17, 65, 12, 60)(8, 56, 19, 67, 13, 61, 28, 76, 30, 78, 20, 68)(10, 58, 23, 71, 31, 79, 43, 91, 37, 85, 24, 72)(18, 66, 33, 81, 42, 90, 38, 86, 22, 70, 34, 82)(26, 74, 35, 83, 27, 75, 36, 84, 44, 92, 41, 89)(39, 87, 46, 94, 40, 88, 47, 95, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 105, 153)(102, 150, 112, 160)(104, 152, 114, 162)(107, 155, 120, 168)(108, 156, 119, 167)(109, 157, 118, 166)(110, 158, 117, 165)(111, 159, 125, 173)(113, 161, 127, 175)(115, 163, 130, 178)(116, 164, 129, 177)(121, 169, 133, 181)(122, 170, 136, 184)(123, 171, 135, 183)(124, 172, 134, 182)(126, 174, 138, 186)(128, 176, 139, 187)(131, 179, 142, 190)(132, 180, 141, 189)(137, 185, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 113)(7, 114)(8, 98)(9, 118)(10, 99)(11, 122)(12, 123)(13, 101)(14, 121)(15, 126)(16, 127)(17, 102)(18, 103)(19, 131)(20, 132)(21, 133)(22, 105)(23, 135)(24, 136)(25, 110)(26, 107)(27, 108)(28, 137)(29, 138)(30, 111)(31, 112)(32, 140)(33, 141)(34, 142)(35, 115)(36, 116)(37, 117)(38, 143)(39, 119)(40, 120)(41, 124)(42, 125)(43, 144)(44, 128)(45, 129)(46, 130)(47, 134)(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 ) } Outer automorphisms :: reflexible Dual of E15.759 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.768 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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^-2 * Y1^-2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y3^6, Y3^-1 * Y1^4 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 15, 63, 5, 53)(3, 51, 11, 59, 27, 75, 35, 83, 20, 68, 8, 56)(4, 52, 14, 62, 6, 54, 18, 66, 21, 69, 16, 64)(9, 57, 24, 72, 10, 58, 26, 74, 17, 65, 25, 73)(12, 60, 29, 77, 13, 61, 31, 79, 36, 84, 30, 78)(22, 70, 37, 85, 23, 71, 39, 87, 28, 76, 38, 86)(32, 80, 40, 88, 33, 81, 41, 89, 34, 82, 42, 90)(43, 91, 47, 95, 44, 92, 48, 96, 45, 93, 46, 94)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 116, 164)(105, 153, 119, 167)(106, 154, 118, 166)(110, 158, 125, 173)(111, 159, 123, 171)(112, 160, 127, 175)(113, 161, 124, 172)(114, 162, 126, 174)(115, 163, 131, 179)(117, 165, 132, 180)(120, 168, 133, 181)(121, 169, 135, 183)(122, 170, 134, 182)(128, 176, 140, 188)(129, 177, 139, 187)(130, 178, 141, 189)(136, 184, 143, 191)(137, 185, 142, 190)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 113)(6, 97)(7, 102)(8, 118)(9, 101)(10, 98)(11, 119)(12, 116)(13, 99)(14, 128)(15, 117)(16, 130)(17, 115)(18, 129)(19, 106)(20, 132)(21, 103)(22, 131)(23, 104)(24, 136)(25, 138)(26, 137)(27, 109)(28, 107)(29, 139)(30, 141)(31, 140)(32, 112)(33, 110)(34, 114)(35, 124)(36, 123)(37, 142)(38, 144)(39, 143)(40, 121)(41, 120)(42, 122)(43, 126)(44, 125)(45, 127)(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, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.757 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.769 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, (Y3 * Y1^-2)^2, Y1^6, (Y2 * Y1^-2)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1^-1 * Y2, (Y1^-1 * Y3)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 16, 64, 5, 53)(3, 51, 9, 57, 25, 73, 37, 85, 18, 66, 11, 59)(4, 52, 12, 60, 31, 79, 38, 86, 19, 67, 13, 61)(7, 55, 20, 68, 14, 62, 32, 80, 34, 82, 22, 70)(8, 56, 23, 71, 15, 63, 33, 81, 35, 83, 24, 72)(10, 58, 21, 69, 36, 84, 46, 94, 43, 91, 28, 76)(26, 74, 39, 87, 29, 77, 41, 89, 47, 95, 44, 92)(27, 75, 40, 88, 30, 78, 42, 90, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 110, 158)(102, 150, 114, 162)(104, 152, 117, 165)(105, 153, 122, 170)(107, 155, 125, 173)(108, 156, 123, 171)(109, 157, 126, 174)(111, 159, 124, 172)(112, 160, 121, 169)(113, 161, 130, 178)(115, 163, 132, 180)(116, 164, 135, 183)(118, 166, 137, 185)(119, 167, 136, 184)(120, 168, 138, 186)(127, 175, 139, 187)(128, 176, 140, 188)(129, 177, 141, 189)(131, 179, 142, 190)(133, 181, 143, 191)(134, 182, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 111)(6, 115)(7, 117)(8, 98)(9, 123)(10, 99)(11, 126)(12, 122)(13, 125)(14, 124)(15, 101)(16, 127)(17, 131)(18, 132)(19, 102)(20, 136)(21, 103)(22, 138)(23, 135)(24, 137)(25, 139)(26, 108)(27, 105)(28, 110)(29, 109)(30, 107)(31, 112)(32, 141)(33, 140)(34, 142)(35, 113)(36, 114)(37, 144)(38, 143)(39, 119)(40, 116)(41, 120)(42, 118)(43, 121)(44, 129)(45, 128)(46, 130)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.758 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.770 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y3^4, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 18, 66, 16, 64, 5, 53)(3, 51, 11, 59, 25, 73, 32, 80, 19, 67, 8, 56)(4, 52, 14, 62, 29, 77, 33, 81, 20, 68, 9, 57)(6, 54, 17, 65, 31, 79, 34, 82, 21, 69, 10, 58)(12, 60, 22, 70, 35, 83, 43, 91, 39, 87, 26, 74)(13, 61, 23, 71, 36, 84, 44, 92, 40, 88, 27, 75)(15, 63, 24, 72, 37, 85, 45, 93, 42, 90, 30, 78)(28, 76, 41, 89, 47, 95, 48, 96, 46, 94, 38, 86)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 115, 163)(105, 153, 119, 167)(106, 154, 118, 166)(110, 158, 123, 171)(111, 159, 124, 172)(112, 160, 121, 169)(113, 161, 122, 170)(114, 162, 128, 176)(116, 164, 132, 180)(117, 165, 131, 179)(120, 168, 134, 182)(125, 173, 136, 184)(126, 174, 137, 185)(127, 175, 135, 183)(129, 177, 140, 188)(130, 178, 139, 187)(133, 181, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 105)(3, 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, 129)(19, 131)(20, 133)(21, 103)(22, 134)(23, 104)(24, 106)(25, 135)(26, 137)(27, 107)(28, 109)(29, 138)(30, 113)(31, 112)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.762 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.771 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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^-1 * Y2)^2, Y1^2 * Y3^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1 * Y2)^2, (Y3 * Y2 * Y1^-1)^2, Y1^-1 * Y3^4 * Y1^-1, Y2 * Y1 * Y3^-1 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 21, 69, 16, 64, 5, 53)(3, 51, 11, 59, 31, 79, 42, 90, 22, 70, 13, 61)(4, 52, 15, 63, 6, 54, 20, 68, 23, 71, 17, 65)(8, 56, 24, 72, 18, 66, 39, 87, 40, 88, 26, 74)(9, 57, 28, 76, 10, 58, 30, 78, 19, 67, 29, 77)(12, 60, 27, 75, 14, 62, 37, 85, 41, 89, 25, 73)(32, 80, 43, 91, 35, 83, 46, 94, 38, 86, 48, 96)(33, 81, 45, 93, 34, 82, 47, 95, 36, 84, 44, 92)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 114, 162)(102, 150, 108, 156)(103, 151, 118, 166)(105, 153, 123, 171)(106, 154, 121, 169)(107, 155, 128, 176)(109, 157, 131, 179)(111, 159, 129, 177)(112, 160, 127, 175)(113, 161, 130, 178)(115, 163, 133, 181)(116, 164, 132, 180)(117, 165, 136, 184)(119, 167, 137, 185)(120, 168, 139, 187)(122, 170, 142, 190)(124, 172, 140, 188)(125, 173, 141, 189)(126, 174, 143, 191)(134, 182, 138, 186)(135, 183, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 102)(8, 121)(9, 101)(10, 98)(11, 129)(12, 118)(13, 132)(14, 99)(15, 128)(16, 119)(17, 134)(18, 123)(19, 117)(20, 131)(21, 106)(22, 137)(23, 103)(24, 140)(25, 136)(26, 143)(27, 104)(28, 139)(29, 144)(30, 142)(31, 110)(32, 113)(33, 109)(34, 107)(35, 111)(36, 138)(37, 114)(38, 116)(39, 141)(40, 133)(41, 127)(42, 130)(43, 125)(44, 122)(45, 120)(46, 124)(47, 135)(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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.756 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.772 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4 * Y1^-2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, (Y2 * Y1^-2)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 21, 69, 18, 66, 5, 53)(3, 51, 11, 59, 31, 79, 44, 92, 22, 70, 13, 61)(4, 52, 9, 57, 23, 71, 41, 89, 38, 86, 16, 64)(6, 54, 10, 58, 24, 72, 42, 90, 39, 87, 19, 67)(8, 56, 25, 73, 17, 65, 36, 84, 40, 88, 27, 75)(12, 60, 28, 76, 47, 95, 37, 85, 43, 91, 33, 81)(14, 62, 32, 80, 48, 96, 26, 74, 45, 93, 35, 83)(15, 63, 29, 77, 46, 94, 34, 82, 20, 68, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 118, 166)(105, 153, 124, 172)(106, 154, 122, 170)(107, 155, 125, 173)(109, 157, 130, 178)(111, 159, 132, 180)(112, 160, 133, 181)(114, 162, 127, 175)(115, 163, 131, 179)(116, 164, 123, 171)(117, 165, 136, 184)(119, 167, 141, 189)(120, 168, 139, 187)(121, 169, 142, 190)(126, 174, 140, 188)(128, 176, 138, 186)(129, 177, 137, 185)(134, 182, 144, 192)(135, 183, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 112)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 124)(12, 123)(13, 129)(14, 99)(15, 120)(16, 126)(17, 131)(18, 134)(19, 101)(20, 102)(21, 137)(22, 139)(23, 142)(24, 103)(25, 141)(26, 140)(27, 144)(28, 104)(29, 138)(30, 106)(31, 143)(32, 107)(33, 136)(34, 115)(35, 109)(36, 110)(37, 113)(38, 116)(39, 114)(40, 128)(41, 130)(42, 117)(43, 132)(44, 133)(45, 118)(46, 135)(47, 121)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.763 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.773 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 * R * Y2^-1, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, Y1^4, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2^6 ] Map:: polytopal 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, 111, 159, 126, 174, 135, 183, 122, 170, 108, 156)(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, 119, 167, 134, 182, 142, 190, 133, 181, 118, 166)(110, 158, 124, 172, 137, 185, 143, 191, 138, 186, 125, 173)(115, 163, 130, 178, 141, 189, 144, 192, 140, 188, 129, 177) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.753 Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.774 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y2^-1 * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^4, Y2^6 ] Map:: polytopal 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, 111, 159, 126, 174, 137, 185, 124, 172, 109, 157)(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, 119, 167, 134, 182, 142, 190, 133, 181, 118, 166)(110, 158, 125, 173, 138, 186, 143, 191, 136, 184, 122, 170)(115, 163, 130, 178, 141, 189, 144, 192, 140, 188, 129, 177) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.754 Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.775 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y2^-1)^2, Y1^4, Y2^6 ] Map:: polytopal 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, 111, 159, 126, 174, 137, 185, 124, 172, 109, 157)(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, 119, 167, 134, 182, 142, 190, 133, 181, 118, 166)(110, 158, 121, 169, 135, 183, 143, 191, 138, 186, 125, 173)(115, 163, 130, 178, 141, 189, 144, 192, 140, 188, 129, 177) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.752 Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.776 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 * Y1^2, (Y3^-1, Y1^-1), Y3^2 * Y1^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, (Y2^-1 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: polytopal 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, 113, 161, 129, 177, 141, 189, 127, 175, 112, 160)(101, 149, 114, 162, 130, 178, 139, 187, 125, 173, 109, 157)(103, 151, 115, 163, 131, 179, 140, 188, 128, 176, 111, 159)(104, 152, 117, 165, 132, 180, 142, 190, 133, 181, 118, 166)(106, 154, 122, 170, 137, 185, 144, 192, 135, 183, 121, 169)(108, 156, 123, 171, 138, 186, 143, 191, 136, 184, 120, 168) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.751 Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.777 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, Y2 * Y3^-1 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^4, Y1 * Y2 * Y3^2 * Y1 * Y2, (Y3^-1 * Y1)^6 ] Map:: polytopal 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, 21, 69)(11, 59, 22, 70)(13, 61, 19, 67)(16, 64, 25, 73)(17, 65, 26, 74)(23, 71, 31, 79)(24, 72, 32, 80)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(33, 81, 41, 89)(34, 82, 42, 90)(39, 87, 44, 92)(40, 88, 43, 91)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 106, 154)(101, 149, 107, 155)(103, 151, 112, 160)(104, 152, 113, 161)(105, 153, 115, 163)(108, 156, 118, 166)(109, 157, 111, 159)(110, 158, 117, 165)(114, 162, 122, 170)(116, 164, 121, 169)(119, 167, 126, 174)(120, 168, 125, 173)(123, 171, 130, 178)(124, 172, 129, 177)(127, 175, 133, 181)(128, 176, 134, 182)(131, 179, 137, 185)(132, 180, 138, 186)(135, 183, 141, 189)(136, 184, 142, 190)(139, 187, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 103)(3, 106)(4, 109)(5, 97)(6, 112)(7, 115)(8, 98)(9, 113)(10, 111)(11, 99)(12, 119)(13, 101)(14, 120)(15, 107)(16, 105)(17, 102)(18, 123)(19, 104)(20, 124)(21, 125)(22, 126)(23, 110)(24, 108)(25, 129)(26, 130)(27, 116)(28, 114)(29, 118)(30, 117)(31, 135)(32, 136)(33, 122)(34, 121)(35, 139)(36, 140)(37, 141)(38, 142)(39, 128)(40, 127)(41, 143)(42, 144)(43, 132)(44, 131)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.782 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.778 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, Y2^4, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^-1 * Y2^2 * Y3^-1, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 10, 58)(5, 53, 9, 57)(6, 54, 8, 56)(11, 59, 16, 64)(12, 60, 18, 66)(13, 61, 17, 65)(14, 62, 20, 68)(15, 63, 19, 67)(21, 69, 26, 74)(22, 70, 25, 73)(23, 71, 27, 75)(24, 72, 28, 76)(29, 77, 33, 81)(30, 78, 34, 82)(31, 79, 35, 83)(32, 80, 36, 84)(37, 85, 41, 89)(38, 86, 42, 90)(39, 87, 44, 92)(40, 88, 43, 91)(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, 110, 158, 102, 150, 111, 159)(104, 152, 115, 163, 106, 154, 116, 164)(108, 156, 117, 165, 109, 157, 118, 166)(113, 161, 121, 169, 114, 162, 122, 170)(119, 167, 127, 175, 120, 168, 128, 176)(123, 171, 131, 179, 124, 172, 132, 180)(125, 173, 133, 181, 126, 174, 134, 182)(129, 177, 137, 185, 130, 178, 138, 186)(135, 183, 141, 189, 136, 184, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192) 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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.781 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.779 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^-2, Y3^-2 * Y2^2, Y2^4, Y3^-1 * Y2^-2 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y1 * Y2 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: polytopal 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, 18, 66)(9, 57, 24, 72)(12, 60, 19, 67)(13, 61, 23, 71)(14, 62, 22, 70)(15, 63, 21, 69)(16, 64, 20, 68)(25, 73, 33, 81)(26, 74, 36, 84)(27, 75, 35, 83)(28, 76, 34, 82)(29, 77, 37, 85)(30, 78, 40, 88)(31, 79, 39, 87)(32, 80, 38, 86)(41, 89, 45, 93)(42, 90, 46, 94)(43, 91, 48, 96)(44, 92, 47, 95)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 115, 163, 105, 153)(100, 148, 111, 159, 102, 150, 112, 160)(104, 152, 118, 166, 106, 154, 119, 167)(107, 155, 121, 169, 113, 161, 122, 170)(109, 157, 123, 171, 110, 158, 124, 172)(114, 162, 125, 173, 120, 168, 126, 174)(116, 164, 127, 175, 117, 165, 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, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 116)(8, 115)(9, 117)(10, 98)(11, 118)(12, 102)(13, 101)(14, 99)(15, 120)(16, 114)(17, 119)(18, 111)(19, 106)(20, 105)(21, 103)(22, 113)(23, 107)(24, 112)(25, 130)(26, 131)(27, 132)(28, 129)(29, 134)(30, 135)(31, 136)(32, 133)(33, 123)(34, 122)(35, 121)(36, 124)(37, 127)(38, 126)(39, 125)(40, 128)(41, 143)(42, 144)(43, 142)(44, 141)(45, 139)(46, 140)(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 ) } Outer automorphisms :: reflexible Dual of E15.780 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.780 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1 * Y3 * Y1, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1^-1 * Y3^-1, (R * Y1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y2, Y2 * Y1^2 * Y2 * Y1^-2, Y1^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 20, 68, 18, 66, 5, 53)(3, 51, 11, 59, 21, 69, 39, 87, 31, 79, 13, 61)(4, 52, 15, 63, 33, 81, 37, 85, 22, 70, 9, 57)(6, 54, 19, 67, 35, 83, 38, 86, 23, 71, 10, 58)(8, 56, 24, 72, 36, 84, 34, 82, 17, 65, 26, 74)(12, 60, 29, 77, 43, 91, 47, 95, 40, 88, 27, 75)(14, 62, 32, 80, 45, 93, 46, 94, 41, 89, 25, 73)(16, 64, 28, 76, 42, 90, 48, 96, 44, 92, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 117, 165)(105, 153, 123, 171)(106, 154, 121, 169)(107, 155, 124, 172)(109, 157, 126, 174)(111, 159, 125, 173)(112, 160, 122, 170)(114, 162, 127, 175)(115, 163, 128, 176)(116, 164, 132, 180)(118, 166, 137, 185)(119, 167, 136, 184)(120, 168, 138, 186)(129, 177, 141, 189)(130, 178, 140, 188)(131, 179, 139, 187)(133, 181, 143, 191)(134, 182, 142, 190)(135, 183, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 111)(6, 97)(7, 118)(8, 121)(9, 124)(10, 98)(11, 123)(12, 122)(13, 125)(14, 99)(15, 126)(16, 102)(17, 128)(18, 129)(19, 101)(20, 133)(21, 136)(22, 138)(23, 103)(24, 137)(25, 107)(26, 110)(27, 104)(28, 106)(29, 113)(30, 115)(31, 139)(32, 109)(33, 140)(34, 141)(35, 114)(36, 142)(37, 144)(38, 116)(39, 143)(40, 120)(41, 117)(42, 119)(43, 130)(44, 131)(45, 127)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.779 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.781 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y3 * Y1 * Y3^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * R * Y2 * R * Y1^-1, Y1^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 20, 68, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 40, 88, 21, 69, 13, 61)(4, 52, 15, 63, 33, 81, 37, 85, 22, 70, 9, 57)(6, 54, 19, 67, 35, 83, 38, 86, 23, 71, 10, 58)(8, 56, 24, 72, 17, 65, 34, 82, 36, 84, 26, 74)(12, 60, 27, 75, 39, 87, 47, 95, 43, 91, 31, 79)(14, 62, 25, 73, 41, 89, 46, 94, 44, 92, 32, 80)(16, 64, 28, 76, 42, 90, 48, 96, 45, 93, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 117, 165)(105, 153, 123, 171)(106, 154, 121, 169)(107, 155, 126, 174)(109, 157, 124, 172)(111, 159, 127, 175)(112, 160, 120, 168)(114, 162, 125, 173)(115, 163, 128, 176)(116, 164, 132, 180)(118, 166, 137, 185)(119, 167, 135, 183)(122, 170, 138, 186)(129, 177, 140, 188)(130, 178, 141, 189)(131, 179, 139, 187)(133, 181, 143, 191)(134, 182, 142, 190)(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, 133)(21, 135)(22, 138)(23, 103)(24, 110)(25, 109)(26, 137)(27, 104)(28, 106)(29, 139)(30, 115)(31, 113)(32, 107)(33, 141)(34, 140)(35, 114)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.778 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.782 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y3^-2 * Y1^2, Y2 * Y1 * Y2 * Y1^-1, Y1^4, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: polytopal 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, 113, 161, 129, 177, 141, 189, 126, 174, 112, 160)(101, 149, 114, 162, 130, 178, 140, 188, 127, 175, 111, 159)(103, 151, 115, 163, 131, 179, 139, 187, 128, 176, 110, 158)(104, 152, 117, 165, 132, 180, 142, 190, 133, 181, 118, 166)(106, 154, 122, 170, 137, 185, 144, 192, 135, 183, 121, 169)(108, 156, 123, 171, 138, 186, 143, 191, 136, 184, 120, 168) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.777 Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.783 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x C2 x ((C6 x C2) : C2) (small group id <96, 219>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^2, Y2^4, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1, (Y3^-1 * Y2^-1 * Y1)^2, Y2^2 * Y1 * Y3^2 * Y1, Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: polytopal 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, 18, 66)(9, 57, 24, 72)(12, 60, 19, 67)(13, 61, 22, 70)(14, 62, 23, 71)(15, 63, 20, 68)(16, 64, 21, 69)(25, 73, 33, 81)(26, 74, 36, 84)(27, 75, 34, 82)(28, 76, 35, 83)(29, 77, 37, 85)(30, 78, 40, 88)(31, 79, 38, 86)(32, 80, 39, 87)(41, 89, 46, 94)(42, 90, 45, 93)(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, 111, 159, 102, 150, 112, 160)(104, 152, 118, 166, 106, 154, 119, 167)(107, 155, 121, 169, 113, 161, 122, 170)(109, 157, 123, 171, 110, 158, 124, 172)(114, 162, 125, 173, 120, 168, 126, 174)(116, 164, 127, 175, 117, 165, 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, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 116)(8, 115)(9, 117)(10, 98)(11, 119)(12, 102)(13, 101)(14, 99)(15, 114)(16, 120)(17, 118)(18, 112)(19, 106)(20, 105)(21, 103)(22, 107)(23, 113)(24, 111)(25, 130)(26, 131)(27, 129)(28, 132)(29, 134)(30, 135)(31, 133)(32, 136)(33, 124)(34, 122)(35, 121)(36, 123)(37, 128)(38, 126)(39, 125)(40, 127)(41, 143)(42, 144)(43, 142)(44, 141)(45, 139)(46, 140)(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 ) } Outer automorphisms :: reflexible Dual of E15.784 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.784 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x C2 x ((C6 x C2) : C2) (small group id <96, 219>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1^-1 * Y3^-1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^4, (R * Y2 * Y3^-1)^2, Y1^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 18, 66, 16, 64, 5, 53)(3, 51, 8, 56, 19, 67, 32, 80, 27, 75, 12, 60)(4, 52, 14, 62, 29, 77, 33, 81, 20, 68, 9, 57)(6, 54, 17, 65, 31, 79, 34, 82, 21, 69, 10, 58)(11, 59, 25, 73, 39, 87, 43, 91, 35, 83, 22, 70)(13, 61, 28, 76, 41, 89, 44, 92, 36, 84, 23, 71)(15, 63, 24, 72, 37, 85, 45, 93, 42, 90, 30, 78)(26, 74, 38, 86, 46, 94, 48, 96, 47, 95, 40, 88)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 108, 156)(102, 150, 107, 155)(103, 151, 115, 163)(105, 153, 119, 167)(106, 154, 118, 166)(110, 158, 124, 172)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 121, 169)(114, 162, 128, 176)(116, 164, 132, 180)(117, 165, 131, 179)(120, 168, 134, 182)(125, 173, 137, 185)(126, 174, 136, 184)(127, 175, 135, 183)(129, 177, 140, 188)(130, 178, 139, 187)(133, 181, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 110)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 122)(12, 121)(13, 99)(14, 126)(15, 102)(16, 125)(17, 101)(18, 129)(19, 131)(20, 133)(21, 103)(22, 134)(23, 104)(24, 106)(25, 136)(26, 109)(27, 135)(28, 108)(29, 138)(30, 113)(31, 112)(32, 139)(33, 141)(34, 114)(35, 142)(36, 115)(37, 117)(38, 119)(39, 143)(40, 124)(41, 123)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.783 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.785 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, (Y3 * Y1 * Y3^-1 * Y1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 13, 61)(7, 55, 16, 64)(8, 56, 18, 66)(9, 57, 19, 67)(10, 58, 21, 69)(12, 60, 24, 72)(14, 62, 26, 74)(15, 63, 22, 70)(17, 65, 29, 77)(20, 68, 32, 80)(23, 71, 35, 83)(25, 73, 38, 86)(27, 75, 40, 88)(28, 76, 41, 89)(30, 78, 44, 92)(31, 79, 36, 84)(33, 81, 37, 85)(34, 82, 43, 91)(39, 87, 42, 90)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 106, 154)(103, 151, 110, 158)(104, 152, 111, 159)(107, 155, 115, 163)(108, 156, 116, 164)(109, 157, 117, 165)(112, 160, 122, 170)(113, 161, 123, 171)(114, 162, 118, 166)(119, 167, 127, 175)(120, 168, 128, 176)(121, 169, 129, 177)(124, 172, 135, 183)(125, 173, 136, 184)(126, 174, 130, 178)(131, 179, 132, 180)(133, 181, 134, 182)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 97)(6, 110)(7, 113)(8, 98)(9, 116)(10, 99)(11, 118)(12, 101)(13, 121)(14, 123)(15, 102)(16, 117)(17, 104)(18, 126)(19, 114)(20, 106)(21, 129)(22, 130)(23, 107)(24, 132)(25, 135)(26, 109)(27, 111)(28, 112)(29, 138)(30, 127)(31, 115)(32, 131)(33, 124)(34, 119)(35, 141)(36, 142)(37, 120)(38, 128)(39, 122)(40, 137)(41, 143)(42, 144)(43, 125)(44, 136)(45, 134)(46, 133)(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) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.808 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.786 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, Y3 * Y2 * Y3, (Y2 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^4, (Y1 * Y3^-1 * Y1 * Y2)^2, (Y3^-1 * Y1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 11, 59)(6, 54, 12, 60)(7, 55, 13, 61)(8, 56, 14, 62)(15, 63, 24, 72)(16, 64, 30, 78)(17, 65, 27, 75)(18, 66, 26, 74)(19, 67, 33, 81)(20, 68, 34, 82)(21, 69, 25, 73)(22, 70, 35, 83)(23, 71, 36, 84)(28, 76, 37, 85)(29, 77, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 45, 93)(42, 90, 48, 96)(43, 91, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 101, 149)(103, 151, 104, 152)(105, 153, 111, 159)(106, 154, 114, 162)(107, 155, 117, 165)(108, 156, 120, 168)(109, 157, 123, 171)(110, 158, 126, 174)(112, 160, 113, 161)(115, 163, 116, 164)(118, 166, 119, 167)(121, 169, 122, 170)(124, 172, 125, 173)(127, 175, 128, 176)(129, 177, 132, 180)(130, 178, 131, 179)(133, 181, 136, 184)(134, 182, 135, 183)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 103)(3, 101)(4, 99)(5, 97)(6, 104)(7, 102)(8, 98)(9, 112)(10, 115)(11, 118)(12, 121)(13, 124)(14, 127)(15, 113)(16, 111)(17, 105)(18, 116)(19, 114)(20, 106)(21, 119)(22, 117)(23, 107)(24, 122)(25, 120)(26, 108)(27, 125)(28, 123)(29, 109)(30, 128)(31, 126)(32, 110)(33, 137)(34, 139)(35, 140)(36, 138)(37, 141)(38, 143)(39, 144)(40, 142)(41, 132)(42, 129)(43, 131)(44, 130)(45, 136)(46, 133)(47, 135)(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 ) } Outer automorphisms :: reflexible Dual of E15.810 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.787 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y2^2, R^2, Y3^-1 * Y2 * Y3 * Y2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, (Y3^-1 * Y1 * Y2 * Y3^-1)^2, (Y2 * Y1)^4 ] Map:: polytopal 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, 24, 72)(11, 59, 26, 74)(13, 61, 30, 78)(16, 64, 28, 76)(17, 65, 33, 81)(19, 67, 38, 86)(21, 69, 34, 82)(22, 70, 29, 77)(23, 71, 32, 80)(25, 73, 37, 85)(27, 75, 36, 84)(31, 79, 35, 83)(39, 87, 43, 91)(40, 88, 45, 93)(41, 89, 48, 96)(42, 90, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 106, 154)(101, 149, 107, 155)(103, 151, 112, 160)(104, 152, 113, 161)(105, 153, 117, 165)(108, 156, 123, 171)(109, 157, 121, 169)(110, 158, 127, 175)(111, 159, 130, 178)(114, 162, 128, 176)(115, 163, 133, 181)(116, 164, 125, 173)(118, 166, 135, 183)(119, 167, 136, 184)(120, 168, 138, 186)(122, 170, 140, 188)(124, 172, 141, 189)(126, 174, 137, 185)(129, 177, 139, 187)(131, 179, 142, 190)(132, 180, 143, 191)(134, 182, 144, 192) L = (1, 100)(2, 103)(3, 106)(4, 109)(5, 97)(6, 112)(7, 115)(8, 98)(9, 118)(10, 121)(11, 99)(12, 124)(13, 101)(14, 128)(15, 131)(16, 133)(17, 102)(18, 120)(19, 104)(20, 123)(21, 135)(22, 137)(23, 105)(24, 139)(25, 107)(26, 116)(27, 141)(28, 140)(29, 108)(30, 136)(31, 114)(32, 138)(33, 110)(34, 142)(35, 144)(36, 111)(37, 113)(38, 143)(39, 126)(40, 117)(41, 119)(42, 129)(43, 127)(44, 125)(45, 122)(46, 134)(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) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.809 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.788 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y1)^2, (R * Y3)^2, Y2^4, (R * Y1)^2, (R * Y2 * Y3)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1 * Y3, R * Y2 * Y1 * R * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 16, 64)(12, 60, 17, 65)(13, 61, 18, 66)(19, 67, 27, 75)(20, 68, 24, 72)(21, 69, 28, 76)(22, 70, 29, 77)(23, 71, 26, 74)(25, 73, 30, 78)(31, 79, 34, 82)(32, 80, 39, 87)(33, 81, 37, 85)(35, 83, 40, 88)(36, 84, 38, 86)(41, 89, 43, 91)(42, 90, 46, 94)(44, 92, 45, 93)(47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 110, 158, 104, 152)(100, 148, 107, 155, 118, 166, 108, 156)(103, 151, 112, 160, 125, 173, 113, 161)(106, 154, 116, 164, 129, 177, 117, 165)(109, 157, 121, 169, 134, 182, 122, 170)(111, 159, 120, 168, 133, 181, 124, 172)(114, 162, 126, 174, 132, 180, 119, 167)(115, 163, 127, 175, 137, 185, 128, 176)(123, 171, 130, 178, 139, 187, 135, 183)(131, 179, 140, 188, 143, 191, 138, 186)(136, 184, 141, 189, 144, 192, 142, 190) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 111)(7, 98)(8, 114)(9, 115)(10, 99)(11, 119)(12, 120)(13, 101)(14, 123)(15, 102)(16, 122)(17, 116)(18, 104)(19, 105)(20, 113)(21, 130)(22, 131)(23, 107)(24, 108)(25, 135)(26, 112)(27, 110)(28, 127)(29, 136)(30, 128)(31, 124)(32, 126)(33, 138)(34, 117)(35, 118)(36, 141)(37, 142)(38, 140)(39, 121)(40, 125)(41, 143)(42, 129)(43, 144)(44, 134)(45, 132)(46, 133)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.806 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.789 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y1 * Y2)^2, (R * Y1)^2, (Y3 * Y1)^2, Y2^4, (R * Y3)^2, (R * Y2 * Y3)^2, Y2 * Y3 * Y2^2 * Y1 * Y3 * Y2, (Y3 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 8, 56)(4, 52, 7, 55)(5, 53, 6, 54)(9, 57, 14, 62)(10, 58, 18, 66)(11, 59, 17, 65)(12, 60, 16, 64)(13, 61, 15, 63)(19, 67, 22, 70)(20, 68, 25, 73)(21, 69, 26, 74)(23, 71, 28, 76)(24, 72, 27, 75)(29, 77, 35, 83)(30, 78, 36, 84)(31, 79, 33, 81)(32, 80, 34, 82)(37, 85, 39, 87)(38, 86, 40, 88)(41, 89, 43, 91)(42, 90, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 110, 158, 104, 152)(100, 148, 107, 155, 118, 166, 108, 156)(103, 151, 112, 160, 115, 163, 113, 161)(106, 154, 116, 164, 111, 159, 117, 165)(109, 157, 121, 169, 114, 162, 122, 170)(119, 167, 127, 175, 123, 171, 128, 176)(120, 168, 129, 177, 124, 172, 130, 178)(125, 173, 133, 181, 132, 180, 134, 182)(126, 174, 135, 183, 131, 179, 136, 184)(137, 185, 141, 189, 140, 188, 144, 192)(138, 186, 143, 191, 139, 187, 142, 190) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 111)(7, 98)(8, 114)(9, 115)(10, 99)(11, 119)(12, 120)(13, 101)(14, 118)(15, 102)(16, 123)(17, 124)(18, 104)(19, 105)(20, 125)(21, 126)(22, 110)(23, 107)(24, 108)(25, 131)(26, 132)(27, 112)(28, 113)(29, 116)(30, 117)(31, 137)(32, 138)(33, 139)(34, 140)(35, 121)(36, 122)(37, 141)(38, 142)(39, 143)(40, 144)(41, 127)(42, 128)(43, 129)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.805 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.790 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3)^2, Y2 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3, (Y3 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 8, 56)(4, 52, 7, 55)(5, 53, 6, 54)(9, 57, 14, 62)(10, 58, 18, 66)(11, 59, 17, 65)(12, 60, 16, 64)(13, 61, 15, 63)(19, 67, 27, 75)(20, 68, 30, 78)(21, 69, 23, 71)(22, 70, 29, 77)(24, 72, 25, 73)(26, 74, 28, 76)(31, 79, 39, 87)(32, 80, 34, 82)(33, 81, 36, 84)(35, 83, 40, 88)(37, 85, 38, 86)(41, 89, 43, 91)(42, 90, 45, 93)(44, 92, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 110, 158, 104, 152)(100, 148, 107, 155, 118, 166, 108, 156)(103, 151, 112, 160, 125, 173, 113, 161)(106, 154, 116, 164, 129, 177, 117, 165)(109, 157, 121, 169, 134, 182, 122, 170)(111, 159, 124, 172, 133, 181, 120, 168)(114, 162, 119, 167, 132, 180, 126, 174)(115, 163, 127, 175, 137, 185, 128, 176)(123, 171, 130, 178, 139, 187, 135, 183)(131, 179, 140, 188, 143, 191, 138, 186)(136, 184, 141, 189, 144, 192, 142, 190) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 111)(7, 98)(8, 114)(9, 115)(10, 99)(11, 119)(12, 120)(13, 101)(14, 123)(15, 102)(16, 121)(17, 117)(18, 104)(19, 105)(20, 130)(21, 113)(22, 131)(23, 107)(24, 108)(25, 112)(26, 135)(27, 110)(28, 127)(29, 136)(30, 128)(31, 124)(32, 126)(33, 138)(34, 116)(35, 118)(36, 141)(37, 142)(38, 140)(39, 122)(40, 125)(41, 143)(42, 129)(43, 144)(44, 134)(45, 132)(46, 133)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.807 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.791 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y1 * Y3 * Y2^-1 * Y3 * Y1 * Y2, (R * Y2 * Y3)^2, Y1 * Y2 * Y3 * Y2 * Y3 * Y2, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 16, 64)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 19, 67)(12, 60, 18, 66)(13, 61, 22, 70)(15, 63, 20, 68)(17, 65, 31, 79)(23, 71, 37, 85)(25, 73, 34, 82)(26, 74, 38, 86)(27, 75, 32, 80)(28, 76, 39, 87)(29, 77, 40, 88)(30, 78, 41, 89)(33, 81, 42, 90)(35, 83, 43, 91)(36, 84, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 113, 161, 104, 152)(100, 148, 108, 156, 123, 171, 109, 157)(103, 151, 115, 163, 130, 178, 116, 164)(105, 153, 117, 165, 131, 179, 119, 167)(107, 155, 118, 166, 132, 180, 122, 170)(110, 158, 124, 172, 126, 174, 112, 160)(111, 159, 125, 173, 129, 177, 114, 162)(120, 168, 133, 181, 141, 189, 135, 183)(121, 169, 134, 182, 142, 190, 136, 184)(127, 175, 137, 185, 143, 191, 139, 187)(128, 176, 138, 186, 144, 192, 140, 188) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 111)(6, 114)(7, 98)(8, 118)(9, 115)(10, 121)(11, 99)(12, 112)(13, 117)(14, 116)(15, 101)(16, 108)(17, 128)(18, 102)(19, 105)(20, 110)(21, 109)(22, 104)(23, 134)(24, 130)(25, 106)(26, 133)(27, 127)(28, 136)(29, 135)(30, 138)(31, 123)(32, 113)(33, 137)(34, 120)(35, 140)(36, 139)(37, 122)(38, 119)(39, 125)(40, 124)(41, 129)(42, 126)(43, 132)(44, 131)(45, 144)(46, 143)(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 ) } Outer automorphisms :: reflexible Dual of E15.798 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.792 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, (R * Y3)^2, Y2^4, (R * Y1)^2, (Y1 * Y2^-1)^3, (Y2^-1 * Y1)^3, (R * Y2 * Y3)^2, Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2, Y2^-2 * Y1 * Y3 * Y2^-2 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 16, 64)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 20, 68)(12, 60, 22, 70)(13, 61, 18, 66)(15, 63, 19, 67)(17, 65, 31, 79)(23, 71, 37, 85)(25, 73, 34, 82)(26, 74, 38, 86)(27, 75, 32, 80)(28, 76, 39, 87)(29, 77, 40, 88)(30, 78, 41, 89)(33, 81, 42, 90)(35, 83, 43, 91)(36, 84, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 113, 161, 104, 152)(100, 148, 108, 156, 123, 171, 109, 157)(103, 151, 115, 163, 130, 178, 116, 164)(105, 153, 117, 165, 131, 179, 119, 167)(107, 155, 122, 170, 132, 180, 118, 166)(110, 158, 124, 172, 126, 174, 112, 160)(111, 159, 114, 162, 129, 177, 125, 173)(120, 168, 133, 181, 141, 189, 135, 183)(121, 169, 136, 184, 142, 190, 134, 182)(127, 175, 137, 185, 143, 191, 139, 187)(128, 176, 140, 188, 144, 192, 138, 186) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 111)(6, 114)(7, 98)(8, 118)(9, 116)(10, 121)(11, 99)(12, 117)(13, 112)(14, 115)(15, 101)(16, 109)(17, 128)(18, 102)(19, 110)(20, 105)(21, 108)(22, 104)(23, 134)(24, 130)(25, 106)(26, 133)(27, 127)(28, 136)(29, 135)(30, 138)(31, 123)(32, 113)(33, 137)(34, 120)(35, 140)(36, 139)(37, 122)(38, 119)(39, 125)(40, 124)(41, 129)(42, 126)(43, 132)(44, 131)(45, 144)(46, 143)(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 ) } Outer automorphisms :: reflexible Dual of E15.802 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.793 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y2^-2 * Y1 * Y2^-1, (R * Y2 * Y3)^2, (Y1 * Y2 * Y1 * Y2^-1)^3 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 16, 64)(8, 56, 21, 69)(10, 58, 25, 73)(11, 59, 20, 68)(12, 60, 22, 70)(13, 61, 18, 66)(15, 63, 19, 67)(17, 65, 30, 78)(23, 71, 33, 81)(24, 72, 35, 83)(26, 74, 36, 84)(27, 75, 34, 82)(28, 76, 37, 85)(29, 77, 39, 87)(31, 79, 40, 88)(32, 80, 38, 86)(41, 89, 45, 93)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 113, 161, 104, 152)(100, 148, 108, 156, 121, 169, 109, 157)(103, 151, 115, 163, 126, 174, 116, 164)(105, 153, 119, 167, 111, 159, 120, 168)(107, 155, 122, 170, 110, 158, 123, 171)(112, 160, 124, 172, 118, 166, 125, 173)(114, 162, 127, 175, 117, 165, 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, 103)(3, 107)(4, 97)(5, 111)(6, 114)(7, 98)(8, 118)(9, 116)(10, 113)(11, 99)(12, 117)(13, 112)(14, 115)(15, 101)(16, 109)(17, 106)(18, 102)(19, 110)(20, 105)(21, 108)(22, 104)(23, 130)(24, 132)(25, 126)(26, 131)(27, 129)(28, 134)(29, 136)(30, 121)(31, 135)(32, 133)(33, 123)(34, 119)(35, 122)(36, 120)(37, 128)(38, 124)(39, 127)(40, 125)(41, 144)(42, 142)(43, 143)(44, 141)(45, 140)(46, 138)(47, 139)(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 ) } Outer automorphisms :: reflexible Dual of E15.799 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.794 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y2^-1 * Y1)^3, Y3^-1 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y2 * Y3 * Y1 * Y2^-1, Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 18, 66)(6, 54, 8, 56)(7, 55, 23, 71)(9, 57, 30, 78)(12, 60, 36, 84)(13, 61, 33, 81)(14, 62, 29, 77)(15, 63, 32, 80)(16, 64, 28, 76)(17, 65, 26, 74)(19, 67, 34, 82)(20, 68, 27, 75)(21, 69, 25, 73)(22, 70, 31, 79)(24, 72, 43, 91)(35, 83, 46, 94)(37, 85, 44, 92)(38, 86, 45, 93)(39, 87, 42, 90)(40, 88, 48, 96)(41, 89, 47, 95)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 120, 168, 105, 153)(100, 148, 111, 159, 134, 182, 113, 161)(102, 150, 117, 165, 133, 181, 118, 166)(104, 152, 123, 171, 141, 189, 125, 173)(106, 154, 129, 177, 140, 188, 130, 178)(107, 155, 126, 174, 143, 191, 131, 179)(109, 157, 122, 170, 116, 164, 127, 175)(110, 158, 128, 176, 115, 163, 121, 169)(112, 160, 137, 185, 139, 187, 135, 183)(114, 162, 136, 184, 138, 186, 119, 167)(124, 172, 144, 192, 132, 180, 142, 190) L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 115)(6, 97)(7, 121)(8, 124)(9, 127)(10, 98)(11, 125)(12, 133)(13, 135)(14, 99)(15, 136)(16, 102)(17, 131)(18, 123)(19, 137)(20, 101)(21, 119)(22, 126)(23, 113)(24, 140)(25, 142)(26, 103)(27, 143)(28, 106)(29, 138)(30, 111)(31, 144)(32, 105)(33, 107)(34, 114)(35, 117)(36, 141)(37, 139)(38, 108)(39, 110)(40, 118)(41, 116)(42, 129)(43, 134)(44, 132)(45, 120)(46, 122)(47, 130)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.803 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.795 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1 * Y2 * Y1)^2, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1, Y2^-1 * Y3^-1 * Y2 * Y1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, (Y2 * Y1)^3, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 18, 66)(6, 54, 8, 56)(7, 55, 23, 71)(9, 57, 30, 78)(12, 60, 36, 84)(13, 61, 34, 82)(14, 62, 27, 75)(15, 63, 26, 74)(16, 64, 28, 76)(17, 65, 32, 80)(19, 67, 33, 81)(20, 68, 29, 77)(21, 69, 31, 79)(22, 70, 25, 73)(24, 72, 43, 91)(35, 83, 46, 94)(37, 85, 44, 92)(38, 86, 45, 93)(39, 87, 42, 90)(40, 88, 48, 96)(41, 89, 47, 95)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 120, 168, 105, 153)(100, 148, 111, 159, 134, 182, 113, 161)(102, 150, 117, 165, 133, 181, 118, 166)(104, 152, 123, 171, 141, 189, 125, 173)(106, 154, 129, 177, 140, 188, 130, 178)(107, 155, 126, 174, 144, 192, 131, 179)(109, 157, 127, 175, 116, 164, 122, 170)(110, 158, 121, 169, 115, 163, 128, 176)(112, 160, 136, 184, 139, 187, 135, 183)(114, 162, 137, 185, 138, 186, 119, 167)(124, 172, 143, 191, 132, 180, 142, 190) L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 115)(6, 97)(7, 121)(8, 124)(9, 127)(10, 98)(11, 123)(12, 133)(13, 135)(14, 99)(15, 131)(16, 102)(17, 137)(18, 125)(19, 136)(20, 101)(21, 126)(22, 119)(23, 111)(24, 140)(25, 142)(26, 103)(27, 138)(28, 106)(29, 144)(30, 113)(31, 143)(32, 105)(33, 114)(34, 107)(35, 118)(36, 141)(37, 139)(38, 108)(39, 110)(40, 116)(41, 117)(42, 130)(43, 134)(44, 132)(45, 120)(46, 122)(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, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.804 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.796 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, (Y3 * Y1)^2, Y3^-1 * Y2^2 * Y1, Y2 * Y3 * Y1 * Y2, (R * Y1)^2, Y3^4, (R * Y3)^2, Y3^2 * Y2 * Y1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y1 * Y3, Y3 * Y2 * Y3^2 * Y2^-1 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 12, 60)(6, 54, 8, 56)(7, 55, 18, 66)(9, 57, 19, 67)(13, 61, 23, 71)(14, 62, 24, 72)(15, 63, 22, 70)(16, 64, 20, 68)(17, 65, 21, 69)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 36, 84)(28, 76, 35, 83)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 40, 88)(32, 80, 39, 87)(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, 103, 151, 102, 150, 105, 153)(100, 148, 110, 158, 118, 166, 112, 160)(104, 152, 117, 165, 111, 159, 119, 167)(107, 155, 121, 169, 109, 157, 122, 170)(108, 156, 123, 171, 113, 161, 124, 172)(114, 162, 125, 173, 116, 164, 126, 174)(115, 163, 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, 104)(3, 108)(4, 111)(5, 107)(6, 97)(7, 115)(8, 118)(9, 114)(10, 98)(11, 119)(12, 117)(13, 99)(14, 116)(15, 102)(16, 120)(17, 101)(18, 112)(19, 110)(20, 103)(21, 109)(22, 106)(23, 113)(24, 105)(25, 130)(26, 129)(27, 131)(28, 132)(29, 134)(30, 133)(31, 135)(32, 136)(33, 124)(34, 123)(35, 121)(36, 122)(37, 128)(38, 127)(39, 125)(40, 126)(41, 144)(42, 141)(43, 142)(44, 143)(45, 140)(46, 137)(47, 138)(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 ) } Outer automorphisms :: reflexible Dual of E15.800 Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.797 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 :: [ Y1^2, R^2, Y3 * Y2^2 * Y1, (Y1 * Y3)^2, Y2 * Y3^-1 * Y1 * Y2, (R * Y3)^2, Y3^4, (R * Y1)^2, Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y1, (R * Y2^-1 * Y3^-1)^2, Y3^-1 * Y2^-2 * Y3 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2 * Y3^-2, Y3^-1 * Y2 * Y3^-1 * 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, 13, 61)(6, 54, 8, 56)(7, 55, 18, 66)(9, 57, 20, 68)(12, 60, 24, 72)(14, 62, 21, 69)(15, 63, 23, 71)(16, 64, 22, 70)(17, 65, 19, 67)(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, 48, 96)(43, 91, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147, 104, 152, 101, 149)(98, 146, 103, 151, 100, 148, 105, 153)(102, 150, 112, 160, 117, 165, 113, 161)(106, 154, 119, 167, 110, 158, 120, 168)(107, 155, 121, 169, 108, 156, 122, 170)(109, 157, 123, 171, 111, 159, 124, 172)(114, 162, 125, 173, 115, 163, 126, 174)(116, 164, 127, 175, 118, 166, 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, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 101)(12, 119)(13, 99)(14, 102)(15, 120)(16, 116)(17, 114)(18, 105)(19, 112)(20, 103)(21, 106)(22, 113)(23, 109)(24, 107)(25, 130)(26, 132)(27, 131)(28, 129)(29, 134)(30, 136)(31, 135)(32, 133)(33, 122)(34, 123)(35, 121)(36, 124)(37, 126)(38, 127)(39, 125)(40, 128)(41, 142)(42, 143)(43, 144)(44, 141)(45, 138)(46, 139)(47, 140)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.801 Graph:: bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.798 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, Y2 * Y1^-3, (R * Y2)^2, (Y3 * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 3, 51, 7, 55, 5, 53)(4, 52, 10, 58, 18, 66, 9, 57, 17, 65, 11, 59)(8, 56, 15, 63, 26, 74, 14, 62, 25, 73, 16, 64)(12, 60, 21, 69, 24, 72, 13, 61, 23, 71, 22, 70)(19, 67, 31, 79, 41, 89, 29, 77, 36, 84, 32, 80)(20, 68, 33, 81, 37, 85, 30, 78, 39, 87, 27, 75)(28, 76, 40, 88, 34, 82, 38, 86, 44, 92, 35, 83)(42, 90, 46, 94, 43, 91, 47, 95, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 105, 153)(101, 149, 102, 150)(104, 152, 110, 158)(106, 154, 113, 161)(107, 155, 114, 162)(108, 156, 109, 157)(111, 159, 121, 169)(112, 160, 122, 170)(115, 163, 125, 173)(116, 164, 126, 174)(117, 165, 119, 167)(118, 166, 120, 168)(123, 171, 133, 181)(124, 172, 134, 182)(127, 175, 132, 180)(128, 176, 137, 185)(129, 177, 135, 183)(130, 178, 131, 179)(136, 184, 140, 188)(138, 186, 143, 191)(139, 187, 141, 189)(142, 190, 144, 192) L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 108)(6, 109)(7, 110)(8, 98)(9, 99)(10, 115)(11, 116)(12, 101)(13, 102)(14, 103)(15, 123)(16, 124)(17, 125)(18, 126)(19, 106)(20, 107)(21, 130)(22, 127)(23, 131)(24, 132)(25, 133)(26, 134)(27, 111)(28, 112)(29, 113)(30, 114)(31, 118)(32, 138)(33, 139)(34, 117)(35, 119)(36, 120)(37, 121)(38, 122)(39, 141)(40, 142)(41, 143)(42, 128)(43, 129)(44, 144)(45, 135)(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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.791 Graph:: bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.799 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^6, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, Y1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 16, 64, 5, 53)(3, 51, 9, 57, 25, 73, 40, 88, 31, 79, 11, 59)(4, 52, 12, 60, 32, 80, 41, 89, 33, 81, 13, 61)(7, 55, 20, 68, 45, 93, 38, 86, 29, 77, 22, 70)(8, 56, 23, 71, 30, 78, 39, 87, 46, 94, 24, 72)(10, 58, 28, 76, 47, 95, 48, 96, 43, 91, 21, 69)(14, 62, 34, 82, 26, 74, 18, 66, 42, 90, 35, 83)(15, 63, 36, 84, 44, 92, 19, 67, 27, 75, 37, 85)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 110, 158)(102, 150, 114, 162)(104, 152, 117, 165)(105, 153, 122, 170)(107, 155, 125, 173)(108, 156, 126, 174)(109, 157, 123, 171)(111, 159, 124, 172)(112, 160, 134, 182)(113, 161, 136, 184)(115, 163, 139, 187)(116, 164, 121, 169)(118, 166, 130, 178)(119, 167, 133, 181)(120, 168, 129, 177)(127, 175, 131, 179)(128, 176, 132, 180)(135, 183, 143, 191)(137, 185, 144, 192)(138, 186, 141, 189)(140, 188, 142, 190) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 111)(6, 115)(7, 117)(8, 98)(9, 123)(10, 99)(11, 126)(12, 125)(13, 122)(14, 124)(15, 101)(16, 135)(17, 137)(18, 139)(19, 102)(20, 129)(21, 103)(22, 133)(23, 130)(24, 121)(25, 120)(26, 109)(27, 105)(28, 110)(29, 108)(30, 107)(31, 132)(32, 131)(33, 116)(34, 119)(35, 128)(36, 127)(37, 118)(38, 143)(39, 112)(40, 144)(41, 113)(42, 142)(43, 114)(44, 141)(45, 140)(46, 138)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.793 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.800 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (Y1^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y3^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y2, Y1^6, (Y1^-1 * R * Y2)^2, Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y3, (R * Y2 * Y3^-1)^2, Y1^2 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 19, 67, 5, 53)(3, 51, 11, 59, 30, 78, 40, 88, 34, 82, 13, 61)(4, 52, 15, 63, 35, 83, 41, 89, 29, 77, 10, 58)(6, 54, 18, 66, 37, 85, 42, 90, 24, 72, 21, 69)(8, 56, 26, 74, 46, 94, 38, 86, 32, 80, 27, 75)(9, 57, 12, 60, 20, 68, 39, 87, 45, 93, 25, 73)(14, 62, 33, 81, 47, 95, 48, 96, 44, 92, 28, 76)(16, 64, 31, 79, 23, 71, 43, 91, 36, 84, 17, 65)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 119, 167)(105, 153, 124, 172)(106, 154, 117, 165)(107, 155, 127, 175)(109, 157, 128, 176)(111, 159, 116, 164)(112, 160, 123, 171)(114, 162, 129, 177)(115, 163, 134, 182)(118, 166, 136, 184)(120, 168, 140, 188)(121, 169, 125, 173)(122, 170, 126, 174)(130, 178, 132, 180)(131, 179, 133, 181)(135, 183, 143, 191)(137, 185, 144, 192)(138, 186, 141, 189)(139, 187, 142, 190) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 120)(8, 117)(9, 107)(10, 98)(11, 106)(12, 123)(13, 129)(14, 99)(15, 109)(16, 102)(17, 111)(18, 128)(19, 135)(20, 101)(21, 127)(22, 137)(23, 125)(24, 122)(25, 103)(26, 121)(27, 110)(28, 104)(29, 126)(30, 140)(31, 124)(32, 116)(33, 113)(34, 131)(35, 115)(36, 143)(37, 132)(38, 133)(39, 130)(40, 141)(41, 139)(42, 118)(43, 138)(44, 119)(45, 142)(46, 144)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.796 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.801 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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^-1 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, Y1 * Y3 * Y2 * Y1 * Y3, Y2 * Y1^-1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3, Y1^6, Y1^2 * Y3^-2 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 19, 67, 5, 53)(3, 51, 11, 59, 30, 78, 40, 88, 34, 82, 13, 61)(4, 52, 15, 63, 35, 83, 41, 89, 29, 77, 10, 58)(6, 54, 18, 66, 37, 85, 42, 90, 24, 72, 21, 69)(8, 56, 26, 74, 46, 94, 38, 86, 33, 81, 16, 64)(9, 57, 14, 62, 20, 68, 39, 87, 45, 93, 25, 73)(12, 60, 31, 79, 47, 95, 48, 96, 44, 92, 27, 75)(17, 65, 32, 80, 28, 76, 23, 71, 43, 91, 36, 84)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 119, 167)(105, 153, 117, 165)(106, 154, 123, 171)(107, 155, 124, 172)(109, 157, 129, 177)(111, 159, 114, 162)(112, 160, 128, 176)(115, 163, 134, 182)(116, 164, 127, 175)(118, 166, 136, 184)(120, 168, 125, 173)(121, 169, 140, 188)(122, 170, 126, 174)(130, 178, 132, 180)(131, 179, 143, 191)(133, 181, 135, 183)(137, 185, 141, 189)(138, 186, 144, 192)(139, 187, 142, 190) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 120)(8, 123)(9, 124)(10, 98)(11, 117)(12, 128)(13, 116)(14, 99)(15, 113)(16, 102)(17, 127)(18, 109)(19, 135)(20, 101)(21, 104)(22, 137)(23, 140)(24, 126)(25, 103)(26, 125)(27, 107)(28, 106)(29, 119)(30, 121)(31, 129)(32, 110)(33, 111)(34, 133)(35, 115)(36, 131)(37, 134)(38, 143)(39, 132)(40, 144)(41, 142)(42, 118)(43, 141)(44, 122)(45, 136)(46, 138)(47, 130)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.797 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.802 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1 * Y2)^2, Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y1^6, Y2 * Y1 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 16, 64, 5, 53)(3, 51, 9, 57, 25, 73, 36, 84, 29, 77, 11, 59)(4, 52, 12, 60, 30, 78, 37, 85, 31, 79, 13, 61)(7, 55, 20, 68, 43, 91, 34, 82, 44, 92, 22, 70)(8, 56, 23, 71, 45, 93, 35, 83, 46, 94, 24, 72)(10, 58, 28, 76, 47, 95, 48, 96, 39, 87, 21, 69)(14, 62, 32, 80, 40, 88, 18, 66, 38, 86, 26, 74)(15, 63, 27, 75, 42, 90, 19, 67, 41, 89, 33, 81)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 110, 158)(102, 150, 114, 162)(104, 152, 117, 165)(105, 153, 122, 170)(107, 155, 116, 164)(108, 156, 120, 168)(109, 157, 123, 171)(111, 159, 124, 172)(112, 160, 130, 178)(113, 161, 132, 180)(115, 163, 135, 183)(118, 166, 134, 182)(119, 167, 138, 186)(121, 169, 140, 188)(125, 173, 136, 184)(126, 174, 137, 185)(127, 175, 141, 189)(128, 176, 139, 187)(129, 177, 142, 190)(131, 179, 143, 191)(133, 181, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 111)(6, 115)(7, 117)(8, 98)(9, 123)(10, 99)(11, 120)(12, 116)(13, 122)(14, 124)(15, 101)(16, 131)(17, 133)(18, 135)(19, 102)(20, 108)(21, 103)(22, 138)(23, 134)(24, 107)(25, 141)(26, 109)(27, 105)(28, 110)(29, 137)(30, 136)(31, 140)(32, 142)(33, 139)(34, 143)(35, 112)(36, 144)(37, 113)(38, 119)(39, 114)(40, 126)(41, 125)(42, 118)(43, 129)(44, 127)(45, 121)(46, 128)(47, 130)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.792 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.803 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-2)^2, (Y3 * Y2 * Y1^-1)^2, (Y2 * Y1^-1)^3, Y3^-2 * Y1^-1 * Y2 * Y1^-2, (Y1^-1 * R * Y2)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 19, 67, 5, 53)(3, 51, 11, 59, 33, 81, 40, 88, 31, 79, 13, 61)(4, 52, 15, 63, 35, 83, 41, 89, 32, 80, 10, 58)(6, 54, 18, 66, 27, 75, 42, 90, 24, 72, 21, 69)(8, 56, 26, 74, 46, 94, 39, 87, 45, 93, 28, 76)(9, 57, 30, 78, 20, 68, 36, 84, 12, 60, 25, 73)(14, 62, 37, 85, 47, 95, 48, 96, 44, 92, 29, 77)(16, 64, 34, 82, 17, 65, 38, 86, 43, 91, 23, 71)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 119, 167)(105, 153, 125, 173)(106, 154, 123, 171)(107, 155, 130, 178)(109, 157, 122, 170)(111, 159, 121, 169)(112, 160, 124, 172)(114, 162, 133, 181)(115, 163, 135, 183)(116, 164, 128, 176)(117, 165, 131, 179)(118, 166, 136, 184)(120, 168, 140, 188)(126, 174, 138, 186)(127, 175, 139, 187)(129, 177, 141, 189)(132, 180, 143, 191)(134, 182, 142, 190)(137, 185, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 120)(8, 123)(9, 127)(10, 98)(11, 131)(12, 124)(13, 133)(14, 99)(15, 129)(16, 102)(17, 128)(18, 122)(19, 132)(20, 101)(21, 130)(22, 137)(23, 111)(24, 141)(25, 103)(26, 116)(27, 139)(28, 110)(29, 104)(30, 142)(31, 106)(32, 109)(33, 140)(34, 143)(35, 115)(36, 107)(37, 113)(38, 138)(39, 117)(40, 126)(41, 134)(42, 118)(43, 125)(44, 119)(45, 121)(46, 144)(47, 135)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.794 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.804 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (Y2 * Y3^-1)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^4, (R * Y3)^2, Y2 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-2)^2, (Y2 * Y1^-1)^3, (Y3^-1 * Y2 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 19, 67, 5, 53)(3, 51, 11, 59, 33, 81, 40, 88, 36, 84, 13, 61)(4, 52, 15, 63, 38, 86, 41, 89, 32, 80, 10, 58)(6, 54, 18, 66, 29, 77, 42, 90, 24, 72, 21, 69)(8, 56, 26, 74, 16, 64, 39, 87, 46, 94, 28, 76)(9, 57, 30, 78, 20, 68, 37, 85, 14, 62, 25, 73)(12, 60, 34, 82, 47, 95, 48, 96, 44, 92, 27, 75)(17, 65, 35, 83, 45, 93, 23, 71, 43, 91, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 113, 161)(102, 150, 108, 156)(103, 151, 119, 167)(105, 153, 125, 173)(106, 154, 123, 171)(107, 155, 127, 175)(109, 157, 122, 170)(111, 159, 120, 168)(112, 160, 131, 179)(114, 162, 128, 176)(115, 163, 135, 183)(116, 164, 130, 178)(117, 165, 133, 181)(118, 166, 136, 184)(121, 169, 140, 188)(124, 172, 139, 187)(126, 174, 137, 185)(129, 177, 142, 190)(132, 180, 141, 189)(134, 182, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 120)(8, 123)(9, 127)(10, 98)(11, 125)(12, 131)(13, 121)(14, 99)(15, 119)(16, 102)(17, 130)(18, 129)(19, 133)(20, 101)(21, 135)(22, 137)(23, 140)(24, 109)(25, 103)(26, 111)(27, 107)(28, 138)(29, 104)(30, 136)(31, 106)(32, 113)(33, 116)(34, 142)(35, 110)(36, 117)(37, 141)(38, 115)(39, 143)(40, 144)(41, 124)(42, 118)(43, 126)(44, 122)(45, 134)(46, 128)(47, 132)(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 ) } Outer automorphisms :: reflexible Dual of E15.795 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.805 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^2, Y1^6, Y3 * Y1 * Y3 * Y1^2 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 14, 62, 5, 53)(3, 51, 9, 57, 21, 69, 32, 80, 16, 64, 7, 55)(4, 52, 11, 59, 25, 73, 33, 81, 28, 76, 12, 60)(8, 56, 19, 67, 39, 87, 31, 79, 42, 90, 20, 68)(10, 58, 23, 71, 41, 89, 46, 94, 45, 93, 24, 72)(13, 61, 29, 77, 36, 84, 17, 65, 35, 83, 30, 78)(18, 66, 37, 85, 48, 96, 43, 91, 26, 74, 38, 86)(22, 70, 40, 88, 27, 75, 34, 82, 47, 95, 44, 92)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 105, 153)(102, 150, 112, 160)(104, 152, 114, 162)(107, 155, 120, 168)(108, 156, 119, 167)(109, 157, 118, 166)(110, 158, 117, 165)(111, 159, 128, 176)(113, 161, 130, 178)(115, 163, 134, 182)(116, 164, 133, 181)(121, 169, 141, 189)(122, 170, 135, 183)(123, 171, 131, 179)(124, 172, 137, 185)(125, 173, 140, 188)(126, 174, 136, 184)(127, 175, 139, 187)(129, 177, 142, 190)(132, 180, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 113)(7, 114)(8, 98)(9, 118)(10, 99)(11, 122)(12, 123)(13, 101)(14, 127)(15, 129)(16, 130)(17, 102)(18, 103)(19, 136)(20, 137)(21, 139)(22, 105)(23, 131)(24, 135)(25, 140)(26, 107)(27, 108)(28, 133)(29, 141)(30, 134)(31, 110)(32, 142)(33, 111)(34, 112)(35, 119)(36, 144)(37, 124)(38, 126)(39, 120)(40, 115)(41, 116)(42, 143)(43, 117)(44, 121)(45, 125)(46, 128)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.789 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.806 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (R * Y2)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-2 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y2)^4, (Y3 * Y1^-1)^4, (Y1^-1 * Y2 * Y1^-1 * Y3)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 10, 58, 16, 64, 5, 53)(3, 51, 9, 57, 13, 61, 4, 52, 12, 60, 11, 59)(7, 55, 17, 65, 20, 68, 8, 56, 19, 67, 18, 66)(14, 62, 25, 73, 28, 76, 15, 63, 27, 75, 26, 74)(21, 69, 33, 81, 36, 84, 22, 70, 35, 83, 34, 82)(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, 106, 154)(101, 149, 110, 158)(102, 150, 111, 159)(104, 152, 112, 160)(105, 153, 117, 165)(107, 155, 119, 167)(108, 156, 118, 166)(109, 157, 120, 168)(113, 161, 125, 173)(114, 162, 127, 175)(115, 163, 126, 174)(116, 164, 128, 176)(121, 169, 135, 183)(122, 170, 129, 177)(123, 171, 136, 184)(124, 172, 131, 179)(130, 178, 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, 104)(3, 106)(4, 97)(5, 111)(6, 110)(7, 112)(8, 98)(9, 118)(10, 99)(11, 120)(12, 117)(13, 119)(14, 102)(15, 101)(16, 103)(17, 126)(18, 128)(19, 125)(20, 127)(21, 108)(22, 105)(23, 109)(24, 107)(25, 136)(26, 131)(27, 135)(28, 129)(29, 115)(30, 113)(31, 116)(32, 114)(33, 124)(34, 140)(35, 122)(36, 139)(37, 142)(38, 141)(39, 123)(40, 121)(41, 144)(42, 143)(43, 132)(44, 130)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.788 Graph:: bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.807 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^2, (Y3 * Y2)^2, Y1^6, Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3, (Y3 * Y1^-3)^2, (Y3 * Y1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 14, 62, 5, 53)(3, 51, 9, 57, 21, 69, 32, 80, 16, 64, 7, 55)(4, 52, 11, 59, 25, 73, 33, 81, 28, 76, 12, 60)(8, 56, 19, 67, 38, 86, 31, 79, 40, 88, 20, 68)(10, 58, 23, 71, 43, 91, 48, 96, 44, 92, 24, 72)(13, 61, 29, 77, 36, 84, 17, 65, 35, 83, 30, 78)(18, 66, 26, 74, 46, 94, 41, 89, 47, 95, 37, 85)(22, 70, 42, 90, 45, 93, 34, 82, 39, 87, 27, 75)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 105, 153)(102, 150, 112, 160)(104, 152, 114, 162)(107, 155, 120, 168)(108, 156, 119, 167)(109, 157, 118, 166)(110, 158, 117, 165)(111, 159, 128, 176)(113, 161, 130, 178)(115, 163, 133, 181)(116, 164, 122, 170)(121, 169, 140, 188)(123, 171, 125, 173)(124, 172, 139, 187)(126, 174, 138, 186)(127, 175, 137, 185)(129, 177, 144, 192)(131, 179, 141, 189)(132, 180, 135, 183)(134, 182, 143, 191)(136, 184, 142, 190) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 113)(7, 114)(8, 98)(9, 118)(10, 99)(11, 122)(12, 123)(13, 101)(14, 127)(15, 129)(16, 130)(17, 102)(18, 103)(19, 135)(20, 120)(21, 137)(22, 105)(23, 125)(24, 116)(25, 141)(26, 107)(27, 108)(28, 143)(29, 119)(30, 142)(31, 110)(32, 144)(33, 111)(34, 112)(35, 140)(36, 133)(37, 132)(38, 139)(39, 115)(40, 138)(41, 117)(42, 136)(43, 134)(44, 131)(45, 121)(46, 126)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.790 Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 4^24, 12^8 ] E15.808 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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 * Y3 * Y2, Y3^3, (R * Y2)^2, (Y1 * Y3)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 31, 79, 14, 62)(4, 52, 16, 64, 35, 83, 17, 65)(6, 54, 20, 68, 26, 74, 9, 57)(7, 55, 21, 69, 28, 76, 10, 58)(11, 59, 29, 77, 38, 86, 22, 70)(12, 60, 30, 78, 40, 88, 23, 71)(15, 63, 27, 75, 39, 87, 32, 80)(18, 66, 24, 72, 41, 89, 36, 84)(19, 67, 25, 73, 42, 90, 37, 85)(33, 81, 45, 93, 47, 95, 43, 91)(34, 82, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 103, 151, 111, 159, 100, 148, 102, 150)(98, 146, 105, 153, 108, 156, 123, 171, 106, 154, 107, 155)(101, 149, 114, 162, 112, 160, 128, 176, 115, 163, 109, 157)(104, 152, 118, 166, 121, 169, 135, 183, 119, 167, 120, 168)(110, 158, 129, 177, 116, 164, 113, 161, 130, 178, 117, 165)(122, 170, 139, 187, 125, 173, 124, 172, 140, 188, 126, 174)(127, 175, 133, 181, 142, 190, 131, 179, 132, 180, 141, 189)(134, 182, 143, 191, 137, 185, 136, 184, 144, 192, 138, 186) L = (1, 100)(2, 106)(3, 102)(4, 103)(5, 115)(6, 111)(7, 97)(8, 119)(9, 107)(10, 108)(11, 123)(12, 98)(13, 128)(14, 130)(15, 99)(16, 101)(17, 129)(18, 109)(19, 112)(20, 110)(21, 113)(22, 120)(23, 121)(24, 135)(25, 104)(26, 140)(27, 105)(28, 139)(29, 122)(30, 124)(31, 132)(32, 114)(33, 117)(34, 116)(35, 133)(36, 142)(37, 141)(38, 144)(39, 118)(40, 143)(41, 134)(42, 136)(43, 126)(44, 125)(45, 131)(46, 127)(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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.785 Graph:: bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.809 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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, (Y2^-1 * Y3)^2, (R * Y1)^2, (Y1 * Y3)^2, Y1^4, (R * Y3)^2, (Y2^-1 * Y1)^2, Y1^2 * Y2^-2 * Y3^-1, Y2^2 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * R * Y2 * R * Y1^-1 * Y2^-1, Y2^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 11, 59)(4, 52, 17, 65, 43, 91, 19, 67)(6, 54, 20, 68, 47, 95, 24, 72)(7, 55, 27, 75, 14, 62, 10, 58)(9, 57, 15, 63, 35, 83, 18, 66)(12, 60, 36, 84, 31, 79, 25, 73)(16, 64, 33, 81, 39, 87, 38, 86)(21, 69, 30, 78, 48, 96, 42, 90)(22, 70, 29, 77, 32, 80, 28, 76)(23, 71, 44, 92, 45, 93, 34, 82)(37, 85, 40, 88, 46, 94, 41, 89)(97, 145, 99, 147, 110, 158, 135, 183, 121, 169, 102, 150)(98, 146, 105, 153, 127, 175, 134, 182, 117, 165, 107, 155)(100, 148, 114, 162, 104, 152, 125, 173, 138, 186, 112, 160)(101, 149, 116, 164, 115, 163, 129, 177, 106, 154, 118, 166)(103, 151, 119, 167, 139, 187, 143, 191, 136, 184, 124, 172)(108, 156, 130, 178, 123, 171, 109, 157, 133, 181, 120, 168)(111, 159, 137, 185, 122, 170, 126, 174, 141, 189, 132, 180)(113, 161, 140, 188, 144, 192, 128, 176, 142, 190, 131, 179) L = (1, 100)(2, 106)(3, 111)(4, 103)(5, 117)(6, 119)(7, 97)(8, 121)(9, 128)(10, 108)(11, 130)(12, 98)(13, 134)(14, 136)(15, 112)(16, 99)(17, 101)(18, 141)(19, 142)(20, 109)(21, 113)(22, 140)(23, 122)(24, 118)(25, 126)(26, 102)(27, 115)(28, 114)(29, 143)(30, 104)(31, 133)(32, 129)(33, 105)(34, 131)(35, 107)(36, 110)(37, 144)(38, 116)(39, 125)(40, 132)(41, 139)(42, 137)(43, 138)(44, 120)(45, 124)(46, 123)(47, 135)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.787 Graph:: bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.810 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 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^-1 * Y1, (Y3 * Y2^-1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^6, (Y2^2 * Y1)^2, Y2 * R * Y1^-1 * Y2^2 * R * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 19, 67, 8, 56)(5, 53, 11, 59, 25, 73, 13, 61)(7, 55, 17, 65, 31, 79, 16, 64)(10, 58, 23, 71, 38, 86, 22, 70)(12, 60, 15, 63, 29, 77, 27, 75)(14, 62, 28, 76, 34, 82, 18, 66)(20, 68, 36, 84, 43, 91, 30, 78)(21, 69, 37, 85, 42, 90, 33, 81)(24, 72, 35, 83, 44, 92, 40, 88)(26, 74, 32, 80, 45, 93, 41, 89)(39, 87, 47, 95, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 120, 168, 110, 158, 101, 149)(98, 146, 103, 151, 114, 162, 131, 179, 116, 164, 104, 152)(100, 148, 107, 155, 122, 170, 136, 184, 119, 167, 108, 156)(102, 150, 111, 159, 126, 174, 140, 188, 128, 176, 112, 160)(105, 153, 117, 165, 109, 157, 124, 172, 135, 183, 118, 166)(113, 161, 129, 177, 115, 163, 132, 180, 142, 190, 130, 178)(121, 169, 133, 181, 123, 171, 134, 182, 143, 191, 137, 185)(125, 173, 138, 186, 127, 175, 141, 189, 144, 192, 139, 187) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 100)(7, 113)(8, 99)(9, 115)(10, 119)(11, 121)(12, 111)(13, 101)(14, 124)(15, 125)(16, 103)(17, 127)(18, 110)(19, 104)(20, 132)(21, 133)(22, 106)(23, 134)(24, 131)(25, 109)(26, 128)(27, 108)(28, 130)(29, 123)(30, 116)(31, 112)(32, 141)(33, 117)(34, 114)(35, 140)(36, 139)(37, 138)(38, 118)(39, 143)(40, 120)(41, 122)(42, 129)(43, 126)(44, 136)(45, 137)(46, 135)(47, 144)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.786 Graph:: bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.811 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 8}) Quotient :: edge 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 :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^6, T2^8 ] Map:: non-degenerate R = (1, 3, 10, 21, 33, 24, 13, 5)(2, 7, 17, 29, 40, 30, 18, 8)(4, 9, 20, 32, 42, 35, 23, 12)(6, 15, 27, 38, 46, 39, 28, 16)(11, 19, 31, 41, 47, 43, 34, 22)(14, 25, 36, 44, 48, 45, 37, 26)(49, 50, 54, 62, 59, 52)(51, 57, 67, 73, 63, 55)(53, 60, 70, 74, 64, 56)(58, 65, 75, 84, 79, 68)(61, 66, 76, 85, 82, 71)(69, 80, 89, 92, 86, 77)(72, 83, 91, 93, 87, 78)(81, 88, 94, 96, 95, 90) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.812 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.812 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 8}) Quotient :: loop 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 :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^6, T2^8 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 21, 69, 33, 81, 24, 72, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 29, 77, 40, 88, 30, 78, 18, 66, 8, 56)(4, 52, 9, 57, 20, 68, 32, 80, 42, 90, 35, 83, 23, 71, 12, 60)(6, 54, 15, 63, 27, 75, 38, 86, 46, 94, 39, 87, 28, 76, 16, 64)(11, 59, 19, 67, 31, 79, 41, 89, 47, 95, 43, 91, 34, 82, 22, 70)(14, 62, 25, 73, 36, 84, 44, 92, 48, 96, 45, 93, 37, 85, 26, 74) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 60)(6, 62)(7, 51)(8, 53)(9, 67)(10, 65)(11, 52)(12, 70)(13, 66)(14, 59)(15, 55)(16, 56)(17, 75)(18, 76)(19, 73)(20, 58)(21, 80)(22, 74)(23, 61)(24, 83)(25, 63)(26, 64)(27, 84)(28, 85)(29, 69)(30, 72)(31, 68)(32, 89)(33, 88)(34, 71)(35, 91)(36, 79)(37, 82)(38, 77)(39, 78)(40, 94)(41, 92)(42, 81)(43, 93)(44, 86)(45, 87)(46, 96)(47, 90)(48, 95) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.811 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.813 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = C2 x (C3 : C8) (small group id <48, 9>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^6, Y2^8, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 11, 59, 4, 52)(3, 51, 9, 57, 19, 67, 25, 73, 15, 63, 7, 55)(5, 53, 12, 60, 22, 70, 26, 74, 16, 64, 8, 56)(10, 58, 17, 65, 27, 75, 36, 84, 31, 79, 20, 68)(13, 61, 18, 66, 28, 76, 37, 85, 34, 82, 23, 71)(21, 69, 32, 80, 41, 89, 44, 92, 38, 86, 29, 77)(24, 72, 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, 106, 154, 117, 165, 129, 177, 120, 168, 109, 157, 101, 149)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 126, 174, 114, 162, 104, 152)(100, 148, 105, 153, 116, 164, 128, 176, 138, 186, 131, 179, 119, 167, 108, 156)(102, 150, 111, 159, 123, 171, 134, 182, 142, 190, 135, 183, 124, 172, 112, 160)(107, 155, 115, 163, 127, 175, 137, 185, 143, 191, 139, 187, 130, 178, 118, 166)(110, 158, 121, 169, 132, 180, 140, 188, 144, 192, 141, 189, 133, 181, 122, 170) L = (1, 100)(2, 97)(3, 103)(4, 107)(5, 104)(6, 98)(7, 111)(8, 112)(9, 99)(10, 116)(11, 110)(12, 101)(13, 119)(14, 102)(15, 121)(16, 122)(17, 106)(18, 109)(19, 105)(20, 127)(21, 125)(22, 108)(23, 130)(24, 126)(25, 115)(26, 118)(27, 113)(28, 114)(29, 134)(30, 135)(31, 132)(32, 117)(33, 138)(34, 133)(35, 120)(36, 123)(37, 124)(38, 140)(39, 141)(40, 129)(41, 128)(42, 143)(43, 131)(44, 137)(45, 139)(46, 136)(47, 144)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 16, 2, 16, 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 E15.814 Graph:: bipartite v = 14 e = 96 f = 54 degree seq :: [ 12^8, 16^6 ] E15.814 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = C2 x (C3 : C8) (small group id <48, 9>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-4 * Y1^-1, Y1^8, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 25, 73, 24, 72, 12, 60, 4, 52)(3, 51, 8, 56, 15, 63, 27, 75, 36, 84, 33, 81, 21, 69, 10, 58)(5, 53, 7, 55, 16, 64, 26, 74, 37, 85, 35, 83, 23, 71, 11, 59)(9, 57, 18, 66, 28, 76, 39, 87, 44, 92, 42, 90, 32, 80, 20, 68)(13, 61, 17, 65, 29, 77, 38, 86, 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)(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, 107)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 100)(11, 118)(12, 117)(13, 101)(14, 122)(15, 124)(16, 102)(17, 126)(18, 104)(19, 109)(20, 106)(21, 128)(22, 127)(23, 108)(24, 131)(25, 132)(26, 134)(27, 110)(28, 136)(29, 112)(30, 114)(31, 116)(32, 137)(33, 120)(34, 119)(35, 139)(36, 140)(37, 121)(38, 142)(39, 123)(40, 125)(41, 130)(42, 129)(43, 143)(44, 144)(45, 133)(46, 135)(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) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E15.813 Graph:: simple bipartite v = 54 e = 96 f = 14 degree seq :: [ 2^48, 16^6 ] E15.815 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 8}) Quotient :: edge Aut^+ = (C3 : C8) : C2 (small group id <48, 10>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1^-1 * T2^2, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T1^6 ] Map:: non-degenerate R = (1, 3, 10, 24, 41, 21, 17, 5)(2, 7, 22, 16, 31, 11, 26, 8)(4, 12, 30, 15, 29, 9, 28, 14)(6, 19, 37, 25, 42, 23, 40, 20)(13, 27, 43, 34, 45, 32, 44, 33)(18, 35, 46, 39, 48, 38, 47, 36)(49, 50, 54, 66, 61, 52)(51, 57, 75, 86, 67, 59)(53, 63, 81, 87, 68, 64)(55, 69, 60, 80, 83, 71)(56, 72, 62, 82, 84, 73)(58, 70, 85, 94, 91, 78)(65, 74, 88, 95, 92, 76)(77, 89, 79, 90, 96, 93) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.816 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.816 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 8}) Quotient :: loop Aut^+ = (C3 : C8) : C2 (small group id <48, 10>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1^-1 * T2^2, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, T1^6 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 24, 72, 41, 89, 21, 69, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 16, 64, 31, 79, 11, 59, 26, 74, 8, 56)(4, 52, 12, 60, 30, 78, 15, 63, 29, 77, 9, 57, 28, 76, 14, 62)(6, 54, 19, 67, 37, 85, 25, 73, 42, 90, 23, 71, 40, 88, 20, 68)(13, 61, 27, 75, 43, 91, 34, 82, 45, 93, 32, 80, 44, 92, 33, 81)(18, 66, 35, 83, 46, 94, 39, 87, 48, 96, 38, 86, 47, 95, 36, 84) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 75)(10, 70)(11, 51)(12, 80)(13, 52)(14, 82)(15, 81)(16, 53)(17, 74)(18, 61)(19, 59)(20, 64)(21, 60)(22, 85)(23, 55)(24, 62)(25, 56)(26, 88)(27, 86)(28, 65)(29, 89)(30, 58)(31, 90)(32, 83)(33, 87)(34, 84)(35, 71)(36, 73)(37, 94)(38, 67)(39, 68)(40, 95)(41, 79)(42, 96)(43, 78)(44, 76)(45, 77)(46, 91)(47, 92)(48, 93) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.815 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.817 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 10>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-2, Y1^6, Y3 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y2^3 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2^-3, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y1^-2 * Y2^-1, Y2^8, (Y3 * Y2 * Y1^-1 * Y2^-1)^2 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 27, 75, 38, 86, 19, 67, 11, 59)(5, 53, 15, 63, 33, 81, 39, 87, 20, 68, 16, 64)(7, 55, 21, 69, 12, 60, 32, 80, 35, 83, 23, 71)(8, 56, 24, 72, 14, 62, 34, 82, 36, 84, 25, 73)(10, 58, 22, 70, 37, 85, 46, 94, 43, 91, 30, 78)(17, 65, 26, 74, 40, 88, 47, 95, 44, 92, 28, 76)(29, 77, 41, 89, 31, 79, 42, 90, 48, 96, 45, 93)(97, 145, 99, 147, 106, 154, 120, 168, 137, 185, 117, 165, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 112, 160, 127, 175, 107, 155, 122, 170, 104, 152)(100, 148, 108, 156, 126, 174, 111, 159, 125, 173, 105, 153, 124, 172, 110, 158)(102, 150, 115, 163, 133, 181, 121, 169, 138, 186, 119, 167, 136, 184, 116, 164)(109, 157, 123, 171, 139, 187, 130, 178, 141, 189, 128, 176, 140, 188, 129, 177)(114, 162, 131, 179, 142, 190, 135, 183, 144, 192, 134, 182, 143, 191, 132, 180) L = (1, 100)(2, 97)(3, 107)(4, 109)(5, 112)(6, 98)(7, 119)(8, 121)(9, 99)(10, 126)(11, 115)(12, 117)(13, 114)(14, 120)(15, 101)(16, 116)(17, 124)(18, 102)(19, 134)(20, 135)(21, 103)(22, 106)(23, 131)(24, 104)(25, 132)(26, 113)(27, 105)(28, 140)(29, 141)(30, 139)(31, 137)(32, 108)(33, 111)(34, 110)(35, 128)(36, 130)(37, 118)(38, 123)(39, 129)(40, 122)(41, 125)(42, 127)(43, 142)(44, 143)(45, 144)(46, 133)(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) :: { ( 2, 16, 2, 16, 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 E15.818 Graph:: bipartite v = 14 e = 96 f = 54 degree seq :: [ 12^8, 16^6 ] E15.818 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 10>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^3, Y3 * Y1^3 * Y3 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-3 * Y3 * Y1^-1, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y3 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 35, 83, 27, 75, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 14, 62, 25, 73, 8, 56, 24, 72, 11, 59)(5, 53, 15, 63, 20, 68, 12, 60, 23, 71, 7, 55, 21, 69, 16, 64)(10, 58, 26, 74, 36, 84, 31, 79, 42, 90, 28, 76, 41, 89, 30, 78)(17, 65, 22, 70, 37, 85, 34, 82, 40, 88, 33, 81, 38, 86, 32, 80)(29, 77, 43, 91, 46, 94, 45, 93, 48, 96, 39, 87, 47, 95, 44, 92)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 125)(11, 114)(12, 128)(13, 120)(14, 100)(15, 129)(16, 130)(17, 101)(18, 112)(19, 132)(20, 102)(21, 109)(22, 135)(23, 131)(24, 137)(25, 138)(26, 104)(27, 111)(28, 105)(29, 113)(30, 110)(31, 107)(32, 141)(33, 139)(34, 140)(35, 121)(36, 142)(37, 116)(38, 117)(39, 122)(40, 119)(41, 143)(42, 144)(43, 124)(44, 127)(45, 126)(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) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E15.817 Graph:: simple bipartite v = 54 e = 96 f = 14 degree seq :: [ 2^48, 16^6 ] E15.819 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 8}) Quotient :: edge Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2 * T1^-1, T1^6, T1^6, T1 * T2^3 * T1 * T2^-1, T2^-1 * T1^-1 * T2^-3 * T1^2 * T2^-2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^3 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 27, 18, 22, 17, 5)(2, 7, 21, 11, 13, 31, 23, 8)(4, 12, 30, 19, 6, 15, 33, 14)(9, 24, 41, 28, 29, 40, 42, 25)(16, 26, 43, 45, 34, 36, 46, 35)(20, 37, 47, 39, 32, 44, 48, 38)(49, 50, 54, 66, 61, 52)(51, 57, 56, 70, 77, 59)(53, 63, 82, 75, 60, 64)(55, 68, 67, 79, 80, 62)(58, 74, 73, 65, 84, 76)(69, 72, 86, 71, 88, 87)(78, 92, 83, 81, 85, 93)(89, 91, 96, 90, 94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.820 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.820 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 8}) Quotient :: loop Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2 * T1^-1, T1^6, T1^6, T1 * T2^3 * T1 * T2^-1, T2^-1 * T1^-1 * T2^-3 * T1^2 * T2^-2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^3 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 18, 66, 22, 70, 17, 65, 5, 53)(2, 50, 7, 55, 21, 69, 11, 59, 13, 61, 31, 79, 23, 71, 8, 56)(4, 52, 12, 60, 30, 78, 19, 67, 6, 54, 15, 63, 33, 81, 14, 62)(9, 57, 24, 72, 41, 89, 28, 76, 29, 77, 40, 88, 42, 90, 25, 73)(16, 64, 26, 74, 43, 91, 45, 93, 34, 82, 36, 84, 46, 94, 35, 83)(20, 68, 37, 85, 47, 95, 39, 87, 32, 80, 44, 92, 48, 96, 38, 86) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 68)(8, 70)(9, 56)(10, 74)(11, 51)(12, 64)(13, 52)(14, 55)(15, 82)(16, 53)(17, 84)(18, 61)(19, 79)(20, 67)(21, 72)(22, 77)(23, 88)(24, 86)(25, 65)(26, 73)(27, 60)(28, 58)(29, 59)(30, 92)(31, 80)(32, 62)(33, 85)(34, 75)(35, 81)(36, 76)(37, 93)(38, 71)(39, 69)(40, 87)(41, 91)(42, 94)(43, 96)(44, 83)(45, 78)(46, 95)(47, 89)(48, 90) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.819 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.821 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * R * Y2^-1 * R, Y2 * Y1 * Y3^-1 * Y2 * Y3, (R * Y2^-1 * Y1)^2, Y3 * Y2^-3 * Y1^-1 * Y2, Y1^6, Y1^-1 * Y3 * Y1^-1 * Y2^4, Y2^2 * Y1 * Y2^2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 8, 56, 22, 70, 29, 77, 11, 59)(5, 53, 15, 63, 34, 82, 27, 75, 12, 60, 16, 64)(7, 55, 20, 68, 19, 67, 31, 79, 32, 80, 14, 62)(10, 58, 26, 74, 25, 73, 17, 65, 36, 84, 28, 76)(21, 69, 24, 72, 38, 86, 23, 71, 40, 88, 39, 87)(30, 78, 44, 92, 35, 83, 33, 81, 37, 85, 45, 93)(41, 89, 43, 91, 48, 96, 42, 90, 46, 94, 47, 95)(97, 145, 99, 147, 106, 154, 123, 171, 114, 162, 118, 166, 113, 161, 101, 149)(98, 146, 103, 151, 117, 165, 107, 155, 109, 157, 127, 175, 119, 167, 104, 152)(100, 148, 108, 156, 126, 174, 115, 163, 102, 150, 111, 159, 129, 177, 110, 158)(105, 153, 120, 168, 137, 185, 124, 172, 125, 173, 136, 184, 138, 186, 121, 169)(112, 160, 122, 170, 139, 187, 141, 189, 130, 178, 132, 180, 142, 190, 131, 179)(116, 164, 133, 181, 143, 191, 135, 183, 128, 176, 140, 188, 144, 192, 134, 182) L = (1, 100)(2, 97)(3, 107)(4, 109)(5, 112)(6, 98)(7, 110)(8, 105)(9, 99)(10, 124)(11, 125)(12, 123)(13, 114)(14, 128)(15, 101)(16, 108)(17, 121)(18, 102)(19, 116)(20, 103)(21, 135)(22, 104)(23, 134)(24, 117)(25, 122)(26, 106)(27, 130)(28, 132)(29, 118)(30, 141)(31, 115)(32, 127)(33, 131)(34, 111)(35, 140)(36, 113)(37, 129)(38, 120)(39, 136)(40, 119)(41, 143)(42, 144)(43, 137)(44, 126)(45, 133)(46, 138)(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) :: { ( 2, 16, 2, 16, 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 E15.822 Graph:: bipartite v = 14 e = 96 f = 54 degree seq :: [ 12^8, 16^6 ] E15.822 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3, Y3^6, (R * Y2 * Y3^-1)^2, Y3^6, Y1^-1 * Y3 * Y1^3 * Y3, Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-2, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 26, 74, 28, 76, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 8, 56, 17, 65, 36, 84, 29, 77, 11, 59)(5, 53, 15, 63, 34, 82, 27, 75, 10, 58, 12, 60, 30, 78, 16, 64)(7, 55, 21, 69, 38, 86, 20, 68, 24, 72, 42, 90, 40, 88, 22, 70)(14, 62, 19, 67, 37, 85, 44, 92, 31, 79, 32, 80, 45, 93, 33, 81)(25, 73, 43, 91, 48, 96, 41, 89, 35, 83, 46, 94, 47, 95, 39, 87)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 107)(8, 98)(9, 121)(10, 122)(11, 124)(12, 127)(13, 128)(14, 100)(15, 110)(16, 105)(17, 101)(18, 111)(19, 118)(20, 102)(21, 135)(22, 109)(23, 117)(24, 104)(25, 123)(26, 113)(27, 132)(28, 120)(29, 138)(30, 139)(31, 114)(32, 116)(33, 126)(34, 142)(35, 112)(36, 131)(37, 143)(38, 133)(39, 125)(40, 141)(41, 119)(42, 137)(43, 140)(44, 130)(45, 144)(46, 129)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E15.821 Graph:: simple bipartite v = 54 e = 96 f = 14 degree seq :: [ 2^48, 16^6 ] E15.823 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 8, 8}) Quotient :: edge Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^2, T1^6, (T1^-1 * T2^-1 * T1^-1)^2, T1 * T2^2 * T1 * T2^-1 * T1^-1 * T2^-1, T1^-3 * T2^-4 ] Map:: non-degenerate R = (1, 3, 10, 27, 16, 35, 15, 5)(2, 7, 20, 23, 12, 30, 22, 8)(4, 11, 29, 18, 6, 17, 31, 13)(9, 24, 41, 34, 21, 39, 42, 25)(14, 32, 46, 44, 28, 26, 43, 33)(19, 37, 47, 40, 36, 45, 48, 38)(49, 50, 54, 64, 60, 52)(51, 57, 71, 83, 69, 56)(53, 59, 76, 75, 65, 62)(55, 67, 61, 78, 84, 66)(58, 74, 82, 63, 80, 73)(68, 72, 88, 70, 87, 86)(77, 93, 81, 79, 85, 92)(89, 91, 96, 90, 94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^6 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.824 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 6^8, 8^6 ] E15.824 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 8, 8}) Quotient :: loop Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^2, T1^6, (T1^-1 * T2^-1 * T1^-1)^2, T1 * T2^2 * T1 * T2^-1 * T1^-1 * T2^-1, T1^-3 * T2^-4 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 16, 64, 35, 83, 15, 63, 5, 53)(2, 50, 7, 55, 20, 68, 23, 71, 12, 60, 30, 78, 22, 70, 8, 56)(4, 52, 11, 59, 29, 77, 18, 66, 6, 54, 17, 65, 31, 79, 13, 61)(9, 57, 24, 72, 41, 89, 34, 82, 21, 69, 39, 87, 42, 90, 25, 73)(14, 62, 32, 80, 46, 94, 44, 92, 28, 76, 26, 74, 43, 91, 33, 81)(19, 67, 37, 85, 47, 95, 40, 88, 36, 84, 45, 93, 48, 96, 38, 86) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 64)(7, 67)(8, 51)(9, 71)(10, 74)(11, 76)(12, 52)(13, 78)(14, 53)(15, 80)(16, 60)(17, 62)(18, 55)(19, 61)(20, 72)(21, 56)(22, 87)(23, 83)(24, 88)(25, 58)(26, 82)(27, 65)(28, 75)(29, 93)(30, 84)(31, 85)(32, 73)(33, 79)(34, 63)(35, 69)(36, 66)(37, 92)(38, 68)(39, 86)(40, 70)(41, 91)(42, 94)(43, 96)(44, 77)(45, 81)(46, 95)(47, 89)(48, 90) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.823 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.825 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^2 * Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^6, Y1^-3 * Y2^-4, Y3^-1 * Y2^-3 * R * Y2^-1 * R, Y2^2 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-2 * Y1^-1, (Y1 * Y2 * Y1 * Y2^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 12, 60, 4, 52)(3, 51, 9, 57, 23, 71, 35, 83, 21, 69, 8, 56)(5, 53, 11, 59, 28, 76, 27, 75, 17, 65, 14, 62)(7, 55, 19, 67, 13, 61, 30, 78, 36, 84, 18, 66)(10, 58, 26, 74, 34, 82, 15, 63, 32, 80, 25, 73)(20, 68, 24, 72, 40, 88, 22, 70, 39, 87, 38, 86)(29, 77, 45, 93, 33, 81, 31, 79, 37, 85, 44, 92)(41, 89, 43, 91, 48, 96, 42, 90, 46, 94, 47, 95)(97, 145, 99, 147, 106, 154, 123, 171, 112, 160, 131, 179, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 119, 167, 108, 156, 126, 174, 118, 166, 104, 152)(100, 148, 107, 155, 125, 173, 114, 162, 102, 150, 113, 161, 127, 175, 109, 157)(105, 153, 120, 168, 137, 185, 130, 178, 117, 165, 135, 183, 138, 186, 121, 169)(110, 158, 128, 176, 142, 190, 140, 188, 124, 172, 122, 170, 139, 187, 129, 177)(115, 163, 133, 181, 143, 191, 136, 184, 132, 180, 141, 189, 144, 192, 134, 182) L = (1, 100)(2, 97)(3, 104)(4, 108)(5, 110)(6, 98)(7, 114)(8, 117)(9, 99)(10, 121)(11, 101)(12, 112)(13, 115)(14, 113)(15, 130)(16, 102)(17, 123)(18, 132)(19, 103)(20, 134)(21, 131)(22, 136)(23, 105)(24, 116)(25, 128)(26, 106)(27, 124)(28, 107)(29, 140)(30, 109)(31, 129)(32, 111)(33, 141)(34, 122)(35, 119)(36, 126)(37, 127)(38, 135)(39, 118)(40, 120)(41, 143)(42, 144)(43, 137)(44, 133)(45, 125)(46, 138)(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) :: { ( 2, 16, 2, 16, 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 E15.826 Graph:: bipartite v = 14 e = 96 f = 54 degree seq :: [ 12^8, 16^6 ] E15.826 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^6, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1 * Y3^-1)^2, Y1^4 * Y3^-3, Y1 * Y3 * Y1 * Y3^-1 * Y1^-2 * Y3^-1, Y1^8, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 27, 75, 31, 79, 12, 60, 4, 52)(3, 51, 9, 57, 23, 71, 20, 68, 15, 63, 34, 82, 21, 69, 8, 56)(5, 53, 11, 59, 28, 76, 25, 73, 10, 58, 26, 74, 35, 83, 14, 62)(7, 55, 19, 67, 38, 86, 32, 80, 22, 70, 40, 88, 37, 85, 18, 66)(13, 61, 30, 78, 46, 94, 45, 93, 29, 77, 17, 65, 36, 84, 33, 81)(24, 72, 42, 90, 48, 96, 39, 87, 43, 91, 44, 92, 47, 95, 41, 89)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 113)(7, 116)(8, 98)(9, 120)(10, 123)(11, 125)(12, 126)(13, 100)(14, 130)(15, 101)(16, 122)(17, 128)(18, 102)(19, 135)(20, 127)(21, 136)(22, 104)(23, 115)(24, 110)(25, 105)(26, 109)(27, 111)(28, 140)(29, 112)(30, 114)(31, 118)(32, 108)(33, 131)(34, 139)(35, 138)(36, 143)(37, 142)(38, 132)(39, 117)(40, 137)(41, 119)(42, 141)(43, 121)(44, 129)(45, 124)(46, 144)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E15.825 Graph:: simple bipartite v = 54 e = 96 f = 14 degree seq :: [ 2^48, 16^6 ] E15.827 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y2^2, R^2, Y3^-3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1 * Y2)^2, Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2, (Y3^-1 * Y1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 12, 60)(7, 55, 15, 63)(8, 56, 16, 64)(9, 57, 17, 65)(10, 58, 18, 66)(13, 61, 23, 71)(14, 62, 24, 72)(19, 67, 33, 81)(20, 68, 34, 82)(21, 69, 35, 83)(22, 70, 36, 84)(25, 73, 39, 87)(26, 74, 30, 78)(27, 75, 31, 79)(28, 76, 40, 88)(29, 77, 41, 89)(32, 80, 42, 90)(37, 85, 45, 93)(38, 86, 46, 94)(43, 91, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 106, 154)(103, 151, 109, 157)(104, 152, 110, 158)(107, 155, 113, 161)(108, 156, 114, 162)(111, 159, 119, 167)(112, 160, 120, 168)(115, 163, 125, 173)(116, 164, 126, 174)(117, 165, 127, 175)(118, 166, 128, 176)(121, 169, 133, 181)(122, 170, 130, 178)(123, 171, 131, 179)(124, 172, 134, 182)(129, 177, 137, 185)(132, 180, 138, 186)(135, 183, 141, 189)(136, 184, 142, 190)(139, 187, 140, 188)(143, 191, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 106)(5, 97)(6, 109)(7, 110)(8, 98)(9, 101)(10, 99)(11, 115)(12, 117)(13, 104)(14, 102)(15, 121)(16, 123)(17, 125)(18, 127)(19, 126)(20, 107)(21, 128)(22, 108)(23, 133)(24, 131)(25, 130)(26, 111)(27, 134)(28, 112)(29, 116)(30, 113)(31, 118)(32, 114)(33, 139)(34, 119)(35, 124)(36, 129)(37, 122)(38, 120)(39, 143)(40, 135)(41, 140)(42, 137)(43, 138)(44, 132)(45, 144)(46, 141)(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) :: { ( 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E15.832 Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.828 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y3^2, R^2, Y2^3, Y1 * Y2 * Y1 * Y2^-1, (R * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y1 * Y2 * Y3 * Y2^-1)^2, Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, R * Y1 * Y2^-1 * Y3 * R * Y2 * Y1 * Y2 * Y3, (Y3 * Y2^-1)^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, 23, 71)(18, 66, 24, 72)(19, 67, 25, 73)(20, 68, 26, 74)(21, 69, 27, 75)(22, 70, 28, 76)(29, 77, 37, 85)(30, 78, 32, 80)(31, 79, 38, 86)(33, 81, 35, 83)(34, 82, 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, 101, 149)(98, 146, 102, 150, 104, 152)(100, 148, 106, 154, 107, 155)(103, 151, 110, 158, 111, 159)(105, 153, 113, 161, 114, 162)(108, 156, 117, 165, 118, 166)(109, 157, 119, 167, 120, 168)(112, 160, 123, 171, 124, 172)(115, 163, 127, 175, 128, 176)(116, 164, 129, 177, 130, 178)(121, 169, 134, 182, 126, 174)(122, 170, 131, 179, 135, 183)(125, 173, 137, 185, 136, 184)(132, 180, 133, 181, 140, 188)(138, 186, 143, 191, 142, 190)(139, 187, 141, 189, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 97)(5, 108)(6, 109)(7, 98)(8, 112)(9, 99)(10, 115)(11, 116)(12, 101)(13, 102)(14, 121)(15, 122)(16, 104)(17, 125)(18, 126)(19, 106)(20, 107)(21, 131)(22, 132)(23, 133)(24, 128)(25, 110)(26, 111)(27, 129)(28, 136)(29, 113)(30, 114)(31, 138)(32, 120)(33, 123)(34, 139)(35, 117)(36, 118)(37, 119)(38, 141)(39, 142)(40, 124)(41, 143)(42, 127)(43, 130)(44, 144)(45, 134)(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) :: { ( 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.831 Graph:: simple bipartite v = 40 e = 96 f = 28 degree seq :: [ 4^24, 6^16 ] E15.829 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y1, (R * Y2 * Y3)^2, Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3, (Y1 * Y2^-1)^12 ] Map:: polytopal 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, 17, 65)(11, 59, 16, 64)(12, 60, 20, 68)(14, 62, 18, 66)(21, 69, 37, 85)(22, 70, 32, 80)(23, 71, 38, 86)(24, 72, 30, 78)(25, 73, 35, 83)(26, 74, 39, 87)(27, 75, 33, 81)(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, 101, 149)(98, 146, 102, 150, 104, 152)(100, 148, 107, 155, 108, 156)(103, 151, 113, 161, 114, 162)(105, 153, 117, 165, 118, 166)(106, 154, 119, 167, 120, 168)(109, 157, 121, 169, 122, 170)(110, 158, 123, 171, 124, 172)(111, 159, 125, 173, 126, 174)(112, 160, 127, 175, 128, 176)(115, 163, 129, 177, 130, 178)(116, 164, 131, 179, 132, 180)(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, 103)(3, 106)(4, 97)(5, 110)(6, 112)(7, 98)(8, 116)(9, 113)(10, 99)(11, 111)(12, 115)(13, 114)(14, 101)(15, 107)(16, 102)(17, 105)(18, 109)(19, 108)(20, 104)(21, 134)(22, 126)(23, 133)(24, 128)(25, 129)(26, 136)(27, 131)(28, 135)(29, 138)(30, 118)(31, 137)(32, 120)(33, 121)(34, 140)(35, 123)(36, 139)(37, 119)(38, 117)(39, 124)(40, 122)(41, 127)(42, 125)(43, 132)(44, 130)(45, 144)(46, 143)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.830 Graph:: simple bipartite v = 40 e = 96 f = 28 degree seq :: [ 4^24, 6^16 ] E15.830 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (Y3 * Y1^-1)^3, Y2 * Y1^6, Y3 * Y1^3 * Y3 * Y1^-3, Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 24, 72, 10, 58, 3, 51, 7, 55, 16, 64, 30, 78, 14, 62, 5, 53)(4, 52, 11, 59, 25, 73, 31, 79, 41, 89, 22, 70, 9, 57, 21, 69, 39, 87, 47, 95, 27, 75, 12, 60)(8, 56, 19, 67, 37, 85, 43, 91, 44, 92, 36, 84, 18, 66, 35, 83, 48, 96, 29, 77, 38, 86, 20, 68)(13, 61, 28, 76, 34, 82, 17, 65, 33, 81, 40, 88, 23, 71, 42, 90, 46, 94, 32, 80, 45, 93, 26, 74)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 105, 153)(101, 149, 106, 154)(102, 150, 112, 160)(104, 152, 114, 162)(107, 155, 117, 165)(108, 156, 118, 166)(109, 157, 119, 167)(110, 158, 120, 168)(111, 159, 126, 174)(113, 161, 128, 176)(115, 163, 131, 179)(116, 164, 132, 180)(121, 169, 135, 183)(122, 170, 136, 184)(123, 171, 137, 185)(124, 172, 138, 186)(125, 173, 139, 187)(127, 175, 143, 191)(129, 177, 141, 189)(130, 178, 142, 190)(133, 181, 144, 192)(134, 182, 140, 188) L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 109)(6, 113)(7, 114)(8, 98)(9, 99)(10, 119)(11, 122)(12, 115)(13, 101)(14, 125)(15, 127)(16, 128)(17, 102)(18, 103)(19, 108)(20, 129)(21, 136)(22, 131)(23, 106)(24, 139)(25, 140)(26, 107)(27, 142)(28, 144)(29, 110)(30, 143)(31, 111)(32, 112)(33, 116)(34, 137)(35, 118)(36, 141)(37, 138)(38, 135)(39, 134)(40, 117)(41, 130)(42, 133)(43, 120)(44, 121)(45, 132)(46, 123)(47, 126)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E15.829 Graph:: bipartite v = 28 e = 96 f = 40 degree seq :: [ 4^24, 24^4 ] E15.831 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2, Y3 * Y1^3 * Y3 * Y1^-3, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-4 * Y3 * Y2 * Y1^-2, Y2 * Y1^3 * Y2 * Y1^-3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 37, 85, 28, 76, 10, 58, 21, 69, 41, 89, 36, 84, 16, 64, 5, 53)(3, 51, 9, 57, 25, 73, 38, 86, 31, 79, 13, 61, 4, 52, 12, 60, 30, 78, 39, 87, 29, 77, 11, 59)(7, 55, 20, 68, 45, 93, 35, 83, 48, 96, 24, 72, 8, 56, 23, 71, 47, 95, 34, 82, 46, 94, 22, 70)(14, 62, 32, 80, 42, 90, 18, 66, 40, 88, 26, 74, 15, 63, 33, 81, 44, 92, 19, 67, 43, 91, 27, 75)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 110, 158)(102, 150, 114, 162)(104, 152, 117, 165)(105, 153, 122, 170)(107, 155, 119, 167)(108, 156, 123, 171)(109, 157, 116, 164)(111, 159, 124, 172)(112, 160, 130, 178)(113, 161, 134, 182)(115, 163, 137, 185)(118, 166, 139, 187)(120, 168, 136, 184)(121, 169, 142, 190)(125, 173, 138, 186)(126, 174, 144, 192)(127, 175, 140, 188)(128, 176, 141, 189)(129, 177, 143, 191)(131, 179, 133, 181)(132, 180, 135, 183) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 111)(6, 115)(7, 117)(8, 98)(9, 123)(10, 99)(11, 116)(12, 122)(13, 119)(14, 124)(15, 101)(16, 131)(17, 135)(18, 137)(19, 102)(20, 107)(21, 103)(22, 136)(23, 109)(24, 139)(25, 144)(26, 108)(27, 105)(28, 110)(29, 140)(30, 142)(31, 138)(32, 143)(33, 141)(34, 133)(35, 112)(36, 134)(37, 130)(38, 132)(39, 113)(40, 118)(41, 114)(42, 127)(43, 120)(44, 125)(45, 129)(46, 126)(47, 128)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E15.828 Graph:: bipartite v = 28 e = 96 f = 40 degree seq :: [ 4^24, 24^4 ] E15.832 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, Y1^3, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2)^2, (Y2^-1 * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y1 * Y2^6 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 14, 62)(4, 52, 9, 57, 7, 55)(6, 54, 18, 66, 8, 56)(10, 58, 26, 74, 17, 65)(12, 60, 30, 78, 32, 80)(13, 61, 25, 73, 15, 63)(16, 64, 22, 70, 28, 76)(19, 67, 24, 72, 21, 69)(20, 68, 37, 85, 39, 87)(23, 71, 34, 82, 36, 84)(27, 75, 45, 93, 33, 81)(29, 77, 40, 88, 35, 83)(31, 79, 43, 91, 48, 96)(38, 86, 41, 89, 44, 92)(42, 90, 46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 127, 175, 140, 188, 120, 168, 105, 153, 121, 169, 141, 189, 138, 186, 116, 164, 102, 150)(98, 146, 104, 152, 119, 167, 139, 187, 128, 176, 118, 166, 103, 151, 115, 163, 136, 184, 142, 190, 123, 171, 106, 154)(100, 148, 112, 160, 133, 181, 143, 191, 125, 173, 107, 155, 101, 149, 113, 161, 134, 182, 144, 192, 132, 180, 111, 159)(109, 157, 130, 178, 114, 162, 135, 183, 124, 172, 126, 174, 110, 158, 131, 179, 117, 165, 137, 185, 122, 170, 129, 177) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 115)(7, 97)(8, 117)(9, 101)(10, 112)(11, 121)(12, 123)(13, 107)(14, 111)(15, 99)(16, 122)(17, 124)(18, 120)(19, 114)(20, 137)(21, 102)(22, 113)(23, 125)(24, 104)(25, 110)(26, 118)(27, 126)(28, 106)(29, 130)(30, 141)(31, 143)(32, 129)(33, 108)(34, 136)(35, 119)(36, 131)(37, 140)(38, 116)(39, 134)(40, 132)(41, 133)(42, 144)(43, 138)(44, 135)(45, 128)(46, 127)(47, 139)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^6 ), ( 4^24 ) } Outer automorphisms :: reflexible Dual of E15.827 Graph:: bipartite v = 20 e = 96 f = 48 degree seq :: [ 6^16, 24^4 ] E15.833 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = C12 x C4 (small group id <48, 20>) Aut = (C12 x C4) : C2 (small group id <96, 81>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^12 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 46, 40, 32, 24, 16, 8)(4, 10, 18, 26, 34, 42, 47, 43, 35, 27, 19, 11)(6, 13, 21, 29, 37, 44, 48, 45, 38, 30, 22, 14)(49, 50, 54, 52)(51, 55, 61, 58)(53, 56, 62, 59)(57, 63, 69, 66)(60, 64, 70, 67)(65, 71, 77, 74)(68, 72, 78, 75)(73, 79, 85, 82)(76, 80, 86, 83)(81, 87, 92, 90)(84, 88, 93, 91)(89, 94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.834 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.834 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = C12 x C4 (small group id <48, 20>) Aut = (C12 x C4) : C2 (small group id <96, 81>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 36, 84, 28, 76, 20, 68, 12, 60, 5, 53)(2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 46, 94, 40, 88, 32, 80, 24, 72, 16, 64, 8, 56)(4, 52, 10, 58, 18, 66, 26, 74, 34, 82, 42, 90, 47, 95, 43, 91, 35, 83, 27, 75, 19, 67, 11, 59)(6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 44, 92, 48, 96, 45, 93, 38, 86, 30, 78, 22, 70, 14, 62) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 52)(7, 61)(8, 62)(9, 63)(10, 51)(11, 53)(12, 64)(13, 58)(14, 59)(15, 69)(16, 70)(17, 71)(18, 57)(19, 60)(20, 72)(21, 66)(22, 67)(23, 77)(24, 78)(25, 79)(26, 65)(27, 68)(28, 80)(29, 74)(30, 75)(31, 85)(32, 86)(33, 87)(34, 73)(35, 76)(36, 88)(37, 82)(38, 83)(39, 92)(40, 93)(41, 94)(42, 81)(43, 84)(44, 90)(45, 91)(46, 96)(47, 89)(48, 95) 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 E15.833 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.835 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C12 x C4 (small group id <48, 20>) Aut = (C12 x C4) : C2 (small group id <96, 81>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^12, Y2^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 7, 55, 13, 61, 10, 58)(5, 53, 8, 56, 14, 62, 11, 59)(9, 57, 15, 63, 21, 69, 18, 66)(12, 60, 16, 64, 22, 70, 19, 67)(17, 65, 23, 71, 29, 77, 26, 74)(20, 68, 24, 72, 30, 78, 27, 75)(25, 73, 31, 79, 37, 85, 34, 82)(28, 76, 32, 80, 38, 86, 35, 83)(33, 81, 39, 87, 44, 92, 42, 90)(36, 84, 40, 88, 45, 93, 43, 91)(41, 89, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 103, 151, 111, 159, 119, 167, 127, 175, 135, 183, 142, 190, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152)(100, 148, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 143, 191, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155)(102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 140, 188, 144, 192, 141, 189, 134, 182, 126, 174, 118, 166, 110, 158) L = (1, 100)(2, 97)(3, 106)(4, 102)(5, 107)(6, 98)(7, 99)(8, 101)(9, 114)(10, 109)(11, 110)(12, 115)(13, 103)(14, 104)(15, 105)(16, 108)(17, 122)(18, 117)(19, 118)(20, 123)(21, 111)(22, 112)(23, 113)(24, 116)(25, 130)(26, 125)(27, 126)(28, 131)(29, 119)(30, 120)(31, 121)(32, 124)(33, 138)(34, 133)(35, 134)(36, 139)(37, 127)(38, 128)(39, 129)(40, 132)(41, 143)(42, 140)(43, 141)(44, 135)(45, 136)(46, 137)(47, 144)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E15.836 Graph:: bipartite v = 16 e = 96 f = 52 degree seq :: [ 8^12, 24^4 ] E15.836 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C12 x C4 (small group id <48, 20>) Aut = (C12 x C4) : C2 (small group id <96, 81>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3^-12, Y1^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 35, 83, 27, 75, 19, 67, 11, 59, 4, 52)(3, 51, 7, 55, 14, 62, 22, 70, 30, 78, 38, 86, 44, 92, 42, 90, 34, 82, 26, 74, 18, 66, 10, 58)(5, 53, 8, 56, 15, 63, 23, 71, 31, 79, 39, 87, 45, 93, 43, 91, 36, 84, 28, 76, 20, 68, 12, 60)(9, 57, 16, 64, 24, 72, 32, 80, 40, 88, 46, 94, 48, 96, 47, 95, 41, 89, 33, 81, 25, 73, 17, 65)(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, 110)(7, 112)(8, 98)(9, 101)(10, 113)(11, 114)(12, 100)(13, 118)(14, 120)(15, 102)(16, 104)(17, 108)(18, 121)(19, 122)(20, 107)(21, 126)(22, 128)(23, 109)(24, 111)(25, 116)(26, 129)(27, 130)(28, 115)(29, 134)(30, 136)(31, 117)(32, 119)(33, 124)(34, 137)(35, 138)(36, 123)(37, 140)(38, 142)(39, 125)(40, 127)(41, 132)(42, 143)(43, 131)(44, 144)(45, 133)(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) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.835 Graph:: simple bipartite v = 52 e = 96 f = 16 degree seq :: [ 2^48, 24^4 ] E15.837 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^12 ] Map:: non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 46, 40, 32, 24, 16, 8)(4, 9, 17, 25, 33, 41, 47, 43, 35, 27, 19, 11)(6, 13, 21, 29, 37, 44, 48, 45, 38, 30, 22, 14)(49, 50, 54, 52)(51, 57, 61, 55)(53, 59, 62, 56)(58, 63, 69, 65)(60, 64, 70, 67)(66, 73, 77, 71)(68, 75, 78, 72)(74, 79, 85, 81)(76, 80, 86, 83)(82, 89, 92, 87)(84, 91, 93, 88)(90, 94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.841 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.838 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1, T1^-1)^2, T2^3 * T1 * T2^3 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 27, 43, 23, 41, 21, 40, 34, 16, 5)(2, 7, 20, 39, 32, 14, 26, 9, 25, 44, 24, 8)(4, 12, 28, 46, 33, 15, 30, 11, 29, 45, 31, 13)(6, 17, 35, 47, 42, 22, 38, 19, 37, 48, 36, 18)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 68, 83, 76)(64, 72, 84, 79)(73, 85, 77, 88)(74, 86, 78, 89)(75, 92, 95, 93)(80, 90, 81, 91)(82, 87, 96, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.843 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.839 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1 * T2^-2 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^2, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 3, 10, 27, 36, 18, 6, 17, 35, 34, 16, 5)(2, 7, 20, 39, 31, 13, 4, 12, 28, 44, 24, 8)(9, 25, 45, 33, 15, 30, 11, 29, 46, 32, 14, 26)(19, 37, 47, 43, 23, 41, 21, 40, 48, 42, 22, 38)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 68, 83, 76)(64, 72, 84, 79)(73, 85, 77, 88)(74, 86, 78, 89)(75, 93, 82, 94)(80, 90, 81, 91)(87, 95, 92, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.842 Transitivity :: ET+ Graph:: bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.840 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-1 * T2^-2 * T1, T2^3 * T1^-1 * T2 * T1^-1, T2 * T1^2 * T2^-1 * T1^-2, (T2^-1, T1)^2, (T2^-1 * T1^-1)^4, (T1 * T2^-1 * T1)^4, T1^12 ] Map:: non-degenerate R = (1, 3, 10, 24, 46, 21, 45, 35, 38, 32, 17, 5)(2, 7, 22, 43, 33, 41, 37, 16, 31, 11, 26, 8)(4, 12, 29, 15, 28, 9, 27, 40, 18, 39, 36, 14)(6, 19, 42, 34, 13, 30, 48, 25, 47, 23, 44, 20)(49, 50, 54, 66, 86, 79, 95, 76, 94, 81, 61, 52)(51, 57, 67, 89, 80, 60, 71, 55, 69, 87, 78, 59)(53, 63, 68, 91, 83, 62, 73, 56, 72, 88, 82, 64)(58, 70, 90, 84, 65, 74, 92, 75, 93, 85, 96, 77) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.844 Transitivity :: ET+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.841 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 18, 66, 26, 74, 34, 82, 42, 90, 36, 84, 28, 76, 20, 68, 12, 60, 5, 53)(2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 46, 94, 40, 88, 32, 80, 24, 72, 16, 64, 8, 56)(4, 52, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 47, 95, 43, 91, 35, 83, 27, 75, 19, 67, 11, 59)(6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 44, 92, 48, 96, 45, 93, 38, 86, 30, 78, 22, 70, 14, 62) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 52)(7, 51)(8, 53)(9, 61)(10, 63)(11, 62)(12, 64)(13, 55)(14, 56)(15, 69)(16, 70)(17, 58)(18, 73)(19, 60)(20, 75)(21, 65)(22, 67)(23, 66)(24, 68)(25, 77)(26, 79)(27, 78)(28, 80)(29, 71)(30, 72)(31, 85)(32, 86)(33, 74)(34, 89)(35, 76)(36, 91)(37, 81)(38, 83)(39, 82)(40, 84)(41, 92)(42, 94)(43, 93)(44, 87)(45, 88)(46, 96)(47, 90)(48, 95) 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 E15.837 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.842 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1, T1^-1)^2, T2^3 * T1 * T2^3 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 43, 91, 23, 71, 41, 89, 21, 69, 40, 88, 34, 82, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 39, 87, 32, 80, 14, 62, 26, 74, 9, 57, 25, 73, 44, 92, 24, 72, 8, 56)(4, 52, 12, 60, 28, 76, 46, 94, 33, 81, 15, 63, 30, 78, 11, 59, 29, 77, 45, 93, 31, 79, 13, 61)(6, 54, 17, 65, 35, 83, 47, 95, 42, 90, 22, 70, 38, 86, 19, 67, 37, 85, 48, 96, 36, 84, 18, 66) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 68)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 72)(17, 59)(18, 63)(19, 60)(20, 83)(21, 55)(22, 61)(23, 56)(24, 84)(25, 85)(26, 86)(27, 92)(28, 58)(29, 88)(30, 89)(31, 64)(32, 90)(33, 91)(34, 87)(35, 76)(36, 79)(37, 77)(38, 78)(39, 96)(40, 73)(41, 74)(42, 81)(43, 80)(44, 95)(45, 75)(46, 82)(47, 93)(48, 94) 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 E15.839 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.843 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1 * T2^-2 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^2, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 36, 84, 18, 66, 6, 54, 17, 65, 35, 83, 34, 82, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 39, 87, 31, 79, 13, 61, 4, 52, 12, 60, 28, 76, 44, 92, 24, 72, 8, 56)(9, 57, 25, 73, 45, 93, 33, 81, 15, 63, 30, 78, 11, 59, 29, 77, 46, 94, 32, 80, 14, 62, 26, 74)(19, 67, 37, 85, 47, 95, 43, 91, 23, 71, 41, 89, 21, 69, 40, 88, 48, 96, 42, 90, 22, 70, 38, 86) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 68)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 72)(17, 59)(18, 63)(19, 60)(20, 83)(21, 55)(22, 61)(23, 56)(24, 84)(25, 85)(26, 86)(27, 93)(28, 58)(29, 88)(30, 89)(31, 64)(32, 90)(33, 91)(34, 94)(35, 76)(36, 79)(37, 77)(38, 78)(39, 95)(40, 73)(41, 74)(42, 81)(43, 80)(44, 96)(45, 82)(46, 75)(47, 92)(48, 87) 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 E15.838 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.844 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T1^2 * T2 * T1^-2 * T2^-1, (T2^-1, T1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-2 * T2 * T1^-1 * T2^-1 * T1^-3 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 27, 75, 14, 62)(6, 54, 18, 66, 39, 87, 19, 67)(9, 57, 25, 73, 15, 63, 26, 74)(11, 59, 28, 76, 16, 64, 30, 78)(13, 61, 29, 77, 45, 93, 33, 81)(17, 65, 36, 84, 47, 95, 37, 85)(20, 68, 41, 89, 23, 71, 42, 90)(22, 70, 43, 91, 24, 72, 44, 92)(31, 79, 46, 94, 34, 82, 35, 83)(32, 80, 38, 86, 48, 96, 40, 88) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 66)(10, 69)(11, 51)(12, 70)(13, 52)(14, 72)(15, 67)(16, 53)(17, 83)(18, 86)(19, 88)(20, 84)(21, 87)(22, 55)(23, 85)(24, 56)(25, 89)(26, 90)(27, 58)(28, 91)(29, 59)(30, 92)(31, 60)(32, 61)(33, 64)(34, 62)(35, 78)(36, 77)(37, 81)(38, 79)(39, 95)(40, 82)(41, 96)(42, 80)(43, 73)(44, 74)(45, 75)(46, 76)(47, 94)(48, 93) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.840 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.845 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y1^-3, Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1^2 * Y2^-1 * Y1, Y3^-1 * Y2^-2 * Y3 * Y2^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^3 * Y1 * Y2^3 * Y1^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-2 * Y3 * Y2^-1 * Y3^-1 * Y2^-3, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 35, 83, 28, 76)(16, 64, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 38, 86, 30, 78, 41, 89)(27, 75, 44, 92, 47, 95, 45, 93)(32, 80, 42, 90, 33, 81, 43, 91)(34, 82, 39, 87, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 123, 171, 139, 187, 119, 167, 137, 185, 117, 165, 136, 184, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 128, 176, 110, 158, 122, 170, 105, 153, 121, 169, 140, 188, 120, 168, 104, 152)(100, 148, 108, 156, 124, 172, 142, 190, 129, 177, 111, 159, 126, 174, 107, 155, 125, 173, 141, 189, 127, 175, 109, 157)(102, 150, 113, 161, 131, 179, 143, 191, 138, 186, 118, 166, 134, 182, 115, 163, 133, 181, 144, 192, 132, 180, 114, 162) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 124)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 127)(17, 105)(18, 110)(19, 103)(20, 106)(21, 108)(22, 104)(23, 109)(24, 112)(25, 136)(26, 137)(27, 141)(28, 131)(29, 133)(30, 134)(31, 132)(32, 139)(33, 138)(34, 142)(35, 116)(36, 120)(37, 121)(38, 122)(39, 130)(40, 125)(41, 126)(42, 128)(43, 129)(44, 123)(45, 143)(46, 144)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 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 E15.851 Graph:: bipartite v = 16 e = 96 f = 52 degree seq :: [ 8^12, 24^4 ] E15.846 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y3^-1, Y1^4, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^12, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 13, 61, 7, 55)(5, 53, 11, 59, 14, 62, 8, 56)(10, 58, 15, 63, 21, 69, 17, 65)(12, 60, 16, 64, 22, 70, 19, 67)(18, 66, 25, 73, 29, 77, 23, 71)(20, 68, 27, 75, 30, 78, 24, 72)(26, 74, 31, 79, 37, 85, 33, 81)(28, 76, 32, 80, 38, 86, 35, 83)(34, 82, 41, 89, 44, 92, 39, 87)(36, 84, 43, 91, 45, 93, 40, 88)(42, 90, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 103, 151, 111, 159, 119, 167, 127, 175, 135, 183, 142, 190, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152)(100, 148, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 143, 191, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155)(102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 140, 188, 144, 192, 141, 189, 134, 182, 126, 174, 118, 166, 110, 158) L = (1, 100)(2, 97)(3, 103)(4, 102)(5, 104)(6, 98)(7, 109)(8, 110)(9, 99)(10, 113)(11, 101)(12, 115)(13, 105)(14, 107)(15, 106)(16, 108)(17, 117)(18, 119)(19, 118)(20, 120)(21, 111)(22, 112)(23, 125)(24, 126)(25, 114)(26, 129)(27, 116)(28, 131)(29, 121)(30, 123)(31, 122)(32, 124)(33, 133)(34, 135)(35, 134)(36, 136)(37, 127)(38, 128)(39, 140)(40, 141)(41, 130)(42, 143)(43, 132)(44, 137)(45, 139)(46, 138)(47, 144)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E15.850 Graph:: bipartite v = 16 e = 96 f = 52 degree seq :: [ 8^12, 24^4 ] E15.847 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^2 * Y1^-2, (Y3 * Y1^-1)^2, Y1^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y1 * Y2^-2 * Y1^-1 * Y2, Y3 * Y2^6 * Y1^-1, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, (Y1 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 35, 83, 28, 76)(16, 64, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 38, 86, 30, 78, 41, 89)(27, 75, 45, 93, 34, 82, 46, 94)(32, 80, 42, 90, 33, 81, 43, 91)(39, 87, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 123, 171, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 127, 175, 109, 157, 100, 148, 108, 156, 124, 172, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 129, 177, 111, 159, 126, 174, 107, 155, 125, 173, 142, 190, 128, 176, 110, 158, 122, 170)(115, 163, 133, 181, 143, 191, 139, 187, 119, 167, 137, 185, 117, 165, 136, 184, 144, 192, 138, 186, 118, 166, 134, 182) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 124)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 127)(17, 105)(18, 110)(19, 103)(20, 106)(21, 108)(22, 104)(23, 109)(24, 112)(25, 136)(26, 137)(27, 142)(28, 131)(29, 133)(30, 134)(31, 132)(32, 139)(33, 138)(34, 141)(35, 116)(36, 120)(37, 121)(38, 122)(39, 144)(40, 125)(41, 126)(42, 128)(43, 129)(44, 143)(45, 123)(46, 130)(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) :: { ( 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 E15.852 Graph:: bipartite v = 16 e = 96 f = 52 degree seq :: [ 8^12, 24^4 ] E15.848 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4 * Y1^-1 * Y2 * Y1 * Y2, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 38, 86, 27, 75, 43, 91, 36, 84, 47, 95, 32, 80, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 40, 88, 37, 85, 45, 93, 34, 82, 14, 62, 25, 73, 8, 56, 24, 72, 11, 59)(5, 53, 15, 63, 20, 68, 12, 60, 23, 71, 7, 55, 21, 69, 39, 87, 29, 77, 48, 96, 33, 81, 16, 64)(10, 58, 22, 70, 41, 89, 35, 83, 17, 65, 26, 74, 42, 90, 31, 79, 46, 94, 28, 76, 44, 92, 30, 78)(97, 145, 99, 147, 106, 154, 125, 173, 143, 191, 121, 169, 142, 190, 119, 167, 134, 182, 133, 181, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 141, 189, 128, 176, 111, 159, 124, 172, 105, 153, 123, 171, 144, 192, 122, 170, 104, 152)(100, 148, 108, 156, 126, 174, 136, 184, 132, 180, 112, 160, 127, 175, 107, 155, 114, 162, 135, 183, 131, 179, 110, 158)(102, 150, 115, 163, 137, 185, 129, 177, 109, 157, 120, 168, 140, 188, 117, 165, 139, 187, 130, 178, 138, 186, 116, 164) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 125)(11, 114)(12, 126)(13, 120)(14, 100)(15, 124)(16, 127)(17, 101)(18, 135)(19, 137)(20, 102)(21, 139)(22, 141)(23, 134)(24, 140)(25, 142)(26, 104)(27, 144)(28, 105)(29, 143)(30, 136)(31, 107)(32, 111)(33, 109)(34, 138)(35, 110)(36, 112)(37, 113)(38, 133)(39, 131)(40, 132)(41, 129)(42, 116)(43, 130)(44, 117)(45, 128)(46, 119)(47, 121)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E15.849 Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 24^8 ] E15.849 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-2 * Y3 * Y2^-2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3^2 * Y2 * Y3^-2 * Y2^-1, (Y2, Y3^-1)^2, Y3^3 * Y2 * Y3^3 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 116, 164, 131, 179, 124, 172)(112, 160, 120, 168, 132, 180, 127, 175)(121, 169, 133, 181, 125, 173, 136, 184)(122, 170, 134, 182, 126, 174, 137, 185)(123, 171, 140, 188, 143, 191, 141, 189)(128, 176, 138, 186, 129, 177, 139, 187)(130, 178, 135, 183, 144, 192, 142, 190) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 123)(11, 125)(12, 124)(13, 100)(14, 122)(15, 126)(16, 101)(17, 131)(18, 102)(19, 133)(20, 135)(21, 136)(22, 134)(23, 137)(24, 104)(25, 140)(26, 105)(27, 139)(28, 142)(29, 141)(30, 107)(31, 109)(32, 110)(33, 111)(34, 112)(35, 143)(36, 114)(37, 144)(38, 115)(39, 128)(40, 130)(41, 117)(42, 118)(43, 119)(44, 120)(45, 127)(46, 129)(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) :: { ( 24, 24 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E15.848 Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.850 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 36, 84, 28, 76, 20, 68, 12, 60, 4, 52)(3, 51, 8, 56, 14, 62, 23, 71, 30, 78, 39, 87, 44, 92, 42, 90, 34, 82, 26, 74, 18, 66, 10, 58)(5, 53, 7, 55, 15, 63, 22, 70, 31, 79, 38, 86, 45, 93, 43, 91, 35, 83, 27, 75, 19, 67, 11, 59)(9, 57, 16, 64, 24, 72, 32, 80, 40, 88, 46, 94, 48, 96, 47, 95, 41, 89, 33, 81, 25, 73, 17, 65)(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, 107)(5, 97)(6, 110)(7, 112)(8, 98)(9, 101)(10, 100)(11, 113)(12, 114)(13, 118)(14, 120)(15, 102)(16, 104)(17, 106)(18, 121)(19, 108)(20, 123)(21, 126)(22, 128)(23, 109)(24, 111)(25, 115)(26, 116)(27, 129)(28, 130)(29, 134)(30, 136)(31, 117)(32, 119)(33, 122)(34, 137)(35, 124)(36, 139)(37, 140)(38, 142)(39, 125)(40, 127)(41, 131)(42, 132)(43, 143)(44, 144)(45, 133)(46, 135)(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) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.846 Graph:: simple bipartite v = 52 e = 96 f = 16 degree seq :: [ 2^48, 24^4 ] E15.851 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3^-2 * Y1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y1^-1 * Y3^2 * Y1^-5, (Y3^-1, Y1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^4, Y3^-1 * Y1^-4 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-4 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 27, 75, 10, 58, 21, 69, 39, 87, 32, 80, 13, 61, 4, 52)(3, 51, 9, 57, 18, 66, 38, 86, 33, 81, 16, 64, 5, 53, 15, 63, 19, 67, 40, 88, 29, 77, 11, 59)(7, 55, 20, 68, 36, 84, 34, 82, 14, 62, 24, 72, 8, 56, 23, 71, 37, 85, 31, 79, 12, 60, 22, 70)(25, 73, 41, 89, 47, 95, 46, 94, 30, 78, 44, 92, 26, 74, 42, 90, 48, 96, 45, 93, 28, 76, 43, 91)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 121)(10, 101)(11, 124)(12, 123)(13, 125)(14, 100)(15, 122)(16, 126)(17, 132)(18, 135)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 111)(26, 105)(27, 110)(28, 112)(29, 131)(30, 107)(31, 141)(32, 133)(33, 109)(34, 142)(35, 129)(36, 128)(37, 113)(38, 143)(39, 115)(40, 144)(41, 119)(42, 116)(43, 120)(44, 118)(45, 130)(46, 127)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.845 Graph:: simple bipartite v = 52 e = 96 f = 16 degree seq :: [ 2^48, 24^4 ] E15.852 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C4 : C4) (small group id <48, 22>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 102>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, (Y3, Y1^-1)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-5, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 30, 78, 44, 92, 26, 74, 42, 90, 32, 80, 13, 61, 4, 52)(3, 51, 9, 57, 18, 66, 38, 86, 31, 79, 12, 60, 22, 70, 7, 55, 20, 68, 36, 84, 29, 77, 11, 59)(5, 53, 15, 63, 19, 67, 40, 88, 34, 82, 14, 62, 24, 72, 8, 56, 23, 71, 37, 85, 33, 81, 16, 64)(10, 58, 21, 69, 39, 87, 47, 95, 46, 94, 28, 76, 43, 91, 25, 73, 41, 89, 48, 96, 45, 93, 27, 75)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 121)(10, 101)(11, 124)(12, 123)(13, 125)(14, 100)(15, 122)(16, 126)(17, 132)(18, 135)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 111)(26, 105)(27, 110)(28, 112)(29, 141)(30, 107)(31, 142)(32, 134)(33, 109)(34, 131)(35, 127)(36, 143)(37, 113)(38, 144)(39, 115)(40, 128)(41, 119)(42, 116)(43, 120)(44, 118)(45, 129)(46, 130)(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, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.847 Graph:: simple bipartite v = 52 e = 96 f = 16 degree seq :: [ 2^48, 24^4 ] E15.853 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-2, T2^6 * T1^-2, (T2^-3 * T1)^2, T2^-1 * T1 * T2^2 * T1^-1 * T2^-4 * T1^-1 * T2^-3 ] Map:: non-degenerate R = (1, 3, 10, 28, 42, 18, 6, 17, 41, 40, 16, 5)(2, 7, 20, 43, 33, 13, 4, 12, 32, 44, 24, 8)(9, 25, 45, 39, 23, 31, 11, 30, 48, 38, 22, 26)(14, 34, 21, 27, 46, 37, 15, 36, 19, 29, 47, 35)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 75, 89, 77)(64, 86, 90, 87)(68, 73, 80, 78)(72, 85, 81, 83)(74, 82, 79, 84)(76, 91, 88, 92)(93, 94, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.855 Transitivity :: ET+ Graph:: bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.854 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1^-1 * T2^2 * T1^-1, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-2, T2^6 * T1^-2, (T2^-3 * T1)^2 ] Map:: non-degenerate R = (1, 3, 10, 28, 42, 18, 6, 17, 41, 40, 16, 5)(2, 7, 20, 43, 33, 13, 4, 12, 32, 44, 24, 8)(9, 25, 45, 39, 22, 31, 11, 30, 48, 38, 23, 26)(14, 34, 19, 27, 46, 37, 15, 36, 21, 29, 47, 35)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 75, 89, 77)(64, 86, 90, 87)(68, 78, 80, 73)(72, 83, 81, 85)(74, 84, 79, 82)(76, 91, 88, 92)(93, 95, 96, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^4 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E15.856 Transitivity :: ET+ Graph:: bipartite v = 16 e = 48 f = 4 degree seq :: [ 4^12, 12^4 ] E15.855 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-2, T2^6 * T1^-2, (T2^-3 * T1)^2, T2^-1 * T1 * T2^2 * T1^-1 * T2^-4 * T1^-1 * T2^-3 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 28, 76, 42, 90, 18, 66, 6, 54, 17, 65, 41, 89, 40, 88, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 43, 91, 33, 81, 13, 61, 4, 52, 12, 60, 32, 80, 44, 92, 24, 72, 8, 56)(9, 57, 25, 73, 45, 93, 39, 87, 23, 71, 31, 79, 11, 59, 30, 78, 48, 96, 38, 86, 22, 70, 26, 74)(14, 62, 34, 82, 21, 69, 27, 75, 46, 94, 37, 85, 15, 63, 36, 84, 19, 67, 29, 77, 47, 95, 35, 83) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 75)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 86)(17, 59)(18, 63)(19, 60)(20, 73)(21, 55)(22, 61)(23, 56)(24, 85)(25, 80)(26, 82)(27, 89)(28, 91)(29, 58)(30, 68)(31, 84)(32, 78)(33, 83)(34, 79)(35, 72)(36, 74)(37, 81)(38, 90)(39, 64)(40, 92)(41, 77)(42, 87)(43, 88)(44, 76)(45, 94)(46, 96)(47, 93)(48, 95) 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 E15.853 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.856 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1^-1 * T2^2 * T1^-1, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-2, T2^6 * T1^-2, (T2^-3 * T1)^2 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 28, 76, 42, 90, 18, 66, 6, 54, 17, 65, 41, 89, 40, 88, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 43, 91, 33, 81, 13, 61, 4, 52, 12, 60, 32, 80, 44, 92, 24, 72, 8, 56)(9, 57, 25, 73, 45, 93, 39, 87, 22, 70, 31, 79, 11, 59, 30, 78, 48, 96, 38, 86, 23, 71, 26, 74)(14, 62, 34, 82, 19, 67, 27, 75, 46, 94, 37, 85, 15, 63, 36, 84, 21, 69, 29, 77, 47, 95, 35, 83) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 75)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 86)(17, 59)(18, 63)(19, 60)(20, 78)(21, 55)(22, 61)(23, 56)(24, 83)(25, 68)(26, 84)(27, 89)(28, 91)(29, 58)(30, 80)(31, 82)(32, 73)(33, 85)(34, 74)(35, 81)(36, 79)(37, 72)(38, 90)(39, 64)(40, 92)(41, 77)(42, 87)(43, 88)(44, 76)(45, 95)(46, 93)(47, 96)(48, 94) 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 E15.854 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 48 f = 16 degree seq :: [ 24^4 ] E15.857 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y3^-1 * Y1, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1 * Y2^-2 * Y3, Y1 * Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y1 * Y2 * R * Y2^2 * R * Y2, Y3 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2, Y2^3 * Y3 * Y2^3 * Y1^-1, Y1 * Y2^2 * R * Y2^-2 * R * Y2^2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 41, 89, 29, 77)(16, 64, 38, 86, 42, 90, 39, 87)(20, 68, 30, 78, 32, 80, 25, 73)(24, 72, 35, 83, 33, 81, 37, 85)(26, 74, 36, 84, 31, 79, 34, 82)(28, 76, 43, 91, 40, 88, 44, 92)(45, 93, 47, 95, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 124, 172, 138, 186, 114, 162, 102, 150, 113, 161, 137, 185, 136, 184, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 139, 187, 129, 177, 109, 157, 100, 148, 108, 156, 128, 176, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 135, 183, 118, 166, 127, 175, 107, 155, 126, 174, 144, 192, 134, 182, 119, 167, 122, 170)(110, 158, 130, 178, 115, 163, 123, 171, 142, 190, 133, 181, 111, 159, 132, 180, 117, 165, 125, 173, 143, 191, 131, 179) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 125)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 135)(17, 105)(18, 110)(19, 103)(20, 121)(21, 108)(22, 104)(23, 109)(24, 133)(25, 128)(26, 130)(27, 106)(28, 140)(29, 137)(30, 116)(31, 132)(32, 126)(33, 131)(34, 127)(35, 120)(36, 122)(37, 129)(38, 112)(39, 138)(40, 139)(41, 123)(42, 134)(43, 124)(44, 136)(45, 142)(46, 144)(47, 141)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E15.860 Graph:: bipartite v = 16 e = 96 f = 52 degree seq :: [ 8^12, 24^4 ] E15.858 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y1 * Y3^-1 * Y2 * Y3 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y3 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2^-2, Y3 * Y2 * Y1^-1 * Y2^-2 * Y3^-1 * Y2, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, Y2^3 * Y3 * Y2^3 * Y1^-1, Y1 * Y2 * R * Y2^-4 * R * Y2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 41, 89, 29, 77)(16, 64, 38, 86, 42, 90, 39, 87)(20, 68, 25, 73, 32, 80, 30, 78)(24, 72, 37, 85, 33, 81, 35, 83)(26, 74, 34, 82, 31, 79, 36, 84)(28, 76, 43, 91, 40, 88, 44, 92)(45, 93, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 106, 154, 124, 172, 138, 186, 114, 162, 102, 150, 113, 161, 137, 185, 136, 184, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 139, 187, 129, 177, 109, 157, 100, 148, 108, 156, 128, 176, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 135, 183, 119, 167, 127, 175, 107, 155, 126, 174, 144, 192, 134, 182, 118, 166, 122, 170)(110, 158, 130, 178, 117, 165, 123, 171, 142, 190, 133, 181, 111, 159, 132, 180, 115, 163, 125, 173, 143, 191, 131, 179) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 125)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 135)(17, 105)(18, 110)(19, 103)(20, 126)(21, 108)(22, 104)(23, 109)(24, 131)(25, 116)(26, 132)(27, 106)(28, 140)(29, 137)(30, 128)(31, 130)(32, 121)(33, 133)(34, 122)(35, 129)(36, 127)(37, 120)(38, 112)(39, 138)(40, 139)(41, 123)(42, 134)(43, 124)(44, 136)(45, 143)(46, 141)(47, 144)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E15.859 Graph:: bipartite v = 16 e = 96 f = 52 degree seq :: [ 8^12, 24^4 ] E15.859 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y1^2 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2 * Y3, (Y1^-1 * Y3 * Y1^-2)^2, (Y3 * Y2^-1)^4, (Y1^-4 * Y3^-1)^3 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 41, 89, 28, 76, 10, 58, 21, 69, 45, 93, 35, 83, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 42, 90, 40, 88, 16, 64, 5, 53, 15, 63, 39, 87, 43, 91, 30, 78, 11, 59)(7, 55, 20, 68, 47, 95, 36, 84, 31, 79, 24, 72, 8, 56, 23, 71, 48, 96, 34, 82, 29, 77, 22, 70)(12, 60, 32, 80, 27, 75, 18, 66, 44, 92, 38, 86, 14, 62, 37, 85, 26, 74, 19, 67, 46, 94, 33, 81)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 122)(10, 101)(11, 125)(12, 124)(13, 130)(14, 100)(15, 123)(16, 127)(17, 138)(18, 141)(19, 102)(20, 135)(21, 104)(22, 128)(23, 121)(24, 133)(25, 116)(26, 111)(27, 105)(28, 110)(29, 112)(30, 134)(31, 107)(32, 120)(33, 126)(34, 137)(35, 139)(36, 109)(37, 118)(38, 136)(39, 119)(40, 129)(41, 132)(42, 131)(43, 113)(44, 144)(45, 115)(46, 143)(47, 140)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.858 Graph:: simple bipartite v = 52 e = 96 f = 16 degree seq :: [ 2^48, 24^4 ] E15.860 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2 * Y3^-1, Y1^-2 * Y3^2 * Y1^-4, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^2)^3 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 41, 89, 28, 76, 10, 58, 21, 69, 45, 93, 35, 83, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 42, 90, 40, 88, 16, 64, 5, 53, 15, 63, 39, 87, 43, 91, 30, 78, 11, 59)(7, 55, 20, 68, 47, 95, 36, 84, 29, 77, 24, 72, 8, 56, 23, 71, 48, 96, 34, 82, 31, 79, 22, 70)(12, 60, 32, 80, 26, 74, 18, 66, 44, 92, 38, 86, 14, 62, 37, 85, 27, 75, 19, 67, 46, 94, 33, 81)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 122)(10, 101)(11, 125)(12, 124)(13, 130)(14, 100)(15, 123)(16, 127)(17, 138)(18, 141)(19, 102)(20, 121)(21, 104)(22, 133)(23, 135)(24, 128)(25, 119)(26, 111)(27, 105)(28, 110)(29, 112)(30, 129)(31, 107)(32, 118)(33, 136)(34, 137)(35, 139)(36, 109)(37, 120)(38, 126)(39, 116)(40, 134)(41, 132)(42, 131)(43, 113)(44, 143)(45, 115)(46, 144)(47, 142)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.857 Graph:: simple bipartite v = 52 e = 96 f = 16 degree seq :: [ 2^48, 24^4 ] E15.861 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 24}) Quotient :: edge Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^4 * T1^-2, (T2^2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1)^24 ] Map:: non-degenerate R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 15, 28, 11, 27, 14, 26)(19, 29, 23, 32, 21, 31, 22, 30)(33, 41, 36, 44, 34, 43, 35, 42)(37, 45, 40, 48, 38, 47, 39, 46)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 68, 64, 72)(73, 81, 75, 82)(74, 83, 76, 84)(77, 85, 79, 86)(78, 87, 80, 88)(89, 93, 91, 95)(90, 94, 92, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^8 ) } Outer automorphisms :: reflexible Dual of E15.865 Transitivity :: ET+ Graph:: bipartite v = 18 e = 48 f = 2 degree seq :: [ 4^12, 8^6 ] E15.862 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 24}) Quotient :: edge Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1^-2 * T2^-1 * T1^2, T2^-2 * T1^-1 * T2^-2 * T1^-3, T2^6 * T1^2, (T2^-1 * T1^-1)^4, T1^8 ] Map:: non-degenerate R = (1, 3, 10, 25, 40, 28, 12, 21, 42, 48, 39, 19, 34, 29, 43, 47, 38, 18, 6, 17, 37, 33, 15, 5)(2, 7, 20, 41, 30, 13, 4, 11, 26, 46, 24, 36, 27, 14, 31, 45, 23, 9, 16, 35, 32, 44, 22, 8)(49, 50, 54, 64, 82, 75, 60, 52)(51, 57, 65, 84, 77, 61, 69, 56)(53, 59, 66, 55, 67, 83, 76, 62)(58, 72, 85, 78, 91, 70, 90, 71)(63, 79, 86, 74, 87, 68, 88, 80)(73, 89, 81, 92, 95, 93, 96, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E15.866 Transitivity :: ET+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.863 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 24}) Quotient :: edge Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T1 * T2^-1 * T1)^2, T2 * T1^-1 * T2^2 * T1 * T2, (T1^-1 * T2^-1 * T1^-1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1^-4 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 32, 45, 25)(17, 36, 47, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 35, 34, 46)(33, 40, 48, 39)(49, 50, 54, 65, 83, 74, 89, 78, 92, 96, 93, 76, 58, 69, 86, 95, 94, 75, 90, 77, 91, 81, 61, 52)(51, 57, 73, 84, 72, 56, 71, 60, 79, 87, 66, 64, 53, 63, 80, 85, 70, 55, 68, 62, 82, 88, 67, 59) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^4 ), ( 16^24 ) } Outer automorphisms :: reflexible Dual of E15.864 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.864 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 24}) Quotient :: loop Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^4 * T1^-2, (T2^2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1)^24 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 18, 66, 6, 54, 17, 65, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 13, 61, 4, 52, 12, 60, 24, 72, 8, 56)(9, 57, 25, 73, 15, 63, 28, 76, 11, 59, 27, 75, 14, 62, 26, 74)(19, 67, 29, 77, 23, 71, 32, 80, 21, 69, 31, 79, 22, 70, 30, 78)(33, 81, 41, 89, 36, 84, 44, 92, 34, 82, 43, 91, 35, 83, 42, 90)(37, 85, 45, 93, 40, 88, 48, 96, 38, 86, 47, 95, 39, 87, 46, 94) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 68)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 72)(17, 59)(18, 63)(19, 60)(20, 64)(21, 55)(22, 61)(23, 56)(24, 58)(25, 81)(26, 83)(27, 82)(28, 84)(29, 85)(30, 87)(31, 86)(32, 88)(33, 75)(34, 73)(35, 76)(36, 74)(37, 79)(38, 77)(39, 80)(40, 78)(41, 93)(42, 94)(43, 95)(44, 96)(45, 91)(46, 92)(47, 89)(48, 90) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.863 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.865 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 24}) Quotient :: loop Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1^-2 * T2^-1 * T1^2, T2^-2 * T1^-1 * T2^-2 * T1^-3, T2^6 * T1^2, (T2^-1 * T1^-1)^4, T1^8 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 25, 73, 40, 88, 28, 76, 12, 60, 21, 69, 42, 90, 48, 96, 39, 87, 19, 67, 34, 82, 29, 77, 43, 91, 47, 95, 38, 86, 18, 66, 6, 54, 17, 65, 37, 85, 33, 81, 15, 63, 5, 53)(2, 50, 7, 55, 20, 68, 41, 89, 30, 78, 13, 61, 4, 52, 11, 59, 26, 74, 46, 94, 24, 72, 36, 84, 27, 75, 14, 62, 31, 79, 45, 93, 23, 71, 9, 57, 16, 64, 35, 83, 32, 80, 44, 92, 22, 70, 8, 56) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 64)(7, 67)(8, 51)(9, 65)(10, 72)(11, 66)(12, 52)(13, 69)(14, 53)(15, 79)(16, 82)(17, 84)(18, 55)(19, 83)(20, 88)(21, 56)(22, 90)(23, 58)(24, 85)(25, 89)(26, 87)(27, 60)(28, 62)(29, 61)(30, 91)(31, 86)(32, 63)(33, 92)(34, 75)(35, 76)(36, 77)(37, 78)(38, 74)(39, 68)(40, 80)(41, 81)(42, 71)(43, 70)(44, 95)(45, 96)(46, 73)(47, 93)(48, 94) 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 ) } Outer automorphisms :: reflexible Dual of E15.861 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 48 f = 18 degree seq :: [ 48^2 ] E15.866 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 24}) Quotient :: loop Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T1 * T2^-1 * T1)^2, T2 * T1^-1 * T2^2 * T1 * T2, (T1^-1 * T2^-1 * T1^-1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1^-4 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 28, 76, 14, 62)(6, 54, 18, 66, 38, 86, 19, 67)(9, 57, 26, 74, 15, 63, 27, 75)(11, 59, 29, 77, 16, 64, 30, 78)(13, 61, 32, 80, 45, 93, 25, 73)(17, 65, 36, 84, 47, 95, 37, 85)(20, 68, 41, 89, 23, 71, 42, 90)(22, 70, 43, 91, 24, 72, 44, 92)(31, 79, 35, 83, 34, 82, 46, 94)(33, 81, 40, 88, 48, 96, 39, 87) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 73)(10, 69)(11, 51)(12, 79)(13, 52)(14, 82)(15, 80)(16, 53)(17, 83)(18, 64)(19, 59)(20, 62)(21, 86)(22, 55)(23, 60)(24, 56)(25, 84)(26, 89)(27, 90)(28, 58)(29, 91)(30, 92)(31, 87)(32, 85)(33, 61)(34, 88)(35, 74)(36, 72)(37, 70)(38, 95)(39, 66)(40, 67)(41, 78)(42, 77)(43, 81)(44, 96)(45, 76)(46, 75)(47, 94)(48, 93) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.862 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.867 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^-1 * Y1^-2 * Y2 * Y1^-2, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y3 * Y2^4 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^2 * Y3 * Y2^2 * Y1^-1, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, R * Y2 * Y3^-1 * Y2^2 * R * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 16, 64, 24, 72)(25, 73, 33, 81, 27, 75, 34, 82)(26, 74, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 45, 93, 43, 91, 47, 95)(42, 90, 46, 94, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 114, 162, 102, 150, 113, 161, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 109, 157, 100, 148, 108, 156, 120, 168, 104, 152)(105, 153, 121, 169, 111, 159, 124, 172, 107, 155, 123, 171, 110, 158, 122, 170)(115, 163, 125, 173, 119, 167, 128, 176, 117, 165, 127, 175, 118, 166, 126, 174)(129, 177, 137, 185, 132, 180, 140, 188, 130, 178, 139, 187, 131, 179, 138, 186)(133, 181, 141, 189, 136, 184, 144, 192, 134, 182, 143, 191, 135, 183, 142, 190) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 120)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 116)(17, 105)(18, 110)(19, 103)(20, 106)(21, 108)(22, 104)(23, 109)(24, 112)(25, 130)(26, 132)(27, 129)(28, 131)(29, 134)(30, 136)(31, 133)(32, 135)(33, 121)(34, 123)(35, 122)(36, 124)(37, 125)(38, 127)(39, 126)(40, 128)(41, 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) :: { ( 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 E15.870 Graph:: bipartite v = 18 e = 96 f = 50 degree seq :: [ 8^12, 16^6 ] E15.868 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^-2 * Y1^-1 * Y2^-2 * Y1^-3, Y2^-4 * Y1 * Y2^2 * Y1, Y1^8, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 34, 82, 27, 75, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 36, 84, 29, 77, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 35, 83, 28, 76, 14, 62)(10, 58, 24, 72, 37, 85, 30, 78, 43, 91, 22, 70, 42, 90, 23, 71)(15, 63, 31, 79, 38, 86, 26, 74, 39, 87, 20, 68, 40, 88, 32, 80)(25, 73, 41, 89, 33, 81, 44, 92, 47, 95, 45, 93, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 121, 169, 136, 184, 124, 172, 108, 156, 117, 165, 138, 186, 144, 192, 135, 183, 115, 163, 130, 178, 125, 173, 139, 187, 143, 191, 134, 182, 114, 162, 102, 150, 113, 161, 133, 181, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 137, 185, 126, 174, 109, 157, 100, 148, 107, 155, 122, 170, 142, 190, 120, 168, 132, 180, 123, 171, 110, 158, 127, 175, 141, 189, 119, 167, 105, 153, 112, 160, 131, 179, 128, 176, 140, 188, 118, 166, 104, 152) L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 113)(7, 116)(8, 98)(9, 112)(10, 121)(11, 122)(12, 117)(13, 100)(14, 127)(15, 101)(16, 131)(17, 133)(18, 102)(19, 130)(20, 137)(21, 138)(22, 104)(23, 105)(24, 132)(25, 136)(26, 142)(27, 110)(28, 108)(29, 139)(30, 109)(31, 141)(32, 140)(33, 111)(34, 125)(35, 128)(36, 123)(37, 129)(38, 114)(39, 115)(40, 124)(41, 126)(42, 144)(43, 143)(44, 118)(45, 119)(46, 120)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.869 Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 16^6, 48^2 ] E15.869 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2 * Y3^2)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^2 * Y3 * Y2, (Y3^2 * Y2^-1)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3^-5 * Y2 * Y3, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 123, 171, 131, 179, 120, 168)(112, 160, 127, 175, 132, 180, 116, 164)(121, 169, 133, 181, 125, 173, 136, 184)(122, 170, 138, 186, 126, 174, 139, 187)(124, 172, 135, 183, 143, 191, 141, 189)(128, 176, 134, 182, 129, 177, 137, 185)(130, 178, 140, 188, 144, 192, 142, 190) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 124)(11, 125)(12, 127)(13, 100)(14, 128)(15, 129)(16, 101)(17, 131)(18, 102)(19, 133)(20, 135)(21, 136)(22, 138)(23, 139)(24, 104)(25, 111)(26, 105)(27, 109)(28, 134)(29, 110)(30, 107)(31, 141)(32, 142)(33, 140)(34, 112)(35, 143)(36, 114)(37, 119)(38, 115)(39, 126)(40, 118)(41, 117)(42, 130)(43, 144)(44, 120)(45, 122)(46, 123)(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) :: { ( 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E15.868 Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.870 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-2)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-3, (Y3 * Y2^-1)^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 26, 74, 41, 89, 30, 78, 44, 92, 48, 96, 45, 93, 28, 76, 10, 58, 21, 69, 38, 86, 47, 95, 46, 94, 27, 75, 42, 90, 29, 77, 43, 91, 33, 81, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 36, 84, 24, 72, 8, 56, 23, 71, 12, 60, 31, 79, 39, 87, 18, 66, 16, 64, 5, 53, 15, 63, 32, 80, 37, 85, 22, 70, 7, 55, 20, 68, 14, 62, 34, 82, 40, 88, 19, 67, 11, 59)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 122)(10, 101)(11, 125)(12, 124)(13, 128)(14, 100)(15, 123)(16, 126)(17, 132)(18, 134)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 109)(26, 111)(27, 105)(28, 110)(29, 112)(30, 107)(31, 131)(32, 141)(33, 136)(34, 142)(35, 130)(36, 143)(37, 113)(38, 115)(39, 129)(40, 144)(41, 119)(42, 116)(43, 120)(44, 118)(45, 121)(46, 127)(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, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.867 Graph:: simple bipartite v = 50 e = 96 f = 18 degree seq :: [ 2^48, 48^2 ] E15.871 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y1^-1 * Y2^-2, Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1, Y3 * Y2^2 * Y1^-1 * Y2^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-5 * Y1^-1, (Y2^-1 * R * Y2^-2)^2, (Y3 * Y2 * Y1 * Y2)^4, Y1^-1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 35, 83, 24, 72)(16, 64, 31, 79, 36, 84, 20, 68)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 42, 90, 30, 78, 43, 91)(28, 76, 39, 87, 47, 95, 45, 93)(32, 80, 38, 86, 33, 81, 41, 89)(34, 82, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 124, 172, 134, 182, 115, 163, 133, 181, 119, 167, 139, 187, 144, 192, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 143, 191, 137, 185, 117, 165, 136, 184, 118, 166, 138, 186, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 126, 174, 107, 155, 125, 173, 110, 158, 128, 176, 142, 190, 123, 171, 109, 157, 100, 148, 108, 156, 127, 175, 141, 189, 122, 170, 105, 153, 121, 169, 111, 159, 129, 177, 140, 188, 120, 168, 104, 152) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 120)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 116)(17, 105)(18, 110)(19, 103)(20, 132)(21, 108)(22, 104)(23, 109)(24, 131)(25, 136)(26, 139)(27, 106)(28, 141)(29, 133)(30, 138)(31, 112)(32, 137)(33, 134)(34, 142)(35, 123)(36, 127)(37, 121)(38, 128)(39, 124)(40, 125)(41, 129)(42, 122)(43, 126)(44, 130)(45, 143)(46, 144)(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) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E15.872 Graph:: bipartite v = 14 e = 96 f = 54 degree seq :: [ 8^12, 48^2 ] E15.872 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y1^-1 * Y3^-1 * Y1^3 * Y3^-1, Y3^-1 * Y1^2 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1 * Y3^-3 * Y1^-1, Y3^-2 * Y1^-1 * Y3^-2 * Y1^-3, (Y3^-1 * Y1^-1)^4, Y1^8, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 34, 82, 27, 75, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 36, 84, 29, 77, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 35, 83, 28, 76, 14, 62)(10, 58, 24, 72, 37, 85, 30, 78, 43, 91, 22, 70, 42, 90, 23, 71)(15, 63, 31, 79, 38, 86, 26, 74, 39, 87, 20, 68, 40, 88, 32, 80)(25, 73, 41, 89, 33, 81, 44, 92, 47, 95, 45, 93, 48, 96, 46, 94)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 113)(7, 116)(8, 98)(9, 112)(10, 121)(11, 122)(12, 117)(13, 100)(14, 127)(15, 101)(16, 131)(17, 133)(18, 102)(19, 130)(20, 137)(21, 138)(22, 104)(23, 105)(24, 132)(25, 136)(26, 142)(27, 110)(28, 108)(29, 139)(30, 109)(31, 141)(32, 140)(33, 111)(34, 125)(35, 128)(36, 123)(37, 129)(38, 114)(39, 115)(40, 124)(41, 126)(42, 144)(43, 143)(44, 118)(45, 119)(46, 120)(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, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E15.871 Graph:: simple bipartite v = 54 e = 96 f = 14 degree seq :: [ 2^48, 16^6 ] E15.873 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 24}) Quotient :: edge Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^3, (T2^2 * T1^-1)^2, T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^24 ] Map:: non-degenerate R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 15, 28, 11, 27, 14, 26)(19, 29, 23, 32, 21, 31, 22, 30)(33, 41, 36, 44, 34, 43, 35, 42)(37, 45, 40, 48, 38, 47, 39, 46)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 68, 64, 72)(73, 81, 75, 82)(74, 83, 76, 84)(77, 85, 79, 86)(78, 87, 80, 88)(89, 95, 91, 93)(90, 96, 92, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 48^4 ), ( 48^8 ) } Outer automorphisms :: reflexible Dual of E15.877 Transitivity :: ET+ Graph:: bipartite v = 18 e = 48 f = 2 degree seq :: [ 4^12, 8^6 ] E15.874 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 24}) Quotient :: edge Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1^-2 * T2^-1 * T1^2, T2 * T1^-1 * T2^-5 * T1, T2^-2 * T1^-1 * T2^-2 * T1^-3, T1^8, (T2^-1 * T1^-1)^4 ] Map:: non-degenerate R = (1, 3, 10, 25, 38, 18, 6, 17, 37, 47, 39, 19, 34, 29, 43, 48, 40, 28, 12, 21, 42, 33, 15, 5)(2, 7, 20, 41, 23, 9, 16, 35, 32, 45, 24, 36, 27, 14, 31, 46, 30, 13, 4, 11, 26, 44, 22, 8)(49, 50, 54, 64, 82, 75, 60, 52)(51, 57, 65, 84, 77, 61, 69, 56)(53, 59, 66, 55, 67, 83, 76, 62)(58, 72, 85, 78, 91, 70, 90, 71)(63, 79, 86, 74, 87, 68, 88, 80)(73, 94, 95, 92, 96, 89, 81, 93) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^8 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E15.878 Transitivity :: ET+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 8^6, 24^2 ] E15.875 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 24}) Quotient :: edge Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T2^4, T2^4, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-2 * T1 * T2, T2^2 * T1 * T2^-2 * T1^-1, (T1^-1 * T2 * T1^-1)^2, (T1^-1 * T2^-1 * T1^-1)^2, T1^-2 * T2^-1 * T1 * T2 * T1^-3, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 32, 45, 25)(17, 36, 47, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 46, 34, 35)(33, 39, 48, 40)(49, 50, 54, 65, 83, 75, 90, 77, 91, 96, 93, 76, 58, 69, 86, 95, 94, 74, 89, 78, 92, 81, 61, 52)(51, 57, 73, 85, 70, 55, 68, 62, 82, 87, 66, 64, 53, 63, 80, 84, 72, 56, 71, 60, 79, 88, 67, 59) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^4 ), ( 16^24 ) } Outer automorphisms :: reflexible Dual of E15.876 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 6 degree seq :: [ 4^12, 24^2 ] E15.876 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 24}) Quotient :: loop Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^3, (T2^2 * T1^-1)^2, T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^24 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 18, 66, 6, 54, 17, 65, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 13, 61, 4, 52, 12, 60, 24, 72, 8, 56)(9, 57, 25, 73, 15, 63, 28, 76, 11, 59, 27, 75, 14, 62, 26, 74)(19, 67, 29, 77, 23, 71, 32, 80, 21, 69, 31, 79, 22, 70, 30, 78)(33, 81, 41, 89, 36, 84, 44, 92, 34, 82, 43, 91, 35, 83, 42, 90)(37, 85, 45, 93, 40, 88, 48, 96, 38, 86, 47, 95, 39, 87, 46, 94) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 68)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 72)(17, 59)(18, 63)(19, 60)(20, 64)(21, 55)(22, 61)(23, 56)(24, 58)(25, 81)(26, 83)(27, 82)(28, 84)(29, 85)(30, 87)(31, 86)(32, 88)(33, 75)(34, 73)(35, 76)(36, 74)(37, 79)(38, 77)(39, 80)(40, 78)(41, 95)(42, 96)(43, 93)(44, 94)(45, 89)(46, 90)(47, 91)(48, 92) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.875 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 14 degree seq :: [ 16^6 ] E15.877 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 24}) Quotient :: loop Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2^-1 * T1^-2, T2 * T1^-2 * T2^-1 * T1^2, T2 * T1^-1 * T2^-5 * T1, T2^-2 * T1^-1 * T2^-2 * T1^-3, T1^8, (T2^-1 * T1^-1)^4 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 25, 73, 38, 86, 18, 66, 6, 54, 17, 65, 37, 85, 47, 95, 39, 87, 19, 67, 34, 82, 29, 77, 43, 91, 48, 96, 40, 88, 28, 76, 12, 60, 21, 69, 42, 90, 33, 81, 15, 63, 5, 53)(2, 50, 7, 55, 20, 68, 41, 89, 23, 71, 9, 57, 16, 64, 35, 83, 32, 80, 45, 93, 24, 72, 36, 84, 27, 75, 14, 62, 31, 79, 46, 94, 30, 78, 13, 61, 4, 52, 11, 59, 26, 74, 44, 92, 22, 70, 8, 56) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 64)(7, 67)(8, 51)(9, 65)(10, 72)(11, 66)(12, 52)(13, 69)(14, 53)(15, 79)(16, 82)(17, 84)(18, 55)(19, 83)(20, 88)(21, 56)(22, 90)(23, 58)(24, 85)(25, 94)(26, 87)(27, 60)(28, 62)(29, 61)(30, 91)(31, 86)(32, 63)(33, 93)(34, 75)(35, 76)(36, 77)(37, 78)(38, 74)(39, 68)(40, 80)(41, 81)(42, 71)(43, 70)(44, 96)(45, 73)(46, 95)(47, 92)(48, 89) 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 ) } Outer automorphisms :: reflexible Dual of E15.873 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 48 f = 18 degree seq :: [ 48^2 ] E15.878 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 24}) Quotient :: loop Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ F^2, T2^4, T2^4, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-2 * T1 * T2, T2^2 * T1 * T2^-2 * T1^-1, (T1^-1 * T2 * T1^-1)^2, (T1^-1 * T2^-1 * T1^-1)^2, T1^-2 * T2^-1 * T1 * T2 * T1^-3, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 28, 76, 14, 62)(6, 54, 18, 66, 38, 86, 19, 67)(9, 57, 26, 74, 15, 63, 27, 75)(11, 59, 29, 77, 16, 64, 30, 78)(13, 61, 32, 80, 45, 93, 25, 73)(17, 65, 36, 84, 47, 95, 37, 85)(20, 68, 41, 89, 23, 71, 42, 90)(22, 70, 43, 91, 24, 72, 44, 92)(31, 79, 46, 94, 34, 82, 35, 83)(33, 81, 39, 87, 48, 96, 40, 88) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 73)(10, 69)(11, 51)(12, 79)(13, 52)(14, 82)(15, 80)(16, 53)(17, 83)(18, 64)(19, 59)(20, 62)(21, 86)(22, 55)(23, 60)(24, 56)(25, 85)(26, 89)(27, 90)(28, 58)(29, 91)(30, 92)(31, 88)(32, 84)(33, 61)(34, 87)(35, 75)(36, 72)(37, 70)(38, 95)(39, 66)(40, 67)(41, 78)(42, 77)(43, 96)(44, 81)(45, 76)(46, 74)(47, 94)(48, 93) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E15.874 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.879 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (Y1 * Y3^-1)^2, Y3^4, (R * Y3)^2, Y1 * Y3^-2 * Y1, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y3^-1 * Y2^4 * Y1, Y2^-1 * Y3^2 * Y2 * Y1^-2, Y2^2 * Y3 * Y2^2 * Y1^-1, Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2 * Y1 * Y2)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 16, 64, 24, 72)(25, 73, 33, 81, 27, 75, 34, 82)(26, 74, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 47, 95, 43, 91, 45, 93)(42, 90, 48, 96, 44, 92, 46, 94)(97, 145, 99, 147, 106, 154, 114, 162, 102, 150, 113, 161, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 109, 157, 100, 148, 108, 156, 120, 168, 104, 152)(105, 153, 121, 169, 111, 159, 124, 172, 107, 155, 123, 171, 110, 158, 122, 170)(115, 163, 125, 173, 119, 167, 128, 176, 117, 165, 127, 175, 118, 166, 126, 174)(129, 177, 137, 185, 132, 180, 140, 188, 130, 178, 139, 187, 131, 179, 138, 186)(133, 181, 141, 189, 136, 184, 144, 192, 134, 182, 143, 191, 135, 183, 142, 190) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 120)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 116)(17, 105)(18, 110)(19, 103)(20, 106)(21, 108)(22, 104)(23, 109)(24, 112)(25, 130)(26, 132)(27, 129)(28, 131)(29, 134)(30, 136)(31, 133)(32, 135)(33, 121)(34, 123)(35, 122)(36, 124)(37, 125)(38, 127)(39, 126)(40, 128)(41, 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) :: { ( 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 E15.882 Graph:: bipartite v = 18 e = 96 f = 50 degree seq :: [ 8^12, 16^6 ] E15.880 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2 * Y1^-3 * Y2 * Y1, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^-2 * Y1^-1 * Y2 * Y1 * Y2^-3, Y2^-2 * Y1^-1 * Y2^-2 * Y1^-3, (Y3^-1 * Y1^-1)^4, Y1^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 34, 82, 27, 75, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 36, 84, 29, 77, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 35, 83, 28, 76, 14, 62)(10, 58, 24, 72, 37, 85, 30, 78, 43, 91, 22, 70, 42, 90, 23, 71)(15, 63, 31, 79, 38, 86, 26, 74, 39, 87, 20, 68, 40, 88, 32, 80)(25, 73, 46, 94, 47, 95, 44, 92, 48, 96, 41, 89, 33, 81, 45, 93)(97, 145, 99, 147, 106, 154, 121, 169, 134, 182, 114, 162, 102, 150, 113, 161, 133, 181, 143, 191, 135, 183, 115, 163, 130, 178, 125, 173, 139, 187, 144, 192, 136, 184, 124, 172, 108, 156, 117, 165, 138, 186, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 137, 185, 119, 167, 105, 153, 112, 160, 131, 179, 128, 176, 141, 189, 120, 168, 132, 180, 123, 171, 110, 158, 127, 175, 142, 190, 126, 174, 109, 157, 100, 148, 107, 155, 122, 170, 140, 188, 118, 166, 104, 152) L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 113)(7, 116)(8, 98)(9, 112)(10, 121)(11, 122)(12, 117)(13, 100)(14, 127)(15, 101)(16, 131)(17, 133)(18, 102)(19, 130)(20, 137)(21, 138)(22, 104)(23, 105)(24, 132)(25, 134)(26, 140)(27, 110)(28, 108)(29, 139)(30, 109)(31, 142)(32, 141)(33, 111)(34, 125)(35, 128)(36, 123)(37, 143)(38, 114)(39, 115)(40, 124)(41, 119)(42, 129)(43, 144)(44, 118)(45, 120)(46, 126)(47, 135)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.881 Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 16^6, 48^2 ] E15.881 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^2 * Y3 * Y2, (Y3^2 * Y2^-1)^2, (Y2^-1 * Y3^-2)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y3^3 * Y2^-1 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 123, 171, 131, 179, 120, 168)(112, 160, 127, 175, 132, 180, 116, 164)(121, 169, 133, 181, 125, 173, 136, 184)(122, 170, 138, 186, 126, 174, 139, 187)(124, 172, 142, 190, 143, 191, 135, 183)(128, 176, 134, 182, 129, 177, 137, 185)(130, 178, 141, 189, 144, 192, 140, 188) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 124)(11, 125)(12, 127)(13, 100)(14, 128)(15, 129)(16, 101)(17, 131)(18, 102)(19, 133)(20, 135)(21, 136)(22, 138)(23, 139)(24, 104)(25, 111)(26, 105)(27, 109)(28, 137)(29, 110)(30, 107)(31, 142)(32, 140)(33, 141)(34, 112)(35, 143)(36, 114)(37, 119)(38, 115)(39, 122)(40, 118)(41, 117)(42, 144)(43, 130)(44, 120)(45, 123)(46, 126)(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) :: { ( 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E15.880 Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.882 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y3 * Y1^-2)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3, Y1^-3 * Y3 * Y1 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^4, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 27, 75, 42, 90, 29, 77, 43, 91, 48, 96, 45, 93, 28, 76, 10, 58, 21, 69, 38, 86, 47, 95, 46, 94, 26, 74, 41, 89, 30, 78, 44, 92, 33, 81, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 37, 85, 22, 70, 7, 55, 20, 68, 14, 62, 34, 82, 39, 87, 18, 66, 16, 64, 5, 53, 15, 63, 32, 80, 36, 84, 24, 72, 8, 56, 23, 71, 12, 60, 31, 79, 40, 88, 19, 67, 11, 59)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 122)(10, 101)(11, 125)(12, 124)(13, 128)(14, 100)(15, 123)(16, 126)(17, 132)(18, 134)(19, 102)(20, 137)(21, 104)(22, 139)(23, 138)(24, 140)(25, 109)(26, 111)(27, 105)(28, 110)(29, 112)(30, 107)(31, 142)(32, 141)(33, 135)(34, 131)(35, 127)(36, 143)(37, 113)(38, 115)(39, 144)(40, 129)(41, 119)(42, 116)(43, 120)(44, 118)(45, 121)(46, 130)(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, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.879 Graph:: simple bipartite v = 50 e = 96 f = 18 degree seq :: [ 2^48, 48^2 ] E15.883 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y3^-1 * Y1^-1, Y1^4, (R * Y3)^2, (R * Y1)^2, Y3 * R * Y2^-1 * Y1^-1 * R * Y2^-1, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y3, Y2^2 * Y3 * Y2^2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^2, Y2^-2 * Y1^-1 * Y2^-2 * Y3, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-2 * Y3^-1 * Y2 * Y1^-1 * Y2^-3, (Y3 * Y2 * Y1 * Y2)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 35, 83, 24, 72)(16, 64, 31, 79, 36, 84, 20, 68)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 42, 90, 30, 78, 43, 91)(28, 76, 46, 94, 47, 95, 39, 87)(32, 80, 38, 86, 33, 81, 41, 89)(34, 82, 45, 93, 48, 96, 44, 92)(97, 145, 99, 147, 106, 154, 124, 172, 137, 185, 117, 165, 136, 184, 118, 166, 138, 186, 144, 192, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 143, 191, 134, 182, 115, 163, 133, 181, 119, 167, 139, 187, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 122, 170, 105, 153, 121, 169, 111, 159, 129, 177, 141, 189, 123, 171, 109, 157, 100, 148, 108, 156, 127, 175, 142, 190, 126, 174, 107, 155, 125, 173, 110, 158, 128, 176, 140, 188, 120, 168, 104, 152) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 120)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 116)(17, 105)(18, 110)(19, 103)(20, 132)(21, 108)(22, 104)(23, 109)(24, 131)(25, 136)(26, 139)(27, 106)(28, 135)(29, 133)(30, 138)(31, 112)(32, 137)(33, 134)(34, 140)(35, 123)(36, 127)(37, 121)(38, 128)(39, 143)(40, 125)(41, 129)(42, 122)(43, 126)(44, 144)(45, 130)(46, 124)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E15.884 Graph:: bipartite v = 14 e = 96 f = 54 degree seq :: [ 8^12, 48^2 ] E15.884 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y3^-1 * Y1^2 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^4 * Y1^-2 * Y3^2, Y1^8, Y3^-2 * Y1^-1 * Y3^-2 * Y1^-3, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 16, 64, 34, 82, 27, 75, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 36, 84, 29, 77, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 35, 83, 28, 76, 14, 62)(10, 58, 24, 72, 37, 85, 30, 78, 43, 91, 22, 70, 42, 90, 23, 71)(15, 63, 31, 79, 38, 86, 26, 74, 39, 87, 20, 68, 40, 88, 32, 80)(25, 73, 46, 94, 47, 95, 44, 92, 48, 96, 41, 89, 33, 81, 45, 93)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 113)(7, 116)(8, 98)(9, 112)(10, 121)(11, 122)(12, 117)(13, 100)(14, 127)(15, 101)(16, 131)(17, 133)(18, 102)(19, 130)(20, 137)(21, 138)(22, 104)(23, 105)(24, 132)(25, 134)(26, 140)(27, 110)(28, 108)(29, 139)(30, 109)(31, 142)(32, 141)(33, 111)(34, 125)(35, 128)(36, 123)(37, 143)(38, 114)(39, 115)(40, 124)(41, 119)(42, 129)(43, 144)(44, 118)(45, 120)(46, 126)(47, 135)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E15.883 Graph:: simple bipartite v = 54 e = 96 f = 14 degree seq :: [ 2^48, 16^6 ] E15.885 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 16, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^16 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 47, 43, 37, 31, 25, 19, 13, 7)(4, 9, 15, 21, 27, 33, 39, 45, 48, 46, 40, 34, 28, 22, 16, 10)(49, 50, 52)(51, 54, 57)(53, 55, 58)(56, 60, 63)(59, 61, 64)(62, 66, 69)(65, 67, 70)(68, 72, 75)(71, 73, 76)(74, 78, 81)(77, 79, 82)(80, 84, 87)(83, 85, 88)(86, 90, 93)(89, 91, 94)(92, 95, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 96^3 ), ( 96^16 ) } Outer automorphisms :: reflexible Dual of E15.889 Transitivity :: ET+ Graph:: simple bipartite v = 19 e = 48 f = 1 degree seq :: [ 3^16, 16^3 ] E15.886 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 16, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^3 * T2^3, T1^-6 * T2^-6, T1 * T2^-15, T1^16 ] Map:: non-degenerate R = (1, 3, 9, 19, 25, 31, 37, 43, 47, 40, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 39, 45, 46, 42, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 38, 44, 48, 41, 34, 30, 23, 14, 13, 5)(49, 50, 54, 62, 70, 76, 82, 88, 94, 92, 85, 81, 74, 67, 59, 52)(51, 55, 63, 61, 66, 72, 78, 84, 90, 96, 91, 87, 80, 73, 69, 58)(53, 56, 64, 71, 77, 83, 89, 95, 93, 86, 79, 75, 68, 57, 65, 60) 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) :: { ( 6^16 ), ( 6^48 ) } Outer automorphisms :: reflexible Dual of E15.890 Transitivity :: ET+ Graph:: bipartite v = 4 e = 48 f = 16 degree seq :: [ 16^3, 48 ] E15.887 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 16, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^16, (T1^-1 * T2^-1)^16 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 13, 14)(10, 15, 17)(12, 19, 20)(16, 21, 23)(18, 25, 26)(22, 27, 29)(24, 31, 32)(28, 33, 35)(30, 37, 38)(34, 39, 41)(36, 43, 44)(40, 45, 47)(42, 46, 48)(49, 50, 54, 60, 66, 72, 78, 84, 90, 95, 89, 83, 77, 71, 65, 59, 53, 56, 62, 68, 74, 80, 86, 92, 96, 93, 87, 81, 75, 69, 63, 57, 51, 55, 61, 67, 73, 79, 85, 91, 94, 88, 82, 76, 70, 64, 58, 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) :: { ( 32^3 ), ( 32^48 ) } Outer automorphisms :: reflexible Dual of E15.888 Transitivity :: ET+ Graph:: bipartite v = 17 e = 48 f = 3 degree seq :: [ 3^16, 48 ] E15.888 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 16, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^16 ] Map:: non-degenerate R = (1, 49, 3, 51, 8, 56, 14, 62, 20, 68, 26, 74, 32, 80, 38, 86, 44, 92, 41, 89, 35, 83, 29, 77, 23, 71, 17, 65, 11, 59, 5, 53)(2, 50, 6, 54, 12, 60, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 47, 95, 43, 91, 37, 85, 31, 79, 25, 73, 19, 67, 13, 61, 7, 55)(4, 52, 9, 57, 15, 63, 21, 69, 27, 75, 33, 81, 39, 87, 45, 93, 48, 96, 46, 94, 40, 88, 34, 82, 28, 76, 22, 70, 16, 64, 10, 58) L = (1, 50)(2, 52)(3, 54)(4, 49)(5, 55)(6, 57)(7, 58)(8, 60)(9, 51)(10, 53)(11, 61)(12, 63)(13, 64)(14, 66)(15, 56)(16, 59)(17, 67)(18, 69)(19, 70)(20, 72)(21, 62)(22, 65)(23, 73)(24, 75)(25, 76)(26, 78)(27, 68)(28, 71)(29, 79)(30, 81)(31, 82)(32, 84)(33, 74)(34, 77)(35, 85)(36, 87)(37, 88)(38, 90)(39, 80)(40, 83)(41, 91)(42, 93)(43, 94)(44, 95)(45, 86)(46, 89)(47, 96)(48, 92) local type(s) :: { ( 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48, 3, 48 ) } Outer automorphisms :: reflexible Dual of E15.887 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 48 f = 17 degree seq :: [ 32^3 ] E15.889 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 16, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^3 * T2^3, T1^-6 * T2^-6, T1 * T2^-15, T1^16 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 19, 67, 25, 73, 31, 79, 37, 85, 43, 91, 47, 95, 40, 88, 36, 84, 29, 77, 22, 70, 18, 66, 8, 56, 2, 50, 7, 55, 17, 65, 11, 59, 21, 69, 27, 75, 33, 81, 39, 87, 45, 93, 46, 94, 42, 90, 35, 83, 28, 76, 24, 72, 16, 64, 6, 54, 15, 63, 12, 60, 4, 52, 10, 58, 20, 68, 26, 74, 32, 80, 38, 86, 44, 92, 48, 96, 41, 89, 34, 82, 30, 78, 23, 71, 14, 62, 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, 70)(15, 61)(16, 71)(17, 60)(18, 72)(19, 59)(20, 57)(21, 58)(22, 76)(23, 77)(24, 78)(25, 69)(26, 67)(27, 68)(28, 82)(29, 83)(30, 84)(31, 75)(32, 73)(33, 74)(34, 88)(35, 89)(36, 90)(37, 81)(38, 79)(39, 80)(40, 94)(41, 95)(42, 96)(43, 87)(44, 85)(45, 86)(46, 92)(47, 93)(48, 91) local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) } Outer automorphisms :: reflexible Dual of E15.885 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 19 degree seq :: [ 96 ] E15.890 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 16, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^16, (T1^-1 * T2^-1)^16 ] Map:: non-degenerate R = (1, 49, 3, 51, 5, 53)(2, 50, 7, 55, 8, 56)(4, 52, 9, 57, 11, 59)(6, 54, 13, 61, 14, 62)(10, 58, 15, 63, 17, 65)(12, 60, 19, 67, 20, 68)(16, 64, 21, 69, 23, 71)(18, 66, 25, 73, 26, 74)(22, 70, 27, 75, 29, 77)(24, 72, 31, 79, 32, 80)(28, 76, 33, 81, 35, 83)(30, 78, 37, 85, 38, 86)(34, 82, 39, 87, 41, 89)(36, 84, 43, 91, 44, 92)(40, 88, 45, 93, 47, 95)(42, 90, 46, 94, 48, 96) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 60)(7, 61)(8, 62)(9, 51)(10, 52)(11, 53)(12, 66)(13, 67)(14, 68)(15, 57)(16, 58)(17, 59)(18, 72)(19, 73)(20, 74)(21, 63)(22, 64)(23, 65)(24, 78)(25, 79)(26, 80)(27, 69)(28, 70)(29, 71)(30, 84)(31, 85)(32, 86)(33, 75)(34, 76)(35, 77)(36, 90)(37, 91)(38, 92)(39, 81)(40, 82)(41, 83)(42, 95)(43, 94)(44, 96)(45, 87)(46, 88)(47, 89)(48, 93) local type(s) :: { ( 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E15.886 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 48 f = 4 degree seq :: [ 6^16 ] E15.891 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 16, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^16, Y3^48 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 6, 54, 9, 57)(5, 53, 7, 55, 10, 58)(8, 56, 12, 60, 15, 63)(11, 59, 13, 61, 16, 64)(14, 62, 18, 66, 21, 69)(17, 65, 19, 67, 22, 70)(20, 68, 24, 72, 27, 75)(23, 71, 25, 73, 28, 76)(26, 74, 30, 78, 33, 81)(29, 77, 31, 79, 34, 82)(32, 80, 36, 84, 39, 87)(35, 83, 37, 85, 40, 88)(38, 86, 42, 90, 45, 93)(41, 89, 43, 91, 46, 94)(44, 92, 47, 95, 48, 96)(97, 145, 99, 147, 104, 152, 110, 158, 116, 164, 122, 170, 128, 176, 134, 182, 140, 188, 137, 185, 131, 179, 125, 173, 119, 167, 113, 161, 107, 155, 101, 149)(98, 146, 102, 150, 108, 156, 114, 162, 120, 168, 126, 174, 132, 180, 138, 186, 143, 191, 139, 187, 133, 181, 127, 175, 121, 169, 115, 163, 109, 157, 103, 151)(100, 148, 105, 153, 111, 159, 117, 165, 123, 171, 129, 177, 135, 183, 141, 189, 144, 192, 142, 190, 136, 184, 130, 178, 124, 172, 118, 166, 112, 160, 106, 154) L = (1, 100)(2, 97)(3, 105)(4, 98)(5, 106)(6, 99)(7, 101)(8, 111)(9, 102)(10, 103)(11, 112)(12, 104)(13, 107)(14, 117)(15, 108)(16, 109)(17, 118)(18, 110)(19, 113)(20, 123)(21, 114)(22, 115)(23, 124)(24, 116)(25, 119)(26, 129)(27, 120)(28, 121)(29, 130)(30, 122)(31, 125)(32, 135)(33, 126)(34, 127)(35, 136)(36, 128)(37, 131)(38, 141)(39, 132)(40, 133)(41, 142)(42, 134)(43, 137)(44, 144)(45, 138)(46, 139)(47, 140)(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 ) } Outer automorphisms :: reflexible Dual of E15.894 Graph:: bipartite v = 19 e = 96 f = 49 degree seq :: [ 6^16, 32^3 ] E15.892 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 16, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^3, (Y3^-1 * Y1^-1)^3, Y2^9 * Y1^-7, Y1^16 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 22, 70, 28, 76, 34, 82, 40, 88, 46, 94, 44, 92, 37, 85, 33, 81, 26, 74, 19, 67, 11, 59, 4, 52)(3, 51, 7, 55, 15, 63, 13, 61, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 48, 96, 43, 91, 39, 87, 32, 80, 25, 73, 21, 69, 10, 58)(5, 53, 8, 56, 16, 64, 23, 71, 29, 77, 35, 83, 41, 89, 47, 95, 45, 93, 38, 86, 31, 79, 27, 75, 20, 68, 9, 57, 17, 65, 12, 60)(97, 145, 99, 147, 105, 153, 115, 163, 121, 169, 127, 175, 133, 181, 139, 187, 143, 191, 136, 184, 132, 180, 125, 173, 118, 166, 114, 162, 104, 152, 98, 146, 103, 151, 113, 161, 107, 155, 117, 165, 123, 171, 129, 177, 135, 183, 141, 189, 142, 190, 138, 186, 131, 179, 124, 172, 120, 168, 112, 160, 102, 150, 111, 159, 108, 156, 100, 148, 106, 154, 116, 164, 122, 170, 128, 176, 134, 182, 140, 188, 144, 192, 137, 185, 130, 178, 126, 174, 119, 167, 110, 158, 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, 109)(15, 108)(16, 102)(17, 107)(18, 104)(19, 121)(20, 122)(21, 123)(22, 114)(23, 110)(24, 112)(25, 127)(26, 128)(27, 129)(28, 120)(29, 118)(30, 119)(31, 133)(32, 134)(33, 135)(34, 126)(35, 124)(36, 125)(37, 139)(38, 140)(39, 141)(40, 132)(41, 130)(42, 131)(43, 143)(44, 144)(45, 142)(46, 138)(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) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 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 E15.893 Graph:: bipartite v = 4 e = 96 f = 64 degree seq :: [ 32^3, 96 ] E15.893 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 16, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y3^-16 * Y2, (Y2^-1 * Y3)^16, (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, 100, 148)(99, 147, 102, 150, 105, 153)(101, 149, 103, 151, 106, 154)(104, 152, 108, 156, 111, 159)(107, 155, 109, 157, 112, 160)(110, 158, 114, 162, 117, 165)(113, 161, 115, 163, 118, 166)(116, 164, 120, 168, 123, 171)(119, 167, 121, 169, 124, 172)(122, 170, 126, 174, 129, 177)(125, 173, 127, 175, 130, 178)(128, 176, 132, 180, 135, 183)(131, 179, 133, 181, 136, 184)(134, 182, 138, 186, 141, 189)(137, 185, 139, 187, 142, 190)(140, 188, 144, 192, 143, 191) L = (1, 99)(2, 102)(3, 104)(4, 105)(5, 97)(6, 108)(7, 98)(8, 110)(9, 111)(10, 100)(11, 101)(12, 114)(13, 103)(14, 116)(15, 117)(16, 106)(17, 107)(18, 120)(19, 109)(20, 122)(21, 123)(22, 112)(23, 113)(24, 126)(25, 115)(26, 128)(27, 129)(28, 118)(29, 119)(30, 132)(31, 121)(32, 134)(33, 135)(34, 124)(35, 125)(36, 138)(37, 127)(38, 140)(39, 141)(40, 130)(41, 131)(42, 144)(43, 133)(44, 139)(45, 143)(46, 136)(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) :: { ( 32, 96 ), ( 32, 96, 32, 96, 32, 96 ) } Outer automorphisms :: reflexible Dual of E15.892 Graph:: simple bipartite v = 64 e = 96 f = 4 degree seq :: [ 2^48, 6^16 ] E15.894 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 16, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^16, 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 ] Map:: R = (1, 49, 2, 50, 6, 54, 12, 60, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 47, 95, 41, 89, 35, 83, 29, 77, 23, 71, 17, 65, 11, 59, 5, 53, 8, 56, 14, 62, 20, 68, 26, 74, 32, 80, 38, 86, 44, 92, 48, 96, 45, 93, 39, 87, 33, 81, 27, 75, 21, 69, 15, 63, 9, 57, 3, 51, 7, 55, 13, 61, 19, 67, 25, 73, 31, 79, 37, 85, 43, 91, 46, 94, 40, 88, 34, 82, 28, 76, 22, 70, 16, 64, 10, 58, 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, 101)(4, 105)(5, 97)(6, 109)(7, 104)(8, 98)(9, 107)(10, 111)(11, 100)(12, 115)(13, 110)(14, 102)(15, 113)(16, 117)(17, 106)(18, 121)(19, 116)(20, 108)(21, 119)(22, 123)(23, 112)(24, 127)(25, 122)(26, 114)(27, 125)(28, 129)(29, 118)(30, 133)(31, 128)(32, 120)(33, 131)(34, 135)(35, 124)(36, 139)(37, 134)(38, 126)(39, 137)(40, 141)(41, 130)(42, 142)(43, 140)(44, 132)(45, 143)(46, 144)(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, 32 ), ( 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32 ) } Outer automorphisms :: reflexible Dual of E15.891 Graph:: bipartite v = 49 e = 96 f = 19 degree seq :: [ 2^48, 96 ] E15.895 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 16, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3^-1 * Y2^16, 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 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 6, 54, 9, 57)(5, 53, 7, 55, 10, 58)(8, 56, 12, 60, 15, 63)(11, 59, 13, 61, 16, 64)(14, 62, 18, 66, 21, 69)(17, 65, 19, 67, 22, 70)(20, 68, 24, 72, 27, 75)(23, 71, 25, 73, 28, 76)(26, 74, 30, 78, 33, 81)(29, 77, 31, 79, 34, 82)(32, 80, 36, 84, 39, 87)(35, 83, 37, 85, 40, 88)(38, 86, 42, 90, 45, 93)(41, 89, 43, 91, 46, 94)(44, 92, 47, 95, 48, 96)(97, 145, 99, 147, 104, 152, 110, 158, 116, 164, 122, 170, 128, 176, 134, 182, 140, 188, 142, 190, 136, 184, 130, 178, 124, 172, 118, 166, 112, 160, 106, 154, 100, 148, 105, 153, 111, 159, 117, 165, 123, 171, 129, 177, 135, 183, 141, 189, 144, 192, 139, 187, 133, 181, 127, 175, 121, 169, 115, 163, 109, 157, 103, 151, 98, 146, 102, 150, 108, 156, 114, 162, 120, 168, 126, 174, 132, 180, 138, 186, 143, 191, 137, 185, 131, 179, 125, 173, 119, 167, 113, 161, 107, 155, 101, 149) L = (1, 100)(2, 97)(3, 105)(4, 98)(5, 106)(6, 99)(7, 101)(8, 111)(9, 102)(10, 103)(11, 112)(12, 104)(13, 107)(14, 117)(15, 108)(16, 109)(17, 118)(18, 110)(19, 113)(20, 123)(21, 114)(22, 115)(23, 124)(24, 116)(25, 119)(26, 129)(27, 120)(28, 121)(29, 130)(30, 122)(31, 125)(32, 135)(33, 126)(34, 127)(35, 136)(36, 128)(37, 131)(38, 141)(39, 132)(40, 133)(41, 142)(42, 134)(43, 137)(44, 144)(45, 138)(46, 139)(47, 140)(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, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.896 Graph:: bipartite v = 17 e = 96 f = 51 degree seq :: [ 6^16, 96 ] E15.896 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 16, 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, (Y3, Y1^-1), Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^-6 * Y3^-6, Y1^-1 * Y3^15, Y1^16, (Y3 * Y2^-1)^48 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 22, 70, 28, 76, 34, 82, 40, 88, 46, 94, 44, 92, 37, 85, 33, 81, 26, 74, 19, 67, 11, 59, 4, 52)(3, 51, 7, 55, 15, 63, 13, 61, 18, 66, 24, 72, 30, 78, 36, 84, 42, 90, 48, 96, 43, 91, 39, 87, 32, 80, 25, 73, 21, 69, 10, 58)(5, 53, 8, 56, 16, 64, 23, 71, 29, 77, 35, 83, 41, 89, 47, 95, 45, 93, 38, 86, 31, 79, 27, 75, 20, 68, 9, 57, 17, 65, 12, 60)(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, 109)(15, 108)(16, 102)(17, 107)(18, 104)(19, 121)(20, 122)(21, 123)(22, 114)(23, 110)(24, 112)(25, 127)(26, 128)(27, 129)(28, 120)(29, 118)(30, 119)(31, 133)(32, 134)(33, 135)(34, 126)(35, 124)(36, 125)(37, 139)(38, 140)(39, 141)(40, 132)(41, 130)(42, 131)(43, 143)(44, 144)(45, 142)(46, 138)(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) :: { ( 6, 96 ), ( 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96 ) } Outer automorphisms :: reflexible Dual of E15.895 Graph:: simple bipartite v = 51 e = 96 f = 17 degree seq :: [ 2^48, 32^3 ] E15.897 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {5, 5, 11}) Quotient :: edge Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X1^5, X2^-1 * X1 * X2 * X1^-1 * X2^-2, X2^-1 * X1 * X2^-3 * X1^-1 * X2^-1 ] Map:: polytopal non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 26, 32, 11)(5, 15, 41, 43, 16)(7, 20, 50, 40, 22)(8, 23, 54, 33, 24)(10, 29, 19, 48, 30)(12, 34, 27, 49, 35)(14, 38, 42, 47, 39)(17, 28, 18, 46, 45)(21, 52, 37, 44, 53)(25, 51, 36, 31, 55)(56, 58, 65, 77, 89, 110, 108, 93, 79, 72, 60)(57, 62, 76, 83, 64, 82, 97, 70, 84, 80, 63)(59, 67, 88, 66, 86, 100, 85, 99, 71, 95, 69)(61, 73, 102, 106, 75, 81, 96, 78, 107, 104, 74)(68, 91, 98, 90, 101, 105, 109, 103, 94, 87, 92) L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110) local type(s) :: { ( 10^5 ), ( 10^11 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 55 f = 11 degree seq :: [ 5^11, 11^5 ] E15.898 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {5, 5, 11}) Quotient :: edge Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X2 * X1^-1 * X2^2 * X1, X1^5, X2 * X1^2 * X2 * X1^2 * X2^-1 * X1, X1^-2 * X2 * X1^-1 * X2^-1 * X1^-2 * X2, X2 * X1 * X2^-5 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 24, 28, 11)(5, 15, 36, 39, 16)(7, 20, 46, 40, 17)(8, 22, 50, 27, 10)(12, 30, 48, 47, 31)(14, 34, 53, 51, 35)(18, 42, 38, 52, 23)(19, 44, 29, 49, 21)(25, 45, 32, 54, 26)(33, 55, 41, 37, 43)(56, 58, 65, 81, 107, 85, 89, 104, 96, 72, 60)(57, 62, 76, 103, 80, 64, 70, 92, 108, 78, 63)(59, 67, 71, 93, 95, 109, 110, 82, 84, 66, 69)(61, 73, 98, 79, 102, 75, 77, 106, 91, 100, 74)(68, 87, 90, 101, 83, 97, 99, 94, 105, 86, 88) L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110) local type(s) :: { ( 10^5 ), ( 10^11 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 55 f = 11 degree seq :: [ 5^11, 11^5 ] E15.899 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {5, 5, 11}) Quotient :: loop Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X1^5, X2^5, X1^-1 * X2^-1 * X1^2 * X2^2, X1^-1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^2, X2 * X1^-2 * X2^-2 * X1 * X2^-1 * X1^-1, X2^-2 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-2 * X2^-1 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 56, 2, 57, 6, 61, 13, 68, 4, 59)(3, 58, 9, 64, 26, 81, 31, 86, 11, 66)(5, 60, 15, 70, 25, 80, 32, 87, 16, 71)(7, 62, 20, 75, 46, 101, 40, 95, 22, 77)(8, 63, 23, 78, 27, 82, 50, 105, 24, 79)(10, 65, 28, 83, 52, 107, 42, 97, 29, 84)(12, 67, 21, 76, 48, 103, 54, 109, 34, 89)(14, 69, 36, 91, 17, 72, 43, 98, 37, 92)(18, 73, 33, 88, 53, 108, 41, 96, 44, 99)(19, 74, 45, 100, 47, 102, 39, 94, 30, 85)(35, 90, 55, 110, 38, 93, 51, 106, 49, 104) L = (1, 58)(2, 62)(3, 65)(4, 67)(5, 56)(6, 73)(7, 76)(8, 57)(9, 82)(10, 72)(11, 85)(12, 88)(13, 84)(14, 59)(15, 94)(16, 96)(17, 60)(18, 64)(19, 61)(20, 102)(21, 80)(22, 104)(23, 106)(24, 107)(25, 63)(26, 103)(27, 74)(28, 108)(29, 75)(30, 109)(31, 91)(32, 66)(33, 93)(34, 79)(35, 68)(36, 105)(37, 95)(38, 69)(39, 99)(40, 70)(41, 78)(42, 71)(43, 89)(44, 92)(45, 98)(46, 81)(47, 90)(48, 83)(49, 86)(50, 77)(51, 97)(52, 100)(53, 101)(54, 110)(55, 87) local type(s) :: { ( 5, 11, 5, 11, 5, 11, 5, 11, 5, 11 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 11 e = 55 f = 16 degree seq :: [ 10^11 ] E15.900 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {5, 5, 11}) Quotient :: loop Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X1^5, X2^5, X1^-1 * X2^-2 * X1^-2 * X2^-1, X2^-1 * X1^-1 * X2^-2 * X1^-2, X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 56, 2, 57, 6, 61, 13, 68, 4, 59)(3, 58, 9, 64, 26, 81, 32, 87, 11, 66)(5, 60, 15, 70, 39, 94, 27, 82, 16, 71)(7, 62, 20, 75, 17, 72, 43, 98, 22, 77)(8, 63, 23, 78, 33, 88, 46, 101, 24, 79)(10, 65, 29, 84, 53, 108, 40, 95, 30, 85)(12, 67, 34, 89, 50, 105, 55, 110, 36, 91)(14, 69, 38, 93, 49, 104, 41, 96, 21, 76)(18, 73, 31, 86, 25, 80, 51, 106, 44, 99)(19, 74, 45, 100, 48, 103, 54, 109, 35, 90)(28, 83, 37, 92, 47, 102, 42, 97, 52, 107) L = (1, 58)(2, 62)(3, 65)(4, 67)(5, 56)(6, 73)(7, 76)(8, 57)(9, 82)(10, 72)(11, 86)(12, 90)(13, 92)(14, 59)(15, 95)(16, 97)(17, 60)(18, 71)(19, 61)(20, 101)(21, 80)(22, 102)(23, 104)(24, 105)(25, 63)(26, 69)(27, 78)(28, 64)(29, 68)(30, 93)(31, 109)(32, 110)(33, 66)(34, 96)(35, 81)(36, 75)(37, 79)(38, 103)(39, 91)(40, 99)(41, 70)(42, 74)(43, 87)(44, 89)(45, 94)(46, 100)(47, 85)(48, 77)(49, 83)(50, 84)(51, 98)(52, 106)(53, 88)(54, 108)(55, 107) local type(s) :: { ( 5, 11, 5, 11, 5, 11, 5, 11, 5, 11 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 11 e = 55 f = 16 degree seq :: [ 10^11 ] E15.901 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {5, 5, 11}) Quotient :: loop Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T1^5, T2^5, T2 * T1 * T2^-2 * T1^-2, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^2, T2^2 * T1^2 * T2^-1 * T1 * T2 * T1^-1, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 17, 5)(2, 7, 21, 25, 8)(4, 12, 33, 38, 14)(6, 18, 9, 27, 19)(11, 30, 54, 55, 32)(13, 29, 20, 47, 35)(15, 39, 44, 37, 40)(16, 41, 23, 51, 42)(22, 49, 31, 36, 50)(24, 52, 45, 43, 34)(26, 48, 28, 53, 46)(56, 57, 61, 68, 59)(58, 64, 81, 86, 66)(60, 70, 80, 87, 71)(62, 75, 101, 95, 77)(63, 78, 82, 105, 79)(65, 83, 107, 97, 84)(67, 76, 103, 109, 89)(69, 91, 72, 98, 92)(73, 88, 108, 96, 99)(74, 100, 102, 94, 85)(90, 110, 93, 106, 104) L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110) local type(s) :: { ( 22^5 ) } Outer automorphisms :: reflexible Dual of E15.903 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 22 e = 55 f = 5 degree seq :: [ 5^22 ] E15.902 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {5, 5, 11}) Quotient :: loop Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T1^5, T2^5, T1^-1 * T2^-2 * T1^-2 * T2^-1, T1^-2 * T2^-1 * T1^-1 * T2^-2, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 17, 5)(2, 7, 21, 25, 8)(4, 12, 35, 26, 14)(6, 18, 16, 42, 19)(9, 27, 23, 49, 28)(11, 31, 54, 53, 33)(13, 37, 24, 50, 29)(15, 40, 44, 34, 41)(20, 46, 45, 39, 36)(22, 47, 30, 38, 48)(32, 55, 52, 51, 43)(56, 57, 61, 68, 59)(58, 64, 81, 87, 66)(60, 70, 94, 82, 71)(62, 75, 72, 98, 77)(63, 78, 88, 101, 79)(65, 84, 108, 95, 85)(67, 89, 105, 110, 91)(69, 93, 104, 96, 76)(73, 86, 80, 106, 99)(74, 100, 103, 109, 90)(83, 92, 102, 97, 107) L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110) local type(s) :: { ( 22^5 ) } Outer automorphisms :: reflexible Dual of E15.904 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 22 e = 55 f = 5 degree seq :: [ 5^22 ] E15.903 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {5, 5, 11}) Quotient :: edge Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T1^5, T2^3 * T1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-3 * T1^-1 * T2^-1, T1^2 * F * T1^-2 * F * T2 ] Map:: polytopal non-degenerate R = (1, 56, 3, 58, 10, 65, 22, 77, 34, 89, 55, 110, 53, 108, 38, 93, 24, 79, 17, 72, 5, 60)(2, 57, 7, 62, 21, 76, 28, 83, 9, 64, 27, 82, 42, 97, 15, 70, 29, 84, 25, 80, 8, 63)(4, 59, 12, 67, 33, 88, 11, 66, 31, 86, 45, 100, 30, 85, 44, 99, 16, 71, 40, 95, 14, 69)(6, 61, 18, 73, 47, 102, 51, 106, 20, 75, 26, 81, 41, 96, 23, 78, 52, 107, 49, 104, 19, 74)(13, 68, 36, 91, 43, 98, 35, 90, 46, 101, 50, 105, 54, 109, 48, 103, 39, 94, 32, 87, 37, 92) L = (1, 57)(2, 61)(3, 64)(4, 56)(5, 70)(6, 68)(7, 75)(8, 78)(9, 81)(10, 84)(11, 58)(12, 89)(13, 59)(14, 93)(15, 96)(16, 60)(17, 83)(18, 101)(19, 103)(20, 105)(21, 107)(22, 62)(23, 109)(24, 63)(25, 106)(26, 87)(27, 104)(28, 73)(29, 74)(30, 65)(31, 110)(32, 66)(33, 79)(34, 82)(35, 67)(36, 86)(37, 99)(38, 97)(39, 69)(40, 77)(41, 98)(42, 102)(43, 71)(44, 108)(45, 72)(46, 100)(47, 94)(48, 85)(49, 90)(50, 95)(51, 91)(52, 92)(53, 76)(54, 88)(55, 80) local type(s) :: { ( 5^22 ) } Outer automorphisms :: reflexible Dual of E15.901 Transitivity :: ET+ VT+ Graph:: v = 5 e = 55 f = 22 degree seq :: [ 22^5 ] E15.904 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {5, 5, 11}) Quotient :: edge Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ F^2, (T2 * F)^2, F * T1 * T2 * F * T1^-1, T2 * T1^-1 * T2^2 * T1, T1^5, T1^2 * T2^-3 * T1^-2 * T2, T2 * T1 * T2^-1 * T1 * T2^2 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 56, 3, 58, 10, 65, 26, 81, 52, 107, 30, 85, 34, 89, 49, 104, 41, 96, 17, 72, 5, 60)(2, 57, 7, 62, 21, 76, 48, 103, 25, 80, 9, 64, 15, 70, 37, 92, 53, 108, 23, 78, 8, 63)(4, 59, 12, 67, 16, 71, 38, 93, 40, 95, 54, 109, 55, 110, 27, 82, 29, 84, 11, 66, 14, 69)(6, 61, 18, 73, 43, 98, 24, 79, 47, 102, 20, 75, 22, 77, 51, 106, 36, 91, 45, 100, 19, 74)(13, 68, 32, 87, 35, 90, 46, 101, 28, 83, 42, 97, 44, 99, 39, 94, 50, 105, 31, 86, 33, 88) L = (1, 57)(2, 61)(3, 64)(4, 56)(5, 70)(6, 68)(7, 75)(8, 77)(9, 79)(10, 63)(11, 58)(12, 85)(13, 59)(14, 89)(15, 91)(16, 60)(17, 62)(18, 97)(19, 99)(20, 101)(21, 74)(22, 105)(23, 73)(24, 83)(25, 100)(26, 80)(27, 65)(28, 66)(29, 104)(30, 103)(31, 67)(32, 109)(33, 110)(34, 108)(35, 69)(36, 94)(37, 98)(38, 107)(39, 71)(40, 72)(41, 92)(42, 93)(43, 88)(44, 84)(45, 87)(46, 95)(47, 86)(48, 102)(49, 76)(50, 82)(51, 90)(52, 78)(53, 106)(54, 81)(55, 96) local type(s) :: { ( 5^22 ) } Outer automorphisms :: reflexible Dual of E15.902 Transitivity :: ET+ VT+ Graph:: v = 5 e = 55 f = 22 degree seq :: [ 22^5 ] E15.905 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 11}) Quotient :: edge^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3^-2 * Y1, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y2 * Y1 * Y2^-1 * Y3 * Y1^-1, Y2^5, Y1^-1 * Y2^-1 * Y1 * Y3^-1 * Y2, Y2^5, Y1 * Y3 * Y2 * Y3^-2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y1^5, Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2, Y2^-2 * Y3^2 * Y1^-2, Y3 * Y2 * Y1^2 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 56, 4, 59, 17, 72, 36, 91, 23, 78, 51, 106, 45, 100, 12, 67, 42, 97, 31, 86, 7, 62)(2, 57, 9, 64, 35, 90, 27, 82, 6, 61, 25, 80, 44, 99, 28, 83, 19, 74, 43, 98, 11, 66)(3, 58, 5, 60, 21, 76, 16, 71, 18, 73, 50, 105, 49, 104, 46, 101, 29, 84, 30, 85, 15, 70)(8, 63, 32, 87, 48, 103, 40, 95, 10, 65, 24, 79, 55, 110, 41, 96, 37, 92, 26, 81, 34, 89)(13, 68, 14, 69, 39, 94, 20, 75, 22, 77, 54, 109, 52, 107, 53, 108, 33, 88, 38, 93, 47, 102)(111, 112, 118, 132, 115)(113, 122, 154, 158, 124)(114, 116, 134, 149, 128)(117, 138, 165, 162, 140)(119, 120, 148, 125, 146)(121, 151, 157, 126, 152)(123, 156, 127, 129, 144)(130, 139, 155, 145, 147)(131, 133, 135, 136, 163)(137, 142, 143, 159, 141)(150, 164, 160, 161, 153)(166, 168, 178, 191, 171)(167, 172, 194, 204, 175)(169, 181, 203, 205, 184)(170, 185, 206, 208, 188)(173, 176, 177, 180, 198)(174, 182, 214, 218, 202)(179, 197, 200, 216, 183)(186, 217, 189, 192, 207)(187, 199, 193, 196, 215)(190, 201, 195, 219, 213)(209, 210, 211, 212, 220) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 4^5 ), ( 4^22 ) } Outer automorphisms :: reflexible Dual of E15.911 Graph:: simple bipartite v = 27 e = 110 f = 55 degree seq :: [ 5^22, 22^5 ] E15.906 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 11}) Quotient :: edge^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y1, Y3 * Y1^-1 * Y3 * Y2^-1, Y1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^5, Y1^5, Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y2^-1 * Y3^-2 * Y1^-1, Y3^11 ] Map:: polytopal non-degenerate R = (1, 56, 4, 59, 17, 72, 48, 103, 52, 107, 21, 76, 12, 67, 39, 94, 31, 86, 27, 82, 7, 62)(2, 57, 9, 64, 32, 87, 51, 106, 25, 80, 6, 61, 23, 78, 53, 108, 38, 93, 37, 92, 11, 66)(3, 58, 5, 60, 19, 74, 26, 81, 55, 110, 43, 98, 40, 95, 47, 102, 46, 101, 16, 71, 15, 70)(8, 63, 28, 83, 49, 104, 22, 77, 36, 91, 10, 65, 34, 89, 42, 97, 24, 79, 41, 96, 30, 85)(13, 68, 14, 69, 33, 88, 44, 99, 29, 84, 45, 100, 54, 109, 35, 90, 50, 105, 18, 73, 20, 75)(111, 112, 118, 130, 115)(113, 122, 148, 152, 124)(114, 116, 132, 154, 125)(117, 133, 134, 164, 136)(119, 120, 143, 153, 137)(121, 144, 145, 156, 127)(123, 150, 158, 135, 151)(126, 149, 142, 140, 155)(128, 157, 141, 163, 159)(129, 131, 161, 146, 160)(138, 139, 165, 162, 147)(166, 168, 178, 189, 171)(167, 172, 184, 200, 175)(169, 181, 194, 173, 176)(170, 183, 193, 203, 186)(174, 196, 205, 185, 195)(177, 180, 198, 201, 197)(179, 199, 202, 213, 208)(182, 212, 215, 187, 190)(188, 192, 220, 209, 214)(191, 210, 206, 216, 217)(204, 211, 219, 207, 218) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 4^5 ), ( 4^22 ) } Outer automorphisms :: reflexible Dual of E15.912 Graph:: simple bipartite v = 27 e = 110 f = 55 degree seq :: [ 5^22, 22^5 ] E15.907 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 11}) Quotient :: edge^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^5, Y2^5, Y1 * Y2^-2 * Y1^-2 * Y2, Y1^-1 * Y2^-1 * Y1^2 * Y2^2, Y2 * Y1 * Y2^-2 * Y1^-2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^2 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^11 ] Map:: polytopal R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 112, 116, 123, 114)(113, 119, 136, 141, 121)(115, 125, 135, 142, 126)(117, 130, 156, 150, 132)(118, 133, 137, 160, 134)(120, 138, 162, 152, 139)(122, 131, 158, 164, 144)(124, 146, 127, 153, 147)(128, 143, 163, 151, 154)(129, 155, 157, 149, 140)(145, 165, 148, 161, 159)(166, 168, 175, 182, 170)(167, 172, 186, 190, 173)(169, 177, 198, 203, 179)(171, 183, 174, 192, 184)(176, 195, 219, 220, 197)(178, 194, 185, 212, 200)(180, 204, 209, 202, 205)(181, 206, 188, 216, 207)(187, 214, 196, 201, 215)(189, 217, 210, 208, 199)(191, 213, 193, 218, 211) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 44, 44 ), ( 44^5 ) } Outer automorphisms :: reflexible Dual of E15.909 Graph:: simple bipartite v = 77 e = 110 f = 5 degree seq :: [ 2^55, 5^22 ] E15.908 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 11}) Quotient :: edge^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^5, Y2^5, Y1^-1 * Y2^-2 * Y1^-2 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2 * Y1^-2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^11 ] Map:: polytopal R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 112, 116, 123, 114)(113, 119, 136, 142, 121)(115, 125, 149, 137, 126)(117, 130, 127, 153, 132)(118, 133, 143, 156, 134)(120, 139, 163, 150, 140)(122, 144, 160, 165, 146)(124, 148, 159, 151, 131)(128, 141, 135, 161, 154)(129, 155, 158, 164, 145)(138, 147, 157, 152, 162)(166, 168, 175, 182, 170)(167, 172, 186, 190, 173)(169, 177, 200, 191, 179)(171, 183, 181, 207, 184)(174, 192, 188, 214, 193)(176, 196, 219, 218, 198)(178, 202, 189, 215, 194)(180, 205, 209, 199, 206)(185, 211, 210, 204, 201)(187, 212, 195, 203, 213)(197, 220, 217, 216, 208) L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 44, 44 ), ( 44^5 ) } Outer automorphisms :: reflexible Dual of E15.910 Graph:: simple bipartite v = 77 e = 110 f = 5 degree seq :: [ 2^55, 5^22 ] E15.909 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 11}) Quotient :: loop^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3^-2 * Y1, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y2 * Y1 * Y2^-1 * Y3 * Y1^-1, Y2^5, Y1^-1 * Y2^-1 * Y1 * Y3^-1 * Y2, Y2^5, Y1 * Y3 * Y2 * Y3^-2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y1^5, Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2, Y2^-2 * Y3^2 * Y1^-2, Y3 * Y2 * Y1^2 * Y3 * Y1^-1 ] Map:: R = (1, 56, 111, 166, 4, 59, 114, 169, 17, 72, 127, 182, 36, 91, 146, 201, 23, 78, 133, 188, 51, 106, 161, 216, 45, 100, 155, 210, 12, 67, 122, 177, 42, 97, 152, 207, 31, 86, 141, 196, 7, 62, 117, 172)(2, 57, 112, 167, 9, 64, 119, 174, 35, 90, 145, 200, 27, 82, 137, 192, 6, 61, 116, 171, 25, 80, 135, 190, 44, 99, 154, 209, 28, 83, 138, 193, 19, 74, 129, 184, 43, 98, 153, 208, 11, 66, 121, 176)(3, 58, 113, 168, 5, 60, 115, 170, 21, 76, 131, 186, 16, 71, 126, 181, 18, 73, 128, 183, 50, 105, 160, 215, 49, 104, 159, 214, 46, 101, 156, 211, 29, 84, 139, 194, 30, 85, 140, 195, 15, 70, 125, 180)(8, 63, 118, 173, 32, 87, 142, 197, 48, 103, 158, 213, 40, 95, 150, 205, 10, 65, 120, 175, 24, 79, 134, 189, 55, 110, 165, 220, 41, 96, 151, 206, 37, 92, 147, 202, 26, 81, 136, 191, 34, 89, 144, 199)(13, 68, 123, 178, 14, 69, 124, 179, 39, 94, 149, 204, 20, 75, 130, 185, 22, 77, 132, 187, 54, 109, 164, 219, 52, 107, 162, 217, 53, 108, 163, 218, 33, 88, 143, 198, 38, 93, 148, 203, 47, 102, 157, 212) L = (1, 57)(2, 63)(3, 67)(4, 61)(5, 56)(6, 79)(7, 83)(8, 77)(9, 65)(10, 93)(11, 96)(12, 99)(13, 101)(14, 58)(15, 91)(16, 97)(17, 74)(18, 59)(19, 89)(20, 84)(21, 78)(22, 60)(23, 80)(24, 94)(25, 81)(26, 108)(27, 87)(28, 110)(29, 100)(30, 62)(31, 82)(32, 88)(33, 104)(34, 68)(35, 92)(36, 64)(37, 75)(38, 70)(39, 73)(40, 109)(41, 102)(42, 66)(43, 95)(44, 103)(45, 90)(46, 72)(47, 71)(48, 69)(49, 86)(50, 106)(51, 98)(52, 85)(53, 76)(54, 105)(55, 107)(111, 168)(112, 172)(113, 178)(114, 181)(115, 185)(116, 166)(117, 194)(118, 176)(119, 182)(120, 167)(121, 177)(122, 180)(123, 191)(124, 197)(125, 198)(126, 203)(127, 214)(128, 179)(129, 169)(130, 206)(131, 217)(132, 199)(133, 170)(134, 192)(135, 201)(136, 171)(137, 207)(138, 196)(139, 204)(140, 219)(141, 215)(142, 200)(143, 173)(144, 193)(145, 216)(146, 195)(147, 174)(148, 205)(149, 175)(150, 184)(151, 208)(152, 186)(153, 188)(154, 210)(155, 211)(156, 212)(157, 220)(158, 190)(159, 218)(160, 187)(161, 183)(162, 189)(163, 202)(164, 213)(165, 209) local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) } Outer automorphisms :: reflexible Dual of E15.907 Transitivity :: VT+ Graph:: v = 5 e = 110 f = 77 degree seq :: [ 44^5 ] E15.910 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 11}) Quotient :: loop^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y1, Y3 * Y1^-1 * Y3 * Y2^-1, Y1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^5, Y1^5, Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y2^-1 * Y3^-2 * Y1^-1, Y3^11 ] Map:: R = (1, 56, 111, 166, 4, 59, 114, 169, 17, 72, 127, 182, 48, 103, 158, 213, 52, 107, 162, 217, 21, 76, 131, 186, 12, 67, 122, 177, 39, 94, 149, 204, 31, 86, 141, 196, 27, 82, 137, 192, 7, 62, 117, 172)(2, 57, 112, 167, 9, 64, 119, 174, 32, 87, 142, 197, 51, 106, 161, 216, 25, 80, 135, 190, 6, 61, 116, 171, 23, 78, 133, 188, 53, 108, 163, 218, 38, 93, 148, 203, 37, 92, 147, 202, 11, 66, 121, 176)(3, 58, 113, 168, 5, 60, 115, 170, 19, 74, 129, 184, 26, 81, 136, 191, 55, 110, 165, 220, 43, 98, 153, 208, 40, 95, 150, 205, 47, 102, 157, 212, 46, 101, 156, 211, 16, 71, 126, 181, 15, 70, 125, 180)(8, 63, 118, 173, 28, 83, 138, 193, 49, 104, 159, 214, 22, 77, 132, 187, 36, 91, 146, 201, 10, 65, 120, 175, 34, 89, 144, 199, 42, 97, 152, 207, 24, 79, 134, 189, 41, 96, 151, 206, 30, 85, 140, 195)(13, 68, 123, 178, 14, 69, 124, 179, 33, 88, 143, 198, 44, 99, 154, 209, 29, 84, 139, 194, 45, 100, 155, 210, 54, 109, 164, 219, 35, 90, 145, 200, 50, 105, 160, 215, 18, 73, 128, 183, 20, 75, 130, 185) L = (1, 57)(2, 63)(3, 67)(4, 61)(5, 56)(6, 77)(7, 78)(8, 75)(9, 65)(10, 88)(11, 89)(12, 93)(13, 95)(14, 58)(15, 59)(16, 94)(17, 66)(18, 102)(19, 76)(20, 60)(21, 106)(22, 99)(23, 79)(24, 109)(25, 96)(26, 62)(27, 64)(28, 84)(29, 110)(30, 100)(31, 108)(32, 85)(33, 98)(34, 90)(35, 101)(36, 105)(37, 83)(38, 97)(39, 87)(40, 103)(41, 68)(42, 69)(43, 82)(44, 70)(45, 71)(46, 72)(47, 86)(48, 80)(49, 73)(50, 74)(51, 91)(52, 92)(53, 104)(54, 81)(55, 107)(111, 168)(112, 172)(113, 178)(114, 181)(115, 183)(116, 166)(117, 184)(118, 176)(119, 196)(120, 167)(121, 169)(122, 180)(123, 189)(124, 199)(125, 198)(126, 194)(127, 212)(128, 193)(129, 200)(130, 195)(131, 170)(132, 190)(133, 192)(134, 171)(135, 182)(136, 210)(137, 220)(138, 203)(139, 173)(140, 174)(141, 205)(142, 177)(143, 201)(144, 202)(145, 175)(146, 197)(147, 213)(148, 186)(149, 211)(150, 185)(151, 216)(152, 218)(153, 179)(154, 214)(155, 206)(156, 219)(157, 215)(158, 208)(159, 188)(160, 187)(161, 217)(162, 191)(163, 204)(164, 207)(165, 209) local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) } Outer automorphisms :: reflexible Dual of E15.908 Transitivity :: VT+ Graph:: v = 5 e = 110 f = 77 degree seq :: [ 44^5 ] E15.911 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 11}) Quotient :: loop^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^5, Y2^5, Y1 * Y2^-2 * Y1^-2 * Y2, Y1^-1 * Y2^-1 * Y1^2 * Y2^2, Y2 * Y1 * Y2^-2 * Y1^-2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^2 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^11 ] Map:: polytopal non-degenerate R = (1, 56, 111, 166)(2, 57, 112, 167)(3, 58, 113, 168)(4, 59, 114, 169)(5, 60, 115, 170)(6, 61, 116, 171)(7, 62, 117, 172)(8, 63, 118, 173)(9, 64, 119, 174)(10, 65, 120, 175)(11, 66, 121, 176)(12, 67, 122, 177)(13, 68, 123, 178)(14, 69, 124, 179)(15, 70, 125, 180)(16, 71, 126, 181)(17, 72, 127, 182)(18, 73, 128, 183)(19, 74, 129, 184)(20, 75, 130, 185)(21, 76, 131, 186)(22, 77, 132, 187)(23, 78, 133, 188)(24, 79, 134, 189)(25, 80, 135, 190)(26, 81, 136, 191)(27, 82, 137, 192)(28, 83, 138, 193)(29, 84, 139, 194)(30, 85, 140, 195)(31, 86, 141, 196)(32, 87, 142, 197)(33, 88, 143, 198)(34, 89, 144, 199)(35, 90, 145, 200)(36, 91, 146, 201)(37, 92, 147, 202)(38, 93, 148, 203)(39, 94, 149, 204)(40, 95, 150, 205)(41, 96, 151, 206)(42, 97, 152, 207)(43, 98, 153, 208)(44, 99, 154, 209)(45, 100, 155, 210)(46, 101, 156, 211)(47, 102, 157, 212)(48, 103, 158, 213)(49, 104, 159, 214)(50, 105, 160, 215)(51, 106, 161, 216)(52, 107, 162, 217)(53, 108, 163, 218)(54, 109, 164, 219)(55, 110, 165, 220) L = (1, 57)(2, 61)(3, 64)(4, 56)(5, 70)(6, 68)(7, 75)(8, 78)(9, 81)(10, 83)(11, 58)(12, 76)(13, 59)(14, 91)(15, 80)(16, 60)(17, 98)(18, 88)(19, 100)(20, 101)(21, 103)(22, 62)(23, 82)(24, 63)(25, 87)(26, 86)(27, 105)(28, 107)(29, 65)(30, 74)(31, 66)(32, 71)(33, 108)(34, 67)(35, 110)(36, 72)(37, 69)(38, 106)(39, 85)(40, 77)(41, 99)(42, 84)(43, 92)(44, 73)(45, 102)(46, 95)(47, 94)(48, 109)(49, 90)(50, 79)(51, 104)(52, 97)(53, 96)(54, 89)(55, 93)(111, 168)(112, 172)(113, 175)(114, 177)(115, 166)(116, 183)(117, 186)(118, 167)(119, 192)(120, 182)(121, 195)(122, 198)(123, 194)(124, 169)(125, 204)(126, 206)(127, 170)(128, 174)(129, 171)(130, 212)(131, 190)(132, 214)(133, 216)(134, 217)(135, 173)(136, 213)(137, 184)(138, 218)(139, 185)(140, 219)(141, 201)(142, 176)(143, 203)(144, 189)(145, 178)(146, 215)(147, 205)(148, 179)(149, 209)(150, 180)(151, 188)(152, 181)(153, 199)(154, 202)(155, 208)(156, 191)(157, 200)(158, 193)(159, 196)(160, 187)(161, 207)(162, 210)(163, 211)(164, 220)(165, 197) local type(s) :: { ( 5, 22, 5, 22 ) } Outer automorphisms :: reflexible Dual of E15.905 Transitivity :: VT+ Graph:: simple v = 55 e = 110 f = 27 degree seq :: [ 4^55 ] E15.912 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 11}) Quotient :: loop^2 Aut^+ = C11 : C5 (small group id <55, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^5, Y2^5, Y1^-1 * Y2^-2 * Y1^-2 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2 * Y1^-2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^11 ] Map:: polytopal non-degenerate R = (1, 56, 111, 166)(2, 57, 112, 167)(3, 58, 113, 168)(4, 59, 114, 169)(5, 60, 115, 170)(6, 61, 116, 171)(7, 62, 117, 172)(8, 63, 118, 173)(9, 64, 119, 174)(10, 65, 120, 175)(11, 66, 121, 176)(12, 67, 122, 177)(13, 68, 123, 178)(14, 69, 124, 179)(15, 70, 125, 180)(16, 71, 126, 181)(17, 72, 127, 182)(18, 73, 128, 183)(19, 74, 129, 184)(20, 75, 130, 185)(21, 76, 131, 186)(22, 77, 132, 187)(23, 78, 133, 188)(24, 79, 134, 189)(25, 80, 135, 190)(26, 81, 136, 191)(27, 82, 137, 192)(28, 83, 138, 193)(29, 84, 139, 194)(30, 85, 140, 195)(31, 86, 141, 196)(32, 87, 142, 197)(33, 88, 143, 198)(34, 89, 144, 199)(35, 90, 145, 200)(36, 91, 146, 201)(37, 92, 147, 202)(38, 93, 148, 203)(39, 94, 149, 204)(40, 95, 150, 205)(41, 96, 151, 206)(42, 97, 152, 207)(43, 98, 153, 208)(44, 99, 154, 209)(45, 100, 155, 210)(46, 101, 156, 211)(47, 102, 157, 212)(48, 103, 158, 213)(49, 104, 159, 214)(50, 105, 160, 215)(51, 106, 161, 216)(52, 107, 162, 217)(53, 108, 163, 218)(54, 109, 164, 219)(55, 110, 165, 220) L = (1, 57)(2, 61)(3, 64)(4, 56)(5, 70)(6, 68)(7, 75)(8, 78)(9, 81)(10, 84)(11, 58)(12, 89)(13, 59)(14, 93)(15, 94)(16, 60)(17, 98)(18, 86)(19, 100)(20, 72)(21, 69)(22, 62)(23, 88)(24, 63)(25, 106)(26, 87)(27, 71)(28, 92)(29, 108)(30, 65)(31, 80)(32, 66)(33, 101)(34, 105)(35, 74)(36, 67)(37, 102)(38, 104)(39, 82)(40, 85)(41, 76)(42, 107)(43, 77)(44, 73)(45, 103)(46, 79)(47, 97)(48, 109)(49, 96)(50, 110)(51, 99)(52, 83)(53, 95)(54, 90)(55, 91)(111, 168)(112, 172)(113, 175)(114, 177)(115, 166)(116, 183)(117, 186)(118, 167)(119, 192)(120, 182)(121, 196)(122, 200)(123, 202)(124, 169)(125, 205)(126, 207)(127, 170)(128, 181)(129, 171)(130, 211)(131, 190)(132, 212)(133, 214)(134, 215)(135, 173)(136, 179)(137, 188)(138, 174)(139, 178)(140, 203)(141, 219)(142, 220)(143, 176)(144, 206)(145, 191)(146, 185)(147, 189)(148, 213)(149, 201)(150, 209)(151, 180)(152, 184)(153, 197)(154, 199)(155, 204)(156, 210)(157, 195)(158, 187)(159, 193)(160, 194)(161, 208)(162, 216)(163, 198)(164, 218)(165, 217) local type(s) :: { ( 5, 22, 5, 22 ) } Outer automorphisms :: reflexible Dual of E15.906 Transitivity :: VT+ Graph:: simple v = 55 e = 110 f = 27 degree seq :: [ 4^55 ] E15.913 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 58, 2, 62, 6, 61, 5, 57)(3, 65, 9, 60, 4, 66, 10, 59)(7, 67, 11, 64, 8, 68, 12, 63)(13, 73, 17, 70, 14, 74, 18, 69)(15, 75, 19, 72, 16, 76, 20, 71)(21, 81, 25, 78, 22, 82, 26, 77)(23, 83, 27, 80, 24, 84, 28, 79)(29, 89, 33, 86, 30, 90, 34, 85)(31, 91, 35, 88, 32, 92, 36, 87)(37, 97, 41, 94, 38, 98, 42, 93)(39, 99, 43, 96, 40, 100, 44, 95)(45, 105, 49, 102, 46, 106, 50, 101)(47, 107, 51, 104, 48, 108, 52, 103)(53, 111, 55, 110, 54, 112, 56, 109) 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, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 60)(58, 64)(59, 62)(61, 63)(65, 70)(66, 69)(67, 72)(68, 71)(73, 78)(74, 77)(75, 80)(76, 79)(81, 86)(82, 85)(83, 88)(84, 87)(89, 94)(90, 93)(91, 96)(92, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 110)(106, 109)(107, 112)(108, 111) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 14 e = 56 f = 14 degree seq :: [ 8^14 ] E15.914 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y1^4, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * 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 ] Map:: R = (1, 58, 2, 61, 5, 60, 4, 57)(3, 63, 7, 66, 10, 64, 8, 59)(6, 67, 11, 65, 9, 68, 12, 62)(13, 73, 17, 70, 14, 74, 18, 69)(15, 75, 19, 72, 16, 76, 20, 71)(21, 81, 25, 78, 22, 82, 26, 77)(23, 83, 27, 80, 24, 84, 28, 79)(29, 89, 33, 86, 30, 90, 34, 85)(31, 91, 35, 88, 32, 92, 36, 87)(37, 97, 41, 94, 38, 98, 42, 93)(39, 99, 43, 96, 40, 100, 44, 95)(45, 105, 49, 102, 46, 106, 50, 101)(47, 107, 51, 104, 48, 108, 52, 103)(53, 111, 55, 110, 54, 112, 56, 109) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 59)(58, 62)(60, 65)(61, 66)(63, 69)(64, 70)(67, 71)(68, 72)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 14 e = 56 f = 14 degree seq :: [ 8^14 ] E15.915 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, Y1^4, (R * Y1)^2, R * Y2 * R * Y3, (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^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 58, 2, 61, 5, 60, 4, 57)(3, 63, 7, 66, 10, 64, 8, 59)(6, 67, 11, 65, 9, 68, 12, 62)(13, 73, 17, 70, 14, 74, 18, 69)(15, 75, 19, 72, 16, 76, 20, 71)(21, 81, 25, 78, 22, 82, 26, 77)(23, 83, 27, 80, 24, 84, 28, 79)(29, 89, 33, 86, 30, 90, 34, 85)(31, 91, 35, 88, 32, 92, 36, 87)(37, 97, 41, 94, 38, 98, 42, 93)(39, 99, 43, 96, 40, 100, 44, 95)(45, 105, 49, 102, 46, 106, 50, 101)(47, 107, 51, 104, 48, 108, 52, 103)(53, 112, 56, 110, 54, 111, 55, 109) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 59)(58, 62)(60, 65)(61, 66)(63, 69)(64, 70)(67, 71)(68, 72)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 14 e = 56 f = 14 degree seq :: [ 8^14 ] E15.916 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y2 * Y1)^2, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, (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 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 4, 60, 6, 62, 5, 61)(2, 58, 7, 63, 3, 59, 8, 64)(9, 65, 13, 69, 10, 66, 14, 70)(11, 67, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112)(113, 114)(115, 118)(116, 121)(117, 122)(119, 123)(120, 124)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 167)(166, 168)(169, 171)(170, 174)(172, 178)(173, 177)(175, 180)(176, 179)(181, 186)(182, 185)(183, 188)(184, 187)(189, 194)(190, 193)(191, 196)(192, 195)(197, 202)(198, 201)(199, 204)(200, 203)(205, 210)(206, 209)(207, 212)(208, 211)(213, 218)(214, 217)(215, 220)(216, 219)(221, 224)(222, 223) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.922 Graph:: simple bipartite v = 70 e = 112 f = 14 degree seq :: [ 2^56, 8^14 ] E15.917 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 3, 59, 8, 64, 4, 60)(2, 58, 5, 61, 11, 67, 6, 62)(7, 63, 13, 69, 9, 65, 14, 70)(10, 66, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112)(113, 114)(115, 119)(116, 121)(117, 122)(118, 124)(120, 123)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 167)(166, 168)(169, 170)(171, 175)(172, 177)(173, 178)(174, 180)(176, 179)(181, 185)(182, 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, 211)(208, 212)(213, 217)(214, 218)(215, 219)(216, 220)(221, 223)(222, 224) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.923 Graph:: simple bipartite v = 70 e = 112 f = 14 degree seq :: [ 2^56, 8^14 ] E15.918 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, R * Y1 * R * Y2, (R * Y3)^2, (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^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 3, 59, 8, 64, 4, 60)(2, 58, 5, 61, 11, 67, 6, 62)(7, 63, 13, 69, 9, 65, 14, 70)(10, 66, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112)(113, 114)(115, 119)(116, 121)(117, 122)(118, 124)(120, 123)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 168)(166, 167)(169, 170)(171, 175)(172, 177)(173, 178)(174, 180)(176, 179)(181, 185)(182, 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, 211)(208, 212)(213, 217)(214, 218)(215, 219)(216, 220)(221, 224)(222, 223) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.924 Graph:: simple bipartite v = 70 e = 112 f = 14 degree seq :: [ 2^56, 8^14 ] E15.919 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = C2 x C4 x D14 (small group id <112, 28>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1^4, Y2^4, (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^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 57, 4, 60)(2, 58, 6, 62)(3, 59, 7, 63)(5, 61, 10, 66)(8, 64, 13, 69)(9, 65, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 54, 110)(51, 107, 55, 111)(52, 108, 56, 112)(113, 114, 117, 115)(116, 120, 122, 121)(118, 123, 119, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 137, 134, 138)(135, 139, 136, 140)(141, 145, 142, 146)(143, 147, 144, 148)(149, 153, 150, 154)(151, 155, 152, 156)(157, 161, 158, 162)(159, 163, 160, 164)(165, 167, 166, 168)(169, 171, 173, 170)(172, 177, 178, 176)(174, 180, 175, 179)(181, 186, 182, 185)(183, 188, 184, 187)(189, 194, 190, 193)(191, 196, 192, 195)(197, 202, 198, 201)(199, 204, 200, 203)(205, 210, 206, 209)(207, 212, 208, 211)(213, 218, 214, 217)(215, 220, 216, 219)(221, 224, 222, 223) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.925 Graph:: simple bipartite v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.920 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1^4, Y2^4, (Y1^-1 * Y3 * Y2^-1)^2, 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, 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 ] Map:: polytopal non-degenerate R = (1, 57, 3, 59)(2, 58, 6, 62)(4, 60, 9, 65)(5, 61, 10, 66)(7, 63, 13, 69)(8, 64, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 54, 110)(51, 107, 55, 111)(52, 108, 56, 112)(113, 114, 117, 116)(115, 119, 122, 120)(118, 123, 121, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 137, 134, 138)(135, 139, 136, 140)(141, 145, 142, 146)(143, 147, 144, 148)(149, 153, 150, 154)(151, 155, 152, 156)(157, 161, 158, 162)(159, 163, 160, 164)(165, 167, 166, 168)(169, 170, 173, 172)(171, 175, 178, 176)(174, 179, 177, 180)(181, 185, 182, 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, 211, 208, 212)(213, 217, 214, 218)(215, 219, 216, 220)(221, 223, 222, 224) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.926 Graph:: simple bipartite v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.921 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, 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^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 57, 3, 59)(2, 58, 6, 62)(4, 60, 9, 65)(5, 61, 10, 66)(7, 63, 13, 69)(8, 64, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 54, 110)(51, 107, 55, 111)(52, 108, 56, 112)(113, 114, 117, 116)(115, 119, 122, 120)(118, 123, 121, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 137, 134, 138)(135, 139, 136, 140)(141, 145, 142, 146)(143, 147, 144, 148)(149, 153, 150, 154)(151, 155, 152, 156)(157, 161, 158, 162)(159, 163, 160, 164)(165, 168, 166, 167)(169, 170, 173, 172)(171, 175, 178, 176)(174, 179, 177, 180)(181, 185, 182, 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, 211, 208, 212)(213, 217, 214, 218)(215, 219, 216, 220)(221, 224, 222, 223) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.927 Graph:: simple bipartite v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.922 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = (C28 x C2) : C2 (small group id <112, 30>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y2 * Y1)^2, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, (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 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 113, 169, 4, 60, 116, 172, 6, 62, 118, 174, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 3, 59, 115, 171, 8, 64, 120, 176)(9, 65, 121, 177, 13, 69, 125, 181, 10, 66, 122, 178, 14, 70, 126, 182)(11, 67, 123, 179, 15, 71, 127, 183, 12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189, 18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191, 20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197, 26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199, 28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205, 34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207, 36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213, 42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215, 44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221, 50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223, 52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 57)(3, 62)(4, 65)(5, 66)(6, 59)(7, 67)(8, 68)(9, 60)(10, 61)(11, 63)(12, 64)(13, 73)(14, 74)(15, 75)(16, 76)(17, 69)(18, 70)(19, 71)(20, 72)(21, 81)(22, 82)(23, 83)(24, 84)(25, 77)(26, 78)(27, 79)(28, 80)(29, 89)(30, 90)(31, 91)(32, 92)(33, 85)(34, 86)(35, 87)(36, 88)(37, 97)(38, 98)(39, 99)(40, 100)(41, 93)(42, 94)(43, 95)(44, 96)(45, 105)(46, 106)(47, 107)(48, 108)(49, 101)(50, 102)(51, 103)(52, 104)(53, 111)(54, 112)(55, 109)(56, 110)(113, 171)(114, 174)(115, 169)(116, 178)(117, 177)(118, 170)(119, 180)(120, 179)(121, 173)(122, 172)(123, 176)(124, 175)(125, 186)(126, 185)(127, 188)(128, 187)(129, 182)(130, 181)(131, 184)(132, 183)(133, 194)(134, 193)(135, 196)(136, 195)(137, 190)(138, 189)(139, 192)(140, 191)(141, 202)(142, 201)(143, 204)(144, 203)(145, 198)(146, 197)(147, 200)(148, 199)(149, 210)(150, 209)(151, 212)(152, 211)(153, 206)(154, 205)(155, 208)(156, 207)(157, 218)(158, 217)(159, 220)(160, 219)(161, 214)(162, 213)(163, 216)(164, 215)(165, 224)(166, 223)(167, 222)(168, 221) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.916 Transitivity :: VT+ Graph:: bipartite v = 14 e = 112 f = 70 degree seq :: [ 16^14 ] E15.923 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 113, 169, 3, 59, 115, 171, 8, 64, 120, 176, 4, 60, 116, 172)(2, 58, 114, 170, 5, 61, 117, 173, 11, 67, 123, 179, 6, 62, 118, 174)(7, 63, 119, 175, 13, 69, 125, 181, 9, 65, 121, 177, 14, 70, 126, 182)(10, 66, 122, 178, 15, 71, 127, 183, 12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189, 18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191, 20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197, 26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199, 28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205, 34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207, 36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213, 42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215, 44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221, 50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223, 52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 57)(3, 63)(4, 65)(5, 66)(6, 68)(7, 59)(8, 67)(9, 60)(10, 61)(11, 64)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 69)(18, 70)(19, 71)(20, 72)(21, 81)(22, 82)(23, 83)(24, 84)(25, 77)(26, 78)(27, 79)(28, 80)(29, 89)(30, 90)(31, 91)(32, 92)(33, 85)(34, 86)(35, 87)(36, 88)(37, 97)(38, 98)(39, 99)(40, 100)(41, 93)(42, 94)(43, 95)(44, 96)(45, 105)(46, 106)(47, 107)(48, 108)(49, 101)(50, 102)(51, 103)(52, 104)(53, 111)(54, 112)(55, 109)(56, 110)(113, 170)(114, 169)(115, 175)(116, 177)(117, 178)(118, 180)(119, 171)(120, 179)(121, 172)(122, 173)(123, 176)(124, 174)(125, 185)(126, 186)(127, 187)(128, 188)(129, 181)(130, 182)(131, 183)(132, 184)(133, 193)(134, 194)(135, 195)(136, 196)(137, 189)(138, 190)(139, 191)(140, 192)(141, 201)(142, 202)(143, 203)(144, 204)(145, 197)(146, 198)(147, 199)(148, 200)(149, 209)(150, 210)(151, 211)(152, 212)(153, 205)(154, 206)(155, 207)(156, 208)(157, 217)(158, 218)(159, 219)(160, 220)(161, 213)(162, 214)(163, 215)(164, 216)(165, 223)(166, 224)(167, 221)(168, 222) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.917 Transitivity :: VT+ Graph:: bipartite v = 14 e = 112 f = 70 degree seq :: [ 16^14 ] E15.924 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, R * Y1 * R * Y2, (R * Y3)^2, (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^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 113, 169, 3, 59, 115, 171, 8, 64, 120, 176, 4, 60, 116, 172)(2, 58, 114, 170, 5, 61, 117, 173, 11, 67, 123, 179, 6, 62, 118, 174)(7, 63, 119, 175, 13, 69, 125, 181, 9, 65, 121, 177, 14, 70, 126, 182)(10, 66, 122, 178, 15, 71, 127, 183, 12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189, 18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191, 20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197, 26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199, 28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205, 34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207, 36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213, 42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215, 44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221, 50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223, 52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 57)(3, 63)(4, 65)(5, 66)(6, 68)(7, 59)(8, 67)(9, 60)(10, 61)(11, 64)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 69)(18, 70)(19, 71)(20, 72)(21, 81)(22, 82)(23, 83)(24, 84)(25, 77)(26, 78)(27, 79)(28, 80)(29, 89)(30, 90)(31, 91)(32, 92)(33, 85)(34, 86)(35, 87)(36, 88)(37, 97)(38, 98)(39, 99)(40, 100)(41, 93)(42, 94)(43, 95)(44, 96)(45, 105)(46, 106)(47, 107)(48, 108)(49, 101)(50, 102)(51, 103)(52, 104)(53, 112)(54, 111)(55, 110)(56, 109)(113, 170)(114, 169)(115, 175)(116, 177)(117, 178)(118, 180)(119, 171)(120, 179)(121, 172)(122, 173)(123, 176)(124, 174)(125, 185)(126, 186)(127, 187)(128, 188)(129, 181)(130, 182)(131, 183)(132, 184)(133, 193)(134, 194)(135, 195)(136, 196)(137, 189)(138, 190)(139, 191)(140, 192)(141, 201)(142, 202)(143, 203)(144, 204)(145, 197)(146, 198)(147, 199)(148, 200)(149, 209)(150, 210)(151, 211)(152, 212)(153, 205)(154, 206)(155, 207)(156, 208)(157, 217)(158, 218)(159, 219)(160, 220)(161, 213)(162, 214)(163, 215)(164, 216)(165, 224)(166, 223)(167, 222)(168, 221) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.918 Transitivity :: VT+ Graph:: bipartite v = 14 e = 112 f = 70 degree seq :: [ 16^14 ] E15.925 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = C2 x C4 x D14 (small group id <112, 28>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1^4, Y2^4, (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^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 6, 62, 118, 174)(3, 59, 115, 171, 7, 63, 119, 175)(5, 61, 117, 173, 10, 66, 122, 178)(8, 64, 120, 176, 13, 69, 125, 181)(9, 65, 121, 177, 14, 70, 126, 182)(11, 67, 123, 179, 15, 71, 127, 183)(12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189)(18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191)(20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197)(26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199)(28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205)(34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207)(36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213)(42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215)(44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221)(50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223)(52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 61)(3, 57)(4, 64)(5, 59)(6, 67)(7, 68)(8, 66)(9, 60)(10, 65)(11, 63)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 70)(18, 69)(19, 72)(20, 71)(21, 81)(22, 82)(23, 83)(24, 84)(25, 78)(26, 77)(27, 80)(28, 79)(29, 89)(30, 90)(31, 91)(32, 92)(33, 86)(34, 85)(35, 88)(36, 87)(37, 97)(38, 98)(39, 99)(40, 100)(41, 94)(42, 93)(43, 96)(44, 95)(45, 105)(46, 106)(47, 107)(48, 108)(49, 102)(50, 101)(51, 104)(52, 103)(53, 111)(54, 112)(55, 110)(56, 109)(113, 171)(114, 169)(115, 173)(116, 177)(117, 170)(118, 180)(119, 179)(120, 172)(121, 178)(122, 176)(123, 174)(124, 175)(125, 186)(126, 185)(127, 188)(128, 187)(129, 181)(130, 182)(131, 183)(132, 184)(133, 194)(134, 193)(135, 196)(136, 195)(137, 189)(138, 190)(139, 191)(140, 192)(141, 202)(142, 201)(143, 204)(144, 203)(145, 197)(146, 198)(147, 199)(148, 200)(149, 210)(150, 209)(151, 212)(152, 211)(153, 205)(154, 206)(155, 207)(156, 208)(157, 218)(158, 217)(159, 220)(160, 219)(161, 213)(162, 214)(163, 215)(164, 216)(165, 224)(166, 223)(167, 221)(168, 222) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.919 Transitivity :: VT+ Graph:: bipartite v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.926 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y1^4, Y2^4, (Y1^-1 * Y3 * Y2^-1)^2, 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, 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 ] Map:: polytopal non-degenerate R = (1, 57, 113, 169, 3, 59, 115, 171)(2, 58, 114, 170, 6, 62, 118, 174)(4, 60, 116, 172, 9, 65, 121, 177)(5, 61, 117, 173, 10, 66, 122, 178)(7, 63, 119, 175, 13, 69, 125, 181)(8, 64, 120, 176, 14, 70, 126, 182)(11, 67, 123, 179, 15, 71, 127, 183)(12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189)(18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191)(20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197)(26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199)(28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205)(34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207)(36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213)(42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215)(44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221)(50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223)(52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 60)(6, 67)(7, 66)(8, 59)(9, 68)(10, 64)(11, 65)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 70)(18, 69)(19, 72)(20, 71)(21, 81)(22, 82)(23, 83)(24, 84)(25, 78)(26, 77)(27, 80)(28, 79)(29, 89)(30, 90)(31, 91)(32, 92)(33, 86)(34, 85)(35, 88)(36, 87)(37, 97)(38, 98)(39, 99)(40, 100)(41, 94)(42, 93)(43, 96)(44, 95)(45, 105)(46, 106)(47, 107)(48, 108)(49, 102)(50, 101)(51, 104)(52, 103)(53, 111)(54, 112)(55, 110)(56, 109)(113, 170)(114, 173)(115, 175)(116, 169)(117, 172)(118, 179)(119, 178)(120, 171)(121, 180)(122, 176)(123, 177)(124, 174)(125, 185)(126, 186)(127, 187)(128, 188)(129, 182)(130, 181)(131, 184)(132, 183)(133, 193)(134, 194)(135, 195)(136, 196)(137, 190)(138, 189)(139, 192)(140, 191)(141, 201)(142, 202)(143, 203)(144, 204)(145, 198)(146, 197)(147, 200)(148, 199)(149, 209)(150, 210)(151, 211)(152, 212)(153, 206)(154, 205)(155, 208)(156, 207)(157, 217)(158, 218)(159, 219)(160, 220)(161, 214)(162, 213)(163, 216)(164, 215)(165, 223)(166, 224)(167, 222)(168, 221) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.920 Transitivity :: VT+ Graph:: bipartite v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.927 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, 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^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 57, 113, 169, 3, 59, 115, 171)(2, 58, 114, 170, 6, 62, 118, 174)(4, 60, 116, 172, 9, 65, 121, 177)(5, 61, 117, 173, 10, 66, 122, 178)(7, 63, 119, 175, 13, 69, 125, 181)(8, 64, 120, 176, 14, 70, 126, 182)(11, 67, 123, 179, 15, 71, 127, 183)(12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189)(18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191)(20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197)(26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199)(28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205)(34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207)(36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213)(42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215)(44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221)(50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223)(52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 60)(6, 67)(7, 66)(8, 59)(9, 68)(10, 64)(11, 65)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 70)(18, 69)(19, 72)(20, 71)(21, 81)(22, 82)(23, 83)(24, 84)(25, 78)(26, 77)(27, 80)(28, 79)(29, 89)(30, 90)(31, 91)(32, 92)(33, 86)(34, 85)(35, 88)(36, 87)(37, 97)(38, 98)(39, 99)(40, 100)(41, 94)(42, 93)(43, 96)(44, 95)(45, 105)(46, 106)(47, 107)(48, 108)(49, 102)(50, 101)(51, 104)(52, 103)(53, 112)(54, 111)(55, 109)(56, 110)(113, 170)(114, 173)(115, 175)(116, 169)(117, 172)(118, 179)(119, 178)(120, 171)(121, 180)(122, 176)(123, 177)(124, 174)(125, 185)(126, 186)(127, 187)(128, 188)(129, 182)(130, 181)(131, 184)(132, 183)(133, 193)(134, 194)(135, 195)(136, 196)(137, 190)(138, 189)(139, 192)(140, 191)(141, 201)(142, 202)(143, 203)(144, 204)(145, 198)(146, 197)(147, 200)(148, 199)(149, 209)(150, 210)(151, 211)(152, 212)(153, 206)(154, 205)(155, 208)(156, 207)(157, 217)(158, 218)(159, 219)(160, 220)(161, 214)(162, 213)(163, 216)(164, 215)(165, 224)(166, 223)(167, 221)(168, 222) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.921 Transitivity :: VT+ Graph:: bipartite v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.928 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * 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 ] Map:: R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 10, 66)(6, 62, 12, 68)(8, 64, 11, 67)(13, 69, 17, 73)(14, 70, 18, 74)(15, 71, 19, 75)(16, 72, 20, 76)(21, 77, 25, 81)(22, 78, 26, 82)(23, 79, 27, 83)(24, 80, 28, 84)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 41, 97)(38, 94, 42, 98)(39, 95, 43, 99)(40, 96, 44, 100)(45, 101, 49, 105)(46, 102, 50, 106)(47, 103, 51, 107)(48, 104, 52, 108)(53, 109, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 120, 176, 116, 172)(114, 170, 117, 173, 123, 179, 118, 174)(119, 175, 125, 181, 121, 177, 126, 182)(122, 178, 127, 183, 124, 180, 128, 184)(129, 185, 133, 189, 130, 186, 134, 190)(131, 187, 135, 191, 132, 188, 136, 192)(137, 193, 141, 197, 138, 194, 142, 198)(139, 195, 143, 199, 140, 196, 144, 200)(145, 201, 149, 205, 146, 202, 150, 206)(147, 203, 151, 207, 148, 204, 152, 208)(153, 209, 157, 213, 154, 210, 158, 214)(155, 211, 159, 215, 156, 212, 160, 216)(161, 217, 165, 221, 162, 218, 166, 222)(163, 219, 167, 223, 164, 220, 168, 224) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.929 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, Y2^4, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-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^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 10, 66)(6, 62, 12, 68)(8, 64, 11, 67)(13, 69, 17, 73)(14, 70, 18, 74)(15, 71, 19, 75)(16, 72, 20, 76)(21, 77, 25, 81)(22, 78, 26, 82)(23, 79, 27, 83)(24, 80, 28, 84)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 41, 97)(38, 94, 42, 98)(39, 95, 43, 99)(40, 96, 44, 100)(45, 101, 49, 105)(46, 102, 50, 106)(47, 103, 51, 107)(48, 104, 52, 108)(53, 109, 56, 112)(54, 110, 55, 111)(113, 169, 115, 171, 120, 176, 116, 172)(114, 170, 117, 173, 123, 179, 118, 174)(119, 175, 125, 181, 121, 177, 126, 182)(122, 178, 127, 183, 124, 180, 128, 184)(129, 185, 133, 189, 130, 186, 134, 190)(131, 187, 135, 191, 132, 188, 136, 192)(137, 193, 141, 197, 138, 194, 142, 198)(139, 195, 143, 199, 140, 196, 144, 200)(145, 201, 149, 205, 146, 202, 150, 206)(147, 203, 151, 207, 148, 204, 152, 208)(153, 209, 157, 213, 154, 210, 158, 214)(155, 211, 159, 215, 156, 212, 160, 216)(161, 217, 165, 221, 162, 218, 166, 222)(163, 219, 167, 223, 164, 220, 168, 224) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.930 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2, Y2^2 * Y3, (R * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * 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^-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, 57, 2, 58)(3, 59, 9, 65)(4, 60, 7, 63)(5, 61, 10, 66)(6, 62, 11, 67)(8, 64, 12, 68)(13, 69, 17, 73)(14, 70, 18, 74)(15, 71, 19, 75)(16, 72, 20, 76)(21, 77, 25, 81)(22, 78, 26, 82)(23, 79, 27, 83)(24, 80, 28, 84)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 41, 97)(38, 94, 42, 98)(39, 95, 43, 99)(40, 96, 44, 100)(45, 101, 49, 105)(46, 102, 50, 106)(47, 103, 51, 107)(48, 104, 52, 108)(53, 109, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 116, 172, 117, 173)(114, 170, 118, 174, 119, 175, 120, 176)(121, 177, 125, 181, 122, 178, 126, 182)(123, 179, 127, 183, 124, 180, 128, 184)(129, 185, 133, 189, 130, 186, 134, 190)(131, 187, 135, 191, 132, 188, 136, 192)(137, 193, 141, 197, 138, 194, 142, 198)(139, 195, 143, 199, 140, 196, 144, 200)(145, 201, 149, 205, 146, 202, 150, 206)(147, 203, 151, 207, 148, 204, 152, 208)(153, 209, 157, 213, 154, 210, 158, 214)(155, 211, 159, 215, 156, 212, 160, 216)(161, 217, 165, 221, 162, 218, 166, 222)(163, 219, 167, 223, 164, 220, 168, 224) L = (1, 116)(2, 119)(3, 117)(4, 113)(5, 115)(6, 120)(7, 114)(8, 118)(9, 122)(10, 121)(11, 124)(12, 123)(13, 126)(14, 125)(15, 128)(16, 127)(17, 130)(18, 129)(19, 132)(20, 131)(21, 134)(22, 133)(23, 136)(24, 135)(25, 138)(26, 137)(27, 140)(28, 139)(29, 142)(30, 141)(31, 144)(32, 143)(33, 146)(34, 145)(35, 148)(36, 147)(37, 150)(38, 149)(39, 152)(40, 151)(41, 154)(42, 153)(43, 156)(44, 155)(45, 158)(46, 157)(47, 160)(48, 159)(49, 162)(50, 161)(51, 164)(52, 163)(53, 166)(54, 165)(55, 168)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.931 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2, Y2^2 * Y3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, 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 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 7, 63)(5, 61, 10, 66)(6, 62, 11, 67)(8, 64, 12, 68)(13, 69, 17, 73)(14, 70, 18, 74)(15, 71, 19, 75)(16, 72, 20, 76)(21, 77, 25, 81)(22, 78, 26, 82)(23, 79, 27, 83)(24, 80, 28, 84)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 41, 97)(38, 94, 42, 98)(39, 95, 43, 99)(40, 96, 44, 100)(45, 101, 49, 105)(46, 102, 50, 106)(47, 103, 51, 107)(48, 104, 52, 108)(53, 109, 56, 112)(54, 110, 55, 111)(113, 169, 115, 171, 116, 172, 117, 173)(114, 170, 118, 174, 119, 175, 120, 176)(121, 177, 125, 181, 122, 178, 126, 182)(123, 179, 127, 183, 124, 180, 128, 184)(129, 185, 133, 189, 130, 186, 134, 190)(131, 187, 135, 191, 132, 188, 136, 192)(137, 193, 141, 197, 138, 194, 142, 198)(139, 195, 143, 199, 140, 196, 144, 200)(145, 201, 149, 205, 146, 202, 150, 206)(147, 203, 151, 207, 148, 204, 152, 208)(153, 209, 157, 213, 154, 210, 158, 214)(155, 211, 159, 215, 156, 212, 160, 216)(161, 217, 165, 221, 162, 218, 166, 222)(163, 219, 167, 223, 164, 220, 168, 224) L = (1, 116)(2, 119)(3, 117)(4, 113)(5, 115)(6, 120)(7, 114)(8, 118)(9, 122)(10, 121)(11, 124)(12, 123)(13, 126)(14, 125)(15, 128)(16, 127)(17, 130)(18, 129)(19, 132)(20, 131)(21, 134)(22, 133)(23, 136)(24, 135)(25, 138)(26, 137)(27, 140)(28, 139)(29, 142)(30, 141)(31, 144)(32, 143)(33, 146)(34, 145)(35, 148)(36, 147)(37, 150)(38, 149)(39, 152)(40, 151)(41, 154)(42, 153)(43, 156)(44, 155)(45, 158)(46, 157)(47, 160)(48, 159)(49, 162)(50, 161)(51, 164)(52, 163)(53, 166)(54, 165)(55, 168)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.932 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^4, (Y2^-2 * Y1)^2, Y2 * Y1 * Y3^2 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^7, Y3^3 * Y1 * Y2 * Y3^2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 20, 76)(9, 65, 26, 82)(12, 68, 21, 77)(13, 69, 30, 86)(14, 70, 23, 79)(15, 71, 28, 84)(16, 72, 25, 81)(18, 74, 35, 91)(19, 75, 24, 80)(22, 78, 39, 95)(27, 83, 44, 100)(29, 85, 47, 103)(31, 87, 41, 97)(32, 88, 40, 96)(33, 89, 49, 105)(34, 90, 46, 102)(36, 92, 51, 107)(37, 93, 43, 99)(38, 94, 53, 109)(42, 98, 50, 106)(45, 101, 52, 108)(48, 104, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 124, 180, 117, 173)(114, 170, 119, 175, 133, 189, 121, 177)(116, 172, 126, 182, 143, 199, 128, 184)(118, 174, 125, 181, 144, 200, 130, 186)(120, 176, 135, 191, 152, 208, 137, 193)(122, 178, 134, 190, 153, 209, 139, 195)(123, 179, 141, 197, 129, 185, 136, 192)(127, 183, 132, 188, 150, 206, 138, 194)(131, 187, 145, 201, 159, 215, 148, 204)(140, 196, 154, 210, 165, 221, 157, 213)(142, 198, 160, 216, 147, 203, 155, 211)(146, 202, 151, 207, 166, 222, 156, 212)(149, 205, 162, 218, 167, 223, 164, 220)(158, 214, 161, 217, 168, 224, 163, 219) L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 130)(6, 113)(7, 134)(8, 136)(9, 139)(10, 114)(11, 135)(12, 143)(13, 145)(14, 115)(15, 146)(16, 117)(17, 137)(18, 148)(19, 118)(20, 126)(21, 152)(22, 154)(23, 119)(24, 155)(25, 121)(26, 128)(27, 157)(28, 122)(29, 160)(30, 123)(31, 150)(32, 124)(33, 162)(34, 149)(35, 129)(36, 164)(37, 131)(38, 166)(39, 132)(40, 141)(41, 133)(42, 161)(43, 158)(44, 138)(45, 163)(46, 140)(47, 144)(48, 168)(49, 142)(50, 151)(51, 147)(52, 156)(53, 153)(54, 167)(55, 159)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.933 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D14 (small group id <56, 4>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-1 * Y3 * Y2, Y2^4, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y1 * Y2^-2)^2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-2 * Y2 * Y3^4, Y3^3 * Y1 * Y2^-1 * Y3^2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 20, 76)(9, 65, 26, 82)(12, 68, 21, 77)(13, 69, 30, 86)(14, 70, 23, 79)(15, 71, 28, 84)(16, 72, 25, 81)(18, 74, 35, 91)(19, 75, 24, 80)(22, 78, 39, 95)(27, 83, 44, 100)(29, 85, 47, 103)(31, 87, 41, 97)(32, 88, 40, 96)(33, 89, 49, 105)(34, 90, 46, 102)(36, 92, 52, 108)(37, 93, 43, 99)(38, 94, 55, 111)(42, 98, 53, 109)(45, 101, 50, 106)(48, 104, 51, 107)(54, 110, 56, 112)(113, 169, 115, 171, 124, 180, 117, 173)(114, 170, 119, 175, 133, 189, 121, 177)(116, 172, 126, 182, 143, 199, 128, 184)(118, 174, 125, 181, 144, 200, 130, 186)(120, 176, 135, 191, 152, 208, 137, 193)(122, 178, 134, 190, 153, 209, 139, 195)(123, 179, 141, 197, 129, 185, 136, 192)(127, 183, 132, 188, 150, 206, 138, 194)(131, 187, 145, 201, 159, 215, 148, 204)(140, 196, 154, 210, 167, 223, 157, 213)(142, 198, 160, 216, 147, 203, 155, 211)(146, 202, 151, 207, 166, 222, 156, 212)(149, 205, 162, 218, 163, 219, 165, 221)(158, 214, 164, 220, 168, 224, 161, 217) L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 130)(6, 113)(7, 134)(8, 136)(9, 139)(10, 114)(11, 135)(12, 143)(13, 145)(14, 115)(15, 146)(16, 117)(17, 137)(18, 148)(19, 118)(20, 126)(21, 152)(22, 154)(23, 119)(24, 155)(25, 121)(26, 128)(27, 157)(28, 122)(29, 160)(30, 123)(31, 150)(32, 124)(33, 162)(34, 163)(35, 129)(36, 165)(37, 131)(38, 166)(39, 132)(40, 141)(41, 133)(42, 164)(43, 168)(44, 138)(45, 161)(46, 140)(47, 144)(48, 158)(49, 142)(50, 156)(51, 159)(52, 147)(53, 151)(54, 149)(55, 153)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.934 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * 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, 58, 2, 62, 6, 61, 5, 57)(3, 65, 9, 60, 4, 66, 10, 59)(7, 67, 11, 64, 8, 68, 12, 63)(13, 73, 17, 70, 14, 74, 18, 69)(15, 75, 19, 72, 16, 76, 20, 71)(21, 81, 25, 78, 22, 82, 26, 77)(23, 83, 27, 80, 24, 84, 28, 79)(29, 89, 33, 86, 30, 90, 34, 85)(31, 91, 35, 88, 32, 92, 36, 87)(37, 97, 41, 94, 38, 98, 42, 93)(39, 99, 43, 96, 40, 100, 44, 95)(45, 105, 49, 102, 46, 106, 50, 101)(47, 107, 51, 104, 48, 108, 52, 103)(53, 112, 56, 110, 54, 111, 55, 109) 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, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 60)(58, 64)(59, 62)(61, 63)(65, 70)(66, 69)(67, 72)(68, 71)(73, 78)(74, 77)(75, 80)(76, 79)(81, 86)(82, 85)(83, 88)(84, 87)(89, 94)(90, 93)(91, 96)(92, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 110)(106, 109)(107, 112)(108, 111) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 14 e = 56 f = 14 degree seq :: [ 8^14 ] E15.935 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 36>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y2 * Y1)^2, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, (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 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 4, 60, 6, 62, 5, 61)(2, 58, 7, 63, 3, 59, 8, 64)(9, 65, 13, 69, 10, 66, 14, 70)(11, 67, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112)(113, 114)(115, 118)(116, 121)(117, 122)(119, 123)(120, 124)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 168)(166, 167)(169, 171)(170, 174)(172, 178)(173, 177)(175, 180)(176, 179)(181, 186)(182, 185)(183, 188)(184, 187)(189, 194)(190, 193)(191, 196)(192, 195)(197, 202)(198, 201)(199, 204)(200, 203)(205, 210)(206, 209)(207, 212)(208, 211)(213, 218)(214, 217)(215, 220)(216, 219)(221, 223)(222, 224) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E15.937 Graph:: simple bipartite v = 70 e = 112 f = 14 degree seq :: [ 2^56, 8^14 ] E15.936 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 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, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * 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, 57, 4, 60)(2, 58, 6, 62)(3, 59, 7, 63)(5, 61, 10, 66)(8, 64, 13, 69)(9, 65, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 54, 110)(51, 107, 55, 111)(52, 108, 56, 112)(113, 114, 117, 115)(116, 120, 122, 121)(118, 123, 119, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 137, 134, 138)(135, 139, 136, 140)(141, 145, 142, 146)(143, 147, 144, 148)(149, 153, 150, 154)(151, 155, 152, 156)(157, 161, 158, 162)(159, 163, 160, 164)(165, 168, 166, 167)(169, 171, 173, 170)(172, 177, 178, 176)(174, 180, 175, 179)(181, 186, 182, 185)(183, 188, 184, 187)(189, 194, 190, 193)(191, 196, 192, 195)(197, 202, 198, 201)(199, 204, 200, 203)(205, 210, 206, 209)(207, 212, 208, 211)(213, 218, 214, 217)(215, 220, 216, 219)(221, 223, 222, 224) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.938 Graph:: simple bipartite v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.937 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 36>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y2 * Y1)^2, Y3^2 * Y2 * Y1, Y2 * Y3^2 * Y1, (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 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 57, 113, 169, 4, 60, 116, 172, 6, 62, 118, 174, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 3, 59, 115, 171, 8, 64, 120, 176)(9, 65, 121, 177, 13, 69, 125, 181, 10, 66, 122, 178, 14, 70, 126, 182)(11, 67, 123, 179, 15, 71, 127, 183, 12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189, 18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191, 20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197, 26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199, 28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205, 34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207, 36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213, 42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215, 44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221, 50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223, 52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 57)(3, 62)(4, 65)(5, 66)(6, 59)(7, 67)(8, 68)(9, 60)(10, 61)(11, 63)(12, 64)(13, 73)(14, 74)(15, 75)(16, 76)(17, 69)(18, 70)(19, 71)(20, 72)(21, 81)(22, 82)(23, 83)(24, 84)(25, 77)(26, 78)(27, 79)(28, 80)(29, 89)(30, 90)(31, 91)(32, 92)(33, 85)(34, 86)(35, 87)(36, 88)(37, 97)(38, 98)(39, 99)(40, 100)(41, 93)(42, 94)(43, 95)(44, 96)(45, 105)(46, 106)(47, 107)(48, 108)(49, 101)(50, 102)(51, 103)(52, 104)(53, 112)(54, 111)(55, 110)(56, 109)(113, 171)(114, 174)(115, 169)(116, 178)(117, 177)(118, 170)(119, 180)(120, 179)(121, 173)(122, 172)(123, 176)(124, 175)(125, 186)(126, 185)(127, 188)(128, 187)(129, 182)(130, 181)(131, 184)(132, 183)(133, 194)(134, 193)(135, 196)(136, 195)(137, 190)(138, 189)(139, 192)(140, 191)(141, 202)(142, 201)(143, 204)(144, 203)(145, 198)(146, 197)(147, 200)(148, 199)(149, 210)(150, 209)(151, 212)(152, 211)(153, 206)(154, 205)(155, 208)(156, 207)(157, 218)(158, 217)(159, 220)(160, 219)(161, 214)(162, 213)(163, 216)(164, 215)(165, 223)(166, 224)(167, 221)(168, 222) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.935 Transitivity :: VT+ Graph:: bipartite v = 14 e = 112 f = 70 degree seq :: [ 16^14 ] E15.938 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 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, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * 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, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 6, 62, 118, 174)(3, 59, 115, 171, 7, 63, 119, 175)(5, 61, 117, 173, 10, 66, 122, 178)(8, 64, 120, 176, 13, 69, 125, 181)(9, 65, 121, 177, 14, 70, 126, 182)(11, 67, 123, 179, 15, 71, 127, 183)(12, 68, 124, 180, 16, 72, 128, 184)(17, 73, 129, 185, 21, 77, 133, 189)(18, 74, 130, 186, 22, 78, 134, 190)(19, 75, 131, 187, 23, 79, 135, 191)(20, 76, 132, 188, 24, 80, 136, 192)(25, 81, 137, 193, 29, 85, 141, 197)(26, 82, 138, 194, 30, 86, 142, 198)(27, 83, 139, 195, 31, 87, 143, 199)(28, 84, 140, 196, 32, 88, 144, 200)(33, 89, 145, 201, 37, 93, 149, 205)(34, 90, 146, 202, 38, 94, 150, 206)(35, 91, 147, 203, 39, 95, 151, 207)(36, 92, 148, 204, 40, 96, 152, 208)(41, 97, 153, 209, 45, 101, 157, 213)(42, 98, 154, 210, 46, 102, 158, 214)(43, 99, 155, 211, 47, 103, 159, 215)(44, 100, 156, 212, 48, 104, 160, 216)(49, 105, 161, 217, 53, 109, 165, 221)(50, 106, 162, 218, 54, 110, 166, 222)(51, 107, 163, 219, 55, 111, 167, 223)(52, 108, 164, 220, 56, 112, 168, 224) L = (1, 58)(2, 61)(3, 57)(4, 64)(5, 59)(6, 67)(7, 68)(8, 66)(9, 60)(10, 65)(11, 63)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 70)(18, 69)(19, 72)(20, 71)(21, 81)(22, 82)(23, 83)(24, 84)(25, 78)(26, 77)(27, 80)(28, 79)(29, 89)(30, 90)(31, 91)(32, 92)(33, 86)(34, 85)(35, 88)(36, 87)(37, 97)(38, 98)(39, 99)(40, 100)(41, 94)(42, 93)(43, 96)(44, 95)(45, 105)(46, 106)(47, 107)(48, 108)(49, 102)(50, 101)(51, 104)(52, 103)(53, 112)(54, 111)(55, 109)(56, 110)(113, 171)(114, 169)(115, 173)(116, 177)(117, 170)(118, 180)(119, 179)(120, 172)(121, 178)(122, 176)(123, 174)(124, 175)(125, 186)(126, 185)(127, 188)(128, 187)(129, 181)(130, 182)(131, 183)(132, 184)(133, 194)(134, 193)(135, 196)(136, 195)(137, 189)(138, 190)(139, 191)(140, 192)(141, 202)(142, 201)(143, 204)(144, 203)(145, 197)(146, 198)(147, 199)(148, 200)(149, 210)(150, 209)(151, 212)(152, 211)(153, 205)(154, 206)(155, 207)(156, 208)(157, 218)(158, 217)(159, 220)(160, 219)(161, 213)(162, 214)(163, 215)(164, 216)(165, 223)(166, 224)(167, 222)(168, 221) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.936 Transitivity :: VT+ Graph:: bipartite v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.939 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 36>) |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, (Y2^-2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, Y3^7, Y3^2 * Y1 * Y2 * Y3^3 * Y1 * Y2 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 20, 76)(9, 65, 26, 82)(12, 68, 21, 77)(13, 69, 30, 86)(14, 70, 25, 81)(15, 71, 28, 84)(16, 72, 23, 79)(18, 74, 35, 91)(19, 75, 24, 80)(22, 78, 39, 95)(27, 83, 44, 100)(29, 85, 47, 103)(31, 87, 41, 97)(32, 88, 40, 96)(33, 89, 49, 105)(34, 90, 46, 102)(36, 92, 51, 107)(37, 93, 43, 99)(38, 94, 53, 109)(42, 98, 52, 108)(45, 101, 50, 106)(48, 104, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 124, 180, 117, 173)(114, 170, 119, 175, 133, 189, 121, 177)(116, 172, 126, 182, 143, 199, 128, 184)(118, 174, 125, 181, 144, 200, 130, 186)(120, 176, 135, 191, 152, 208, 137, 193)(122, 178, 134, 190, 153, 209, 139, 195)(123, 179, 136, 192, 129, 185, 141, 197)(127, 183, 138, 194, 150, 206, 132, 188)(131, 187, 145, 201, 159, 215, 148, 204)(140, 196, 154, 210, 165, 221, 157, 213)(142, 198, 155, 211, 147, 203, 160, 216)(146, 202, 156, 212, 166, 222, 151, 207)(149, 205, 162, 218, 167, 223, 164, 220)(158, 214, 163, 219, 168, 224, 161, 217) L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 130)(6, 113)(7, 134)(8, 136)(9, 139)(10, 114)(11, 137)(12, 143)(13, 145)(14, 115)(15, 146)(16, 117)(17, 135)(18, 148)(19, 118)(20, 128)(21, 152)(22, 154)(23, 119)(24, 155)(25, 121)(26, 126)(27, 157)(28, 122)(29, 160)(30, 123)(31, 150)(32, 124)(33, 162)(34, 149)(35, 129)(36, 164)(37, 131)(38, 166)(39, 132)(40, 141)(41, 133)(42, 163)(43, 158)(44, 138)(45, 161)(46, 140)(47, 144)(48, 168)(49, 142)(50, 156)(51, 147)(52, 151)(53, 153)(54, 167)(55, 159)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.940 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = C2 x ((C14 x C2) : C2) (small group id <112, 36>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y1 * Y3^-1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2^4, (R * Y1)^2, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^3 * Y1 * Y2 * Y1 * Y2^-1 * Y3^2 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 20, 76)(9, 65, 26, 82)(12, 68, 21, 77)(13, 69, 30, 86)(14, 70, 25, 81)(15, 71, 28, 84)(16, 72, 23, 79)(18, 74, 35, 91)(19, 75, 24, 80)(22, 78, 39, 95)(27, 83, 44, 100)(29, 85, 47, 103)(31, 87, 41, 97)(32, 88, 40, 96)(33, 89, 49, 105)(34, 90, 46, 102)(36, 92, 52, 108)(37, 93, 43, 99)(38, 94, 55, 111)(42, 98, 50, 106)(45, 101, 53, 109)(48, 104, 51, 107)(54, 110, 56, 112)(113, 169, 115, 171, 124, 180, 117, 173)(114, 170, 119, 175, 133, 189, 121, 177)(116, 172, 126, 182, 143, 199, 128, 184)(118, 174, 125, 181, 144, 200, 130, 186)(120, 176, 135, 191, 152, 208, 137, 193)(122, 178, 134, 190, 153, 209, 139, 195)(123, 179, 136, 192, 129, 185, 141, 197)(127, 183, 138, 194, 150, 206, 132, 188)(131, 187, 145, 201, 159, 215, 148, 204)(140, 196, 154, 210, 167, 223, 157, 213)(142, 198, 155, 211, 147, 203, 160, 216)(146, 202, 156, 212, 166, 222, 151, 207)(149, 205, 162, 218, 163, 219, 165, 221)(158, 214, 161, 217, 168, 224, 164, 220) L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 130)(6, 113)(7, 134)(8, 136)(9, 139)(10, 114)(11, 137)(12, 143)(13, 145)(14, 115)(15, 146)(16, 117)(17, 135)(18, 148)(19, 118)(20, 128)(21, 152)(22, 154)(23, 119)(24, 155)(25, 121)(26, 126)(27, 157)(28, 122)(29, 160)(30, 123)(31, 150)(32, 124)(33, 162)(34, 163)(35, 129)(36, 165)(37, 131)(38, 166)(39, 132)(40, 141)(41, 133)(42, 161)(43, 168)(44, 138)(45, 164)(46, 140)(47, 144)(48, 158)(49, 142)(50, 151)(51, 159)(52, 147)(53, 156)(54, 149)(55, 153)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 42 e = 112 f = 42 degree seq :: [ 4^28, 8^14 ] E15.941 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 5}) Quotient :: halfedge^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y1^-1 * Y3 * Y1, Y1^-1 * Y3 * Y1 * Y2, R * Y3 * R * Y2, (R * Y1)^2, Y1^5, Y3 * Y1 * Y3 * Y1^2 * Y2, (Y1^-1 * Y2 * Y3)^3 ] Map:: polytopal non-degenerate R = (1, 62, 2, 66, 6, 75, 15, 65, 5, 61)(3, 69, 9, 82, 22, 79, 19, 71, 11, 63)(4, 67, 7, 78, 18, 90, 30, 73, 13, 64)(8, 76, 16, 72, 12, 87, 27, 81, 21, 68)(10, 83, 23, 74, 14, 91, 31, 86, 26, 70)(17, 93, 33, 80, 20, 96, 36, 92, 32, 77)(24, 99, 39, 85, 25, 103, 43, 102, 42, 84)(28, 106, 46, 89, 29, 110, 50, 109, 49, 88)(34, 100, 40, 95, 35, 101, 41, 111, 51, 94)(37, 107, 47, 98, 38, 108, 48, 115, 55, 97)(44, 112, 52, 105, 45, 113, 53, 114, 54, 104)(56, 118, 58, 117, 57, 119, 59, 120, 60, 116) L = (1, 3)(2, 7)(4, 12)(5, 14)(6, 16)(8, 20)(9, 23)(10, 25)(11, 18)(13, 29)(15, 33)(17, 31)(19, 35)(21, 38)(22, 39)(24, 41)(26, 45)(27, 46)(28, 48)(30, 40)(32, 53)(34, 50)(36, 47)(37, 54)(42, 57)(43, 52)(44, 59)(49, 56)(51, 58)(55, 60)(61, 64)(62, 68)(63, 70)(65, 71)(66, 77)(67, 79)(69, 84)(72, 88)(73, 76)(74, 92)(75, 83)(78, 94)(80, 97)(81, 93)(82, 100)(85, 104)(86, 99)(87, 107)(89, 111)(90, 106)(91, 112)(95, 102)(96, 105)(98, 109)(101, 116)(103, 118)(108, 119)(110, 120)(113, 115)(114, 117) local type(s) :: { ( 6^10 ) } Outer automorphisms :: reflexible Dual of E15.942 Transitivity :: VT+ AT Graph:: v = 12 e = 60 f = 20 degree seq :: [ 10^12 ] E15.942 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 5}) Quotient :: halfedge^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^3, (Y3 * Y1^-1)^3, (Y2 * Y1^-1)^3, (Y2 * Y3)^3, (Y2 * Y3 * Y2 * Y1^-1)^2, (Y3 * Y2 * Y3 * Y1^-1)^2, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y1 * Y2 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 62, 2, 65, 5, 61)(3, 68, 8, 70, 10, 63)(4, 71, 11, 73, 13, 64)(6, 76, 16, 78, 18, 66)(7, 79, 19, 81, 21, 67)(9, 84, 24, 86, 26, 69)(12, 90, 30, 91, 31, 72)(14, 93, 33, 82, 22, 74)(15, 95, 35, 89, 29, 75)(17, 98, 38, 100, 40, 77)(20, 103, 43, 104, 44, 80)(23, 107, 47, 109, 49, 83)(25, 110, 50, 99, 39, 85)(27, 112, 52, 102, 42, 87)(28, 106, 46, 113, 53, 88)(32, 114, 54, 97, 37, 92)(34, 111, 51, 116, 56, 94)(36, 108, 48, 118, 58, 96)(41, 119, 59, 117, 57, 101)(45, 120, 60, 115, 55, 105) L = (1, 3)(2, 6)(4, 12)(5, 14)(7, 20)(8, 22)(9, 25)(10, 16)(11, 28)(13, 32)(15, 36)(17, 39)(18, 33)(19, 42)(21, 45)(23, 48)(24, 40)(26, 51)(27, 44)(29, 47)(30, 37)(31, 46)(34, 50)(35, 57)(38, 56)(41, 58)(43, 55)(49, 59)(52, 60)(53, 54)(61, 64)(62, 67)(63, 69)(65, 75)(66, 77)(68, 83)(70, 87)(71, 89)(72, 85)(73, 79)(74, 94)(76, 97)(78, 101)(80, 99)(81, 95)(82, 106)(84, 102)(86, 107)(88, 111)(90, 104)(91, 108)(92, 100)(93, 115)(96, 110)(98, 117)(103, 118)(105, 116)(109, 112)(113, 120)(114, 119) local type(s) :: { ( 10^6 ) } Outer automorphisms :: reflexible Dual of E15.941 Transitivity :: VT+ AT Graph:: simple v = 20 e = 60 f = 12 degree seq :: [ 6^20 ] E15.943 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 5}) Quotient :: edge^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y3)^3, (Y1 * Y3^-1)^3, (Y2 * Y1)^3, (Y1 * Y2 * Y1 * Y3^-1)^2, (Y3 * Y2 * Y3 * Y1)^2, (Y1 * Y3^-1 * Y2)^5 ] Map:: polytopal R = (1, 61, 4, 64, 5, 65)(2, 62, 7, 67, 8, 68)(3, 63, 10, 70, 11, 71)(6, 66, 17, 77, 18, 78)(9, 69, 23, 83, 24, 84)(12, 72, 21, 81, 30, 90)(13, 73, 28, 88, 32, 92)(14, 74, 34, 94, 19, 79)(15, 75, 36, 96, 26, 86)(16, 76, 37, 97, 38, 98)(20, 80, 42, 102, 45, 105)(22, 82, 48, 108, 40, 100)(25, 85, 43, 103, 49, 109)(27, 87, 50, 110, 46, 106)(29, 89, 51, 111, 39, 99)(31, 91, 53, 113, 47, 107)(33, 93, 41, 101, 55, 115)(35, 95, 44, 104, 57, 117)(52, 112, 59, 119, 58, 118)(54, 114, 60, 120, 56, 116)(121, 122)(123, 129)(124, 132)(125, 134)(126, 136)(127, 139)(128, 141)(130, 145)(131, 147)(133, 151)(135, 155)(137, 159)(138, 161)(140, 164)(142, 167)(143, 166)(144, 163)(146, 162)(148, 160)(149, 158)(150, 154)(152, 174)(153, 157)(156, 178)(165, 179)(168, 180)(169, 170)(171, 175)(172, 177)(173, 176)(181, 183)(182, 186)(184, 193)(185, 195)(187, 200)(188, 202)(189, 196)(190, 206)(191, 208)(192, 209)(194, 213)(197, 220)(198, 222)(199, 223)(201, 226)(203, 227)(204, 224)(205, 221)(207, 219)(210, 232)(211, 218)(212, 216)(214, 236)(215, 217)(225, 228)(229, 240)(230, 239)(231, 238)(233, 237)(234, 235) 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, 20 ), ( 20^6 ) } Outer automorphisms :: reflexible Dual of E15.946 Graph:: simple bipartite v = 80 e = 120 f = 12 degree seq :: [ 2^60, 6^20 ] E15.944 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 5}) Quotient :: edge^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^5, Y3^2 * Y1 * Y3^-2 * Y2, (Y2 * Y1)^3, (Y3 * Y2)^3, (Y3 * Y1)^3, Y3^-1 * Y1 * Y3^2 * Y2 * Y3 * Y1, (Y1 * Y2 * Y3^-1 * Y2)^2 ] Map:: polytopal R = (1, 61, 4, 64, 14, 74, 17, 77, 5, 65)(2, 62, 7, 67, 23, 83, 26, 86, 8, 68)(3, 63, 10, 70, 31, 91, 34, 94, 11, 71)(6, 66, 19, 79, 47, 107, 50, 110, 20, 80)(9, 69, 27, 87, 55, 115, 56, 116, 28, 88)(12, 72, 24, 84, 30, 90, 16, 76, 36, 96)(13, 73, 33, 93, 43, 103, 29, 89, 38, 98)(15, 75, 41, 101, 25, 85, 39, 99, 21, 81)(18, 78, 44, 104, 59, 119, 60, 120, 45, 105)(22, 82, 49, 109, 54, 114, 46, 106, 35, 95)(32, 92, 42, 102, 51, 111, 57, 117, 52, 112)(37, 97, 58, 118, 40, 100, 48, 108, 53, 113)(121, 122)(123, 129)(124, 132)(125, 135)(126, 138)(127, 141)(128, 144)(130, 149)(131, 152)(133, 157)(134, 151)(136, 162)(137, 163)(139, 166)(140, 168)(142, 171)(143, 167)(145, 173)(146, 174)(147, 172)(148, 158)(150, 169)(153, 161)(154, 156)(155, 165)(159, 170)(160, 164)(175, 179)(176, 178)(177, 180)(181, 183)(182, 186)(184, 193)(185, 196)(187, 202)(188, 205)(189, 198)(190, 210)(191, 213)(192, 215)(194, 219)(195, 220)(197, 206)(199, 221)(200, 229)(201, 218)(203, 216)(204, 232)(207, 233)(208, 231)(209, 228)(211, 237)(212, 226)(214, 236)(217, 225)(222, 224)(223, 235)(227, 238)(230, 240)(234, 239) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12, 12 ), ( 12^10 ) } Outer automorphisms :: reflexible Dual of E15.945 Graph:: simple bipartite v = 72 e = 120 f = 20 degree seq :: [ 2^60, 10^12 ] E15.945 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 5}) Quotient :: loop^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y3)^3, (Y1 * Y3^-1)^3, (Y2 * Y1)^3, (Y1 * Y2 * Y1 * Y3^-1)^2, (Y3 * Y2 * Y3 * Y1)^2, (Y1 * Y3^-1 * Y2)^5 ] Map:: R = (1, 61, 121, 181, 4, 64, 124, 184, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 8, 68, 128, 188)(3, 63, 123, 183, 10, 70, 130, 190, 11, 71, 131, 191)(6, 66, 126, 186, 17, 77, 137, 197, 18, 78, 138, 198)(9, 69, 129, 189, 23, 83, 143, 203, 24, 84, 144, 204)(12, 72, 132, 192, 21, 81, 141, 201, 30, 90, 150, 210)(13, 73, 133, 193, 28, 88, 148, 208, 32, 92, 152, 212)(14, 74, 134, 194, 34, 94, 154, 214, 19, 79, 139, 199)(15, 75, 135, 195, 36, 96, 156, 216, 26, 86, 146, 206)(16, 76, 136, 196, 37, 97, 157, 217, 38, 98, 158, 218)(20, 80, 140, 200, 42, 102, 162, 222, 45, 105, 165, 225)(22, 82, 142, 202, 48, 108, 168, 228, 40, 100, 160, 220)(25, 85, 145, 205, 43, 103, 163, 223, 49, 109, 169, 229)(27, 87, 147, 207, 50, 110, 170, 230, 46, 106, 166, 226)(29, 89, 149, 209, 51, 111, 171, 231, 39, 99, 159, 219)(31, 91, 151, 211, 53, 113, 173, 233, 47, 107, 167, 227)(33, 93, 153, 213, 41, 101, 161, 221, 55, 115, 175, 235)(35, 95, 155, 215, 44, 104, 164, 224, 57, 117, 177, 237)(52, 112, 172, 232, 59, 119, 179, 239, 58, 118, 178, 238)(54, 114, 174, 234, 60, 120, 180, 240, 56, 116, 176, 236) L = (1, 62)(2, 61)(3, 69)(4, 72)(5, 74)(6, 76)(7, 79)(8, 81)(9, 63)(10, 85)(11, 87)(12, 64)(13, 91)(14, 65)(15, 95)(16, 66)(17, 99)(18, 101)(19, 67)(20, 104)(21, 68)(22, 107)(23, 106)(24, 103)(25, 70)(26, 102)(27, 71)(28, 100)(29, 98)(30, 94)(31, 73)(32, 114)(33, 97)(34, 90)(35, 75)(36, 118)(37, 93)(38, 89)(39, 77)(40, 88)(41, 78)(42, 86)(43, 84)(44, 80)(45, 119)(46, 83)(47, 82)(48, 120)(49, 110)(50, 109)(51, 115)(52, 117)(53, 116)(54, 92)(55, 111)(56, 113)(57, 112)(58, 96)(59, 105)(60, 108)(121, 183)(122, 186)(123, 181)(124, 193)(125, 195)(126, 182)(127, 200)(128, 202)(129, 196)(130, 206)(131, 208)(132, 209)(133, 184)(134, 213)(135, 185)(136, 189)(137, 220)(138, 222)(139, 223)(140, 187)(141, 226)(142, 188)(143, 227)(144, 224)(145, 221)(146, 190)(147, 219)(148, 191)(149, 192)(150, 232)(151, 218)(152, 216)(153, 194)(154, 236)(155, 217)(156, 212)(157, 215)(158, 211)(159, 207)(160, 197)(161, 205)(162, 198)(163, 199)(164, 204)(165, 228)(166, 201)(167, 203)(168, 225)(169, 240)(170, 239)(171, 238)(172, 210)(173, 237)(174, 235)(175, 234)(176, 214)(177, 233)(178, 231)(179, 230)(180, 229) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E15.944 Transitivity :: VT+ Graph:: v = 20 e = 120 f = 72 degree seq :: [ 12^20 ] E15.946 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 5}) Quotient :: loop^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^5, Y3^2 * Y1 * Y3^-2 * Y2, (Y2 * Y1)^3, (Y3 * Y2)^3, (Y3 * Y1)^3, Y3^-1 * Y1 * Y3^2 * Y2 * Y3 * Y1, (Y1 * Y2 * Y3^-1 * Y2)^2 ] Map:: R = (1, 61, 121, 181, 4, 64, 124, 184, 14, 74, 134, 194, 17, 77, 137, 197, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 23, 83, 143, 203, 26, 86, 146, 206, 8, 68, 128, 188)(3, 63, 123, 183, 10, 70, 130, 190, 31, 91, 151, 211, 34, 94, 154, 214, 11, 71, 131, 191)(6, 66, 126, 186, 19, 79, 139, 199, 47, 107, 167, 227, 50, 110, 170, 230, 20, 80, 140, 200)(9, 69, 129, 189, 27, 87, 147, 207, 55, 115, 175, 235, 56, 116, 176, 236, 28, 88, 148, 208)(12, 72, 132, 192, 24, 84, 144, 204, 30, 90, 150, 210, 16, 76, 136, 196, 36, 96, 156, 216)(13, 73, 133, 193, 33, 93, 153, 213, 43, 103, 163, 223, 29, 89, 149, 209, 38, 98, 158, 218)(15, 75, 135, 195, 41, 101, 161, 221, 25, 85, 145, 205, 39, 99, 159, 219, 21, 81, 141, 201)(18, 78, 138, 198, 44, 104, 164, 224, 59, 119, 179, 239, 60, 120, 180, 240, 45, 105, 165, 225)(22, 82, 142, 202, 49, 109, 169, 229, 54, 114, 174, 234, 46, 106, 166, 226, 35, 95, 155, 215)(32, 92, 152, 212, 42, 102, 162, 222, 51, 111, 171, 231, 57, 117, 177, 237, 52, 112, 172, 232)(37, 97, 157, 217, 58, 118, 178, 238, 40, 100, 160, 220, 48, 108, 168, 228, 53, 113, 173, 233) L = (1, 62)(2, 61)(3, 69)(4, 72)(5, 75)(6, 78)(7, 81)(8, 84)(9, 63)(10, 89)(11, 92)(12, 64)(13, 97)(14, 91)(15, 65)(16, 102)(17, 103)(18, 66)(19, 106)(20, 108)(21, 67)(22, 111)(23, 107)(24, 68)(25, 113)(26, 114)(27, 112)(28, 98)(29, 70)(30, 109)(31, 74)(32, 71)(33, 101)(34, 96)(35, 105)(36, 94)(37, 73)(38, 88)(39, 110)(40, 104)(41, 93)(42, 76)(43, 77)(44, 100)(45, 95)(46, 79)(47, 83)(48, 80)(49, 90)(50, 99)(51, 82)(52, 87)(53, 85)(54, 86)(55, 119)(56, 118)(57, 120)(58, 116)(59, 115)(60, 117)(121, 183)(122, 186)(123, 181)(124, 193)(125, 196)(126, 182)(127, 202)(128, 205)(129, 198)(130, 210)(131, 213)(132, 215)(133, 184)(134, 219)(135, 220)(136, 185)(137, 206)(138, 189)(139, 221)(140, 229)(141, 218)(142, 187)(143, 216)(144, 232)(145, 188)(146, 197)(147, 233)(148, 231)(149, 228)(150, 190)(151, 237)(152, 226)(153, 191)(154, 236)(155, 192)(156, 203)(157, 225)(158, 201)(159, 194)(160, 195)(161, 199)(162, 224)(163, 235)(164, 222)(165, 217)(166, 212)(167, 238)(168, 209)(169, 200)(170, 240)(171, 208)(172, 204)(173, 207)(174, 239)(175, 223)(176, 214)(177, 211)(178, 227)(179, 234)(180, 230) local type(s) :: { ( 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 E15.943 Transitivity :: VT+ Graph:: v = 12 e = 120 f = 80 degree seq :: [ 20^12 ] E15.947 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 7, 67)(5, 65, 13, 73)(6, 66, 15, 75)(8, 68, 19, 79)(10, 70, 18, 78)(11, 71, 20, 80)(12, 72, 16, 76)(14, 74, 17, 77)(21, 81, 37, 97)(22, 82, 39, 99)(23, 83, 40, 100)(24, 84, 38, 98)(25, 85, 41, 101)(26, 86, 43, 103)(27, 87, 44, 104)(28, 88, 42, 102)(29, 89, 45, 105)(30, 90, 47, 107)(31, 91, 48, 108)(32, 92, 46, 106)(33, 93, 49, 109)(34, 94, 51, 111)(35, 95, 52, 112)(36, 96, 50, 110)(53, 113, 60, 120)(54, 114, 59, 119)(55, 115, 57, 117)(56, 116, 58, 118)(121, 181, 123, 183, 125, 185)(122, 182, 126, 186, 128, 188)(124, 184, 131, 191, 132, 192)(127, 187, 137, 197, 138, 198)(129, 189, 141, 201, 142, 202)(130, 190, 143, 203, 144, 204)(133, 193, 145, 205, 146, 206)(134, 194, 147, 207, 148, 208)(135, 195, 149, 209, 150, 210)(136, 196, 151, 211, 152, 212)(139, 199, 153, 213, 154, 214)(140, 200, 155, 215, 156, 216)(157, 217, 171, 231, 173, 233)(158, 218, 174, 234, 172, 232)(159, 219, 168, 228, 175, 235)(160, 220, 176, 236, 167, 227)(161, 221, 177, 237, 170, 230)(162, 222, 169, 229, 178, 238)(163, 223, 179, 239, 165, 225)(164, 224, 166, 226, 180, 240) L = (1, 124)(2, 127)(3, 130)(4, 121)(5, 134)(6, 136)(7, 122)(8, 140)(9, 138)(10, 123)(11, 139)(12, 135)(13, 137)(14, 125)(15, 132)(16, 126)(17, 133)(18, 129)(19, 131)(20, 128)(21, 158)(22, 160)(23, 159)(24, 157)(25, 162)(26, 164)(27, 163)(28, 161)(29, 166)(30, 168)(31, 167)(32, 165)(33, 170)(34, 172)(35, 171)(36, 169)(37, 144)(38, 141)(39, 143)(40, 142)(41, 148)(42, 145)(43, 147)(44, 146)(45, 152)(46, 149)(47, 151)(48, 150)(49, 156)(50, 153)(51, 155)(52, 154)(53, 179)(54, 180)(55, 178)(56, 177)(57, 176)(58, 175)(59, 173)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E15.953 Graph:: simple bipartite v = 50 e = 120 f = 42 degree seq :: [ 4^30, 6^20 ] E15.948 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y2^-1)^5, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2 * 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, 16, 76)(10, 70, 15, 75)(11, 71, 14, 74)(12, 72, 13, 73)(17, 77, 28, 88)(18, 78, 27, 87)(19, 79, 26, 86)(20, 80, 25, 85)(21, 81, 24, 84)(22, 82, 23, 83)(29, 89, 44, 104)(30, 90, 43, 103)(31, 91, 42, 102)(32, 92, 41, 101)(33, 93, 40, 100)(34, 94, 39, 99)(35, 95, 38, 98)(36, 96, 37, 97)(45, 105, 58, 118)(46, 106, 60, 120)(47, 107, 50, 110)(48, 108, 59, 119)(49, 109, 55, 115)(51, 111, 53, 113)(52, 112, 57, 117)(54, 114, 56, 116)(121, 181, 123, 183, 125, 185)(122, 182, 126, 186, 128, 188)(124, 184, 130, 190, 131, 191)(127, 187, 134, 194, 135, 195)(129, 189, 137, 197, 138, 198)(132, 192, 141, 201, 142, 202)(133, 193, 143, 203, 144, 204)(136, 196, 147, 207, 148, 208)(139, 199, 151, 211, 152, 212)(140, 200, 153, 213, 154, 214)(145, 205, 159, 219, 160, 220)(146, 206, 161, 221, 162, 222)(149, 209, 165, 225, 166, 226)(150, 210, 167, 227, 168, 228)(155, 215, 172, 232, 173, 233)(156, 216, 174, 234, 169, 229)(157, 217, 175, 235, 176, 236)(158, 218, 171, 231, 177, 237)(163, 223, 179, 239, 170, 230)(164, 224, 180, 240, 178, 238) L = (1, 124)(2, 127)(3, 129)(4, 121)(5, 132)(6, 133)(7, 122)(8, 136)(9, 123)(10, 139)(11, 140)(12, 125)(13, 126)(14, 145)(15, 146)(16, 128)(17, 149)(18, 150)(19, 130)(20, 131)(21, 155)(22, 156)(23, 157)(24, 158)(25, 134)(26, 135)(27, 163)(28, 164)(29, 137)(30, 138)(31, 169)(32, 170)(33, 171)(34, 165)(35, 141)(36, 142)(37, 143)(38, 144)(39, 178)(40, 173)(41, 167)(42, 175)(43, 147)(44, 148)(45, 154)(46, 176)(47, 161)(48, 172)(49, 151)(50, 152)(51, 153)(52, 168)(53, 160)(54, 180)(55, 162)(56, 166)(57, 179)(58, 159)(59, 177)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E15.952 Graph:: simple bipartite v = 50 e = 120 f = 42 degree seq :: [ 4^30, 6^20 ] E15.949 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y1 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1)^3, Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y1 * Y3^-1, (Y3 * Y2^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 11, 71)(4, 64, 10, 70)(5, 65, 16, 76)(6, 66, 8, 68)(7, 67, 21, 81)(9, 69, 26, 86)(12, 72, 32, 92)(13, 73, 25, 85)(14, 74, 28, 88)(15, 75, 23, 83)(17, 77, 39, 99)(18, 78, 24, 84)(19, 79, 35, 95)(20, 80, 41, 101)(22, 82, 37, 97)(27, 87, 36, 96)(29, 89, 46, 106)(30, 90, 44, 104)(31, 91, 38, 98)(33, 93, 51, 111)(34, 94, 42, 102)(40, 100, 53, 113)(43, 103, 50, 110)(45, 105, 49, 109)(47, 107, 48, 108)(52, 112, 55, 115)(54, 114, 58, 118)(56, 116, 60, 120)(57, 117, 59, 119)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 134, 194, 135, 195)(126, 186, 139, 199, 140, 200)(128, 188, 144, 204, 145, 205)(130, 190, 149, 209, 150, 210)(131, 191, 146, 206, 151, 211)(132, 192, 153, 213, 147, 207)(133, 193, 154, 214, 155, 215)(136, 196, 158, 218, 141, 201)(137, 197, 142, 202, 160, 220)(138, 198, 161, 221, 162, 222)(143, 203, 167, 227, 166, 226)(148, 208, 164, 224, 168, 228)(152, 212, 163, 223, 172, 232)(156, 216, 176, 236, 170, 230)(157, 217, 169, 229, 177, 237)(159, 219, 174, 234, 165, 225)(171, 231, 175, 235, 180, 240)(173, 233, 179, 239, 178, 238) L = (1, 124)(2, 128)(3, 132)(4, 126)(5, 137)(6, 121)(7, 142)(8, 130)(9, 147)(10, 122)(11, 145)(12, 133)(13, 123)(14, 156)(15, 157)(16, 144)(17, 138)(18, 125)(19, 163)(20, 165)(21, 135)(22, 143)(23, 127)(24, 159)(25, 152)(26, 134)(27, 148)(28, 129)(29, 169)(30, 170)(31, 160)(32, 131)(33, 173)(34, 174)(35, 150)(36, 146)(37, 141)(38, 153)(39, 136)(40, 171)(41, 149)(42, 172)(43, 164)(44, 139)(45, 166)(46, 140)(47, 176)(48, 177)(49, 161)(50, 155)(51, 151)(52, 178)(53, 158)(54, 175)(55, 154)(56, 179)(57, 180)(58, 162)(59, 167)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E15.954 Graph:: simple bipartite v = 50 e = 120 f = 42 degree seq :: [ 4^30, 6^20 ] E15.950 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y2)^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y3^5, (Y3 * Y2^-1 * Y1)^2, (Y3^-1 * Y1 * Y2^-1)^2, Y1 * Y2^-1 * Y3^-2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y3^2 * Y2^-1 * Y3 * Y1, (Y3 * Y2^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 11, 71)(4, 64, 10, 70)(5, 65, 17, 77)(6, 66, 8, 68)(7, 67, 21, 81)(9, 69, 27, 87)(12, 72, 32, 92)(13, 73, 26, 86)(14, 74, 24, 84)(15, 75, 30, 90)(16, 76, 23, 83)(18, 78, 40, 100)(19, 79, 42, 102)(20, 80, 25, 85)(22, 82, 46, 106)(28, 88, 41, 101)(29, 89, 45, 105)(31, 91, 44, 104)(33, 93, 55, 115)(34, 94, 56, 116)(35, 95, 39, 99)(36, 96, 52, 112)(37, 97, 49, 109)(38, 98, 57, 117)(43, 103, 60, 120)(47, 107, 54, 114)(48, 108, 53, 113)(50, 110, 59, 119)(51, 111, 58, 118)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 134, 194, 136, 196)(126, 186, 139, 199, 132, 192)(128, 188, 144, 204, 146, 206)(130, 190, 149, 209, 142, 202)(131, 191, 151, 211, 145, 205)(133, 193, 154, 214, 138, 198)(135, 195, 141, 201, 156, 216)(137, 197, 158, 218, 159, 219)(140, 200, 165, 225, 163, 223)(143, 203, 168, 228, 148, 208)(147, 207, 170, 230, 157, 217)(150, 210, 162, 222, 171, 231)(152, 212, 174, 234, 173, 233)(153, 213, 164, 224, 169, 229)(155, 215, 167, 227, 172, 232)(160, 220, 179, 239, 178, 238)(161, 221, 177, 237, 180, 240)(166, 226, 175, 235, 176, 236) L = (1, 124)(2, 128)(3, 132)(4, 135)(5, 138)(6, 121)(7, 142)(8, 145)(9, 148)(10, 122)(11, 146)(12, 153)(13, 123)(14, 125)(15, 140)(16, 157)(17, 144)(18, 161)(19, 163)(20, 126)(21, 136)(22, 167)(23, 127)(24, 129)(25, 150)(26, 159)(27, 134)(28, 160)(29, 171)(30, 130)(31, 173)(32, 131)(33, 155)(34, 172)(35, 133)(36, 176)(37, 174)(38, 178)(39, 175)(40, 137)(41, 147)(42, 151)(43, 179)(44, 139)(45, 156)(46, 141)(47, 169)(48, 164)(49, 143)(50, 180)(51, 177)(52, 149)(53, 170)(54, 166)(55, 152)(56, 158)(57, 154)(58, 165)(59, 168)(60, 162)(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, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E15.955 Graph:: simple bipartite v = 50 e = 120 f = 42 degree seq :: [ 4^30, 6^20 ] E15.951 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3^-1 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^5, Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-1 * Y1)^2, (Y2^-1 * Y3^-1)^3, (Y1 * Y2^-1)^3, (Y3^2 * Y2^-1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2, Y1 * Y3^-1 * Y2 * Y3^2 * Y1 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 11, 71)(4, 64, 10, 70)(5, 65, 17, 77)(6, 66, 8, 68)(7, 67, 23, 83)(9, 69, 29, 89)(12, 72, 36, 96)(13, 73, 28, 88)(14, 74, 31, 91)(15, 75, 34, 94)(16, 76, 25, 85)(18, 78, 46, 106)(19, 79, 26, 86)(20, 80, 40, 100)(21, 81, 49, 109)(22, 82, 27, 87)(24, 84, 51, 111)(30, 90, 53, 113)(32, 92, 38, 98)(33, 93, 52, 112)(35, 95, 45, 105)(37, 97, 56, 116)(39, 99, 42, 102)(41, 101, 57, 117)(43, 103, 48, 108)(44, 104, 54, 114)(47, 107, 59, 119)(50, 110, 55, 115)(58, 118, 60, 120)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 134, 194, 136, 196)(126, 186, 140, 200, 141, 201)(128, 188, 146, 206, 148, 208)(130, 190, 152, 212, 153, 213)(131, 191, 149, 209, 155, 215)(132, 192, 157, 217, 150, 210)(133, 193, 159, 219, 160, 220)(135, 195, 163, 223, 161, 221)(137, 197, 165, 225, 143, 203)(138, 198, 144, 204, 168, 228)(139, 199, 169, 229, 162, 222)(142, 202, 167, 227, 173, 233)(145, 205, 170, 230, 158, 218)(147, 207, 176, 236, 174, 234)(151, 211, 172, 232, 175, 235)(154, 214, 178, 238, 166, 226)(156, 216, 179, 239, 164, 224)(171, 231, 180, 240, 177, 237) L = (1, 124)(2, 128)(3, 132)(4, 135)(5, 138)(6, 121)(7, 144)(8, 147)(9, 150)(10, 122)(11, 148)(12, 158)(13, 123)(14, 162)(15, 142)(16, 164)(17, 146)(18, 167)(19, 125)(20, 171)(21, 172)(22, 126)(23, 136)(24, 160)(25, 127)(26, 175)(27, 154)(28, 177)(29, 134)(30, 178)(31, 129)(32, 156)(33, 169)(34, 130)(35, 168)(36, 131)(37, 141)(38, 161)(39, 151)(40, 174)(41, 133)(42, 180)(43, 165)(44, 140)(45, 157)(46, 137)(47, 170)(48, 153)(49, 176)(50, 139)(51, 143)(52, 163)(53, 149)(54, 145)(55, 179)(56, 155)(57, 152)(58, 159)(59, 166)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E15.956 Graph:: simple bipartite v = 50 e = 120 f = 42 degree seq :: [ 4^30, 6^20 ] E15.952 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y1 * Y2)^2, (R * Y3)^2, Y1^5, (Y3 * Y1^-1)^3, Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 14, 74, 5, 65)(3, 63, 9, 69, 20, 80, 15, 75, 7, 67)(4, 64, 11, 71, 24, 84, 26, 86, 12, 72)(8, 68, 18, 78, 34, 94, 35, 95, 19, 79)(10, 70, 22, 82, 39, 99, 40, 100, 23, 83)(13, 73, 27, 87, 44, 104, 42, 102, 25, 85)(16, 76, 30, 90, 49, 109, 50, 110, 31, 91)(17, 77, 32, 92, 51, 111, 52, 112, 33, 93)(21, 81, 37, 97, 57, 117, 54, 114, 38, 98)(28, 88, 46, 106, 58, 118, 60, 120, 45, 105)(29, 89, 47, 107, 41, 101, 59, 119, 48, 108)(36, 96, 55, 115, 53, 113, 43, 103, 56, 116)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 129, 189)(126, 186, 135, 195)(128, 188, 137, 197)(131, 191, 143, 203)(132, 192, 142, 202)(133, 193, 141, 201)(134, 194, 140, 200)(136, 196, 149, 209)(138, 198, 153, 213)(139, 199, 152, 212)(144, 204, 160, 220)(145, 205, 157, 217)(146, 206, 159, 219)(147, 207, 158, 218)(148, 208, 156, 216)(150, 210, 168, 228)(151, 211, 167, 227)(154, 214, 172, 232)(155, 215, 171, 231)(161, 221, 170, 230)(162, 222, 177, 237)(163, 223, 178, 238)(164, 224, 174, 234)(165, 225, 175, 235)(166, 226, 176, 236)(169, 229, 179, 239)(173, 233, 180, 240) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 133)(6, 136)(7, 137)(8, 122)(9, 141)(10, 123)(11, 145)(12, 138)(13, 125)(14, 148)(15, 149)(16, 126)(17, 127)(18, 132)(19, 150)(20, 156)(21, 129)(22, 153)(23, 157)(24, 161)(25, 131)(26, 163)(27, 165)(28, 134)(29, 135)(30, 139)(31, 166)(32, 168)(33, 142)(34, 173)(35, 174)(36, 140)(37, 143)(38, 175)(39, 178)(40, 170)(41, 144)(42, 179)(43, 146)(44, 171)(45, 147)(46, 151)(47, 176)(48, 152)(49, 177)(50, 160)(51, 164)(52, 180)(53, 154)(54, 155)(55, 158)(56, 167)(57, 169)(58, 159)(59, 162)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.948 Graph:: simple bipartite v = 42 e = 120 f = 50 degree seq :: [ 4^30, 10^12 ] E15.953 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^5, (Y3 * Y1^-1)^3, Y1^-1 * Y3 * Y1^-1 * Y2 * Y1 * Y2, Y3 * Y1^-2 * Y2 * Y1^-2 * Y3 * Y1^2, (Y1^2 * Y2)^3 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 16, 76, 5, 65)(3, 63, 9, 69, 24, 84, 28, 88, 11, 71)(4, 64, 12, 72, 29, 89, 30, 90, 13, 73)(7, 67, 19, 79, 40, 100, 41, 101, 21, 81)(8, 68, 22, 82, 42, 102, 43, 103, 23, 83)(10, 70, 25, 85, 46, 106, 36, 96, 20, 80)(14, 74, 27, 87, 48, 108, 53, 113, 31, 91)(15, 75, 32, 92, 54, 114, 47, 107, 26, 86)(17, 77, 35, 95, 49, 109, 57, 117, 37, 97)(18, 78, 38, 98, 58, 118, 50, 110, 39, 99)(33, 93, 52, 112, 59, 119, 44, 104, 55, 115)(34, 94, 56, 116, 45, 105, 60, 120, 51, 111)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 134, 194)(126, 186, 137, 197)(128, 188, 140, 200)(129, 189, 142, 202)(131, 191, 146, 206)(132, 192, 147, 207)(133, 193, 141, 201)(135, 195, 145, 205)(136, 196, 153, 213)(138, 198, 156, 216)(139, 199, 158, 218)(143, 203, 157, 217)(144, 204, 164, 224)(148, 208, 169, 229)(149, 209, 170, 230)(150, 210, 165, 225)(151, 211, 171, 231)(152, 212, 172, 232)(154, 214, 166, 226)(155, 215, 176, 236)(159, 219, 175, 235)(160, 220, 173, 233)(161, 221, 179, 239)(162, 222, 180, 240)(163, 223, 174, 234)(167, 227, 178, 238)(168, 228, 177, 237) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 135)(6, 138)(7, 140)(8, 122)(9, 141)(10, 123)(11, 147)(12, 146)(13, 142)(14, 145)(15, 125)(16, 154)(17, 156)(18, 126)(19, 157)(20, 127)(21, 129)(22, 133)(23, 158)(24, 165)(25, 134)(26, 132)(27, 131)(28, 170)(29, 169)(30, 164)(31, 172)(32, 171)(33, 166)(34, 136)(35, 175)(36, 137)(37, 139)(38, 143)(39, 176)(40, 174)(41, 180)(42, 179)(43, 173)(44, 150)(45, 144)(46, 153)(47, 177)(48, 178)(49, 149)(50, 148)(51, 152)(52, 151)(53, 163)(54, 160)(55, 155)(56, 159)(57, 167)(58, 168)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.947 Graph:: simple bipartite v = 42 e = 120 f = 50 degree seq :: [ 4^30, 10^12 ] E15.954 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^5, (Y3 * Y1^-2)^2, Y3^-1 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y2, Y1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y2 * Y1^-1)^3, Y1 * Y3^-1 * Y2 * Y1 * Y3 * Y1^-1 * Y3^-1, Y1^2 * Y2 * Y1^-2 * Y2 * Y3 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 5, 65)(3, 63, 11, 71, 34, 94, 41, 101, 13, 73)(4, 64, 15, 75, 43, 103, 25, 85, 16, 76)(6, 66, 21, 81, 52, 112, 55, 115, 22, 82)(8, 68, 26, 86, 48, 108, 50, 110, 28, 88)(9, 69, 30, 90, 59, 119, 53, 113, 31, 91)(10, 70, 32, 92, 18, 78, 46, 106, 33, 93)(12, 72, 38, 98, 23, 83, 56, 116, 39, 99)(14, 74, 42, 102, 60, 120, 58, 118, 29, 89)(17, 77, 49, 109, 54, 114, 57, 117, 35, 95)(20, 80, 37, 97, 24, 84, 40, 100, 44, 104)(27, 87, 45, 105, 51, 111, 47, 107, 36, 96)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 134, 194)(125, 185, 137, 197)(126, 186, 132, 192)(127, 187, 143, 203)(129, 189, 149, 209)(130, 190, 147, 207)(131, 191, 155, 215)(133, 193, 146, 206)(135, 195, 151, 211)(136, 196, 166, 226)(138, 198, 162, 222)(139, 199, 171, 231)(140, 200, 170, 230)(141, 201, 160, 220)(142, 202, 156, 216)(144, 204, 178, 238)(145, 205, 177, 237)(148, 208, 176, 236)(150, 210, 157, 217)(152, 212, 175, 235)(153, 213, 174, 234)(154, 214, 163, 223)(158, 218, 167, 227)(159, 219, 164, 224)(161, 221, 173, 233)(165, 225, 169, 229)(168, 228, 179, 239)(172, 232, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 126)(5, 138)(6, 121)(7, 144)(8, 147)(9, 130)(10, 122)(11, 156)(12, 134)(13, 160)(14, 123)(15, 164)(16, 167)(17, 170)(18, 140)(19, 172)(20, 125)(21, 146)(22, 155)(23, 177)(24, 145)(25, 127)(26, 174)(27, 149)(28, 175)(29, 128)(30, 142)(31, 169)(32, 176)(33, 133)(34, 152)(35, 150)(36, 157)(37, 131)(38, 166)(39, 151)(40, 153)(41, 180)(42, 137)(43, 148)(44, 165)(45, 135)(46, 179)(47, 168)(48, 136)(49, 159)(50, 162)(51, 161)(52, 173)(53, 139)(54, 141)(55, 163)(56, 154)(57, 178)(58, 143)(59, 158)(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) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.949 Graph:: simple bipartite v = 42 e = 120 f = 50 degree seq :: [ 4^30, 10^12 ] E15.955 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^5, Y1^5, Y1 * Y2 * Y1^-2 * Y3^-2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y2 * Y1^-1, Y1 * Y3 * Y1^-1 * Y2 * Y1 * Y2, Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y2 * Y1 * Y3^-2 * Y2 * Y1^-1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 20, 80, 5, 65)(3, 63, 11, 71, 38, 98, 43, 103, 13, 73)(4, 64, 15, 75, 42, 102, 29, 89, 17, 77)(6, 66, 22, 82, 54, 114, 26, 86, 23, 83)(8, 68, 28, 88, 49, 109, 16, 76, 30, 90)(9, 69, 32, 92, 21, 81, 51, 111, 34, 94)(10, 70, 35, 95, 41, 101, 53, 113, 36, 96)(12, 72, 40, 100, 19, 79, 48, 108, 27, 87)(14, 74, 45, 105, 60, 120, 55, 115, 31, 91)(18, 78, 39, 99, 57, 117, 44, 104, 50, 110)(24, 84, 25, 85, 47, 107, 59, 119, 33, 93)(37, 97, 52, 112, 58, 118, 46, 106, 56, 116)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 134, 194)(125, 185, 138, 198)(126, 186, 132, 192)(127, 187, 145, 205)(129, 189, 151, 211)(130, 190, 149, 209)(131, 191, 156, 216)(133, 193, 154, 214)(135, 195, 167, 227)(136, 196, 166, 226)(137, 197, 170, 230)(139, 199, 165, 225)(140, 200, 172, 232)(141, 201, 155, 215)(142, 202, 162, 222)(143, 203, 159, 219)(144, 204, 161, 221)(146, 206, 175, 235)(147, 207, 171, 231)(148, 208, 168, 228)(150, 210, 174, 234)(152, 212, 178, 238)(153, 213, 177, 237)(157, 217, 160, 220)(158, 218, 176, 236)(163, 223, 179, 239)(164, 224, 169, 229)(173, 233, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 136)(5, 139)(6, 121)(7, 146)(8, 149)(9, 153)(10, 122)(11, 159)(12, 161)(13, 162)(14, 123)(15, 152)(16, 144)(17, 158)(18, 155)(19, 163)(20, 173)(21, 125)(22, 154)(23, 156)(24, 126)(25, 171)(26, 176)(27, 127)(28, 131)(29, 160)(30, 141)(31, 128)(32, 143)(33, 157)(34, 169)(35, 174)(36, 168)(37, 130)(38, 175)(39, 178)(40, 177)(41, 166)(42, 140)(43, 150)(44, 133)(45, 138)(46, 134)(47, 148)(48, 135)(49, 180)(50, 147)(51, 137)(52, 142)(53, 164)(54, 179)(55, 145)(56, 170)(57, 151)(58, 167)(59, 165)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.950 Graph:: simple bipartite v = 42 e = 120 f = 50 degree seq :: [ 4^30, 10^12 ] E15.956 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 5}) Quotient :: dipole Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^5, Y1^5, (Y1^-1 * R * Y2)^2, Y3 * Y1 * Y3^-1 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y3 * Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^3, (Y2 * Y1^-1)^3, Y2 * Y3 * Y1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 5, 65)(3, 63, 11, 71, 34, 94, 33, 93, 13, 73)(4, 64, 15, 75, 41, 101, 32, 92, 10, 70)(6, 66, 18, 78, 27, 87, 49, 109, 21, 81)(8, 68, 26, 86, 54, 114, 53, 113, 28, 88)(9, 69, 30, 90, 56, 116, 39, 99, 25, 85)(12, 72, 38, 98, 42, 102, 20, 80, 37, 97)(14, 74, 40, 100, 58, 118, 52, 112, 29, 89)(16, 76, 43, 103, 36, 96, 51, 111, 23, 83)(17, 77, 44, 104, 50, 110, 22, 82, 35, 95)(24, 84, 45, 105, 59, 119, 55, 115, 47, 107)(31, 91, 57, 117, 48, 108, 60, 120, 46, 106)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 134, 194)(125, 185, 137, 197)(126, 186, 132, 192)(127, 187, 143, 203)(129, 189, 149, 209)(130, 190, 147, 207)(131, 191, 155, 215)(133, 193, 146, 206)(135, 195, 145, 205)(136, 196, 148, 208)(138, 198, 160, 220)(139, 199, 166, 226)(140, 200, 165, 225)(141, 201, 156, 216)(142, 202, 159, 219)(144, 204, 172, 232)(150, 210, 167, 227)(151, 211, 171, 231)(152, 212, 168, 228)(153, 213, 175, 235)(154, 214, 176, 236)(157, 217, 178, 238)(158, 218, 163, 223)(161, 221, 170, 230)(162, 222, 173, 233)(164, 224, 180, 240)(169, 229, 177, 237)(174, 234, 179, 239) L = (1, 124)(2, 129)(3, 132)(4, 136)(5, 138)(6, 121)(7, 144)(8, 147)(9, 151)(10, 122)(11, 156)(12, 159)(13, 160)(14, 123)(15, 162)(16, 142)(17, 165)(18, 146)(19, 157)(20, 125)(21, 155)(22, 126)(23, 135)(24, 164)(25, 127)(26, 168)(27, 175)(28, 134)(29, 128)(30, 141)(31, 153)(32, 133)(33, 130)(34, 177)(35, 178)(36, 167)(37, 131)(38, 161)(39, 148)(40, 137)(41, 179)(42, 180)(43, 154)(44, 173)(45, 152)(46, 150)(47, 139)(48, 140)(49, 176)(50, 163)(51, 149)(52, 143)(53, 145)(54, 170)(55, 171)(56, 158)(57, 174)(58, 166)(59, 169)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.951 Graph:: simple bipartite v = 42 e = 120 f = 50 degree seq :: [ 4^30, 10^12 ] E15.957 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 30}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, 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 ] Map:: non-degenerate R = (1, 61, 2, 62)(3, 63, 5, 65)(4, 64, 8, 68)(6, 66, 10, 70)(7, 67, 11, 71)(9, 69, 13, 73)(12, 72, 16, 76)(14, 74, 18, 78)(15, 75, 19, 79)(17, 77, 21, 81)(20, 80, 24, 84)(22, 82, 26, 86)(23, 83, 27, 87)(25, 85, 47, 107)(28, 88, 49, 109)(29, 89, 51, 111)(30, 90, 53, 113)(31, 91, 55, 115)(32, 92, 58, 118)(33, 93, 57, 117)(34, 94, 59, 119)(35, 95, 60, 120)(36, 96, 52, 112)(37, 97, 50, 110)(38, 98, 54, 114)(39, 99, 56, 116)(40, 100, 48, 108)(41, 101, 46, 106)(42, 102, 45, 105)(43, 103, 44, 104)(121, 181, 123, 183)(122, 182, 125, 185)(124, 184, 127, 187)(126, 186, 129, 189)(128, 188, 131, 191)(130, 190, 133, 193)(132, 192, 135, 195)(134, 194, 137, 197)(136, 196, 139, 199)(138, 198, 141, 201)(140, 200, 143, 203)(142, 202, 145, 205)(144, 204, 147, 207)(146, 206, 167, 227)(148, 208, 158, 218)(149, 209, 151, 211)(150, 210, 153, 213)(152, 212, 155, 215)(154, 214, 157, 217)(156, 216, 159, 219)(160, 220, 162, 222)(161, 221, 163, 223)(164, 224, 166, 226)(165, 225, 168, 228)(169, 229, 174, 234)(170, 230, 179, 239)(171, 231, 175, 235)(172, 232, 176, 236)(173, 233, 177, 237)(178, 238, 180, 240) L = (1, 124)(2, 126)(3, 127)(4, 121)(5, 129)(6, 122)(7, 123)(8, 132)(9, 125)(10, 134)(11, 135)(12, 128)(13, 137)(14, 130)(15, 131)(16, 140)(17, 133)(18, 142)(19, 143)(20, 136)(21, 145)(22, 138)(23, 139)(24, 148)(25, 141)(26, 159)(27, 158)(28, 144)(29, 172)(30, 174)(31, 176)(32, 173)(33, 169)(34, 171)(35, 177)(36, 167)(37, 175)(38, 147)(39, 146)(40, 178)(41, 179)(42, 180)(43, 170)(44, 168)(45, 166)(46, 165)(47, 156)(48, 164)(49, 153)(50, 163)(51, 154)(52, 149)(53, 152)(54, 150)(55, 157)(56, 151)(57, 155)(58, 160)(59, 161)(60, 162)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E15.958 Graph:: simple bipartite v = 60 e = 120 f = 32 degree seq :: [ 4^60 ] E15.958 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 30}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y1^8 * Y3 * Y1^-7 * Y2, Y1^2 * Y3 * Y1^-1 * Y2 * Y1^6 * Y3 * Y2 * Y1^6 * Y3 * Y2 ] Map:: non-degenerate R = (1, 61, 2, 62, 6, 66, 13, 73, 21, 81, 29, 89, 37, 97, 45, 105, 53, 113, 58, 118, 50, 110, 42, 102, 34, 94, 26, 86, 18, 78, 10, 70, 16, 76, 24, 84, 32, 92, 40, 100, 48, 108, 56, 116, 60, 120, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80, 12, 72, 5, 65)(3, 63, 9, 69, 17, 77, 25, 85, 33, 93, 41, 101, 49, 109, 57, 117, 55, 115, 47, 107, 39, 99, 31, 91, 23, 83, 15, 75, 8, 68, 4, 64, 11, 71, 19, 79, 27, 87, 35, 95, 43, 103, 51, 111, 59, 119, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 14, 74, 7, 67)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 129, 189)(126, 186, 134, 194)(128, 188, 136, 196)(131, 191, 138, 198)(132, 192, 137, 197)(133, 193, 142, 202)(135, 195, 144, 204)(139, 199, 146, 206)(140, 200, 145, 205)(141, 201, 150, 210)(143, 203, 152, 212)(147, 207, 154, 214)(148, 208, 153, 213)(149, 209, 158, 218)(151, 211, 160, 220)(155, 215, 162, 222)(156, 216, 161, 221)(157, 217, 166, 226)(159, 219, 168, 228)(163, 223, 170, 230)(164, 224, 169, 229)(165, 225, 174, 234)(167, 227, 176, 236)(171, 231, 178, 238)(172, 232, 177, 237)(173, 233, 179, 239)(175, 235, 180, 240) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 131)(6, 135)(7, 136)(8, 122)(9, 138)(10, 123)(11, 125)(12, 139)(13, 143)(14, 144)(15, 126)(16, 127)(17, 146)(18, 129)(19, 132)(20, 147)(21, 151)(22, 152)(23, 133)(24, 134)(25, 154)(26, 137)(27, 140)(28, 155)(29, 159)(30, 160)(31, 141)(32, 142)(33, 162)(34, 145)(35, 148)(36, 163)(37, 167)(38, 168)(39, 149)(40, 150)(41, 170)(42, 153)(43, 156)(44, 171)(45, 175)(46, 176)(47, 157)(48, 158)(49, 178)(50, 161)(51, 164)(52, 179)(53, 177)(54, 180)(55, 165)(56, 166)(57, 173)(58, 169)(59, 172)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^4 ), ( 4^60 ) } Outer automorphisms :: reflexible Dual of E15.957 Graph:: bipartite v = 32 e = 120 f = 60 degree seq :: [ 4^30, 60^2 ] E15.959 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 30}) Quotient :: edge Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1^4, (F * T1)^2, T2 * T1 * T2 * T1^-1, T1^-2 * T2^15 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 58, 50, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 51, 59, 56, 48, 40, 32, 24, 16, 8)(61, 62, 66, 64)(63, 68, 73, 70)(65, 67, 74, 71)(69, 76, 81, 78)(72, 75, 82, 79)(77, 84, 89, 86)(80, 83, 90, 87)(85, 92, 97, 94)(88, 91, 98, 95)(93, 100, 105, 102)(96, 99, 106, 103)(101, 108, 113, 110)(104, 107, 114, 111)(109, 116, 120, 118)(112, 115, 117, 119) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^4 ), ( 8^30 ) } Outer automorphisms :: reflexible Dual of E15.960 Transitivity :: ET+ Graph:: bipartite v = 17 e = 60 f = 15 degree seq :: [ 4^15, 30^2 ] E15.960 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 30}) Quotient :: loop Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ F^2, T2^4, T1^2 * T2^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 61, 3, 63, 6, 66, 5, 65)(2, 62, 7, 67, 4, 64, 8, 68)(9, 69, 13, 73, 10, 70, 14, 74)(11, 71, 15, 75, 12, 72, 16, 76)(17, 77, 21, 81, 18, 78, 22, 82)(19, 79, 23, 83, 20, 80, 24, 84)(25, 85, 29, 89, 26, 86, 30, 90)(27, 87, 45, 105, 28, 88, 47, 107)(31, 91, 49, 109, 34, 94, 51, 111)(32, 92, 52, 112, 33, 93, 54, 114)(35, 95, 57, 117, 36, 96, 59, 119)(37, 97, 58, 118, 38, 98, 60, 120)(39, 99, 55, 115, 40, 100, 53, 113)(41, 101, 50, 110, 42, 102, 56, 116)(43, 103, 46, 106, 44, 104, 48, 108) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 70)(6, 64)(7, 71)(8, 72)(9, 65)(10, 63)(11, 68)(12, 67)(13, 77)(14, 78)(15, 79)(16, 80)(17, 74)(18, 73)(19, 76)(20, 75)(21, 85)(22, 86)(23, 87)(24, 88)(25, 82)(26, 81)(27, 84)(28, 83)(29, 94)(30, 91)(31, 89)(32, 105)(33, 107)(34, 90)(35, 111)(36, 109)(37, 114)(38, 112)(39, 119)(40, 117)(41, 120)(42, 118)(43, 113)(44, 115)(45, 93)(46, 116)(47, 92)(48, 110)(49, 95)(50, 106)(51, 96)(52, 97)(53, 104)(54, 98)(55, 103)(56, 108)(57, 99)(58, 101)(59, 100)(60, 102) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E15.959 Transitivity :: ET+ VT+ AT Graph:: v = 15 e = 60 f = 17 degree seq :: [ 8^15 ] E15.961 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 30}) Quotient :: dipole Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1 * Y2^7 * Y1 * Y2^-7, Y2^30 ] Map:: R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 8, 68, 13, 73, 10, 70)(5, 65, 7, 67, 14, 74, 11, 71)(9, 69, 16, 76, 21, 81, 18, 78)(12, 72, 15, 75, 22, 82, 19, 79)(17, 77, 24, 84, 29, 89, 26, 86)(20, 80, 23, 83, 30, 90, 27, 87)(25, 85, 32, 92, 37, 97, 34, 94)(28, 88, 31, 91, 38, 98, 35, 95)(33, 93, 40, 100, 45, 105, 42, 102)(36, 96, 39, 99, 46, 106, 43, 103)(41, 101, 48, 108, 53, 113, 50, 110)(44, 104, 47, 107, 54, 114, 51, 111)(49, 109, 56, 116, 60, 120, 58, 118)(52, 112, 55, 115, 57, 117, 59, 119)(121, 181, 123, 183, 129, 189, 137, 197, 145, 205, 153, 213, 161, 221, 169, 229, 177, 237, 174, 234, 166, 226, 158, 218, 150, 210, 142, 202, 134, 194, 126, 186, 133, 193, 141, 201, 149, 209, 157, 217, 165, 225, 173, 233, 180, 240, 172, 232, 164, 224, 156, 216, 148, 208, 140, 200, 132, 192, 125, 185)(122, 182, 127, 187, 135, 195, 143, 203, 151, 211, 159, 219, 167, 227, 175, 235, 178, 238, 170, 230, 162, 222, 154, 214, 146, 206, 138, 198, 130, 190, 124, 184, 131, 191, 139, 199, 147, 207, 155, 215, 163, 223, 171, 231, 179, 239, 176, 236, 168, 228, 160, 220, 152, 212, 144, 204, 136, 196, 128, 188) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 133)(7, 135)(8, 122)(9, 137)(10, 124)(11, 139)(12, 125)(13, 141)(14, 126)(15, 143)(16, 128)(17, 145)(18, 130)(19, 147)(20, 132)(21, 149)(22, 134)(23, 151)(24, 136)(25, 153)(26, 138)(27, 155)(28, 140)(29, 157)(30, 142)(31, 159)(32, 144)(33, 161)(34, 146)(35, 163)(36, 148)(37, 165)(38, 150)(39, 167)(40, 152)(41, 169)(42, 154)(43, 171)(44, 156)(45, 173)(46, 158)(47, 175)(48, 160)(49, 177)(50, 162)(51, 179)(52, 164)(53, 180)(54, 166)(55, 178)(56, 168)(57, 174)(58, 170)(59, 176)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.962 Graph:: bipartite v = 17 e = 120 f = 75 degree seq :: [ 8^15, 60^2 ] E15.962 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 30}) Quotient :: dipole Aut^+ = C15 : C4 (small group id <60, 3>) Aut = (C30 x C2) : C2 (small group id <120, 30>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^15, (Y3^-1 * Y1^-1)^30 ] Map:: R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 124, 184)(123, 183, 128, 188, 133, 193, 130, 190)(125, 185, 127, 187, 134, 194, 131, 191)(129, 189, 136, 196, 141, 201, 138, 198)(132, 192, 135, 195, 142, 202, 139, 199)(137, 197, 144, 204, 149, 209, 146, 206)(140, 200, 143, 203, 150, 210, 147, 207)(145, 205, 152, 212, 157, 217, 154, 214)(148, 208, 151, 211, 158, 218, 155, 215)(153, 213, 160, 220, 165, 225, 162, 222)(156, 216, 159, 219, 166, 226, 163, 223)(161, 221, 168, 228, 173, 233, 170, 230)(164, 224, 167, 227, 174, 234, 171, 231)(169, 229, 176, 236, 180, 240, 178, 238)(172, 232, 175, 235, 177, 237, 179, 239) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 133)(7, 135)(8, 122)(9, 137)(10, 124)(11, 139)(12, 125)(13, 141)(14, 126)(15, 143)(16, 128)(17, 145)(18, 130)(19, 147)(20, 132)(21, 149)(22, 134)(23, 151)(24, 136)(25, 153)(26, 138)(27, 155)(28, 140)(29, 157)(30, 142)(31, 159)(32, 144)(33, 161)(34, 146)(35, 163)(36, 148)(37, 165)(38, 150)(39, 167)(40, 152)(41, 169)(42, 154)(43, 171)(44, 156)(45, 173)(46, 158)(47, 175)(48, 160)(49, 177)(50, 162)(51, 179)(52, 164)(53, 180)(54, 166)(55, 178)(56, 168)(57, 174)(58, 170)(59, 176)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8, 60 ), ( 8, 60, 8, 60, 8, 60, 8, 60 ) } Outer automorphisms :: reflexible Dual of E15.961 Graph:: simple bipartite v = 75 e = 120 f = 17 degree seq :: [ 2^60, 8^15 ] E15.963 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 60, 60}) Quotient :: regular Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^30 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 39, 35, 31, 34, 38, 42, 44, 46, 48, 60, 57, 53, 50, 51, 54, 49, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 40, 36, 32, 29, 30, 33, 37, 41, 43, 45, 47, 59, 56, 52, 55, 58, 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, 40)(28, 49)(29, 31)(30, 34)(32, 35)(33, 38)(36, 39)(37, 42)(41, 44)(43, 46)(45, 48)(47, 60)(50, 52)(51, 55)(53, 56)(54, 58)(57, 59) local type(s) :: { ( 60^60 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 30 f = 1 degree seq :: [ 60 ] E15.964 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 60, 60}) Quotient :: edge Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^30 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 29, 31, 34, 36, 38, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 45, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 33, 30, 32, 35, 37, 39, 41, 43, 50, 47, 49, 52, 54, 56, 58, 60, 28, 24, 20, 16, 12, 8, 4)(61, 62)(63, 65)(64, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 93)(88, 105)(89, 90)(91, 92)(94, 95)(96, 97)(98, 99)(100, 101)(102, 103)(104, 110)(106, 107)(108, 109)(111, 112)(113, 114)(115, 116)(117, 118)(119, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 120, 120 ), ( 120^60 ) } Outer automorphisms :: reflexible Dual of E15.965 Transitivity :: ET+ Graph:: bipartite v = 31 e = 60 f = 1 degree seq :: [ 2^30, 60 ] E15.965 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 60, 60}) Quotient :: loop Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^30 * T1 ] Map:: R = (1, 61, 3, 63, 7, 67, 11, 71, 15, 75, 19, 79, 23, 83, 27, 87, 29, 89, 31, 91, 34, 94, 36, 96, 38, 98, 40, 100, 42, 102, 44, 104, 46, 106, 48, 108, 51, 111, 53, 113, 55, 115, 57, 117, 59, 119, 45, 105, 26, 86, 22, 82, 18, 78, 14, 74, 10, 70, 6, 66, 2, 62, 5, 65, 9, 69, 13, 73, 17, 77, 21, 81, 25, 85, 33, 93, 30, 90, 32, 92, 35, 95, 37, 97, 39, 99, 41, 101, 43, 103, 50, 110, 47, 107, 49, 109, 52, 112, 54, 114, 56, 116, 58, 118, 60, 120, 28, 88, 24, 84, 20, 80, 16, 76, 12, 72, 8, 68, 4, 64) L = (1, 62)(2, 61)(3, 65)(4, 66)(5, 63)(6, 64)(7, 69)(8, 70)(9, 67)(10, 68)(11, 73)(12, 74)(13, 71)(14, 72)(15, 77)(16, 78)(17, 75)(18, 76)(19, 81)(20, 82)(21, 79)(22, 80)(23, 85)(24, 86)(25, 83)(26, 84)(27, 93)(28, 105)(29, 90)(30, 89)(31, 92)(32, 91)(33, 87)(34, 95)(35, 94)(36, 97)(37, 96)(38, 99)(39, 98)(40, 101)(41, 100)(42, 103)(43, 102)(44, 110)(45, 88)(46, 107)(47, 106)(48, 109)(49, 108)(50, 104)(51, 112)(52, 111)(53, 114)(54, 113)(55, 116)(56, 115)(57, 118)(58, 117)(59, 120)(60, 119) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E15.964 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 60 f = 31 degree seq :: [ 120 ] E15.966 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 60, 60}) Quotient :: dipole Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |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, Y2^30 * Y1, (Y3 * Y2^-1)^60 ] Map:: R = (1, 61, 2, 62)(3, 63, 5, 65)(4, 64, 6, 66)(7, 67, 9, 69)(8, 68, 10, 70)(11, 71, 13, 73)(12, 72, 14, 74)(15, 75, 17, 77)(16, 76, 18, 78)(19, 79, 21, 81)(20, 80, 22, 82)(23, 83, 25, 85)(24, 84, 26, 86)(27, 87, 32, 92)(28, 88, 45, 105)(29, 89, 30, 90)(31, 91, 33, 93)(34, 94, 35, 95)(36, 96, 37, 97)(38, 98, 39, 99)(40, 100, 41, 101)(42, 102, 43, 103)(44, 104, 49, 109)(46, 106, 47, 107)(48, 108, 50, 110)(51, 111, 52, 112)(53, 113, 54, 114)(55, 115, 56, 116)(57, 117, 58, 118)(59, 119, 60, 120)(121, 181, 123, 183, 127, 187, 131, 191, 135, 195, 139, 199, 143, 203, 147, 207, 150, 210, 153, 213, 155, 215, 157, 217, 159, 219, 161, 221, 163, 223, 169, 229, 166, 226, 168, 228, 171, 231, 173, 233, 175, 235, 177, 237, 179, 239, 165, 225, 146, 206, 142, 202, 138, 198, 134, 194, 130, 190, 126, 186, 122, 182, 125, 185, 129, 189, 133, 193, 137, 197, 141, 201, 145, 205, 152, 212, 149, 209, 151, 211, 154, 214, 156, 216, 158, 218, 160, 220, 162, 222, 164, 224, 167, 227, 170, 230, 172, 232, 174, 234, 176, 236, 178, 238, 180, 240, 148, 208, 144, 204, 140, 200, 136, 196, 132, 192, 128, 188, 124, 184) L = (1, 122)(2, 121)(3, 125)(4, 126)(5, 123)(6, 124)(7, 129)(8, 130)(9, 127)(10, 128)(11, 133)(12, 134)(13, 131)(14, 132)(15, 137)(16, 138)(17, 135)(18, 136)(19, 141)(20, 142)(21, 139)(22, 140)(23, 145)(24, 146)(25, 143)(26, 144)(27, 152)(28, 165)(29, 150)(30, 149)(31, 153)(32, 147)(33, 151)(34, 155)(35, 154)(36, 157)(37, 156)(38, 159)(39, 158)(40, 161)(41, 160)(42, 163)(43, 162)(44, 169)(45, 148)(46, 167)(47, 166)(48, 170)(49, 164)(50, 168)(51, 172)(52, 171)(53, 174)(54, 173)(55, 176)(56, 175)(57, 178)(58, 177)(59, 180)(60, 179)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) } Outer automorphisms :: reflexible Dual of E15.967 Graph:: bipartite v = 31 e = 120 f = 61 degree seq :: [ 4^30, 120 ] E15.967 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 60, 60}) Quotient :: dipole Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^30 ] Map:: R = (1, 61, 2, 62, 5, 65, 9, 69, 13, 73, 17, 77, 21, 81, 25, 85, 43, 103, 39, 99, 35, 95, 31, 91, 34, 94, 38, 98, 42, 102, 46, 106, 48, 108, 50, 110, 60, 120, 58, 118, 56, 116, 54, 114, 52, 112, 51, 111, 27, 87, 23, 83, 19, 79, 15, 75, 11, 71, 7, 67, 3, 63, 6, 66, 10, 70, 14, 74, 18, 78, 22, 82, 26, 86, 44, 104, 40, 100, 36, 96, 32, 92, 29, 89, 30, 90, 33, 93, 37, 97, 41, 101, 45, 105, 47, 107, 49, 109, 59, 119, 57, 117, 55, 115, 53, 113, 28, 88, 24, 84, 20, 80, 16, 76, 12, 72, 8, 68, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 126)(3, 121)(4, 127)(5, 130)(6, 122)(7, 124)(8, 131)(9, 134)(10, 125)(11, 128)(12, 135)(13, 138)(14, 129)(15, 132)(16, 139)(17, 142)(18, 133)(19, 136)(20, 143)(21, 146)(22, 137)(23, 140)(24, 147)(25, 164)(26, 141)(27, 144)(28, 171)(29, 151)(30, 154)(31, 149)(32, 155)(33, 158)(34, 150)(35, 152)(36, 159)(37, 162)(38, 153)(39, 156)(40, 163)(41, 166)(42, 157)(43, 160)(44, 145)(45, 168)(46, 161)(47, 170)(48, 165)(49, 180)(50, 167)(51, 148)(52, 173)(53, 172)(54, 175)(55, 174)(56, 177)(57, 176)(58, 179)(59, 178)(60, 169)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 120 ), ( 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120 ) } Outer automorphisms :: reflexible Dual of E15.966 Graph:: bipartite v = 61 e = 120 f = 31 degree seq :: [ 2^60, 120 ] E15.968 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 31, 62}) Quotient :: regular Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-31 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 62, 58, 43, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 29, 30, 31, 33, 35, 37, 39, 41, 47, 49, 51, 53, 55, 57, 59, 60, 61, 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, 29)(28, 43)(30, 32)(31, 34)(33, 36)(35, 38)(37, 40)(39, 42)(41, 44)(45, 47)(46, 49)(48, 51)(50, 53)(52, 55)(54, 57)(56, 59)(58, 61)(60, 62) local type(s) :: { ( 31^62 ) } Outer automorphisms :: reflexible Dual of E15.969 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 31 f = 2 degree seq :: [ 62 ] E15.969 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 31, 62}) Quotient :: regular Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^31 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 44, 40, 36, 32, 29, 30, 33, 37, 41, 45, 48, 51, 60, 58, 56, 54, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 50, 47, 43, 39, 35, 31, 34, 38, 42, 46, 49, 52, 62, 61, 59, 57, 55, 53, 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, 50)(28, 53)(29, 31)(30, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 49)(48, 52)(51, 62)(54, 55)(56, 57)(58, 59)(60, 61) local type(s) :: { ( 62^31 ) } Outer automorphisms :: reflexible Dual of E15.968 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 31 f = 1 degree seq :: [ 31^2 ] E15.970 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 31, 62}) Quotient :: edge Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^31 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 30, 33, 35, 37, 39, 41, 43, 49, 46, 48, 51, 53, 55, 57, 59, 61, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 32, 29, 31, 34, 36, 38, 40, 42, 44, 47, 50, 52, 54, 56, 58, 60, 62, 45, 26, 22, 18, 14, 10, 6)(63, 64)(65, 67)(66, 68)(69, 71)(70, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 83)(82, 84)(85, 87)(86, 88)(89, 94)(90, 107)(91, 92)(93, 95)(96, 97)(98, 99)(100, 101)(102, 103)(104, 105)(106, 111)(108, 109)(110, 112)(113, 114)(115, 116)(117, 118)(119, 120)(121, 122)(123, 124) L = (1, 63)(2, 64)(3, 65)(4, 66)(5, 67)(6, 68)(7, 69)(8, 70)(9, 71)(10, 72)(11, 73)(12, 74)(13, 75)(14, 76)(15, 77)(16, 78)(17, 79)(18, 80)(19, 81)(20, 82)(21, 83)(22, 84)(23, 85)(24, 86)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 92)(31, 93)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 124, 124 ), ( 124^31 ) } Outer automorphisms :: reflexible Dual of E15.974 Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 62 f = 1 degree seq :: [ 2^31, 31^2 ] E15.971 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 31, 62}) Quotient :: edge Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^29, T2^-2 * T1^13 * T2^-16 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 53, 58, 57, 60, 62, 51, 50, 47, 46, 41, 38, 32, 37, 34, 40, 44, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 54, 55, 56, 59, 61, 52, 49, 48, 45, 42, 36, 35, 31, 33, 39, 43, 28, 23, 20, 15, 12, 6, 5)(63, 64, 68, 73, 77, 81, 85, 89, 105, 102, 95, 99, 97, 100, 104, 108, 110, 112, 114, 124, 121, 119, 117, 115, 92, 87, 84, 79, 76, 71, 66)(65, 69, 67, 70, 74, 78, 82, 86, 90, 106, 101, 96, 93, 94, 98, 103, 107, 109, 111, 113, 123, 122, 118, 120, 116, 91, 88, 83, 80, 75, 72) L = (1, 63)(2, 64)(3, 65)(4, 66)(5, 67)(6, 68)(7, 69)(8, 70)(9, 71)(10, 72)(11, 73)(12, 74)(13, 75)(14, 76)(15, 77)(16, 78)(17, 79)(18, 80)(19, 81)(20, 82)(21, 83)(22, 84)(23, 85)(24, 86)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 92)(31, 93)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 4^31 ), ( 4^62 ) } Outer automorphisms :: reflexible Dual of E15.975 Transitivity :: ET+ Graph:: bipartite v = 3 e = 62 f = 31 degree seq :: [ 31^2, 62 ] E15.972 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 31, 62}) Quotient :: edge Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-31 ] 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, 34)(28, 45)(29, 31)(30, 33)(32, 36)(35, 38)(37, 40)(39, 42)(41, 44)(43, 51)(46, 48)(47, 50)(49, 53)(52, 55)(54, 57)(56, 59)(58, 61)(60, 62)(63, 64, 67, 71, 75, 79, 83, 87, 91, 92, 94, 97, 99, 101, 103, 105, 108, 109, 111, 114, 116, 118, 120, 122, 107, 89, 85, 81, 77, 73, 69, 65, 68, 72, 76, 80, 84, 88, 96, 93, 95, 98, 100, 102, 104, 106, 113, 110, 112, 115, 117, 119, 121, 123, 124, 90, 86, 82, 78, 74, 70, 66) L = (1, 63)(2, 64)(3, 65)(4, 66)(5, 67)(6, 68)(7, 69)(8, 70)(9, 71)(10, 72)(11, 73)(12, 74)(13, 75)(14, 76)(15, 77)(16, 78)(17, 79)(18, 80)(19, 81)(20, 82)(21, 83)(22, 84)(23, 85)(24, 86)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 92)(31, 93)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124) local type(s) :: { ( 62, 62 ), ( 62^62 ) } Outer automorphisms :: reflexible Dual of E15.973 Transitivity :: ET+ Graph:: bipartite v = 32 e = 62 f = 2 degree seq :: [ 2^31, 62 ] E15.973 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 31, 62}) Quotient :: loop Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^31 ] Map:: R = (1, 63, 3, 65, 7, 69, 11, 73, 15, 77, 19, 81, 23, 85, 27, 89, 34, 96, 30, 92, 33, 95, 37, 99, 39, 101, 41, 103, 43, 105, 45, 107, 55, 117, 51, 113, 48, 110, 50, 112, 54, 116, 57, 119, 59, 121, 61, 123, 28, 90, 24, 86, 20, 82, 16, 78, 12, 74, 8, 70, 4, 66)(2, 64, 5, 67, 9, 71, 13, 75, 17, 79, 21, 83, 25, 87, 36, 98, 32, 94, 29, 91, 31, 93, 35, 97, 38, 100, 40, 102, 42, 104, 44, 106, 46, 108, 53, 115, 49, 111, 52, 114, 56, 118, 58, 120, 60, 122, 62, 124, 47, 109, 26, 88, 22, 84, 18, 80, 14, 76, 10, 72, 6, 68) L = (1, 64)(2, 63)(3, 67)(4, 68)(5, 65)(6, 66)(7, 71)(8, 72)(9, 69)(10, 70)(11, 75)(12, 76)(13, 73)(14, 74)(15, 79)(16, 80)(17, 77)(18, 78)(19, 83)(20, 84)(21, 81)(22, 82)(23, 87)(24, 88)(25, 85)(26, 86)(27, 98)(28, 109)(29, 92)(30, 91)(31, 95)(32, 96)(33, 93)(34, 94)(35, 99)(36, 89)(37, 97)(38, 101)(39, 100)(40, 103)(41, 102)(42, 105)(43, 104)(44, 107)(45, 106)(46, 117)(47, 90)(48, 111)(49, 110)(50, 114)(51, 115)(52, 112)(53, 113)(54, 118)(55, 108)(56, 116)(57, 120)(58, 119)(59, 122)(60, 121)(61, 124)(62, 123) local type(s) :: { ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.972 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 62 f = 32 degree seq :: [ 62^2 ] E15.974 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 31, 62}) Quotient :: loop Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^29, T2^-2 * T1^13 * T2^-16 ] Map:: R = (1, 63, 3, 65, 9, 71, 13, 75, 17, 79, 21, 83, 25, 87, 29, 91, 47, 109, 62, 124, 59, 121, 58, 120, 55, 117, 54, 116, 50, 112, 53, 115, 45, 107, 44, 106, 41, 103, 40, 102, 37, 99, 36, 98, 32, 94, 35, 97, 27, 89, 24, 86, 19, 81, 16, 78, 11, 73, 8, 70, 2, 64, 7, 69, 4, 66, 10, 72, 14, 76, 18, 80, 22, 84, 26, 88, 30, 92, 48, 110, 61, 123, 60, 122, 57, 119, 56, 118, 52, 114, 51, 113, 49, 111, 46, 108, 43, 105, 42, 104, 39, 101, 38, 100, 34, 96, 33, 95, 31, 93, 28, 90, 23, 85, 20, 82, 15, 77, 12, 74, 6, 68, 5, 67) L = (1, 64)(2, 68)(3, 69)(4, 63)(5, 70)(6, 73)(7, 67)(8, 74)(9, 66)(10, 65)(11, 77)(12, 78)(13, 72)(14, 71)(15, 81)(16, 82)(17, 76)(18, 75)(19, 85)(20, 86)(21, 80)(22, 79)(23, 89)(24, 90)(25, 84)(26, 83)(27, 93)(28, 97)(29, 88)(30, 87)(31, 94)(32, 96)(33, 98)(34, 99)(35, 95)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 111)(46, 115)(47, 92)(48, 91)(49, 112)(50, 114)(51, 116)(52, 117)(53, 113)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 109)(62, 110) local type(s) :: { ( 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31, 2, 31 ) } Outer automorphisms :: reflexible Dual of E15.970 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 62 f = 33 degree seq :: [ 124 ] E15.975 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 31, 62}) Quotient :: loop Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-31 ] Map:: non-degenerate R = (1, 63, 3, 65)(2, 64, 6, 68)(4, 66, 7, 69)(5, 67, 10, 72)(8, 70, 11, 73)(9, 71, 14, 76)(12, 74, 15, 77)(13, 75, 18, 80)(16, 78, 19, 81)(17, 79, 22, 84)(20, 82, 23, 85)(21, 83, 26, 88)(24, 86, 27, 89)(25, 87, 40, 102)(28, 90, 49, 111)(29, 91, 31, 93)(30, 92, 34, 96)(32, 94, 35, 97)(33, 95, 38, 100)(36, 98, 39, 101)(37, 99, 42, 104)(41, 103, 44, 106)(43, 105, 46, 108)(45, 107, 48, 110)(47, 109, 61, 123)(50, 112, 52, 114)(51, 113, 55, 117)(53, 115, 56, 118)(54, 116, 59, 121)(57, 119, 60, 122)(58, 120, 62, 124) L = (1, 64)(2, 67)(3, 68)(4, 63)(5, 71)(6, 72)(7, 65)(8, 66)(9, 75)(10, 76)(11, 69)(12, 70)(13, 79)(14, 80)(15, 73)(16, 74)(17, 83)(18, 84)(19, 77)(20, 78)(21, 87)(22, 88)(23, 81)(24, 82)(25, 101)(26, 102)(27, 85)(28, 86)(29, 92)(30, 95)(31, 96)(32, 91)(33, 99)(34, 100)(35, 93)(36, 94)(37, 103)(38, 104)(39, 97)(40, 98)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 122)(48, 123)(49, 89)(50, 113)(51, 116)(52, 117)(53, 112)(54, 120)(55, 121)(56, 114)(57, 115)(58, 111)(59, 124)(60, 118)(61, 119)(62, 90) local type(s) :: { ( 31, 62, 31, 62 ) } Outer automorphisms :: reflexible Dual of E15.971 Transitivity :: ET+ VT+ AT Graph:: v = 31 e = 62 f = 3 degree seq :: [ 4^31 ] E15.976 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 31, 62}) Quotient :: dipole Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 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, Y2^31, (Y3 * Y2^-1)^62 ] Map:: R = (1, 63, 2, 64)(3, 65, 5, 67)(4, 66, 6, 68)(7, 69, 9, 71)(8, 70, 10, 72)(11, 73, 13, 75)(12, 74, 14, 76)(15, 77, 17, 79)(16, 78, 18, 80)(19, 81, 21, 83)(20, 82, 22, 84)(23, 85, 25, 87)(24, 86, 26, 88)(27, 89, 36, 98)(28, 90, 47, 109)(29, 91, 30, 92)(31, 93, 33, 95)(32, 94, 34, 96)(35, 97, 37, 99)(38, 100, 39, 101)(40, 102, 41, 103)(42, 104, 43, 105)(44, 106, 45, 107)(46, 108, 55, 117)(48, 110, 49, 111)(50, 112, 52, 114)(51, 113, 53, 115)(54, 116, 56, 118)(57, 119, 58, 120)(59, 121, 60, 122)(61, 123, 62, 124)(125, 187, 127, 189, 131, 193, 135, 197, 139, 201, 143, 205, 147, 209, 151, 213, 158, 220, 154, 216, 157, 219, 161, 223, 163, 225, 165, 227, 167, 229, 169, 231, 179, 241, 175, 237, 172, 234, 174, 236, 178, 240, 181, 243, 183, 245, 185, 247, 152, 214, 148, 210, 144, 206, 140, 202, 136, 198, 132, 194, 128, 190)(126, 188, 129, 191, 133, 195, 137, 199, 141, 203, 145, 207, 149, 211, 160, 222, 156, 218, 153, 215, 155, 217, 159, 221, 162, 224, 164, 226, 166, 228, 168, 230, 170, 232, 177, 239, 173, 235, 176, 238, 180, 242, 182, 244, 184, 246, 186, 248, 171, 233, 150, 212, 146, 208, 142, 204, 138, 200, 134, 196, 130, 192) L = (1, 126)(2, 125)(3, 129)(4, 130)(5, 127)(6, 128)(7, 133)(8, 134)(9, 131)(10, 132)(11, 137)(12, 138)(13, 135)(14, 136)(15, 141)(16, 142)(17, 139)(18, 140)(19, 145)(20, 146)(21, 143)(22, 144)(23, 149)(24, 150)(25, 147)(26, 148)(27, 160)(28, 171)(29, 154)(30, 153)(31, 157)(32, 158)(33, 155)(34, 156)(35, 161)(36, 151)(37, 159)(38, 163)(39, 162)(40, 165)(41, 164)(42, 167)(43, 166)(44, 169)(45, 168)(46, 179)(47, 152)(48, 173)(49, 172)(50, 176)(51, 177)(52, 174)(53, 175)(54, 180)(55, 170)(56, 178)(57, 182)(58, 181)(59, 184)(60, 183)(61, 186)(62, 185)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 197)(74, 198)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 209)(86, 210)(87, 211)(88, 212)(89, 213)(90, 214)(91, 215)(92, 216)(93, 217)(94, 218)(95, 219)(96, 220)(97, 221)(98, 222)(99, 223)(100, 224)(101, 225)(102, 226)(103, 227)(104, 228)(105, 229)(106, 230)(107, 231)(108, 232)(109, 233)(110, 234)(111, 235)(112, 236)(113, 237)(114, 238)(115, 239)(116, 240)(117, 241)(118, 242)(119, 243)(120, 244)(121, 245)(122, 246)(123, 247)(124, 248) local type(s) :: { ( 2, 124, 2, 124 ), ( 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124, 2, 124 ) } Outer automorphisms :: reflexible Dual of E15.979 Graph:: bipartite v = 33 e = 124 f = 63 degree seq :: [ 4^31, 62^2 ] E15.977 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 31, 62}) Quotient :: dipole Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, Y2^14 * Y1^14, Y1^13 * Y2^-1 * Y1 * Y2^-15 * Y1, Y1^31, Y2^-138 * Y1^-14 ] Map:: R = (1, 63, 2, 64, 6, 68, 11, 73, 15, 77, 19, 81, 23, 85, 27, 89, 33, 95, 37, 99, 35, 97, 38, 100, 40, 102, 42, 104, 44, 106, 46, 108, 48, 110, 54, 116, 51, 113, 52, 114, 56, 118, 59, 121, 61, 123, 49, 111, 30, 92, 25, 87, 22, 84, 17, 79, 14, 76, 9, 71, 4, 66)(3, 65, 7, 69, 5, 67, 8, 70, 12, 74, 16, 78, 20, 82, 24, 86, 28, 90, 34, 96, 31, 93, 32, 94, 36, 98, 39, 101, 41, 103, 43, 105, 45, 107, 47, 109, 53, 115, 57, 119, 55, 117, 58, 120, 60, 122, 62, 124, 50, 112, 29, 91, 26, 88, 21, 83, 18, 80, 13, 75, 10, 72)(125, 187, 127, 189, 133, 195, 137, 199, 141, 203, 145, 207, 149, 211, 153, 215, 173, 235, 186, 248, 183, 245, 182, 244, 176, 238, 181, 243, 178, 240, 171, 233, 170, 232, 167, 229, 166, 228, 163, 225, 162, 224, 156, 218, 161, 223, 158, 220, 151, 213, 148, 210, 143, 205, 140, 202, 135, 197, 132, 194, 126, 188, 131, 193, 128, 190, 134, 196, 138, 200, 142, 204, 146, 208, 150, 212, 154, 216, 174, 236, 185, 247, 184, 246, 180, 242, 179, 241, 175, 237, 177, 239, 172, 234, 169, 231, 168, 230, 165, 227, 164, 226, 160, 222, 159, 221, 155, 217, 157, 219, 152, 214, 147, 209, 144, 206, 139, 201, 136, 198, 130, 192, 129, 191) L = (1, 127)(2, 131)(3, 133)(4, 134)(5, 125)(6, 129)(7, 128)(8, 126)(9, 137)(10, 138)(11, 132)(12, 130)(13, 141)(14, 142)(15, 136)(16, 135)(17, 145)(18, 146)(19, 140)(20, 139)(21, 149)(22, 150)(23, 144)(24, 143)(25, 153)(26, 154)(27, 148)(28, 147)(29, 173)(30, 174)(31, 157)(32, 161)(33, 152)(34, 151)(35, 155)(36, 159)(37, 158)(38, 156)(39, 162)(40, 160)(41, 164)(42, 163)(43, 166)(44, 165)(45, 168)(46, 167)(47, 170)(48, 169)(49, 186)(50, 185)(51, 177)(52, 181)(53, 172)(54, 171)(55, 175)(56, 179)(57, 178)(58, 176)(59, 182)(60, 180)(61, 184)(62, 183)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 197)(74, 198)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 209)(86, 210)(87, 211)(88, 212)(89, 213)(90, 214)(91, 215)(92, 216)(93, 217)(94, 218)(95, 219)(96, 220)(97, 221)(98, 222)(99, 223)(100, 224)(101, 225)(102, 226)(103, 227)(104, 228)(105, 229)(106, 230)(107, 231)(108, 232)(109, 233)(110, 234)(111, 235)(112, 236)(113, 237)(114, 238)(115, 239)(116, 240)(117, 241)(118, 242)(119, 243)(120, 244)(121, 245)(122, 246)(123, 247)(124, 248) 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 ) } Outer automorphisms :: reflexible Dual of E15.978 Graph:: bipartite v = 3 e = 124 f = 93 degree seq :: [ 62^2, 124 ] E15.978 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 31, 62}) Quotient :: dipole Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^31 * Y2, (Y3^-1 * Y1^-1)^62 ] Map:: R = (1, 63)(2, 64)(3, 65)(4, 66)(5, 67)(6, 68)(7, 69)(8, 70)(9, 71)(10, 72)(11, 73)(12, 74)(13, 75)(14, 76)(15, 77)(16, 78)(17, 79)(18, 80)(19, 81)(20, 82)(21, 83)(22, 84)(23, 85)(24, 86)(25, 87)(26, 88)(27, 89)(28, 90)(29, 91)(30, 92)(31, 93)(32, 94)(33, 95)(34, 96)(35, 97)(36, 98)(37, 99)(38, 100)(39, 101)(40, 102)(41, 103)(42, 104)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 113)(52, 114)(53, 115)(54, 116)(55, 117)(56, 118)(57, 119)(58, 120)(59, 121)(60, 122)(61, 123)(62, 124)(125, 187, 126, 188)(127, 189, 129, 191)(128, 190, 130, 192)(131, 193, 133, 195)(132, 194, 134, 196)(135, 197, 137, 199)(136, 198, 138, 200)(139, 201, 141, 203)(140, 202, 142, 204)(143, 205, 145, 207)(144, 206, 146, 208)(147, 209, 149, 211)(148, 210, 150, 212)(151, 213, 157, 219)(152, 214, 169, 231)(153, 215, 154, 216)(155, 217, 156, 218)(158, 220, 159, 221)(160, 222, 161, 223)(162, 224, 163, 225)(164, 226, 165, 227)(166, 228, 167, 229)(168, 230, 174, 236)(170, 232, 171, 233)(172, 234, 173, 235)(175, 237, 176, 238)(177, 239, 178, 240)(179, 241, 180, 242)(181, 243, 182, 244)(183, 245, 184, 246)(185, 247, 186, 248) L = (1, 127)(2, 129)(3, 131)(4, 125)(5, 133)(6, 126)(7, 135)(8, 128)(9, 137)(10, 130)(11, 139)(12, 132)(13, 141)(14, 134)(15, 143)(16, 136)(17, 145)(18, 138)(19, 147)(20, 140)(21, 149)(22, 142)(23, 151)(24, 144)(25, 157)(26, 146)(27, 153)(28, 148)(29, 155)(30, 156)(31, 158)(32, 159)(33, 154)(34, 160)(35, 161)(36, 162)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 174)(44, 170)(45, 150)(46, 172)(47, 173)(48, 175)(49, 176)(50, 171)(51, 177)(52, 178)(53, 179)(54, 180)(55, 181)(56, 182)(57, 183)(58, 184)(59, 185)(60, 186)(61, 169)(62, 152)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 197)(74, 198)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 209)(86, 210)(87, 211)(88, 212)(89, 213)(90, 214)(91, 215)(92, 216)(93, 217)(94, 218)(95, 219)(96, 220)(97, 221)(98, 222)(99, 223)(100, 224)(101, 225)(102, 226)(103, 227)(104, 228)(105, 229)(106, 230)(107, 231)(108, 232)(109, 233)(110, 234)(111, 235)(112, 236)(113, 237)(114, 238)(115, 239)(116, 240)(117, 241)(118, 242)(119, 243)(120, 244)(121, 245)(122, 246)(123, 247)(124, 248) local type(s) :: { ( 62, 124 ), ( 62, 124, 62, 124 ) } Outer automorphisms :: reflexible Dual of E15.977 Graph:: simple bipartite v = 93 e = 124 f = 3 degree seq :: [ 2^62, 4^31 ] E15.979 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 31, 62}) Quotient :: dipole Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-31 ] Map:: R = (1, 63, 2, 64, 5, 67, 9, 71, 13, 75, 17, 79, 21, 83, 25, 87, 35, 97, 31, 93, 34, 96, 38, 100, 40, 102, 42, 104, 44, 106, 46, 108, 55, 117, 51, 113, 48, 110, 49, 111, 52, 114, 56, 118, 58, 120, 60, 122, 47, 109, 27, 89, 23, 85, 19, 81, 15, 77, 11, 73, 7, 69, 3, 65, 6, 68, 10, 72, 14, 76, 18, 80, 22, 84, 26, 88, 36, 98, 32, 94, 29, 91, 30, 92, 33, 95, 37, 99, 39, 101, 41, 103, 43, 105, 45, 107, 54, 116, 50, 112, 53, 115, 57, 119, 59, 121, 61, 123, 62, 124, 28, 90, 24, 86, 20, 82, 16, 78, 12, 74, 8, 70, 4, 66)(125, 187)(126, 188)(127, 189)(128, 190)(129, 191)(130, 192)(131, 193)(132, 194)(133, 195)(134, 196)(135, 197)(136, 198)(137, 199)(138, 200)(139, 201)(140, 202)(141, 203)(142, 204)(143, 205)(144, 206)(145, 207)(146, 208)(147, 209)(148, 210)(149, 211)(150, 212)(151, 213)(152, 214)(153, 215)(154, 216)(155, 217)(156, 218)(157, 219)(158, 220)(159, 221)(160, 222)(161, 223)(162, 224)(163, 225)(164, 226)(165, 227)(166, 228)(167, 229)(168, 230)(169, 231)(170, 232)(171, 233)(172, 234)(173, 235)(174, 236)(175, 237)(176, 238)(177, 239)(178, 240)(179, 241)(180, 242)(181, 243)(182, 244)(183, 245)(184, 246)(185, 247)(186, 248) L = (1, 127)(2, 130)(3, 125)(4, 131)(5, 134)(6, 126)(7, 128)(8, 135)(9, 138)(10, 129)(11, 132)(12, 139)(13, 142)(14, 133)(15, 136)(16, 143)(17, 146)(18, 137)(19, 140)(20, 147)(21, 150)(22, 141)(23, 144)(24, 151)(25, 160)(26, 145)(27, 148)(28, 171)(29, 155)(30, 158)(31, 153)(32, 159)(33, 162)(34, 154)(35, 156)(36, 149)(37, 164)(38, 157)(39, 166)(40, 161)(41, 168)(42, 163)(43, 170)(44, 165)(45, 179)(46, 167)(47, 152)(48, 174)(49, 177)(50, 172)(51, 178)(52, 181)(53, 173)(54, 175)(55, 169)(56, 183)(57, 176)(58, 185)(59, 180)(60, 186)(61, 182)(62, 184)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 197)(74, 198)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 209)(86, 210)(87, 211)(88, 212)(89, 213)(90, 214)(91, 215)(92, 216)(93, 217)(94, 218)(95, 219)(96, 220)(97, 221)(98, 222)(99, 223)(100, 224)(101, 225)(102, 226)(103, 227)(104, 228)(105, 229)(106, 230)(107, 231)(108, 232)(109, 233)(110, 234)(111, 235)(112, 236)(113, 237)(114, 238)(115, 239)(116, 240)(117, 241)(118, 242)(119, 243)(120, 244)(121, 245)(122, 246)(123, 247)(124, 248) local type(s) :: { ( 4, 62 ), ( 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62, 4, 62 ) } Outer automorphisms :: reflexible Dual of E15.976 Graph:: bipartite v = 63 e = 124 f = 33 degree seq :: [ 2^62, 124 ] E15.980 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 31, 62}) Quotient :: dipole Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 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, Y2^31 * Y1, (Y3 * Y2^-1)^31 ] Map:: R = (1, 63, 2, 64)(3, 65, 5, 67)(4, 66, 6, 68)(7, 69, 9, 71)(8, 70, 10, 72)(11, 73, 13, 75)(12, 74, 14, 76)(15, 77, 17, 79)(16, 78, 18, 80)(19, 81, 21, 83)(20, 82, 22, 84)(23, 85, 25, 87)(24, 86, 26, 88)(27, 89, 32, 94)(28, 90, 45, 107)(29, 91, 30, 92)(31, 93, 33, 95)(34, 96, 35, 97)(36, 98, 37, 99)(38, 100, 39, 101)(40, 102, 41, 103)(42, 104, 43, 105)(44, 106, 49, 111)(46, 108, 47, 109)(48, 110, 50, 112)(51, 113, 52, 114)(53, 115, 54, 116)(55, 117, 56, 118)(57, 119, 58, 120)(59, 121, 60, 122)(61, 123, 62, 124)(125, 187, 127, 189, 131, 193, 135, 197, 139, 201, 143, 205, 147, 209, 151, 213, 154, 216, 157, 219, 159, 221, 161, 223, 163, 225, 165, 227, 167, 229, 173, 235, 170, 232, 172, 234, 175, 237, 177, 239, 179, 241, 181, 243, 183, 245, 185, 247, 169, 231, 150, 212, 146, 208, 142, 204, 138, 200, 134, 196, 130, 192, 126, 188, 129, 191, 133, 195, 137, 199, 141, 203, 145, 207, 149, 211, 156, 218, 153, 215, 155, 217, 158, 220, 160, 222, 162, 224, 164, 226, 166, 228, 168, 230, 171, 233, 174, 236, 176, 238, 178, 240, 180, 242, 182, 244, 184, 246, 186, 248, 152, 214, 148, 210, 144, 206, 140, 202, 136, 198, 132, 194, 128, 190) L = (1, 126)(2, 125)(3, 129)(4, 130)(5, 127)(6, 128)(7, 133)(8, 134)(9, 131)(10, 132)(11, 137)(12, 138)(13, 135)(14, 136)(15, 141)(16, 142)(17, 139)(18, 140)(19, 145)(20, 146)(21, 143)(22, 144)(23, 149)(24, 150)(25, 147)(26, 148)(27, 156)(28, 169)(29, 154)(30, 153)(31, 157)(32, 151)(33, 155)(34, 159)(35, 158)(36, 161)(37, 160)(38, 163)(39, 162)(40, 165)(41, 164)(42, 167)(43, 166)(44, 173)(45, 152)(46, 171)(47, 170)(48, 174)(49, 168)(50, 172)(51, 176)(52, 175)(53, 178)(54, 177)(55, 180)(56, 179)(57, 182)(58, 181)(59, 184)(60, 183)(61, 186)(62, 185)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 197)(74, 198)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 209)(86, 210)(87, 211)(88, 212)(89, 213)(90, 214)(91, 215)(92, 216)(93, 217)(94, 218)(95, 219)(96, 220)(97, 221)(98, 222)(99, 223)(100, 224)(101, 225)(102, 226)(103, 227)(104, 228)(105, 229)(106, 230)(107, 231)(108, 232)(109, 233)(110, 234)(111, 235)(112, 236)(113, 237)(114, 238)(115, 239)(116, 240)(117, 241)(118, 242)(119, 243)(120, 244)(121, 245)(122, 246)(123, 247)(124, 248) local type(s) :: { ( 2, 62, 2, 62 ), ( 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62, 2, 62 ) } Outer automorphisms :: reflexible Dual of E15.981 Graph:: bipartite v = 32 e = 124 f = 64 degree seq :: [ 4^31, 124 ] E15.981 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 31, 62}) Quotient :: dipole Aut^+ = C62 (small group id <62, 2>) Aut = D124 (small group id <124, 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 * Y1^13 * Y3^-16, Y3^-2 * Y1^29, (Y3 * Y2^-1)^62 ] Map:: R = (1, 63, 2, 64, 6, 68, 11, 73, 15, 77, 19, 81, 23, 85, 27, 89, 35, 97, 33, 95, 36, 98, 38, 100, 40, 102, 42, 104, 44, 106, 46, 108, 49, 111, 50, 112, 52, 114, 55, 117, 57, 119, 59, 121, 61, 123, 47, 109, 30, 92, 25, 87, 22, 84, 17, 79, 14, 76, 9, 71, 4, 66)(3, 65, 7, 69, 5, 67, 8, 70, 12, 74, 16, 78, 20, 82, 24, 86, 28, 90, 31, 93, 32, 94, 34, 96, 37, 99, 39, 101, 41, 103, 43, 105, 45, 107, 53, 115, 51, 113, 54, 116, 56, 118, 58, 120, 60, 122, 62, 124, 48, 110, 29, 91, 26, 88, 21, 83, 18, 80, 13, 75, 10, 72)(125, 187)(126, 188)(127, 189)(128, 190)(129, 191)(130, 192)(131, 193)(132, 194)(133, 195)(134, 196)(135, 197)(136, 198)(137, 199)(138, 200)(139, 201)(140, 202)(141, 203)(142, 204)(143, 205)(144, 206)(145, 207)(146, 208)(147, 209)(148, 210)(149, 211)(150, 212)(151, 213)(152, 214)(153, 215)(154, 216)(155, 217)(156, 218)(157, 219)(158, 220)(159, 221)(160, 222)(161, 223)(162, 224)(163, 225)(164, 226)(165, 227)(166, 228)(167, 229)(168, 230)(169, 231)(170, 232)(171, 233)(172, 234)(173, 235)(174, 236)(175, 237)(176, 238)(177, 239)(178, 240)(179, 241)(180, 242)(181, 243)(182, 244)(183, 245)(184, 246)(185, 247)(186, 248) L = (1, 127)(2, 131)(3, 133)(4, 134)(5, 125)(6, 129)(7, 128)(8, 126)(9, 137)(10, 138)(11, 132)(12, 130)(13, 141)(14, 142)(15, 136)(16, 135)(17, 145)(18, 146)(19, 140)(20, 139)(21, 149)(22, 150)(23, 144)(24, 143)(25, 153)(26, 154)(27, 148)(28, 147)(29, 171)(30, 172)(31, 151)(32, 159)(33, 155)(34, 157)(35, 152)(36, 156)(37, 160)(38, 158)(39, 162)(40, 161)(41, 164)(42, 163)(43, 166)(44, 165)(45, 168)(46, 167)(47, 186)(48, 185)(49, 169)(50, 177)(51, 173)(52, 175)(53, 170)(54, 174)(55, 178)(56, 176)(57, 180)(58, 179)(59, 182)(60, 181)(61, 184)(62, 183)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 197)(74, 198)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 209)(86, 210)(87, 211)(88, 212)(89, 213)(90, 214)(91, 215)(92, 216)(93, 217)(94, 218)(95, 219)(96, 220)(97, 221)(98, 222)(99, 223)(100, 224)(101, 225)(102, 226)(103, 227)(104, 228)(105, 229)(106, 230)(107, 231)(108, 232)(109, 233)(110, 234)(111, 235)(112, 236)(113, 237)(114, 238)(115, 239)(116, 240)(117, 241)(118, 242)(119, 243)(120, 244)(121, 245)(122, 246)(123, 247)(124, 248) local type(s) :: { ( 4, 124 ), ( 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124, 4, 124 ) } Outer automorphisms :: reflexible Dual of E15.980 Graph:: simple bipartite v = 64 e = 124 f = 32 degree seq :: [ 2^62, 62^2 ] E15.982 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 5, 69)(4, 68, 8, 72)(6, 70, 10, 74)(7, 71, 11, 75)(9, 73, 13, 77)(12, 76, 16, 80)(14, 78, 18, 82)(15, 79, 19, 83)(17, 81, 21, 85)(20, 84, 24, 88)(22, 86, 26, 90)(23, 87, 27, 91)(25, 89, 29, 93)(28, 92, 32, 96)(30, 94, 35, 99)(31, 95, 34, 98)(33, 97, 49, 113)(36, 100, 54, 118)(37, 101, 53, 117)(38, 102, 52, 116)(39, 103, 55, 119)(40, 104, 56, 120)(41, 105, 57, 121)(42, 106, 58, 122)(43, 107, 59, 123)(44, 108, 60, 124)(45, 109, 61, 125)(46, 110, 62, 126)(47, 111, 63, 127)(48, 112, 50, 114)(51, 115, 64, 128)(129, 193, 131, 195)(130, 194, 133, 197)(132, 196, 135, 199)(134, 198, 137, 201)(136, 200, 139, 203)(138, 202, 141, 205)(140, 204, 143, 207)(142, 206, 145, 209)(144, 208, 147, 211)(146, 210, 149, 213)(148, 212, 151, 215)(150, 214, 153, 217)(152, 216, 155, 219)(154, 218, 157, 221)(156, 220, 159, 223)(158, 222, 177, 241)(160, 224, 162, 226)(161, 225, 163, 227)(164, 228, 166, 230)(165, 229, 167, 231)(168, 232, 170, 234)(169, 233, 171, 235)(172, 236, 174, 238)(173, 237, 175, 239)(176, 240, 179, 243)(178, 242, 192, 256)(180, 244, 182, 246)(181, 245, 183, 247)(184, 248, 186, 250)(185, 249, 187, 251)(188, 252, 190, 254)(189, 253, 191, 255) L = (1, 132)(2, 134)(3, 135)(4, 129)(5, 137)(6, 130)(7, 131)(8, 140)(9, 133)(10, 142)(11, 143)(12, 136)(13, 145)(14, 138)(15, 139)(16, 148)(17, 141)(18, 150)(19, 151)(20, 144)(21, 153)(22, 146)(23, 147)(24, 156)(25, 149)(26, 158)(27, 159)(28, 152)(29, 177)(30, 154)(31, 155)(32, 180)(33, 181)(34, 182)(35, 183)(36, 184)(37, 185)(38, 186)(39, 187)(40, 188)(41, 189)(42, 190)(43, 191)(44, 178)(45, 176)(46, 192)(47, 179)(48, 173)(49, 157)(50, 172)(51, 175)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 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, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.987 Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.983 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y2^2, R^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y1 * Y3 * Y1 * Y2)^2, (Y1 * Y2)^4, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 10, 74)(6, 70, 12, 76)(8, 72, 15, 79)(11, 75, 20, 84)(13, 77, 18, 82)(14, 78, 21, 85)(16, 80, 19, 83)(17, 81, 27, 91)(22, 86, 32, 96)(23, 87, 29, 93)(24, 88, 28, 92)(25, 89, 34, 98)(26, 90, 35, 99)(30, 94, 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, 62, 126)(59, 123, 63, 127)(129, 193, 131, 195)(130, 194, 133, 197)(132, 196, 136, 200)(134, 198, 139, 203)(135, 199, 141, 205)(137, 201, 144, 208)(138, 202, 146, 210)(140, 204, 149, 213)(142, 206, 151, 215)(143, 207, 152, 216)(145, 209, 154, 218)(147, 211, 156, 220)(148, 212, 157, 221)(150, 214, 159, 223)(153, 217, 161, 225)(155, 219, 162, 226)(158, 222, 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, 179, 243)(175, 239, 181, 245)(176, 240, 183, 247)(178, 242, 185, 249)(180, 244, 187, 251)(182, 246, 189, 253)(184, 248, 191, 255)(186, 250, 192, 256)(188, 252, 190, 254) L = (1, 132)(2, 134)(3, 136)(4, 129)(5, 139)(6, 130)(7, 142)(8, 131)(9, 145)(10, 147)(11, 133)(12, 150)(13, 151)(14, 135)(15, 153)(16, 154)(17, 137)(18, 156)(19, 138)(20, 158)(21, 159)(22, 140)(23, 141)(24, 161)(25, 143)(26, 144)(27, 164)(28, 146)(29, 165)(30, 148)(31, 149)(32, 168)(33, 152)(34, 170)(35, 171)(36, 155)(37, 157)(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) :: { ( 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.989 Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.984 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y2^2, R^2, Y3^4, (R * Y1)^2, (Y2 * Y3)^2, (R * Y3)^2, Y3^4, (Y3^-2 * Y1)^2, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1, (Y3 * 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, 15, 79)(7, 71, 18, 82)(8, 72, 20, 84)(10, 74, 16, 80)(11, 75, 17, 81)(13, 77, 19, 83)(21, 85, 31, 95)(22, 86, 32, 96)(23, 87, 34, 98)(24, 88, 33, 97)(25, 89, 35, 99)(26, 90, 36, 100)(27, 91, 37, 101)(28, 92, 39, 103)(29, 93, 38, 102)(30, 94, 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, 63, 127)(59, 123, 62, 126)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 139, 203)(133, 197, 138, 202)(135, 199, 145, 209)(136, 200, 144, 208)(137, 201, 149, 213)(140, 204, 151, 215)(141, 205, 152, 216)(142, 206, 150, 214)(143, 207, 154, 218)(146, 210, 156, 220)(147, 211, 157, 221)(148, 212, 155, 219)(153, 217, 161, 225)(158, 222, 166, 230)(159, 223, 169, 233)(160, 224, 171, 235)(162, 226, 170, 234)(163, 227, 172, 236)(164, 228, 173, 237)(165, 229, 175, 239)(167, 231, 174, 238)(168, 232, 176, 240)(177, 241, 185, 249)(178, 242, 187, 251)(179, 243, 186, 250)(180, 244, 188, 252)(181, 245, 189, 253)(182, 246, 191, 255)(183, 247, 190, 254)(184, 248, 192, 256) L = (1, 132)(2, 135)(3, 138)(4, 141)(5, 129)(6, 144)(7, 147)(8, 130)(9, 150)(10, 152)(11, 131)(12, 153)(13, 133)(14, 149)(15, 155)(16, 157)(17, 134)(18, 158)(19, 136)(20, 154)(21, 140)(22, 161)(23, 137)(24, 139)(25, 142)(26, 146)(27, 166)(28, 143)(29, 145)(30, 148)(31, 170)(32, 172)(33, 151)(34, 169)(35, 171)(36, 174)(37, 176)(38, 156)(39, 173)(40, 175)(41, 160)(42, 163)(43, 159)(44, 162)(45, 165)(46, 168)(47, 164)(48, 167)(49, 186)(50, 188)(51, 185)(52, 187)(53, 190)(54, 192)(55, 189)(56, 191)(57, 178)(58, 180)(59, 177)(60, 179)(61, 182)(62, 184)(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) :: { ( 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.988 Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.985 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^2 * Y2 * Y1 * Y3^-1 * 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, 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, 138, 202)(133, 197, 137, 201)(135, 199, 143, 207)(136, 200, 142, 206)(139, 203, 149, 213)(140, 204, 148, 212)(141, 205, 147, 211)(144, 208, 154, 218)(145, 209, 153, 217)(146, 210, 152, 216)(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, 174, 238)(168, 232, 173, 237)(171, 235, 178, 242)(172, 236, 177, 241)(175, 239, 182, 246)(176, 240, 181, 245)(179, 243, 186, 250)(180, 244, 185, 249)(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) :: { ( 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.990 Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.986 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y2 * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y2 * Y1 * Y2 * Y3, 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, 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, 139, 203)(133, 197, 138, 202)(135, 199, 145, 209)(136, 200, 144, 208)(137, 201, 147, 211)(140, 204, 149, 213)(141, 205, 143, 207)(142, 206, 150, 214)(146, 210, 153, 217)(148, 212, 154, 218)(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, 174, 238)(168, 232, 173, 237)(171, 235, 178, 242)(172, 236, 177, 241)(175, 239, 181, 245)(176, 240, 182, 246)(179, 243, 185, 249)(180, 244, 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, 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) :: { ( 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.991 Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.987 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (Y1^-1 * Y2)^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, 54, 118, 46, 110, 38, 102, 30, 94, 22, 86, 14, 78, 7, 71)(4, 68, 11, 75, 19, 83, 27, 91, 35, 99, 43, 107, 51, 115, 59, 123, 61, 125, 55, 119, 47, 111, 39, 103, 31, 95, 23, 87, 15, 79, 8, 72)(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, 137, 201)(134, 198, 142, 206)(136, 200, 144, 208)(139, 203, 146, 210)(140, 204, 145, 209)(141, 205, 150, 214)(143, 207, 152, 216)(147, 211, 154, 218)(148, 212, 153, 217)(149, 213, 158, 222)(151, 215, 160, 224)(155, 219, 162, 226)(156, 220, 161, 225)(157, 221, 166, 230)(159, 223, 168, 232)(163, 227, 170, 234)(164, 228, 169, 233)(165, 229, 174, 238)(167, 231, 176, 240)(171, 235, 178, 242)(172, 236, 177, 241)(173, 237, 182, 246)(175, 239, 184, 248)(179, 243, 186, 250)(180, 244, 185, 249)(181, 245, 188, 252)(183, 247, 190, 254)(187, 251, 191, 255)(189, 253, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 139)(6, 143)(7, 144)(8, 130)(9, 146)(10, 131)(11, 133)(12, 147)(13, 151)(14, 152)(15, 134)(16, 135)(17, 154)(18, 137)(19, 140)(20, 155)(21, 159)(22, 160)(23, 141)(24, 142)(25, 162)(26, 145)(27, 148)(28, 163)(29, 167)(30, 168)(31, 149)(32, 150)(33, 170)(34, 153)(35, 156)(36, 171)(37, 175)(38, 176)(39, 157)(40, 158)(41, 178)(42, 161)(43, 164)(44, 179)(45, 183)(46, 184)(47, 165)(48, 166)(49, 186)(50, 169)(51, 172)(52, 187)(53, 189)(54, 190)(55, 173)(56, 174)(57, 191)(58, 177)(59, 180)(60, 192)(61, 181)(62, 182)(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) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.982 Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.988 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2 * Y1^2 * Y2 * Y1^-2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1^7, Y1^-4 * Y2 * Y1^-3 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 48, 112, 42, 106, 24, 88, 38, 102, 21, 85, 35, 99, 53, 117, 47, 111, 29, 93, 14, 78, 5, 69)(3, 67, 9, 73, 16, 80, 33, 97, 49, 113, 46, 110, 28, 92, 13, 77, 20, 84, 7, 71, 18, 82, 31, 95, 51, 115, 43, 107, 25, 89, 11, 75)(4, 68, 12, 76, 26, 90, 44, 108, 59, 123, 64, 128, 55, 119, 39, 103, 56, 120, 41, 105, 58, 122, 61, 125, 50, 114, 32, 96, 17, 81, 8, 72)(10, 74, 23, 87, 40, 104, 57, 121, 63, 127, 52, 116, 36, 100, 19, 83, 37, 101, 27, 91, 45, 109, 60, 124, 62, 126, 54, 118, 34, 98, 22, 86)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 141, 205)(134, 198, 144, 208)(136, 200, 147, 211)(137, 201, 149, 213)(139, 203, 152, 216)(140, 204, 155, 219)(142, 206, 153, 217)(143, 207, 159, 223)(145, 209, 162, 226)(146, 210, 163, 227)(148, 212, 166, 230)(150, 214, 167, 231)(151, 215, 169, 233)(154, 218, 168, 232)(156, 220, 170, 234)(157, 221, 174, 238)(158, 222, 177, 241)(160, 224, 180, 244)(161, 225, 181, 245)(164, 228, 183, 247)(165, 229, 184, 248)(171, 235, 176, 240)(172, 236, 188, 252)(173, 237, 186, 250)(175, 239, 179, 243)(178, 242, 190, 254)(182, 246, 192, 256)(185, 249, 189, 253)(187, 251, 191, 255) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 140)(6, 145)(7, 147)(8, 130)(9, 150)(10, 131)(11, 151)(12, 133)(13, 155)(14, 154)(15, 160)(16, 162)(17, 134)(18, 164)(19, 135)(20, 165)(21, 167)(22, 137)(23, 139)(24, 169)(25, 168)(26, 142)(27, 141)(28, 173)(29, 172)(30, 178)(31, 180)(32, 143)(33, 182)(34, 144)(35, 183)(36, 146)(37, 148)(38, 184)(39, 149)(40, 153)(41, 152)(42, 186)(43, 185)(44, 157)(45, 156)(46, 188)(47, 187)(48, 189)(49, 190)(50, 158)(51, 191)(52, 159)(53, 192)(54, 161)(55, 163)(56, 166)(57, 171)(58, 170)(59, 175)(60, 174)(61, 176)(62, 177)(63, 179)(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) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.984 Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.989 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, Y3^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y1^-2 * Y2)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^3 * Y2 * Y1^-5 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 48, 112, 42, 106, 22, 86, 35, 99, 25, 89, 38, 102, 54, 118, 47, 111, 29, 93, 14, 78, 5, 69)(3, 67, 9, 73, 21, 85, 39, 103, 52, 116, 31, 95, 20, 84, 7, 71, 18, 82, 13, 77, 28, 92, 46, 110, 49, 113, 34, 98, 16, 80, 11, 75)(4, 68, 12, 76, 26, 90, 44, 108, 59, 123, 64, 128, 56, 120, 43, 107, 55, 119, 41, 105, 58, 122, 61, 125, 50, 114, 32, 96, 17, 81, 8, 72)(10, 74, 24, 88, 33, 97, 53, 117, 62, 126, 60, 124, 45, 109, 27, 91, 36, 100, 19, 83, 37, 101, 51, 115, 63, 127, 57, 121, 40, 104, 23, 87)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 141, 205)(134, 198, 144, 208)(136, 200, 147, 211)(137, 201, 150, 214)(139, 203, 153, 217)(140, 204, 155, 219)(142, 206, 149, 213)(143, 207, 159, 223)(145, 209, 161, 225)(146, 210, 163, 227)(148, 212, 166, 230)(151, 215, 169, 233)(152, 216, 171, 235)(154, 218, 168, 232)(156, 220, 170, 234)(157, 221, 174, 238)(158, 222, 177, 241)(160, 224, 179, 243)(162, 226, 182, 246)(164, 228, 183, 247)(165, 229, 184, 248)(167, 231, 176, 240)(172, 236, 188, 252)(173, 237, 186, 250)(175, 239, 180, 244)(178, 242, 190, 254)(181, 245, 192, 256)(185, 249, 189, 253)(187, 251, 191, 255) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 140)(6, 145)(7, 147)(8, 130)(9, 151)(10, 131)(11, 152)(12, 133)(13, 155)(14, 154)(15, 160)(16, 161)(17, 134)(18, 164)(19, 135)(20, 165)(21, 168)(22, 169)(23, 137)(24, 139)(25, 171)(26, 142)(27, 141)(28, 173)(29, 172)(30, 178)(31, 179)(32, 143)(33, 144)(34, 181)(35, 183)(36, 146)(37, 148)(38, 184)(39, 185)(40, 149)(41, 150)(42, 186)(43, 153)(44, 157)(45, 156)(46, 188)(47, 187)(48, 189)(49, 190)(50, 158)(51, 159)(52, 191)(53, 162)(54, 192)(55, 163)(56, 166)(57, 167)(58, 170)(59, 175)(60, 174)(61, 176)(62, 177)(63, 180)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.983 Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.990 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y2)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^8, Y1^-1 * Y3^-1 * Y1^3 * Y3 * Y1^-4 ] Map:: polytopal 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, 48, 112, 32, 96, 17, 81, 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, 35, 99, 21, 85, 9, 73, 6, 70, 16, 80, 31, 95, 47, 111, 51, 115, 36, 100, 20, 84, 10, 74)(12, 76, 23, 87, 37, 101, 54, 118, 62, 126, 58, 122, 43, 107, 26, 90, 13, 77, 22, 86, 38, 102, 53, 117, 63, 127, 59, 123, 42, 106, 27, 91)(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, 154, 218)(143, 207, 156, 220)(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, 171, 235)(158, 222, 172, 236)(159, 223, 170, 234)(160, 224, 169, 233)(161, 225, 178, 242)(163, 227, 182, 246)(164, 228, 181, 245)(167, 231, 184, 248)(173, 237, 186, 250)(174, 238, 188, 252)(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, 140)(4, 143)(5, 144)(6, 129)(7, 148)(8, 150)(9, 152)(10, 130)(11, 154)(12, 156)(13, 131)(14, 133)(15, 134)(16, 158)(17, 157)(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, 142)(31, 145)(32, 175)(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, 160)(46, 159)(47, 177)(48, 180)(49, 173)(50, 190)(51, 176)(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) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.985 Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.991 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1 * Y3^-1)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y3 * Y2)^2, (Y3^-1 * Y1^-1)^2, Y2 * Y3 * Y1^-1 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y1^2 * Y2)^2, Y1^-4 * Y2 * Y1 * Y2 * Y1^-3 ] Map:: polytopal 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, 52, 116, 36, 100, 19, 83, 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, 39, 103, 23, 87, 9, 73, 6, 70, 18, 82, 35, 99, 51, 115, 55, 119, 40, 104, 22, 86, 10, 74)(12, 76, 25, 89, 41, 105, 57, 121, 63, 127, 61, 125, 47, 111, 31, 95, 14, 78, 27, 91, 43, 107, 59, 123, 64, 128, 62, 126, 46, 110, 32, 96)(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, 160, 224)(144, 208, 152, 216)(146, 210, 159, 223)(147, 211, 157, 221)(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, 174, 238)(164, 228, 178, 242)(165, 229, 182, 246)(167, 231, 187, 251)(168, 232, 185, 249)(170, 234, 188, 252)(173, 237, 181, 245)(177, 241, 190, 254)(179, 243, 189, 253)(180, 244, 186, 250)(183, 247, 192, 256)(184, 248, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 146)(6, 129)(7, 150)(8, 153)(9, 156)(10, 130)(11, 159)(12, 152)(13, 155)(14, 131)(15, 133)(16, 134)(17, 160)(18, 158)(19, 161)(20, 167)(21, 169)(22, 172)(23, 135)(24, 142)(25, 141)(26, 171)(27, 136)(28, 138)(29, 174)(30, 143)(31, 145)(32, 139)(33, 176)(34, 175)(35, 147)(36, 179)(37, 183)(38, 185)(39, 188)(40, 148)(41, 154)(42, 187)(43, 149)(44, 151)(45, 189)(46, 162)(47, 157)(48, 163)(49, 164)(50, 190)(51, 181)(52, 184)(53, 177)(54, 191)(55, 180)(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) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.986 Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.992 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2^-1 * T1^-1 * T2^-2 * T1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 25, 13)(6, 16, 28, 17)(9, 23, 14, 24)(11, 26, 15, 27)(18, 29, 21, 30)(20, 31, 22, 32)(33, 41, 35, 42)(34, 43, 36, 44)(37, 45, 39, 46)(38, 47, 40, 48)(49, 57, 51, 58)(50, 59, 52, 60)(53, 61, 55, 62)(54, 63, 56, 64)(65, 66, 70, 68)(67, 73, 80, 75)(69, 78, 81, 79)(71, 82, 76, 84)(72, 85, 77, 86)(74, 83, 92, 89)(87, 97, 90, 98)(88, 99, 91, 100)(93, 101, 95, 102)(94, 103, 96, 104)(105, 113, 107, 114)(106, 115, 108, 116)(109, 117, 111, 118)(110, 119, 112, 120)(121, 127, 123, 125)(122, 128, 124, 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) :: { ( 32^4 ) } Outer automorphisms :: reflexible Dual of E15.997 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 64 f = 4 degree seq :: [ 4^32 ] E15.993 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2^-2 * T1, (T2^-1 * T1 * T2^-1 * T1^-1)^2, (T2 * T1^-1)^4, T2^-3 * T1 * T2^2 * T1 * T2^-3 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 46, 54, 36, 18, 6, 17, 35, 53, 52, 34, 16, 5)(2, 7, 20, 39, 56, 48, 28, 13, 4, 12, 31, 49, 60, 44, 24, 8)(9, 25, 14, 32, 50, 62, 47, 30, 11, 29, 15, 33, 51, 61, 45, 26)(19, 37, 22, 42, 58, 64, 57, 41, 21, 40, 23, 43, 59, 63, 55, 38)(65, 66, 70, 68)(67, 73, 81, 75)(69, 78, 82, 79)(71, 83, 76, 85)(72, 86, 77, 87)(74, 88, 99, 92)(80, 84, 100, 95)(89, 101, 93, 104)(90, 106, 94, 107)(91, 109, 117, 111)(96, 102, 97, 105)(98, 114, 118, 115)(103, 119, 113, 121)(108, 122, 112, 123)(110, 124, 116, 120)(125, 128, 126, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.995 Transitivity :: ET+ Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.994 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T1^-1 * T2^-2 * T1 * T2^-2, (T2 * T1^-1)^4, (T2^-1 * T1 * T2^-1 * T1^-1)^2, T2^5 * T1^-1 * T2^-3 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 27, 46, 55, 38, 19, 37, 22, 42, 58, 52, 34, 16, 5)(2, 7, 20, 39, 56, 47, 30, 11, 29, 15, 33, 51, 60, 44, 24, 8)(4, 12, 31, 49, 61, 45, 26, 9, 25, 14, 32, 50, 62, 48, 28, 13)(6, 17, 35, 53, 63, 57, 41, 21, 40, 23, 43, 59, 64, 54, 36, 18)(65, 66, 70, 68)(67, 73, 81, 75)(69, 78, 82, 79)(71, 83, 76, 85)(72, 86, 77, 87)(74, 88, 99, 92)(80, 84, 100, 95)(89, 101, 93, 104)(90, 106, 94, 107)(91, 109, 117, 111)(96, 102, 97, 105)(98, 114, 118, 115)(103, 119, 113, 121)(108, 122, 112, 123)(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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.996 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.995 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2^-1 * T1^-1 * T2^-2 * T1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 65, 3, 67, 10, 74, 5, 69)(2, 66, 7, 71, 19, 83, 8, 72)(4, 68, 12, 76, 25, 89, 13, 77)(6, 70, 16, 80, 28, 92, 17, 81)(9, 73, 23, 87, 14, 78, 24, 88)(11, 75, 26, 90, 15, 79, 27, 91)(18, 82, 29, 93, 21, 85, 30, 94)(20, 84, 31, 95, 22, 86, 32, 96)(33, 97, 41, 105, 35, 99, 42, 106)(34, 98, 43, 107, 36, 100, 44, 108)(37, 101, 45, 109, 39, 103, 46, 110)(38, 102, 47, 111, 40, 104, 48, 112)(49, 113, 57, 121, 51, 115, 58, 122)(50, 114, 59, 123, 52, 116, 60, 124)(53, 117, 61, 125, 55, 119, 62, 126)(54, 118, 63, 127, 56, 120, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 83)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 92)(20, 71)(21, 77)(22, 72)(23, 97)(24, 99)(25, 74)(26, 98)(27, 100)(28, 89)(29, 101)(30, 103)(31, 102)(32, 104)(33, 90)(34, 87)(35, 91)(36, 88)(37, 95)(38, 93)(39, 96)(40, 94)(41, 113)(42, 115)(43, 114)(44, 116)(45, 117)(46, 119)(47, 118)(48, 120)(49, 107)(50, 105)(51, 108)(52, 106)(53, 111)(54, 109)(55, 112)(56, 110)(57, 127)(58, 128)(59, 125)(60, 126)(61, 121)(62, 122)(63, 123)(64, 124) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.993 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.996 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^16 ] Map:: non-degenerate R = (1, 65, 3, 67, 10, 74, 5, 69)(2, 66, 7, 71, 19, 83, 8, 72)(4, 68, 12, 76, 25, 89, 13, 77)(6, 70, 16, 80, 28, 92, 17, 81)(9, 73, 23, 87, 14, 78, 24, 88)(11, 75, 26, 90, 15, 79, 27, 91)(18, 82, 29, 93, 21, 85, 30, 94)(20, 84, 31, 95, 22, 86, 32, 96)(33, 97, 41, 105, 35, 99, 42, 106)(34, 98, 43, 107, 36, 100, 44, 108)(37, 101, 45, 109, 39, 103, 46, 110)(38, 102, 47, 111, 40, 104, 48, 112)(49, 113, 57, 121, 51, 115, 58, 122)(50, 114, 59, 123, 52, 116, 60, 124)(53, 117, 61, 125, 55, 119, 62, 126)(54, 118, 63, 127, 56, 120, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 83)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 92)(20, 71)(21, 77)(22, 72)(23, 97)(24, 99)(25, 74)(26, 98)(27, 100)(28, 89)(29, 101)(30, 103)(31, 102)(32, 104)(33, 90)(34, 87)(35, 91)(36, 88)(37, 95)(38, 93)(39, 96)(40, 94)(41, 113)(42, 115)(43, 114)(44, 116)(45, 117)(46, 119)(47, 118)(48, 120)(49, 107)(50, 105)(51, 108)(52, 106)(53, 111)(54, 109)(55, 112)(56, 110)(57, 126)(58, 125)(59, 128)(60, 127)(61, 124)(62, 123)(63, 122)(64, 121) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.994 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.997 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2^-2 * T1, (T2^-1 * T1 * T2^-1 * T1^-1)^2, (T2 * T1^-1)^4, T2^-3 * T1 * T2^2 * T1 * T2^-3 ] Map:: non-degenerate R = (1, 65, 3, 67, 10, 74, 27, 91, 46, 110, 54, 118, 36, 100, 18, 82, 6, 70, 17, 81, 35, 99, 53, 117, 52, 116, 34, 98, 16, 80, 5, 69)(2, 66, 7, 71, 20, 84, 39, 103, 56, 120, 48, 112, 28, 92, 13, 77, 4, 68, 12, 76, 31, 95, 49, 113, 60, 124, 44, 108, 24, 88, 8, 72)(9, 73, 25, 89, 14, 78, 32, 96, 50, 114, 62, 126, 47, 111, 30, 94, 11, 75, 29, 93, 15, 79, 33, 97, 51, 115, 61, 125, 45, 109, 26, 90)(19, 83, 37, 101, 22, 86, 42, 106, 58, 122, 64, 128, 57, 121, 41, 105, 21, 85, 40, 104, 23, 87, 43, 107, 59, 123, 63, 127, 55, 119, 38, 102) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 83)(8, 86)(9, 81)(10, 88)(11, 67)(12, 85)(13, 87)(14, 82)(15, 69)(16, 84)(17, 75)(18, 79)(19, 76)(20, 100)(21, 71)(22, 77)(23, 72)(24, 99)(25, 101)(26, 106)(27, 109)(28, 74)(29, 104)(30, 107)(31, 80)(32, 102)(33, 105)(34, 114)(35, 92)(36, 95)(37, 93)(38, 97)(39, 119)(40, 89)(41, 96)(42, 94)(43, 90)(44, 122)(45, 117)(46, 124)(47, 91)(48, 123)(49, 121)(50, 118)(51, 98)(52, 120)(53, 111)(54, 115)(55, 113)(56, 110)(57, 103)(58, 112)(59, 108)(60, 116)(61, 128)(62, 127)(63, 125)(64, 126) local type(s) :: { ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.992 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 64 f = 32 degree seq :: [ 32^4 ] E15.998 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1^4, Y1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^16 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 16, 80, 11, 75)(5, 69, 14, 78, 17, 81, 15, 79)(7, 71, 18, 82, 12, 76, 20, 84)(8, 72, 21, 85, 13, 77, 22, 86)(10, 74, 19, 83, 28, 92, 25, 89)(23, 87, 33, 97, 26, 90, 34, 98)(24, 88, 35, 99, 27, 91, 36, 100)(29, 93, 37, 101, 31, 95, 38, 102)(30, 94, 39, 103, 32, 96, 40, 104)(41, 105, 49, 113, 43, 107, 50, 114)(42, 106, 51, 115, 44, 108, 52, 116)(45, 109, 53, 117, 47, 111, 54, 118)(46, 110, 55, 119, 48, 112, 56, 120)(57, 121, 62, 126, 59, 123, 64, 128)(58, 122, 61, 125, 60, 124, 63, 127)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 135, 199, 147, 211, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(134, 198, 144, 208, 156, 220, 145, 209)(137, 201, 151, 215, 142, 206, 152, 216)(139, 203, 154, 218, 143, 207, 155, 219)(146, 210, 157, 221, 149, 213, 158, 222)(148, 212, 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, 129)(3, 139)(4, 134)(5, 143)(6, 130)(7, 148)(8, 150)(9, 131)(10, 153)(11, 144)(12, 146)(13, 149)(14, 133)(15, 145)(16, 137)(17, 142)(18, 135)(19, 138)(20, 140)(21, 136)(22, 141)(23, 162)(24, 164)(25, 156)(26, 161)(27, 163)(28, 147)(29, 166)(30, 168)(31, 165)(32, 167)(33, 151)(34, 154)(35, 152)(36, 155)(37, 157)(38, 159)(39, 158)(40, 160)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 169)(50, 171)(51, 170)(52, 172)(53, 173)(54, 175)(55, 174)(56, 176)(57, 192)(58, 191)(59, 190)(60, 189)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.1003 Graph:: bipartite v = 32 e = 128 f = 68 degree seq :: [ 8^32 ] E15.999 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y1^-1 * Y2^-8 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 17, 81, 11, 75)(5, 69, 14, 78, 18, 82, 15, 79)(7, 71, 19, 83, 12, 76, 21, 85)(8, 72, 22, 86, 13, 77, 23, 87)(10, 74, 24, 88, 35, 99, 28, 92)(16, 80, 20, 84, 36, 100, 31, 95)(25, 89, 37, 101, 29, 93, 40, 104)(26, 90, 42, 106, 30, 94, 43, 107)(27, 91, 45, 109, 53, 117, 47, 111)(32, 96, 38, 102, 33, 97, 41, 105)(34, 98, 50, 114, 54, 118, 51, 115)(39, 103, 55, 119, 49, 113, 57, 121)(44, 108, 58, 122, 48, 112, 59, 123)(46, 110, 60, 124, 52, 116, 56, 120)(61, 125, 64, 128, 62, 126, 63, 127)(129, 193, 131, 195, 138, 202, 155, 219, 174, 238, 182, 246, 164, 228, 146, 210, 134, 198, 145, 209, 163, 227, 181, 245, 180, 244, 162, 226, 144, 208, 133, 197)(130, 194, 135, 199, 148, 212, 167, 231, 184, 248, 176, 240, 156, 220, 141, 205, 132, 196, 140, 204, 159, 223, 177, 241, 188, 252, 172, 236, 152, 216, 136, 200)(137, 201, 153, 217, 142, 206, 160, 224, 178, 242, 190, 254, 175, 239, 158, 222, 139, 203, 157, 221, 143, 207, 161, 225, 179, 243, 189, 253, 173, 237, 154, 218)(147, 211, 165, 229, 150, 214, 170, 234, 186, 250, 192, 256, 185, 249, 169, 233, 149, 213, 168, 232, 151, 215, 171, 235, 187, 251, 191, 255, 183, 247, 166, 230) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 155)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 142)(26, 137)(27, 174)(28, 141)(29, 143)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 150)(38, 147)(39, 184)(40, 151)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 182)(47, 158)(48, 156)(49, 188)(50, 190)(51, 189)(52, 162)(53, 180)(54, 164)(55, 166)(56, 176)(57, 169)(58, 192)(59, 191)(60, 172)(61, 173)(62, 175)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1002 Graph:: bipartite v = 20 e = 128 f = 80 degree seq :: [ 8^16, 32^4 ] E15.1000 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^2 * Y1^-1, (Y2^-1 * Y1 * Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y2 * Y1^-1 * Y2^-7 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 17, 81, 11, 75)(5, 69, 14, 78, 18, 82, 15, 79)(7, 71, 19, 83, 12, 76, 21, 85)(8, 72, 22, 86, 13, 77, 23, 87)(10, 74, 24, 88, 35, 99, 28, 92)(16, 80, 20, 84, 36, 100, 31, 95)(25, 89, 37, 101, 29, 93, 40, 104)(26, 90, 42, 106, 30, 94, 43, 107)(27, 91, 45, 109, 53, 117, 47, 111)(32, 96, 38, 102, 33, 97, 41, 105)(34, 98, 50, 114, 54, 118, 51, 115)(39, 103, 55, 119, 49, 113, 57, 121)(44, 108, 58, 122, 48, 112, 59, 123)(46, 110, 60, 124, 63, 127, 62, 126)(52, 116, 56, 120, 64, 128, 61, 125)(129, 193, 131, 195, 138, 202, 155, 219, 174, 238, 183, 247, 166, 230, 147, 211, 165, 229, 150, 214, 170, 234, 186, 250, 180, 244, 162, 226, 144, 208, 133, 197)(130, 194, 135, 199, 148, 212, 167, 231, 184, 248, 175, 239, 158, 222, 139, 203, 157, 221, 143, 207, 161, 225, 179, 243, 188, 252, 172, 236, 152, 216, 136, 200)(132, 196, 140, 204, 159, 223, 177, 241, 189, 253, 173, 237, 154, 218, 137, 201, 153, 217, 142, 206, 160, 224, 178, 242, 190, 254, 176, 240, 156, 220, 141, 205)(134, 198, 145, 209, 163, 227, 181, 245, 191, 255, 185, 249, 169, 233, 149, 213, 168, 232, 151, 215, 171, 235, 187, 251, 192, 256, 182, 246, 164, 228, 146, 210) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 155)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 142)(26, 137)(27, 174)(28, 141)(29, 143)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 150)(38, 147)(39, 184)(40, 151)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 183)(47, 158)(48, 156)(49, 189)(50, 190)(51, 188)(52, 162)(53, 191)(54, 164)(55, 166)(56, 175)(57, 169)(58, 180)(59, 192)(60, 172)(61, 173)(62, 176)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1001 Graph:: bipartite v = 20 e = 128 f = 80 degree seq :: [ 8^16, 32^4 ] E15.1001 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3^-2 * Y2^-1 * Y3^-2 * Y2, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-3 * Y2 * Y3^2 * Y2 * Y3^-3, (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, 132, 196)(131, 195, 137, 201, 145, 209, 139, 203)(133, 197, 142, 206, 146, 210, 143, 207)(135, 199, 147, 211, 140, 204, 149, 213)(136, 200, 150, 214, 141, 205, 151, 215)(138, 202, 152, 216, 163, 227, 156, 220)(144, 208, 148, 212, 164, 228, 159, 223)(153, 217, 165, 229, 157, 221, 168, 232)(154, 218, 170, 234, 158, 222, 171, 235)(155, 219, 173, 237, 181, 245, 175, 239)(160, 224, 166, 230, 161, 225, 169, 233)(162, 226, 178, 242, 182, 246, 179, 243)(167, 231, 183, 247, 177, 241, 185, 249)(172, 236, 186, 250, 176, 240, 187, 251)(174, 238, 188, 252, 180, 244, 184, 248)(189, 253, 192, 256, 190, 254, 191, 255) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 155)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 142)(26, 137)(27, 174)(28, 141)(29, 143)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 150)(38, 147)(39, 184)(40, 151)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 182)(47, 158)(48, 156)(49, 188)(50, 190)(51, 189)(52, 162)(53, 180)(54, 164)(55, 166)(56, 176)(57, 169)(58, 192)(59, 191)(60, 172)(61, 173)(62, 175)(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, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E15.1000 Graph:: simple bipartite v = 80 e = 128 f = 20 degree seq :: [ 2^64, 8^16 ] E15.1002 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-5 * Y2 * Y3 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^16 ] Map:: polytopal 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, 132, 196)(131, 195, 137, 201, 145, 209, 139, 203)(133, 197, 142, 206, 146, 210, 143, 207)(135, 199, 147, 211, 140, 204, 149, 213)(136, 200, 150, 214, 141, 205, 151, 215)(138, 202, 152, 216, 163, 227, 156, 220)(144, 208, 148, 212, 164, 228, 159, 223)(153, 217, 165, 229, 157, 221, 168, 232)(154, 218, 170, 234, 158, 222, 171, 235)(155, 219, 173, 237, 181, 245, 175, 239)(160, 224, 166, 230, 161, 225, 169, 233)(162, 226, 178, 242, 182, 246, 179, 243)(167, 231, 183, 247, 177, 241, 185, 249)(172, 236, 186, 250, 176, 240, 187, 251)(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, 145)(7, 148)(8, 130)(9, 153)(10, 155)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 142)(26, 137)(27, 174)(28, 141)(29, 143)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 150)(38, 147)(39, 184)(40, 151)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 183)(47, 158)(48, 156)(49, 189)(50, 190)(51, 188)(52, 162)(53, 191)(54, 164)(55, 166)(56, 175)(57, 169)(58, 180)(59, 192)(60, 172)(61, 173)(62, 176)(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) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E15.999 Graph:: simple bipartite v = 80 e = 128 f = 20 degree seq :: [ 2^64, 8^16 ] E15.1003 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = Q16 : C4 (small group id <64, 39>) Aut = $<128, 918>$ (small group id <128, 918>) |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 * Y1^2 * Y3^-1 * Y1^2, (Y1^-1 * Y3 * Y1^-1 * Y3^-1)^2, (Y3 * Y1^-1)^4, (Y3 * Y2^-1)^4, Y1^-2 * Y3^2 * Y1^-6 ] Map:: 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, 50, 114, 32, 96, 13, 77, 4, 68)(3, 67, 9, 73, 25, 89, 45, 109, 55, 119, 40, 104, 19, 83, 16, 80, 5, 69, 15, 79, 33, 97, 52, 116, 54, 118, 39, 103, 18, 82, 11, 75)(7, 71, 20, 84, 12, 76, 31, 95, 49, 113, 58, 122, 37, 101, 24, 88, 8, 72, 23, 87, 14, 78, 34, 98, 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)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 146)(7, 149)(8, 130)(9, 154)(10, 133)(11, 157)(12, 156)(13, 153)(14, 132)(15, 155)(16, 158)(17, 164)(18, 166)(19, 134)(20, 169)(21, 136)(22, 171)(23, 170)(24, 172)(25, 174)(26, 143)(27, 137)(28, 142)(29, 144)(30, 139)(31, 175)(32, 177)(33, 141)(34, 176)(35, 182)(36, 184)(37, 145)(38, 147)(39, 187)(40, 188)(41, 151)(42, 148)(43, 152)(44, 150)(45, 189)(46, 161)(47, 162)(48, 159)(49, 181)(50, 183)(51, 160)(52, 190)(53, 179)(54, 178)(55, 163)(56, 165)(57, 191)(58, 192)(59, 168)(60, 167)(61, 180)(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) :: { ( 8, 8 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E15.998 Graph:: simple bipartite v = 68 e = 128 f = 32 degree seq :: [ 2^64, 32^4 ] E15.1004 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2 * T1^-2 * T2^-1 * T1^-2, (T2^-2 * T1^-1)^2, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 ] 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, 66, 70, 68)(67, 73, 80, 75)(69, 78, 81, 79)(71, 82, 76, 84)(72, 85, 77, 86)(74, 89, 92, 83)(87, 97, 90, 98)(88, 99, 91, 100)(93, 101, 95, 102)(94, 103, 96, 104)(105, 113, 107, 114)(106, 115, 108, 116)(109, 117, 111, 118)(110, 119, 112, 120)(121, 127, 123, 125)(122, 126, 124, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32^4 ) } Outer automorphisms :: reflexible Dual of E15.1009 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 64 f = 4 degree seq :: [ 4^32 ] E15.1005 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, (T2^2 * T1)^2, (T2^2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-6 * T1 * T2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 48, 54, 36, 18, 6, 17, 35, 53, 52, 34, 16, 5)(2, 7, 20, 39, 57, 46, 27, 13, 4, 12, 31, 49, 60, 44, 24, 8)(9, 25, 15, 33, 51, 62, 47, 30, 11, 29, 14, 32, 50, 61, 45, 26)(19, 37, 23, 43, 59, 64, 56, 41, 21, 40, 22, 42, 58, 63, 55, 38)(65, 66, 70, 68)(67, 73, 81, 75)(69, 78, 82, 79)(71, 83, 76, 85)(72, 86, 77, 87)(74, 91, 99, 88)(80, 95, 100, 84)(89, 104, 93, 101)(90, 107, 94, 106)(92, 111, 117, 109)(96, 105, 97, 102)(98, 115, 118, 114)(103, 120, 113, 119)(108, 123, 110, 122)(112, 124, 116, 121)(125, 127, 126, 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.1007 Transitivity :: ET+ Graph:: bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.1006 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (T2 * T1^-1)^2, (F * T1)^2, T1 * T2^-2 * T1^-2 * T2^2 * T1, (T2^3 * T1)^2, (T2^-1 * T1^-1)^4, T2^6 * T1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 24, 48, 55, 38, 17, 37, 27, 43, 59, 52, 32, 14, 5)(2, 7, 18, 40, 57, 46, 23, 33, 30, 13, 29, 50, 60, 44, 20, 8)(4, 11, 26, 49, 61, 45, 22, 9, 21, 35, 31, 51, 62, 47, 28, 12)(6, 15, 34, 53, 63, 56, 39, 25, 42, 19, 41, 58, 64, 54, 36, 16)(65, 66, 70, 68)(67, 73, 83, 72)(69, 75, 89, 77)(71, 81, 99, 80)(74, 87, 98, 86)(76, 79, 97, 91)(78, 93, 100, 95)(82, 103, 90, 102)(84, 105, 92, 107)(85, 101, 94, 106)(88, 111, 122, 110)(96, 115, 120, 104)(108, 123, 109, 117)(112, 124, 127, 126)(113, 118, 114, 119)(116, 121, 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.1008 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.1007 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2 * T1^-2 * T2^-1 * T1^-2, (T2^-2 * T1^-1)^2, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 ] Map:: polytopal non-degenerate R = (1, 65, 3, 67, 10, 74, 5, 69)(2, 66, 7, 71, 19, 83, 8, 72)(4, 68, 12, 76, 25, 89, 13, 77)(6, 70, 16, 80, 28, 92, 17, 81)(9, 73, 23, 87, 15, 79, 24, 88)(11, 75, 26, 90, 14, 78, 27, 91)(18, 82, 29, 93, 22, 86, 30, 94)(20, 84, 31, 95, 21, 85, 32, 96)(33, 97, 41, 105, 36, 100, 42, 106)(34, 98, 43, 107, 35, 99, 44, 108)(37, 101, 45, 109, 40, 104, 46, 110)(38, 102, 47, 111, 39, 103, 48, 112)(49, 113, 57, 121, 52, 116, 58, 122)(50, 114, 59, 123, 51, 115, 60, 124)(53, 117, 61, 125, 56, 120, 62, 126)(54, 118, 63, 127, 55, 119, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 89)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 74)(20, 71)(21, 77)(22, 72)(23, 97)(24, 99)(25, 92)(26, 98)(27, 100)(28, 83)(29, 101)(30, 103)(31, 102)(32, 104)(33, 90)(34, 87)(35, 91)(36, 88)(37, 95)(38, 93)(39, 96)(40, 94)(41, 113)(42, 115)(43, 114)(44, 116)(45, 117)(46, 119)(47, 118)(48, 120)(49, 107)(50, 105)(51, 108)(52, 106)(53, 111)(54, 109)(55, 112)(56, 110)(57, 127)(58, 126)(59, 125)(60, 128)(61, 121)(62, 124)(63, 123)(64, 122) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1005 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.1008 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T2 * T1^-2)^2, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^16 ] Map:: non-degenerate R = (1, 65, 3, 67, 10, 74, 5, 69)(2, 66, 7, 71, 19, 83, 8, 72)(4, 68, 12, 76, 25, 89, 13, 77)(6, 70, 16, 80, 28, 92, 17, 81)(9, 73, 23, 87, 14, 78, 24, 88)(11, 75, 26, 90, 15, 79, 27, 91)(18, 82, 29, 93, 21, 85, 30, 94)(20, 84, 31, 95, 22, 86, 32, 96)(33, 97, 41, 105, 35, 99, 42, 106)(34, 98, 43, 107, 36, 100, 44, 108)(37, 101, 45, 109, 39, 103, 46, 110)(38, 102, 47, 111, 40, 104, 48, 112)(49, 113, 57, 121, 51, 115, 58, 122)(50, 114, 59, 123, 52, 116, 60, 124)(53, 117, 61, 125, 55, 119, 62, 126)(54, 118, 63, 127, 56, 120, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 81)(10, 83)(11, 67)(12, 86)(13, 84)(14, 80)(15, 69)(16, 79)(17, 75)(18, 77)(19, 92)(20, 71)(21, 76)(22, 72)(23, 97)(24, 99)(25, 74)(26, 100)(27, 98)(28, 89)(29, 101)(30, 103)(31, 104)(32, 102)(33, 91)(34, 87)(35, 90)(36, 88)(37, 96)(38, 93)(39, 95)(40, 94)(41, 113)(42, 115)(43, 116)(44, 114)(45, 117)(46, 119)(47, 120)(48, 118)(49, 108)(50, 105)(51, 107)(52, 106)(53, 112)(54, 109)(55, 111)(56, 110)(57, 126)(58, 125)(59, 128)(60, 127)(61, 123)(62, 124)(63, 121)(64, 122) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1006 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.1009 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, (T2^2 * T1)^2, (T2^2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-6 * T1 * T2 ] Map:: non-degenerate R = (1, 65, 3, 67, 10, 74, 28, 92, 48, 112, 54, 118, 36, 100, 18, 82, 6, 70, 17, 81, 35, 99, 53, 117, 52, 116, 34, 98, 16, 80, 5, 69)(2, 66, 7, 71, 20, 84, 39, 103, 57, 121, 46, 110, 27, 91, 13, 77, 4, 68, 12, 76, 31, 95, 49, 113, 60, 124, 44, 108, 24, 88, 8, 72)(9, 73, 25, 89, 15, 79, 33, 97, 51, 115, 62, 126, 47, 111, 30, 94, 11, 75, 29, 93, 14, 78, 32, 96, 50, 114, 61, 125, 45, 109, 26, 90)(19, 83, 37, 101, 23, 87, 43, 107, 59, 123, 64, 128, 56, 120, 41, 105, 21, 85, 40, 104, 22, 86, 42, 106, 58, 122, 63, 127, 55, 119, 38, 102) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 83)(8, 86)(9, 81)(10, 91)(11, 67)(12, 85)(13, 87)(14, 82)(15, 69)(16, 95)(17, 75)(18, 79)(19, 76)(20, 80)(21, 71)(22, 77)(23, 72)(24, 74)(25, 104)(26, 107)(27, 99)(28, 111)(29, 101)(30, 106)(31, 100)(32, 105)(33, 102)(34, 115)(35, 88)(36, 84)(37, 89)(38, 96)(39, 120)(40, 93)(41, 97)(42, 90)(43, 94)(44, 123)(45, 92)(46, 122)(47, 117)(48, 124)(49, 119)(50, 98)(51, 118)(52, 121)(53, 109)(54, 114)(55, 103)(56, 113)(57, 112)(58, 108)(59, 110)(60, 116)(61, 127)(62, 128)(63, 126)(64, 125) local type(s) :: { ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.1004 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 64 f = 32 degree seq :: [ 32^4 ] E15.1010 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, (Y2 * Y1^-2)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^16 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 17, 81, 11, 75)(5, 69, 14, 78, 16, 80, 15, 79)(7, 71, 18, 82, 13, 77, 20, 84)(8, 72, 21, 85, 12, 76, 22, 86)(10, 74, 19, 83, 28, 92, 25, 89)(23, 87, 33, 97, 27, 91, 34, 98)(24, 88, 35, 99, 26, 90, 36, 100)(29, 93, 37, 101, 32, 96, 38, 102)(30, 94, 39, 103, 31, 95, 40, 104)(41, 105, 49, 113, 44, 108, 50, 114)(42, 106, 51, 115, 43, 107, 52, 116)(45, 109, 53, 117, 48, 112, 54, 118)(46, 110, 55, 119, 47, 111, 56, 120)(57, 121, 62, 126, 60, 124, 63, 127)(58, 122, 61, 125, 59, 123, 64, 128)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 135, 199, 147, 211, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(134, 198, 144, 208, 156, 220, 145, 209)(137, 201, 151, 215, 142, 206, 152, 216)(139, 203, 154, 218, 143, 207, 155, 219)(146, 210, 157, 221, 149, 213, 158, 222)(148, 212, 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, 129)(3, 139)(4, 134)(5, 143)(6, 130)(7, 148)(8, 150)(9, 131)(10, 153)(11, 145)(12, 149)(13, 146)(14, 133)(15, 144)(16, 142)(17, 137)(18, 135)(19, 138)(20, 141)(21, 136)(22, 140)(23, 162)(24, 164)(25, 156)(26, 163)(27, 161)(28, 147)(29, 166)(30, 168)(31, 167)(32, 165)(33, 151)(34, 155)(35, 152)(36, 154)(37, 157)(38, 160)(39, 158)(40, 159)(41, 178)(42, 180)(43, 179)(44, 177)(45, 182)(46, 184)(47, 183)(48, 181)(49, 169)(50, 172)(51, 170)(52, 171)(53, 173)(54, 176)(55, 174)(56, 175)(57, 191)(58, 192)(59, 189)(60, 190)(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) :: { ( 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.1015 Graph:: bipartite v = 32 e = 128 f = 68 degree seq :: [ 8^32 ] E15.1011 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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 * Y3^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, (Y2^2 * Y1^-1)^2, (Y2^-1 * Y1^-1 * Y2^-1)^2, (Y2 * Y1 * Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^2 * Y1 * Y2^-6 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 17, 81, 11, 75)(5, 69, 14, 78, 18, 82, 15, 79)(7, 71, 19, 83, 12, 76, 21, 85)(8, 72, 22, 86, 13, 77, 23, 87)(10, 74, 27, 91, 35, 99, 24, 88)(16, 80, 31, 95, 36, 100, 20, 84)(25, 89, 40, 104, 29, 93, 37, 101)(26, 90, 43, 107, 30, 94, 42, 106)(28, 92, 47, 111, 53, 117, 45, 109)(32, 96, 41, 105, 33, 97, 38, 102)(34, 98, 51, 115, 54, 118, 50, 114)(39, 103, 56, 120, 49, 113, 55, 119)(44, 108, 59, 123, 46, 110, 58, 122)(48, 112, 60, 124, 52, 116, 57, 121)(61, 125, 63, 127, 62, 126, 64, 128)(129, 193, 131, 195, 138, 202, 156, 220, 176, 240, 182, 246, 164, 228, 146, 210, 134, 198, 145, 209, 163, 227, 181, 245, 180, 244, 162, 226, 144, 208, 133, 197)(130, 194, 135, 199, 148, 212, 167, 231, 185, 249, 174, 238, 155, 219, 141, 205, 132, 196, 140, 204, 159, 223, 177, 241, 188, 252, 172, 236, 152, 216, 136, 200)(137, 201, 153, 217, 143, 207, 161, 225, 179, 243, 190, 254, 175, 239, 158, 222, 139, 203, 157, 221, 142, 206, 160, 224, 178, 242, 189, 253, 173, 237, 154, 218)(147, 211, 165, 229, 151, 215, 171, 235, 187, 251, 192, 256, 184, 248, 169, 233, 149, 213, 168, 232, 150, 214, 170, 234, 186, 250, 191, 255, 183, 247, 166, 230) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 156)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 143)(26, 137)(27, 141)(28, 176)(29, 142)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 151)(38, 147)(39, 185)(40, 150)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 155)(47, 158)(48, 182)(49, 188)(50, 189)(51, 190)(52, 162)(53, 180)(54, 164)(55, 166)(56, 169)(57, 174)(58, 191)(59, 192)(60, 172)(61, 173)(62, 175)(63, 183)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1014 Graph:: bipartite v = 20 e = 128 f = 80 degree seq :: [ 8^16, 32^4 ] E15.1012 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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 * Y3^-1, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, Y1^4, Y1^2 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-1, (Y2^3 * Y1)^2, (Y3^-1 * Y1^-1)^4, Y2^6 * Y1 * Y2^-2 * Y1^-1 ] Map:: 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, 131)(2, 135)(3, 138)(4, 139)(5, 129)(6, 143)(7, 146)(8, 130)(9, 149)(10, 152)(11, 154)(12, 132)(13, 157)(14, 133)(15, 162)(16, 134)(17, 165)(18, 168)(19, 169)(20, 136)(21, 163)(22, 137)(23, 161)(24, 176)(25, 170)(26, 177)(27, 171)(28, 140)(29, 178)(30, 141)(31, 179)(32, 142)(33, 158)(34, 181)(35, 159)(36, 144)(37, 155)(38, 145)(39, 153)(40, 185)(41, 186)(42, 147)(43, 187)(44, 148)(45, 150)(46, 151)(47, 156)(48, 183)(49, 189)(50, 188)(51, 190)(52, 160)(53, 191)(54, 164)(55, 166)(56, 167)(57, 174)(58, 192)(59, 180)(60, 172)(61, 173)(62, 175)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1013 Graph:: bipartite v = 20 e = 128 f = 80 degree seq :: [ 8^16, 32^4 ] E15.1013 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (Y3^2 * Y2)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2^-1)^2, (Y3^-1 * Y2 * Y3^-1 * Y2^-1)^2, Y2^-1 * Y3^-8 * 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, 132, 196)(131, 195, 137, 201, 145, 209, 139, 203)(133, 197, 142, 206, 146, 210, 143, 207)(135, 199, 147, 211, 140, 204, 149, 213)(136, 200, 150, 214, 141, 205, 151, 215)(138, 202, 155, 219, 163, 227, 152, 216)(144, 208, 159, 223, 164, 228, 148, 212)(153, 217, 168, 232, 157, 221, 165, 229)(154, 218, 171, 235, 158, 222, 170, 234)(156, 220, 175, 239, 181, 245, 173, 237)(160, 224, 169, 233, 161, 225, 166, 230)(162, 226, 179, 243, 182, 246, 178, 242)(167, 231, 184, 248, 177, 241, 183, 247)(172, 236, 187, 251, 174, 238, 186, 250)(176, 240, 188, 252, 180, 244, 185, 249)(189, 253, 191, 255, 190, 254, 192, 256) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 156)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 143)(26, 137)(27, 141)(28, 176)(29, 142)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 151)(38, 147)(39, 185)(40, 150)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 155)(47, 158)(48, 182)(49, 188)(50, 189)(51, 190)(52, 162)(53, 180)(54, 164)(55, 166)(56, 169)(57, 174)(58, 191)(59, 192)(60, 172)(61, 173)(62, 175)(63, 183)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E15.1012 Graph:: simple bipartite v = 80 e = 128 f = 20 degree seq :: [ 2^64, 8^16 ] E15.1014 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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, R^2, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3 * Y2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y2)^4, (Y3^3 * Y2^-1)^2, Y3 * Y2^-1 * Y3^-7 * Y2^-1, (Y3^-1 * Y1^-1)^16 ] Map:: polytopal 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, 132, 196)(131, 195, 137, 201, 149, 213, 139, 203)(133, 197, 141, 205, 146, 210, 135, 199)(136, 200, 147, 211, 162, 226, 143, 207)(138, 202, 151, 215, 161, 225, 153, 217)(140, 204, 144, 208, 163, 227, 156, 220)(142, 206, 159, 223, 164, 228, 157, 221)(145, 209, 165, 229, 155, 219, 167, 231)(148, 212, 171, 235, 150, 214, 169, 233)(152, 216, 175, 239, 187, 251, 172, 236)(154, 218, 168, 232, 158, 222, 170, 234)(160, 224, 177, 241, 183, 247, 179, 243)(166, 230, 184, 248, 178, 242, 182, 246)(173, 237, 181, 245, 174, 238, 186, 250)(176, 240, 188, 252, 191, 255, 189, 253)(180, 244, 185, 249, 192, 256, 190, 254) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 143)(7, 145)(8, 130)(9, 132)(10, 152)(11, 154)(12, 155)(13, 157)(14, 133)(15, 161)(16, 134)(17, 166)(18, 168)(19, 169)(20, 136)(21, 171)(22, 137)(23, 139)(24, 176)(25, 162)(26, 163)(27, 177)(28, 170)(29, 178)(30, 141)(31, 179)(32, 142)(33, 181)(34, 158)(35, 159)(36, 144)(37, 146)(38, 185)(39, 156)(40, 149)(41, 186)(42, 147)(43, 187)(44, 148)(45, 150)(46, 151)(47, 153)(48, 184)(49, 190)(50, 189)(51, 188)(52, 160)(53, 191)(54, 164)(55, 165)(56, 167)(57, 174)(58, 180)(59, 192)(60, 172)(61, 173)(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) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E15.1011 Graph:: simple bipartite v = 80 e = 128 f = 20 degree seq :: [ 2^64, 8^16 ] E15.1015 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |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^-2)^2, (Y1^-2 * Y3^-1)^2, (Y3 * Y1^-1)^4, (Y3 * Y2^-1)^4, Y1^-2 * Y3^-2 * Y1^-6 ] Map:: 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, 33, 97, 13, 77, 4, 68)(3, 67, 9, 73, 25, 89, 45, 109, 55, 119, 39, 103, 18, 82, 16, 80, 5, 69, 15, 79, 32, 96, 50, 114, 54, 118, 40, 104, 19, 83, 11, 75)(7, 71, 20, 84, 14, 78, 34, 98, 51, 115, 57, 121, 36, 100, 24, 88, 8, 72, 23, 87, 12, 76, 31, 95, 49, 113, 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)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 146)(7, 149)(8, 130)(9, 154)(10, 133)(11, 157)(12, 156)(13, 160)(14, 132)(15, 155)(16, 158)(17, 164)(18, 166)(19, 134)(20, 169)(21, 136)(22, 171)(23, 170)(24, 172)(25, 141)(26, 143)(27, 137)(28, 142)(29, 144)(30, 139)(31, 176)(32, 174)(33, 179)(34, 175)(35, 182)(36, 184)(37, 145)(38, 147)(39, 187)(40, 188)(41, 151)(42, 148)(43, 152)(44, 150)(45, 189)(46, 153)(47, 159)(48, 162)(49, 161)(50, 190)(51, 181)(52, 183)(53, 177)(54, 180)(55, 163)(56, 165)(57, 191)(58, 192)(59, 168)(60, 167)(61, 178)(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) :: { ( 8, 8 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E15.1010 Graph:: simple bipartite v = 68 e = 128 f = 32 degree seq :: [ 2^64, 32^4 ] E15.1016 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = C16 : C4 (small group id <64, 47>) Aut = $<128, 947>$ (small group id <128, 947>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^16 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 62, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 63, 58, 50, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 53, 60, 64, 61, 54, 46, 38, 30, 22, 14)(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, 101, 98)(92, 95, 102, 99)(97, 104, 109, 106)(100, 103, 110, 107)(105, 112, 117, 114)(108, 111, 118, 115)(113, 120, 124, 122)(116, 119, 125, 123)(121, 126, 128, 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.1017 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.1017 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = C16 : C4 (small group id <64, 47>) Aut = $<128, 947>$ (small group id <128, 947>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^16 ] Map:: non-degenerate R = (1, 65, 3, 67, 6, 70, 5, 69)(2, 66, 7, 71, 4, 68, 8, 72)(9, 73, 13, 77, 10, 74, 14, 78)(11, 75, 15, 79, 12, 76, 16, 80)(17, 81, 21, 85, 18, 82, 22, 86)(19, 83, 23, 87, 20, 84, 24, 88)(25, 89, 29, 93, 26, 90, 30, 94)(27, 91, 31, 95, 28, 92, 32, 96)(33, 97, 37, 101, 34, 98, 38, 102)(35, 99, 39, 103, 36, 100, 40, 104)(41, 105, 45, 109, 42, 106, 46, 110)(43, 107, 47, 111, 44, 108, 48, 112)(49, 113, 53, 117, 50, 114, 54, 118)(51, 115, 55, 119, 52, 116, 56, 120)(57, 121, 61, 125, 58, 122, 62, 126)(59, 123, 63, 127, 60, 124, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 74)(6, 68)(7, 75)(8, 76)(9, 69)(10, 67)(11, 72)(12, 71)(13, 81)(14, 82)(15, 83)(16, 84)(17, 78)(18, 77)(19, 80)(20, 79)(21, 89)(22, 90)(23, 91)(24, 92)(25, 86)(26, 85)(27, 88)(28, 87)(29, 97)(30, 98)(31, 99)(32, 100)(33, 94)(34, 93)(35, 96)(36, 95)(37, 105)(38, 106)(39, 107)(40, 108)(41, 102)(42, 101)(43, 104)(44, 103)(45, 113)(46, 114)(47, 115)(48, 116)(49, 110)(50, 109)(51, 112)(52, 111)(53, 121)(54, 122)(55, 123)(56, 124)(57, 118)(58, 117)(59, 120)(60, 119)(61, 127)(62, 128)(63, 126)(64, 125) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1016 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.1018 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = C16 : C4 (small group id <64, 47>) Aut = $<128, 947>$ (small group id <128, 947>) |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, Y2^16 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 8, 72, 13, 77, 10, 74)(5, 69, 7, 71, 14, 78, 11, 75)(9, 73, 16, 80, 21, 85, 18, 82)(12, 76, 15, 79, 22, 86, 19, 83)(17, 81, 24, 88, 29, 93, 26, 90)(20, 84, 23, 87, 30, 94, 27, 91)(25, 89, 32, 96, 37, 101, 34, 98)(28, 92, 31, 95, 38, 102, 35, 99)(33, 97, 40, 104, 45, 109, 42, 106)(36, 100, 39, 103, 46, 110, 43, 107)(41, 105, 48, 112, 53, 117, 50, 114)(44, 108, 47, 111, 54, 118, 51, 115)(49, 113, 56, 120, 60, 124, 58, 122)(52, 116, 55, 119, 61, 125, 59, 123)(57, 121, 62, 126, 64, 128, 63, 127)(129, 193, 131, 195, 137, 201, 145, 209, 153, 217, 161, 225, 169, 233, 177, 241, 185, 249, 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, 186, 250, 178, 242, 170, 234, 162, 226, 154, 218, 146, 210, 138, 202)(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, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 141)(7, 143)(8, 130)(9, 145)(10, 132)(11, 147)(12, 133)(13, 149)(14, 134)(15, 151)(16, 136)(17, 153)(18, 138)(19, 155)(20, 140)(21, 157)(22, 142)(23, 159)(24, 144)(25, 161)(26, 146)(27, 163)(28, 148)(29, 165)(30, 150)(31, 167)(32, 152)(33, 169)(34, 154)(35, 171)(36, 156)(37, 173)(38, 158)(39, 175)(40, 160)(41, 177)(42, 162)(43, 179)(44, 164)(45, 181)(46, 166)(47, 183)(48, 168)(49, 185)(50, 170)(51, 187)(52, 172)(53, 188)(54, 174)(55, 190)(56, 176)(57, 180)(58, 178)(59, 191)(60, 192)(61, 182)(62, 184)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1019 Graph:: bipartite v = 20 e = 128 f = 80 degree seq :: [ 8^16, 32^4 ] E15.1019 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = C16 : C4 (small group id <64, 47>) Aut = $<128, 947>$ (small group id <128, 947>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^7 * Y2 * Y3^-9 * 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, 132, 196)(131, 195, 136, 200, 141, 205, 138, 202)(133, 197, 135, 199, 142, 206, 139, 203)(137, 201, 144, 208, 149, 213, 146, 210)(140, 204, 143, 207, 150, 214, 147, 211)(145, 209, 152, 216, 157, 221, 154, 218)(148, 212, 151, 215, 158, 222, 155, 219)(153, 217, 160, 224, 165, 229, 162, 226)(156, 220, 159, 223, 166, 230, 163, 227)(161, 225, 168, 232, 173, 237, 170, 234)(164, 228, 167, 231, 174, 238, 171, 235)(169, 233, 176, 240, 181, 245, 178, 242)(172, 236, 175, 239, 182, 246, 179, 243)(177, 241, 184, 248, 188, 252, 186, 250)(180, 244, 183, 247, 189, 253, 187, 251)(185, 249, 190, 254, 192, 256, 191, 255) L = (1, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 141)(7, 143)(8, 130)(9, 145)(10, 132)(11, 147)(12, 133)(13, 149)(14, 134)(15, 151)(16, 136)(17, 153)(18, 138)(19, 155)(20, 140)(21, 157)(22, 142)(23, 159)(24, 144)(25, 161)(26, 146)(27, 163)(28, 148)(29, 165)(30, 150)(31, 167)(32, 152)(33, 169)(34, 154)(35, 171)(36, 156)(37, 173)(38, 158)(39, 175)(40, 160)(41, 177)(42, 162)(43, 179)(44, 164)(45, 181)(46, 166)(47, 183)(48, 168)(49, 185)(50, 170)(51, 187)(52, 172)(53, 188)(54, 174)(55, 190)(56, 176)(57, 180)(58, 178)(59, 191)(60, 192)(61, 182)(62, 184)(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) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E15.1018 Graph:: simple bipartite v = 80 e = 128 f = 20 degree seq :: [ 2^64, 8^16 ] E15.1020 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 16}) Quotient :: edge Aut^+ = C16 : C4 (small group id <64, 48>) Aut = $<128, 950>$ (small group id <128, 950>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T1 * T2^-2 * T1^-1 * T2^-2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1 * T2^-1 * T1^-1)^2, T2^3 * T1 * T2^-5 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 46, 57, 41, 21, 40, 23, 43, 59, 52, 34, 16, 5)(2, 7, 20, 39, 56, 45, 26, 9, 25, 14, 32, 50, 60, 44, 24, 8)(4, 12, 31, 49, 62, 47, 30, 11, 29, 15, 33, 51, 61, 48, 28, 13)(6, 17, 35, 53, 63, 55, 38, 19, 37, 22, 42, 58, 64, 54, 36, 18)(65, 66, 70, 68)(67, 73, 81, 75)(69, 78, 82, 79)(71, 83, 76, 85)(72, 86, 77, 87)(74, 88, 99, 92)(80, 84, 100, 95)(89, 101, 93, 104)(90, 106, 94, 107)(91, 109, 117, 111)(96, 102, 97, 105)(98, 114, 118, 115)(103, 119, 113, 121)(108, 122, 112, 123)(110, 124, 127, 125)(116, 120, 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) :: { ( 8^4 ), ( 8^16 ) } Outer automorphisms :: reflexible Dual of E15.1021 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 64 f = 16 degree seq :: [ 4^16, 16^4 ] E15.1021 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 16}) Quotient :: loop Aut^+ = C16 : C4 (small group id <64, 48>) Aut = $<128, 950>$ (small group id <128, 950>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T2^4, T1 * T2 * T1^-2 * T2^-1 * T1, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^16 ] Map:: polytopal non-degenerate R = (1, 65, 3, 67, 10, 74, 5, 69)(2, 66, 7, 71, 19, 83, 8, 72)(4, 68, 12, 76, 25, 89, 13, 77)(6, 70, 16, 80, 28, 92, 17, 81)(9, 73, 23, 87, 14, 78, 24, 88)(11, 75, 26, 90, 15, 79, 27, 91)(18, 82, 29, 93, 21, 85, 30, 94)(20, 84, 31, 95, 22, 86, 32, 96)(33, 97, 41, 105, 35, 99, 42, 106)(34, 98, 43, 107, 36, 100, 44, 108)(37, 101, 45, 109, 39, 103, 46, 110)(38, 102, 47, 111, 40, 104, 48, 112)(49, 113, 57, 121, 51, 115, 58, 122)(50, 114, 59, 123, 52, 116, 60, 124)(53, 117, 61, 125, 55, 119, 62, 126)(54, 118, 63, 127, 56, 120, 64, 128) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 78)(6, 68)(7, 82)(8, 85)(9, 80)(10, 83)(11, 67)(12, 84)(13, 86)(14, 81)(15, 69)(16, 75)(17, 79)(18, 76)(19, 92)(20, 71)(21, 77)(22, 72)(23, 97)(24, 99)(25, 74)(26, 98)(27, 100)(28, 89)(29, 101)(30, 103)(31, 102)(32, 104)(33, 90)(34, 87)(35, 91)(36, 88)(37, 95)(38, 93)(39, 96)(40, 94)(41, 113)(42, 115)(43, 114)(44, 116)(45, 117)(46, 119)(47, 118)(48, 120)(49, 107)(50, 105)(51, 108)(52, 106)(53, 111)(54, 109)(55, 112)(56, 110)(57, 128)(58, 127)(59, 126)(60, 125)(61, 122)(62, 121)(63, 124)(64, 123) local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1020 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 64 f = 20 degree seq :: [ 8^16 ] E15.1022 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = C16 : C4 (small group id <64, 48>) Aut = $<128, 950>$ (small group id <128, 950>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-2 * Y1^-1 * Y2^-2 * Y1, (Y2^-1 * Y1 * Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^3 * Y1 * Y2^-5 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 17, 81, 11, 75)(5, 69, 14, 78, 18, 82, 15, 79)(7, 71, 19, 83, 12, 76, 21, 85)(8, 72, 22, 86, 13, 77, 23, 87)(10, 74, 24, 88, 35, 99, 28, 92)(16, 80, 20, 84, 36, 100, 31, 95)(25, 89, 37, 101, 29, 93, 40, 104)(26, 90, 42, 106, 30, 94, 43, 107)(27, 91, 45, 109, 53, 117, 47, 111)(32, 96, 38, 102, 33, 97, 41, 105)(34, 98, 50, 114, 54, 118, 51, 115)(39, 103, 55, 119, 49, 113, 57, 121)(44, 108, 58, 122, 48, 112, 59, 123)(46, 110, 60, 124, 63, 127, 61, 125)(52, 116, 56, 120, 64, 128, 62, 126)(129, 193, 131, 195, 138, 202, 155, 219, 174, 238, 185, 249, 169, 233, 149, 213, 168, 232, 151, 215, 171, 235, 187, 251, 180, 244, 162, 226, 144, 208, 133, 197)(130, 194, 135, 199, 148, 212, 167, 231, 184, 248, 173, 237, 154, 218, 137, 201, 153, 217, 142, 206, 160, 224, 178, 242, 188, 252, 172, 236, 152, 216, 136, 200)(132, 196, 140, 204, 159, 223, 177, 241, 190, 254, 175, 239, 158, 222, 139, 203, 157, 221, 143, 207, 161, 225, 179, 243, 189, 253, 176, 240, 156, 220, 141, 205)(134, 198, 145, 209, 163, 227, 181, 245, 191, 255, 183, 247, 166, 230, 147, 211, 165, 229, 150, 214, 170, 234, 186, 250, 192, 256, 182, 246, 164, 228, 146, 210) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 155)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 142)(26, 137)(27, 174)(28, 141)(29, 143)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 150)(38, 147)(39, 184)(40, 151)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 185)(47, 158)(48, 156)(49, 190)(50, 188)(51, 189)(52, 162)(53, 191)(54, 164)(55, 166)(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, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1023 Graph:: bipartite v = 20 e = 128 f = 80 degree seq :: [ 8^16, 32^4 ] E15.1023 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16}) Quotient :: dipole Aut^+ = C16 : C4 (small group id <64, 48>) Aut = $<128, 950>$ (small group id <128, 950>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^3 * Y2 * Y3^-5 * Y2^-1, (Y3^-1 * Y1^-1)^16 ] Map:: polytopal 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, 132, 196)(131, 195, 137, 201, 145, 209, 139, 203)(133, 197, 142, 206, 146, 210, 143, 207)(135, 199, 147, 211, 140, 204, 149, 213)(136, 200, 150, 214, 141, 205, 151, 215)(138, 202, 152, 216, 163, 227, 156, 220)(144, 208, 148, 212, 164, 228, 159, 223)(153, 217, 165, 229, 157, 221, 168, 232)(154, 218, 170, 234, 158, 222, 171, 235)(155, 219, 173, 237, 181, 245, 175, 239)(160, 224, 166, 230, 161, 225, 169, 233)(162, 226, 178, 242, 182, 246, 179, 243)(167, 231, 183, 247, 177, 241, 185, 249)(172, 236, 186, 250, 176, 240, 187, 251)(174, 238, 188, 252, 191, 255, 189, 253)(180, 244, 184, 248, 192, 256, 190, 254) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 145)(7, 148)(8, 130)(9, 153)(10, 155)(11, 157)(12, 159)(13, 132)(14, 160)(15, 161)(16, 133)(17, 163)(18, 134)(19, 165)(20, 167)(21, 168)(22, 170)(23, 171)(24, 136)(25, 142)(26, 137)(27, 174)(28, 141)(29, 143)(30, 139)(31, 177)(32, 178)(33, 179)(34, 144)(35, 181)(36, 146)(37, 150)(38, 147)(39, 184)(40, 151)(41, 149)(42, 186)(43, 187)(44, 152)(45, 154)(46, 185)(47, 158)(48, 156)(49, 190)(50, 188)(51, 189)(52, 162)(53, 191)(54, 164)(55, 166)(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) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E15.1022 Graph:: simple bipartite v = 80 e = 128 f = 20 degree seq :: [ 2^64, 8^16 ] E15.1024 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 32, 32}) Quotient :: regular Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^32 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 43, 39, 35, 38, 42, 46, 48, 50, 52, 54, 64, 62, 59, 56, 57, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 44, 40, 36, 33, 34, 37, 41, 45, 47, 49, 51, 53, 63, 61, 58, 60, 55, 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, 44)(32, 55)(33, 35)(34, 38)(36, 39)(37, 42)(40, 43)(41, 46)(45, 48)(47, 50)(49, 52)(51, 54)(53, 64)(56, 58)(57, 60)(59, 61)(62, 63) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.1025 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 32, 32}) Quotient :: edge Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^32 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 42, 38, 34, 37, 41, 45, 47, 49, 51, 53, 64, 62, 59, 56, 58, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 44, 40, 36, 33, 35, 39, 43, 46, 48, 50, 52, 54, 63, 61, 57, 60, 55, 30, 26, 22, 18, 14, 10, 6)(65, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 108)(96, 119)(97, 98)(99, 101)(100, 102)(103, 105)(104, 106)(107, 109)(110, 111)(112, 113)(114, 115)(116, 117)(118, 128)(120, 121)(122, 124)(123, 125)(126, 127) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.1026 Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.1026 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 32, 32}) Quotient :: loop Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^32 ] Map:: R = (1, 65, 3, 67, 7, 71, 11, 75, 15, 79, 19, 83, 23, 87, 27, 91, 31, 95, 36, 100, 33, 97, 35, 99, 39, 103, 42, 106, 44, 108, 46, 110, 48, 112, 50, 114, 52, 116, 57, 121, 54, 118, 56, 120, 60, 124, 63, 127, 32, 96, 28, 92, 24, 88, 20, 84, 16, 80, 12, 76, 8, 72, 4, 68)(2, 66, 5, 69, 9, 73, 13, 77, 17, 81, 21, 85, 25, 89, 29, 93, 41, 105, 38, 102, 34, 98, 37, 101, 40, 104, 43, 107, 45, 109, 47, 111, 49, 113, 51, 115, 62, 126, 59, 123, 55, 119, 58, 122, 61, 125, 64, 128, 53, 117, 30, 94, 26, 90, 22, 86, 18, 82, 14, 78, 10, 74, 6, 70) L = (1, 66)(2, 65)(3, 69)(4, 70)(5, 67)(6, 68)(7, 73)(8, 74)(9, 71)(10, 72)(11, 77)(12, 78)(13, 75)(14, 76)(15, 81)(16, 82)(17, 79)(18, 80)(19, 85)(20, 86)(21, 83)(22, 84)(23, 89)(24, 90)(25, 87)(26, 88)(27, 93)(28, 94)(29, 91)(30, 92)(31, 105)(32, 117)(33, 98)(34, 97)(35, 101)(36, 102)(37, 99)(38, 100)(39, 104)(40, 103)(41, 95)(42, 107)(43, 106)(44, 109)(45, 108)(46, 111)(47, 110)(48, 113)(49, 112)(50, 115)(51, 114)(52, 126)(53, 96)(54, 119)(55, 118)(56, 122)(57, 123)(58, 120)(59, 121)(60, 125)(61, 124)(62, 116)(63, 128)(64, 127) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.1025 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.1027 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 32, 32}) Quotient :: dipole Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^32, (Y3 * Y2^-1)^32 ] Map:: R = (1, 65, 2, 66)(3, 67, 5, 69)(4, 68, 6, 70)(7, 71, 9, 73)(8, 72, 10, 74)(11, 75, 13, 77)(12, 76, 14, 78)(15, 79, 17, 81)(16, 80, 18, 82)(19, 83, 21, 85)(20, 84, 22, 86)(23, 87, 25, 89)(24, 88, 26, 90)(27, 91, 29, 93)(28, 92, 30, 94)(31, 95, 40, 104)(32, 96, 53, 117)(33, 97, 34, 98)(35, 99, 37, 101)(36, 100, 38, 102)(39, 103, 41, 105)(42, 106, 43, 107)(44, 108, 45, 109)(46, 110, 47, 111)(48, 112, 49, 113)(50, 114, 51, 115)(52, 116, 61, 125)(54, 118, 55, 119)(56, 120, 58, 122)(57, 121, 59, 123)(60, 124, 62, 126)(63, 127, 64, 128)(129, 193, 131, 195, 135, 199, 139, 203, 143, 207, 147, 211, 151, 215, 155, 219, 159, 223, 166, 230, 162, 226, 165, 229, 169, 233, 171, 235, 173, 237, 175, 239, 177, 241, 179, 243, 189, 253, 185, 249, 182, 246, 184, 248, 188, 252, 191, 255, 160, 224, 156, 220, 152, 216, 148, 212, 144, 208, 140, 204, 136, 200, 132, 196)(130, 194, 133, 197, 137, 201, 141, 205, 145, 209, 149, 213, 153, 217, 157, 221, 168, 232, 164, 228, 161, 225, 163, 227, 167, 231, 170, 234, 172, 236, 174, 238, 176, 240, 178, 242, 180, 244, 187, 251, 183, 247, 186, 250, 190, 254, 192, 256, 181, 245, 158, 222, 154, 218, 150, 214, 146, 210, 142, 206, 138, 202, 134, 198) L = (1, 130)(2, 129)(3, 133)(4, 134)(5, 131)(6, 132)(7, 137)(8, 138)(9, 135)(10, 136)(11, 141)(12, 142)(13, 139)(14, 140)(15, 145)(16, 146)(17, 143)(18, 144)(19, 149)(20, 150)(21, 147)(22, 148)(23, 153)(24, 154)(25, 151)(26, 152)(27, 157)(28, 158)(29, 155)(30, 156)(31, 168)(32, 181)(33, 162)(34, 161)(35, 165)(36, 166)(37, 163)(38, 164)(39, 169)(40, 159)(41, 167)(42, 171)(43, 170)(44, 173)(45, 172)(46, 175)(47, 174)(48, 177)(49, 176)(50, 179)(51, 178)(52, 189)(53, 160)(54, 183)(55, 182)(56, 186)(57, 187)(58, 184)(59, 185)(60, 190)(61, 180)(62, 188)(63, 192)(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) :: { ( 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 E15.1028 Graph:: bipartite v = 34 e = 128 f = 66 degree seq :: [ 4^32, 64^2 ] E15.1028 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-32, Y1^32 ] Map:: R = (1, 65, 2, 66, 5, 69, 9, 73, 13, 77, 17, 81, 21, 85, 25, 89, 29, 93, 39, 103, 35, 99, 38, 102, 42, 106, 44, 108, 46, 110, 48, 112, 50, 114, 52, 116, 61, 125, 57, 121, 54, 118, 55, 119, 58, 122, 62, 126, 32, 96, 28, 92, 24, 88, 20, 84, 16, 80, 12, 76, 8, 72, 4, 68)(3, 67, 6, 70, 10, 74, 14, 78, 18, 82, 22, 86, 26, 90, 30, 94, 40, 104, 36, 100, 33, 97, 34, 98, 37, 101, 41, 105, 43, 107, 45, 109, 47, 111, 49, 113, 51, 115, 60, 124, 56, 120, 59, 123, 63, 127, 64, 128, 53, 117, 31, 95, 27, 91, 23, 87, 19, 83, 15, 79, 11, 75, 7, 71)(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, 134)(3, 129)(4, 135)(5, 138)(6, 130)(7, 132)(8, 139)(9, 142)(10, 133)(11, 136)(12, 143)(13, 146)(14, 137)(15, 140)(16, 147)(17, 150)(18, 141)(19, 144)(20, 151)(21, 154)(22, 145)(23, 148)(24, 155)(25, 158)(26, 149)(27, 152)(28, 159)(29, 168)(30, 153)(31, 156)(32, 181)(33, 163)(34, 166)(35, 161)(36, 167)(37, 170)(38, 162)(39, 164)(40, 157)(41, 172)(42, 165)(43, 174)(44, 169)(45, 176)(46, 171)(47, 178)(48, 173)(49, 180)(50, 175)(51, 189)(52, 177)(53, 160)(54, 184)(55, 187)(56, 182)(57, 188)(58, 191)(59, 183)(60, 185)(61, 179)(62, 192)(63, 186)(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, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 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 E15.1027 Graph:: simple bipartite v = 66 e = 128 f = 34 degree seq :: [ 2^64, 64^2 ] E15.1029 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 32, 32}) Quotient :: regular Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |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, T2 * T1 * T2 * T1^15, T1^-6 * T2 * T1^-9 * T2 * T1^-1, T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 57, 49, 41, 33, 25, 16, 24, 15, 23, 32, 40, 48, 56, 64, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 59, 51, 43, 35, 27, 18, 9, 14, 6, 13, 21, 31, 38, 47, 54, 63, 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, 61)(60, 63) local type(s) :: { ( 32^32 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 32 f = 2 degree seq :: [ 32^2 ] E15.1030 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 32, 32}) Quotient :: edge Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, T2^15 * T1 * T2 * T1, T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-1 * T1 ] Map:: R = (1, 3, 8, 17, 26, 34, 42, 50, 58, 63, 55, 47, 39, 31, 23, 13, 21, 11, 20, 29, 37, 45, 53, 61, 60, 52, 44, 36, 28, 19, 10, 4)(2, 5, 12, 22, 30, 38, 46, 54, 62, 59, 51, 43, 35, 27, 18, 9, 16, 7, 15, 25, 33, 41, 49, 57, 64, 56, 48, 40, 32, 24, 14, 6)(65, 66)(67, 71)(68, 73)(69, 75)(70, 77)(72, 76)(74, 78)(79, 84)(80, 85)(81, 89)(82, 87)(83, 91)(86, 93)(88, 95)(90, 94)(92, 96)(97, 101)(98, 105)(99, 103)(100, 107)(102, 109)(104, 111)(106, 110)(108, 112)(113, 117)(114, 121)(115, 119)(116, 123)(118, 125)(120, 127)(122, 126)(124, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64, 64 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E15.1031 Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 64 f = 2 degree seq :: [ 2^32, 32^2 ] E15.1031 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 32, 32}) Quotient :: loop Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, T2^15 * T1 * T2 * T1, T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-1 * T1 ] Map:: R = (1, 65, 3, 67, 8, 72, 17, 81, 26, 90, 34, 98, 42, 106, 50, 114, 58, 122, 63, 127, 55, 119, 47, 111, 39, 103, 31, 95, 23, 87, 13, 77, 21, 85, 11, 75, 20, 84, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 19, 83, 10, 74, 4, 68)(2, 66, 5, 69, 12, 76, 22, 86, 30, 94, 38, 102, 46, 110, 54, 118, 62, 126, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 18, 82, 9, 73, 16, 80, 7, 71, 15, 79, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 64, 128, 56, 120, 48, 112, 40, 104, 32, 96, 24, 88, 14, 78, 6, 70) L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 75)(6, 77)(7, 67)(8, 76)(9, 68)(10, 78)(11, 69)(12, 72)(13, 70)(14, 74)(15, 84)(16, 85)(17, 89)(18, 87)(19, 91)(20, 79)(21, 80)(22, 93)(23, 82)(24, 95)(25, 81)(26, 94)(27, 83)(28, 96)(29, 86)(30, 90)(31, 88)(32, 92)(33, 101)(34, 105)(35, 103)(36, 107)(37, 97)(38, 109)(39, 99)(40, 111)(41, 98)(42, 110)(43, 100)(44, 112)(45, 102)(46, 106)(47, 104)(48, 108)(49, 117)(50, 121)(51, 119)(52, 123)(53, 113)(54, 125)(55, 115)(56, 127)(57, 114)(58, 126)(59, 116)(60, 128)(61, 118)(62, 122)(63, 120)(64, 124) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.1030 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 64 f = 34 degree seq :: [ 64^2 ] E15.1032 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 32, 32}) Quotient :: dipole Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |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, Y2^15 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^32 ] Map:: 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, 20, 84)(16, 80, 21, 85)(17, 81, 25, 89)(18, 82, 23, 87)(19, 83, 27, 91)(22, 86, 29, 93)(24, 88, 31, 95)(26, 90, 30, 94)(28, 92, 32, 96)(33, 97, 37, 101)(34, 98, 41, 105)(35, 99, 39, 103)(36, 100, 43, 107)(38, 102, 45, 109)(40, 104, 47, 111)(42, 106, 46, 110)(44, 108, 48, 112)(49, 113, 53, 117)(50, 114, 57, 121)(51, 115, 55, 119)(52, 116, 59, 123)(54, 118, 61, 125)(56, 120, 63, 127)(58, 122, 62, 126)(60, 124, 64, 128)(129, 193, 131, 195, 136, 200, 145, 209, 154, 218, 162, 226, 170, 234, 178, 242, 186, 250, 191, 255, 183, 247, 175, 239, 167, 231, 159, 223, 151, 215, 141, 205, 149, 213, 139, 203, 148, 212, 157, 221, 165, 229, 173, 237, 181, 245, 189, 253, 188, 252, 180, 244, 172, 236, 164, 228, 156, 220, 147, 211, 138, 202, 132, 196)(130, 194, 133, 197, 140, 204, 150, 214, 158, 222, 166, 230, 174, 238, 182, 246, 190, 254, 187, 251, 179, 243, 171, 235, 163, 227, 155, 219, 146, 210, 137, 201, 144, 208, 135, 199, 143, 207, 153, 217, 161, 225, 169, 233, 177, 241, 185, 249, 192, 256, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 142, 206, 134, 198) 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, 148)(16, 149)(17, 153)(18, 151)(19, 155)(20, 143)(21, 144)(22, 157)(23, 146)(24, 159)(25, 145)(26, 158)(27, 147)(28, 160)(29, 150)(30, 154)(31, 152)(32, 156)(33, 165)(34, 169)(35, 167)(36, 171)(37, 161)(38, 173)(39, 163)(40, 175)(41, 162)(42, 174)(43, 164)(44, 176)(45, 166)(46, 170)(47, 168)(48, 172)(49, 181)(50, 185)(51, 183)(52, 187)(53, 177)(54, 189)(55, 179)(56, 191)(57, 178)(58, 190)(59, 180)(60, 192)(61, 182)(62, 186)(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) :: { ( 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 E15.1033 Graph:: bipartite v = 34 e = 128 f = 66 degree seq :: [ 4^32, 64^2 ] E15.1033 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1 * Y3 * Y1^-2 * Y3 * Y1, (Y1 * Y3 * Y1^-1 * Y3)^2, Y1^-2 * Y3 * Y1^-13 * Y3 * Y1^-1 ] Map:: R = (1, 65, 2, 66, 5, 69, 11, 75, 20, 84, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 57, 121, 49, 113, 41, 105, 33, 97, 25, 89, 16, 80, 24, 88, 15, 79, 23, 87, 32, 96, 40, 104, 48, 112, 56, 120, 64, 128, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 19, 83, 10, 74, 4, 68)(3, 67, 7, 71, 12, 76, 22, 86, 30, 94, 39, 103, 46, 110, 55, 119, 62, 126, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 18, 82, 9, 73, 14, 78, 6, 70, 13, 77, 21, 85, 31, 95, 38, 102, 47, 111, 54, 118, 63, 127, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90, 17, 81, 8, 72)(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, 134)(3, 129)(4, 137)(5, 140)(6, 130)(7, 143)(8, 144)(9, 132)(10, 145)(11, 149)(12, 133)(13, 151)(14, 152)(15, 135)(16, 136)(17, 138)(18, 153)(19, 155)(20, 158)(21, 139)(22, 160)(23, 141)(24, 142)(25, 146)(26, 161)(27, 147)(28, 162)(29, 166)(30, 148)(31, 168)(32, 150)(33, 154)(34, 156)(35, 169)(36, 171)(37, 174)(38, 157)(39, 176)(40, 159)(41, 163)(42, 177)(43, 164)(44, 178)(45, 182)(46, 165)(47, 184)(48, 167)(49, 170)(50, 172)(51, 185)(52, 187)(53, 190)(54, 173)(55, 192)(56, 175)(57, 179)(58, 189)(59, 180)(60, 191)(61, 186)(62, 181)(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, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 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 E15.1032 Graph:: simple bipartite v = 66 e = 128 f = 34 degree seq :: [ 2^64, 64^2 ] E15.1034 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 22, 33}) Quotient :: regular Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1^-3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^4 * T2 * T1^4 * T2 * T1^3 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 59, 47, 33, 17, 29, 44, 31, 45, 58, 65, 66, 60, 48, 34, 46, 32, 16, 28, 43, 57, 64, 52, 38, 22, 10, 4)(3, 7, 15, 24, 41, 56, 62, 50, 36, 20, 9, 19, 26, 12, 25, 42, 54, 63, 51, 37, 21, 30, 14, 6, 13, 27, 40, 55, 61, 49, 35, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 32)(20, 33)(22, 35)(23, 40)(25, 43)(26, 44)(27, 45)(30, 46)(36, 48)(37, 47)(38, 50)(39, 54)(41, 57)(42, 58)(49, 59)(51, 60)(52, 63)(53, 62)(55, 64)(56, 65)(61, 66) local type(s) :: { ( 22^33 ) } Outer automorphisms :: reflexible Dual of E15.1035 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 33 f = 3 degree seq :: [ 33^2 ] E15.1035 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 22, 33}) Quotient :: regular Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^-1 * T2 * T1^2 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, T2 * T1 * T2 * T1^9 * T2 * T1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 61, 55, 41, 54, 40, 53, 39, 52, 66, 60, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 62, 58, 44, 29, 38, 24, 37, 23, 36, 50, 65, 57, 43, 28, 17, 8)(6, 13, 21, 34, 48, 63, 56, 42, 27, 16, 26, 15, 25, 35, 51, 64, 59, 45, 30, 18, 9, 14) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 55)(45, 58)(46, 59)(47, 62)(49, 64)(51, 66)(56, 61)(57, 63)(60, 65) local type(s) :: { ( 33^22 ) } Outer automorphisms :: reflexible Dual of E15.1034 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 3 e = 33 f = 2 degree seq :: [ 22^3 ] E15.1036 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 22, 33}) Quotient :: edge Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T2^9 * T1 * T2 * T1 * T2 * T1, T2^3 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 3, 8, 17, 28, 43, 57, 64, 52, 36, 50, 34, 48, 32, 47, 61, 60, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 63, 58, 44, 29, 42, 27, 40, 25, 39, 55, 66, 54, 38, 24, 14, 6)(7, 15, 26, 41, 56, 65, 53, 37, 23, 13, 21, 11, 20, 33, 49, 62, 59, 45, 30, 18, 9, 16)(67, 68)(69, 73)(70, 75)(71, 77)(72, 79)(74, 78)(76, 80)(81, 91)(82, 93)(83, 92)(84, 95)(85, 96)(86, 98)(87, 100)(88, 99)(89, 102)(90, 103)(94, 101)(97, 104)(105, 113)(106, 114)(107, 121)(108, 116)(109, 122)(110, 118)(111, 124)(112, 125)(115, 127)(117, 128)(119, 130)(120, 131)(123, 129)(126, 132) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 66, 66 ), ( 66^22 ) } Outer automorphisms :: reflexible Dual of E15.1040 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 66 f = 2 degree seq :: [ 2^33, 22^3 ] E15.1037 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 22, 33}) Quotient :: edge Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-2 * T2, T1 * T2^-2 * T1 * T2^4, T1 * T2^-1 * T1^4 * T2^-2 * T1^3, T1^22, T1^-1 * T2^2 * T1^2 * T2^-1 * T1^2 * T2^2 * T1^2 * T2^-1 * T1^2 * T2^2 * T1^2 * T2^-1 * T1^2 * T2^2 * T1^-2 * T2^2 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 47, 61, 59, 38, 18, 6, 17, 36, 57, 41, 30, 52, 66, 54, 34, 21, 42, 60, 39, 20, 13, 28, 50, 64, 55, 43, 33, 15, 5)(2, 7, 19, 40, 26, 49, 65, 56, 35, 16, 14, 31, 46, 24, 11, 27, 51, 62, 53, 37, 32, 45, 23, 9, 4, 12, 29, 48, 63, 58, 44, 22, 8)(67, 68, 72, 82, 100, 119, 130, 114, 91, 106, 123, 112, 126, 111, 99, 110, 125, 131, 118, 93, 79, 70)(69, 75, 83, 74, 87, 101, 121, 128, 113, 95, 107, 85, 105, 97, 81, 98, 104, 124, 132, 115, 94, 77)(71, 80, 84, 103, 120, 129, 116, 92, 76, 90, 102, 89, 108, 88, 109, 122, 127, 117, 96, 78, 86, 73) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 4^22 ), ( 4^33 ) } Outer automorphisms :: reflexible Dual of E15.1041 Transitivity :: ET+ Graph:: bipartite v = 5 e = 66 f = 33 degree seq :: [ 22^3, 33^2 ] E15.1038 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 22, 33}) Quotient :: edge Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1^-3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^4 * T2 * T1^4 * T2 * T1^3 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 32)(20, 33)(22, 35)(23, 40)(25, 43)(26, 44)(27, 45)(30, 46)(36, 48)(37, 47)(38, 50)(39, 54)(41, 57)(42, 58)(49, 59)(51, 60)(52, 63)(53, 62)(55, 64)(56, 65)(61, 66)(67, 68, 71, 77, 89, 105, 119, 125, 113, 99, 83, 95, 110, 97, 111, 124, 131, 132, 126, 114, 100, 112, 98, 82, 94, 109, 123, 130, 118, 104, 88, 76, 70)(69, 73, 81, 90, 107, 122, 128, 116, 102, 86, 75, 85, 92, 78, 91, 108, 120, 129, 117, 103, 87, 96, 80, 72, 79, 93, 106, 121, 127, 115, 101, 84, 74) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 44, 44 ), ( 44^33 ) } Outer automorphisms :: reflexible Dual of E15.1039 Transitivity :: ET+ Graph:: simple bipartite v = 35 e = 66 f = 3 degree seq :: [ 2^33, 33^2 ] E15.1039 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 22, 33}) Quotient :: loop Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T2^9 * T1 * T2 * T1 * T2 * T1, T2^3 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 67, 3, 69, 8, 74, 17, 83, 28, 94, 43, 109, 57, 123, 64, 130, 52, 118, 36, 102, 50, 116, 34, 100, 48, 114, 32, 98, 47, 113, 61, 127, 60, 126, 46, 112, 31, 97, 19, 85, 10, 76, 4, 70)(2, 68, 5, 71, 12, 78, 22, 88, 35, 101, 51, 117, 63, 129, 58, 124, 44, 110, 29, 95, 42, 108, 27, 93, 40, 106, 25, 91, 39, 105, 55, 121, 66, 132, 54, 120, 38, 104, 24, 90, 14, 80, 6, 72)(7, 73, 15, 81, 26, 92, 41, 107, 56, 122, 65, 131, 53, 119, 37, 103, 23, 89, 13, 79, 21, 87, 11, 77, 20, 86, 33, 99, 49, 115, 62, 128, 59, 125, 45, 111, 30, 96, 18, 84, 9, 75, 16, 82) 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, 91)(16, 93)(17, 92)(18, 95)(19, 96)(20, 98)(21, 100)(22, 99)(23, 102)(24, 103)(25, 81)(26, 83)(27, 82)(28, 101)(29, 84)(30, 85)(31, 104)(32, 86)(33, 88)(34, 87)(35, 94)(36, 89)(37, 90)(38, 97)(39, 113)(40, 114)(41, 121)(42, 116)(43, 122)(44, 118)(45, 124)(46, 125)(47, 105)(48, 106)(49, 127)(50, 108)(51, 128)(52, 110)(53, 130)(54, 131)(55, 107)(56, 109)(57, 129)(58, 111)(59, 112)(60, 132)(61, 115)(62, 117)(63, 123)(64, 119)(65, 120)(66, 126) local type(s) :: { ( 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33, 2, 33 ) } Outer automorphisms :: reflexible Dual of E15.1038 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 66 f = 35 degree seq :: [ 44^3 ] E15.1040 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 22, 33}) Quotient :: loop Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-2 * T2, T1 * T2^-2 * T1 * T2^4, T1 * T2^-1 * T1^4 * T2^-2 * T1^3, T1^22, T1^-1 * T2^2 * T1^2 * T2^-1 * T1^2 * T2^2 * T1^2 * T2^-1 * T1^2 * T2^2 * T1^2 * T2^-1 * T1^2 * T2^2 * T1^-2 * T2^2 * T1^-1 * T2 ] Map:: R = (1, 67, 3, 69, 10, 76, 25, 91, 47, 113, 61, 127, 59, 125, 38, 104, 18, 84, 6, 72, 17, 83, 36, 102, 57, 123, 41, 107, 30, 96, 52, 118, 66, 132, 54, 120, 34, 100, 21, 87, 42, 108, 60, 126, 39, 105, 20, 86, 13, 79, 28, 94, 50, 116, 64, 130, 55, 121, 43, 109, 33, 99, 15, 81, 5, 71)(2, 68, 7, 73, 19, 85, 40, 106, 26, 92, 49, 115, 65, 131, 56, 122, 35, 101, 16, 82, 14, 80, 31, 97, 46, 112, 24, 90, 11, 77, 27, 93, 51, 117, 62, 128, 53, 119, 37, 103, 32, 98, 45, 111, 23, 89, 9, 75, 4, 70, 12, 78, 29, 95, 48, 114, 63, 129, 58, 124, 44, 110, 22, 88, 8, 74) L = (1, 68)(2, 72)(3, 75)(4, 67)(5, 80)(6, 82)(7, 71)(8, 87)(9, 83)(10, 90)(11, 69)(12, 86)(13, 70)(14, 84)(15, 98)(16, 100)(17, 74)(18, 103)(19, 105)(20, 73)(21, 101)(22, 109)(23, 108)(24, 102)(25, 106)(26, 76)(27, 79)(28, 77)(29, 107)(30, 78)(31, 81)(32, 104)(33, 110)(34, 119)(35, 121)(36, 89)(37, 120)(38, 124)(39, 97)(40, 123)(41, 85)(42, 88)(43, 122)(44, 125)(45, 99)(46, 126)(47, 95)(48, 91)(49, 94)(50, 92)(51, 96)(52, 93)(53, 130)(54, 129)(55, 128)(56, 127)(57, 112)(58, 132)(59, 131)(60, 111)(61, 117)(62, 113)(63, 116)(64, 114)(65, 118)(66, 115) local type(s) :: { ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E15.1036 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 66 f = 36 degree seq :: [ 66^2 ] E15.1041 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 22, 33}) Quotient :: loop Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1^-3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^4 * T2 * T1^4 * T2 * T1^3 ] Map:: polytopal non-degenerate R = (1, 67, 3, 69)(2, 68, 6, 72)(4, 70, 9, 75)(5, 71, 12, 78)(7, 73, 16, 82)(8, 74, 17, 83)(10, 76, 21, 87)(11, 77, 24, 90)(13, 79, 28, 94)(14, 80, 29, 95)(15, 81, 31, 97)(18, 84, 34, 100)(19, 85, 32, 98)(20, 86, 33, 99)(22, 88, 35, 101)(23, 89, 40, 106)(25, 91, 43, 109)(26, 92, 44, 110)(27, 93, 45, 111)(30, 96, 46, 112)(36, 102, 48, 114)(37, 103, 47, 113)(38, 104, 50, 116)(39, 105, 54, 120)(41, 107, 57, 123)(42, 108, 58, 124)(49, 115, 59, 125)(51, 117, 60, 126)(52, 118, 63, 129)(53, 119, 62, 128)(55, 121, 64, 130)(56, 122, 65, 131)(61, 127, 66, 132) L = (1, 68)(2, 71)(3, 73)(4, 67)(5, 77)(6, 79)(7, 81)(8, 69)(9, 85)(10, 70)(11, 89)(12, 91)(13, 93)(14, 72)(15, 90)(16, 94)(17, 95)(18, 74)(19, 92)(20, 75)(21, 96)(22, 76)(23, 105)(24, 107)(25, 108)(26, 78)(27, 106)(28, 109)(29, 110)(30, 80)(31, 111)(32, 82)(33, 83)(34, 112)(35, 84)(36, 86)(37, 87)(38, 88)(39, 119)(40, 121)(41, 122)(42, 120)(43, 123)(44, 97)(45, 124)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)(53, 125)(54, 129)(55, 127)(56, 128)(57, 130)(58, 131)(59, 113)(60, 114)(61, 115)(62, 116)(63, 117)(64, 118)(65, 132)(66, 126) local type(s) :: { ( 22, 33, 22, 33 ) } Outer automorphisms :: reflexible Dual of E15.1037 Transitivity :: ET+ VT+ AT Graph:: simple v = 33 e = 66 f = 5 degree seq :: [ 4^33 ] E15.1042 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 33}) Quotient :: dipole Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^5 * Y1 * Y2^3 * Y1 * Y2 * Y1 * Y2^2, (Y3 * Y2^-1)^33 ] 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, 25, 91)(16, 82, 27, 93)(17, 83, 26, 92)(18, 84, 29, 95)(19, 85, 30, 96)(20, 86, 32, 98)(21, 87, 34, 100)(22, 88, 33, 99)(23, 89, 36, 102)(24, 90, 37, 103)(28, 94, 35, 101)(31, 97, 38, 104)(39, 105, 47, 113)(40, 106, 48, 114)(41, 107, 55, 121)(42, 108, 50, 116)(43, 109, 56, 122)(44, 110, 52, 118)(45, 111, 58, 124)(46, 112, 59, 125)(49, 115, 61, 127)(51, 117, 62, 128)(53, 119, 64, 130)(54, 120, 65, 131)(57, 123, 63, 129)(60, 126, 66, 132)(133, 199, 135, 201, 140, 206, 149, 215, 160, 226, 175, 241, 189, 255, 196, 262, 184, 250, 168, 234, 182, 248, 166, 232, 180, 246, 164, 230, 179, 245, 193, 259, 192, 258, 178, 244, 163, 229, 151, 217, 142, 208, 136, 202)(134, 200, 137, 203, 144, 210, 154, 220, 167, 233, 183, 249, 195, 261, 190, 256, 176, 242, 161, 227, 174, 240, 159, 225, 172, 238, 157, 223, 171, 237, 187, 253, 198, 264, 186, 252, 170, 236, 156, 222, 146, 212, 138, 204)(139, 205, 147, 213, 158, 224, 173, 239, 188, 254, 197, 263, 185, 251, 169, 235, 155, 221, 145, 211, 153, 219, 143, 209, 152, 218, 165, 231, 181, 247, 194, 260, 191, 257, 177, 243, 162, 228, 150, 216, 141, 207, 148, 214) L = (1, 134)(2, 133)(3, 139)(4, 141)(5, 143)(6, 145)(7, 135)(8, 144)(9, 136)(10, 146)(11, 137)(12, 140)(13, 138)(14, 142)(15, 157)(16, 159)(17, 158)(18, 161)(19, 162)(20, 164)(21, 166)(22, 165)(23, 168)(24, 169)(25, 147)(26, 149)(27, 148)(28, 167)(29, 150)(30, 151)(31, 170)(32, 152)(33, 154)(34, 153)(35, 160)(36, 155)(37, 156)(38, 163)(39, 179)(40, 180)(41, 187)(42, 182)(43, 188)(44, 184)(45, 190)(46, 191)(47, 171)(48, 172)(49, 193)(50, 174)(51, 194)(52, 176)(53, 196)(54, 197)(55, 173)(56, 175)(57, 195)(58, 177)(59, 178)(60, 198)(61, 181)(62, 183)(63, 189)(64, 185)(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) :: { ( 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) } Outer automorphisms :: reflexible Dual of E15.1045 Graph:: bipartite v = 36 e = 132 f = 68 degree seq :: [ 4^33, 44^3 ] E15.1043 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 33}) Quotient :: dipole Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (Y1^-1 * Y2^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y1 * Y2^-2 * Y1 * Y2^4, Y2^-1 * Y1^5 * Y2^-1 * Y1 * Y2^-3, Y1^-1 * Y2^2 * Y1^-1 * Y2^3 * Y1^-2 * Y2^2 ] Map:: R = (1, 67, 2, 68, 6, 72, 16, 82, 34, 100, 53, 119, 64, 130, 48, 114, 25, 91, 40, 106, 57, 123, 46, 112, 60, 126, 45, 111, 33, 99, 44, 110, 59, 125, 65, 131, 52, 118, 27, 93, 13, 79, 4, 70)(3, 69, 9, 75, 17, 83, 8, 74, 21, 87, 35, 101, 55, 121, 62, 128, 47, 113, 29, 95, 41, 107, 19, 85, 39, 105, 31, 97, 15, 81, 32, 98, 38, 104, 58, 124, 66, 132, 49, 115, 28, 94, 11, 77)(5, 71, 14, 80, 18, 84, 37, 103, 54, 120, 63, 129, 50, 116, 26, 92, 10, 76, 24, 90, 36, 102, 23, 89, 42, 108, 22, 88, 43, 109, 56, 122, 61, 127, 51, 117, 30, 96, 12, 78, 20, 86, 7, 73)(133, 199, 135, 201, 142, 208, 157, 223, 179, 245, 193, 259, 191, 257, 170, 236, 150, 216, 138, 204, 149, 215, 168, 234, 189, 255, 173, 239, 162, 228, 184, 250, 198, 264, 186, 252, 166, 232, 153, 219, 174, 240, 192, 258, 171, 237, 152, 218, 145, 211, 160, 226, 182, 248, 196, 262, 187, 253, 175, 241, 165, 231, 147, 213, 137, 203)(134, 200, 139, 205, 151, 217, 172, 238, 158, 224, 181, 247, 197, 263, 188, 254, 167, 233, 148, 214, 146, 212, 163, 229, 178, 244, 156, 222, 143, 209, 159, 225, 183, 249, 194, 260, 185, 251, 169, 235, 164, 230, 177, 243, 155, 221, 141, 207, 136, 202, 144, 210, 161, 227, 180, 246, 195, 261, 190, 256, 176, 242, 154, 220, 140, 206) L = (1, 135)(2, 139)(3, 142)(4, 144)(5, 133)(6, 149)(7, 151)(8, 134)(9, 136)(10, 157)(11, 159)(12, 161)(13, 160)(14, 163)(15, 137)(16, 146)(17, 168)(18, 138)(19, 172)(20, 145)(21, 174)(22, 140)(23, 141)(24, 143)(25, 179)(26, 181)(27, 183)(28, 182)(29, 180)(30, 184)(31, 178)(32, 177)(33, 147)(34, 153)(35, 148)(36, 189)(37, 164)(38, 150)(39, 152)(40, 158)(41, 162)(42, 192)(43, 165)(44, 154)(45, 155)(46, 156)(47, 193)(48, 195)(49, 197)(50, 196)(51, 194)(52, 198)(53, 169)(54, 166)(55, 175)(56, 167)(57, 173)(58, 176)(59, 170)(60, 171)(61, 191)(62, 185)(63, 190)(64, 187)(65, 188)(66, 186)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E15.1044 Graph:: bipartite v = 5 e = 132 f = 99 degree seq :: [ 44^3, 66^2 ] E15.1044 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 33}) Quotient :: dipole Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^3 * Y2 * Y3^-2, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3, Y3^9 * Y2 * Y3 * Y2 * Y3, (Y3^-1 * Y1^-1)^33 ] Map:: polytopal R = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)(133, 199, 134, 200)(135, 201, 139, 205)(136, 202, 141, 207)(137, 203, 143, 209)(138, 204, 145, 211)(140, 206, 149, 215)(142, 208, 153, 219)(144, 210, 157, 223)(146, 212, 161, 227)(147, 213, 155, 221)(148, 214, 159, 225)(150, 216, 158, 224)(151, 217, 156, 222)(152, 218, 160, 226)(154, 220, 162, 228)(163, 229, 173, 239)(164, 230, 172, 238)(165, 231, 171, 237)(166, 232, 174, 240)(167, 233, 179, 245)(168, 234, 177, 243)(169, 235, 176, 242)(170, 236, 182, 248)(175, 241, 185, 251)(178, 244, 188, 254)(180, 246, 186, 252)(181, 247, 192, 258)(183, 249, 189, 255)(184, 250, 195, 261)(187, 253, 197, 263)(190, 256, 198, 264)(191, 257, 196, 262)(193, 259, 194, 260) L = (1, 135)(2, 137)(3, 140)(4, 133)(5, 144)(6, 134)(7, 147)(8, 150)(9, 151)(10, 136)(11, 155)(12, 158)(13, 159)(14, 138)(15, 163)(16, 139)(17, 165)(18, 167)(19, 166)(20, 141)(21, 164)(22, 142)(23, 171)(24, 143)(25, 173)(26, 175)(27, 174)(28, 145)(29, 172)(30, 146)(31, 179)(32, 148)(33, 180)(34, 149)(35, 181)(36, 152)(37, 153)(38, 154)(39, 185)(40, 156)(41, 186)(42, 157)(43, 187)(44, 160)(45, 161)(46, 162)(47, 191)(48, 192)(49, 193)(50, 168)(51, 169)(52, 170)(53, 196)(54, 197)(55, 194)(56, 176)(57, 177)(58, 178)(59, 190)(60, 195)(61, 188)(62, 182)(63, 183)(64, 184)(65, 198)(66, 189)(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) :: { ( 44, 66 ), ( 44, 66, 44, 66 ) } Outer automorphisms :: reflexible Dual of E15.1043 Graph:: simple bipartite v = 99 e = 132 f = 5 degree seq :: [ 2^66, 4^33 ] E15.1045 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 33}) Quotient :: dipole Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3, Y1^3 * Y3 * Y1^-3 * Y3, Y1^4 * Y3 * Y1^4 * Y3 * Y1^3 ] Map:: R = (1, 67, 2, 68, 5, 71, 11, 77, 23, 89, 39, 105, 53, 119, 59, 125, 47, 113, 33, 99, 17, 83, 29, 95, 44, 110, 31, 97, 45, 111, 58, 124, 65, 131, 66, 132, 60, 126, 48, 114, 34, 100, 46, 112, 32, 98, 16, 82, 28, 94, 43, 109, 57, 123, 64, 130, 52, 118, 38, 104, 22, 88, 10, 76, 4, 70)(3, 69, 7, 73, 15, 81, 24, 90, 41, 107, 56, 122, 62, 128, 50, 116, 36, 102, 20, 86, 9, 75, 19, 85, 26, 92, 12, 78, 25, 91, 42, 108, 54, 120, 63, 129, 51, 117, 37, 103, 21, 87, 30, 96, 14, 80, 6, 72, 13, 79, 27, 93, 40, 106, 55, 121, 61, 127, 49, 115, 35, 101, 18, 84, 8, 74)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264) L = (1, 135)(2, 138)(3, 133)(4, 141)(5, 144)(6, 134)(7, 148)(8, 149)(9, 136)(10, 153)(11, 156)(12, 137)(13, 160)(14, 161)(15, 163)(16, 139)(17, 140)(18, 166)(19, 164)(20, 165)(21, 142)(22, 167)(23, 172)(24, 143)(25, 175)(26, 176)(27, 177)(28, 145)(29, 146)(30, 178)(31, 147)(32, 151)(33, 152)(34, 150)(35, 154)(36, 180)(37, 179)(38, 182)(39, 186)(40, 155)(41, 189)(42, 190)(43, 157)(44, 158)(45, 159)(46, 162)(47, 169)(48, 168)(49, 191)(50, 170)(51, 192)(52, 195)(53, 194)(54, 171)(55, 196)(56, 197)(57, 173)(58, 174)(59, 181)(60, 183)(61, 198)(62, 185)(63, 184)(64, 187)(65, 188)(66, 193)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E15.1042 Graph:: simple bipartite v = 68 e = 132 f = 36 degree seq :: [ 2^66, 66^2 ] E15.1046 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 33}) Quotient :: dipole Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^3 * Y1 * Y2^-3, Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, (Y2^-1 * R * Y2^-2)^2, Y2^-4 * Y1 * Y2^-4 * Y1 * Y2^-3, (Y3 * Y2^-1)^22 ] Map:: R = (1, 67, 2, 68)(3, 69, 7, 73)(4, 70, 9, 75)(5, 71, 11, 77)(6, 72, 13, 79)(8, 74, 17, 83)(10, 76, 21, 87)(12, 78, 25, 91)(14, 80, 29, 95)(15, 81, 23, 89)(16, 82, 27, 93)(18, 84, 26, 92)(19, 85, 24, 90)(20, 86, 28, 94)(22, 88, 30, 96)(31, 97, 41, 107)(32, 98, 40, 106)(33, 99, 39, 105)(34, 100, 42, 108)(35, 101, 47, 113)(36, 102, 45, 111)(37, 103, 44, 110)(38, 104, 50, 116)(43, 109, 53, 119)(46, 112, 56, 122)(48, 114, 54, 120)(49, 115, 60, 126)(51, 117, 57, 123)(52, 118, 63, 129)(55, 121, 65, 131)(58, 124, 66, 132)(59, 125, 64, 130)(61, 127, 62, 128)(133, 199, 135, 201, 140, 206, 150, 216, 167, 233, 181, 247, 193, 259, 188, 254, 176, 242, 160, 226, 145, 211, 159, 225, 174, 240, 157, 223, 173, 239, 186, 252, 197, 263, 198, 264, 189, 255, 177, 243, 161, 227, 172, 238, 156, 222, 143, 209, 155, 221, 171, 237, 185, 251, 196, 262, 184, 250, 170, 236, 154, 220, 142, 208, 136, 202)(134, 200, 137, 203, 144, 210, 158, 224, 175, 241, 187, 253, 194, 260, 182, 248, 168, 234, 152, 218, 141, 207, 151, 217, 166, 232, 149, 215, 165, 231, 180, 246, 192, 258, 195, 261, 183, 249, 169, 235, 153, 219, 164, 230, 148, 214, 139, 205, 147, 213, 163, 229, 179, 245, 191, 257, 190, 256, 178, 244, 162, 228, 146, 212, 138, 204) L = (1, 134)(2, 133)(3, 139)(4, 141)(5, 143)(6, 145)(7, 135)(8, 149)(9, 136)(10, 153)(11, 137)(12, 157)(13, 138)(14, 161)(15, 155)(16, 159)(17, 140)(18, 158)(19, 156)(20, 160)(21, 142)(22, 162)(23, 147)(24, 151)(25, 144)(26, 150)(27, 148)(28, 152)(29, 146)(30, 154)(31, 173)(32, 172)(33, 171)(34, 174)(35, 179)(36, 177)(37, 176)(38, 182)(39, 165)(40, 164)(41, 163)(42, 166)(43, 185)(44, 169)(45, 168)(46, 188)(47, 167)(48, 186)(49, 192)(50, 170)(51, 189)(52, 195)(53, 175)(54, 180)(55, 197)(56, 178)(57, 183)(58, 198)(59, 196)(60, 181)(61, 194)(62, 193)(63, 184)(64, 191)(65, 187)(66, 190)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 2, 44, 2, 44 ), ( 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44 ) } Outer automorphisms :: reflexible Dual of E15.1047 Graph:: bipartite v = 35 e = 132 f = 69 degree seq :: [ 4^33, 66^2 ] E15.1047 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 33}) Quotient :: dipole Aut^+ = C11 x S3 (small group id <66, 1>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1^-2 * Y3, (R * Y2 * Y3^-1)^2, Y1 * Y3^-2 * Y1 * Y3^4, Y1 * Y3^-1 * Y1^4 * Y3^-2 * Y1^3, Y1^22, (Y3 * Y2^-1)^33 ] Map:: R = (1, 67, 2, 68, 6, 72, 16, 82, 34, 100, 53, 119, 64, 130, 48, 114, 25, 91, 40, 106, 57, 123, 46, 112, 60, 126, 45, 111, 33, 99, 44, 110, 59, 125, 65, 131, 52, 118, 27, 93, 13, 79, 4, 70)(3, 69, 9, 75, 17, 83, 8, 74, 21, 87, 35, 101, 55, 121, 62, 128, 47, 113, 29, 95, 41, 107, 19, 85, 39, 105, 31, 97, 15, 81, 32, 98, 38, 104, 58, 124, 66, 132, 49, 115, 28, 94, 11, 77)(5, 71, 14, 80, 18, 84, 37, 103, 54, 120, 63, 129, 50, 116, 26, 92, 10, 76, 24, 90, 36, 102, 23, 89, 42, 108, 22, 88, 43, 109, 56, 122, 61, 127, 51, 117, 30, 96, 12, 78, 20, 86, 7, 73)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264) L = (1, 135)(2, 139)(3, 142)(4, 144)(5, 133)(6, 149)(7, 151)(8, 134)(9, 136)(10, 157)(11, 159)(12, 161)(13, 160)(14, 163)(15, 137)(16, 146)(17, 168)(18, 138)(19, 172)(20, 145)(21, 174)(22, 140)(23, 141)(24, 143)(25, 179)(26, 181)(27, 183)(28, 182)(29, 180)(30, 184)(31, 178)(32, 177)(33, 147)(34, 153)(35, 148)(36, 189)(37, 164)(38, 150)(39, 152)(40, 158)(41, 162)(42, 192)(43, 165)(44, 154)(45, 155)(46, 156)(47, 193)(48, 195)(49, 197)(50, 196)(51, 194)(52, 198)(53, 169)(54, 166)(55, 175)(56, 167)(57, 173)(58, 176)(59, 170)(60, 171)(61, 191)(62, 185)(63, 190)(64, 187)(65, 188)(66, 186)(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, 66 ), ( 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66, 4, 66 ) } Outer automorphisms :: reflexible Dual of E15.1046 Graph:: simple bipartite v = 69 e = 132 f = 35 degree seq :: [ 2^66, 44^3 ] E15.1048 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 14, 35}) Quotient :: regular Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^-1 * T2 * T1^-3, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 34, 17, 29, 45, 59, 68, 53, 35, 48, 62, 69, 65, 50, 54, 64, 70, 66, 51, 32, 47, 61, 67, 52, 33, 16, 28, 42, 22, 10, 4)(3, 7, 15, 31, 38, 20, 9, 19, 37, 55, 57, 40, 21, 39, 56, 60, 43, 24, 41, 58, 63, 46, 26, 12, 25, 44, 49, 30, 14, 6, 13, 27, 36, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 40)(25, 42)(26, 45)(27, 47)(30, 48)(31, 50)(36, 54)(37, 51)(38, 53)(39, 52)(43, 59)(44, 61)(46, 62)(49, 64)(55, 65)(56, 66)(57, 68)(58, 67)(60, 69)(63, 70) local type(s) :: { ( 14^35 ) } Outer automorphisms :: reflexible Dual of E15.1049 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 35 f = 5 degree seq :: [ 35^2 ] E15.1049 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 14, 35}) Quotient :: regular Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^14 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 61, 60, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 62, 70, 68, 58, 43, 28, 17, 8)(6, 13, 21, 34, 48, 63, 69, 67, 59, 45, 30, 18, 9, 14)(15, 25, 35, 51, 64, 54, 66, 53, 65, 52, 42, 27, 16, 26)(23, 36, 50, 41, 57, 40, 56, 39, 55, 44, 29, 38, 24, 37) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 51)(45, 55)(46, 59)(47, 62)(49, 64)(56, 67)(57, 63)(58, 65)(60, 68)(61, 69)(66, 70) local type(s) :: { ( 35^14 ) } Outer automorphisms :: reflexible Dual of E15.1048 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 5 e = 35 f = 2 degree seq :: [ 14^5 ] E15.1050 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 14, 35}) Quotient :: edge Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2 * T1 * T2^3 * T1 * T2 * T1 * T2 * T1 * T2 * T1, T2^14 ] Map:: R = (1, 3, 8, 17, 28, 43, 58, 68, 60, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 64, 70, 66, 54, 38, 24, 14, 6)(7, 15, 26, 41, 56, 63, 69, 61, 59, 45, 30, 18, 9, 16)(11, 20, 33, 49, 62, 57, 67, 55, 65, 53, 37, 23, 13, 21)(25, 39, 52, 36, 50, 34, 48, 32, 47, 44, 29, 42, 27, 40)(71, 72)(73, 77)(74, 79)(75, 81)(76, 83)(78, 82)(80, 84)(85, 95)(86, 97)(87, 96)(88, 99)(89, 100)(90, 102)(91, 104)(92, 103)(93, 106)(94, 107)(98, 105)(101, 108)(109, 123)(110, 125)(111, 122)(112, 127)(113, 126)(114, 119)(115, 117)(116, 129)(118, 131)(120, 133)(121, 132)(124, 135)(128, 134)(130, 136)(137, 140)(138, 139) L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 70, 70 ), ( 70^14 ) } Outer automorphisms :: reflexible Dual of E15.1054 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 70 f = 2 degree seq :: [ 2^35, 14^5 ] E15.1051 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 14, 35}) Quotient :: edge Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ F^2, (T1 * T2)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T2^-2 * T1^2 * T2^-3, T1 * T2 * T1^-1 * T2^-1 * T1^2 * T2^2, T2^-1 * T1 * T2^-1 * T1^11 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 18, 6, 17, 36, 55, 53, 34, 21, 41, 58, 68, 66, 54, 42, 49, 63, 70, 67, 57, 40, 30, 48, 62, 56, 38, 20, 13, 28, 33, 15, 5)(2, 7, 19, 39, 35, 16, 14, 31, 50, 64, 52, 37, 32, 51, 65, 69, 60, 45, 26, 46, 61, 59, 44, 24, 11, 27, 47, 43, 23, 9, 4, 12, 29, 22, 8)(71, 72, 76, 86, 104, 122, 136, 139, 140, 131, 118, 97, 83, 74)(73, 79, 87, 78, 91, 105, 124, 134, 137, 135, 132, 116, 98, 81)(75, 84, 88, 107, 123, 130, 138, 129, 133, 117, 100, 82, 90, 77)(80, 94, 106, 93, 111, 92, 112, 109, 127, 120, 126, 121, 103, 96)(85, 102, 95, 115, 125, 114, 128, 113, 119, 99, 110, 89, 108, 101) L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 4^14 ), ( 4^35 ) } Outer automorphisms :: reflexible Dual of E15.1055 Transitivity :: ET+ Graph:: bipartite v = 7 e = 70 f = 35 degree seq :: [ 14^5, 35^2 ] E15.1052 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 14, 35}) Quotient :: edge Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^-1 * T2 * T1^-3, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 ] 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, 40)(25, 42)(26, 45)(27, 47)(30, 48)(31, 50)(36, 54)(37, 51)(38, 53)(39, 52)(43, 59)(44, 61)(46, 62)(49, 64)(55, 65)(56, 66)(57, 68)(58, 67)(60, 69)(63, 70)(71, 72, 75, 81, 93, 104, 87, 99, 115, 129, 138, 123, 105, 118, 132, 139, 135, 120, 124, 134, 140, 136, 121, 102, 117, 131, 137, 122, 103, 86, 98, 112, 92, 80, 74)(73, 77, 85, 101, 108, 90, 79, 89, 107, 125, 127, 110, 91, 109, 126, 130, 113, 94, 111, 128, 133, 116, 96, 82, 95, 114, 119, 100, 84, 76, 83, 97, 106, 88, 78) L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140) local type(s) :: { ( 28, 28 ), ( 28^35 ) } Outer automorphisms :: reflexible Dual of E15.1053 Transitivity :: ET+ Graph:: simple bipartite v = 37 e = 70 f = 5 degree seq :: [ 2^35, 35^2 ] E15.1053 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 14, 35}) Quotient :: loop Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2 * T1 * T2^3 * T1 * T2 * T1 * T2 * T1 * T2 * T1, T2^14 ] Map:: R = (1, 71, 3, 73, 8, 78, 17, 87, 28, 98, 43, 113, 58, 128, 68, 138, 60, 130, 46, 116, 31, 101, 19, 89, 10, 80, 4, 74)(2, 72, 5, 75, 12, 82, 22, 92, 35, 105, 51, 121, 64, 134, 70, 140, 66, 136, 54, 124, 38, 108, 24, 94, 14, 84, 6, 76)(7, 77, 15, 85, 26, 96, 41, 111, 56, 126, 63, 133, 69, 139, 61, 131, 59, 129, 45, 115, 30, 100, 18, 88, 9, 79, 16, 86)(11, 81, 20, 90, 33, 103, 49, 119, 62, 132, 57, 127, 67, 137, 55, 125, 65, 135, 53, 123, 37, 107, 23, 93, 13, 83, 21, 91)(25, 95, 39, 109, 52, 122, 36, 106, 50, 120, 34, 104, 48, 118, 32, 102, 47, 117, 44, 114, 29, 99, 42, 112, 27, 97, 40, 110) L = (1, 72)(2, 71)(3, 77)(4, 79)(5, 81)(6, 83)(7, 73)(8, 82)(9, 74)(10, 84)(11, 75)(12, 78)(13, 76)(14, 80)(15, 95)(16, 97)(17, 96)(18, 99)(19, 100)(20, 102)(21, 104)(22, 103)(23, 106)(24, 107)(25, 85)(26, 87)(27, 86)(28, 105)(29, 88)(30, 89)(31, 108)(32, 90)(33, 92)(34, 91)(35, 98)(36, 93)(37, 94)(38, 101)(39, 123)(40, 125)(41, 122)(42, 127)(43, 126)(44, 119)(45, 117)(46, 129)(47, 115)(48, 131)(49, 114)(50, 133)(51, 132)(52, 111)(53, 109)(54, 135)(55, 110)(56, 113)(57, 112)(58, 134)(59, 116)(60, 136)(61, 118)(62, 121)(63, 120)(64, 128)(65, 124)(66, 130)(67, 140)(68, 139)(69, 138)(70, 137) local type(s) :: { ( 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35, 2, 35 ) } Outer automorphisms :: reflexible Dual of E15.1052 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 70 f = 37 degree seq :: [ 28^5 ] E15.1054 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 14, 35}) Quotient :: loop Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ F^2, (T1 * T2)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T2^-2 * T1^2 * T2^-3, T1 * T2 * T1^-1 * T2^-1 * T1^2 * T2^2, T2^-1 * T1 * T2^-1 * T1^11 ] Map:: R = (1, 71, 3, 73, 10, 80, 25, 95, 18, 88, 6, 76, 17, 87, 36, 106, 55, 125, 53, 123, 34, 104, 21, 91, 41, 111, 58, 128, 68, 138, 66, 136, 54, 124, 42, 112, 49, 119, 63, 133, 70, 140, 67, 137, 57, 127, 40, 110, 30, 100, 48, 118, 62, 132, 56, 126, 38, 108, 20, 90, 13, 83, 28, 98, 33, 103, 15, 85, 5, 75)(2, 72, 7, 77, 19, 89, 39, 109, 35, 105, 16, 86, 14, 84, 31, 101, 50, 120, 64, 134, 52, 122, 37, 107, 32, 102, 51, 121, 65, 135, 69, 139, 60, 130, 45, 115, 26, 96, 46, 116, 61, 131, 59, 129, 44, 114, 24, 94, 11, 81, 27, 97, 47, 117, 43, 113, 23, 93, 9, 79, 4, 74, 12, 82, 29, 99, 22, 92, 8, 78) L = (1, 72)(2, 76)(3, 79)(4, 71)(5, 84)(6, 86)(7, 75)(8, 91)(9, 87)(10, 94)(11, 73)(12, 90)(13, 74)(14, 88)(15, 102)(16, 104)(17, 78)(18, 107)(19, 108)(20, 77)(21, 105)(22, 112)(23, 111)(24, 106)(25, 115)(26, 80)(27, 83)(28, 81)(29, 110)(30, 82)(31, 85)(32, 95)(33, 96)(34, 122)(35, 124)(36, 93)(37, 123)(38, 101)(39, 127)(40, 89)(41, 92)(42, 109)(43, 119)(44, 128)(45, 125)(46, 98)(47, 100)(48, 97)(49, 99)(50, 126)(51, 103)(52, 136)(53, 130)(54, 134)(55, 114)(56, 121)(57, 120)(58, 113)(59, 133)(60, 138)(61, 118)(62, 116)(63, 117)(64, 137)(65, 132)(66, 139)(67, 135)(68, 129)(69, 140)(70, 131) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.1050 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 70 f = 40 degree seq :: [ 70^2 ] E15.1055 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 14, 35}) Quotient :: loop Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^-1 * T2 * T1^-3, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 71, 3, 73)(2, 72, 6, 76)(4, 74, 9, 79)(5, 75, 12, 82)(7, 77, 16, 86)(8, 78, 17, 87)(10, 80, 21, 91)(11, 81, 24, 94)(13, 83, 28, 98)(14, 84, 29, 99)(15, 85, 32, 102)(18, 88, 35, 105)(19, 89, 33, 103)(20, 90, 34, 104)(22, 92, 41, 111)(23, 93, 40, 110)(25, 95, 42, 112)(26, 96, 45, 115)(27, 97, 47, 117)(30, 100, 48, 118)(31, 101, 50, 120)(36, 106, 54, 124)(37, 107, 51, 121)(38, 108, 53, 123)(39, 109, 52, 122)(43, 113, 59, 129)(44, 114, 61, 131)(46, 116, 62, 132)(49, 119, 64, 134)(55, 125, 65, 135)(56, 126, 66, 136)(57, 127, 68, 138)(58, 128, 67, 137)(60, 130, 69, 139)(63, 133, 70, 140) L = (1, 72)(2, 75)(3, 77)(4, 71)(5, 81)(6, 83)(7, 85)(8, 73)(9, 89)(10, 74)(11, 93)(12, 95)(13, 97)(14, 76)(15, 101)(16, 98)(17, 99)(18, 78)(19, 107)(20, 79)(21, 109)(22, 80)(23, 104)(24, 111)(25, 114)(26, 82)(27, 106)(28, 112)(29, 115)(30, 84)(31, 108)(32, 117)(33, 86)(34, 87)(35, 118)(36, 88)(37, 125)(38, 90)(39, 126)(40, 91)(41, 128)(42, 92)(43, 94)(44, 119)(45, 129)(46, 96)(47, 131)(48, 132)(49, 100)(50, 124)(51, 102)(52, 103)(53, 105)(54, 134)(55, 127)(56, 130)(57, 110)(58, 133)(59, 138)(60, 113)(61, 137)(62, 139)(63, 116)(64, 140)(65, 120)(66, 121)(67, 122)(68, 123)(69, 135)(70, 136) local type(s) :: { ( 14, 35, 14, 35 ) } Outer automorphisms :: reflexible Dual of E15.1051 Transitivity :: ET+ VT+ AT Graph:: simple v = 35 e = 70 f = 7 degree seq :: [ 4^35 ] E15.1056 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 35}) Quotient :: dipole Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |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^-3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^14, (Y3 * Y2^-1)^35 ] Map:: R = (1, 71, 2, 72)(3, 73, 7, 77)(4, 74, 9, 79)(5, 75, 11, 81)(6, 76, 13, 83)(8, 78, 12, 82)(10, 80, 14, 84)(15, 85, 25, 95)(16, 86, 27, 97)(17, 87, 26, 96)(18, 88, 29, 99)(19, 89, 30, 100)(20, 90, 32, 102)(21, 91, 34, 104)(22, 92, 33, 103)(23, 93, 36, 106)(24, 94, 37, 107)(28, 98, 35, 105)(31, 101, 38, 108)(39, 109, 53, 123)(40, 110, 55, 125)(41, 111, 52, 122)(42, 112, 57, 127)(43, 113, 56, 126)(44, 114, 49, 119)(45, 115, 47, 117)(46, 116, 59, 129)(48, 118, 61, 131)(50, 120, 63, 133)(51, 121, 62, 132)(54, 124, 65, 135)(58, 128, 64, 134)(60, 130, 66, 136)(67, 137, 70, 140)(68, 138, 69, 139)(141, 211, 143, 213, 148, 218, 157, 227, 168, 238, 183, 253, 198, 268, 208, 278, 200, 270, 186, 256, 171, 241, 159, 229, 150, 220, 144, 214)(142, 212, 145, 215, 152, 222, 162, 232, 175, 245, 191, 261, 204, 274, 210, 280, 206, 276, 194, 264, 178, 248, 164, 234, 154, 224, 146, 216)(147, 217, 155, 225, 166, 236, 181, 251, 196, 266, 203, 273, 209, 279, 201, 271, 199, 269, 185, 255, 170, 240, 158, 228, 149, 219, 156, 226)(151, 221, 160, 230, 173, 243, 189, 259, 202, 272, 197, 267, 207, 277, 195, 265, 205, 275, 193, 263, 177, 247, 163, 233, 153, 223, 161, 231)(165, 235, 179, 249, 192, 262, 176, 246, 190, 260, 174, 244, 188, 258, 172, 242, 187, 257, 184, 254, 169, 239, 182, 252, 167, 237, 180, 250) L = (1, 142)(2, 141)(3, 147)(4, 149)(5, 151)(6, 153)(7, 143)(8, 152)(9, 144)(10, 154)(11, 145)(12, 148)(13, 146)(14, 150)(15, 165)(16, 167)(17, 166)(18, 169)(19, 170)(20, 172)(21, 174)(22, 173)(23, 176)(24, 177)(25, 155)(26, 157)(27, 156)(28, 175)(29, 158)(30, 159)(31, 178)(32, 160)(33, 162)(34, 161)(35, 168)(36, 163)(37, 164)(38, 171)(39, 193)(40, 195)(41, 192)(42, 197)(43, 196)(44, 189)(45, 187)(46, 199)(47, 185)(48, 201)(49, 184)(50, 203)(51, 202)(52, 181)(53, 179)(54, 205)(55, 180)(56, 183)(57, 182)(58, 204)(59, 186)(60, 206)(61, 188)(62, 191)(63, 190)(64, 198)(65, 194)(66, 200)(67, 210)(68, 209)(69, 208)(70, 207)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E15.1059 Graph:: bipartite v = 40 e = 140 f = 72 degree seq :: [ 4^35, 28^5 ] E15.1057 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 35}) Quotient :: dipole Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y1 * Y2)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y1^-3 * Y2^-1 * Y1 * Y2^-1, Y1^2 * Y2^-5, Y2^-1 * Y1 * Y2^-1 * Y1^11 ] Map:: R = (1, 71, 2, 72, 6, 76, 16, 86, 34, 104, 52, 122, 66, 136, 69, 139, 70, 140, 61, 131, 48, 118, 27, 97, 13, 83, 4, 74)(3, 73, 9, 79, 17, 87, 8, 78, 21, 91, 35, 105, 54, 124, 64, 134, 67, 137, 65, 135, 62, 132, 46, 116, 28, 98, 11, 81)(5, 75, 14, 84, 18, 88, 37, 107, 53, 123, 60, 130, 68, 138, 59, 129, 63, 133, 47, 117, 30, 100, 12, 82, 20, 90, 7, 77)(10, 80, 24, 94, 36, 106, 23, 93, 41, 111, 22, 92, 42, 112, 39, 109, 57, 127, 50, 120, 56, 126, 51, 121, 33, 103, 26, 96)(15, 85, 32, 102, 25, 95, 45, 115, 55, 125, 44, 114, 58, 128, 43, 113, 49, 119, 29, 99, 40, 110, 19, 89, 38, 108, 31, 101)(141, 211, 143, 213, 150, 220, 165, 235, 158, 228, 146, 216, 157, 227, 176, 246, 195, 265, 193, 263, 174, 244, 161, 231, 181, 251, 198, 268, 208, 278, 206, 276, 194, 264, 182, 252, 189, 259, 203, 273, 210, 280, 207, 277, 197, 267, 180, 250, 170, 240, 188, 258, 202, 272, 196, 266, 178, 248, 160, 230, 153, 223, 168, 238, 173, 243, 155, 225, 145, 215)(142, 212, 147, 217, 159, 229, 179, 249, 175, 245, 156, 226, 154, 224, 171, 241, 190, 260, 204, 274, 192, 262, 177, 247, 172, 242, 191, 261, 205, 275, 209, 279, 200, 270, 185, 255, 166, 236, 186, 256, 201, 271, 199, 269, 184, 254, 164, 234, 151, 221, 167, 237, 187, 257, 183, 253, 163, 233, 149, 219, 144, 214, 152, 222, 169, 239, 162, 232, 148, 218) L = (1, 143)(2, 147)(3, 150)(4, 152)(5, 141)(6, 157)(7, 159)(8, 142)(9, 144)(10, 165)(11, 167)(12, 169)(13, 168)(14, 171)(15, 145)(16, 154)(17, 176)(18, 146)(19, 179)(20, 153)(21, 181)(22, 148)(23, 149)(24, 151)(25, 158)(26, 186)(27, 187)(28, 173)(29, 162)(30, 188)(31, 190)(32, 191)(33, 155)(34, 161)(35, 156)(36, 195)(37, 172)(38, 160)(39, 175)(40, 170)(41, 198)(42, 189)(43, 163)(44, 164)(45, 166)(46, 201)(47, 183)(48, 202)(49, 203)(50, 204)(51, 205)(52, 177)(53, 174)(54, 182)(55, 193)(56, 178)(57, 180)(58, 208)(59, 184)(60, 185)(61, 199)(62, 196)(63, 210)(64, 192)(65, 209)(66, 194)(67, 197)(68, 206)(69, 200)(70, 207)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E15.1058 Graph:: bipartite v = 7 e = 140 f = 105 degree seq :: [ 28^5, 70^2 ] E15.1058 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 35}) Quotient :: dipole Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |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^-5 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, (Y3^-1 * Y1^-1)^35 ] Map:: polytopal R = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)(141, 211, 142, 212)(143, 213, 147, 217)(144, 214, 149, 219)(145, 215, 151, 221)(146, 216, 153, 223)(148, 218, 157, 227)(150, 220, 161, 231)(152, 222, 165, 235)(154, 224, 169, 239)(155, 225, 163, 233)(156, 226, 167, 237)(158, 228, 175, 245)(159, 229, 164, 234)(160, 230, 168, 238)(162, 232, 181, 251)(166, 236, 186, 256)(170, 240, 190, 260)(171, 241, 184, 254)(172, 242, 188, 258)(173, 243, 182, 252)(174, 244, 187, 257)(176, 246, 180, 250)(177, 247, 185, 255)(178, 248, 189, 259)(179, 249, 183, 253)(191, 261, 206, 276)(192, 262, 200, 270)(193, 263, 204, 274)(194, 264, 203, 273)(195, 265, 202, 272)(196, 266, 201, 271)(197, 267, 205, 275)(198, 268, 199, 269)(207, 277, 209, 279)(208, 278, 210, 280) L = (1, 143)(2, 145)(3, 148)(4, 141)(5, 152)(6, 142)(7, 155)(8, 158)(9, 159)(10, 144)(11, 163)(12, 166)(13, 167)(14, 146)(15, 171)(16, 147)(17, 173)(18, 176)(19, 177)(20, 149)(21, 179)(22, 150)(23, 182)(24, 151)(25, 184)(26, 178)(27, 187)(28, 153)(29, 188)(30, 154)(31, 170)(32, 156)(33, 192)(34, 157)(35, 181)(36, 168)(37, 195)(38, 160)(39, 196)(40, 161)(41, 198)(42, 162)(43, 164)(44, 200)(45, 165)(46, 190)(47, 203)(48, 204)(49, 169)(50, 206)(51, 172)(52, 191)(53, 174)(54, 175)(55, 197)(56, 208)(57, 180)(58, 207)(59, 183)(60, 199)(61, 185)(62, 186)(63, 205)(64, 210)(65, 189)(66, 209)(67, 193)(68, 194)(69, 201)(70, 202)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 28, 70 ), ( 28, 70, 28, 70 ) } Outer automorphisms :: reflexible Dual of E15.1057 Graph:: simple bipartite v = 105 e = 140 f = 7 degree seq :: [ 2^70, 4^35 ] E15.1059 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 35}) Quotient :: dipole Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3, Y1^4 * Y3 * Y1 * Y3 * Y1^2, Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-1 ] Map:: R = (1, 71, 2, 72, 5, 75, 11, 81, 23, 93, 34, 104, 17, 87, 29, 99, 45, 115, 59, 129, 68, 138, 53, 123, 35, 105, 48, 118, 62, 132, 69, 139, 65, 135, 50, 120, 54, 124, 64, 134, 70, 140, 66, 136, 51, 121, 32, 102, 47, 117, 61, 131, 67, 137, 52, 122, 33, 103, 16, 86, 28, 98, 42, 112, 22, 92, 10, 80, 4, 74)(3, 73, 7, 77, 15, 85, 31, 101, 38, 108, 20, 90, 9, 79, 19, 89, 37, 107, 55, 125, 57, 127, 40, 110, 21, 91, 39, 109, 56, 126, 60, 130, 43, 113, 24, 94, 41, 111, 58, 128, 63, 133, 46, 116, 26, 96, 12, 82, 25, 95, 44, 114, 49, 119, 30, 100, 14, 84, 6, 76, 13, 83, 27, 97, 36, 106, 18, 88, 8, 78)(141, 211)(142, 212)(143, 213)(144, 214)(145, 215)(146, 216)(147, 217)(148, 218)(149, 219)(150, 220)(151, 221)(152, 222)(153, 223)(154, 224)(155, 225)(156, 226)(157, 227)(158, 228)(159, 229)(160, 230)(161, 231)(162, 232)(163, 233)(164, 234)(165, 235)(166, 236)(167, 237)(168, 238)(169, 239)(170, 240)(171, 241)(172, 242)(173, 243)(174, 244)(175, 245)(176, 246)(177, 247)(178, 248)(179, 249)(180, 250)(181, 251)(182, 252)(183, 253)(184, 254)(185, 255)(186, 256)(187, 257)(188, 258)(189, 259)(190, 260)(191, 261)(192, 262)(193, 263)(194, 264)(195, 265)(196, 266)(197, 267)(198, 268)(199, 269)(200, 270)(201, 271)(202, 272)(203, 273)(204, 274)(205, 275)(206, 276)(207, 277)(208, 278)(209, 279)(210, 280) L = (1, 143)(2, 146)(3, 141)(4, 149)(5, 152)(6, 142)(7, 156)(8, 157)(9, 144)(10, 161)(11, 164)(12, 145)(13, 168)(14, 169)(15, 172)(16, 147)(17, 148)(18, 175)(19, 173)(20, 174)(21, 150)(22, 181)(23, 180)(24, 151)(25, 182)(26, 185)(27, 187)(28, 153)(29, 154)(30, 188)(31, 190)(32, 155)(33, 159)(34, 160)(35, 158)(36, 194)(37, 191)(38, 193)(39, 192)(40, 163)(41, 162)(42, 165)(43, 199)(44, 201)(45, 166)(46, 202)(47, 167)(48, 170)(49, 204)(50, 171)(51, 177)(52, 179)(53, 178)(54, 176)(55, 205)(56, 206)(57, 208)(58, 207)(59, 183)(60, 209)(61, 184)(62, 186)(63, 210)(64, 189)(65, 195)(66, 196)(67, 198)(68, 197)(69, 200)(70, 203)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E15.1056 Graph:: simple bipartite v = 72 e = 140 f = 40 degree seq :: [ 2^70, 70^2 ] E15.1060 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 35}) Quotient :: dipole Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^-3 * Y1 * Y2^-1 * Y1 * Y2^-3, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^14 ] Map:: R = (1, 71, 2, 72)(3, 73, 7, 77)(4, 74, 9, 79)(5, 75, 11, 81)(6, 76, 13, 83)(8, 78, 17, 87)(10, 80, 21, 91)(12, 82, 25, 95)(14, 84, 29, 99)(15, 85, 23, 93)(16, 86, 27, 97)(18, 88, 35, 105)(19, 89, 24, 94)(20, 90, 28, 98)(22, 92, 41, 111)(26, 96, 46, 116)(30, 100, 50, 120)(31, 101, 44, 114)(32, 102, 48, 118)(33, 103, 42, 112)(34, 104, 47, 117)(36, 106, 40, 110)(37, 107, 45, 115)(38, 108, 49, 119)(39, 109, 43, 113)(51, 121, 66, 136)(52, 122, 60, 130)(53, 123, 64, 134)(54, 124, 63, 133)(55, 125, 62, 132)(56, 126, 61, 131)(57, 127, 65, 135)(58, 128, 59, 129)(67, 137, 69, 139)(68, 138, 70, 140)(141, 211, 143, 213, 148, 218, 158, 228, 176, 246, 168, 238, 153, 223, 167, 237, 187, 257, 203, 273, 205, 275, 189, 259, 169, 239, 188, 258, 204, 274, 210, 280, 202, 272, 186, 256, 190, 260, 206, 276, 209, 279, 201, 271, 185, 255, 165, 235, 184, 254, 200, 270, 199, 269, 183, 253, 164, 234, 151, 221, 163, 233, 182, 252, 162, 232, 150, 220, 144, 214)(142, 212, 145, 215, 152, 222, 166, 236, 178, 248, 160, 230, 149, 219, 159, 229, 177, 247, 195, 265, 197, 267, 180, 250, 161, 231, 179, 249, 196, 266, 208, 278, 194, 264, 175, 245, 181, 251, 198, 268, 207, 277, 193, 263, 174, 244, 157, 227, 173, 243, 192, 262, 191, 261, 172, 242, 156, 226, 147, 217, 155, 225, 171, 241, 170, 240, 154, 224, 146, 216) L = (1, 142)(2, 141)(3, 147)(4, 149)(5, 151)(6, 153)(7, 143)(8, 157)(9, 144)(10, 161)(11, 145)(12, 165)(13, 146)(14, 169)(15, 163)(16, 167)(17, 148)(18, 175)(19, 164)(20, 168)(21, 150)(22, 181)(23, 155)(24, 159)(25, 152)(26, 186)(27, 156)(28, 160)(29, 154)(30, 190)(31, 184)(32, 188)(33, 182)(34, 187)(35, 158)(36, 180)(37, 185)(38, 189)(39, 183)(40, 176)(41, 162)(42, 173)(43, 179)(44, 171)(45, 177)(46, 166)(47, 174)(48, 172)(49, 178)(50, 170)(51, 206)(52, 200)(53, 204)(54, 203)(55, 202)(56, 201)(57, 205)(58, 199)(59, 198)(60, 192)(61, 196)(62, 195)(63, 194)(64, 193)(65, 197)(66, 191)(67, 209)(68, 210)(69, 207)(70, 208)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 2, 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 E15.1061 Graph:: bipartite v = 37 e = 140 f = 75 degree seq :: [ 4^35, 70^2 ] E15.1061 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 35}) Quotient :: dipole Aut^+ = C7 x D10 (small group id <70, 1>) Aut = D10 x D14 (small group id <140, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1 * Y3)^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y1^-3 * Y3^-1 * Y1 * Y3^-1, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^2 * Y3^-3, Y3^-1 * Y1 * Y3^-1 * Y1^11, (Y3 * Y2^-1)^35 ] Map:: R = (1, 71, 2, 72, 6, 76, 16, 86, 34, 104, 52, 122, 66, 136, 69, 139, 70, 140, 61, 131, 48, 118, 27, 97, 13, 83, 4, 74)(3, 73, 9, 79, 17, 87, 8, 78, 21, 91, 35, 105, 54, 124, 64, 134, 67, 137, 65, 135, 62, 132, 46, 116, 28, 98, 11, 81)(5, 75, 14, 84, 18, 88, 37, 107, 53, 123, 60, 130, 68, 138, 59, 129, 63, 133, 47, 117, 30, 100, 12, 82, 20, 90, 7, 77)(10, 80, 24, 94, 36, 106, 23, 93, 41, 111, 22, 92, 42, 112, 39, 109, 57, 127, 50, 120, 56, 126, 51, 121, 33, 103, 26, 96)(15, 85, 32, 102, 25, 95, 45, 115, 55, 125, 44, 114, 58, 128, 43, 113, 49, 119, 29, 99, 40, 110, 19, 89, 38, 108, 31, 101)(141, 211)(142, 212)(143, 213)(144, 214)(145, 215)(146, 216)(147, 217)(148, 218)(149, 219)(150, 220)(151, 221)(152, 222)(153, 223)(154, 224)(155, 225)(156, 226)(157, 227)(158, 228)(159, 229)(160, 230)(161, 231)(162, 232)(163, 233)(164, 234)(165, 235)(166, 236)(167, 237)(168, 238)(169, 239)(170, 240)(171, 241)(172, 242)(173, 243)(174, 244)(175, 245)(176, 246)(177, 247)(178, 248)(179, 249)(180, 250)(181, 251)(182, 252)(183, 253)(184, 254)(185, 255)(186, 256)(187, 257)(188, 258)(189, 259)(190, 260)(191, 261)(192, 262)(193, 263)(194, 264)(195, 265)(196, 266)(197, 267)(198, 268)(199, 269)(200, 270)(201, 271)(202, 272)(203, 273)(204, 274)(205, 275)(206, 276)(207, 277)(208, 278)(209, 279)(210, 280) L = (1, 143)(2, 147)(3, 150)(4, 152)(5, 141)(6, 157)(7, 159)(8, 142)(9, 144)(10, 165)(11, 167)(12, 169)(13, 168)(14, 171)(15, 145)(16, 154)(17, 176)(18, 146)(19, 179)(20, 153)(21, 181)(22, 148)(23, 149)(24, 151)(25, 158)(26, 186)(27, 187)(28, 173)(29, 162)(30, 188)(31, 190)(32, 191)(33, 155)(34, 161)(35, 156)(36, 195)(37, 172)(38, 160)(39, 175)(40, 170)(41, 198)(42, 189)(43, 163)(44, 164)(45, 166)(46, 201)(47, 183)(48, 202)(49, 203)(50, 204)(51, 205)(52, 177)(53, 174)(54, 182)(55, 193)(56, 178)(57, 180)(58, 208)(59, 184)(60, 185)(61, 199)(62, 196)(63, 210)(64, 192)(65, 209)(66, 194)(67, 197)(68, 206)(69, 200)(70, 207)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280) local type(s) :: { ( 4, 70 ), ( 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70, 4, 70 ) } Outer automorphisms :: reflexible Dual of E15.1060 Graph:: simple bipartite v = 75 e = 140 f = 37 degree seq :: [ 2^70, 28^5 ] E15.1062 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 9}) Quotient :: dipole Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^4, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2, (Y3 * Y1)^9 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 10, 82)(6, 78, 12, 84)(8, 80, 15, 87)(11, 83, 20, 92)(13, 85, 18, 90)(14, 86, 24, 96)(16, 88, 27, 99)(17, 89, 29, 101)(19, 91, 25, 97)(21, 93, 23, 95)(22, 94, 32, 104)(26, 98, 35, 107)(28, 100, 36, 108)(30, 102, 39, 111)(31, 103, 40, 112)(33, 105, 41, 113)(34, 106, 37, 109)(38, 110, 46, 118)(42, 114, 50, 122)(43, 115, 51, 123)(44, 116, 52, 124)(45, 117, 53, 125)(47, 119, 55, 127)(48, 120, 56, 128)(49, 121, 57, 129)(54, 126, 62, 134)(58, 130, 66, 138)(59, 131, 67, 139)(60, 132, 68, 140)(61, 133, 69, 141)(63, 135, 70, 142)(64, 136, 71, 143)(65, 137, 72, 144)(145, 217, 147, 219)(146, 218, 149, 221)(148, 220, 152, 224)(150, 222, 155, 227)(151, 223, 157, 229)(153, 225, 160, 232)(154, 226, 162, 234)(156, 228, 165, 237)(158, 230, 167, 239)(159, 231, 169, 241)(161, 233, 172, 244)(163, 235, 171, 243)(164, 236, 168, 240)(166, 238, 175, 247)(170, 242, 178, 250)(173, 245, 181, 253)(174, 246, 177, 249)(176, 248, 185, 257)(179, 251, 180, 252)(182, 254, 189, 261)(183, 255, 184, 256)(186, 258, 193, 265)(187, 259, 188, 260)(190, 262, 195, 267)(191, 263, 192, 264)(194, 266, 199, 271)(196, 268, 197, 269)(198, 270, 203, 275)(200, 272, 201, 273)(202, 274, 207, 279)(204, 276, 205, 277)(206, 278, 212, 284)(208, 280, 209, 281)(210, 282, 215, 287)(211, 283, 213, 285)(214, 286, 216, 288) L = (1, 148)(2, 150)(3, 152)(4, 145)(5, 155)(6, 146)(7, 158)(8, 147)(9, 161)(10, 163)(11, 149)(12, 166)(13, 167)(14, 151)(15, 170)(16, 172)(17, 153)(18, 171)(19, 154)(20, 174)(21, 175)(22, 156)(23, 157)(24, 177)(25, 178)(26, 159)(27, 162)(28, 160)(29, 182)(30, 164)(31, 165)(32, 186)(33, 168)(34, 169)(35, 187)(36, 188)(37, 189)(38, 173)(39, 191)(40, 192)(41, 193)(42, 176)(43, 179)(44, 180)(45, 181)(46, 198)(47, 183)(48, 184)(49, 185)(50, 202)(51, 203)(52, 204)(53, 205)(54, 190)(55, 207)(56, 208)(57, 209)(58, 194)(59, 195)(60, 196)(61, 197)(62, 210)(63, 199)(64, 200)(65, 201)(66, 206)(67, 216)(68, 215)(69, 214)(70, 213)(71, 212)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E15.1065 Graph:: simple bipartite v = 72 e = 144 f = 44 degree seq :: [ 4^72 ] E15.1063 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 9}) Quotient :: dipole Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (Y3 * Y1)^9, (Y2 * Y1)^9 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 10, 82)(6, 78, 12, 84)(8, 80, 15, 87)(11, 83, 20, 92)(13, 85, 23, 95)(14, 86, 25, 97)(16, 88, 28, 100)(17, 89, 30, 102)(18, 90, 31, 103)(19, 91, 33, 105)(21, 93, 36, 108)(22, 94, 38, 110)(24, 96, 35, 107)(26, 98, 37, 109)(27, 99, 32, 104)(29, 101, 34, 106)(39, 111, 49, 121)(40, 112, 50, 122)(41, 113, 51, 123)(42, 114, 52, 124)(43, 115, 48, 120)(44, 116, 53, 125)(45, 117, 54, 126)(46, 118, 55, 127)(47, 119, 56, 128)(57, 129, 65, 137)(58, 130, 66, 138)(59, 131, 67, 139)(60, 132, 68, 140)(61, 133, 69, 141)(62, 134, 70, 142)(63, 135, 71, 143)(64, 136, 72, 144)(145, 217, 147, 219)(146, 218, 149, 221)(148, 220, 152, 224)(150, 222, 155, 227)(151, 223, 157, 229)(153, 225, 160, 232)(154, 226, 162, 234)(156, 228, 165, 237)(158, 230, 168, 240)(159, 231, 170, 242)(161, 233, 173, 245)(163, 235, 176, 248)(164, 236, 178, 250)(166, 238, 181, 253)(167, 239, 183, 255)(169, 241, 185, 257)(171, 243, 187, 259)(172, 244, 186, 258)(174, 246, 184, 256)(175, 247, 188, 260)(177, 249, 190, 262)(179, 251, 192, 264)(180, 252, 191, 263)(182, 254, 189, 261)(193, 265, 201, 273)(194, 266, 203, 275)(195, 267, 204, 276)(196, 268, 202, 274)(197, 269, 205, 277)(198, 270, 207, 279)(199, 271, 208, 280)(200, 272, 206, 278)(209, 281, 213, 285)(210, 282, 215, 287)(211, 283, 214, 286)(212, 284, 216, 288) L = (1, 148)(2, 150)(3, 152)(4, 145)(5, 155)(6, 146)(7, 158)(8, 147)(9, 161)(10, 163)(11, 149)(12, 166)(13, 168)(14, 151)(15, 171)(16, 173)(17, 153)(18, 176)(19, 154)(20, 179)(21, 181)(22, 156)(23, 184)(24, 157)(25, 186)(26, 187)(27, 159)(28, 185)(29, 160)(30, 183)(31, 189)(32, 162)(33, 191)(34, 192)(35, 164)(36, 190)(37, 165)(38, 188)(39, 174)(40, 167)(41, 172)(42, 169)(43, 170)(44, 182)(45, 175)(46, 180)(47, 177)(48, 178)(49, 202)(50, 204)(51, 203)(52, 201)(53, 206)(54, 208)(55, 207)(56, 205)(57, 196)(58, 193)(59, 195)(60, 194)(61, 200)(62, 197)(63, 199)(64, 198)(65, 216)(66, 214)(67, 215)(68, 213)(69, 212)(70, 210)(71, 211)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E15.1064 Graph:: simple bipartite v = 72 e = 144 f = 44 degree seq :: [ 4^72 ] E15.1064 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 9}) Quotient :: dipole Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1 * Y2 * Y1^-2 * Y2, Y1^2 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y1^9 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 6, 78, 15, 87, 33, 105, 52, 124, 32, 104, 14, 86, 5, 77)(3, 75, 9, 81, 21, 93, 34, 106, 55, 127, 61, 133, 45, 117, 26, 98, 11, 83)(4, 76, 12, 84, 27, 99, 46, 118, 62, 134, 54, 126, 35, 107, 17, 89, 8, 80)(7, 79, 18, 90, 38, 110, 53, 125, 66, 138, 51, 123, 31, 103, 25, 97, 20, 92)(10, 82, 24, 96, 43, 115, 60, 132, 70, 142, 68, 140, 56, 128, 41, 113, 23, 95)(13, 85, 29, 101, 22, 94, 16, 88, 36, 108, 57, 129, 65, 137, 50, 122, 30, 102)(19, 91, 40, 112, 44, 116, 47, 119, 63, 135, 72, 144, 67, 139, 59, 131, 39, 111)(28, 100, 48, 120, 64, 136, 71, 143, 69, 141, 58, 130, 37, 109, 42, 114, 49, 121)(145, 217, 147, 219)(146, 218, 151, 223)(148, 220, 154, 226)(149, 221, 157, 229)(150, 222, 160, 232)(152, 224, 163, 235)(153, 225, 166, 238)(155, 227, 169, 241)(156, 228, 172, 244)(158, 230, 175, 247)(159, 231, 178, 250)(161, 233, 181, 253)(162, 234, 165, 237)(164, 236, 173, 245)(167, 239, 186, 258)(168, 240, 188, 260)(170, 242, 174, 246)(171, 243, 191, 263)(176, 248, 189, 261)(177, 249, 197, 269)(179, 251, 200, 272)(180, 252, 182, 254)(183, 255, 185, 257)(184, 256, 193, 265)(187, 259, 192, 264)(190, 262, 204, 276)(194, 266, 195, 267)(196, 268, 209, 281)(198, 270, 211, 283)(199, 271, 201, 273)(202, 274, 203, 275)(205, 277, 210, 282)(206, 278, 215, 287)(207, 279, 208, 280)(212, 284, 213, 285)(214, 286, 216, 288) L = (1, 148)(2, 152)(3, 154)(4, 145)(5, 156)(6, 161)(7, 163)(8, 146)(9, 167)(10, 147)(11, 168)(12, 149)(13, 172)(14, 171)(15, 179)(16, 181)(17, 150)(18, 183)(19, 151)(20, 184)(21, 185)(22, 186)(23, 153)(24, 155)(25, 188)(26, 187)(27, 158)(28, 157)(29, 193)(30, 192)(31, 191)(32, 190)(33, 198)(34, 200)(35, 159)(36, 202)(37, 160)(38, 203)(39, 162)(40, 164)(41, 165)(42, 166)(43, 170)(44, 169)(45, 204)(46, 176)(47, 175)(48, 174)(49, 173)(50, 208)(51, 207)(52, 206)(53, 211)(54, 177)(55, 212)(56, 178)(57, 213)(58, 180)(59, 182)(60, 189)(61, 214)(62, 196)(63, 195)(64, 194)(65, 215)(66, 216)(67, 197)(68, 199)(69, 201)(70, 205)(71, 209)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^4 ), ( 4^18 ) } Outer automorphisms :: reflexible Dual of E15.1063 Graph:: simple bipartite v = 44 e = 144 f = 72 degree seq :: [ 4^36, 18^8 ] E15.1065 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 9}) Quotient :: dipole Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y1^2 * Y2 * Y3 * Y1^-1 * Y2 * Y1 * Y2, (Y2 * Y1^-1)^4, Y1^9 ] Map:: polytopal non-degenerate R = (1, 73, 2, 74, 6, 78, 15, 87, 33, 105, 52, 124, 32, 104, 14, 86, 5, 77)(3, 75, 9, 81, 21, 93, 45, 117, 60, 132, 56, 128, 34, 106, 26, 98, 11, 83)(4, 76, 12, 84, 27, 99, 49, 121, 64, 136, 54, 126, 35, 107, 17, 89, 8, 80)(7, 79, 18, 90, 39, 111, 31, 103, 51, 123, 66, 138, 53, 125, 44, 116, 20, 92)(10, 82, 24, 96, 43, 115, 55, 127, 68, 140, 71, 143, 61, 133, 47, 119, 23, 95)(13, 85, 29, 101, 50, 122, 65, 137, 59, 131, 38, 110, 16, 88, 36, 108, 30, 102)(19, 91, 42, 114, 58, 130, 67, 139, 70, 142, 63, 135, 48, 120, 22, 94, 41, 113)(25, 97, 37, 109, 57, 129, 69, 141, 72, 144, 62, 134, 46, 118, 28, 100, 40, 112)(145, 217, 147, 219)(146, 218, 151, 223)(148, 220, 154, 226)(149, 221, 157, 229)(150, 222, 160, 232)(152, 224, 163, 235)(153, 225, 166, 238)(155, 227, 169, 241)(156, 228, 172, 244)(158, 230, 175, 247)(159, 231, 178, 250)(161, 233, 181, 253)(162, 234, 184, 256)(164, 236, 187, 259)(165, 237, 190, 262)(167, 239, 183, 255)(168, 240, 180, 252)(170, 242, 186, 258)(171, 243, 192, 264)(173, 245, 191, 263)(174, 246, 185, 257)(176, 248, 189, 261)(177, 249, 197, 269)(179, 251, 199, 271)(182, 254, 202, 274)(188, 260, 201, 273)(193, 265, 205, 277)(194, 266, 207, 279)(195, 267, 206, 278)(196, 268, 209, 281)(198, 270, 211, 283)(200, 272, 213, 285)(203, 275, 212, 284)(204, 276, 214, 286)(208, 280, 216, 288)(210, 282, 215, 287) L = (1, 148)(2, 152)(3, 154)(4, 145)(5, 156)(6, 161)(7, 163)(8, 146)(9, 167)(10, 147)(11, 168)(12, 149)(13, 172)(14, 171)(15, 179)(16, 181)(17, 150)(18, 185)(19, 151)(20, 186)(21, 191)(22, 183)(23, 153)(24, 155)(25, 180)(26, 187)(27, 158)(28, 157)(29, 190)(30, 184)(31, 192)(32, 193)(33, 198)(34, 199)(35, 159)(36, 169)(37, 160)(38, 201)(39, 166)(40, 174)(41, 162)(42, 164)(43, 170)(44, 202)(45, 205)(46, 173)(47, 165)(48, 175)(49, 176)(50, 206)(51, 207)(52, 208)(53, 211)(54, 177)(55, 178)(56, 212)(57, 182)(58, 188)(59, 213)(60, 215)(61, 189)(62, 194)(63, 195)(64, 196)(65, 216)(66, 214)(67, 197)(68, 200)(69, 203)(70, 210)(71, 204)(72, 209)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^4 ), ( 4^18 ) } Outer automorphisms :: reflexible Dual of E15.1062 Graph:: simple bipartite v = 44 e = 144 f = 72 degree seq :: [ 4^36, 18^8 ] E15.1066 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 9}) Quotient :: edge Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2 * T1^-1)^2, (T2^-2 * T1^-1)^2, T2^9 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 43, 47, 29, 14, 5)(2, 7, 18, 36, 54, 56, 38, 20, 8)(4, 11, 26, 45, 61, 59, 42, 23, 12)(6, 15, 31, 50, 64, 66, 52, 33, 16)(9, 21, 13, 28, 46, 62, 58, 41, 22)(17, 34, 19, 37, 55, 68, 67, 53, 35)(25, 39, 27, 40, 57, 69, 70, 60, 44)(30, 48, 32, 51, 65, 72, 71, 63, 49)(73, 74, 78, 76)(75, 81, 91, 80)(77, 83, 97, 85)(79, 89, 104, 88)(82, 95, 112, 94)(84, 87, 102, 99)(86, 100, 107, 90)(92, 109, 121, 103)(93, 111, 120, 106)(96, 110, 122, 114)(98, 105, 123, 116)(101, 108, 124, 117)(113, 129, 135, 127)(115, 130, 140, 128)(118, 132, 137, 125)(119, 133, 142, 134)(126, 139, 144, 138)(131, 136, 143, 141) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8^4 ), ( 8^9 ) } Outer automorphisms :: reflexible Dual of E15.1067 Transitivity :: ET+ Graph:: simple bipartite v = 26 e = 72 f = 18 degree seq :: [ 4^18, 9^8 ] E15.1067 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 9}) Quotient :: loop Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T2 * T1^-2)^2, (T2^-2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 73, 3, 75, 10, 82, 5, 77)(2, 74, 7, 79, 19, 91, 8, 80)(4, 76, 12, 84, 25, 97, 13, 85)(6, 78, 16, 88, 28, 100, 17, 89)(9, 81, 23, 95, 15, 87, 24, 96)(11, 83, 26, 98, 14, 86, 27, 99)(18, 90, 29, 101, 22, 94, 30, 102)(20, 92, 31, 103, 21, 93, 32, 104)(33, 105, 41, 113, 36, 108, 42, 114)(34, 106, 43, 115, 35, 107, 44, 116)(37, 109, 45, 117, 40, 112, 46, 118)(38, 110, 47, 119, 39, 111, 48, 120)(49, 121, 57, 129, 52, 124, 58, 130)(50, 122, 59, 131, 51, 123, 60, 132)(53, 125, 61, 133, 56, 128, 62, 134)(54, 126, 63, 135, 55, 127, 64, 136)(65, 137, 69, 141, 68, 140, 72, 144)(66, 138, 71, 143, 67, 139, 70, 142) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 76)(7, 90)(8, 93)(9, 89)(10, 97)(11, 75)(12, 94)(13, 92)(14, 88)(15, 77)(16, 87)(17, 83)(18, 85)(19, 82)(20, 79)(21, 84)(22, 80)(23, 105)(24, 107)(25, 100)(26, 108)(27, 106)(28, 91)(29, 109)(30, 111)(31, 112)(32, 110)(33, 99)(34, 95)(35, 98)(36, 96)(37, 104)(38, 101)(39, 103)(40, 102)(41, 121)(42, 123)(43, 124)(44, 122)(45, 125)(46, 127)(47, 128)(48, 126)(49, 116)(50, 113)(51, 115)(52, 114)(53, 120)(54, 117)(55, 119)(56, 118)(57, 137)(58, 139)(59, 140)(60, 138)(61, 141)(62, 143)(63, 144)(64, 142)(65, 132)(66, 129)(67, 131)(68, 130)(69, 136)(70, 133)(71, 135)(72, 134) local type(s) :: { ( 4, 9, 4, 9, 4, 9, 4, 9 ) } Outer automorphisms :: reflexible Dual of E15.1066 Transitivity :: ET+ VT+ AT Graph:: v = 18 e = 72 f = 26 degree seq :: [ 8^18 ] E15.1068 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 9}) Quotient :: dipole Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2^-1 * Y1)^2, (Y2^-2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^9 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 19, 91, 8, 80)(5, 77, 11, 83, 25, 97, 13, 85)(7, 79, 17, 89, 32, 104, 16, 88)(10, 82, 23, 95, 40, 112, 22, 94)(12, 84, 15, 87, 30, 102, 27, 99)(14, 86, 28, 100, 35, 107, 18, 90)(20, 92, 37, 109, 49, 121, 31, 103)(21, 93, 39, 111, 48, 120, 34, 106)(24, 96, 38, 110, 50, 122, 42, 114)(26, 98, 33, 105, 51, 123, 44, 116)(29, 101, 36, 108, 52, 124, 45, 117)(41, 113, 57, 129, 63, 135, 55, 127)(43, 115, 58, 130, 68, 140, 56, 128)(46, 118, 60, 132, 65, 137, 53, 125)(47, 119, 61, 133, 70, 142, 62, 134)(54, 126, 67, 139, 72, 144, 66, 138)(59, 131, 64, 136, 71, 143, 69, 141)(145, 217, 147, 219, 154, 226, 168, 240, 187, 259, 191, 263, 173, 245, 158, 230, 149, 221)(146, 218, 151, 223, 162, 234, 180, 252, 198, 270, 200, 272, 182, 254, 164, 236, 152, 224)(148, 220, 155, 227, 170, 242, 189, 261, 205, 277, 203, 275, 186, 258, 167, 239, 156, 228)(150, 222, 159, 231, 175, 247, 194, 266, 208, 280, 210, 282, 196, 268, 177, 249, 160, 232)(153, 225, 165, 237, 157, 229, 172, 244, 190, 262, 206, 278, 202, 274, 185, 257, 166, 238)(161, 233, 178, 250, 163, 235, 181, 253, 199, 271, 212, 284, 211, 283, 197, 269, 179, 251)(169, 241, 183, 255, 171, 243, 184, 256, 201, 273, 213, 285, 214, 286, 204, 276, 188, 260)(174, 246, 192, 264, 176, 248, 195, 267, 209, 281, 216, 288, 215, 287, 207, 279, 193, 265) L = (1, 147)(2, 151)(3, 154)(4, 155)(5, 145)(6, 159)(7, 162)(8, 146)(9, 165)(10, 168)(11, 170)(12, 148)(13, 172)(14, 149)(15, 175)(16, 150)(17, 178)(18, 180)(19, 181)(20, 152)(21, 157)(22, 153)(23, 156)(24, 187)(25, 183)(26, 189)(27, 184)(28, 190)(29, 158)(30, 192)(31, 194)(32, 195)(33, 160)(34, 163)(35, 161)(36, 198)(37, 199)(38, 164)(39, 171)(40, 201)(41, 166)(42, 167)(43, 191)(44, 169)(45, 205)(46, 206)(47, 173)(48, 176)(49, 174)(50, 208)(51, 209)(52, 177)(53, 179)(54, 200)(55, 212)(56, 182)(57, 213)(58, 185)(59, 186)(60, 188)(61, 203)(62, 202)(63, 193)(64, 210)(65, 216)(66, 196)(67, 197)(68, 211)(69, 214)(70, 204)(71, 207)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 8, 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 E15.1069 Graph:: bipartite v = 26 e = 144 f = 90 degree seq :: [ 8^18, 18^8 ] E15.1069 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 9}) Quotient :: dipole Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y3^-1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^9 ] Map:: polytopal R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 148, 220)(147, 219, 153, 225, 165, 237, 155, 227)(149, 221, 157, 229, 162, 234, 151, 223)(152, 224, 163, 235, 175, 247, 159, 231)(154, 226, 167, 239, 181, 253, 164, 236)(156, 228, 160, 232, 176, 248, 171, 243)(158, 230, 170, 242, 188, 260, 172, 244)(161, 233, 178, 250, 195, 267, 177, 249)(166, 238, 174, 246, 192, 264, 183, 255)(168, 240, 182, 254, 193, 265, 185, 257)(169, 241, 184, 256, 194, 266, 180, 252)(173, 245, 179, 251, 196, 268, 189, 261)(186, 258, 201, 273, 207, 279, 199, 271)(187, 259, 202, 274, 213, 285, 203, 275)(190, 262, 204, 276, 209, 281, 197, 269)(191, 263, 206, 278, 211, 283, 198, 270)(200, 272, 212, 284, 215, 287, 208, 280)(205, 277, 210, 282, 216, 288, 214, 286) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 159)(7, 161)(8, 146)(9, 148)(10, 168)(11, 169)(12, 170)(13, 172)(14, 149)(15, 174)(16, 150)(17, 179)(18, 180)(19, 181)(20, 152)(21, 183)(22, 153)(23, 155)(24, 187)(25, 157)(26, 189)(27, 184)(28, 190)(29, 158)(30, 193)(31, 194)(32, 195)(33, 160)(34, 162)(35, 198)(36, 163)(37, 199)(38, 164)(39, 201)(40, 165)(41, 166)(42, 167)(43, 191)(44, 171)(45, 205)(46, 206)(47, 173)(48, 175)(49, 208)(50, 176)(51, 209)(52, 177)(53, 178)(54, 200)(55, 212)(56, 182)(57, 213)(58, 185)(59, 186)(60, 188)(61, 202)(62, 203)(63, 192)(64, 210)(65, 216)(66, 196)(67, 197)(68, 211)(69, 214)(70, 204)(71, 207)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18 ) } Outer automorphisms :: reflexible Dual of E15.1068 Graph:: simple bipartite v = 90 e = 144 f = 26 degree seq :: [ 2^72, 8^18 ] E15.1070 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 18, 18}) Quotient :: regular Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1 * T2 * T1 * T2 * T1^-2 * T2, T1^18, T1^-1 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-3 * T2 * T1^-2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 31, 39, 47, 55, 63, 62, 54, 46, 38, 30, 22, 10, 4)(3, 7, 15, 24, 33, 42, 48, 57, 66, 70, 67, 59, 51, 43, 35, 27, 18, 8)(6, 13, 26, 32, 41, 50, 56, 65, 72, 69, 61, 53, 45, 37, 29, 21, 17, 14)(9, 19, 16, 12, 25, 34, 40, 49, 58, 64, 71, 68, 60, 52, 44, 36, 28, 20) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 15)(14, 19)(18, 20)(22, 27)(23, 32)(25, 26)(28, 29)(30, 36)(31, 40)(33, 34)(35, 37)(38, 45)(39, 48)(41, 42)(43, 44)(46, 51)(47, 56)(49, 50)(52, 53)(54, 60)(55, 64)(57, 58)(59, 61)(62, 69)(63, 70)(65, 66)(67, 68)(71, 72) local type(s) :: { ( 18^18 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 4 e = 36 f = 4 degree seq :: [ 18^4 ] E15.1071 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 18}) Quotient :: edge Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^18, T2^-1 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-3 * T1 * T2^-2 ] Map:: R = (1, 3, 8, 18, 27, 35, 43, 51, 59, 67, 62, 54, 46, 38, 30, 22, 10, 4)(2, 5, 12, 23, 31, 39, 47, 55, 63, 70, 64, 56, 48, 40, 32, 24, 14, 6)(7, 15, 25, 33, 41, 49, 57, 65, 71, 69, 61, 53, 45, 37, 29, 21, 13, 16)(9, 19, 11, 17, 26, 34, 42, 50, 58, 66, 72, 68, 60, 52, 44, 36, 28, 20)(73, 74)(75, 79)(76, 81)(77, 83)(78, 85)(80, 89)(82, 93)(84, 87)(86, 92)(88, 91)(90, 95)(94, 96)(97, 98)(99, 105)(100, 101)(102, 108)(103, 106)(104, 109)(107, 114)(110, 117)(111, 113)(112, 116)(115, 119)(118, 120)(121, 122)(123, 129)(124, 125)(126, 132)(127, 130)(128, 133)(131, 138)(134, 141)(135, 137)(136, 140)(139, 142)(143, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36, 36 ), ( 36^18 ) } Outer automorphisms :: reflexible Dual of E15.1072 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 72 f = 4 degree seq :: [ 2^36, 18^4 ] E15.1072 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 18}) Quotient :: loop Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^18, T2^-1 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-3 * T1 * T2^-2 ] Map:: R = (1, 73, 3, 75, 8, 80, 18, 90, 27, 99, 35, 107, 43, 115, 51, 123, 59, 131, 67, 139, 62, 134, 54, 126, 46, 118, 38, 110, 30, 102, 22, 94, 10, 82, 4, 76)(2, 74, 5, 77, 12, 84, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 70, 142, 64, 136, 56, 128, 48, 120, 40, 112, 32, 104, 24, 96, 14, 86, 6, 78)(7, 79, 15, 87, 25, 97, 33, 105, 41, 113, 49, 121, 57, 129, 65, 137, 71, 143, 69, 141, 61, 133, 53, 125, 45, 117, 37, 109, 29, 101, 21, 93, 13, 85, 16, 88)(9, 81, 19, 91, 11, 83, 17, 89, 26, 98, 34, 106, 42, 114, 50, 122, 58, 130, 66, 138, 72, 144, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92) L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 83)(6, 85)(7, 75)(8, 89)(9, 76)(10, 93)(11, 77)(12, 87)(13, 78)(14, 92)(15, 84)(16, 91)(17, 80)(18, 95)(19, 88)(20, 86)(21, 82)(22, 96)(23, 90)(24, 94)(25, 98)(26, 97)(27, 105)(28, 101)(29, 100)(30, 108)(31, 106)(32, 109)(33, 99)(34, 103)(35, 114)(36, 102)(37, 104)(38, 117)(39, 113)(40, 116)(41, 111)(42, 107)(43, 119)(44, 112)(45, 110)(46, 120)(47, 115)(48, 118)(49, 122)(50, 121)(51, 129)(52, 125)(53, 124)(54, 132)(55, 130)(56, 133)(57, 123)(58, 127)(59, 138)(60, 126)(61, 128)(62, 141)(63, 137)(64, 140)(65, 135)(66, 131)(67, 142)(68, 136)(69, 134)(70, 139)(71, 144)(72, 143) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E15.1071 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 72 f = 40 degree seq :: [ 36^4 ] E15.1073 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 18}) Quotient :: dipole Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, Y1 * Y2 * R * Y2^2 * R * Y2, Y2^18, (Y3 * Y2^-1)^18 ] Map:: R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 11, 83)(6, 78, 13, 85)(8, 80, 17, 89)(10, 82, 21, 93)(12, 84, 15, 87)(14, 86, 20, 92)(16, 88, 19, 91)(18, 90, 23, 95)(22, 94, 24, 96)(25, 97, 26, 98)(27, 99, 33, 105)(28, 100, 29, 101)(30, 102, 36, 108)(31, 103, 34, 106)(32, 104, 37, 109)(35, 107, 42, 114)(38, 110, 45, 117)(39, 111, 41, 113)(40, 112, 44, 116)(43, 115, 47, 119)(46, 118, 48, 120)(49, 121, 50, 122)(51, 123, 57, 129)(52, 124, 53, 125)(54, 126, 60, 132)(55, 127, 58, 130)(56, 128, 61, 133)(59, 131, 66, 138)(62, 134, 69, 141)(63, 135, 65, 137)(64, 136, 68, 140)(67, 139, 70, 142)(71, 143, 72, 144)(145, 217, 147, 219, 152, 224, 162, 234, 171, 243, 179, 251, 187, 259, 195, 267, 203, 275, 211, 283, 206, 278, 198, 270, 190, 262, 182, 254, 174, 246, 166, 238, 154, 226, 148, 220)(146, 218, 149, 221, 156, 228, 167, 239, 175, 247, 183, 255, 191, 263, 199, 271, 207, 279, 214, 286, 208, 280, 200, 272, 192, 264, 184, 256, 176, 248, 168, 240, 158, 230, 150, 222)(151, 223, 159, 231, 169, 241, 177, 249, 185, 257, 193, 265, 201, 273, 209, 281, 215, 287, 213, 285, 205, 277, 197, 269, 189, 261, 181, 253, 173, 245, 165, 237, 157, 229, 160, 232)(153, 225, 163, 235, 155, 227, 161, 233, 170, 242, 178, 250, 186, 258, 194, 266, 202, 274, 210, 282, 216, 288, 212, 284, 204, 276, 196, 268, 188, 260, 180, 252, 172, 244, 164, 236) L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 161)(9, 148)(10, 165)(11, 149)(12, 159)(13, 150)(14, 164)(15, 156)(16, 163)(17, 152)(18, 167)(19, 160)(20, 158)(21, 154)(22, 168)(23, 162)(24, 166)(25, 170)(26, 169)(27, 177)(28, 173)(29, 172)(30, 180)(31, 178)(32, 181)(33, 171)(34, 175)(35, 186)(36, 174)(37, 176)(38, 189)(39, 185)(40, 188)(41, 183)(42, 179)(43, 191)(44, 184)(45, 182)(46, 192)(47, 187)(48, 190)(49, 194)(50, 193)(51, 201)(52, 197)(53, 196)(54, 204)(55, 202)(56, 205)(57, 195)(58, 199)(59, 210)(60, 198)(61, 200)(62, 213)(63, 209)(64, 212)(65, 207)(66, 203)(67, 214)(68, 208)(69, 206)(70, 211)(71, 216)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E15.1074 Graph:: bipartite v = 40 e = 144 f = 76 degree seq :: [ 4^36, 36^4 ] E15.1074 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 18}) Quotient :: dipole Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>) Aut = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^18, Y1^-3 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-1 ] Map:: R = (1, 73, 2, 74, 5, 77, 11, 83, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 62, 134, 54, 126, 46, 118, 38, 110, 30, 102, 22, 94, 10, 82, 4, 76)(3, 75, 7, 79, 15, 87, 24, 96, 33, 105, 42, 114, 48, 120, 57, 129, 66, 138, 70, 142, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 18, 90, 8, 80)(6, 78, 13, 85, 26, 98, 32, 104, 41, 113, 50, 122, 56, 128, 65, 137, 72, 144, 69, 141, 61, 133, 53, 125, 45, 117, 37, 109, 29, 101, 21, 93, 17, 89, 14, 86)(9, 81, 19, 91, 16, 88, 12, 84, 25, 97, 34, 106, 40, 112, 49, 121, 58, 130, 64, 136, 71, 143, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 150)(3, 145)(4, 153)(5, 156)(6, 146)(7, 160)(8, 161)(9, 148)(10, 165)(11, 168)(12, 149)(13, 159)(14, 163)(15, 157)(16, 151)(17, 152)(18, 164)(19, 158)(20, 162)(21, 154)(22, 171)(23, 176)(24, 155)(25, 170)(26, 169)(27, 166)(28, 173)(29, 172)(30, 180)(31, 184)(32, 167)(33, 178)(34, 177)(35, 181)(36, 174)(37, 179)(38, 189)(39, 192)(40, 175)(41, 186)(42, 185)(43, 188)(44, 187)(45, 182)(46, 195)(47, 200)(48, 183)(49, 194)(50, 193)(51, 190)(52, 197)(53, 196)(54, 204)(55, 208)(56, 191)(57, 202)(58, 201)(59, 205)(60, 198)(61, 203)(62, 213)(63, 214)(64, 199)(65, 210)(66, 209)(67, 212)(68, 211)(69, 206)(70, 207)(71, 216)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 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 E15.1073 Graph:: simple bipartite v = 76 e = 144 f = 40 degree seq :: [ 2^72, 36^4 ] E15.1075 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 40}) Quotient :: regular Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T1^4 * T2)^2, T1^-5 * T2 * T1 * T2 * T1^-4, (T1^-2 * T2)^4 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 66, 58, 33, 16, 28, 48, 69, 61, 76, 80, 78, 57, 32, 52, 72, 60, 35, 53, 73, 79, 77, 56, 75, 59, 34, 17, 29, 49, 70, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 67, 54, 30, 14, 6, 13, 27, 51, 41, 64, 74, 50, 26, 12, 25, 47, 40, 21, 39, 63, 71, 46, 24, 45, 38, 20, 9, 19, 37, 62, 68, 44, 36, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 77)(63, 78)(64, 66)(65, 68)(71, 79)(74, 80) local type(s) :: { ( 8^40 ) } Outer automorphisms :: reflexible Dual of E15.1076 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 40 f = 10 degree seq :: [ 40^2 ] E15.1076 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 40}) Quotient :: regular Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, 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, T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-10 ] 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, 77, 76, 80, 75, 79, 74, 78) 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) local type(s) :: { ( 40^8 ) } Outer automorphisms :: reflexible Dual of E15.1075 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 40 f = 2 degree seq :: [ 8^10 ] E15.1077 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 40}) Quotient :: edge Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^8, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^40 ] 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, 82)(83, 87)(84, 89)(85, 91)(86, 93)(88, 92)(90, 94)(95, 105)(96, 107)(97, 106)(98, 109)(99, 110)(100, 111)(101, 113)(102, 112)(103, 115)(104, 116)(108, 114)(117, 127)(118, 129)(119, 128)(120, 130)(121, 131)(122, 132)(123, 134)(124, 133)(125, 135)(126, 136)(137, 145)(138, 146)(139, 147)(140, 148)(141, 149)(142, 150)(143, 151)(144, 152)(153, 157)(154, 158)(155, 159)(156, 160) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^8 ) } Outer automorphisms :: reflexible Dual of E15.1081 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 80 f = 2 degree seq :: [ 2^40, 8^10 ] E15.1078 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 40}) Quotient :: edge Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (T1^-1 * T2^-1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-1 * T1^-3, T2^-1 * T1 * T2^-1 * T1^5, T2^8 * T1 * T2^-1 * T1^-1 * T2, T2^-2 * T1^-1 * T2^3 * T1 * T2^-1 * T1 * T2^2 * T1^2 * T2^2 * T1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 64, 71, 55, 39, 20, 13, 28, 43, 59, 75, 80, 72, 56, 41, 30, 34, 21, 42, 58, 74, 79, 70, 54, 38, 18, 6, 17, 36, 53, 69, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 61, 45, 23, 9, 4, 12, 29, 49, 65, 77, 62, 46, 24, 11, 27, 37, 32, 51, 67, 78, 63, 47, 26, 35, 16, 14, 31, 50, 66, 76, 60, 44, 22, 8)(81, 82, 86, 96, 114, 107, 93, 84)(83, 89, 97, 88, 101, 115, 108, 91)(85, 94, 98, 117, 110, 92, 100, 87)(90, 104, 116, 103, 122, 102, 123, 106)(95, 112, 118, 109, 121, 99, 119, 111)(105, 127, 133, 126, 138, 125, 139, 124)(113, 129, 134, 120, 136, 130, 135, 131)(128, 140, 149, 143, 154, 142, 155, 141)(132, 137, 150, 146, 152, 147, 151, 145)(144, 153, 148, 156, 159, 158, 160, 157) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^40 ) } Outer automorphisms :: reflexible Dual of E15.1082 Transitivity :: ET+ Graph:: bipartite v = 12 e = 80 f = 40 degree seq :: [ 8^10, 40^2 ] E15.1079 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 40}) Quotient :: edge Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T1^4 * T2)^2, T1^-5 * T2 * T1 * T2 * T1^-4, (T1^-2 * T2)^4 ] 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, 77)(63, 78)(64, 66)(65, 68)(71, 79)(74, 80)(81, 82, 85, 91, 103, 123, 146, 138, 113, 96, 108, 128, 149, 141, 156, 160, 158, 137, 112, 132, 152, 140, 115, 133, 153, 159, 157, 136, 155, 139, 114, 97, 109, 129, 150, 145, 122, 102, 90, 84)(83, 87, 95, 111, 135, 147, 134, 110, 94, 86, 93, 107, 131, 121, 144, 154, 130, 106, 92, 105, 127, 120, 101, 119, 143, 151, 126, 104, 125, 118, 100, 89, 99, 117, 142, 148, 124, 116, 98, 88) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 16 ), ( 16^40 ) } Outer automorphisms :: reflexible Dual of E15.1080 Transitivity :: ET+ Graph:: simple bipartite v = 42 e = 80 f = 10 degree seq :: [ 2^40, 40^2 ] E15.1080 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 40}) Quotient :: loop Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^8, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^40 ] Map:: R = (1, 81, 3, 83, 8, 88, 17, 97, 28, 108, 19, 99, 10, 90, 4, 84)(2, 82, 5, 85, 12, 92, 22, 102, 34, 114, 24, 104, 14, 94, 6, 86)(7, 87, 15, 95, 26, 106, 39, 119, 30, 110, 18, 98, 9, 89, 16, 96)(11, 91, 20, 100, 32, 112, 44, 124, 36, 116, 23, 103, 13, 93, 21, 101)(25, 105, 37, 117, 48, 128, 41, 121, 29, 109, 40, 120, 27, 107, 38, 118)(31, 111, 42, 122, 53, 133, 46, 126, 35, 115, 45, 125, 33, 113, 43, 123)(47, 127, 57, 137, 51, 131, 60, 140, 50, 130, 59, 139, 49, 129, 58, 138)(52, 132, 61, 141, 56, 136, 64, 144, 55, 135, 63, 143, 54, 134, 62, 142)(65, 145, 73, 153, 68, 148, 76, 156, 67, 147, 75, 155, 66, 146, 74, 154)(69, 149, 77, 157, 72, 152, 80, 160, 71, 151, 79, 159, 70, 150, 78, 158) L = (1, 82)(2, 81)(3, 87)(4, 89)(5, 91)(6, 93)(7, 83)(8, 92)(9, 84)(10, 94)(11, 85)(12, 88)(13, 86)(14, 90)(15, 105)(16, 107)(17, 106)(18, 109)(19, 110)(20, 111)(21, 113)(22, 112)(23, 115)(24, 116)(25, 95)(26, 97)(27, 96)(28, 114)(29, 98)(30, 99)(31, 100)(32, 102)(33, 101)(34, 108)(35, 103)(36, 104)(37, 127)(38, 129)(39, 128)(40, 130)(41, 131)(42, 132)(43, 134)(44, 133)(45, 135)(46, 136)(47, 117)(48, 119)(49, 118)(50, 120)(51, 121)(52, 122)(53, 124)(54, 123)(55, 125)(56, 126)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(73, 157)(74, 158)(75, 159)(76, 160)(77, 153)(78, 154)(79, 155)(80, 156) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E15.1079 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 80 f = 42 degree seq :: [ 16^10 ] E15.1081 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 40}) Quotient :: loop Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (T1^-1 * T2^-1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-1 * T1^-3, T2^-1 * T1 * T2^-1 * T1^5, T2^8 * T1 * T2^-1 * T1^-1 * T2, T2^-2 * T1^-1 * T2^3 * T1 * T2^-1 * T1 * T2^2 * T1^2 * T2^2 * T1 ] Map:: R = (1, 81, 3, 83, 10, 90, 25, 105, 48, 128, 64, 144, 71, 151, 55, 135, 39, 119, 20, 100, 13, 93, 28, 108, 43, 123, 59, 139, 75, 155, 80, 160, 72, 152, 56, 136, 41, 121, 30, 110, 34, 114, 21, 101, 42, 122, 58, 138, 74, 154, 79, 159, 70, 150, 54, 134, 38, 118, 18, 98, 6, 86, 17, 97, 36, 116, 53, 133, 69, 149, 68, 148, 52, 132, 33, 113, 15, 95, 5, 85)(2, 82, 7, 87, 19, 99, 40, 120, 57, 137, 73, 153, 61, 141, 45, 125, 23, 103, 9, 89, 4, 84, 12, 92, 29, 109, 49, 129, 65, 145, 77, 157, 62, 142, 46, 126, 24, 104, 11, 91, 27, 107, 37, 117, 32, 112, 51, 131, 67, 147, 78, 158, 63, 143, 47, 127, 26, 106, 35, 115, 16, 96, 14, 94, 31, 111, 50, 130, 66, 146, 76, 156, 60, 140, 44, 124, 22, 102, 8, 88) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 94)(6, 96)(7, 85)(8, 101)(9, 97)(10, 104)(11, 83)(12, 100)(13, 84)(14, 98)(15, 112)(16, 114)(17, 88)(18, 117)(19, 119)(20, 87)(21, 115)(22, 123)(23, 122)(24, 116)(25, 127)(26, 90)(27, 93)(28, 91)(29, 121)(30, 92)(31, 95)(32, 118)(33, 129)(34, 107)(35, 108)(36, 103)(37, 110)(38, 109)(39, 111)(40, 136)(41, 99)(42, 102)(43, 106)(44, 105)(45, 139)(46, 138)(47, 133)(48, 140)(49, 134)(50, 135)(51, 113)(52, 137)(53, 126)(54, 120)(55, 131)(56, 130)(57, 150)(58, 125)(59, 124)(60, 149)(61, 128)(62, 155)(63, 154)(64, 153)(65, 132)(66, 152)(67, 151)(68, 156)(69, 143)(70, 146)(71, 145)(72, 147)(73, 148)(74, 142)(75, 141)(76, 159)(77, 144)(78, 160)(79, 158)(80, 157) 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 ) } Outer automorphisms :: reflexible Dual of E15.1077 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 80 f = 50 degree seq :: [ 80^2 ] E15.1082 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 40}) Quotient :: loop Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T1^4 * T2)^2, T1^-5 * T2 * T1 * T2 * T1^-4, (T1^-2 * T2)^4 ] Map:: polytopal non-degenerate R = (1, 81, 3, 83)(2, 82, 6, 86)(4, 84, 9, 89)(5, 85, 12, 92)(7, 87, 16, 96)(8, 88, 17, 97)(10, 90, 21, 101)(11, 91, 24, 104)(13, 93, 28, 108)(14, 94, 29, 109)(15, 95, 32, 112)(18, 98, 35, 115)(19, 99, 33, 113)(20, 100, 34, 114)(22, 102, 41, 121)(23, 103, 44, 124)(25, 105, 48, 128)(26, 106, 49, 129)(27, 107, 52, 132)(30, 110, 53, 133)(31, 111, 56, 136)(36, 116, 61, 141)(37, 117, 57, 137)(38, 118, 60, 140)(39, 119, 58, 138)(40, 120, 59, 139)(42, 122, 55, 135)(43, 123, 67, 147)(45, 125, 69, 149)(46, 126, 70, 150)(47, 127, 72, 152)(50, 130, 73, 153)(51, 131, 75, 155)(54, 134, 76, 156)(62, 142, 77, 157)(63, 143, 78, 158)(64, 144, 66, 146)(65, 145, 68, 148)(71, 151, 79, 159)(74, 154, 80, 160) L = (1, 82)(2, 85)(3, 87)(4, 81)(5, 91)(6, 93)(7, 95)(8, 83)(9, 99)(10, 84)(11, 103)(12, 105)(13, 107)(14, 86)(15, 111)(16, 108)(17, 109)(18, 88)(19, 117)(20, 89)(21, 119)(22, 90)(23, 123)(24, 125)(25, 127)(26, 92)(27, 131)(28, 128)(29, 129)(30, 94)(31, 135)(32, 132)(33, 96)(34, 97)(35, 133)(36, 98)(37, 142)(38, 100)(39, 143)(40, 101)(41, 144)(42, 102)(43, 146)(44, 116)(45, 118)(46, 104)(47, 120)(48, 149)(49, 150)(50, 106)(51, 121)(52, 152)(53, 153)(54, 110)(55, 147)(56, 155)(57, 112)(58, 113)(59, 114)(60, 115)(61, 156)(62, 148)(63, 151)(64, 154)(65, 122)(66, 138)(67, 134)(68, 124)(69, 141)(70, 145)(71, 126)(72, 140)(73, 159)(74, 130)(75, 139)(76, 160)(77, 136)(78, 137)(79, 157)(80, 158) local type(s) :: { ( 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E15.1078 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 80 f = 12 degree seq :: [ 4^40 ] E15.1083 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |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^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^40 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 12, 92)(10, 90, 14, 94)(15, 95, 25, 105)(16, 96, 27, 107)(17, 97, 26, 106)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 31, 111)(21, 101, 33, 113)(22, 102, 32, 112)(23, 103, 35, 115)(24, 104, 36, 116)(28, 108, 34, 114)(37, 117, 47, 127)(38, 118, 49, 129)(39, 119, 48, 128)(40, 120, 50, 130)(41, 121, 51, 131)(42, 122, 52, 132)(43, 123, 54, 134)(44, 124, 53, 133)(45, 125, 55, 135)(46, 126, 56, 136)(57, 137, 65, 145)(58, 138, 66, 146)(59, 139, 67, 147)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 70, 150)(63, 143, 71, 151)(64, 144, 72, 152)(73, 153, 77, 157)(74, 154, 78, 158)(75, 155, 79, 159)(76, 156, 80, 160)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 194, 274, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 186, 266, 199, 279, 190, 270, 178, 258, 169, 249, 176, 256)(171, 251, 180, 260, 192, 272, 204, 284, 196, 276, 183, 263, 173, 253, 181, 261)(185, 265, 197, 277, 208, 288, 201, 281, 189, 269, 200, 280, 187, 267, 198, 278)(191, 271, 202, 282, 213, 293, 206, 286, 195, 275, 205, 285, 193, 273, 203, 283)(207, 287, 217, 297, 211, 291, 220, 300, 210, 290, 219, 299, 209, 289, 218, 298)(212, 292, 221, 301, 216, 296, 224, 304, 215, 295, 223, 303, 214, 294, 222, 302)(225, 305, 233, 313, 228, 308, 236, 316, 227, 307, 235, 315, 226, 306, 234, 314)(229, 309, 237, 317, 232, 312, 240, 320, 231, 311, 239, 319, 230, 310, 238, 318) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 172)(9, 164)(10, 174)(11, 165)(12, 168)(13, 166)(14, 170)(15, 185)(16, 187)(17, 186)(18, 189)(19, 190)(20, 191)(21, 193)(22, 192)(23, 195)(24, 196)(25, 175)(26, 177)(27, 176)(28, 194)(29, 178)(30, 179)(31, 180)(32, 182)(33, 181)(34, 188)(35, 183)(36, 184)(37, 207)(38, 209)(39, 208)(40, 210)(41, 211)(42, 212)(43, 214)(44, 213)(45, 215)(46, 216)(47, 197)(48, 199)(49, 198)(50, 200)(51, 201)(52, 202)(53, 204)(54, 203)(55, 205)(56, 206)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 217)(66, 218)(67, 219)(68, 220)(69, 221)(70, 222)(71, 223)(72, 224)(73, 237)(74, 238)(75, 239)(76, 240)(77, 233)(78, 234)(79, 235)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E15.1086 Graph:: bipartite v = 50 e = 160 f = 82 degree seq :: [ 4^40, 16^10 ] E15.1084 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, R * Y2 * R * Y3, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^-3 * Y2^-1 * Y1 * Y2^-1, Y2^-2 * Y1^3 * Y2^-2 * Y1, Y1 * Y2^-8 * Y1 * Y2^2 ] Map:: R = (1, 81, 2, 82, 6, 86, 16, 96, 34, 114, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 17, 97, 8, 88, 21, 101, 35, 115, 28, 108, 11, 91)(5, 85, 14, 94, 18, 98, 37, 117, 30, 110, 12, 92, 20, 100, 7, 87)(10, 90, 24, 104, 36, 116, 23, 103, 42, 122, 22, 102, 43, 123, 26, 106)(15, 95, 32, 112, 38, 118, 29, 109, 41, 121, 19, 99, 39, 119, 31, 111)(25, 105, 47, 127, 53, 133, 46, 126, 58, 138, 45, 125, 59, 139, 44, 124)(33, 113, 49, 129, 54, 134, 40, 120, 56, 136, 50, 130, 55, 135, 51, 131)(48, 128, 60, 140, 69, 149, 63, 143, 74, 154, 62, 142, 75, 155, 61, 141)(52, 132, 57, 137, 70, 150, 66, 146, 72, 152, 67, 147, 71, 151, 65, 145)(64, 144, 73, 153, 68, 148, 76, 156, 79, 159, 78, 158, 80, 160, 77, 157)(161, 241, 163, 243, 170, 250, 185, 265, 208, 288, 224, 304, 231, 311, 215, 295, 199, 279, 180, 260, 173, 253, 188, 268, 203, 283, 219, 299, 235, 315, 240, 320, 232, 312, 216, 296, 201, 281, 190, 270, 194, 274, 181, 261, 202, 282, 218, 298, 234, 314, 239, 319, 230, 310, 214, 294, 198, 278, 178, 258, 166, 246, 177, 257, 196, 276, 213, 293, 229, 309, 228, 308, 212, 292, 193, 273, 175, 255, 165, 245)(162, 242, 167, 247, 179, 259, 200, 280, 217, 297, 233, 313, 221, 301, 205, 285, 183, 263, 169, 249, 164, 244, 172, 252, 189, 269, 209, 289, 225, 305, 237, 317, 222, 302, 206, 286, 184, 264, 171, 251, 187, 267, 197, 277, 192, 272, 211, 291, 227, 307, 238, 318, 223, 303, 207, 287, 186, 266, 195, 275, 176, 256, 174, 254, 191, 271, 210, 290, 226, 306, 236, 316, 220, 300, 204, 284, 182, 262, 168, 248) L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 179)(8, 162)(9, 164)(10, 185)(11, 187)(12, 189)(13, 188)(14, 191)(15, 165)(16, 174)(17, 196)(18, 166)(19, 200)(20, 173)(21, 202)(22, 168)(23, 169)(24, 171)(25, 208)(26, 195)(27, 197)(28, 203)(29, 209)(30, 194)(31, 210)(32, 211)(33, 175)(34, 181)(35, 176)(36, 213)(37, 192)(38, 178)(39, 180)(40, 217)(41, 190)(42, 218)(43, 219)(44, 182)(45, 183)(46, 184)(47, 186)(48, 224)(49, 225)(50, 226)(51, 227)(52, 193)(53, 229)(54, 198)(55, 199)(56, 201)(57, 233)(58, 234)(59, 235)(60, 204)(61, 205)(62, 206)(63, 207)(64, 231)(65, 237)(66, 236)(67, 238)(68, 212)(69, 228)(70, 214)(71, 215)(72, 216)(73, 221)(74, 239)(75, 240)(76, 220)(77, 222)(78, 223)(79, 230)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E15.1085 Graph:: bipartite v = 12 e = 160 f = 120 degree seq :: [ 16^10, 80^2 ] E15.1085 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-4 * Y2)^2, (Y3^2 * Y2)^4, Y3^-6 * Y2 * Y3 * Y2 * Y3^-3, (Y3^-1 * Y1^-1)^40 ] Map:: polytopal R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242)(163, 243, 167, 247)(164, 244, 169, 249)(165, 245, 171, 251)(166, 246, 173, 253)(168, 248, 177, 257)(170, 250, 181, 261)(172, 252, 185, 265)(174, 254, 189, 269)(175, 255, 183, 263)(176, 256, 187, 267)(178, 258, 195, 275)(179, 259, 184, 264)(180, 260, 188, 268)(182, 262, 201, 281)(186, 266, 207, 287)(190, 270, 213, 293)(191, 271, 205, 285)(192, 272, 211, 291)(193, 273, 203, 283)(194, 274, 209, 289)(196, 276, 214, 294)(197, 277, 206, 286)(198, 278, 212, 292)(199, 279, 204, 284)(200, 280, 210, 290)(202, 282, 208, 288)(215, 295, 230, 310)(216, 296, 235, 315)(217, 297, 228, 308)(218, 298, 234, 314)(219, 299, 226, 306)(220, 300, 233, 313)(221, 301, 232, 312)(222, 302, 231, 311)(223, 303, 229, 309)(224, 304, 227, 307)(225, 305, 236, 316)(237, 317, 239, 319)(238, 318, 240, 320) L = (1, 163)(2, 165)(3, 168)(4, 161)(5, 172)(6, 162)(7, 175)(8, 178)(9, 179)(10, 164)(11, 183)(12, 186)(13, 187)(14, 166)(15, 191)(16, 167)(17, 193)(18, 196)(19, 197)(20, 169)(21, 199)(22, 170)(23, 203)(24, 171)(25, 205)(26, 208)(27, 209)(28, 173)(29, 211)(30, 174)(31, 215)(32, 176)(33, 217)(34, 177)(35, 219)(36, 221)(37, 222)(38, 180)(39, 223)(40, 181)(41, 224)(42, 182)(43, 226)(44, 184)(45, 228)(46, 185)(47, 230)(48, 232)(49, 233)(50, 188)(51, 234)(52, 189)(53, 235)(54, 190)(55, 201)(56, 192)(57, 200)(58, 194)(59, 198)(60, 195)(61, 227)(62, 236)(63, 238)(64, 237)(65, 202)(66, 213)(67, 204)(68, 212)(69, 206)(70, 210)(71, 207)(72, 216)(73, 225)(74, 240)(75, 239)(76, 214)(77, 218)(78, 220)(79, 229)(80, 231)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 16, 80 ), ( 16, 80, 16, 80 ) } Outer automorphisms :: reflexible Dual of E15.1084 Graph:: simple bipartite v = 120 e = 160 f = 12 degree seq :: [ 2^80, 4^40 ] E15.1086 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y1^4 * Y3)^2, Y1^-4 * Y3 * Y1 * Y3 * Y1^-5, (Y3 * Y1^-2)^4 ] Map:: R = (1, 81, 2, 82, 5, 85, 11, 91, 23, 103, 43, 123, 66, 146, 58, 138, 33, 113, 16, 96, 28, 108, 48, 128, 69, 149, 61, 141, 76, 156, 80, 160, 78, 158, 57, 137, 32, 112, 52, 132, 72, 152, 60, 140, 35, 115, 53, 133, 73, 153, 79, 159, 77, 157, 56, 136, 75, 155, 59, 139, 34, 114, 17, 97, 29, 109, 49, 129, 70, 150, 65, 145, 42, 122, 22, 102, 10, 90, 4, 84)(3, 83, 7, 87, 15, 95, 31, 111, 55, 135, 67, 147, 54, 134, 30, 110, 14, 94, 6, 86, 13, 93, 27, 107, 51, 131, 41, 121, 64, 144, 74, 154, 50, 130, 26, 106, 12, 92, 25, 105, 47, 127, 40, 120, 21, 101, 39, 119, 63, 143, 71, 151, 46, 126, 24, 104, 45, 125, 38, 118, 20, 100, 9, 89, 19, 99, 37, 117, 62, 142, 68, 148, 44, 124, 36, 116, 18, 98, 8, 88)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 166)(3, 161)(4, 169)(5, 172)(6, 162)(7, 176)(8, 177)(9, 164)(10, 181)(11, 184)(12, 165)(13, 188)(14, 189)(15, 192)(16, 167)(17, 168)(18, 195)(19, 193)(20, 194)(21, 170)(22, 201)(23, 204)(24, 171)(25, 208)(26, 209)(27, 212)(28, 173)(29, 174)(30, 213)(31, 216)(32, 175)(33, 179)(34, 180)(35, 178)(36, 221)(37, 217)(38, 220)(39, 218)(40, 219)(41, 182)(42, 215)(43, 227)(44, 183)(45, 229)(46, 230)(47, 232)(48, 185)(49, 186)(50, 233)(51, 235)(52, 187)(53, 190)(54, 236)(55, 202)(56, 191)(57, 197)(58, 199)(59, 200)(60, 198)(61, 196)(62, 237)(63, 238)(64, 226)(65, 228)(66, 224)(67, 203)(68, 225)(69, 205)(70, 206)(71, 239)(72, 207)(73, 210)(74, 240)(75, 211)(76, 214)(77, 222)(78, 223)(79, 231)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 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 E15.1083 Graph:: simple bipartite v = 82 e = 160 f = 50 degree seq :: [ 2^80, 80^2 ] E15.1087 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |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^-6 * Y1 * Y2 * Y1 * Y2^-3, (Y2^2 * Y1)^4, (Y2^-2 * R * Y2^-3)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 17, 97)(10, 90, 21, 101)(12, 92, 25, 105)(14, 94, 29, 109)(15, 95, 23, 103)(16, 96, 27, 107)(18, 98, 35, 115)(19, 99, 24, 104)(20, 100, 28, 108)(22, 102, 41, 121)(26, 106, 47, 127)(30, 110, 53, 133)(31, 111, 45, 125)(32, 112, 51, 131)(33, 113, 43, 123)(34, 114, 49, 129)(36, 116, 54, 134)(37, 117, 46, 126)(38, 118, 52, 132)(39, 119, 44, 124)(40, 120, 50, 130)(42, 122, 48, 128)(55, 135, 70, 150)(56, 136, 75, 155)(57, 137, 68, 148)(58, 138, 74, 154)(59, 139, 66, 146)(60, 140, 73, 153)(61, 141, 72, 152)(62, 142, 71, 151)(63, 143, 69, 149)(64, 144, 67, 147)(65, 145, 76, 156)(77, 157, 79, 159)(78, 158, 80, 160)(161, 241, 163, 243, 168, 248, 178, 258, 196, 276, 221, 301, 227, 307, 204, 284, 184, 264, 171, 251, 183, 263, 203, 283, 226, 306, 213, 293, 235, 315, 239, 319, 229, 309, 206, 286, 185, 265, 205, 285, 228, 308, 212, 292, 189, 269, 211, 291, 234, 314, 240, 320, 231, 311, 207, 287, 230, 310, 210, 290, 188, 268, 173, 253, 187, 267, 209, 289, 233, 313, 225, 305, 202, 282, 182, 262, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 186, 266, 208, 288, 232, 312, 216, 296, 192, 272, 176, 256, 167, 247, 175, 255, 191, 271, 215, 295, 201, 281, 224, 304, 237, 317, 218, 298, 194, 274, 177, 257, 193, 273, 217, 297, 200, 280, 181, 261, 199, 279, 223, 303, 238, 318, 220, 300, 195, 275, 219, 299, 198, 278, 180, 260, 169, 249, 179, 259, 197, 277, 222, 302, 236, 316, 214, 294, 190, 270, 174, 254, 166, 246) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 177)(9, 164)(10, 181)(11, 165)(12, 185)(13, 166)(14, 189)(15, 183)(16, 187)(17, 168)(18, 195)(19, 184)(20, 188)(21, 170)(22, 201)(23, 175)(24, 179)(25, 172)(26, 207)(27, 176)(28, 180)(29, 174)(30, 213)(31, 205)(32, 211)(33, 203)(34, 209)(35, 178)(36, 214)(37, 206)(38, 212)(39, 204)(40, 210)(41, 182)(42, 208)(43, 193)(44, 199)(45, 191)(46, 197)(47, 186)(48, 202)(49, 194)(50, 200)(51, 192)(52, 198)(53, 190)(54, 196)(55, 230)(56, 235)(57, 228)(58, 234)(59, 226)(60, 233)(61, 232)(62, 231)(63, 229)(64, 227)(65, 236)(66, 219)(67, 224)(68, 217)(69, 223)(70, 215)(71, 222)(72, 221)(73, 220)(74, 218)(75, 216)(76, 225)(77, 239)(78, 240)(79, 237)(80, 238)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E15.1088 Graph:: bipartite v = 42 e = 160 f = 90 degree seq :: [ 4^40, 80^2 ] E15.1088 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C8 x D10 (small group id <80, 4>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y1^-1 * Y3 * Y1^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-1 * Y1^2, Y1^8, Y1 * Y3^-8 * Y1 * Y3^2, (Y3 * Y2^-1)^40 ] Map:: R = (1, 81, 2, 82, 6, 86, 16, 96, 34, 114, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 17, 97, 8, 88, 21, 101, 35, 115, 28, 108, 11, 91)(5, 85, 14, 94, 18, 98, 37, 117, 30, 110, 12, 92, 20, 100, 7, 87)(10, 90, 24, 104, 36, 116, 23, 103, 42, 122, 22, 102, 43, 123, 26, 106)(15, 95, 32, 112, 38, 118, 29, 109, 41, 121, 19, 99, 39, 119, 31, 111)(25, 105, 47, 127, 53, 133, 46, 126, 58, 138, 45, 125, 59, 139, 44, 124)(33, 113, 49, 129, 54, 134, 40, 120, 56, 136, 50, 130, 55, 135, 51, 131)(48, 128, 60, 140, 69, 149, 63, 143, 74, 154, 62, 142, 75, 155, 61, 141)(52, 132, 57, 137, 70, 150, 66, 146, 72, 152, 67, 147, 71, 151, 65, 145)(64, 144, 73, 153, 68, 148, 76, 156, 79, 159, 78, 158, 80, 160, 77, 157)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 179)(8, 162)(9, 164)(10, 185)(11, 187)(12, 189)(13, 188)(14, 191)(15, 165)(16, 174)(17, 196)(18, 166)(19, 200)(20, 173)(21, 202)(22, 168)(23, 169)(24, 171)(25, 208)(26, 195)(27, 197)(28, 203)(29, 209)(30, 194)(31, 210)(32, 211)(33, 175)(34, 181)(35, 176)(36, 213)(37, 192)(38, 178)(39, 180)(40, 217)(41, 190)(42, 218)(43, 219)(44, 182)(45, 183)(46, 184)(47, 186)(48, 224)(49, 225)(50, 226)(51, 227)(52, 193)(53, 229)(54, 198)(55, 199)(56, 201)(57, 233)(58, 234)(59, 235)(60, 204)(61, 205)(62, 206)(63, 207)(64, 231)(65, 237)(66, 236)(67, 238)(68, 212)(69, 228)(70, 214)(71, 215)(72, 216)(73, 221)(74, 239)(75, 240)(76, 220)(77, 222)(78, 223)(79, 230)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 80 ), ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ) } Outer automorphisms :: reflexible Dual of E15.1087 Graph:: simple bipartite v = 90 e = 160 f = 42 degree seq :: [ 2^80, 16^10 ] E15.1089 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 40}) Quotient :: regular Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T1^-1 * T2 * T1^-3)^2, T1^3 * T2 * T1^-7 * T2, (T1^-2 * T2)^4 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 66, 56, 75, 59, 34, 17, 29, 49, 70, 79, 77, 57, 32, 52, 72, 60, 35, 53, 73, 80, 78, 58, 33, 16, 28, 48, 69, 61, 76, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 71, 46, 24, 45, 38, 20, 9, 19, 37, 62, 74, 50, 26, 12, 25, 47, 40, 21, 39, 63, 67, 54, 30, 14, 6, 13, 27, 51, 41, 64, 68, 44, 36, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 66)(63, 77)(64, 78)(65, 74)(68, 79)(71, 80) local type(s) :: { ( 8^40 ) } Outer automorphisms :: reflexible Dual of E15.1090 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 40 f = 10 degree seq :: [ 40^2 ] E15.1090 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 40}) Quotient :: regular Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * 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 ] 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, 79, 76, 78, 75, 77, 74, 80) 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) local type(s) :: { ( 40^8 ) } Outer automorphisms :: reflexible Dual of E15.1089 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 40 f = 2 degree seq :: [ 8^10 ] E15.1091 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 40}) Quotient :: edge Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^8, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^40 ] 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, 82)(83, 87)(84, 89)(85, 91)(86, 93)(88, 92)(90, 94)(95, 105)(96, 107)(97, 106)(98, 109)(99, 110)(100, 111)(101, 113)(102, 112)(103, 115)(104, 116)(108, 114)(117, 127)(118, 129)(119, 128)(120, 130)(121, 131)(122, 132)(123, 134)(124, 133)(125, 135)(126, 136)(137, 145)(138, 146)(139, 147)(140, 148)(141, 149)(142, 150)(143, 151)(144, 152)(153, 159)(154, 160)(155, 157)(156, 158) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 80, 80 ), ( 80^8 ) } Outer automorphisms :: reflexible Dual of E15.1095 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 80 f = 2 degree seq :: [ 2^40, 8^10 ] E15.1092 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 40}) Quotient :: edge Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1^3, (T2^3 * T1^-1)^2, T2^7 * T1 * T2^-3 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 64, 70, 54, 38, 18, 6, 17, 36, 53, 69, 79, 72, 56, 41, 30, 34, 21, 42, 58, 74, 80, 71, 55, 39, 20, 13, 28, 43, 59, 75, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 63, 47, 26, 35, 16, 14, 31, 50, 66, 78, 62, 46, 24, 11, 27, 37, 32, 51, 67, 77, 61, 45, 23, 9, 4, 12, 29, 49, 65, 76, 60, 44, 22, 8)(81, 82, 86, 96, 114, 107, 93, 84)(83, 89, 97, 88, 101, 115, 108, 91)(85, 94, 98, 117, 110, 92, 100, 87)(90, 104, 116, 103, 122, 102, 123, 106)(95, 112, 118, 109, 121, 99, 119, 111)(105, 127, 133, 126, 138, 125, 139, 124)(113, 129, 134, 120, 136, 130, 135, 131)(128, 140, 149, 143, 154, 142, 155, 141)(132, 137, 150, 146, 152, 147, 151, 145)(144, 157, 159, 156, 160, 153, 148, 158) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4^8 ), ( 4^40 ) } Outer automorphisms :: reflexible Dual of E15.1096 Transitivity :: ET+ Graph:: bipartite v = 12 e = 80 f = 40 degree seq :: [ 8^10, 40^2 ] E15.1093 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 40}) Quotient :: edge Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T1^-1 * T2 * T1^-3)^2, T1^3 * T2 * T1^-7 * T2, (T1^-2 * T2)^4 ] 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, 66)(63, 77)(64, 78)(65, 74)(68, 79)(71, 80)(81, 82, 85, 91, 103, 123, 146, 136, 155, 139, 114, 97, 109, 129, 150, 159, 157, 137, 112, 132, 152, 140, 115, 133, 153, 160, 158, 138, 113, 96, 108, 128, 149, 141, 156, 145, 122, 102, 90, 84)(83, 87, 95, 111, 135, 151, 126, 104, 125, 118, 100, 89, 99, 117, 142, 154, 130, 106, 92, 105, 127, 120, 101, 119, 143, 147, 134, 110, 94, 86, 93, 107, 131, 121, 144, 148, 124, 116, 98, 88) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 16, 16 ), ( 16^40 ) } Outer automorphisms :: reflexible Dual of E15.1094 Transitivity :: ET+ Graph:: simple bipartite v = 42 e = 80 f = 10 degree seq :: [ 2^40, 40^2 ] E15.1094 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 40}) Quotient :: loop Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^8, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^40 ] Map:: R = (1, 81, 3, 83, 8, 88, 17, 97, 28, 108, 19, 99, 10, 90, 4, 84)(2, 82, 5, 85, 12, 92, 22, 102, 34, 114, 24, 104, 14, 94, 6, 86)(7, 87, 15, 95, 26, 106, 39, 119, 30, 110, 18, 98, 9, 89, 16, 96)(11, 91, 20, 100, 32, 112, 44, 124, 36, 116, 23, 103, 13, 93, 21, 101)(25, 105, 37, 117, 48, 128, 41, 121, 29, 109, 40, 120, 27, 107, 38, 118)(31, 111, 42, 122, 53, 133, 46, 126, 35, 115, 45, 125, 33, 113, 43, 123)(47, 127, 57, 137, 51, 131, 60, 140, 50, 130, 59, 139, 49, 129, 58, 138)(52, 132, 61, 141, 56, 136, 64, 144, 55, 135, 63, 143, 54, 134, 62, 142)(65, 145, 73, 153, 68, 148, 76, 156, 67, 147, 75, 155, 66, 146, 74, 154)(69, 149, 77, 157, 72, 152, 80, 160, 71, 151, 79, 159, 70, 150, 78, 158) L = (1, 82)(2, 81)(3, 87)(4, 89)(5, 91)(6, 93)(7, 83)(8, 92)(9, 84)(10, 94)(11, 85)(12, 88)(13, 86)(14, 90)(15, 105)(16, 107)(17, 106)(18, 109)(19, 110)(20, 111)(21, 113)(22, 112)(23, 115)(24, 116)(25, 95)(26, 97)(27, 96)(28, 114)(29, 98)(30, 99)(31, 100)(32, 102)(33, 101)(34, 108)(35, 103)(36, 104)(37, 127)(38, 129)(39, 128)(40, 130)(41, 131)(42, 132)(43, 134)(44, 133)(45, 135)(46, 136)(47, 117)(48, 119)(49, 118)(50, 120)(51, 121)(52, 122)(53, 124)(54, 123)(55, 125)(56, 126)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(73, 159)(74, 160)(75, 157)(76, 158)(77, 155)(78, 156)(79, 153)(80, 154) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E15.1093 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 80 f = 42 degree seq :: [ 16^10 ] E15.1095 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 40}) Quotient :: loop Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1^3, (T2^3 * T1^-1)^2, T2^7 * T1 * T2^-3 * T1^-1 ] Map:: R = (1, 81, 3, 83, 10, 90, 25, 105, 48, 128, 64, 144, 70, 150, 54, 134, 38, 118, 18, 98, 6, 86, 17, 97, 36, 116, 53, 133, 69, 149, 79, 159, 72, 152, 56, 136, 41, 121, 30, 110, 34, 114, 21, 101, 42, 122, 58, 138, 74, 154, 80, 160, 71, 151, 55, 135, 39, 119, 20, 100, 13, 93, 28, 108, 43, 123, 59, 139, 75, 155, 68, 148, 52, 132, 33, 113, 15, 95, 5, 85)(2, 82, 7, 87, 19, 99, 40, 120, 57, 137, 73, 153, 63, 143, 47, 127, 26, 106, 35, 115, 16, 96, 14, 94, 31, 111, 50, 130, 66, 146, 78, 158, 62, 142, 46, 126, 24, 104, 11, 91, 27, 107, 37, 117, 32, 112, 51, 131, 67, 147, 77, 157, 61, 141, 45, 125, 23, 103, 9, 89, 4, 84, 12, 92, 29, 109, 49, 129, 65, 145, 76, 156, 60, 140, 44, 124, 22, 102, 8, 88) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 94)(6, 96)(7, 85)(8, 101)(9, 97)(10, 104)(11, 83)(12, 100)(13, 84)(14, 98)(15, 112)(16, 114)(17, 88)(18, 117)(19, 119)(20, 87)(21, 115)(22, 123)(23, 122)(24, 116)(25, 127)(26, 90)(27, 93)(28, 91)(29, 121)(30, 92)(31, 95)(32, 118)(33, 129)(34, 107)(35, 108)(36, 103)(37, 110)(38, 109)(39, 111)(40, 136)(41, 99)(42, 102)(43, 106)(44, 105)(45, 139)(46, 138)(47, 133)(48, 140)(49, 134)(50, 135)(51, 113)(52, 137)(53, 126)(54, 120)(55, 131)(56, 130)(57, 150)(58, 125)(59, 124)(60, 149)(61, 128)(62, 155)(63, 154)(64, 157)(65, 132)(66, 152)(67, 151)(68, 158)(69, 143)(70, 146)(71, 145)(72, 147)(73, 148)(74, 142)(75, 141)(76, 160)(77, 159)(78, 144)(79, 156)(80, 153) 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 ) } Outer automorphisms :: reflexible Dual of E15.1091 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 80 f = 50 degree seq :: [ 80^2 ] E15.1096 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 40}) Quotient :: loop Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T1^-1 * T2 * T1^-3)^2, T1^3 * T2 * T1^-7 * T2, (T1^-2 * T2)^4 ] Map:: polytopal non-degenerate R = (1, 81, 3, 83)(2, 82, 6, 86)(4, 84, 9, 89)(5, 85, 12, 92)(7, 87, 16, 96)(8, 88, 17, 97)(10, 90, 21, 101)(11, 91, 24, 104)(13, 93, 28, 108)(14, 94, 29, 109)(15, 95, 32, 112)(18, 98, 35, 115)(19, 99, 33, 113)(20, 100, 34, 114)(22, 102, 41, 121)(23, 103, 44, 124)(25, 105, 48, 128)(26, 106, 49, 129)(27, 107, 52, 132)(30, 110, 53, 133)(31, 111, 56, 136)(36, 116, 61, 141)(37, 117, 57, 137)(38, 118, 60, 140)(39, 119, 58, 138)(40, 120, 59, 139)(42, 122, 55, 135)(43, 123, 67, 147)(45, 125, 69, 149)(46, 126, 70, 150)(47, 127, 72, 152)(50, 130, 73, 153)(51, 131, 75, 155)(54, 134, 76, 156)(62, 142, 66, 146)(63, 143, 77, 157)(64, 144, 78, 158)(65, 145, 74, 154)(68, 148, 79, 159)(71, 151, 80, 160) L = (1, 82)(2, 85)(3, 87)(4, 81)(5, 91)(6, 93)(7, 95)(8, 83)(9, 99)(10, 84)(11, 103)(12, 105)(13, 107)(14, 86)(15, 111)(16, 108)(17, 109)(18, 88)(19, 117)(20, 89)(21, 119)(22, 90)(23, 123)(24, 125)(25, 127)(26, 92)(27, 131)(28, 128)(29, 129)(30, 94)(31, 135)(32, 132)(33, 96)(34, 97)(35, 133)(36, 98)(37, 142)(38, 100)(39, 143)(40, 101)(41, 144)(42, 102)(43, 146)(44, 116)(45, 118)(46, 104)(47, 120)(48, 149)(49, 150)(50, 106)(51, 121)(52, 152)(53, 153)(54, 110)(55, 151)(56, 155)(57, 112)(58, 113)(59, 114)(60, 115)(61, 156)(62, 154)(63, 147)(64, 148)(65, 122)(66, 136)(67, 134)(68, 124)(69, 141)(70, 159)(71, 126)(72, 140)(73, 160)(74, 130)(75, 139)(76, 145)(77, 137)(78, 138)(79, 157)(80, 158) local type(s) :: { ( 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E15.1092 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 80 f = 12 degree seq :: [ 4^40 ] E15.1097 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^40 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 12, 92)(10, 90, 14, 94)(15, 95, 25, 105)(16, 96, 27, 107)(17, 97, 26, 106)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 31, 111)(21, 101, 33, 113)(22, 102, 32, 112)(23, 103, 35, 115)(24, 104, 36, 116)(28, 108, 34, 114)(37, 117, 47, 127)(38, 118, 49, 129)(39, 119, 48, 128)(40, 120, 50, 130)(41, 121, 51, 131)(42, 122, 52, 132)(43, 123, 54, 134)(44, 124, 53, 133)(45, 125, 55, 135)(46, 126, 56, 136)(57, 137, 65, 145)(58, 138, 66, 146)(59, 139, 67, 147)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 70, 150)(63, 143, 71, 151)(64, 144, 72, 152)(73, 153, 79, 159)(74, 154, 80, 160)(75, 155, 77, 157)(76, 156, 78, 158)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 194, 274, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 186, 266, 199, 279, 190, 270, 178, 258, 169, 249, 176, 256)(171, 251, 180, 260, 192, 272, 204, 284, 196, 276, 183, 263, 173, 253, 181, 261)(185, 265, 197, 277, 208, 288, 201, 281, 189, 269, 200, 280, 187, 267, 198, 278)(191, 271, 202, 282, 213, 293, 206, 286, 195, 275, 205, 285, 193, 273, 203, 283)(207, 287, 217, 297, 211, 291, 220, 300, 210, 290, 219, 299, 209, 289, 218, 298)(212, 292, 221, 301, 216, 296, 224, 304, 215, 295, 223, 303, 214, 294, 222, 302)(225, 305, 233, 313, 228, 308, 236, 316, 227, 307, 235, 315, 226, 306, 234, 314)(229, 309, 237, 317, 232, 312, 240, 320, 231, 311, 239, 319, 230, 310, 238, 318) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 172)(9, 164)(10, 174)(11, 165)(12, 168)(13, 166)(14, 170)(15, 185)(16, 187)(17, 186)(18, 189)(19, 190)(20, 191)(21, 193)(22, 192)(23, 195)(24, 196)(25, 175)(26, 177)(27, 176)(28, 194)(29, 178)(30, 179)(31, 180)(32, 182)(33, 181)(34, 188)(35, 183)(36, 184)(37, 207)(38, 209)(39, 208)(40, 210)(41, 211)(42, 212)(43, 214)(44, 213)(45, 215)(46, 216)(47, 197)(48, 199)(49, 198)(50, 200)(51, 201)(52, 202)(53, 204)(54, 203)(55, 205)(56, 206)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 217)(66, 218)(67, 219)(68, 220)(69, 221)(70, 222)(71, 223)(72, 224)(73, 239)(74, 240)(75, 237)(76, 238)(77, 235)(78, 236)(79, 233)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 80, 2, 80 ), ( 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E15.1100 Graph:: bipartite v = 50 e = 160 f = 82 degree seq :: [ 4^40, 16^10 ] E15.1098 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y1 * Y2)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1^-1 * Y2 * Y1^3, Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1^2, (Y1^-1 * Y2 * Y1^-2)^2, Y2^-1 * Y1 * Y2^8 * Y1 * Y2^-1 ] Map:: R = (1, 81, 2, 82, 6, 86, 16, 96, 34, 114, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 17, 97, 8, 88, 21, 101, 35, 115, 28, 108, 11, 91)(5, 85, 14, 94, 18, 98, 37, 117, 30, 110, 12, 92, 20, 100, 7, 87)(10, 90, 24, 104, 36, 116, 23, 103, 42, 122, 22, 102, 43, 123, 26, 106)(15, 95, 32, 112, 38, 118, 29, 109, 41, 121, 19, 99, 39, 119, 31, 111)(25, 105, 47, 127, 53, 133, 46, 126, 58, 138, 45, 125, 59, 139, 44, 124)(33, 113, 49, 129, 54, 134, 40, 120, 56, 136, 50, 130, 55, 135, 51, 131)(48, 128, 60, 140, 69, 149, 63, 143, 74, 154, 62, 142, 75, 155, 61, 141)(52, 132, 57, 137, 70, 150, 66, 146, 72, 152, 67, 147, 71, 151, 65, 145)(64, 144, 77, 157, 79, 159, 76, 156, 80, 160, 73, 153, 68, 148, 78, 158)(161, 241, 163, 243, 170, 250, 185, 265, 208, 288, 224, 304, 230, 310, 214, 294, 198, 278, 178, 258, 166, 246, 177, 257, 196, 276, 213, 293, 229, 309, 239, 319, 232, 312, 216, 296, 201, 281, 190, 270, 194, 274, 181, 261, 202, 282, 218, 298, 234, 314, 240, 320, 231, 311, 215, 295, 199, 279, 180, 260, 173, 253, 188, 268, 203, 283, 219, 299, 235, 315, 228, 308, 212, 292, 193, 273, 175, 255, 165, 245)(162, 242, 167, 247, 179, 259, 200, 280, 217, 297, 233, 313, 223, 303, 207, 287, 186, 266, 195, 275, 176, 256, 174, 254, 191, 271, 210, 290, 226, 306, 238, 318, 222, 302, 206, 286, 184, 264, 171, 251, 187, 267, 197, 277, 192, 272, 211, 291, 227, 307, 237, 317, 221, 301, 205, 285, 183, 263, 169, 249, 164, 244, 172, 252, 189, 269, 209, 289, 225, 305, 236, 316, 220, 300, 204, 284, 182, 262, 168, 248) L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 179)(8, 162)(9, 164)(10, 185)(11, 187)(12, 189)(13, 188)(14, 191)(15, 165)(16, 174)(17, 196)(18, 166)(19, 200)(20, 173)(21, 202)(22, 168)(23, 169)(24, 171)(25, 208)(26, 195)(27, 197)(28, 203)(29, 209)(30, 194)(31, 210)(32, 211)(33, 175)(34, 181)(35, 176)(36, 213)(37, 192)(38, 178)(39, 180)(40, 217)(41, 190)(42, 218)(43, 219)(44, 182)(45, 183)(46, 184)(47, 186)(48, 224)(49, 225)(50, 226)(51, 227)(52, 193)(53, 229)(54, 198)(55, 199)(56, 201)(57, 233)(58, 234)(59, 235)(60, 204)(61, 205)(62, 206)(63, 207)(64, 230)(65, 236)(66, 238)(67, 237)(68, 212)(69, 239)(70, 214)(71, 215)(72, 216)(73, 223)(74, 240)(75, 228)(76, 220)(77, 221)(78, 222)(79, 232)(80, 231)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E15.1099 Graph:: bipartite v = 12 e = 160 f = 120 degree seq :: [ 16^10, 80^2 ] E15.1099 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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^-5 * Y2 * Y3^3 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^40 ] Map:: polytopal R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242)(163, 243, 167, 247)(164, 244, 169, 249)(165, 245, 171, 251)(166, 246, 173, 253)(168, 248, 177, 257)(170, 250, 181, 261)(172, 252, 185, 265)(174, 254, 189, 269)(175, 255, 183, 263)(176, 256, 187, 267)(178, 258, 195, 275)(179, 259, 184, 264)(180, 260, 188, 268)(182, 262, 201, 281)(186, 266, 207, 287)(190, 270, 213, 293)(191, 271, 205, 285)(192, 272, 211, 291)(193, 273, 203, 283)(194, 274, 209, 289)(196, 276, 214, 294)(197, 277, 206, 286)(198, 278, 212, 292)(199, 279, 204, 284)(200, 280, 210, 290)(202, 282, 208, 288)(215, 295, 230, 310)(216, 296, 235, 315)(217, 297, 228, 308)(218, 298, 234, 314)(219, 299, 226, 306)(220, 300, 233, 313)(221, 301, 237, 317)(222, 302, 231, 311)(223, 303, 229, 309)(224, 304, 227, 307)(225, 305, 238, 318)(232, 312, 239, 319)(236, 316, 240, 320) L = (1, 163)(2, 165)(3, 168)(4, 161)(5, 172)(6, 162)(7, 175)(8, 178)(9, 179)(10, 164)(11, 183)(12, 186)(13, 187)(14, 166)(15, 191)(16, 167)(17, 193)(18, 196)(19, 197)(20, 169)(21, 199)(22, 170)(23, 203)(24, 171)(25, 205)(26, 208)(27, 209)(28, 173)(29, 211)(30, 174)(31, 215)(32, 176)(33, 217)(34, 177)(35, 219)(36, 221)(37, 222)(38, 180)(39, 223)(40, 181)(41, 224)(42, 182)(43, 226)(44, 184)(45, 228)(46, 185)(47, 230)(48, 232)(49, 233)(50, 188)(51, 234)(52, 189)(53, 235)(54, 190)(55, 201)(56, 192)(57, 200)(58, 194)(59, 198)(60, 195)(61, 231)(62, 238)(63, 237)(64, 236)(65, 202)(66, 213)(67, 204)(68, 212)(69, 206)(70, 210)(71, 207)(72, 220)(73, 240)(74, 239)(75, 225)(76, 214)(77, 216)(78, 218)(79, 227)(80, 229)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 16, 80 ), ( 16, 80, 16, 80 ) } Outer automorphisms :: reflexible Dual of E15.1098 Graph:: simple bipartite v = 120 e = 160 f = 12 degree seq :: [ 2^80, 4^40 ] E15.1100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y1^-3 * Y3 * Y1^-1)^2, Y1^3 * Y3 * Y1^-7 * Y3, (Y1^-2 * Y3)^4 ] Map:: R = (1, 81, 2, 82, 5, 85, 11, 91, 23, 103, 43, 123, 66, 146, 56, 136, 75, 155, 59, 139, 34, 114, 17, 97, 29, 109, 49, 129, 70, 150, 79, 159, 77, 157, 57, 137, 32, 112, 52, 132, 72, 152, 60, 140, 35, 115, 53, 133, 73, 153, 80, 160, 78, 158, 58, 138, 33, 113, 16, 96, 28, 108, 48, 128, 69, 149, 61, 141, 76, 156, 65, 145, 42, 122, 22, 102, 10, 90, 4, 84)(3, 83, 7, 87, 15, 95, 31, 111, 55, 135, 71, 151, 46, 126, 24, 104, 45, 125, 38, 118, 20, 100, 9, 89, 19, 99, 37, 117, 62, 142, 74, 154, 50, 130, 26, 106, 12, 92, 25, 105, 47, 127, 40, 120, 21, 101, 39, 119, 63, 143, 67, 147, 54, 134, 30, 110, 14, 94, 6, 86, 13, 93, 27, 107, 51, 131, 41, 121, 64, 144, 68, 148, 44, 124, 36, 116, 18, 98, 8, 88)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 166)(3, 161)(4, 169)(5, 172)(6, 162)(7, 176)(8, 177)(9, 164)(10, 181)(11, 184)(12, 165)(13, 188)(14, 189)(15, 192)(16, 167)(17, 168)(18, 195)(19, 193)(20, 194)(21, 170)(22, 201)(23, 204)(24, 171)(25, 208)(26, 209)(27, 212)(28, 173)(29, 174)(30, 213)(31, 216)(32, 175)(33, 179)(34, 180)(35, 178)(36, 221)(37, 217)(38, 220)(39, 218)(40, 219)(41, 182)(42, 215)(43, 227)(44, 183)(45, 229)(46, 230)(47, 232)(48, 185)(49, 186)(50, 233)(51, 235)(52, 187)(53, 190)(54, 236)(55, 202)(56, 191)(57, 197)(58, 199)(59, 200)(60, 198)(61, 196)(62, 226)(63, 237)(64, 238)(65, 234)(66, 222)(67, 203)(68, 239)(69, 205)(70, 206)(71, 240)(72, 207)(73, 210)(74, 225)(75, 211)(76, 214)(77, 223)(78, 224)(79, 228)(80, 231)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 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 E15.1097 Graph:: simple bipartite v = 82 e = 160 f = 50 degree seq :: [ 2^80, 80^2 ] E15.1101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |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^-1 * Y1 * R * Y2^-2)^2, (Y2^4 * Y1)^2, Y2^3 * Y1 * Y2^-7 * Y1, (Y2^2 * Y1)^4, (Y3 * Y2^-1)^8 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 17, 97)(10, 90, 21, 101)(12, 92, 25, 105)(14, 94, 29, 109)(15, 95, 23, 103)(16, 96, 27, 107)(18, 98, 35, 115)(19, 99, 24, 104)(20, 100, 28, 108)(22, 102, 41, 121)(26, 106, 47, 127)(30, 110, 53, 133)(31, 111, 45, 125)(32, 112, 51, 131)(33, 113, 43, 123)(34, 114, 49, 129)(36, 116, 54, 134)(37, 117, 46, 126)(38, 118, 52, 132)(39, 119, 44, 124)(40, 120, 50, 130)(42, 122, 48, 128)(55, 135, 70, 150)(56, 136, 75, 155)(57, 137, 68, 148)(58, 138, 74, 154)(59, 139, 66, 146)(60, 140, 73, 153)(61, 141, 77, 157)(62, 142, 71, 151)(63, 143, 69, 149)(64, 144, 67, 147)(65, 145, 78, 158)(72, 152, 79, 159)(76, 156, 80, 160)(161, 241, 163, 243, 168, 248, 178, 258, 196, 276, 221, 301, 231, 311, 207, 287, 230, 310, 210, 290, 188, 268, 173, 253, 187, 267, 209, 289, 233, 313, 240, 320, 229, 309, 206, 286, 185, 265, 205, 285, 228, 308, 212, 292, 189, 269, 211, 291, 234, 314, 239, 319, 227, 307, 204, 284, 184, 264, 171, 251, 183, 263, 203, 283, 226, 306, 213, 293, 235, 315, 225, 305, 202, 282, 182, 262, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 186, 266, 208, 288, 232, 312, 220, 300, 195, 275, 219, 299, 198, 278, 180, 260, 169, 249, 179, 259, 197, 277, 222, 302, 238, 318, 218, 298, 194, 274, 177, 257, 193, 273, 217, 297, 200, 280, 181, 261, 199, 279, 223, 303, 237, 317, 216, 296, 192, 272, 176, 256, 167, 247, 175, 255, 191, 271, 215, 295, 201, 281, 224, 304, 236, 316, 214, 294, 190, 270, 174, 254, 166, 246) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 177)(9, 164)(10, 181)(11, 165)(12, 185)(13, 166)(14, 189)(15, 183)(16, 187)(17, 168)(18, 195)(19, 184)(20, 188)(21, 170)(22, 201)(23, 175)(24, 179)(25, 172)(26, 207)(27, 176)(28, 180)(29, 174)(30, 213)(31, 205)(32, 211)(33, 203)(34, 209)(35, 178)(36, 214)(37, 206)(38, 212)(39, 204)(40, 210)(41, 182)(42, 208)(43, 193)(44, 199)(45, 191)(46, 197)(47, 186)(48, 202)(49, 194)(50, 200)(51, 192)(52, 198)(53, 190)(54, 196)(55, 230)(56, 235)(57, 228)(58, 234)(59, 226)(60, 233)(61, 237)(62, 231)(63, 229)(64, 227)(65, 238)(66, 219)(67, 224)(68, 217)(69, 223)(70, 215)(71, 222)(72, 239)(73, 220)(74, 218)(75, 216)(76, 240)(77, 221)(78, 225)(79, 232)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E15.1102 Graph:: bipartite v = 42 e = 160 f = 90 degree seq :: [ 4^40, 80^2 ] E15.1102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 40}) Quotient :: dipole Aut^+ = C40 : C2 (small group id <80, 5>) Aut = (D8 x D10) : C2 (small group id <160, 135>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^2 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3 * Y1^-1 * Y3^2 * Y1^-1, Y1^8, Y1^2 * Y3^-10, (Y3 * Y2^-1)^40 ] Map:: R = (1, 81, 2, 82, 6, 86, 16, 96, 34, 114, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 17, 97, 8, 88, 21, 101, 35, 115, 28, 108, 11, 91)(5, 85, 14, 94, 18, 98, 37, 117, 30, 110, 12, 92, 20, 100, 7, 87)(10, 90, 24, 104, 36, 116, 23, 103, 42, 122, 22, 102, 43, 123, 26, 106)(15, 95, 32, 112, 38, 118, 29, 109, 41, 121, 19, 99, 39, 119, 31, 111)(25, 105, 47, 127, 53, 133, 46, 126, 58, 138, 45, 125, 59, 139, 44, 124)(33, 113, 49, 129, 54, 134, 40, 120, 56, 136, 50, 130, 55, 135, 51, 131)(48, 128, 60, 140, 69, 149, 63, 143, 74, 154, 62, 142, 75, 155, 61, 141)(52, 132, 57, 137, 70, 150, 66, 146, 72, 152, 67, 147, 71, 151, 65, 145)(64, 144, 77, 157, 79, 159, 76, 156, 80, 160, 73, 153, 68, 148, 78, 158)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320) L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 179)(8, 162)(9, 164)(10, 185)(11, 187)(12, 189)(13, 188)(14, 191)(15, 165)(16, 174)(17, 196)(18, 166)(19, 200)(20, 173)(21, 202)(22, 168)(23, 169)(24, 171)(25, 208)(26, 195)(27, 197)(28, 203)(29, 209)(30, 194)(31, 210)(32, 211)(33, 175)(34, 181)(35, 176)(36, 213)(37, 192)(38, 178)(39, 180)(40, 217)(41, 190)(42, 218)(43, 219)(44, 182)(45, 183)(46, 184)(47, 186)(48, 224)(49, 225)(50, 226)(51, 227)(52, 193)(53, 229)(54, 198)(55, 199)(56, 201)(57, 233)(58, 234)(59, 235)(60, 204)(61, 205)(62, 206)(63, 207)(64, 230)(65, 236)(66, 238)(67, 237)(68, 212)(69, 239)(70, 214)(71, 215)(72, 216)(73, 223)(74, 240)(75, 228)(76, 220)(77, 221)(78, 222)(79, 232)(80, 231)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 80 ), ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ) } Outer automorphisms :: reflexible Dual of E15.1101 Graph:: simple bipartite v = 90 e = 160 f = 42 degree seq :: [ 2^80, 16^10 ] E15.1103 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 6}) Quotient :: halfedge^2 Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y3 * Y2)^3, (Y3 * Y1)^14 ] Map:: non-degenerate R = (1, 86, 2, 85)(3, 91, 7, 87)(4, 93, 9, 88)(5, 95, 11, 89)(6, 97, 13, 90)(8, 96, 12, 92)(10, 98, 14, 94)(15, 107, 23, 99)(16, 108, 24, 100)(17, 109, 25, 101)(18, 110, 26, 102)(19, 111, 27, 103)(20, 112, 28, 104)(21, 113, 29, 105)(22, 114, 30, 106)(31, 121, 37, 115)(32, 122, 38, 116)(33, 123, 39, 117)(34, 124, 40, 118)(35, 125, 41, 119)(36, 126, 42, 120)(43, 133, 49, 127)(44, 134, 50, 128)(45, 135, 51, 129)(46, 136, 52, 130)(47, 137, 53, 131)(48, 138, 54, 132)(55, 145, 61, 139)(56, 146, 62, 140)(57, 147, 63, 141)(58, 148, 64, 142)(59, 149, 65, 143)(60, 150, 66, 144)(67, 157, 73, 151)(68, 158, 74, 152)(69, 159, 75, 153)(70, 160, 76, 154)(71, 161, 77, 155)(72, 162, 78, 156)(79, 166, 82, 163)(80, 167, 83, 164)(81, 168, 84, 165) 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, 58)(53, 60)(54, 59)(61, 67)(62, 69)(63, 68)(64, 70)(65, 72)(66, 71)(73, 79)(74, 81)(75, 80)(76, 82)(77, 84)(78, 83)(85, 88)(86, 90)(87, 92)(89, 96)(91, 100)(93, 99)(94, 101)(95, 104)(97, 103)(98, 105)(102, 109)(106, 113)(107, 116)(108, 115)(110, 117)(111, 119)(112, 118)(114, 120)(121, 128)(122, 127)(123, 129)(124, 131)(125, 130)(126, 132)(133, 140)(134, 139)(135, 141)(136, 143)(137, 142)(138, 144)(145, 152)(146, 151)(147, 153)(148, 155)(149, 154)(150, 156)(157, 164)(158, 163)(159, 165)(160, 167)(161, 166)(162, 168) local type(s) :: { ( 12^4 ) } Outer automorphisms :: reflexible Dual of E15.1104 Transitivity :: VT+ AT Graph:: simple bipartite v = 42 e = 84 f = 14 degree seq :: [ 4^42 ] E15.1104 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 6}) Quotient :: halfedge^2 Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ R^2, Y2^2, 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 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 86, 2, 90, 6, 98, 14, 94, 10, 89, 5, 85)(3, 93, 9, 99, 15, 96, 12, 88, 4, 95, 11, 87)(7, 100, 16, 97, 13, 102, 18, 92, 8, 101, 17, 91)(19, 109, 25, 105, 21, 111, 27, 104, 20, 110, 26, 103)(22, 112, 28, 108, 24, 114, 30, 107, 23, 113, 29, 106)(31, 121, 37, 117, 33, 123, 39, 116, 32, 122, 38, 115)(34, 124, 40, 120, 36, 126, 42, 119, 35, 125, 41, 118)(43, 133, 49, 129, 45, 135, 51, 128, 44, 134, 50, 127)(46, 136, 52, 132, 48, 138, 54, 131, 47, 137, 53, 130)(55, 145, 61, 141, 57, 147, 63, 140, 56, 146, 62, 139)(58, 148, 64, 144, 60, 150, 66, 143, 59, 149, 65, 142)(67, 157, 73, 153, 69, 159, 75, 152, 68, 158, 74, 151)(70, 160, 76, 156, 72, 162, 78, 155, 71, 161, 77, 154)(79, 168, 84, 165, 81, 167, 83, 164, 80, 166, 82, 163) L = (1, 3)(2, 7)(4, 6)(5, 13)(8, 14)(9, 19)(10, 15)(11, 21)(12, 20)(16, 22)(17, 24)(18, 23)(25, 31)(26, 33)(27, 32)(28, 34)(29, 36)(30, 35)(37, 43)(38, 45)(39, 44)(40, 46)(41, 48)(42, 47)(49, 55)(50, 57)(51, 56)(52, 58)(53, 60)(54, 59)(61, 67)(62, 69)(63, 68)(64, 70)(65, 72)(66, 71)(73, 79)(74, 81)(75, 80)(76, 82)(77, 84)(78, 83)(85, 88)(86, 92)(87, 94)(89, 91)(90, 99)(93, 104)(95, 103)(96, 105)(97, 98)(100, 107)(101, 106)(102, 108)(109, 116)(110, 115)(111, 117)(112, 119)(113, 118)(114, 120)(121, 128)(122, 127)(123, 129)(124, 131)(125, 130)(126, 132)(133, 140)(134, 139)(135, 141)(136, 143)(137, 142)(138, 144)(145, 152)(146, 151)(147, 153)(148, 155)(149, 154)(150, 156)(157, 164)(158, 163)(159, 165)(160, 167)(161, 166)(162, 168) local type(s) :: { ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1103 Transitivity :: VT+ AT Graph:: bipartite v = 14 e = 84 f = 42 degree seq :: [ 12^14 ] E15.1105 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 6}) Quotient :: edge^2 Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (Y2 * Y1)^3, (Y3 * Y2)^14 ] Map:: R = (1, 85, 4, 88)(2, 86, 6, 90)(3, 87, 8, 92)(5, 89, 12, 96)(7, 91, 15, 99)(9, 93, 17, 101)(10, 94, 18, 102)(11, 95, 19, 103)(13, 97, 21, 105)(14, 98, 22, 106)(16, 100, 23, 107)(20, 104, 27, 111)(24, 108, 31, 115)(25, 109, 32, 116)(26, 110, 33, 117)(28, 112, 34, 118)(29, 113, 35, 119)(30, 114, 36, 120)(37, 121, 43, 127)(38, 122, 44, 128)(39, 123, 45, 129)(40, 124, 46, 130)(41, 125, 47, 131)(42, 126, 48, 132)(49, 133, 55, 139)(50, 134, 56, 140)(51, 135, 57, 141)(52, 136, 58, 142)(53, 137, 59, 143)(54, 138, 60, 144)(61, 145, 67, 151)(62, 146, 68, 152)(63, 147, 69, 153)(64, 148, 70, 154)(65, 149, 71, 155)(66, 150, 72, 156)(73, 157, 79, 163)(74, 158, 80, 164)(75, 159, 81, 165)(76, 160, 82, 166)(77, 161, 83, 167)(78, 162, 84, 168)(169, 170)(171, 175)(172, 177)(173, 179)(174, 181)(176, 184)(178, 183)(180, 188)(182, 187)(185, 192)(186, 194)(189, 196)(190, 198)(191, 197)(193, 195)(199, 205)(200, 207)(201, 206)(202, 208)(203, 210)(204, 209)(211, 217)(212, 219)(213, 218)(214, 220)(215, 222)(216, 221)(223, 229)(224, 231)(225, 230)(226, 232)(227, 234)(228, 233)(235, 241)(236, 243)(237, 242)(238, 244)(239, 246)(240, 245)(247, 250)(248, 252)(249, 251)(253, 255)(254, 257)(256, 262)(258, 266)(259, 263)(260, 265)(261, 264)(267, 272)(268, 271)(269, 277)(270, 276)(273, 281)(274, 280)(275, 282)(278, 279)(283, 290)(284, 289)(285, 291)(286, 293)(287, 292)(288, 294)(295, 302)(296, 301)(297, 303)(298, 305)(299, 304)(300, 306)(307, 314)(308, 313)(309, 315)(310, 317)(311, 316)(312, 318)(319, 326)(320, 325)(321, 327)(322, 329)(323, 328)(324, 330)(331, 335)(332, 334)(333, 336) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 24, 24 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E15.1108 Graph:: simple bipartite v = 126 e = 168 f = 14 degree seq :: [ 2^84, 4^42 ] E15.1106 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 6}) Quotient :: edge^2 Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-1 * 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 ] Map:: R = (1, 85, 4, 88, 6, 90, 15, 99, 9, 93, 5, 89)(2, 86, 7, 91, 3, 87, 10, 94, 14, 98, 8, 92)(11, 95, 19, 103, 12, 96, 21, 105, 13, 97, 20, 104)(16, 100, 22, 106, 17, 101, 24, 108, 18, 102, 23, 107)(25, 109, 31, 115, 26, 110, 33, 117, 27, 111, 32, 116)(28, 112, 34, 118, 29, 113, 36, 120, 30, 114, 35, 119)(37, 121, 43, 127, 38, 122, 45, 129, 39, 123, 44, 128)(40, 124, 46, 130, 41, 125, 48, 132, 42, 126, 47, 131)(49, 133, 55, 139, 50, 134, 57, 141, 51, 135, 56, 140)(52, 136, 58, 142, 53, 137, 60, 144, 54, 138, 59, 143)(61, 145, 67, 151, 62, 146, 69, 153, 63, 147, 68, 152)(64, 148, 70, 154, 65, 149, 72, 156, 66, 150, 71, 155)(73, 157, 79, 163, 74, 158, 81, 165, 75, 159, 80, 164)(76, 160, 82, 166, 77, 161, 84, 168, 78, 162, 83, 167)(169, 170)(171, 177)(172, 179)(173, 180)(174, 182)(175, 184)(176, 185)(178, 186)(181, 183)(187, 193)(188, 194)(189, 195)(190, 196)(191, 197)(192, 198)(199, 205)(200, 206)(201, 207)(202, 208)(203, 209)(204, 210)(211, 217)(212, 218)(213, 219)(214, 220)(215, 221)(216, 222)(223, 229)(224, 230)(225, 231)(226, 232)(227, 233)(228, 234)(235, 241)(236, 242)(237, 243)(238, 244)(239, 245)(240, 246)(247, 251)(248, 250)(249, 252)(253, 255)(254, 258)(256, 264)(257, 265)(259, 269)(260, 270)(261, 266)(262, 268)(263, 267)(271, 278)(272, 279)(273, 277)(274, 281)(275, 282)(276, 280)(283, 290)(284, 291)(285, 289)(286, 293)(287, 294)(288, 292)(295, 302)(296, 303)(297, 301)(298, 305)(299, 306)(300, 304)(307, 314)(308, 315)(309, 313)(310, 317)(311, 318)(312, 316)(319, 326)(320, 327)(321, 325)(322, 329)(323, 330)(324, 328)(331, 334)(332, 336)(333, 335) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 8, 8 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.1107 Graph:: simple bipartite v = 98 e = 168 f = 42 degree seq :: [ 2^84, 12^14 ] E15.1107 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 6}) Quotient :: loop^2 Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (Y2 * Y1)^3, (Y3 * Y2)^14 ] Map:: R = (1, 85, 169, 253, 4, 88, 172, 256)(2, 86, 170, 254, 6, 90, 174, 258)(3, 87, 171, 255, 8, 92, 176, 260)(5, 89, 173, 257, 12, 96, 180, 264)(7, 91, 175, 259, 15, 99, 183, 267)(9, 93, 177, 261, 17, 101, 185, 269)(10, 94, 178, 262, 18, 102, 186, 270)(11, 95, 179, 263, 19, 103, 187, 271)(13, 97, 181, 265, 21, 105, 189, 273)(14, 98, 182, 266, 22, 106, 190, 274)(16, 100, 184, 268, 23, 107, 191, 275)(20, 104, 188, 272, 27, 111, 195, 279)(24, 108, 192, 276, 31, 115, 199, 283)(25, 109, 193, 277, 32, 116, 200, 284)(26, 110, 194, 278, 33, 117, 201, 285)(28, 112, 196, 280, 34, 118, 202, 286)(29, 113, 197, 281, 35, 119, 203, 287)(30, 114, 198, 282, 36, 120, 204, 288)(37, 121, 205, 289, 43, 127, 211, 295)(38, 122, 206, 290, 44, 128, 212, 296)(39, 123, 207, 291, 45, 129, 213, 297)(40, 124, 208, 292, 46, 130, 214, 298)(41, 125, 209, 293, 47, 131, 215, 299)(42, 126, 210, 294, 48, 132, 216, 300)(49, 133, 217, 301, 55, 139, 223, 307)(50, 134, 218, 302, 56, 140, 224, 308)(51, 135, 219, 303, 57, 141, 225, 309)(52, 136, 220, 304, 58, 142, 226, 310)(53, 137, 221, 305, 59, 143, 227, 311)(54, 138, 222, 306, 60, 144, 228, 312)(61, 145, 229, 313, 67, 151, 235, 319)(62, 146, 230, 314, 68, 152, 236, 320)(63, 147, 231, 315, 69, 153, 237, 321)(64, 148, 232, 316, 70, 154, 238, 322)(65, 149, 233, 317, 71, 155, 239, 323)(66, 150, 234, 318, 72, 156, 240, 324)(73, 157, 241, 325, 79, 163, 247, 331)(74, 158, 242, 326, 80, 164, 248, 332)(75, 159, 243, 327, 81, 165, 249, 333)(76, 160, 244, 328, 82, 166, 250, 334)(77, 161, 245, 329, 83, 167, 251, 335)(78, 162, 246, 330, 84, 168, 252, 336) L = (1, 86)(2, 85)(3, 91)(4, 93)(5, 95)(6, 97)(7, 87)(8, 100)(9, 88)(10, 99)(11, 89)(12, 104)(13, 90)(14, 103)(15, 94)(16, 92)(17, 108)(18, 110)(19, 98)(20, 96)(21, 112)(22, 114)(23, 113)(24, 101)(25, 111)(26, 102)(27, 109)(28, 105)(29, 107)(30, 106)(31, 121)(32, 123)(33, 122)(34, 124)(35, 126)(36, 125)(37, 115)(38, 117)(39, 116)(40, 118)(41, 120)(42, 119)(43, 133)(44, 135)(45, 134)(46, 136)(47, 138)(48, 137)(49, 127)(50, 129)(51, 128)(52, 130)(53, 132)(54, 131)(55, 145)(56, 147)(57, 146)(58, 148)(59, 150)(60, 149)(61, 139)(62, 141)(63, 140)(64, 142)(65, 144)(66, 143)(67, 157)(68, 159)(69, 158)(70, 160)(71, 162)(72, 161)(73, 151)(74, 153)(75, 152)(76, 154)(77, 156)(78, 155)(79, 166)(80, 168)(81, 167)(82, 163)(83, 165)(84, 164)(169, 255)(170, 257)(171, 253)(172, 262)(173, 254)(174, 266)(175, 263)(176, 265)(177, 264)(178, 256)(179, 259)(180, 261)(181, 260)(182, 258)(183, 272)(184, 271)(185, 277)(186, 276)(187, 268)(188, 267)(189, 281)(190, 280)(191, 282)(192, 270)(193, 269)(194, 279)(195, 278)(196, 274)(197, 273)(198, 275)(199, 290)(200, 289)(201, 291)(202, 293)(203, 292)(204, 294)(205, 284)(206, 283)(207, 285)(208, 287)(209, 286)(210, 288)(211, 302)(212, 301)(213, 303)(214, 305)(215, 304)(216, 306)(217, 296)(218, 295)(219, 297)(220, 299)(221, 298)(222, 300)(223, 314)(224, 313)(225, 315)(226, 317)(227, 316)(228, 318)(229, 308)(230, 307)(231, 309)(232, 311)(233, 310)(234, 312)(235, 326)(236, 325)(237, 327)(238, 329)(239, 328)(240, 330)(241, 320)(242, 319)(243, 321)(244, 323)(245, 322)(246, 324)(247, 335)(248, 334)(249, 336)(250, 332)(251, 331)(252, 333) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E15.1106 Transitivity :: VT+ Graph:: bipartite v = 42 e = 168 f = 98 degree seq :: [ 8^42 ] E15.1108 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 6}) Quotient :: loop^2 Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-1 * 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 ] Map:: R = (1, 85, 169, 253, 4, 88, 172, 256, 6, 90, 174, 258, 15, 99, 183, 267, 9, 93, 177, 261, 5, 89, 173, 257)(2, 86, 170, 254, 7, 91, 175, 259, 3, 87, 171, 255, 10, 94, 178, 262, 14, 98, 182, 266, 8, 92, 176, 260)(11, 95, 179, 263, 19, 103, 187, 271, 12, 96, 180, 264, 21, 105, 189, 273, 13, 97, 181, 265, 20, 104, 188, 272)(16, 100, 184, 268, 22, 106, 190, 274, 17, 101, 185, 269, 24, 108, 192, 276, 18, 102, 186, 270, 23, 107, 191, 275)(25, 109, 193, 277, 31, 115, 199, 283, 26, 110, 194, 278, 33, 117, 201, 285, 27, 111, 195, 279, 32, 116, 200, 284)(28, 112, 196, 280, 34, 118, 202, 286, 29, 113, 197, 281, 36, 120, 204, 288, 30, 114, 198, 282, 35, 119, 203, 287)(37, 121, 205, 289, 43, 127, 211, 295, 38, 122, 206, 290, 45, 129, 213, 297, 39, 123, 207, 291, 44, 128, 212, 296)(40, 124, 208, 292, 46, 130, 214, 298, 41, 125, 209, 293, 48, 132, 216, 300, 42, 126, 210, 294, 47, 131, 215, 299)(49, 133, 217, 301, 55, 139, 223, 307, 50, 134, 218, 302, 57, 141, 225, 309, 51, 135, 219, 303, 56, 140, 224, 308)(52, 136, 220, 304, 58, 142, 226, 310, 53, 137, 221, 305, 60, 144, 228, 312, 54, 138, 222, 306, 59, 143, 227, 311)(61, 145, 229, 313, 67, 151, 235, 319, 62, 146, 230, 314, 69, 153, 237, 321, 63, 147, 231, 315, 68, 152, 236, 320)(64, 148, 232, 316, 70, 154, 238, 322, 65, 149, 233, 317, 72, 156, 240, 324, 66, 150, 234, 318, 71, 155, 239, 323)(73, 157, 241, 325, 79, 163, 247, 331, 74, 158, 242, 326, 81, 165, 249, 333, 75, 159, 243, 327, 80, 164, 248, 332)(76, 160, 244, 328, 82, 166, 250, 334, 77, 161, 245, 329, 84, 168, 252, 336, 78, 162, 246, 330, 83, 167, 251, 335) L = (1, 86)(2, 85)(3, 93)(4, 95)(5, 96)(6, 98)(7, 100)(8, 101)(9, 87)(10, 102)(11, 88)(12, 89)(13, 99)(14, 90)(15, 97)(16, 91)(17, 92)(18, 94)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156)(79, 167)(80, 166)(81, 168)(82, 164)(83, 163)(84, 165)(169, 255)(170, 258)(171, 253)(172, 264)(173, 265)(174, 254)(175, 269)(176, 270)(177, 266)(178, 268)(179, 267)(180, 256)(181, 257)(182, 261)(183, 263)(184, 262)(185, 259)(186, 260)(187, 278)(188, 279)(189, 277)(190, 281)(191, 282)(192, 280)(193, 273)(194, 271)(195, 272)(196, 276)(197, 274)(198, 275)(199, 290)(200, 291)(201, 289)(202, 293)(203, 294)(204, 292)(205, 285)(206, 283)(207, 284)(208, 288)(209, 286)(210, 287)(211, 302)(212, 303)(213, 301)(214, 305)(215, 306)(216, 304)(217, 297)(218, 295)(219, 296)(220, 300)(221, 298)(222, 299)(223, 314)(224, 315)(225, 313)(226, 317)(227, 318)(228, 316)(229, 309)(230, 307)(231, 308)(232, 312)(233, 310)(234, 311)(235, 326)(236, 327)(237, 325)(238, 329)(239, 330)(240, 328)(241, 321)(242, 319)(243, 320)(244, 324)(245, 322)(246, 323)(247, 334)(248, 336)(249, 335)(250, 331)(251, 333)(252, 332) 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 E15.1105 Transitivity :: VT+ Graph:: bipartite v = 14 e = 168 f = 126 degree seq :: [ 24^14 ] E15.1109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, 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, Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86)(3, 87, 7, 91)(4, 88, 9, 93)(5, 89, 10, 94)(6, 90, 12, 96)(8, 92, 15, 99)(11, 95, 20, 104)(13, 97, 23, 107)(14, 98, 21, 105)(16, 100, 19, 103)(17, 101, 28, 112)(18, 102, 29, 113)(22, 106, 34, 118)(24, 108, 37, 121)(25, 109, 36, 120)(26, 110, 39, 123)(27, 111, 40, 124)(30, 114, 44, 128)(31, 115, 43, 127)(32, 116, 46, 130)(33, 117, 47, 131)(35, 119, 49, 133)(38, 122, 53, 137)(41, 125, 48, 132)(42, 126, 57, 141)(45, 129, 61, 145)(50, 134, 67, 151)(51, 135, 66, 150)(52, 136, 63, 147)(54, 138, 64, 148)(55, 139, 60, 144)(56, 140, 62, 146)(58, 142, 74, 158)(59, 143, 73, 157)(65, 149, 79, 163)(68, 152, 83, 167)(69, 153, 82, 166)(70, 154, 78, 162)(71, 155, 77, 161)(72, 156, 84, 168)(75, 159, 80, 164)(76, 160, 81, 165)(169, 253, 171, 255)(170, 254, 173, 257)(172, 256, 176, 260)(174, 258, 179, 263)(175, 259, 181, 265)(177, 261, 184, 268)(178, 262, 186, 270)(180, 264, 189, 273)(182, 266, 192, 276)(183, 267, 193, 277)(185, 269, 195, 279)(187, 271, 198, 282)(188, 272, 199, 283)(190, 274, 201, 285)(191, 275, 203, 287)(194, 278, 206, 290)(196, 280, 207, 291)(197, 281, 210, 294)(200, 284, 213, 297)(202, 286, 214, 298)(204, 288, 218, 302)(205, 289, 219, 303)(208, 292, 223, 307)(209, 293, 222, 306)(211, 295, 226, 310)(212, 296, 227, 311)(215, 299, 231, 315)(216, 300, 230, 314)(217, 301, 233, 317)(220, 304, 236, 320)(221, 305, 237, 321)(224, 308, 239, 323)(225, 309, 240, 324)(228, 312, 243, 327)(229, 313, 244, 328)(232, 316, 246, 330)(234, 318, 248, 332)(235, 319, 249, 333)(238, 322, 252, 336)(241, 325, 251, 335)(242, 326, 250, 334)(245, 329, 247, 331) L = (1, 172)(2, 174)(3, 176)(4, 169)(5, 179)(6, 170)(7, 182)(8, 171)(9, 185)(10, 187)(11, 173)(12, 190)(13, 192)(14, 175)(15, 194)(16, 195)(17, 177)(18, 198)(19, 178)(20, 200)(21, 201)(22, 180)(23, 204)(24, 181)(25, 206)(26, 183)(27, 184)(28, 209)(29, 211)(30, 186)(31, 213)(32, 188)(33, 189)(34, 216)(35, 218)(36, 191)(37, 220)(38, 193)(39, 222)(40, 224)(41, 196)(42, 226)(43, 197)(44, 228)(45, 199)(46, 230)(47, 232)(48, 202)(49, 234)(50, 203)(51, 236)(52, 205)(53, 238)(54, 207)(55, 239)(56, 208)(57, 241)(58, 210)(59, 243)(60, 212)(61, 245)(62, 214)(63, 246)(64, 215)(65, 248)(66, 217)(67, 250)(68, 219)(69, 252)(70, 221)(71, 223)(72, 251)(73, 225)(74, 249)(75, 227)(76, 247)(77, 229)(78, 231)(79, 244)(80, 233)(81, 242)(82, 235)(83, 240)(84, 237)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.1113 Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 4^84 ] E15.1110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y3^-2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1, Y3^14, (Y3^-6 * Y2 * Y1)^2 ] Map:: non-degenerate R = (1, 85, 2, 86)(3, 87, 9, 93)(4, 88, 12, 96)(5, 89, 14, 98)(6, 90, 16, 100)(7, 91, 19, 103)(8, 92, 21, 105)(10, 94, 24, 108)(11, 95, 26, 110)(13, 97, 22, 106)(15, 99, 20, 104)(17, 101, 29, 113)(18, 102, 28, 112)(23, 107, 31, 115)(25, 109, 37, 121)(27, 111, 33, 117)(30, 114, 42, 126)(32, 116, 38, 122)(34, 118, 45, 129)(35, 119, 39, 123)(36, 120, 41, 125)(40, 124, 51, 135)(43, 127, 48, 132)(44, 128, 47, 131)(46, 130, 54, 138)(49, 133, 50, 134)(52, 136, 61, 145)(53, 137, 57, 141)(55, 139, 66, 150)(56, 140, 62, 146)(58, 142, 69, 153)(59, 143, 63, 147)(60, 144, 65, 149)(64, 148, 75, 159)(67, 151, 72, 156)(68, 152, 71, 155)(70, 154, 78, 162)(73, 157, 74, 158)(76, 160, 81, 165)(77, 161, 80, 164)(79, 163, 83, 167)(82, 166, 84, 168)(169, 253, 171, 255)(170, 254, 174, 258)(172, 256, 179, 263)(173, 257, 178, 262)(175, 259, 186, 270)(176, 260, 185, 269)(177, 261, 188, 272)(180, 264, 195, 279)(181, 265, 184, 268)(182, 266, 194, 278)(183, 267, 193, 277)(187, 271, 199, 283)(189, 273, 196, 280)(190, 274, 202, 286)(191, 275, 203, 287)(192, 276, 206, 290)(197, 281, 209, 293)(198, 282, 201, 285)(200, 284, 208, 292)(204, 288, 214, 298)(205, 289, 215, 299)(207, 291, 218, 302)(210, 294, 221, 305)(211, 295, 213, 297)(212, 296, 220, 304)(216, 300, 226, 310)(217, 301, 227, 311)(219, 303, 230, 314)(222, 306, 233, 317)(223, 307, 225, 309)(224, 308, 232, 316)(228, 312, 238, 322)(229, 313, 239, 323)(231, 315, 242, 326)(234, 318, 245, 329)(235, 319, 237, 321)(236, 320, 244, 328)(240, 324, 249, 333)(241, 325, 250, 334)(243, 327, 251, 335)(246, 330, 252, 336)(247, 331, 248, 332) L = (1, 172)(2, 175)(3, 178)(4, 181)(5, 169)(6, 185)(7, 188)(8, 170)(9, 186)(10, 193)(11, 171)(12, 196)(13, 198)(14, 199)(15, 173)(16, 179)(17, 202)(18, 174)(19, 194)(20, 203)(21, 195)(22, 176)(23, 177)(24, 187)(25, 208)(26, 189)(27, 209)(28, 182)(29, 180)(30, 211)(31, 206)(32, 183)(33, 184)(34, 214)(35, 215)(36, 190)(37, 191)(38, 218)(39, 192)(40, 220)(41, 221)(42, 197)(43, 223)(44, 200)(45, 201)(46, 226)(47, 227)(48, 204)(49, 205)(50, 230)(51, 207)(52, 232)(53, 233)(54, 210)(55, 235)(56, 212)(57, 213)(58, 238)(59, 239)(60, 216)(61, 217)(62, 242)(63, 219)(64, 244)(65, 245)(66, 222)(67, 247)(68, 224)(69, 225)(70, 249)(71, 250)(72, 228)(73, 229)(74, 251)(75, 231)(76, 248)(77, 252)(78, 234)(79, 236)(80, 237)(81, 241)(82, 240)(83, 246)(84, 243)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.1114 Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 4^84 ] E15.1111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86)(3, 87, 7, 91)(4, 88, 9, 93)(5, 89, 10, 94)(6, 90, 12, 96)(8, 92, 15, 99)(11, 95, 20, 104)(13, 97, 23, 107)(14, 98, 25, 109)(16, 100, 28, 112)(17, 101, 30, 114)(18, 102, 31, 115)(19, 103, 33, 117)(21, 105, 36, 120)(22, 106, 38, 122)(24, 108, 41, 125)(26, 110, 44, 128)(27, 111, 37, 121)(29, 113, 35, 119)(32, 116, 50, 134)(34, 118, 53, 137)(39, 123, 57, 141)(40, 124, 55, 139)(42, 126, 51, 135)(43, 127, 56, 140)(45, 129, 60, 144)(46, 130, 49, 133)(47, 131, 52, 136)(48, 132, 64, 148)(54, 138, 67, 151)(58, 142, 73, 157)(59, 143, 74, 158)(61, 145, 72, 156)(62, 146, 70, 154)(63, 147, 69, 153)(65, 149, 79, 163)(66, 150, 80, 164)(68, 152, 78, 162)(71, 155, 82, 166)(75, 159, 83, 167)(76, 160, 77, 161)(81, 165, 84, 168)(169, 253, 171, 255)(170, 254, 173, 257)(172, 256, 176, 260)(174, 258, 179, 263)(175, 259, 181, 265)(177, 261, 184, 268)(178, 262, 186, 270)(180, 264, 189, 273)(182, 266, 192, 276)(183, 267, 194, 278)(185, 269, 197, 281)(187, 271, 200, 284)(188, 272, 202, 286)(190, 274, 205, 289)(191, 275, 207, 291)(193, 277, 210, 294)(195, 279, 213, 297)(196, 280, 214, 298)(198, 282, 211, 295)(199, 283, 216, 300)(201, 285, 219, 303)(203, 287, 222, 306)(204, 288, 223, 307)(206, 290, 220, 304)(208, 292, 226, 310)(209, 293, 227, 311)(212, 296, 229, 313)(215, 299, 231, 315)(217, 301, 233, 317)(218, 302, 234, 318)(221, 305, 236, 320)(224, 308, 238, 322)(225, 309, 239, 323)(228, 312, 243, 327)(230, 314, 244, 328)(232, 316, 245, 329)(235, 319, 249, 333)(237, 321, 250, 334)(240, 324, 248, 332)(241, 325, 247, 331)(242, 326, 246, 330)(251, 335, 252, 336) L = (1, 172)(2, 174)(3, 176)(4, 169)(5, 179)(6, 170)(7, 182)(8, 171)(9, 185)(10, 187)(11, 173)(12, 190)(13, 192)(14, 175)(15, 195)(16, 197)(17, 177)(18, 200)(19, 178)(20, 203)(21, 205)(22, 180)(23, 208)(24, 181)(25, 211)(26, 213)(27, 183)(28, 215)(29, 184)(30, 210)(31, 217)(32, 186)(33, 220)(34, 222)(35, 188)(36, 224)(37, 189)(38, 219)(39, 226)(40, 191)(41, 228)(42, 198)(43, 193)(44, 230)(45, 194)(46, 231)(47, 196)(48, 233)(49, 199)(50, 235)(51, 206)(52, 201)(53, 237)(54, 202)(55, 238)(56, 204)(57, 240)(58, 207)(59, 243)(60, 209)(61, 244)(62, 212)(63, 214)(64, 246)(65, 216)(66, 249)(67, 218)(68, 250)(69, 221)(70, 223)(71, 248)(72, 225)(73, 251)(74, 245)(75, 227)(76, 229)(77, 242)(78, 232)(79, 252)(80, 239)(81, 234)(82, 236)(83, 241)(84, 247)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.1112 Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 4^84 ] E15.1112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 6, 90, 15, 99, 14, 98, 5, 89)(3, 87, 9, 93, 16, 100, 31, 115, 25, 109, 11, 95)(4, 88, 12, 96, 26, 110, 30, 114, 17, 101, 8, 92)(7, 91, 18, 102, 29, 113, 28, 112, 13, 97, 20, 104)(10, 94, 23, 107, 40, 124, 47, 131, 32, 116, 22, 106)(19, 103, 35, 119, 27, 111, 43, 127, 45, 129, 34, 118)(21, 105, 37, 121, 46, 130, 42, 126, 24, 108, 39, 123)(33, 117, 48, 132, 44, 128, 52, 136, 36, 120, 50, 134)(38, 122, 55, 139, 41, 125, 57, 141, 60, 144, 54, 138)(49, 133, 63, 147, 51, 135, 65, 149, 59, 143, 62, 146)(53, 137, 67, 151, 58, 142, 71, 155, 56, 140, 69, 153)(61, 145, 73, 157, 66, 150, 77, 161, 64, 148, 75, 159)(68, 152, 80, 164, 70, 154, 81, 165, 72, 156, 79, 163)(74, 158, 83, 167, 76, 160, 84, 168, 78, 162, 82, 166)(169, 253, 171, 255)(170, 254, 175, 259)(172, 256, 178, 262)(173, 257, 181, 265)(174, 258, 184, 268)(176, 260, 187, 271)(177, 261, 189, 273)(179, 263, 192, 276)(180, 264, 195, 279)(182, 266, 193, 277)(183, 267, 197, 281)(185, 269, 200, 284)(186, 270, 201, 285)(188, 272, 204, 288)(190, 274, 206, 290)(191, 275, 209, 293)(194, 278, 208, 292)(196, 280, 212, 296)(198, 282, 213, 297)(199, 283, 214, 298)(202, 286, 217, 301)(203, 287, 219, 303)(205, 289, 221, 305)(207, 291, 224, 308)(210, 294, 226, 310)(211, 295, 227, 311)(215, 299, 228, 312)(216, 300, 229, 313)(218, 302, 232, 316)(220, 304, 234, 318)(222, 306, 236, 320)(223, 307, 238, 322)(225, 309, 240, 324)(230, 314, 242, 326)(231, 315, 244, 328)(233, 317, 246, 330)(235, 319, 245, 329)(237, 321, 241, 325)(239, 323, 243, 327)(247, 331, 252, 336)(248, 332, 250, 334)(249, 333, 251, 335) L = (1, 172)(2, 176)(3, 178)(4, 169)(5, 180)(6, 185)(7, 187)(8, 170)(9, 190)(10, 171)(11, 191)(12, 173)(13, 195)(14, 194)(15, 198)(16, 200)(17, 174)(18, 202)(19, 175)(20, 203)(21, 206)(22, 177)(23, 179)(24, 209)(25, 208)(26, 182)(27, 181)(28, 211)(29, 213)(30, 183)(31, 215)(32, 184)(33, 217)(34, 186)(35, 188)(36, 219)(37, 222)(38, 189)(39, 223)(40, 193)(41, 192)(42, 225)(43, 196)(44, 227)(45, 197)(46, 228)(47, 199)(48, 230)(49, 201)(50, 231)(51, 204)(52, 233)(53, 236)(54, 205)(55, 207)(56, 238)(57, 210)(58, 240)(59, 212)(60, 214)(61, 242)(62, 216)(63, 218)(64, 244)(65, 220)(66, 246)(67, 247)(68, 221)(69, 248)(70, 224)(71, 249)(72, 226)(73, 250)(74, 229)(75, 251)(76, 232)(77, 252)(78, 234)(79, 235)(80, 237)(81, 239)(82, 241)(83, 243)(84, 245)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1111 Graph:: simple bipartite v = 56 e = 168 f = 84 degree seq :: [ 4^42, 12^14 ] E15.1113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^6, (Y1^-1 * Y2 * Y1^-1)^2, Y1^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y1^-1, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 6, 90, 15, 99, 14, 98, 5, 89)(3, 87, 9, 93, 21, 105, 32, 116, 16, 100, 11, 95)(4, 88, 12, 96, 26, 110, 30, 114, 17, 101, 8, 92)(7, 91, 18, 102, 13, 97, 28, 112, 29, 113, 20, 104)(10, 94, 24, 108, 31, 115, 46, 130, 37, 121, 23, 107)(19, 103, 35, 119, 45, 129, 43, 127, 27, 111, 34, 118)(22, 106, 38, 122, 25, 109, 42, 126, 47, 131, 40, 124)(33, 117, 48, 132, 36, 120, 52, 136, 44, 128, 50, 134)(39, 123, 55, 139, 60, 144, 57, 141, 41, 125, 54, 138)(49, 133, 63, 147, 59, 143, 65, 149, 51, 135, 62, 146)(53, 137, 67, 151, 56, 140, 71, 155, 58, 142, 69, 153)(61, 145, 73, 157, 64, 148, 77, 161, 66, 150, 75, 159)(68, 152, 81, 165, 72, 156, 83, 167, 70, 154, 80, 164)(74, 158, 79, 163, 78, 162, 82, 166, 76, 160, 84, 168)(169, 253, 171, 255)(170, 254, 175, 259)(172, 256, 178, 262)(173, 257, 181, 265)(174, 258, 184, 268)(176, 260, 187, 271)(177, 261, 190, 274)(179, 263, 193, 277)(180, 264, 195, 279)(182, 266, 189, 273)(183, 267, 197, 281)(185, 269, 199, 283)(186, 270, 201, 285)(188, 272, 204, 288)(191, 275, 207, 291)(192, 276, 209, 293)(194, 278, 205, 289)(196, 280, 212, 296)(198, 282, 213, 297)(200, 284, 215, 299)(202, 286, 217, 301)(203, 287, 219, 303)(206, 290, 221, 305)(208, 292, 224, 308)(210, 294, 226, 310)(211, 295, 227, 311)(214, 298, 228, 312)(216, 300, 229, 313)(218, 302, 232, 316)(220, 304, 234, 318)(222, 306, 236, 320)(223, 307, 238, 322)(225, 309, 240, 324)(230, 314, 242, 326)(231, 315, 244, 328)(233, 317, 246, 330)(235, 319, 247, 331)(237, 321, 250, 334)(239, 323, 252, 336)(241, 325, 251, 335)(243, 327, 248, 332)(245, 329, 249, 333) L = (1, 172)(2, 176)(3, 178)(4, 169)(5, 180)(6, 185)(7, 187)(8, 170)(9, 191)(10, 171)(11, 192)(12, 173)(13, 195)(14, 194)(15, 198)(16, 199)(17, 174)(18, 202)(19, 175)(20, 203)(21, 205)(22, 207)(23, 177)(24, 179)(25, 209)(26, 182)(27, 181)(28, 211)(29, 213)(30, 183)(31, 184)(32, 214)(33, 217)(34, 186)(35, 188)(36, 219)(37, 189)(38, 222)(39, 190)(40, 223)(41, 193)(42, 225)(43, 196)(44, 227)(45, 197)(46, 200)(47, 228)(48, 230)(49, 201)(50, 231)(51, 204)(52, 233)(53, 236)(54, 206)(55, 208)(56, 238)(57, 210)(58, 240)(59, 212)(60, 215)(61, 242)(62, 216)(63, 218)(64, 244)(65, 220)(66, 246)(67, 248)(68, 221)(69, 249)(70, 224)(71, 251)(72, 226)(73, 252)(74, 229)(75, 247)(76, 232)(77, 250)(78, 234)(79, 243)(80, 235)(81, 237)(82, 245)(83, 239)(84, 241)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1109 Graph:: simple bipartite v = 56 e = 168 f = 84 degree seq :: [ 4^42, 12^14 ] E15.1114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ R^2, Y2^2, 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 * Y3 * Y2 * Y1 * Y2 * Y3^-1, 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 ] Map:: non-degenerate R = (1, 85, 2, 86, 4, 88, 8, 92, 6, 90, 5, 89)(3, 87, 9, 93, 10, 94, 18, 102, 12, 96, 11, 95)(7, 91, 14, 98, 13, 97, 20, 104, 16, 100, 15, 99)(17, 101, 23, 107, 19, 103, 26, 110, 25, 109, 24, 108)(21, 105, 28, 112, 22, 106, 30, 114, 27, 111, 29, 113)(31, 115, 37, 121, 32, 116, 39, 123, 33, 117, 38, 122)(34, 118, 40, 124, 35, 119, 42, 126, 36, 120, 41, 125)(43, 127, 49, 133, 44, 128, 51, 135, 45, 129, 50, 134)(46, 130, 52, 136, 47, 131, 54, 138, 48, 132, 53, 137)(55, 139, 61, 145, 56, 140, 63, 147, 57, 141, 62, 146)(58, 142, 64, 148, 59, 143, 66, 150, 60, 144, 65, 149)(67, 151, 73, 157, 68, 152, 75, 159, 69, 153, 74, 158)(70, 154, 76, 160, 71, 155, 78, 162, 72, 156, 77, 161)(79, 163, 83, 167, 80, 164, 84, 168, 81, 165, 82, 166)(169, 253, 171, 255)(170, 254, 175, 259)(172, 256, 180, 264)(173, 257, 181, 265)(174, 258, 178, 262)(176, 260, 184, 268)(177, 261, 185, 269)(179, 263, 187, 271)(182, 266, 189, 273)(183, 267, 190, 274)(186, 270, 193, 277)(188, 272, 195, 279)(191, 275, 199, 283)(192, 276, 200, 284)(194, 278, 201, 285)(196, 280, 202, 286)(197, 281, 203, 287)(198, 282, 204, 288)(205, 289, 211, 295)(206, 290, 212, 296)(207, 291, 213, 297)(208, 292, 214, 298)(209, 293, 215, 299)(210, 294, 216, 300)(217, 301, 223, 307)(218, 302, 224, 308)(219, 303, 225, 309)(220, 304, 226, 310)(221, 305, 227, 311)(222, 306, 228, 312)(229, 313, 235, 319)(230, 314, 236, 320)(231, 315, 237, 321)(232, 316, 238, 322)(233, 317, 239, 323)(234, 318, 240, 324)(241, 325, 247, 331)(242, 326, 248, 332)(243, 327, 249, 333)(244, 328, 250, 334)(245, 329, 251, 335)(246, 330, 252, 336) L = (1, 172)(2, 176)(3, 178)(4, 174)(5, 170)(6, 169)(7, 181)(8, 173)(9, 186)(10, 180)(11, 177)(12, 171)(13, 184)(14, 188)(15, 182)(16, 175)(17, 187)(18, 179)(19, 193)(20, 183)(21, 190)(22, 195)(23, 194)(24, 191)(25, 185)(26, 192)(27, 189)(28, 198)(29, 196)(30, 197)(31, 200)(32, 201)(33, 199)(34, 203)(35, 204)(36, 202)(37, 207)(38, 205)(39, 206)(40, 210)(41, 208)(42, 209)(43, 212)(44, 213)(45, 211)(46, 215)(47, 216)(48, 214)(49, 219)(50, 217)(51, 218)(52, 222)(53, 220)(54, 221)(55, 224)(56, 225)(57, 223)(58, 227)(59, 228)(60, 226)(61, 231)(62, 229)(63, 230)(64, 234)(65, 232)(66, 233)(67, 236)(68, 237)(69, 235)(70, 239)(71, 240)(72, 238)(73, 243)(74, 241)(75, 242)(76, 246)(77, 244)(78, 245)(79, 248)(80, 249)(81, 247)(82, 251)(83, 252)(84, 250)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1110 Graph:: bipartite v = 56 e = 168 f = 84 degree seq :: [ 4^42, 12^14 ] E15.1115 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = (C7 : C4) : C3 (small group id <84, 1>) Aut = (C7 : C4) : C3 (small group id <84, 1>) |r| :: 1 Presentation :: [ X1^3, X2^4, X2^4, X2^4, X2^-1 * X1^-1 * X2^-2 * X1 * X2^-1, X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1, (X1 * X2^-1 * X1 * X2)^3 ] Map:: non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 15, 17)(7, 18, 19)(9, 16, 22)(11, 25, 26)(12, 27, 28)(20, 33, 34)(21, 35, 36)(23, 37, 38)(24, 39, 40)(29, 45, 46)(30, 47, 48)(31, 49, 50)(32, 51, 52)(41, 61, 62)(42, 63, 64)(43, 65, 66)(44, 67, 68)(53, 77, 73)(54, 78, 74)(55, 71, 79)(56, 72, 80)(57, 81, 75)(58, 82, 76)(59, 83, 69)(60, 84, 70)(85, 87, 93, 89)(86, 90, 100, 91)(88, 95, 106, 96)(92, 104, 97, 105)(94, 107, 98, 108)(99, 113, 102, 114)(101, 115, 103, 116)(109, 125, 111, 126)(110, 127, 112, 128)(117, 137, 119, 138)(118, 139, 120, 140)(121, 141, 123, 142)(122, 143, 124, 144)(129, 153, 131, 154)(130, 155, 132, 156)(133, 157, 135, 158)(134, 159, 136, 160)(145, 165, 147, 166)(146, 163, 148, 164)(149, 167, 151, 168)(150, 161, 152, 162) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 24^3 ), ( 24^4 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 49 e = 84 f = 7 degree seq :: [ 3^28, 4^21 ] E15.1116 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = (C7 : C4) : C3 (small group id <84, 1>) Aut = (C7 : C4) : C3 (small group id <84, 1>) |r| :: 1 Presentation :: [ X1^4, X1^4, X1^-1 * X2 * X1^-2 * X2^-1 * X1^-1, (X2 * X1)^3, X1 * X2 * X1^-1 * X2 * X1^-1 * X2, X2^6 * X1^2, X2^2 * X1^-1 * X2^-3 * X1^-1 * X2^-2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 6, 4)(3, 9, 17, 11)(5, 14, 18, 15)(7, 19, 12, 21)(8, 22, 13, 23)(10, 26, 37, 28)(16, 34, 38, 35)(20, 40, 30, 42)(24, 46, 31, 47)(25, 49, 29, 50)(27, 53, 36, 54)(32, 57, 33, 59)(39, 63, 43, 64)(41, 67, 48, 68)(44, 71, 45, 73)(51, 77, 56, 78)(52, 79, 55, 80)(58, 72, 60, 74)(61, 75, 62, 76)(65, 81, 70, 82)(66, 83, 69, 84)(85, 87, 94, 111, 122, 102, 90, 101, 121, 120, 100, 89)(86, 91, 104, 125, 115, 97, 88, 96, 114, 132, 108, 92)(93, 106, 128, 156, 140, 113, 95, 107, 129, 158, 135, 109)(98, 116, 142, 149, 123, 103, 99, 117, 144, 154, 127, 105)(110, 133, 150, 124, 147, 139, 112, 134, 153, 126, 148, 136)(118, 145, 152, 168, 161, 141, 119, 146, 151, 167, 162, 143)(130, 159, 137, 163, 165, 155, 131, 160, 138, 164, 166, 157) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 6^4 ), ( 6^12 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: bipartite v = 28 e = 84 f = 28 degree seq :: [ 4^21, 12^7 ] E15.1117 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = (C7 : C4) : C3 (small group id <84, 1>) Aut = (C7 : C4) : C3 (small group id <84, 1>) |r| :: 1 Presentation :: [ X2^3, X1^2 * X2 * X1 * X2^-1 * X1 * X2, X2 * X1 * X2 * X1^-5, (X2^-1 * X1^-1)^4, X1^-1 * X2 * X1^3 * X2 * X1^-2 * X2 ] Map:: non-degenerate R = (1, 2, 6, 16, 42, 24, 48, 41, 56, 32, 12, 4)(3, 9, 23, 57, 74, 37, 35, 13, 34, 63, 27, 10)(5, 14, 36, 50, 20, 7, 19, 28, 65, 76, 40, 15)(8, 21, 52, 72, 45, 17, 39, 51, 82, 58, 55, 22)(11, 29, 66, 73, 79, 59, 25, 33, 71, 84, 68, 30)(18, 46, 75, 38, 64, 43, 54, 78, 61, 26, 60, 47)(31, 44, 77, 83, 53, 81, 67, 70, 62, 80, 49, 69)(85, 87, 89)(86, 91, 92)(88, 95, 97)(90, 101, 102)(93, 108, 109)(94, 110, 112)(96, 115, 117)(98, 121, 122)(99, 123, 125)(100, 127, 128)(103, 132, 119)(104, 133, 135)(105, 124, 137)(106, 138, 140)(107, 114, 142)(111, 146, 148)(113, 126, 151)(116, 131, 154)(118, 143, 156)(120, 145, 157)(129, 152, 162)(130, 139, 163)(134, 155, 165)(136, 164, 141)(144, 158, 161)(147, 166, 167)(149, 159, 168)(150, 153, 160) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 8^3 ), ( 8^12 ) } Outer automorphisms :: chiral Dual of E15.1119 Transitivity :: ET+ Graph:: simple bipartite v = 35 e = 84 f = 21 degree seq :: [ 3^28, 12^7 ] E15.1118 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = (C7 : C4) : C3 (small group id <84, 1>) Aut = (C7 : C4) : C3 (small group id <84, 1>) |r| :: 1 Presentation :: [ X1^3, X2^4, X2^4, X2^4, X2^-1 * X1^-1 * X2^-2 * X1 * X2^-1, X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1, (X1 * X2^-1 * X1 * X2)^3 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 4, 88)(3, 87, 8, 92, 10, 94)(5, 89, 13, 97, 14, 98)(6, 90, 15, 99, 17, 101)(7, 91, 18, 102, 19, 103)(9, 93, 16, 100, 22, 106)(11, 95, 25, 109, 26, 110)(12, 96, 27, 111, 28, 112)(20, 104, 33, 117, 34, 118)(21, 105, 35, 119, 36, 120)(23, 107, 37, 121, 38, 122)(24, 108, 39, 123, 40, 124)(29, 113, 45, 129, 46, 130)(30, 114, 47, 131, 48, 132)(31, 115, 49, 133, 50, 134)(32, 116, 51, 135, 52, 136)(41, 125, 61, 145, 62, 146)(42, 126, 63, 147, 64, 148)(43, 127, 65, 149, 66, 150)(44, 128, 67, 151, 68, 152)(53, 137, 77, 161, 73, 157)(54, 138, 78, 162, 74, 158)(55, 139, 71, 155, 79, 163)(56, 140, 72, 156, 80, 164)(57, 141, 81, 165, 75, 159)(58, 142, 82, 166, 76, 160)(59, 143, 83, 167, 69, 153)(60, 144, 84, 168, 70, 154) L = (1, 87)(2, 90)(3, 93)(4, 95)(5, 85)(6, 100)(7, 86)(8, 104)(9, 89)(10, 107)(11, 106)(12, 88)(13, 105)(14, 108)(15, 113)(16, 91)(17, 115)(18, 114)(19, 116)(20, 97)(21, 92)(22, 96)(23, 98)(24, 94)(25, 125)(26, 127)(27, 126)(28, 128)(29, 102)(30, 99)(31, 103)(32, 101)(33, 137)(34, 139)(35, 138)(36, 140)(37, 141)(38, 143)(39, 142)(40, 144)(41, 111)(42, 109)(43, 112)(44, 110)(45, 153)(46, 155)(47, 154)(48, 156)(49, 157)(50, 159)(51, 158)(52, 160)(53, 119)(54, 117)(55, 120)(56, 118)(57, 123)(58, 121)(59, 124)(60, 122)(61, 165)(62, 163)(63, 166)(64, 164)(65, 167)(66, 161)(67, 168)(68, 162)(69, 131)(70, 129)(71, 132)(72, 130)(73, 135)(74, 133)(75, 136)(76, 134)(77, 152)(78, 150)(79, 148)(80, 146)(81, 147)(82, 145)(83, 151)(84, 149) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple bipartite v = 28 e = 84 f = 28 degree seq :: [ 6^28 ] E15.1119 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = (C7 : C4) : C3 (small group id <84, 1>) Aut = (C7 : C4) : C3 (small group id <84, 1>) |r| :: 1 Presentation :: [ X1^4, X1^4, X1^-1 * X2 * X1^-2 * X2^-1 * X1^-1, (X2 * X1)^3, X1 * X2 * X1^-1 * X2 * X1^-1 * X2, X2^6 * X1^2, X2^2 * X1^-1 * X2^-3 * X1^-1 * X2^-2 * X1^-1 ] Map:: non-degenerate R = (1, 85, 2, 86, 6, 90, 4, 88)(3, 87, 9, 93, 17, 101, 11, 95)(5, 89, 14, 98, 18, 102, 15, 99)(7, 91, 19, 103, 12, 96, 21, 105)(8, 92, 22, 106, 13, 97, 23, 107)(10, 94, 26, 110, 37, 121, 28, 112)(16, 100, 34, 118, 38, 122, 35, 119)(20, 104, 40, 124, 30, 114, 42, 126)(24, 108, 46, 130, 31, 115, 47, 131)(25, 109, 49, 133, 29, 113, 50, 134)(27, 111, 53, 137, 36, 120, 54, 138)(32, 116, 57, 141, 33, 117, 59, 143)(39, 123, 63, 147, 43, 127, 64, 148)(41, 125, 67, 151, 48, 132, 68, 152)(44, 128, 71, 155, 45, 129, 73, 157)(51, 135, 77, 161, 56, 140, 78, 162)(52, 136, 79, 163, 55, 139, 80, 164)(58, 142, 72, 156, 60, 144, 74, 158)(61, 145, 75, 159, 62, 146, 76, 160)(65, 149, 81, 165, 70, 154, 82, 166)(66, 150, 83, 167, 69, 153, 84, 168) L = (1, 87)(2, 91)(3, 94)(4, 96)(5, 85)(6, 101)(7, 104)(8, 86)(9, 106)(10, 111)(11, 107)(12, 114)(13, 88)(14, 116)(15, 117)(16, 89)(17, 121)(18, 90)(19, 99)(20, 125)(21, 98)(22, 128)(23, 129)(24, 92)(25, 93)(26, 133)(27, 122)(28, 134)(29, 95)(30, 132)(31, 97)(32, 142)(33, 144)(34, 145)(35, 146)(36, 100)(37, 120)(38, 102)(39, 103)(40, 147)(41, 115)(42, 148)(43, 105)(44, 156)(45, 158)(46, 159)(47, 160)(48, 108)(49, 150)(50, 153)(51, 109)(52, 110)(53, 163)(54, 164)(55, 112)(56, 113)(57, 119)(58, 149)(59, 118)(60, 154)(61, 152)(62, 151)(63, 139)(64, 136)(65, 123)(66, 124)(67, 167)(68, 168)(69, 126)(70, 127)(71, 131)(72, 140)(73, 130)(74, 135)(75, 137)(76, 138)(77, 141)(78, 143)(79, 165)(80, 166)(81, 155)(82, 157)(83, 162)(84, 161) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: chiral Dual of E15.1117 Transitivity :: ET+ VT+ Graph:: v = 21 e = 84 f = 35 degree seq :: [ 8^21 ] E15.1120 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = (C7 : C4) : C3 (small group id <84, 1>) Aut = (C7 : C4) : C3 (small group id <84, 1>) |r| :: 1 Presentation :: [ X2^3, X1^2 * X2 * X1 * X2^-1 * X1 * X2, X2 * X1 * X2 * X1^-5, (X2^-1 * X1^-1)^4, X1^-1 * X2 * X1^3 * X2 * X1^-2 * X2 ] Map:: non-degenerate R = (1, 85, 2, 86, 6, 90, 16, 100, 42, 126, 24, 108, 48, 132, 41, 125, 56, 140, 32, 116, 12, 96, 4, 88)(3, 87, 9, 93, 23, 107, 57, 141, 74, 158, 37, 121, 35, 119, 13, 97, 34, 118, 63, 147, 27, 111, 10, 94)(5, 89, 14, 98, 36, 120, 50, 134, 20, 104, 7, 91, 19, 103, 28, 112, 65, 149, 76, 160, 40, 124, 15, 99)(8, 92, 21, 105, 52, 136, 72, 156, 45, 129, 17, 101, 39, 123, 51, 135, 82, 166, 58, 142, 55, 139, 22, 106)(11, 95, 29, 113, 66, 150, 73, 157, 79, 163, 59, 143, 25, 109, 33, 117, 71, 155, 84, 168, 68, 152, 30, 114)(18, 102, 46, 130, 75, 159, 38, 122, 64, 148, 43, 127, 54, 138, 78, 162, 61, 145, 26, 110, 60, 144, 47, 131)(31, 115, 44, 128, 77, 161, 83, 167, 53, 137, 81, 165, 67, 151, 70, 154, 62, 146, 80, 164, 49, 133, 69, 153) L = (1, 87)(2, 91)(3, 89)(4, 95)(5, 85)(6, 101)(7, 92)(8, 86)(9, 108)(10, 110)(11, 97)(12, 115)(13, 88)(14, 121)(15, 123)(16, 127)(17, 102)(18, 90)(19, 132)(20, 133)(21, 124)(22, 138)(23, 114)(24, 109)(25, 93)(26, 112)(27, 146)(28, 94)(29, 126)(30, 142)(31, 117)(32, 131)(33, 96)(34, 143)(35, 103)(36, 145)(37, 122)(38, 98)(39, 125)(40, 137)(41, 99)(42, 151)(43, 128)(44, 100)(45, 152)(46, 139)(47, 154)(48, 119)(49, 135)(50, 155)(51, 104)(52, 164)(53, 105)(54, 140)(55, 163)(56, 106)(57, 136)(58, 107)(59, 156)(60, 158)(61, 157)(62, 148)(63, 166)(64, 111)(65, 159)(66, 153)(67, 113)(68, 162)(69, 160)(70, 116)(71, 165)(72, 118)(73, 120)(74, 161)(75, 168)(76, 150)(77, 144)(78, 129)(79, 130)(80, 141)(81, 134)(82, 167)(83, 147)(84, 149) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 7 e = 84 f = 49 degree seq :: [ 24^7 ] E15.1121 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 31}) Quotient :: edge Aut^+ = C31 : C3 (small group id <93, 1>) Aut = C31 : C3 (small group id <93, 1>) |r| :: 1 Presentation :: [ X1^3, (X2 * X1^-1)^3, (X2^-1 * X1^-1)^3, X2^5 * X1 * X2^-1 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 28, 30)(12, 31, 22)(15, 35, 36)(17, 39, 41)(21, 45, 46)(23, 49, 44)(25, 53, 54)(27, 56, 51)(29, 59, 60)(32, 62, 63)(33, 65, 42)(34, 58, 67)(37, 52, 69)(38, 70, 48)(40, 73, 74)(43, 76, 61)(47, 72, 79)(50, 80, 78)(55, 85, 83)(57, 86, 87)(64, 89, 91)(66, 84, 75)(68, 88, 82)(71, 92, 81)(77, 93, 90)(94, 96, 102, 118, 135, 111, 124, 149, 178, 168, 134, 163, 155, 179, 186, 167, 172, 185, 182, 152, 169, 139, 171, 181, 151, 121, 113, 137, 130, 108, 98)(95, 99, 110, 133, 154, 123, 106, 126, 159, 183, 153, 160, 128, 146, 176, 180, 184, 175, 145, 117, 144, 156, 174, 143, 116, 101, 115, 141, 140, 114, 100)(97, 104, 122, 150, 120, 103, 112, 136, 170, 148, 119, 142, 138, 166, 177, 147, 162, 173, 165, 132, 158, 129, 161, 164, 131, 109, 107, 127, 157, 125, 105) L = (1, 94)(2, 95)(3, 96)(4, 97)(5, 98)(6, 99)(7, 100)(8, 101)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 107)(15, 108)(16, 109)(17, 110)(18, 111)(19, 112)(20, 113)(21, 114)(22, 115)(23, 116)(24, 117)(25, 118)(26, 119)(27, 120)(28, 121)(29, 122)(30, 123)(31, 124)(32, 125)(33, 126)(34, 127)(35, 128)(36, 129)(37, 130)(38, 131)(39, 132)(40, 133)(41, 134)(42, 135)(43, 136)(44, 137)(45, 138)(46, 139)(47, 140)(48, 141)(49, 142)(50, 143)(51, 144)(52, 145)(53, 146)(54, 147)(55, 148)(56, 149)(57, 150)(58, 151)(59, 152)(60, 153)(61, 154)(62, 155)(63, 156)(64, 157)(65, 158)(66, 159)(67, 160)(68, 161)(69, 162)(70, 163)(71, 164)(72, 165)(73, 166)(74, 167)(75, 168)(76, 169)(77, 170)(78, 171)(79, 172)(80, 173)(81, 174)(82, 175)(83, 176)(84, 177)(85, 178)(86, 179)(87, 180)(88, 181)(89, 182)(90, 183)(91, 184)(92, 185)(93, 186) local type(s) :: { ( 6^3 ), ( 6^31 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 93 f = 31 degree seq :: [ 3^31, 31^3 ] E15.1122 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 31}) Quotient :: loop Aut^+ = C31 : C3 (small group id <93, 1>) Aut = C31 : C3 (small group id <93, 1>) |r| :: 1 Presentation :: [ X1^3, X2^3, (X2 * X1^-1)^3, X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 94, 2, 95, 4, 97)(3, 96, 8, 101, 9, 102)(5, 98, 12, 105, 13, 106)(6, 99, 14, 107, 15, 108)(7, 100, 16, 109, 17, 110)(10, 103, 21, 114, 22, 115)(11, 104, 23, 116, 24, 117)(18, 111, 33, 126, 34, 127)(19, 112, 26, 119, 35, 128)(20, 113, 36, 129, 37, 130)(25, 118, 42, 135, 43, 136)(27, 120, 44, 137, 45, 138)(28, 121, 46, 139, 47, 140)(29, 122, 31, 124, 48, 141)(30, 123, 49, 142, 50, 143)(32, 125, 51, 144, 52, 145)(38, 131, 59, 152, 60, 153)(39, 132, 40, 133, 61, 154)(41, 134, 62, 155, 63, 156)(53, 146, 73, 166, 76, 169)(54, 147, 56, 149, 77, 170)(55, 148, 78, 171, 79, 172)(57, 150, 66, 159, 80, 173)(58, 151, 81, 174, 82, 175)(64, 157, 87, 180, 88, 181)(65, 158, 89, 182, 68, 161)(67, 160, 69, 162, 71, 164)(70, 163, 90, 183, 91, 184)(72, 165, 74, 167, 92, 185)(75, 168, 83, 176, 84, 177)(85, 178, 86, 179, 93, 186) L = (1, 96)(2, 99)(3, 98)(4, 103)(5, 94)(6, 100)(7, 95)(8, 111)(9, 109)(10, 104)(11, 97)(12, 118)(13, 119)(14, 121)(15, 116)(16, 113)(17, 124)(18, 112)(19, 101)(20, 102)(21, 131)(22, 105)(23, 123)(24, 133)(25, 115)(26, 120)(27, 106)(28, 122)(29, 107)(30, 108)(31, 125)(32, 110)(33, 146)(34, 129)(35, 149)(36, 148)(37, 144)(38, 132)(39, 114)(40, 134)(41, 117)(42, 157)(43, 137)(44, 158)(45, 159)(46, 161)(47, 142)(48, 164)(49, 163)(50, 155)(51, 151)(52, 167)(53, 147)(54, 126)(55, 127)(56, 150)(57, 128)(58, 130)(59, 175)(60, 135)(61, 177)(62, 166)(63, 179)(64, 153)(65, 136)(66, 160)(67, 138)(68, 162)(69, 139)(70, 140)(71, 165)(72, 141)(73, 143)(74, 168)(75, 145)(76, 171)(77, 156)(78, 184)(79, 174)(80, 186)(81, 180)(82, 176)(83, 152)(84, 178)(85, 154)(86, 170)(87, 172)(88, 182)(89, 183)(90, 181)(91, 169)(92, 173)(93, 185) local type(s) :: { ( 3, 31, 3, 31, 3, 31 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 31 e = 93 f = 34 degree seq :: [ 6^31 ] E15.1123 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {3, 3, 31}) Quotient :: loop Aut^+ = C31 : C3 (small group id <93, 1>) Aut = (C31 : C3) : C2 (small group id <186, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, F * T1 * F * T2, (T2 * T1^-1)^3, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 6, 7)(4, 10, 11)(8, 18, 19)(9, 16, 20)(12, 25, 22)(13, 26, 27)(14, 28, 29)(15, 23, 30)(17, 31, 32)(21, 38, 39)(24, 40, 41)(33, 53, 54)(34, 36, 55)(35, 56, 57)(37, 51, 58)(42, 64, 60)(43, 44, 65)(45, 66, 67)(46, 68, 69)(47, 49, 70)(48, 71, 72)(50, 62, 73)(52, 74, 75)(59, 82, 83)(61, 84, 85)(63, 86, 77)(76, 78, 91)(79, 81, 87)(80, 93, 92)(88, 89, 90)(94, 95, 97)(96, 101, 102)(98, 105, 106)(99, 107, 108)(100, 109, 110)(103, 114, 115)(104, 116, 117)(111, 126, 127)(112, 119, 128)(113, 129, 130)(118, 135, 136)(120, 137, 138)(121, 139, 140)(122, 124, 141)(123, 142, 143)(125, 144, 145)(131, 152, 153)(132, 133, 154)(134, 155, 156)(146, 166, 169)(147, 149, 170)(148, 171, 172)(150, 159, 173)(151, 174, 175)(157, 180, 181)(158, 182, 161)(160, 162, 164)(163, 183, 184)(165, 167, 185)(168, 176, 177)(178, 179, 186) L = (1, 94)(2, 95)(3, 96)(4, 97)(5, 98)(6, 99)(7, 100)(8, 101)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 107)(15, 108)(16, 109)(17, 110)(18, 111)(19, 112)(20, 113)(21, 114)(22, 115)(23, 116)(24, 117)(25, 118)(26, 119)(27, 120)(28, 121)(29, 122)(30, 123)(31, 124)(32, 125)(33, 126)(34, 127)(35, 128)(36, 129)(37, 130)(38, 131)(39, 132)(40, 133)(41, 134)(42, 135)(43, 136)(44, 137)(45, 138)(46, 139)(47, 140)(48, 141)(49, 142)(50, 143)(51, 144)(52, 145)(53, 146)(54, 147)(55, 148)(56, 149)(57, 150)(58, 151)(59, 152)(60, 153)(61, 154)(62, 155)(63, 156)(64, 157)(65, 158)(66, 159)(67, 160)(68, 161)(69, 162)(70, 163)(71, 164)(72, 165)(73, 166)(74, 167)(75, 168)(76, 169)(77, 170)(78, 171)(79, 172)(80, 173)(81, 174)(82, 175)(83, 176)(84, 177)(85, 178)(86, 179)(87, 180)(88, 181)(89, 182)(90, 183)(91, 184)(92, 185)(93, 186) local type(s) :: { ( 62^3 ) } Outer automorphisms :: reflexible Dual of E15.1124 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 62 e = 93 f = 3 degree seq :: [ 3^62 ] E15.1124 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {3, 3, 31}) Quotient :: edge Aut^+ = C31 : C3 (small group id <93, 1>) Aut = (C31 : C3) : C2 (small group id <186, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, F * T1 * T2 * F * T1^-1, (T1^-1 * T2^-1)^3, (T2^-1 * T1)^3, (T2^-1 * T1^-1)^3, T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1, T2 * T1^-1 * T2^-5 * T1, (T1^-1 * T2^2 * T1 * F)^2 ] Map:: polytopal non-degenerate R = (1, 94, 3, 96, 9, 102, 25, 118, 42, 135, 18, 111, 31, 124, 56, 149, 85, 178, 75, 168, 41, 134, 70, 163, 62, 155, 86, 179, 93, 186, 74, 167, 79, 172, 92, 185, 89, 182, 59, 152, 76, 169, 46, 139, 78, 171, 88, 181, 58, 151, 28, 121, 20, 113, 44, 137, 37, 130, 15, 108, 5, 98)(2, 95, 6, 99, 17, 110, 40, 133, 61, 154, 30, 123, 13, 106, 33, 126, 66, 159, 90, 183, 60, 153, 67, 160, 35, 128, 53, 146, 83, 176, 87, 180, 91, 184, 82, 175, 52, 145, 24, 117, 51, 144, 63, 156, 81, 174, 50, 143, 23, 116, 8, 101, 22, 115, 48, 141, 47, 140, 21, 114, 7, 100)(4, 97, 11, 104, 29, 122, 57, 150, 27, 120, 10, 103, 19, 112, 43, 136, 77, 170, 55, 148, 26, 119, 49, 142, 45, 138, 73, 166, 84, 177, 54, 147, 69, 162, 80, 173, 72, 165, 39, 132, 65, 158, 36, 129, 68, 161, 71, 164, 38, 131, 16, 109, 14, 107, 34, 127, 64, 157, 32, 125, 12, 105) L = (1, 95)(2, 97)(3, 101)(4, 94)(5, 106)(6, 109)(7, 112)(8, 103)(9, 117)(10, 96)(11, 121)(12, 124)(13, 107)(14, 98)(15, 128)(16, 111)(17, 132)(18, 99)(19, 113)(20, 100)(21, 138)(22, 105)(23, 142)(24, 119)(25, 146)(26, 102)(27, 149)(28, 123)(29, 152)(30, 104)(31, 115)(32, 155)(33, 158)(34, 151)(35, 129)(36, 108)(37, 145)(38, 163)(39, 134)(40, 166)(41, 110)(42, 126)(43, 169)(44, 116)(45, 139)(46, 114)(47, 165)(48, 131)(49, 137)(50, 173)(51, 120)(52, 162)(53, 147)(54, 118)(55, 178)(56, 144)(57, 179)(58, 160)(59, 153)(60, 122)(61, 136)(62, 156)(63, 125)(64, 182)(65, 135)(66, 177)(67, 127)(68, 181)(69, 130)(70, 141)(71, 185)(72, 172)(73, 167)(74, 133)(75, 159)(76, 154)(77, 186)(78, 143)(79, 140)(80, 171)(81, 164)(82, 161)(83, 148)(84, 168)(85, 176)(86, 180)(87, 150)(88, 175)(89, 184)(90, 170)(91, 157)(92, 174)(93, 183) local type(s) :: { ( 3^62 ) } Outer automorphisms :: reflexible Dual of E15.1123 Transitivity :: ET+ VT+ Graph:: v = 3 e = 93 f = 62 degree seq :: [ 62^3 ] E15.1125 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 31}) Quotient :: edge^2 Aut^+ = C31 : C3 (small group id <93, 1>) Aut = (C31 : C3) : C2 (small group id <186, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, Y1^3, Y2 * Y1^-1 * Y3^-1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1, (Y3 * Y1^-1)^3, Y3 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^3, Y2 * Y3^3 * Y1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 94, 4, 97, 15, 108, 40, 133, 24, 117, 26, 119, 11, 104, 32, 125, 70, 163, 58, 151, 60, 153, 63, 156, 35, 128, 72, 165, 90, 183, 91, 184, 92, 185, 93, 186, 75, 168, 47, 140, 66, 159, 68, 161, 87, 180, 85, 178, 48, 141, 19, 112, 30, 123, 50, 143, 57, 150, 23, 116, 7, 100)(2, 95, 8, 101, 25, 118, 59, 152, 44, 137, 46, 139, 21, 114, 52, 145, 88, 181, 82, 175, 83, 176, 84, 177, 55, 148, 42, 135, 71, 164, 73, 166, 76, 169, 81, 174, 43, 136, 17, 110, 33, 126, 36, 129, 74, 167, 51, 144, 20, 113, 6, 99, 12, 105, 34, 127, 69, 162, 31, 124, 10, 103)(3, 96, 5, 98, 18, 111, 45, 138, 38, 131, 14, 107, 16, 109, 29, 122, 65, 158, 77, 170, 39, 132, 41, 134, 49, 142, 67, 160, 61, 154, 78, 171, 79, 172, 80, 173, 86, 179, 62, 155, 27, 120, 53, 146, 56, 149, 89, 182, 64, 157, 28, 121, 9, 102, 22, 115, 54, 147, 37, 130, 13, 106)(187, 188, 191)(189, 197, 198)(190, 192, 202)(193, 207, 208)(194, 195, 212)(196, 215, 216)(199, 221, 222)(200, 218, 219)(201, 203, 227)(204, 205, 232)(206, 235, 236)(209, 241, 242)(210, 238, 239)(211, 213, 246)(214, 249, 220)(217, 253, 254)(223, 261, 262)(224, 258, 259)(225, 256, 257)(226, 228, 265)(229, 266, 243)(230, 251, 252)(231, 233, 269)(234, 270, 240)(237, 272, 273)(244, 274, 264)(245, 247, 277)(248, 278, 255)(250, 279, 260)(263, 276, 268)(267, 275, 271)(280, 282, 285)(281, 286, 288)(283, 293, 296)(284, 289, 298)(287, 303, 306)(290, 292, 312)(291, 305, 307)(294, 318, 321)(295, 299, 309)(297, 323, 326)(300, 302, 332)(301, 325, 327)(304, 337, 340)(308, 310, 345)(311, 317, 350)(313, 339, 341)(314, 316, 352)(315, 342, 343)(319, 357, 331)(320, 322, 329)(324, 361, 351)(328, 330, 347)(333, 362, 354)(334, 336, 358)(335, 363, 364)(338, 369, 344)(346, 348, 370)(349, 356, 367)(353, 371, 365)(355, 372, 368)(359, 360, 366) L = (1, 187)(2, 188)(3, 189)(4, 190)(5, 191)(6, 192)(7, 193)(8, 194)(9, 195)(10, 196)(11, 197)(12, 198)(13, 199)(14, 200)(15, 201)(16, 202)(17, 203)(18, 204)(19, 205)(20, 206)(21, 207)(22, 208)(23, 209)(24, 210)(25, 211)(26, 212)(27, 213)(28, 214)(29, 215)(30, 216)(31, 217)(32, 218)(33, 219)(34, 220)(35, 221)(36, 222)(37, 223)(38, 224)(39, 225)(40, 226)(41, 227)(42, 228)(43, 229)(44, 230)(45, 231)(46, 232)(47, 233)(48, 234)(49, 235)(50, 236)(51, 237)(52, 238)(53, 239)(54, 240)(55, 241)(56, 242)(57, 243)(58, 244)(59, 245)(60, 246)(61, 247)(62, 248)(63, 249)(64, 250)(65, 251)(66, 252)(67, 253)(68, 254)(69, 255)(70, 256)(71, 257)(72, 258)(73, 259)(74, 260)(75, 261)(76, 262)(77, 263)(78, 264)(79, 265)(80, 266)(81, 267)(82, 268)(83, 269)(84, 270)(85, 271)(86, 272)(87, 273)(88, 274)(89, 275)(90, 276)(91, 277)(92, 278)(93, 279)(94, 280)(95, 281)(96, 282)(97, 283)(98, 284)(99, 285)(100, 286)(101, 287)(102, 288)(103, 289)(104, 290)(105, 291)(106, 292)(107, 293)(108, 294)(109, 295)(110, 296)(111, 297)(112, 298)(113, 299)(114, 300)(115, 301)(116, 302)(117, 303)(118, 304)(119, 305)(120, 306)(121, 307)(122, 308)(123, 309)(124, 310)(125, 311)(126, 312)(127, 313)(128, 314)(129, 315)(130, 316)(131, 317)(132, 318)(133, 319)(134, 320)(135, 321)(136, 322)(137, 323)(138, 324)(139, 325)(140, 326)(141, 327)(142, 328)(143, 329)(144, 330)(145, 331)(146, 332)(147, 333)(148, 334)(149, 335)(150, 336)(151, 337)(152, 338)(153, 339)(154, 340)(155, 341)(156, 342)(157, 343)(158, 344)(159, 345)(160, 346)(161, 347)(162, 348)(163, 349)(164, 350)(165, 351)(166, 352)(167, 353)(168, 354)(169, 355)(170, 356)(171, 357)(172, 358)(173, 359)(174, 360)(175, 361)(176, 362)(177, 363)(178, 364)(179, 365)(180, 366)(181, 367)(182, 368)(183, 369)(184, 370)(185, 371)(186, 372) local type(s) :: { ( 4^3 ), ( 4^62 ) } Outer automorphisms :: reflexible Dual of E15.1128 Graph:: simple bipartite v = 65 e = 186 f = 93 degree seq :: [ 3^62, 62^3 ] E15.1126 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 31}) Quotient :: edge^2 Aut^+ = C31 : C3 (small group id <93, 1>) Aut = (C31 : C3) : C2 (small group id <186, 1>) |r| :: 2 Presentation :: [ Y3, R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1^-1)^3, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^31 ] Map:: polytopal R = (1, 94)(2, 95)(3, 96)(4, 97)(5, 98)(6, 99)(7, 100)(8, 101)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 107)(15, 108)(16, 109)(17, 110)(18, 111)(19, 112)(20, 113)(21, 114)(22, 115)(23, 116)(24, 117)(25, 118)(26, 119)(27, 120)(28, 121)(29, 122)(30, 123)(31, 124)(32, 125)(33, 126)(34, 127)(35, 128)(36, 129)(37, 130)(38, 131)(39, 132)(40, 133)(41, 134)(42, 135)(43, 136)(44, 137)(45, 138)(46, 139)(47, 140)(48, 141)(49, 142)(50, 143)(51, 144)(52, 145)(53, 146)(54, 147)(55, 148)(56, 149)(57, 150)(58, 151)(59, 152)(60, 153)(61, 154)(62, 155)(63, 156)(64, 157)(65, 158)(66, 159)(67, 160)(68, 161)(69, 162)(70, 163)(71, 164)(72, 165)(73, 166)(74, 167)(75, 168)(76, 169)(77, 170)(78, 171)(79, 172)(80, 173)(81, 174)(82, 175)(83, 176)(84, 177)(85, 178)(86, 179)(87, 180)(88, 181)(89, 182)(90, 183)(91, 184)(92, 185)(93, 186)(187, 188, 190)(189, 194, 195)(191, 198, 199)(192, 200, 201)(193, 202, 203)(196, 207, 208)(197, 209, 210)(204, 219, 220)(205, 212, 221)(206, 222, 223)(211, 228, 229)(213, 230, 231)(214, 232, 233)(215, 217, 234)(216, 235, 236)(218, 237, 238)(224, 245, 246)(225, 226, 247)(227, 248, 249)(239, 259, 262)(240, 242, 263)(241, 264, 265)(243, 252, 266)(244, 267, 268)(250, 273, 274)(251, 275, 254)(253, 255, 257)(256, 276, 277)(258, 260, 278)(261, 269, 270)(271, 272, 279)(280, 282, 284)(281, 285, 286)(283, 289, 290)(287, 297, 298)(288, 295, 299)(291, 304, 301)(292, 305, 306)(293, 307, 308)(294, 302, 309)(296, 310, 311)(300, 317, 318)(303, 319, 320)(312, 332, 333)(313, 315, 334)(314, 335, 336)(316, 330, 337)(321, 343, 339)(322, 323, 344)(324, 345, 346)(325, 347, 348)(326, 328, 349)(327, 350, 351)(329, 341, 352)(331, 353, 354)(338, 361, 362)(340, 363, 364)(342, 365, 356)(355, 357, 370)(358, 360, 366)(359, 372, 371)(367, 368, 369) L = (1, 187)(2, 188)(3, 189)(4, 190)(5, 191)(6, 192)(7, 193)(8, 194)(9, 195)(10, 196)(11, 197)(12, 198)(13, 199)(14, 200)(15, 201)(16, 202)(17, 203)(18, 204)(19, 205)(20, 206)(21, 207)(22, 208)(23, 209)(24, 210)(25, 211)(26, 212)(27, 213)(28, 214)(29, 215)(30, 216)(31, 217)(32, 218)(33, 219)(34, 220)(35, 221)(36, 222)(37, 223)(38, 224)(39, 225)(40, 226)(41, 227)(42, 228)(43, 229)(44, 230)(45, 231)(46, 232)(47, 233)(48, 234)(49, 235)(50, 236)(51, 237)(52, 238)(53, 239)(54, 240)(55, 241)(56, 242)(57, 243)(58, 244)(59, 245)(60, 246)(61, 247)(62, 248)(63, 249)(64, 250)(65, 251)(66, 252)(67, 253)(68, 254)(69, 255)(70, 256)(71, 257)(72, 258)(73, 259)(74, 260)(75, 261)(76, 262)(77, 263)(78, 264)(79, 265)(80, 266)(81, 267)(82, 268)(83, 269)(84, 270)(85, 271)(86, 272)(87, 273)(88, 274)(89, 275)(90, 276)(91, 277)(92, 278)(93, 279)(94, 280)(95, 281)(96, 282)(97, 283)(98, 284)(99, 285)(100, 286)(101, 287)(102, 288)(103, 289)(104, 290)(105, 291)(106, 292)(107, 293)(108, 294)(109, 295)(110, 296)(111, 297)(112, 298)(113, 299)(114, 300)(115, 301)(116, 302)(117, 303)(118, 304)(119, 305)(120, 306)(121, 307)(122, 308)(123, 309)(124, 310)(125, 311)(126, 312)(127, 313)(128, 314)(129, 315)(130, 316)(131, 317)(132, 318)(133, 319)(134, 320)(135, 321)(136, 322)(137, 323)(138, 324)(139, 325)(140, 326)(141, 327)(142, 328)(143, 329)(144, 330)(145, 331)(146, 332)(147, 333)(148, 334)(149, 335)(150, 336)(151, 337)(152, 338)(153, 339)(154, 340)(155, 341)(156, 342)(157, 343)(158, 344)(159, 345)(160, 346)(161, 347)(162, 348)(163, 349)(164, 350)(165, 351)(166, 352)(167, 353)(168, 354)(169, 355)(170, 356)(171, 357)(172, 358)(173, 359)(174, 360)(175, 361)(176, 362)(177, 363)(178, 364)(179, 365)(180, 366)(181, 367)(182, 368)(183, 369)(184, 370)(185, 371)(186, 372) local type(s) :: { ( 124, 124 ), ( 124^3 ) } Outer automorphisms :: reflexible Dual of E15.1127 Graph:: simple bipartite v = 155 e = 186 f = 3 degree seq :: [ 2^93, 3^62 ] E15.1127 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 31}) Quotient :: loop^2 Aut^+ = C31 : C3 (small group id <93, 1>) Aut = (C31 : C3) : C2 (small group id <186, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, Y1^3, Y2 * Y1^-1 * Y3^-1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1, (Y3 * Y1^-1)^3, Y3 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^3, Y2 * Y3^3 * Y1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 ] Map:: R = (1, 94, 187, 280, 4, 97, 190, 283, 15, 108, 201, 294, 40, 133, 226, 319, 24, 117, 210, 303, 26, 119, 212, 305, 11, 104, 197, 290, 32, 125, 218, 311, 70, 163, 256, 349, 58, 151, 244, 337, 60, 153, 246, 339, 63, 156, 249, 342, 35, 128, 221, 314, 72, 165, 258, 351, 90, 183, 276, 369, 91, 184, 277, 370, 92, 185, 278, 371, 93, 186, 279, 372, 75, 168, 261, 354, 47, 140, 233, 326, 66, 159, 252, 345, 68, 161, 254, 347, 87, 180, 273, 366, 85, 178, 271, 364, 48, 141, 234, 327, 19, 112, 205, 298, 30, 123, 216, 309, 50, 143, 236, 329, 57, 150, 243, 336, 23, 116, 209, 302, 7, 100, 193, 286)(2, 95, 188, 281, 8, 101, 194, 287, 25, 118, 211, 304, 59, 152, 245, 338, 44, 137, 230, 323, 46, 139, 232, 325, 21, 114, 207, 300, 52, 145, 238, 331, 88, 181, 274, 367, 82, 175, 268, 361, 83, 176, 269, 362, 84, 177, 270, 363, 55, 148, 241, 334, 42, 135, 228, 321, 71, 164, 257, 350, 73, 166, 259, 352, 76, 169, 262, 355, 81, 174, 267, 360, 43, 136, 229, 322, 17, 110, 203, 296, 33, 126, 219, 312, 36, 129, 222, 315, 74, 167, 260, 353, 51, 144, 237, 330, 20, 113, 206, 299, 6, 99, 192, 285, 12, 105, 198, 291, 34, 127, 220, 313, 69, 162, 255, 348, 31, 124, 217, 310, 10, 103, 196, 289)(3, 96, 189, 282, 5, 98, 191, 284, 18, 111, 204, 297, 45, 138, 231, 324, 38, 131, 224, 317, 14, 107, 200, 293, 16, 109, 202, 295, 29, 122, 215, 308, 65, 158, 251, 344, 77, 170, 263, 356, 39, 132, 225, 318, 41, 134, 227, 320, 49, 142, 235, 328, 67, 160, 253, 346, 61, 154, 247, 340, 78, 171, 264, 357, 79, 172, 265, 358, 80, 173, 266, 359, 86, 179, 272, 365, 62, 155, 248, 341, 27, 120, 213, 306, 53, 146, 239, 332, 56, 149, 242, 335, 89, 182, 275, 368, 64, 157, 250, 343, 28, 121, 214, 307, 9, 102, 195, 288, 22, 115, 208, 301, 54, 147, 240, 333, 37, 130, 223, 316, 13, 106, 199, 292) L = (1, 95)(2, 98)(3, 104)(4, 99)(5, 94)(6, 109)(7, 114)(8, 102)(9, 119)(10, 122)(11, 105)(12, 96)(13, 128)(14, 125)(15, 110)(16, 97)(17, 134)(18, 112)(19, 139)(20, 142)(21, 115)(22, 100)(23, 148)(24, 145)(25, 120)(26, 101)(27, 153)(28, 156)(29, 123)(30, 103)(31, 160)(32, 126)(33, 107)(34, 121)(35, 129)(36, 106)(37, 168)(38, 165)(39, 163)(40, 135)(41, 108)(42, 172)(43, 173)(44, 158)(45, 140)(46, 111)(47, 176)(48, 177)(49, 143)(50, 113)(51, 179)(52, 146)(53, 117)(54, 141)(55, 149)(56, 116)(57, 136)(58, 181)(59, 154)(60, 118)(61, 184)(62, 185)(63, 127)(64, 186)(65, 159)(66, 137)(67, 161)(68, 124)(69, 155)(70, 164)(71, 132)(72, 166)(73, 131)(74, 157)(75, 169)(76, 130)(77, 183)(78, 151)(79, 133)(80, 150)(81, 182)(82, 170)(83, 138)(84, 147)(85, 174)(86, 180)(87, 144)(88, 171)(89, 178)(90, 175)(91, 152)(92, 162)(93, 167)(187, 282)(188, 286)(189, 285)(190, 293)(191, 289)(192, 280)(193, 288)(194, 303)(195, 281)(196, 298)(197, 292)(198, 305)(199, 312)(200, 296)(201, 318)(202, 299)(203, 283)(204, 323)(205, 284)(206, 309)(207, 302)(208, 325)(209, 332)(210, 306)(211, 337)(212, 307)(213, 287)(214, 291)(215, 310)(216, 295)(217, 345)(218, 317)(219, 290)(220, 339)(221, 316)(222, 342)(223, 352)(224, 350)(225, 321)(226, 357)(227, 322)(228, 294)(229, 329)(230, 326)(231, 361)(232, 327)(233, 297)(234, 301)(235, 330)(236, 320)(237, 347)(238, 319)(239, 300)(240, 362)(241, 336)(242, 363)(243, 358)(244, 340)(245, 369)(246, 341)(247, 304)(248, 313)(249, 343)(250, 315)(251, 338)(252, 308)(253, 348)(254, 328)(255, 370)(256, 356)(257, 311)(258, 324)(259, 314)(260, 371)(261, 333)(262, 372)(263, 367)(264, 331)(265, 334)(266, 360)(267, 366)(268, 351)(269, 354)(270, 364)(271, 335)(272, 353)(273, 359)(274, 349)(275, 355)(276, 344)(277, 346)(278, 365)(279, 368) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E15.1126 Transitivity :: VT+ Graph:: v = 3 e = 186 f = 155 degree seq :: [ 124^3 ] E15.1128 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 31}) Quotient :: loop^2 Aut^+ = C31 : C3 (small group id <93, 1>) Aut = (C31 : C3) : C2 (small group id <186, 1>) |r| :: 2 Presentation :: [ Y3, R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1^-1)^3, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^31 ] Map:: polytopal non-degenerate R = (1, 94, 187, 280)(2, 95, 188, 281)(3, 96, 189, 282)(4, 97, 190, 283)(5, 98, 191, 284)(6, 99, 192, 285)(7, 100, 193, 286)(8, 101, 194, 287)(9, 102, 195, 288)(10, 103, 196, 289)(11, 104, 197, 290)(12, 105, 198, 291)(13, 106, 199, 292)(14, 107, 200, 293)(15, 108, 201, 294)(16, 109, 202, 295)(17, 110, 203, 296)(18, 111, 204, 297)(19, 112, 205, 298)(20, 113, 206, 299)(21, 114, 207, 300)(22, 115, 208, 301)(23, 116, 209, 302)(24, 117, 210, 303)(25, 118, 211, 304)(26, 119, 212, 305)(27, 120, 213, 306)(28, 121, 214, 307)(29, 122, 215, 308)(30, 123, 216, 309)(31, 124, 217, 310)(32, 125, 218, 311)(33, 126, 219, 312)(34, 127, 220, 313)(35, 128, 221, 314)(36, 129, 222, 315)(37, 130, 223, 316)(38, 131, 224, 317)(39, 132, 225, 318)(40, 133, 226, 319)(41, 134, 227, 320)(42, 135, 228, 321)(43, 136, 229, 322)(44, 137, 230, 323)(45, 138, 231, 324)(46, 139, 232, 325)(47, 140, 233, 326)(48, 141, 234, 327)(49, 142, 235, 328)(50, 143, 236, 329)(51, 144, 237, 330)(52, 145, 238, 331)(53, 146, 239, 332)(54, 147, 240, 333)(55, 148, 241, 334)(56, 149, 242, 335)(57, 150, 243, 336)(58, 151, 244, 337)(59, 152, 245, 338)(60, 153, 246, 339)(61, 154, 247, 340)(62, 155, 248, 341)(63, 156, 249, 342)(64, 157, 250, 343)(65, 158, 251, 344)(66, 159, 252, 345)(67, 160, 253, 346)(68, 161, 254, 347)(69, 162, 255, 348)(70, 163, 256, 349)(71, 164, 257, 350)(72, 165, 258, 351)(73, 166, 259, 352)(74, 167, 260, 353)(75, 168, 261, 354)(76, 169, 262, 355)(77, 170, 263, 356)(78, 171, 264, 357)(79, 172, 265, 358)(80, 173, 266, 359)(81, 174, 267, 360)(82, 175, 268, 361)(83, 176, 269, 362)(84, 177, 270, 363)(85, 178, 271, 364)(86, 179, 272, 365)(87, 180, 273, 366)(88, 181, 274, 367)(89, 182, 275, 368)(90, 183, 276, 369)(91, 184, 277, 370)(92, 185, 278, 371)(93, 186, 279, 372) L = (1, 95)(2, 97)(3, 101)(4, 94)(5, 105)(6, 107)(7, 109)(8, 102)(9, 96)(10, 114)(11, 116)(12, 106)(13, 98)(14, 108)(15, 99)(16, 110)(17, 100)(18, 126)(19, 119)(20, 129)(21, 115)(22, 103)(23, 117)(24, 104)(25, 135)(26, 128)(27, 137)(28, 139)(29, 124)(30, 142)(31, 141)(32, 144)(33, 127)(34, 111)(35, 112)(36, 130)(37, 113)(38, 152)(39, 133)(40, 154)(41, 155)(42, 136)(43, 118)(44, 138)(45, 120)(46, 140)(47, 121)(48, 122)(49, 143)(50, 123)(51, 145)(52, 125)(53, 166)(54, 149)(55, 171)(56, 170)(57, 159)(58, 174)(59, 153)(60, 131)(61, 132)(62, 156)(63, 134)(64, 180)(65, 182)(66, 173)(67, 162)(68, 158)(69, 164)(70, 183)(71, 160)(72, 167)(73, 169)(74, 185)(75, 176)(76, 146)(77, 147)(78, 172)(79, 148)(80, 150)(81, 175)(82, 151)(83, 177)(84, 168)(85, 179)(86, 186)(87, 181)(88, 157)(89, 161)(90, 184)(91, 163)(92, 165)(93, 178)(187, 282)(188, 285)(189, 284)(190, 289)(191, 280)(192, 286)(193, 281)(194, 297)(195, 295)(196, 290)(197, 283)(198, 304)(199, 305)(200, 307)(201, 302)(202, 299)(203, 310)(204, 298)(205, 287)(206, 288)(207, 317)(208, 291)(209, 309)(210, 319)(211, 301)(212, 306)(213, 292)(214, 308)(215, 293)(216, 294)(217, 311)(218, 296)(219, 332)(220, 315)(221, 335)(222, 334)(223, 330)(224, 318)(225, 300)(226, 320)(227, 303)(228, 343)(229, 323)(230, 344)(231, 345)(232, 347)(233, 328)(234, 350)(235, 349)(236, 341)(237, 337)(238, 353)(239, 333)(240, 312)(241, 313)(242, 336)(243, 314)(244, 316)(245, 361)(246, 321)(247, 363)(248, 352)(249, 365)(250, 339)(251, 322)(252, 346)(253, 324)(254, 348)(255, 325)(256, 326)(257, 351)(258, 327)(259, 329)(260, 354)(261, 331)(262, 357)(263, 342)(264, 370)(265, 360)(266, 372)(267, 366)(268, 362)(269, 338)(270, 364)(271, 340)(272, 356)(273, 358)(274, 368)(275, 369)(276, 367)(277, 355)(278, 359)(279, 371) local type(s) :: { ( 3, 62, 3, 62 ) } Outer automorphisms :: reflexible Dual of E15.1125 Transitivity :: VT+ Graph:: simple v = 93 e = 186 f = 65 degree seq :: [ 4^93 ] E15.1129 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 8}) Quotient :: edge Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T1 * T2^-2)^3, (T2^-2 * T1 * T2^-1 * T1^-1)^2, (T2 * T1 * T2^-2 * T1^-1)^2, (T2^-1 * T1 * T2^-1 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 27, 12)(8, 20, 46, 21)(10, 24, 55, 25)(13, 31, 65, 32)(14, 33, 69, 34)(15, 35, 71, 36)(17, 39, 75, 40)(18, 41, 77, 42)(19, 43, 79, 44)(22, 50, 60, 51)(23, 52, 37, 53)(26, 57, 88, 58)(28, 45, 81, 61)(29, 62, 87, 63)(30, 48, 84, 64)(38, 72, 59, 73)(47, 82, 67, 83)(49, 85, 66, 86)(54, 89, 70, 90)(56, 91, 68, 92)(74, 93, 80, 94)(76, 95, 78, 96)(97, 98, 100)(99, 104, 106)(101, 109, 110)(102, 111, 113)(103, 114, 115)(105, 118, 119)(107, 122, 124)(108, 125, 126)(112, 133, 134)(116, 141, 143)(117, 144, 145)(120, 150, 131)(121, 152, 137)(123, 155, 156)(127, 157, 162)(128, 160, 163)(129, 164, 132)(130, 166, 138)(135, 170, 153)(136, 172, 158)(139, 174, 154)(140, 176, 159)(142, 165, 169)(146, 167, 175)(147, 173, 171)(148, 183, 177)(149, 184, 180)(151, 168, 161)(178, 189, 185)(179, 192, 187)(181, 191, 186)(182, 190, 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) :: { ( 16^3 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E15.1133 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 3^32, 4^24 ] E15.1130 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 8}) Quotient :: edge Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T1 * T2^-1)^3, (T1^-1 * T2^-1)^3, T1 * T2^-1 * T1^-1 * T2^3 * T1^-1 * T2^-1, T1^-1 * T2^-1 * T1^-2 * T2^-3 * T1^-1, T2^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 29, 67, 42, 16, 5)(2, 7, 20, 52, 84, 60, 24, 8)(4, 12, 33, 55, 79, 49, 36, 13)(6, 17, 44, 37, 61, 25, 48, 18)(9, 26, 62, 75, 43, 23, 57, 27)(11, 22, 56, 76, 45, 35, 70, 31)(14, 38, 54, 21, 46, 77, 72, 34)(15, 39, 71, 32, 47, 78, 50, 19)(28, 65, 91, 73, 41, 64, 90, 66)(30, 63, 89, 74, 40, 69, 92, 68)(51, 82, 95, 87, 59, 81, 94, 83)(53, 80, 93, 88, 58, 86, 96, 85)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 133, 111)(103, 115, 145, 117)(104, 118, 151, 119)(106, 124, 140, 126)(108, 128, 156, 130)(109, 131, 148, 122)(112, 136, 144, 137)(113, 139, 138, 141)(114, 142, 125, 143)(116, 147, 129, 149)(120, 154, 132, 155)(123, 159, 172, 160)(127, 165, 171, 161)(134, 169, 174, 164)(135, 162, 173, 170)(146, 176, 168, 177)(150, 182, 167, 178)(152, 183, 158, 181)(153, 179, 166, 184)(157, 180, 163, 175)(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) :: { ( 6^4 ), ( 6^8 ) } Outer automorphisms :: reflexible Dual of E15.1134 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.1131 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 8}) Quotient :: edge Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1 * T2 * T1^-2 * T2, (T2 * T1^-3)^2, (T2^-1 * T1^-1)^4, T1^8, (T1^-1 * T2 * T1^-2)^2, T2 * T1^-1 * T2 * T1^-1 * T2^2 * T1^2 * T2, (T1^2 * T2)^3, (T2 * T1^2 * T2 * T1^-1)^2 ] 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, 43, 44)(19, 49, 50)(20, 51, 52)(21, 36, 54)(22, 29, 56)(23, 58, 59)(27, 30, 65)(32, 68, 69)(34, 72, 73)(35, 74, 60)(40, 64, 80)(42, 76, 66)(45, 82, 83)(46, 84, 70)(47, 53, 85)(48, 75, 87)(55, 90, 92)(57, 89, 79)(61, 93, 81)(62, 63, 94)(67, 95, 91)(71, 96, 88)(77, 78, 86)(97, 98, 102, 112, 138, 128, 108, 100)(99, 105, 119, 153, 146, 140, 123, 106)(101, 110, 132, 164, 170, 175, 136, 111)(103, 115, 144, 182, 179, 162, 124, 116)(104, 117, 149, 127, 135, 174, 151, 118)(107, 125, 163, 158, 121, 114, 143, 126)(109, 130, 133, 172, 192, 190, 171, 131)(113, 141, 176, 191, 189, 165, 148, 142)(120, 156, 178, 152, 184, 145, 137, 157)(122, 159, 180, 173, 134, 155, 181, 160)(129, 166, 168, 139, 177, 188, 154, 167)(147, 185, 169, 187, 150, 183, 161, 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) :: { ( 8^3 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E15.1132 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 96 f = 24 degree seq :: [ 3^32, 8^12 ] E15.1132 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 8}) Quotient :: loop Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T1 * T2^-2)^3, (T2^-2 * T1 * T2^-1 * T1^-1)^2, (T2 * T1 * T2^-2 * T1^-1)^2, (T2^-1 * T1 * T2^-1 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 9, 105, 5, 101)(2, 98, 6, 102, 16, 112, 7, 103)(4, 100, 11, 107, 27, 123, 12, 108)(8, 104, 20, 116, 46, 142, 21, 117)(10, 106, 24, 120, 55, 151, 25, 121)(13, 109, 31, 127, 65, 161, 32, 128)(14, 110, 33, 129, 69, 165, 34, 130)(15, 111, 35, 131, 71, 167, 36, 132)(17, 113, 39, 135, 75, 171, 40, 136)(18, 114, 41, 137, 77, 173, 42, 138)(19, 115, 43, 139, 79, 175, 44, 140)(22, 118, 50, 146, 60, 156, 51, 147)(23, 119, 52, 148, 37, 133, 53, 149)(26, 122, 57, 153, 88, 184, 58, 154)(28, 124, 45, 141, 81, 177, 61, 157)(29, 125, 62, 158, 87, 183, 63, 159)(30, 126, 48, 144, 84, 180, 64, 160)(38, 134, 72, 168, 59, 155, 73, 169)(47, 143, 82, 178, 67, 163, 83, 179)(49, 145, 85, 181, 66, 162, 86, 182)(54, 150, 89, 185, 70, 166, 90, 186)(56, 152, 91, 187, 68, 164, 92, 188)(74, 170, 93, 189, 80, 176, 94, 190)(76, 172, 95, 191, 78, 174, 96, 192) L = (1, 98)(2, 100)(3, 104)(4, 97)(5, 109)(6, 111)(7, 114)(8, 106)(9, 118)(10, 99)(11, 122)(12, 125)(13, 110)(14, 101)(15, 113)(16, 133)(17, 102)(18, 115)(19, 103)(20, 141)(21, 144)(22, 119)(23, 105)(24, 150)(25, 152)(26, 124)(27, 155)(28, 107)(29, 126)(30, 108)(31, 157)(32, 160)(33, 164)(34, 166)(35, 120)(36, 129)(37, 134)(38, 112)(39, 170)(40, 172)(41, 121)(42, 130)(43, 174)(44, 176)(45, 143)(46, 165)(47, 116)(48, 145)(49, 117)(50, 167)(51, 173)(52, 183)(53, 184)(54, 131)(55, 168)(56, 137)(57, 135)(58, 139)(59, 156)(60, 123)(61, 162)(62, 136)(63, 140)(64, 163)(65, 151)(66, 127)(67, 128)(68, 132)(69, 169)(70, 138)(71, 175)(72, 161)(73, 142)(74, 153)(75, 147)(76, 158)(77, 171)(78, 154)(79, 146)(80, 159)(81, 148)(82, 189)(83, 192)(84, 149)(85, 191)(86, 190)(87, 177)(88, 180)(89, 178)(90, 181)(91, 179)(92, 182)(93, 185)(94, 188)(95, 186)(96, 187) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E15.1131 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 96 f = 44 degree seq :: [ 8^24 ] E15.1133 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 8}) Quotient :: loop Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T1 * T2^-1)^3, (T1^-1 * T2^-1)^3, T1 * T2^-1 * T1^-1 * T2^3 * T1^-1 * T2^-1, T1^-1 * T2^-1 * T1^-2 * T2^-3 * T1^-1, T2^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 29, 125, 67, 163, 42, 138, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 52, 148, 84, 180, 60, 156, 24, 120, 8, 104)(4, 100, 12, 108, 33, 129, 55, 151, 79, 175, 49, 145, 36, 132, 13, 109)(6, 102, 17, 113, 44, 140, 37, 133, 61, 157, 25, 121, 48, 144, 18, 114)(9, 105, 26, 122, 62, 158, 75, 171, 43, 139, 23, 119, 57, 153, 27, 123)(11, 107, 22, 118, 56, 152, 76, 172, 45, 141, 35, 131, 70, 166, 31, 127)(14, 110, 38, 134, 54, 150, 21, 117, 46, 142, 77, 173, 72, 168, 34, 130)(15, 111, 39, 135, 71, 167, 32, 128, 47, 143, 78, 174, 50, 146, 19, 115)(28, 124, 65, 161, 91, 187, 73, 169, 41, 137, 64, 160, 90, 186, 66, 162)(30, 126, 63, 159, 89, 185, 74, 170, 40, 136, 69, 165, 92, 188, 68, 164)(51, 147, 82, 178, 95, 191, 87, 183, 59, 155, 81, 177, 94, 190, 83, 179)(53, 149, 80, 176, 93, 189, 88, 184, 58, 154, 86, 182, 96, 192, 85, 181) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 124)(11, 99)(12, 128)(13, 131)(14, 133)(15, 101)(16, 136)(17, 139)(18, 142)(19, 145)(20, 147)(21, 103)(22, 151)(23, 104)(24, 154)(25, 107)(26, 109)(27, 159)(28, 140)(29, 143)(30, 106)(31, 165)(32, 156)(33, 149)(34, 108)(35, 148)(36, 155)(37, 111)(38, 169)(39, 162)(40, 144)(41, 112)(42, 141)(43, 138)(44, 126)(45, 113)(46, 125)(47, 114)(48, 137)(49, 117)(50, 176)(51, 129)(52, 122)(53, 116)(54, 182)(55, 119)(56, 183)(57, 179)(58, 132)(59, 120)(60, 130)(61, 180)(62, 181)(63, 172)(64, 123)(65, 127)(66, 173)(67, 175)(68, 134)(69, 171)(70, 184)(71, 178)(72, 177)(73, 174)(74, 135)(75, 161)(76, 160)(77, 170)(78, 164)(79, 157)(80, 168)(81, 146)(82, 150)(83, 166)(84, 163)(85, 152)(86, 167)(87, 158)(88, 153)(89, 189)(90, 192)(91, 191)(92, 190)(93, 187)(94, 186)(95, 185)(96, 188) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E15.1129 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1134 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 8}) Quotient :: loop Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1 * T2 * T1^-2 * T2, (T2 * T1^-3)^2, (T2^-1 * T1^-1)^4, T1^8, (T1^-1 * T2 * T1^-2)^2, T2 * T1^-1 * T2 * T1^-1 * T2^2 * T1^2 * T2, (T1^2 * T2)^3, (T2 * T1^2 * T2 * T1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 5, 101)(2, 98, 7, 103, 8, 104)(4, 100, 11, 107, 13, 109)(6, 102, 17, 113, 18, 114)(9, 105, 24, 120, 25, 121)(10, 106, 26, 122, 28, 124)(12, 108, 31, 127, 33, 129)(14, 110, 37, 133, 38, 134)(15, 111, 39, 135, 41, 137)(16, 112, 43, 139, 44, 140)(19, 115, 49, 145, 50, 146)(20, 116, 51, 147, 52, 148)(21, 117, 36, 132, 54, 150)(22, 118, 29, 125, 56, 152)(23, 119, 58, 154, 59, 155)(27, 123, 30, 126, 65, 161)(32, 128, 68, 164, 69, 165)(34, 130, 72, 168, 73, 169)(35, 131, 74, 170, 60, 156)(40, 136, 64, 160, 80, 176)(42, 138, 76, 172, 66, 162)(45, 141, 82, 178, 83, 179)(46, 142, 84, 180, 70, 166)(47, 143, 53, 149, 85, 181)(48, 144, 75, 171, 87, 183)(55, 151, 90, 186, 92, 188)(57, 153, 89, 185, 79, 175)(61, 157, 93, 189, 81, 177)(62, 158, 63, 159, 94, 190)(67, 163, 95, 191, 91, 187)(71, 167, 96, 192, 88, 184)(77, 173, 78, 174, 86, 182) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 115)(8, 117)(9, 119)(10, 99)(11, 125)(12, 100)(13, 130)(14, 132)(15, 101)(16, 138)(17, 141)(18, 143)(19, 144)(20, 103)(21, 149)(22, 104)(23, 153)(24, 156)(25, 114)(26, 159)(27, 106)(28, 116)(29, 163)(30, 107)(31, 135)(32, 108)(33, 166)(34, 133)(35, 109)(36, 164)(37, 172)(38, 155)(39, 174)(40, 111)(41, 157)(42, 128)(43, 177)(44, 123)(45, 176)(46, 113)(47, 126)(48, 182)(49, 137)(50, 140)(51, 185)(52, 142)(53, 127)(54, 183)(55, 118)(56, 184)(57, 146)(58, 167)(59, 181)(60, 178)(61, 120)(62, 121)(63, 180)(64, 122)(65, 186)(66, 124)(67, 158)(68, 170)(69, 148)(70, 168)(71, 129)(72, 139)(73, 187)(74, 175)(75, 131)(76, 192)(77, 134)(78, 151)(79, 136)(80, 191)(81, 188)(82, 152)(83, 162)(84, 173)(85, 160)(86, 179)(87, 161)(88, 145)(89, 169)(90, 147)(91, 150)(92, 154)(93, 165)(94, 171)(95, 189)(96, 190) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1130 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 6^32 ] E15.1135 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (R * Y2^-1 * Y3^-1)^2, Y2^-1 * Y1 * R * Y2^2 * Y1 * R * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1 * Y2^-2 * Y1 * Y2^-2 * Y3^-1 * Y2^-2, Y2^-1 * Y3 * Y2 * Y1 * Y2^-2 * Y1^-1 * Y2 * Y3^-1 * Y2^-1, Y2 * Y1 * Y2^-2 * Y3 * Y2 * Y3^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y2^-1 * Y1)^8 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 13, 109, 14, 110)(6, 102, 15, 111, 17, 113)(7, 103, 18, 114, 19, 115)(9, 105, 22, 118, 23, 119)(11, 107, 26, 122, 28, 124)(12, 108, 29, 125, 30, 126)(16, 112, 37, 133, 38, 134)(20, 116, 45, 141, 47, 143)(21, 117, 48, 144, 49, 145)(24, 120, 54, 150, 35, 131)(25, 121, 56, 152, 41, 137)(27, 123, 59, 155, 60, 156)(31, 127, 61, 157, 66, 162)(32, 128, 64, 160, 67, 163)(33, 129, 68, 164, 36, 132)(34, 130, 70, 166, 42, 138)(39, 135, 74, 170, 57, 153)(40, 136, 76, 172, 62, 158)(43, 139, 78, 174, 58, 154)(44, 140, 80, 176, 63, 159)(46, 142, 69, 165, 73, 169)(50, 146, 71, 167, 79, 175)(51, 147, 77, 173, 75, 171)(52, 148, 87, 183, 81, 177)(53, 149, 88, 184, 84, 180)(55, 151, 72, 168, 65, 161)(82, 178, 93, 189, 89, 185)(83, 179, 96, 192, 91, 187)(85, 181, 95, 191, 90, 186)(86, 182, 94, 190, 92, 188)(193, 289, 195, 291, 201, 297, 197, 293)(194, 290, 198, 294, 208, 304, 199, 295)(196, 292, 203, 299, 219, 315, 204, 300)(200, 296, 212, 308, 238, 334, 213, 309)(202, 298, 216, 312, 247, 343, 217, 313)(205, 301, 223, 319, 257, 353, 224, 320)(206, 302, 225, 321, 261, 357, 226, 322)(207, 303, 227, 323, 263, 359, 228, 324)(209, 305, 231, 327, 267, 363, 232, 328)(210, 306, 233, 329, 269, 365, 234, 330)(211, 307, 235, 331, 271, 367, 236, 332)(214, 310, 242, 338, 252, 348, 243, 339)(215, 311, 244, 340, 229, 325, 245, 341)(218, 314, 249, 345, 280, 376, 250, 346)(220, 316, 237, 333, 273, 369, 253, 349)(221, 317, 254, 350, 279, 375, 255, 351)(222, 318, 240, 336, 276, 372, 256, 352)(230, 326, 264, 360, 251, 347, 265, 361)(239, 335, 274, 370, 259, 355, 275, 371)(241, 337, 277, 373, 258, 354, 278, 374)(246, 342, 281, 377, 262, 358, 282, 378)(248, 344, 283, 379, 260, 356, 284, 380)(266, 362, 285, 381, 272, 368, 286, 382)(268, 364, 287, 383, 270, 366, 288, 384) L = (1, 196)(2, 193)(3, 202)(4, 194)(5, 206)(6, 209)(7, 211)(8, 195)(9, 215)(10, 200)(11, 220)(12, 222)(13, 197)(14, 205)(15, 198)(16, 230)(17, 207)(18, 199)(19, 210)(20, 239)(21, 241)(22, 201)(23, 214)(24, 227)(25, 233)(26, 203)(27, 252)(28, 218)(29, 204)(30, 221)(31, 258)(32, 259)(33, 228)(34, 234)(35, 246)(36, 260)(37, 208)(38, 229)(39, 249)(40, 254)(41, 248)(42, 262)(43, 250)(44, 255)(45, 212)(46, 265)(47, 237)(48, 213)(49, 240)(50, 271)(51, 267)(52, 273)(53, 276)(54, 216)(55, 257)(56, 217)(57, 266)(58, 270)(59, 219)(60, 251)(61, 223)(62, 268)(63, 272)(64, 224)(65, 264)(66, 253)(67, 256)(68, 225)(69, 238)(70, 226)(71, 242)(72, 247)(73, 261)(74, 231)(75, 269)(76, 232)(77, 243)(78, 235)(79, 263)(80, 236)(81, 279)(82, 281)(83, 283)(84, 280)(85, 282)(86, 284)(87, 244)(88, 245)(89, 285)(90, 287)(91, 288)(92, 286)(93, 274)(94, 278)(95, 277)(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, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E15.1138 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 6^32, 8^24 ] E15.1136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2^-1)^3, (Y1^-1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, Y1^-1 * Y2^-1 * Y1^-2 * Y2^-3 * Y1^-1, Y1 * Y2^-1 * Y1^-1 * Y2^3 * Y1^-1 * Y2^-1, Y2^8 ] 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, 49, 145, 21, 117)(8, 104, 22, 118, 55, 151, 23, 119)(10, 106, 28, 124, 44, 140, 30, 126)(12, 108, 32, 128, 60, 156, 34, 130)(13, 109, 35, 131, 52, 148, 26, 122)(16, 112, 40, 136, 48, 144, 41, 137)(17, 113, 43, 139, 42, 138, 45, 141)(18, 114, 46, 142, 29, 125, 47, 143)(20, 116, 51, 147, 33, 129, 53, 149)(24, 120, 58, 154, 36, 132, 59, 155)(27, 123, 63, 159, 76, 172, 64, 160)(31, 127, 69, 165, 75, 171, 65, 161)(38, 134, 73, 169, 78, 174, 68, 164)(39, 135, 66, 162, 77, 173, 74, 170)(50, 146, 80, 176, 72, 168, 81, 177)(54, 150, 86, 182, 71, 167, 82, 178)(56, 152, 87, 183, 62, 158, 85, 181)(57, 153, 83, 179, 70, 166, 88, 184)(61, 157, 84, 180, 67, 163, 79, 175)(89, 185, 93, 189, 91, 187, 95, 191)(90, 186, 96, 192, 92, 188, 94, 190)(193, 289, 195, 291, 202, 298, 221, 317, 259, 355, 234, 330, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 244, 340, 276, 372, 252, 348, 216, 312, 200, 296)(196, 292, 204, 300, 225, 321, 247, 343, 271, 367, 241, 337, 228, 324, 205, 301)(198, 294, 209, 305, 236, 332, 229, 325, 253, 349, 217, 313, 240, 336, 210, 306)(201, 297, 218, 314, 254, 350, 267, 363, 235, 331, 215, 311, 249, 345, 219, 315)(203, 299, 214, 310, 248, 344, 268, 364, 237, 333, 227, 323, 262, 358, 223, 319)(206, 302, 230, 326, 246, 342, 213, 309, 238, 334, 269, 365, 264, 360, 226, 322)(207, 303, 231, 327, 263, 359, 224, 320, 239, 335, 270, 366, 242, 338, 211, 307)(220, 316, 257, 353, 283, 379, 265, 361, 233, 329, 256, 352, 282, 378, 258, 354)(222, 318, 255, 351, 281, 377, 266, 362, 232, 328, 261, 357, 284, 380, 260, 356)(243, 339, 274, 370, 287, 383, 279, 375, 251, 347, 273, 369, 286, 382, 275, 371)(245, 341, 272, 368, 285, 381, 280, 376, 250, 346, 278, 374, 288, 384, 277, 373) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 221)(11, 214)(12, 225)(13, 196)(14, 230)(15, 231)(16, 197)(17, 236)(18, 198)(19, 207)(20, 244)(21, 238)(22, 248)(23, 249)(24, 200)(25, 240)(26, 254)(27, 201)(28, 257)(29, 259)(30, 255)(31, 203)(32, 239)(33, 247)(34, 206)(35, 262)(36, 205)(37, 253)(38, 246)(39, 263)(40, 261)(41, 256)(42, 208)(43, 215)(44, 229)(45, 227)(46, 269)(47, 270)(48, 210)(49, 228)(50, 211)(51, 274)(52, 276)(53, 272)(54, 213)(55, 271)(56, 268)(57, 219)(58, 278)(59, 273)(60, 216)(61, 217)(62, 267)(63, 281)(64, 282)(65, 283)(66, 220)(67, 234)(68, 222)(69, 284)(70, 223)(71, 224)(72, 226)(73, 233)(74, 232)(75, 235)(76, 237)(77, 264)(78, 242)(79, 241)(80, 285)(81, 286)(82, 287)(83, 243)(84, 252)(85, 245)(86, 288)(87, 251)(88, 250)(89, 266)(90, 258)(91, 265)(92, 260)(93, 280)(94, 275)(95, 279)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E15.1137 Graph:: bipartite v = 36 e = 192 f = 128 degree seq :: [ 8^24, 16^12 ] E15.1137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^2 * Y2, (Y3 * Y2^-1)^4, (Y2 * Y3^3)^2, (Y2^-1 * Y3^2)^3, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-4, (Y3^2 * Y2^-1 * Y3^-1 * Y2^-1)^2, (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, 196, 292)(195, 291, 200, 296, 202, 298)(197, 293, 205, 301, 206, 302)(198, 294, 208, 304, 210, 306)(199, 295, 211, 307, 212, 308)(201, 297, 216, 312, 218, 314)(203, 299, 221, 317, 223, 319)(204, 300, 224, 320, 225, 321)(207, 303, 231, 327, 232, 328)(209, 305, 214, 310, 237, 333)(213, 309, 242, 338, 243, 339)(215, 311, 246, 342, 229, 325)(217, 313, 249, 345, 251, 347)(219, 315, 254, 350, 240, 336)(220, 316, 256, 352, 257, 353)(222, 318, 234, 330, 260, 356)(226, 322, 264, 360, 230, 326)(227, 323, 265, 361, 266, 362)(228, 324, 261, 357, 267, 363)(233, 329, 272, 368, 236, 332)(235, 331, 274, 370, 241, 337)(238, 334, 250, 346, 262, 358)(239, 335, 279, 375, 280, 376)(244, 340, 283, 379, 259, 355)(245, 341, 248, 344, 273, 369)(247, 343, 285, 381, 286, 382)(252, 348, 287, 383, 284, 380)(253, 349, 270, 366, 275, 371)(255, 351, 276, 372, 268, 364)(258, 354, 288, 384, 263, 359)(269, 365, 277, 373, 282, 378)(271, 367, 281, 377, 278, 374) L = (1, 195)(2, 198)(3, 201)(4, 203)(5, 193)(6, 209)(7, 194)(8, 214)(9, 217)(10, 219)(11, 222)(12, 196)(13, 227)(14, 229)(15, 197)(16, 234)(17, 236)(18, 238)(19, 239)(20, 241)(21, 199)(22, 245)(23, 200)(24, 248)(25, 250)(26, 252)(27, 255)(28, 202)(29, 216)(30, 259)(31, 261)(32, 220)(33, 263)(34, 204)(35, 210)(36, 205)(37, 269)(38, 206)(39, 270)(40, 212)(41, 207)(42, 273)(43, 208)(44, 267)(45, 276)(46, 278)(47, 223)(48, 211)(49, 247)(50, 282)(51, 225)(52, 213)(53, 232)(54, 281)(55, 215)(56, 230)(57, 226)(58, 233)(59, 279)(60, 242)(61, 218)(62, 249)(63, 274)(64, 253)(65, 283)(66, 221)(67, 254)(68, 271)(69, 284)(70, 224)(71, 275)(72, 286)(73, 277)(74, 251)(75, 244)(76, 228)(77, 258)(78, 266)(79, 231)(80, 256)(81, 243)(82, 287)(83, 235)(84, 264)(85, 237)(86, 288)(87, 285)(88, 272)(89, 240)(90, 280)(91, 265)(92, 246)(93, 260)(94, 257)(95, 262)(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, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.1136 Graph:: simple bipartite v = 128 e = 192 f = 36 degree seq :: [ 2^96, 6^32 ] E15.1138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^2 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y1^-3)^2, Y1^8, (Y3^-1 * Y1^-1)^4, (Y1^-1 * Y3 * Y1^-2)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^2 * Y3, (Y1^2 * Y3)^3, (Y3 * Y1^2 * Y3 * Y1^-1)^2 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 16, 112, 42, 138, 32, 128, 12, 108, 4, 100)(3, 99, 9, 105, 23, 119, 57, 153, 50, 146, 44, 140, 27, 123, 10, 106)(5, 101, 14, 110, 36, 132, 68, 164, 74, 170, 79, 175, 40, 136, 15, 111)(7, 103, 19, 115, 48, 144, 86, 182, 83, 179, 66, 162, 28, 124, 20, 116)(8, 104, 21, 117, 53, 149, 31, 127, 39, 135, 78, 174, 55, 151, 22, 118)(11, 107, 29, 125, 67, 163, 62, 158, 25, 121, 18, 114, 47, 143, 30, 126)(13, 109, 34, 130, 37, 133, 76, 172, 96, 192, 94, 190, 75, 171, 35, 131)(17, 113, 45, 141, 80, 176, 95, 191, 93, 189, 69, 165, 52, 148, 46, 142)(24, 120, 60, 156, 82, 178, 56, 152, 88, 184, 49, 145, 41, 137, 61, 157)(26, 122, 63, 159, 84, 180, 77, 173, 38, 134, 59, 155, 85, 181, 64, 160)(33, 129, 70, 166, 72, 168, 43, 139, 81, 177, 92, 188, 58, 154, 71, 167)(51, 147, 89, 185, 73, 169, 91, 187, 54, 150, 87, 183, 65, 161, 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, 197)(4, 203)(5, 193)(6, 209)(7, 200)(8, 194)(9, 216)(10, 218)(11, 205)(12, 223)(13, 196)(14, 229)(15, 231)(16, 235)(17, 210)(18, 198)(19, 241)(20, 243)(21, 228)(22, 221)(23, 250)(24, 217)(25, 201)(26, 220)(27, 222)(28, 202)(29, 248)(30, 257)(31, 225)(32, 260)(33, 204)(34, 264)(35, 266)(36, 246)(37, 230)(38, 206)(39, 233)(40, 256)(41, 207)(42, 268)(43, 236)(44, 208)(45, 274)(46, 276)(47, 245)(48, 267)(49, 242)(50, 211)(51, 244)(52, 212)(53, 277)(54, 213)(55, 282)(56, 214)(57, 281)(58, 251)(59, 215)(60, 227)(61, 285)(62, 255)(63, 286)(64, 272)(65, 219)(66, 234)(67, 287)(68, 261)(69, 224)(70, 238)(71, 288)(72, 265)(73, 226)(74, 252)(75, 279)(76, 258)(77, 270)(78, 278)(79, 249)(80, 232)(81, 253)(82, 275)(83, 237)(84, 262)(85, 239)(86, 269)(87, 240)(88, 263)(89, 271)(90, 284)(91, 259)(92, 247)(93, 273)(94, 254)(95, 283)(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) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.1135 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3 * Y1^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2 * Y1 * Y2^-2 * Y3^-1, Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-2, Y1 * Y2^-3 * Y3^-1 * Y2^-3, (Y2^-2 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^8, Y2 * Y1^-1 * Y2^3 * Y3 * Y2^2, Y3 * Y2 * Y1^-1 * Y2 * Y1^-2 * Y2^-2 * Y3, Y1 * Y2^2 * Y1 * Y2^2 * Y3^-1 * Y2^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 13, 109, 14, 110)(6, 102, 16, 112, 18, 114)(7, 103, 19, 115, 20, 116)(9, 105, 24, 120, 26, 122)(11, 107, 29, 125, 31, 127)(12, 108, 32, 128, 33, 129)(15, 111, 39, 135, 40, 136)(17, 113, 44, 140, 46, 142)(21, 117, 36, 132, 51, 147)(22, 118, 53, 149, 55, 151)(23, 119, 56, 152, 57, 153)(25, 121, 60, 156, 52, 148)(27, 123, 30, 126, 64, 160)(28, 124, 35, 131, 65, 161)(34, 130, 49, 145, 71, 167)(37, 133, 74, 170, 75, 171)(38, 134, 76, 172, 42, 138)(41, 137, 68, 164, 80, 176)(43, 139, 82, 178, 83, 179)(45, 141, 85, 181, 72, 168)(47, 143, 48, 144, 87, 183)(50, 146, 61, 157, 67, 163)(54, 150, 77, 173, 91, 187)(58, 154, 81, 177, 89, 185)(59, 155, 88, 184, 78, 174)(62, 158, 63, 159, 86, 182)(66, 162, 90, 186, 84, 180)(69, 165, 70, 166, 93, 189)(73, 169, 96, 192, 94, 190)(79, 175, 95, 191, 92, 188)(193, 289, 195, 291, 201, 297, 217, 313, 253, 349, 233, 329, 207, 303, 197, 293)(194, 290, 198, 294, 209, 305, 237, 333, 247, 343, 244, 340, 213, 309, 199, 295)(196, 292, 203, 299, 222, 318, 260, 356, 268, 364, 264, 360, 226, 322, 204, 300)(200, 296, 214, 310, 246, 342, 285, 381, 281, 377, 242, 338, 212, 308, 215, 311)(202, 298, 219, 315, 255, 351, 231, 327, 224, 320, 262, 358, 258, 354, 220, 316)(205, 301, 227, 323, 265, 361, 239, 335, 210, 306, 218, 314, 254, 350, 228, 324)(206, 302, 229, 325, 221, 317, 259, 355, 287, 383, 279, 375, 269, 365, 230, 326)(208, 304, 234, 330, 273, 369, 257, 353, 284, 380, 245, 341, 225, 321, 235, 331)(211, 307, 240, 336, 280, 376, 261, 357, 223, 319, 238, 334, 278, 374, 241, 337)(216, 312, 250, 346, 263, 359, 288, 384, 274, 370, 272, 368, 249, 345, 251, 347)(232, 328, 270, 366, 266, 362, 252, 348, 275, 371, 276, 372, 236, 332, 271, 367)(243, 339, 282, 378, 248, 344, 277, 373, 267, 363, 286, 382, 256, 352, 283, 379) L = (1, 196)(2, 193)(3, 202)(4, 194)(5, 206)(6, 210)(7, 212)(8, 195)(9, 218)(10, 200)(11, 223)(12, 225)(13, 197)(14, 205)(15, 232)(16, 198)(17, 238)(18, 208)(19, 199)(20, 211)(21, 243)(22, 247)(23, 249)(24, 201)(25, 244)(26, 216)(27, 256)(28, 257)(29, 203)(30, 219)(31, 221)(32, 204)(33, 224)(34, 263)(35, 220)(36, 213)(37, 267)(38, 234)(39, 207)(40, 231)(41, 272)(42, 268)(43, 275)(44, 209)(45, 264)(46, 236)(47, 279)(48, 239)(49, 226)(50, 259)(51, 228)(52, 252)(53, 214)(54, 283)(55, 245)(56, 215)(57, 248)(58, 281)(59, 270)(60, 217)(61, 242)(62, 278)(63, 254)(64, 222)(65, 227)(66, 276)(67, 253)(68, 233)(69, 285)(70, 261)(71, 241)(72, 277)(73, 286)(74, 229)(75, 266)(76, 230)(77, 246)(78, 280)(79, 284)(80, 260)(81, 250)(82, 235)(83, 274)(84, 282)(85, 237)(86, 255)(87, 240)(88, 251)(89, 273)(90, 258)(91, 269)(92, 287)(93, 262)(94, 288)(95, 271)(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 ) } Outer automorphisms :: reflexible Dual of E15.1140 Graph:: bipartite v = 44 e = 192 f = 120 degree seq :: [ 6^32, 16^12 ] E15.1140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3^-1)^3, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3, Y3^3 * Y1^2 * Y3 * Y1^-2, (Y3 * Y2^-1)^8 ] Map:: polytopal 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, 49, 145, 21, 117)(8, 104, 22, 118, 55, 151, 23, 119)(10, 106, 28, 124, 44, 140, 30, 126)(12, 108, 32, 128, 60, 156, 34, 130)(13, 109, 35, 131, 52, 148, 26, 122)(16, 112, 40, 136, 48, 144, 41, 137)(17, 113, 43, 139, 42, 138, 45, 141)(18, 114, 46, 142, 29, 125, 47, 143)(20, 116, 51, 147, 33, 129, 53, 149)(24, 120, 58, 154, 36, 132, 59, 155)(27, 123, 63, 159, 76, 172, 64, 160)(31, 127, 69, 165, 75, 171, 65, 161)(38, 134, 73, 169, 78, 174, 68, 164)(39, 135, 66, 162, 77, 173, 74, 170)(50, 146, 80, 176, 72, 168, 81, 177)(54, 150, 86, 182, 71, 167, 82, 178)(56, 152, 87, 183, 62, 158, 85, 181)(57, 153, 83, 179, 70, 166, 88, 184)(61, 157, 84, 180, 67, 163, 79, 175)(89, 185, 93, 189, 91, 187, 95, 191)(90, 186, 96, 192, 92, 188, 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, 209)(7, 212)(8, 194)(9, 218)(10, 221)(11, 214)(12, 225)(13, 196)(14, 230)(15, 231)(16, 197)(17, 236)(18, 198)(19, 207)(20, 244)(21, 238)(22, 248)(23, 249)(24, 200)(25, 240)(26, 254)(27, 201)(28, 257)(29, 259)(30, 255)(31, 203)(32, 239)(33, 247)(34, 206)(35, 262)(36, 205)(37, 253)(38, 246)(39, 263)(40, 261)(41, 256)(42, 208)(43, 215)(44, 229)(45, 227)(46, 269)(47, 270)(48, 210)(49, 228)(50, 211)(51, 274)(52, 276)(53, 272)(54, 213)(55, 271)(56, 268)(57, 219)(58, 278)(59, 273)(60, 216)(61, 217)(62, 267)(63, 281)(64, 282)(65, 283)(66, 220)(67, 234)(68, 222)(69, 284)(70, 223)(71, 224)(72, 226)(73, 233)(74, 232)(75, 235)(76, 237)(77, 264)(78, 242)(79, 241)(80, 285)(81, 286)(82, 287)(83, 243)(84, 252)(85, 245)(86, 288)(87, 251)(88, 250)(89, 266)(90, 258)(91, 265)(92, 260)(93, 280)(94, 275)(95, 279)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E15.1139 Graph:: simple bipartite v = 120 e = 192 f = 44 degree seq :: [ 2^96, 8^24 ] E15.1141 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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, T1^3, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 22, 12)(8, 20, 13, 21)(10, 23, 14, 24)(15, 29, 18, 30)(17, 31, 19, 32)(25, 41, 27, 42)(26, 43, 28, 44)(33, 53, 35, 54)(34, 55, 36, 56)(37, 57, 39, 58)(38, 59, 40, 60)(45, 69, 47, 70)(46, 71, 48, 72)(49, 73, 51, 74)(50, 75, 52, 76)(61, 83, 63, 85)(62, 79, 64, 80)(65, 81, 67, 82)(66, 87, 68, 88)(77, 91, 78, 92)(84, 93, 86, 94)(89, 95, 90, 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, 130)(117, 131, 132)(119, 133, 134)(120, 135, 136)(125, 141, 142)(126, 143, 144)(127, 145, 146)(128, 147, 148)(137, 157, 158)(138, 159, 160)(139, 161, 162)(140, 163, 164)(149, 173, 171)(150, 174, 172)(151, 175, 167)(152, 176, 168)(153, 177, 169)(154, 178, 170)(155, 179, 180)(156, 181, 182)(165, 185, 183)(166, 186, 184)(187, 191, 189)(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) :: { ( 16^3 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E15.1145 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 3^32, 4^24 ] E15.1142 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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 * T2)^2, (F * T1)^2, T2 * T1^-1 * T2 * T1 * T2 * T1^-1, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^8, T2^3 * T1 * T2^3 * T1 * T2^-1 * T1^-1, T2 * T1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 54, 36, 16, 5)(2, 7, 20, 41, 75, 48, 24, 8)(4, 12, 30, 58, 90, 59, 31, 13)(6, 17, 37, 68, 92, 69, 38, 18)(9, 22, 44, 80, 66, 74, 51, 25)(11, 23, 45, 82, 67, 76, 57, 29)(14, 32, 61, 86, 53, 78, 43, 21)(15, 33, 63, 85, 55, 72, 39, 19)(26, 49, 87, 62, 34, 64, 89, 52)(28, 50, 88, 60, 35, 65, 91, 56)(40, 70, 93, 81, 46, 83, 95, 73)(42, 71, 94, 79, 47, 84, 96, 77)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 122, 133, 124)(112, 130, 134, 131)(116, 136, 126, 138)(120, 142, 127, 143)(121, 145, 125, 146)(123, 149, 164, 151)(128, 156, 129, 158)(132, 162, 165, 163)(135, 166, 139, 167)(137, 170, 154, 172)(140, 175, 141, 177)(144, 181, 155, 182)(147, 173, 153, 169)(148, 174, 152, 168)(150, 171, 188, 186)(157, 180, 159, 179)(160, 178, 161, 176)(183, 191, 184, 192)(185, 189, 187, 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) :: { ( 6^4 ), ( 6^8 ) } Outer automorphisms :: reflexible Dual of E15.1146 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.1143 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, T1^8, T2 * T1 * T2^-1 * T1^-3 * T2 * T1^-2, T2 * T1^-1 * T2 * T1^-2 * T2^-1 * T1 * T2^-1 * T1^-2 ] 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, 43, 44)(19, 48, 35)(20, 49, 51)(21, 40, 53)(22, 54, 56)(23, 30, 58)(27, 63, 65)(29, 59, 68)(32, 72, 73)(34, 60, 76)(36, 62, 78)(42, 82, 83)(45, 85, 69)(46, 55, 87)(47, 64, 89)(50, 57, 93)(52, 91, 74)(61, 79, 88)(66, 80, 86)(67, 71, 94)(70, 95, 77)(75, 90, 81)(84, 92, 96)(97, 98, 102, 112, 138, 128, 108, 100)(99, 105, 119, 153, 178, 160, 123, 106)(101, 110, 132, 173, 179, 177, 136, 111)(103, 115, 124, 162, 168, 188, 146, 116)(104, 117, 148, 164, 169, 174, 151, 118)(107, 125, 163, 159, 139, 150, 165, 126)(109, 130, 171, 180, 140, 175, 133, 131)(113, 135, 147, 167, 127, 166, 182, 141)(114, 142, 156, 121, 129, 170, 184, 143)(120, 144, 137, 152, 185, 192, 191, 155)(122, 157, 190, 149, 189, 172, 181, 158)(134, 161, 187, 145, 186, 154, 183, 176) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^3 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E15.1144 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 96 f = 24 degree seq :: [ 3^32, 8^12 ] E15.1144 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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, T1^3, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 9, 105, 5, 101)(2, 98, 6, 102, 16, 112, 7, 103)(4, 100, 11, 107, 22, 118, 12, 108)(8, 104, 20, 116, 13, 109, 21, 117)(10, 106, 23, 119, 14, 110, 24, 120)(15, 111, 29, 125, 18, 114, 30, 126)(17, 113, 31, 127, 19, 115, 32, 128)(25, 121, 41, 137, 27, 123, 42, 138)(26, 122, 43, 139, 28, 124, 44, 140)(33, 129, 53, 149, 35, 131, 54, 150)(34, 130, 55, 151, 36, 132, 56, 152)(37, 133, 57, 153, 39, 135, 58, 154)(38, 134, 59, 155, 40, 136, 60, 156)(45, 141, 69, 165, 47, 143, 70, 166)(46, 142, 71, 167, 48, 144, 72, 168)(49, 145, 73, 169, 51, 147, 74, 170)(50, 146, 75, 171, 52, 148, 76, 172)(61, 157, 83, 179, 63, 159, 85, 181)(62, 158, 79, 175, 64, 160, 80, 176)(65, 161, 81, 177, 67, 163, 82, 178)(66, 162, 87, 183, 68, 164, 88, 184)(77, 173, 91, 187, 78, 174, 92, 188)(84, 180, 93, 189, 86, 182, 94, 190)(89, 185, 95, 191, 90, 186, 96, 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, 131)(22, 105)(23, 133)(24, 135)(25, 122)(26, 107)(27, 124)(28, 108)(29, 141)(30, 143)(31, 145)(32, 147)(33, 130)(34, 116)(35, 132)(36, 117)(37, 134)(38, 119)(39, 136)(40, 120)(41, 157)(42, 159)(43, 161)(44, 163)(45, 142)(46, 125)(47, 144)(48, 126)(49, 146)(50, 127)(51, 148)(52, 128)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 181)(61, 158)(62, 137)(63, 160)(64, 138)(65, 162)(66, 139)(67, 164)(68, 140)(69, 185)(70, 186)(71, 151)(72, 152)(73, 153)(74, 154)(75, 149)(76, 150)(77, 171)(78, 172)(79, 167)(80, 168)(81, 169)(82, 170)(83, 180)(84, 155)(85, 182)(86, 156)(87, 165)(88, 166)(89, 183)(90, 184)(91, 191)(92, 192)(93, 187)(94, 188)(95, 189)(96, 190) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E15.1143 Transitivity :: ET+ VT+ AT Graph:: v = 24 e = 96 f = 44 degree seq :: [ 8^24 ] E15.1145 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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 * T2)^2, (F * T1)^2, T2 * T1^-1 * T2 * T1 * T2 * T1^-1, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^8, T2^3 * T1 * T2^3 * T1 * T2^-1 * T1^-1, T2 * T1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 27, 123, 54, 150, 36, 132, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 41, 137, 75, 171, 48, 144, 24, 120, 8, 104)(4, 100, 12, 108, 30, 126, 58, 154, 90, 186, 59, 155, 31, 127, 13, 109)(6, 102, 17, 113, 37, 133, 68, 164, 92, 188, 69, 165, 38, 134, 18, 114)(9, 105, 22, 118, 44, 140, 80, 176, 66, 162, 74, 170, 51, 147, 25, 121)(11, 107, 23, 119, 45, 141, 82, 178, 67, 163, 76, 172, 57, 153, 29, 125)(14, 110, 32, 128, 61, 157, 86, 182, 53, 149, 78, 174, 43, 139, 21, 117)(15, 111, 33, 129, 63, 159, 85, 181, 55, 151, 72, 168, 39, 135, 19, 115)(26, 122, 49, 145, 87, 183, 62, 158, 34, 130, 64, 160, 89, 185, 52, 148)(28, 124, 50, 146, 88, 184, 60, 156, 35, 131, 65, 161, 91, 187, 56, 152)(40, 136, 70, 166, 93, 189, 81, 177, 46, 142, 83, 179, 95, 191, 73, 169)(42, 138, 71, 167, 94, 190, 79, 175, 47, 143, 84, 180, 96, 192, 77, 173) 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, 136)(21, 103)(22, 109)(23, 104)(24, 142)(25, 145)(26, 133)(27, 149)(28, 106)(29, 146)(30, 138)(31, 143)(32, 156)(33, 158)(34, 134)(35, 112)(36, 162)(37, 124)(38, 131)(39, 166)(40, 126)(41, 170)(42, 116)(43, 167)(44, 175)(45, 177)(46, 127)(47, 120)(48, 181)(49, 125)(50, 121)(51, 173)(52, 174)(53, 164)(54, 171)(55, 123)(56, 168)(57, 169)(58, 172)(59, 182)(60, 129)(61, 180)(62, 128)(63, 179)(64, 178)(65, 176)(66, 165)(67, 132)(68, 151)(69, 163)(70, 139)(71, 135)(72, 148)(73, 147)(74, 154)(75, 188)(76, 137)(77, 153)(78, 152)(79, 141)(80, 160)(81, 140)(82, 161)(83, 157)(84, 159)(85, 155)(86, 144)(87, 191)(88, 192)(89, 189)(90, 150)(91, 190)(92, 186)(93, 187)(94, 185)(95, 184)(96, 183) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E15.1141 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1146 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, T1^8, T2 * T1 * T2^-1 * T1^-3 * T2 * T1^-2, T2 * T1^-1 * T2 * T1^-2 * T2^-1 * T1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 5, 101)(2, 98, 7, 103, 8, 104)(4, 100, 11, 107, 13, 109)(6, 102, 17, 113, 18, 114)(9, 105, 24, 120, 25, 121)(10, 106, 26, 122, 28, 124)(12, 108, 31, 127, 33, 129)(14, 110, 37, 133, 38, 134)(15, 111, 39, 135, 41, 137)(16, 112, 43, 139, 44, 140)(19, 115, 48, 144, 35, 131)(20, 116, 49, 145, 51, 147)(21, 117, 40, 136, 53, 149)(22, 118, 54, 150, 56, 152)(23, 119, 30, 126, 58, 154)(27, 123, 63, 159, 65, 161)(29, 125, 59, 155, 68, 164)(32, 128, 72, 168, 73, 169)(34, 130, 60, 156, 76, 172)(36, 132, 62, 158, 78, 174)(42, 138, 82, 178, 83, 179)(45, 141, 85, 181, 69, 165)(46, 142, 55, 151, 87, 183)(47, 143, 64, 160, 89, 185)(50, 146, 57, 153, 93, 189)(52, 148, 91, 187, 74, 170)(61, 157, 79, 175, 88, 184)(66, 162, 80, 176, 86, 182)(67, 163, 71, 167, 94, 190)(70, 166, 95, 191, 77, 173)(75, 171, 90, 186, 81, 177)(84, 180, 92, 188, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 115)(8, 117)(9, 119)(10, 99)(11, 125)(12, 100)(13, 130)(14, 132)(15, 101)(16, 138)(17, 135)(18, 142)(19, 124)(20, 103)(21, 148)(22, 104)(23, 153)(24, 144)(25, 129)(26, 157)(27, 106)(28, 162)(29, 163)(30, 107)(31, 166)(32, 108)(33, 170)(34, 171)(35, 109)(36, 173)(37, 131)(38, 161)(39, 147)(40, 111)(41, 152)(42, 128)(43, 150)(44, 175)(45, 113)(46, 156)(47, 114)(48, 137)(49, 186)(50, 116)(51, 167)(52, 164)(53, 189)(54, 165)(55, 118)(56, 185)(57, 178)(58, 183)(59, 120)(60, 121)(61, 190)(62, 122)(63, 139)(64, 123)(65, 187)(66, 168)(67, 159)(68, 169)(69, 126)(70, 182)(71, 127)(72, 188)(73, 174)(74, 184)(75, 180)(76, 181)(77, 179)(78, 151)(79, 133)(80, 134)(81, 136)(82, 160)(83, 177)(84, 140)(85, 158)(86, 141)(87, 176)(88, 143)(89, 192)(90, 154)(91, 145)(92, 146)(93, 172)(94, 149)(95, 155)(96, 191) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1142 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 6^32 ] E15.1147 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^8 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 13, 109, 14, 110)(6, 102, 15, 111, 17, 113)(7, 103, 18, 114, 19, 115)(9, 105, 16, 112, 22, 118)(11, 107, 25, 121, 26, 122)(12, 108, 27, 123, 28, 124)(20, 116, 33, 129, 34, 130)(21, 117, 35, 131, 36, 132)(23, 119, 37, 133, 38, 134)(24, 120, 39, 135, 40, 136)(29, 125, 45, 141, 46, 142)(30, 126, 47, 143, 48, 144)(31, 127, 49, 145, 50, 146)(32, 128, 51, 147, 52, 148)(41, 137, 61, 157, 62, 158)(42, 138, 63, 159, 64, 160)(43, 139, 65, 161, 66, 162)(44, 140, 67, 163, 68, 164)(53, 149, 77, 173, 75, 171)(54, 150, 78, 174, 76, 172)(55, 151, 79, 175, 71, 167)(56, 152, 80, 176, 72, 168)(57, 153, 81, 177, 73, 169)(58, 154, 82, 178, 74, 170)(59, 155, 83, 179, 84, 180)(60, 156, 85, 181, 86, 182)(69, 165, 89, 185, 87, 183)(70, 166, 90, 186, 88, 184)(91, 187, 95, 191, 93, 189)(92, 188, 96, 192, 94, 190)(193, 289, 195, 291, 201, 297, 197, 293)(194, 290, 198, 294, 208, 304, 199, 295)(196, 292, 203, 299, 214, 310, 204, 300)(200, 296, 212, 308, 205, 301, 213, 309)(202, 298, 215, 311, 206, 302, 216, 312)(207, 303, 221, 317, 210, 306, 222, 318)(209, 305, 223, 319, 211, 307, 224, 320)(217, 313, 233, 329, 219, 315, 234, 330)(218, 314, 235, 331, 220, 316, 236, 332)(225, 321, 245, 341, 227, 323, 246, 342)(226, 322, 247, 343, 228, 324, 248, 344)(229, 325, 249, 345, 231, 327, 250, 346)(230, 326, 251, 347, 232, 328, 252, 348)(237, 333, 261, 357, 239, 335, 262, 358)(238, 334, 263, 359, 240, 336, 264, 360)(241, 337, 265, 361, 243, 339, 266, 362)(242, 338, 267, 363, 244, 340, 268, 364)(253, 349, 275, 371, 255, 351, 277, 373)(254, 350, 271, 367, 256, 352, 272, 368)(257, 353, 273, 369, 259, 355, 274, 370)(258, 354, 279, 375, 260, 356, 280, 376)(269, 365, 283, 379, 270, 366, 284, 380)(276, 372, 285, 381, 278, 374, 286, 382)(281, 377, 287, 383, 282, 378, 288, 384) L = (1, 196)(2, 193)(3, 202)(4, 194)(5, 206)(6, 209)(7, 211)(8, 195)(9, 214)(10, 200)(11, 218)(12, 220)(13, 197)(14, 205)(15, 198)(16, 201)(17, 207)(18, 199)(19, 210)(20, 226)(21, 228)(22, 208)(23, 230)(24, 232)(25, 203)(26, 217)(27, 204)(28, 219)(29, 238)(30, 240)(31, 242)(32, 244)(33, 212)(34, 225)(35, 213)(36, 227)(37, 215)(38, 229)(39, 216)(40, 231)(41, 254)(42, 256)(43, 258)(44, 260)(45, 221)(46, 237)(47, 222)(48, 239)(49, 223)(50, 241)(51, 224)(52, 243)(53, 267)(54, 268)(55, 263)(56, 264)(57, 265)(58, 266)(59, 276)(60, 278)(61, 233)(62, 253)(63, 234)(64, 255)(65, 235)(66, 257)(67, 236)(68, 259)(69, 279)(70, 280)(71, 271)(72, 272)(73, 273)(74, 274)(75, 269)(76, 270)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 275)(85, 252)(86, 277)(87, 281)(88, 282)(89, 261)(90, 262)(91, 285)(92, 286)(93, 287)(94, 288)(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, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E15.1150 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 6^32, 8^24 ] E15.1148 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, (Y1 * Y2)^3, (Y3^-1 * Y1^-1)^3, Y2^8, Y2^-4 * Y1 * Y2^-4 * 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, 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, 95, 191, 88, 184, 96, 192)(89, 185, 93, 189, 91, 187, 94, 190)(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, 214, 310, 236, 332, 272, 368, 258, 354, 266, 362, 243, 339, 217, 313)(203, 299, 215, 311, 237, 333, 274, 370, 259, 355, 268, 364, 249, 345, 221, 317)(206, 302, 224, 320, 253, 349, 278, 374, 245, 341, 270, 366, 235, 331, 213, 309)(207, 303, 225, 321, 255, 351, 277, 373, 247, 343, 264, 360, 231, 327, 211, 307)(218, 314, 241, 337, 279, 375, 254, 350, 226, 322, 256, 352, 281, 377, 244, 340)(220, 316, 242, 338, 280, 376, 252, 348, 227, 323, 257, 353, 283, 379, 248, 344)(232, 328, 262, 358, 285, 381, 273, 369, 238, 334, 275, 371, 287, 383, 265, 361)(234, 330, 263, 359, 286, 382, 271, 367, 239, 335, 276, 372, 288, 384, 269, 365) 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) :: { ( 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 E15.1149 Graph:: bipartite v = 36 e = 192 f = 128 degree seq :: [ 8^24, 16^12 ] E15.1149 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3 * Y2^-1)^4, Y3^3 * Y2 * Y3^2 * Y2 * Y3^-1 * 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, 196, 292)(195, 291, 200, 296, 202, 298)(197, 293, 205, 301, 206, 302)(198, 294, 208, 304, 210, 306)(199, 295, 211, 307, 212, 308)(201, 297, 216, 312, 218, 314)(203, 299, 221, 317, 223, 319)(204, 300, 224, 320, 225, 321)(207, 303, 231, 327, 232, 328)(209, 305, 236, 332, 238, 334)(213, 309, 214, 310, 243, 339)(215, 311, 240, 336, 246, 342)(217, 313, 250, 346, 252, 348)(219, 315, 228, 324, 241, 337)(220, 316, 242, 338, 254, 350)(222, 318, 257, 353, 230, 326)(226, 322, 234, 330, 262, 358)(227, 323, 264, 360, 256, 352)(229, 325, 266, 362, 259, 355)(233, 329, 272, 368, 273, 369)(235, 331, 260, 356, 275, 371)(237, 333, 277, 373, 270, 366)(239, 335, 261, 357, 280, 376)(244, 340, 284, 380, 265, 361)(245, 341, 269, 365, 274, 370)(247, 343, 248, 344, 276, 372)(249, 345, 281, 377, 263, 359)(251, 347, 278, 374, 286, 382)(253, 349, 268, 364, 279, 375)(255, 351, 282, 378, 258, 354)(267, 363, 283, 379, 271, 367)(285, 381, 288, 384, 287, 383) L = (1, 195)(2, 198)(3, 201)(4, 203)(5, 193)(6, 209)(7, 194)(8, 214)(9, 217)(10, 219)(11, 222)(12, 196)(13, 227)(14, 229)(15, 197)(16, 234)(17, 237)(18, 228)(19, 240)(20, 242)(21, 199)(22, 245)(23, 200)(24, 248)(25, 251)(26, 212)(27, 224)(28, 202)(29, 231)(30, 258)(31, 241)(32, 260)(33, 261)(34, 204)(35, 265)(36, 205)(37, 267)(38, 206)(39, 269)(40, 270)(41, 207)(42, 274)(43, 208)(44, 247)(45, 278)(46, 225)(47, 210)(48, 281)(49, 211)(50, 271)(51, 282)(52, 213)(53, 266)(54, 268)(55, 215)(56, 256)(57, 216)(58, 239)(59, 233)(60, 246)(61, 218)(62, 284)(63, 220)(64, 221)(65, 276)(66, 286)(67, 223)(68, 273)(69, 283)(70, 252)(71, 226)(72, 279)(73, 285)(74, 272)(75, 262)(76, 230)(77, 280)(78, 275)(79, 232)(80, 236)(81, 287)(82, 254)(83, 253)(84, 235)(85, 259)(86, 244)(87, 238)(88, 249)(89, 288)(90, 264)(91, 243)(92, 257)(93, 250)(94, 263)(95, 255)(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 ) } Outer automorphisms :: reflexible Dual of E15.1148 Graph:: simple bipartite v = 128 e = 192 f = 36 degree seq :: [ 2^96, 6^32 ] E15.1150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y1^8, Y3 * Y1 * Y3^-1 * Y1^-3 * Y3 * Y1^-2, Y3 * Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-2 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 16, 112, 42, 138, 32, 128, 12, 108, 4, 100)(3, 99, 9, 105, 23, 119, 57, 153, 82, 178, 64, 160, 27, 123, 10, 106)(5, 101, 14, 110, 36, 132, 77, 173, 83, 179, 81, 177, 40, 136, 15, 111)(7, 103, 19, 115, 28, 124, 66, 162, 72, 168, 92, 188, 50, 146, 20, 116)(8, 104, 21, 117, 52, 148, 68, 164, 73, 169, 78, 174, 55, 151, 22, 118)(11, 107, 29, 125, 67, 163, 63, 159, 43, 139, 54, 150, 69, 165, 30, 126)(13, 109, 34, 130, 75, 171, 84, 180, 44, 140, 79, 175, 37, 133, 35, 131)(17, 113, 39, 135, 51, 147, 71, 167, 31, 127, 70, 166, 86, 182, 45, 141)(18, 114, 46, 142, 60, 156, 25, 121, 33, 129, 74, 170, 88, 184, 47, 143)(24, 120, 48, 144, 41, 137, 56, 152, 89, 185, 96, 192, 95, 191, 59, 155)(26, 122, 61, 157, 94, 190, 53, 149, 93, 189, 76, 172, 85, 181, 62, 158)(38, 134, 65, 161, 91, 187, 49, 145, 90, 186, 58, 154, 87, 183, 80, 176)(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, 197)(4, 203)(5, 193)(6, 209)(7, 200)(8, 194)(9, 216)(10, 218)(11, 205)(12, 223)(13, 196)(14, 229)(15, 231)(16, 235)(17, 210)(18, 198)(19, 240)(20, 241)(21, 232)(22, 246)(23, 222)(24, 217)(25, 201)(26, 220)(27, 255)(28, 202)(29, 251)(30, 250)(31, 225)(32, 264)(33, 204)(34, 252)(35, 211)(36, 254)(37, 230)(38, 206)(39, 233)(40, 245)(41, 207)(42, 274)(43, 236)(44, 208)(45, 277)(46, 247)(47, 256)(48, 227)(49, 243)(50, 249)(51, 212)(52, 283)(53, 213)(54, 248)(55, 279)(56, 214)(57, 285)(58, 215)(59, 260)(60, 268)(61, 271)(62, 270)(63, 257)(64, 281)(65, 219)(66, 272)(67, 263)(68, 221)(69, 237)(70, 287)(71, 286)(72, 265)(73, 224)(74, 244)(75, 282)(76, 226)(77, 262)(78, 228)(79, 280)(80, 278)(81, 267)(82, 275)(83, 234)(84, 284)(85, 261)(86, 258)(87, 238)(88, 253)(89, 239)(90, 273)(91, 266)(92, 288)(93, 242)(94, 259)(95, 269)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.1147 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y3 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^2, (Y3 * Y2^-1)^4, Y2^8, Y1 * Y2 * R * Y2^3 * R * Y2^-2, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2 * Y3 * Y2^-2, Y2 * Y1 * Y2^-2 * Y3^-1 * Y2^-3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1 * Y2^-1 * Y3^-1 * Y2^2 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 13, 109, 14, 110)(6, 102, 16, 112, 18, 114)(7, 103, 19, 115, 20, 116)(9, 105, 24, 120, 26, 122)(11, 107, 29, 125, 31, 127)(12, 108, 32, 128, 33, 129)(15, 111, 39, 135, 40, 136)(17, 113, 36, 132, 45, 141)(21, 117, 50, 146, 51, 147)(22, 118, 42, 138, 38, 134)(23, 119, 53, 149, 54, 150)(25, 121, 57, 153, 59, 155)(27, 123, 34, 130, 63, 159)(28, 124, 64, 160, 65, 161)(30, 126, 48, 144, 69, 165)(35, 131, 43, 139, 73, 169)(37, 133, 46, 142, 76, 172)(41, 137, 80, 176, 81, 177)(44, 140, 83, 179, 55, 151)(47, 143, 67, 163, 88, 184)(49, 145, 70, 166, 90, 186)(52, 148, 92, 188, 61, 157)(56, 152, 89, 185, 74, 170)(58, 154, 84, 180, 94, 190)(60, 156, 66, 162, 85, 181)(62, 158, 91, 187, 79, 175)(68, 164, 77, 173, 82, 178)(71, 167, 75, 171, 86, 182)(72, 168, 78, 174, 87, 183)(93, 189, 96, 192, 95, 191)(193, 289, 195, 291, 201, 297, 217, 313, 250, 346, 233, 329, 207, 303, 197, 293)(194, 290, 198, 294, 209, 305, 236, 332, 276, 372, 244, 340, 213, 309, 199, 295)(196, 292, 203, 299, 222, 318, 260, 356, 286, 382, 263, 359, 226, 322, 204, 300)(200, 296, 214, 310, 212, 308, 241, 337, 272, 368, 285, 381, 247, 343, 215, 311)(202, 298, 219, 315, 254, 350, 265, 361, 273, 369, 261, 357, 258, 354, 220, 316)(205, 301, 227, 323, 264, 360, 242, 338, 249, 345, 256, 352, 266, 362, 228, 324)(206, 302, 229, 325, 267, 363, 287, 383, 251, 347, 259, 355, 221, 317, 230, 326)(208, 304, 234, 330, 225, 321, 257, 353, 284, 380, 288, 384, 274, 370, 235, 331)(210, 306, 232, 328, 271, 367, 280, 376, 253, 349, 218, 314, 252, 348, 238, 334)(211, 307, 239, 335, 279, 375, 255, 351, 275, 371, 268, 364, 281, 377, 240, 336)(216, 312, 224, 320, 246, 342, 270, 366, 231, 327, 269, 365, 282, 378, 248, 344)(223, 319, 243, 339, 283, 379, 245, 341, 278, 374, 237, 333, 277, 373, 262, 358) L = (1, 196)(2, 193)(3, 202)(4, 194)(5, 206)(6, 210)(7, 212)(8, 195)(9, 218)(10, 200)(11, 223)(12, 225)(13, 197)(14, 205)(15, 232)(16, 198)(17, 237)(18, 208)(19, 199)(20, 211)(21, 243)(22, 230)(23, 246)(24, 201)(25, 251)(26, 216)(27, 255)(28, 257)(29, 203)(30, 261)(31, 221)(32, 204)(33, 224)(34, 219)(35, 265)(36, 209)(37, 268)(38, 234)(39, 207)(40, 231)(41, 273)(42, 214)(43, 227)(44, 247)(45, 228)(46, 229)(47, 280)(48, 222)(49, 282)(50, 213)(51, 242)(52, 253)(53, 215)(54, 245)(55, 275)(56, 266)(57, 217)(58, 286)(59, 249)(60, 277)(61, 284)(62, 271)(63, 226)(64, 220)(65, 256)(66, 252)(67, 239)(68, 274)(69, 240)(70, 241)(71, 278)(72, 279)(73, 235)(74, 281)(75, 263)(76, 238)(77, 260)(78, 264)(79, 283)(80, 233)(81, 272)(82, 269)(83, 236)(84, 250)(85, 258)(86, 267)(87, 270)(88, 259)(89, 248)(90, 262)(91, 254)(92, 244)(93, 287)(94, 276)(95, 288)(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 ) } Outer automorphisms :: reflexible Dual of E15.1152 Graph:: bipartite v = 44 e = 192 f = 120 degree seq :: [ 6^32, 16^12 ] E15.1152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y1^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3^-2 * Y1^-1 * Y3 * Y1^-1 * Y3^-2 * Y1^-1, Y1^-1 * Y3^4 * Y1 * Y3^-4, (Y3 * Y2^-1)^8 ] Map:: polytopal 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, 95, 191, 88, 184, 96, 192)(89, 185, 93, 189, 91, 187, 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, 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) :: { ( 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E15.1151 Graph:: simple bipartite v = 120 e = 192 f = 44 degree seq :: [ 2^96, 8^24 ] E15.1153 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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, T1^3, T2^4, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 27, 12)(8, 20, 45, 21)(10, 24, 54, 25)(13, 31, 64, 32)(14, 33, 67, 34)(15, 35, 69, 36)(17, 39, 75, 40)(18, 41, 76, 42)(19, 43, 78, 44)(22, 49, 79, 50)(23, 51, 77, 52)(26, 46, 82, 57)(28, 60, 90, 61)(29, 48, 83, 62)(30, 56, 88, 63)(37, 70, 55, 71)(38, 72, 47, 73)(53, 84, 95, 89)(58, 81, 68, 85)(59, 86, 65, 91)(66, 80, 94, 87)(74, 92, 96, 93)(97, 98, 100)(99, 104, 106)(101, 109, 110)(102, 111, 113)(103, 114, 115)(105, 118, 119)(107, 122, 124)(108, 125, 126)(112, 133, 134)(116, 131, 142)(117, 143, 144)(120, 149, 138)(121, 151, 152)(123, 154, 155)(127, 132, 161)(128, 156, 162)(129, 136, 164)(130, 140, 159)(135, 170, 158)(137, 153, 173)(139, 157, 175)(141, 176, 177)(145, 165, 180)(146, 181, 167)(147, 182, 168)(148, 183, 184)(150, 186, 171)(160, 179, 172)(163, 169, 185)(166, 178, 188)(174, 187, 189)(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) :: { ( 16^3 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E15.1157 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 3^32, 4^24 ] E15.1154 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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 * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-2 * T1 * T2, (T2^-1 * T1^-1)^3, T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1, T2^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 59, 38, 16, 5)(2, 7, 20, 47, 80, 52, 24, 8)(4, 12, 29, 60, 89, 57, 35, 13)(6, 17, 40, 71, 93, 76, 44, 18)(9, 26, 55, 33, 65, 37, 14, 27)(11, 30, 51, 22, 46, 19, 15, 31)(21, 48, 75, 42, 70, 39, 23, 49)(25, 53, 84, 95, 79, 67, 36, 54)(32, 43, 73, 41, 72, 66, 34, 64)(45, 77, 62, 90, 61, 83, 50, 78)(56, 87, 63, 86, 68, 85, 58, 88)(69, 91, 82, 96, 81, 94, 74, 92)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 132, 111)(103, 115, 141, 117)(104, 118, 146, 119)(106, 116, 136, 125)(108, 128, 159, 129)(109, 130, 152, 122)(112, 120, 140, 131)(113, 135, 165, 137)(114, 138, 170, 139)(123, 153, 168, 154)(124, 151, 180, 147)(126, 157, 166, 148)(127, 158, 171, 143)(133, 156, 169, 164)(134, 161, 175, 142)(144, 177, 160, 172)(145, 178, 162, 167)(149, 181, 190, 174)(150, 182, 192, 179)(155, 176, 189, 185)(163, 183, 187, 186)(173, 191, 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) :: { ( 6^4 ), ( 6^8 ) } Outer automorphisms :: reflexible Dual of E15.1158 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 32 degree seq :: [ 4^24, 8^12 ] E15.1155 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2^-1 * T1, T2 * T1^2 * T2^-1 * T1^-2, (T1 * T2^-1)^4, T1^8, (T2^-1 * T1^-1)^4, T2^-1 * T1^-1 * T2^-1 * T1^2 * T2 * T1 * T2 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 23, 24)(10, 25, 27)(12, 26, 30)(14, 32, 33)(15, 34, 35)(16, 37, 38)(19, 41, 42)(20, 43, 44)(21, 45, 46)(22, 47, 48)(28, 55, 57)(29, 56, 58)(31, 60, 49)(36, 65, 66)(39, 69, 70)(40, 71, 72)(50, 68, 81)(51, 82, 64)(52, 83, 84)(53, 79, 85)(54, 86, 61)(59, 88, 73)(62, 90, 91)(63, 92, 67)(74, 93, 80)(75, 94, 89)(76, 95, 77)(78, 87, 96)(97, 98, 102, 112, 132, 125, 108, 100)(99, 105, 113, 135, 161, 149, 122, 106)(101, 110, 114, 136, 162, 155, 126, 111)(103, 115, 133, 163, 152, 124, 107, 116)(104, 117, 134, 164, 154, 127, 109, 118)(119, 145, 165, 144, 175, 142, 121, 146)(120, 147, 166, 186, 181, 150, 123, 148)(128, 157, 167, 180, 184, 160, 130, 158)(129, 151, 168, 139, 169, 137, 131, 159)(138, 170, 188, 183, 153, 172, 140, 171)(141, 173, 177, 185, 156, 176, 143, 174)(178, 191, 187, 190, 182, 189, 179, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^3 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E15.1156 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 96 f = 24 degree seq :: [ 3^32, 8^12 ] E15.1156 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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, T1^3, T2^4, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 9, 105, 5, 101)(2, 98, 6, 102, 16, 112, 7, 103)(4, 100, 11, 107, 27, 123, 12, 108)(8, 104, 20, 116, 45, 141, 21, 117)(10, 106, 24, 120, 54, 150, 25, 121)(13, 109, 31, 127, 64, 160, 32, 128)(14, 110, 33, 129, 67, 163, 34, 130)(15, 111, 35, 131, 69, 165, 36, 132)(17, 113, 39, 135, 75, 171, 40, 136)(18, 114, 41, 137, 76, 172, 42, 138)(19, 115, 43, 139, 78, 174, 44, 140)(22, 118, 49, 145, 79, 175, 50, 146)(23, 119, 51, 147, 77, 173, 52, 148)(26, 122, 46, 142, 82, 178, 57, 153)(28, 124, 60, 156, 90, 186, 61, 157)(29, 125, 48, 144, 83, 179, 62, 158)(30, 126, 56, 152, 88, 184, 63, 159)(37, 133, 70, 166, 55, 151, 71, 167)(38, 134, 72, 168, 47, 143, 73, 169)(53, 149, 84, 180, 95, 191, 89, 185)(58, 154, 81, 177, 68, 164, 85, 181)(59, 155, 86, 182, 65, 161, 91, 187)(66, 162, 80, 176, 94, 190, 87, 183)(74, 170, 92, 188, 96, 192, 93, 189) L = (1, 98)(2, 100)(3, 104)(4, 97)(5, 109)(6, 111)(7, 114)(8, 106)(9, 118)(10, 99)(11, 122)(12, 125)(13, 110)(14, 101)(15, 113)(16, 133)(17, 102)(18, 115)(19, 103)(20, 131)(21, 143)(22, 119)(23, 105)(24, 149)(25, 151)(26, 124)(27, 154)(28, 107)(29, 126)(30, 108)(31, 132)(32, 156)(33, 136)(34, 140)(35, 142)(36, 161)(37, 134)(38, 112)(39, 170)(40, 164)(41, 153)(42, 120)(43, 157)(44, 159)(45, 176)(46, 116)(47, 144)(48, 117)(49, 165)(50, 181)(51, 182)(52, 183)(53, 138)(54, 186)(55, 152)(56, 121)(57, 173)(58, 155)(59, 123)(60, 162)(61, 175)(62, 135)(63, 130)(64, 179)(65, 127)(66, 128)(67, 169)(68, 129)(69, 180)(70, 178)(71, 146)(72, 147)(73, 185)(74, 158)(75, 150)(76, 160)(77, 137)(78, 187)(79, 139)(80, 177)(81, 141)(82, 188)(83, 172)(84, 145)(85, 167)(86, 168)(87, 184)(88, 148)(89, 163)(90, 171)(91, 189)(92, 166)(93, 174)(94, 191)(95, 192)(96, 190) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E15.1155 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 96 f = 44 degree seq :: [ 8^24 ] E15.1157 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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 * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-2 * T1 * T2, (T2^-1 * T1^-1)^3, T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-1, T2^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 59, 155, 38, 134, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 47, 143, 80, 176, 52, 148, 24, 120, 8, 104)(4, 100, 12, 108, 29, 125, 60, 156, 89, 185, 57, 153, 35, 131, 13, 109)(6, 102, 17, 113, 40, 136, 71, 167, 93, 189, 76, 172, 44, 140, 18, 114)(9, 105, 26, 122, 55, 151, 33, 129, 65, 161, 37, 133, 14, 110, 27, 123)(11, 107, 30, 126, 51, 147, 22, 118, 46, 142, 19, 115, 15, 111, 31, 127)(21, 117, 48, 144, 75, 171, 42, 138, 70, 166, 39, 135, 23, 119, 49, 145)(25, 121, 53, 149, 84, 180, 95, 191, 79, 175, 67, 163, 36, 132, 54, 150)(32, 128, 43, 139, 73, 169, 41, 137, 72, 168, 66, 162, 34, 130, 64, 160)(45, 141, 77, 173, 62, 158, 90, 186, 61, 157, 83, 179, 50, 146, 78, 174)(56, 152, 87, 183, 63, 159, 86, 182, 68, 164, 85, 181, 58, 154, 88, 184)(69, 165, 91, 187, 82, 178, 96, 192, 81, 177, 94, 190, 74, 170, 92, 188) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 116)(11, 99)(12, 128)(13, 130)(14, 132)(15, 101)(16, 120)(17, 135)(18, 138)(19, 141)(20, 136)(21, 103)(22, 146)(23, 104)(24, 140)(25, 107)(26, 109)(27, 153)(28, 151)(29, 106)(30, 157)(31, 158)(32, 159)(33, 108)(34, 152)(35, 112)(36, 111)(37, 156)(38, 161)(39, 165)(40, 125)(41, 113)(42, 170)(43, 114)(44, 131)(45, 117)(46, 134)(47, 127)(48, 177)(49, 178)(50, 119)(51, 124)(52, 126)(53, 181)(54, 182)(55, 180)(56, 122)(57, 168)(58, 123)(59, 176)(60, 169)(61, 166)(62, 171)(63, 129)(64, 172)(65, 175)(66, 167)(67, 183)(68, 133)(69, 137)(70, 148)(71, 145)(72, 154)(73, 164)(74, 139)(75, 143)(76, 144)(77, 191)(78, 149)(79, 142)(80, 189)(81, 160)(82, 162)(83, 150)(84, 147)(85, 190)(86, 192)(87, 187)(88, 188)(89, 155)(90, 163)(91, 186)(92, 173)(93, 185)(94, 174)(95, 184)(96, 179) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E15.1153 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1158 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2^-1 * T1, T2 * T1^2 * T2^-1 * T1^-2, (T1 * T2^-1)^4, T1^8, (T2^-1 * T1^-1)^4, T2^-1 * T1^-1 * T2^-1 * T1^2 * T2 * T1 * T2 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 5, 101)(2, 98, 7, 103, 8, 104)(4, 100, 11, 107, 13, 109)(6, 102, 17, 113, 18, 114)(9, 105, 23, 119, 24, 120)(10, 106, 25, 121, 27, 123)(12, 108, 26, 122, 30, 126)(14, 110, 32, 128, 33, 129)(15, 111, 34, 130, 35, 131)(16, 112, 37, 133, 38, 134)(19, 115, 41, 137, 42, 138)(20, 116, 43, 139, 44, 140)(21, 117, 45, 141, 46, 142)(22, 118, 47, 143, 48, 144)(28, 124, 55, 151, 57, 153)(29, 125, 56, 152, 58, 154)(31, 127, 60, 156, 49, 145)(36, 132, 65, 161, 66, 162)(39, 135, 69, 165, 70, 166)(40, 136, 71, 167, 72, 168)(50, 146, 68, 164, 81, 177)(51, 147, 82, 178, 64, 160)(52, 148, 83, 179, 84, 180)(53, 149, 79, 175, 85, 181)(54, 150, 86, 182, 61, 157)(59, 155, 88, 184, 73, 169)(62, 158, 90, 186, 91, 187)(63, 159, 92, 188, 67, 163)(74, 170, 93, 189, 80, 176)(75, 171, 94, 190, 89, 185)(76, 172, 95, 191, 77, 173)(78, 174, 87, 183, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 115)(8, 117)(9, 113)(10, 99)(11, 116)(12, 100)(13, 118)(14, 114)(15, 101)(16, 132)(17, 135)(18, 136)(19, 133)(20, 103)(21, 134)(22, 104)(23, 145)(24, 147)(25, 146)(26, 106)(27, 148)(28, 107)(29, 108)(30, 111)(31, 109)(32, 157)(33, 151)(34, 158)(35, 159)(36, 125)(37, 163)(38, 164)(39, 161)(40, 162)(41, 131)(42, 170)(43, 169)(44, 171)(45, 173)(46, 121)(47, 174)(48, 175)(49, 165)(50, 119)(51, 166)(52, 120)(53, 122)(54, 123)(55, 168)(56, 124)(57, 172)(58, 127)(59, 126)(60, 176)(61, 167)(62, 128)(63, 129)(64, 130)(65, 149)(66, 155)(67, 152)(68, 154)(69, 144)(70, 186)(71, 180)(72, 139)(73, 137)(74, 188)(75, 138)(76, 140)(77, 177)(78, 141)(79, 142)(80, 143)(81, 185)(82, 191)(83, 192)(84, 184)(85, 150)(86, 189)(87, 153)(88, 160)(89, 156)(90, 181)(91, 190)(92, 183)(93, 179)(94, 182)(95, 187)(96, 178) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1154 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 32 e = 96 f = 36 degree seq :: [ 6^32 ] E15.1159 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1 * Y2, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2^-2 * Y1^-1 * Y2^-2 * Y3^-1 * Y2^-1, Y2^-2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^2 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 13, 109, 14, 110)(6, 102, 15, 111, 17, 113)(7, 103, 18, 114, 19, 115)(9, 105, 22, 118, 23, 119)(11, 107, 26, 122, 28, 124)(12, 108, 29, 125, 30, 126)(16, 112, 37, 133, 38, 134)(20, 116, 35, 131, 46, 142)(21, 117, 47, 143, 48, 144)(24, 120, 53, 149, 42, 138)(25, 121, 55, 151, 56, 152)(27, 123, 58, 154, 59, 155)(31, 127, 36, 132, 65, 161)(32, 128, 60, 156, 66, 162)(33, 129, 40, 136, 68, 164)(34, 130, 44, 140, 63, 159)(39, 135, 74, 170, 62, 158)(41, 137, 57, 153, 77, 173)(43, 139, 61, 157, 79, 175)(45, 141, 80, 176, 81, 177)(49, 145, 69, 165, 84, 180)(50, 146, 85, 181, 71, 167)(51, 147, 86, 182, 72, 168)(52, 148, 87, 183, 88, 184)(54, 150, 90, 186, 75, 171)(64, 160, 83, 179, 76, 172)(67, 163, 73, 169, 89, 185)(70, 166, 82, 178, 92, 188)(78, 174, 91, 187, 93, 189)(94, 190, 95, 191, 96, 192)(193, 289, 195, 291, 201, 297, 197, 293)(194, 290, 198, 294, 208, 304, 199, 295)(196, 292, 203, 299, 219, 315, 204, 300)(200, 296, 212, 308, 237, 333, 213, 309)(202, 298, 216, 312, 246, 342, 217, 313)(205, 301, 223, 319, 256, 352, 224, 320)(206, 302, 225, 321, 259, 355, 226, 322)(207, 303, 227, 323, 261, 357, 228, 324)(209, 305, 231, 327, 267, 363, 232, 328)(210, 306, 233, 329, 268, 364, 234, 330)(211, 307, 235, 331, 270, 366, 236, 332)(214, 310, 241, 337, 271, 367, 242, 338)(215, 311, 243, 339, 269, 365, 244, 340)(218, 314, 238, 334, 274, 370, 249, 345)(220, 316, 252, 348, 282, 378, 253, 349)(221, 317, 240, 336, 275, 371, 254, 350)(222, 318, 248, 344, 280, 376, 255, 351)(229, 325, 262, 358, 247, 343, 263, 359)(230, 326, 264, 360, 239, 335, 265, 361)(245, 341, 276, 372, 287, 383, 281, 377)(250, 346, 273, 369, 260, 356, 277, 373)(251, 347, 278, 374, 257, 353, 283, 379)(258, 354, 272, 368, 286, 382, 279, 375)(266, 362, 284, 380, 288, 384, 285, 381) L = (1, 196)(2, 193)(3, 202)(4, 194)(5, 206)(6, 209)(7, 211)(8, 195)(9, 215)(10, 200)(11, 220)(12, 222)(13, 197)(14, 205)(15, 198)(16, 230)(17, 207)(18, 199)(19, 210)(20, 238)(21, 240)(22, 201)(23, 214)(24, 234)(25, 248)(26, 203)(27, 251)(28, 218)(29, 204)(30, 221)(31, 257)(32, 258)(33, 260)(34, 255)(35, 212)(36, 223)(37, 208)(38, 229)(39, 254)(40, 225)(41, 269)(42, 245)(43, 271)(44, 226)(45, 273)(46, 227)(47, 213)(48, 239)(49, 276)(50, 263)(51, 264)(52, 280)(53, 216)(54, 267)(55, 217)(56, 247)(57, 233)(58, 219)(59, 250)(60, 224)(61, 235)(62, 266)(63, 236)(64, 268)(65, 228)(66, 252)(67, 281)(68, 232)(69, 241)(70, 284)(71, 277)(72, 278)(73, 259)(74, 231)(75, 282)(76, 275)(77, 249)(78, 285)(79, 253)(80, 237)(81, 272)(82, 262)(83, 256)(84, 261)(85, 242)(86, 243)(87, 244)(88, 279)(89, 265)(90, 246)(91, 270)(92, 274)(93, 283)(94, 288)(95, 286)(96, 287)(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 ) } Outer automorphisms :: reflexible Dual of E15.1162 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 6^32, 8^24 ] E15.1160 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y1^4, (Y1^-1 * Y2^-1)^3, Y2^2 * Y1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y1 * Y2^-3 * Y1 * Y2^-1 * Y1 * Y2^-1, Y2^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 36, 132, 15, 111)(7, 103, 19, 115, 45, 141, 21, 117)(8, 104, 22, 118, 50, 146, 23, 119)(10, 106, 20, 116, 40, 136, 29, 125)(12, 108, 32, 128, 63, 159, 33, 129)(13, 109, 34, 130, 56, 152, 26, 122)(16, 112, 24, 120, 44, 140, 35, 131)(17, 113, 39, 135, 69, 165, 41, 137)(18, 114, 42, 138, 74, 170, 43, 139)(27, 123, 57, 153, 72, 168, 58, 154)(28, 124, 55, 151, 84, 180, 51, 147)(30, 126, 61, 157, 70, 166, 52, 148)(31, 127, 62, 158, 75, 171, 47, 143)(37, 133, 60, 156, 73, 169, 68, 164)(38, 134, 65, 161, 79, 175, 46, 142)(48, 144, 81, 177, 64, 160, 76, 172)(49, 145, 82, 178, 66, 162, 71, 167)(53, 149, 85, 181, 94, 190, 78, 174)(54, 150, 86, 182, 96, 192, 83, 179)(59, 155, 80, 176, 93, 189, 89, 185)(67, 163, 87, 183, 91, 187, 90, 186)(77, 173, 95, 191, 88, 184, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 251, 347, 230, 326, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 239, 335, 272, 368, 244, 340, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 252, 348, 281, 377, 249, 345, 227, 323, 205, 301)(198, 294, 209, 305, 232, 328, 263, 359, 285, 381, 268, 364, 236, 332, 210, 306)(201, 297, 218, 314, 247, 343, 225, 321, 257, 353, 229, 325, 206, 302, 219, 315)(203, 299, 222, 318, 243, 339, 214, 310, 238, 334, 211, 307, 207, 303, 223, 319)(213, 309, 240, 336, 267, 363, 234, 330, 262, 358, 231, 327, 215, 311, 241, 337)(217, 313, 245, 341, 276, 372, 287, 383, 271, 367, 259, 355, 228, 324, 246, 342)(224, 320, 235, 331, 265, 361, 233, 329, 264, 360, 258, 354, 226, 322, 256, 352)(237, 333, 269, 365, 254, 350, 282, 378, 253, 349, 275, 371, 242, 338, 270, 366)(248, 344, 279, 375, 255, 351, 278, 374, 260, 356, 277, 373, 250, 346, 280, 376)(261, 357, 283, 379, 274, 370, 288, 384, 273, 369, 286, 382, 266, 362, 284, 380) 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, 232)(18, 198)(19, 207)(20, 239)(21, 240)(22, 238)(23, 241)(24, 200)(25, 245)(26, 247)(27, 201)(28, 251)(29, 252)(30, 243)(31, 203)(32, 235)(33, 257)(34, 256)(35, 205)(36, 246)(37, 206)(38, 208)(39, 215)(40, 263)(41, 264)(42, 262)(43, 265)(44, 210)(45, 269)(46, 211)(47, 272)(48, 267)(49, 213)(50, 270)(51, 214)(52, 216)(53, 276)(54, 217)(55, 225)(56, 279)(57, 227)(58, 280)(59, 230)(60, 281)(61, 275)(62, 282)(63, 278)(64, 224)(65, 229)(66, 226)(67, 228)(68, 277)(69, 283)(70, 231)(71, 285)(72, 258)(73, 233)(74, 284)(75, 234)(76, 236)(77, 254)(78, 237)(79, 259)(80, 244)(81, 286)(82, 288)(83, 242)(84, 287)(85, 250)(86, 260)(87, 255)(88, 248)(89, 249)(90, 253)(91, 274)(92, 261)(93, 268)(94, 266)(95, 271)(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, 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 E15.1161 Graph:: bipartite v = 36 e = 192 f = 128 degree seq :: [ 8^24, 16^12 ] E15.1161 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^2 * Y2^-1 * Y3^-1, (Y2 * Y3)^4, (Y3 * Y2^-1)^4, (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, 196, 292)(195, 291, 200, 296, 202, 298)(197, 293, 205, 301, 206, 302)(198, 294, 208, 304, 210, 306)(199, 295, 211, 307, 212, 308)(201, 297, 209, 305, 217, 313)(203, 299, 220, 316, 221, 317)(204, 300, 222, 318, 223, 319)(207, 303, 213, 309, 224, 320)(214, 310, 236, 332, 238, 334)(215, 311, 239, 335, 240, 336)(216, 312, 237, 333, 242, 338)(218, 314, 244, 340, 233, 329)(219, 315, 245, 341, 246, 342)(225, 321, 249, 345, 253, 349)(226, 322, 255, 351, 228, 324)(227, 323, 254, 350, 256, 352)(229, 325, 258, 354, 259, 355)(230, 326, 257, 353, 261, 357)(231, 327, 262, 358, 251, 347)(232, 328, 263, 359, 264, 360)(234, 330, 266, 362, 247, 343)(235, 331, 265, 361, 267, 363)(241, 337, 260, 356, 274, 370)(243, 339, 275, 371, 272, 368)(248, 344, 279, 375, 280, 376)(250, 346, 281, 377, 269, 365)(252, 348, 282, 378, 268, 364)(270, 366, 287, 383, 278, 374)(271, 367, 288, 384, 284, 380)(273, 369, 285, 381, 276, 372)(277, 373, 283, 379, 286, 382) L = (1, 195)(2, 198)(3, 201)(4, 203)(5, 193)(6, 209)(7, 194)(8, 214)(9, 216)(10, 218)(11, 217)(12, 196)(13, 215)(14, 219)(15, 197)(16, 228)(17, 230)(18, 231)(19, 229)(20, 232)(21, 199)(22, 237)(23, 200)(24, 241)(25, 243)(26, 242)(27, 202)(28, 247)(29, 249)(30, 248)(31, 250)(32, 204)(33, 205)(34, 206)(35, 207)(36, 257)(37, 208)(38, 260)(39, 261)(40, 210)(41, 211)(42, 212)(43, 213)(44, 223)(45, 269)(46, 270)(47, 268)(48, 271)(49, 227)(50, 258)(51, 274)(52, 276)(53, 277)(54, 265)(55, 275)(56, 220)(57, 272)(58, 221)(59, 222)(60, 224)(61, 273)(62, 225)(63, 278)(64, 226)(65, 246)(66, 256)(67, 284)(68, 235)(69, 279)(70, 285)(71, 286)(72, 282)(73, 233)(74, 287)(75, 234)(76, 236)(77, 254)(78, 281)(79, 238)(80, 239)(81, 240)(82, 252)(83, 264)(84, 259)(85, 244)(86, 245)(87, 267)(88, 288)(89, 283)(90, 251)(91, 253)(92, 255)(93, 280)(94, 262)(95, 263)(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, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E15.1160 Graph:: simple bipartite v = 128 e = 192 f = 36 degree seq :: [ 2^96, 6^32 ] E15.1162 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y3^3, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1^-1)^4, Y1^8, (Y3 * Y1^-1)^4, Y3^-1 * Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 16, 112, 36, 132, 29, 125, 12, 108, 4, 100)(3, 99, 9, 105, 17, 113, 39, 135, 65, 161, 53, 149, 26, 122, 10, 106)(5, 101, 14, 110, 18, 114, 40, 136, 66, 162, 59, 155, 30, 126, 15, 111)(7, 103, 19, 115, 37, 133, 67, 163, 56, 152, 28, 124, 11, 107, 20, 116)(8, 104, 21, 117, 38, 134, 68, 164, 58, 154, 31, 127, 13, 109, 22, 118)(23, 119, 49, 145, 69, 165, 48, 144, 79, 175, 46, 142, 25, 121, 50, 146)(24, 120, 51, 147, 70, 166, 90, 186, 85, 181, 54, 150, 27, 123, 52, 148)(32, 128, 61, 157, 71, 167, 84, 180, 88, 184, 64, 160, 34, 130, 62, 158)(33, 129, 55, 151, 72, 168, 43, 139, 73, 169, 41, 137, 35, 131, 63, 159)(42, 138, 74, 170, 92, 188, 87, 183, 57, 153, 76, 172, 44, 140, 75, 171)(45, 141, 77, 173, 81, 177, 89, 185, 60, 156, 80, 176, 47, 143, 78, 174)(82, 178, 95, 191, 91, 187, 94, 190, 86, 182, 93, 189, 83, 179, 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, 197)(4, 203)(5, 193)(6, 209)(7, 200)(8, 194)(9, 215)(10, 217)(11, 205)(12, 218)(13, 196)(14, 224)(15, 226)(16, 229)(17, 210)(18, 198)(19, 233)(20, 235)(21, 237)(22, 239)(23, 216)(24, 201)(25, 219)(26, 222)(27, 202)(28, 247)(29, 248)(30, 204)(31, 252)(32, 225)(33, 206)(34, 227)(35, 207)(36, 257)(37, 230)(38, 208)(39, 261)(40, 263)(41, 234)(42, 211)(43, 236)(44, 212)(45, 238)(46, 213)(47, 240)(48, 214)(49, 223)(50, 260)(51, 274)(52, 275)(53, 271)(54, 278)(55, 249)(56, 250)(57, 220)(58, 221)(59, 280)(60, 241)(61, 246)(62, 282)(63, 284)(64, 243)(65, 258)(66, 228)(67, 255)(68, 273)(69, 262)(70, 231)(71, 264)(72, 232)(73, 251)(74, 285)(75, 286)(76, 287)(77, 268)(78, 279)(79, 277)(80, 266)(81, 242)(82, 256)(83, 276)(84, 244)(85, 245)(86, 253)(87, 288)(88, 265)(89, 267)(90, 283)(91, 254)(92, 259)(93, 272)(94, 281)(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) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.1159 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1163 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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^-1 * Y1^-1, Y1^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2, Y2^8, (Y3 * Y2^-1)^4, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 13, 109, 14, 110)(6, 102, 16, 112, 18, 114)(7, 103, 19, 115, 20, 116)(9, 105, 17, 113, 25, 121)(11, 107, 28, 124, 29, 125)(12, 108, 30, 126, 31, 127)(15, 111, 21, 117, 32, 128)(22, 118, 44, 140, 46, 142)(23, 119, 47, 143, 48, 144)(24, 120, 45, 141, 50, 146)(26, 122, 52, 148, 41, 137)(27, 123, 53, 149, 54, 150)(33, 129, 57, 153, 61, 157)(34, 130, 63, 159, 36, 132)(35, 131, 62, 158, 64, 160)(37, 133, 66, 162, 67, 163)(38, 134, 65, 161, 69, 165)(39, 135, 70, 166, 59, 155)(40, 136, 71, 167, 72, 168)(42, 138, 74, 170, 55, 151)(43, 139, 73, 169, 75, 171)(49, 145, 68, 164, 82, 178)(51, 147, 83, 179, 80, 176)(56, 152, 87, 183, 88, 184)(58, 154, 89, 185, 77, 173)(60, 156, 90, 186, 76, 172)(78, 174, 95, 191, 86, 182)(79, 175, 96, 192, 92, 188)(81, 177, 93, 189, 84, 180)(85, 181, 91, 187, 94, 190)(193, 289, 195, 291, 201, 297, 216, 312, 241, 337, 227, 323, 207, 303, 197, 293)(194, 290, 198, 294, 209, 305, 230, 326, 260, 356, 235, 331, 213, 309, 199, 295)(196, 292, 203, 299, 217, 313, 243, 339, 274, 370, 252, 348, 224, 320, 204, 300)(200, 296, 214, 310, 237, 333, 269, 365, 254, 350, 225, 321, 205, 301, 215, 311)(202, 298, 218, 314, 242, 338, 258, 354, 256, 352, 226, 322, 206, 302, 219, 315)(208, 304, 228, 324, 257, 353, 246, 342, 265, 361, 233, 329, 211, 307, 229, 325)(210, 306, 231, 327, 261, 357, 279, 375, 267, 363, 234, 330, 212, 308, 232, 328)(220, 316, 247, 343, 275, 371, 264, 360, 282, 378, 251, 347, 222, 318, 248, 344)(221, 317, 249, 345, 272, 368, 239, 335, 268, 364, 236, 332, 223, 319, 250, 346)(238, 334, 270, 366, 281, 377, 283, 379, 253, 349, 273, 369, 240, 336, 271, 367)(244, 340, 276, 372, 259, 355, 284, 380, 255, 351, 278, 374, 245, 341, 277, 373)(262, 358, 285, 381, 280, 376, 288, 384, 266, 362, 287, 383, 263, 359, 286, 382) L = (1, 196)(2, 193)(3, 202)(4, 194)(5, 206)(6, 210)(7, 212)(8, 195)(9, 217)(10, 200)(11, 221)(12, 223)(13, 197)(14, 205)(15, 224)(16, 198)(17, 201)(18, 208)(19, 199)(20, 211)(21, 207)(22, 238)(23, 240)(24, 242)(25, 209)(26, 233)(27, 246)(28, 203)(29, 220)(30, 204)(31, 222)(32, 213)(33, 253)(34, 228)(35, 256)(36, 255)(37, 259)(38, 261)(39, 251)(40, 264)(41, 244)(42, 247)(43, 267)(44, 214)(45, 216)(46, 236)(47, 215)(48, 239)(49, 274)(50, 237)(51, 272)(52, 218)(53, 219)(54, 245)(55, 266)(56, 280)(57, 225)(58, 269)(59, 262)(60, 268)(61, 249)(62, 227)(63, 226)(64, 254)(65, 230)(66, 229)(67, 258)(68, 241)(69, 257)(70, 231)(71, 232)(72, 263)(73, 235)(74, 234)(75, 265)(76, 282)(77, 281)(78, 278)(79, 284)(80, 275)(81, 276)(82, 260)(83, 243)(84, 285)(85, 286)(86, 287)(87, 248)(88, 279)(89, 250)(90, 252)(91, 277)(92, 288)(93, 273)(94, 283)(95, 270)(96, 271)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E15.1164 Graph:: bipartite v = 44 e = 192 f = 120 degree seq :: [ 6^32, 16^12 ] E15.1164 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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, Y1^4, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y1 * Y3^-3 * Y1 * Y3^-1 * Y1 * Y3^-1, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 36, 132, 15, 111)(7, 103, 19, 115, 45, 141, 21, 117)(8, 104, 22, 118, 50, 146, 23, 119)(10, 106, 20, 116, 40, 136, 29, 125)(12, 108, 32, 128, 63, 159, 33, 129)(13, 109, 34, 130, 56, 152, 26, 122)(16, 112, 24, 120, 44, 140, 35, 131)(17, 113, 39, 135, 69, 165, 41, 137)(18, 114, 42, 138, 74, 170, 43, 139)(27, 123, 57, 153, 72, 168, 58, 154)(28, 124, 55, 151, 84, 180, 51, 147)(30, 126, 61, 157, 70, 166, 52, 148)(31, 127, 62, 158, 75, 171, 47, 143)(37, 133, 60, 156, 73, 169, 68, 164)(38, 134, 65, 161, 79, 175, 46, 142)(48, 144, 81, 177, 64, 160, 76, 172)(49, 145, 82, 178, 66, 162, 71, 167)(53, 149, 85, 181, 94, 190, 78, 174)(54, 150, 86, 182, 96, 192, 83, 179)(59, 155, 80, 176, 93, 189, 89, 185)(67, 163, 87, 183, 91, 187, 90, 186)(77, 173, 95, 191, 88, 184, 92, 188)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 220)(11, 222)(12, 221)(13, 196)(14, 219)(15, 223)(16, 197)(17, 232)(18, 198)(19, 207)(20, 239)(21, 240)(22, 238)(23, 241)(24, 200)(25, 245)(26, 247)(27, 201)(28, 251)(29, 252)(30, 243)(31, 203)(32, 235)(33, 257)(34, 256)(35, 205)(36, 246)(37, 206)(38, 208)(39, 215)(40, 263)(41, 264)(42, 262)(43, 265)(44, 210)(45, 269)(46, 211)(47, 272)(48, 267)(49, 213)(50, 270)(51, 214)(52, 216)(53, 276)(54, 217)(55, 225)(56, 279)(57, 227)(58, 280)(59, 230)(60, 281)(61, 275)(62, 282)(63, 278)(64, 224)(65, 229)(66, 226)(67, 228)(68, 277)(69, 283)(70, 231)(71, 285)(72, 258)(73, 233)(74, 284)(75, 234)(76, 236)(77, 254)(78, 237)(79, 259)(80, 244)(81, 286)(82, 288)(83, 242)(84, 287)(85, 250)(86, 260)(87, 255)(88, 248)(89, 249)(90, 253)(91, 274)(92, 261)(93, 268)(94, 266)(95, 271)(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) :: { ( 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E15.1163 Graph:: simple bipartite v = 120 e = 192 f = 44 degree seq :: [ 2^96, 8^24 ] E15.1165 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2 * T1^-4)^2, (T1^-2 * T2)^4, T1^12 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 43, 66, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 77, 87, 68, 44, 36, 18, 8)(6, 13, 27, 51, 41, 64, 83, 85, 67, 54, 30, 14)(9, 19, 37, 62, 81, 89, 71, 46, 24, 45, 38, 20)(12, 25, 47, 40, 21, 39, 63, 82, 84, 74, 50, 26)(16, 28, 48, 69, 61, 76, 90, 96, 91, 80, 58, 33)(17, 29, 49, 70, 86, 94, 92, 78, 56, 75, 59, 34)(32, 52, 72, 60, 35, 53, 73, 88, 95, 93, 79, 57) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 84)(68, 86)(71, 88)(74, 90)(77, 91)(82, 92)(83, 93)(85, 94)(87, 95)(89, 96) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.1166 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.1166 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, (T1^-1 * T2)^12 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 12, 22, 31, 28, 17, 8)(6, 13, 21, 32, 30, 18, 9, 14)(15, 25, 33, 43, 40, 27, 16, 26)(23, 34, 42, 41, 29, 36, 24, 35)(37, 47, 52, 50, 39, 49, 38, 48)(44, 53, 51, 56, 46, 55, 45, 54)(57, 65, 60, 68, 59, 67, 58, 66)(61, 69, 64, 72, 63, 71, 62, 70)(73, 81, 76, 84, 75, 83, 74, 82)(77, 85, 80, 88, 79, 87, 78, 86)(89, 95, 92, 94, 91, 93, 90, 96) 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) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.1165 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.1167 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^8, (T2^-1 * T1)^12 ] Map:: polytopal R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 26, 39, 30, 18, 9, 16)(11, 20, 32, 44, 36, 23, 13, 21)(25, 37, 48, 41, 29, 40, 27, 38)(31, 42, 53, 46, 35, 45, 33, 43)(47, 57, 51, 60, 50, 59, 49, 58)(52, 61, 56, 64, 55, 63, 54, 62)(65, 73, 68, 76, 67, 75, 66, 74)(69, 77, 72, 80, 71, 79, 70, 78)(81, 89, 84, 92, 83, 91, 82, 90)(85, 93, 88, 96, 87, 95, 86, 94)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 108)(106, 110)(111, 121)(112, 123)(113, 122)(114, 125)(115, 126)(116, 127)(117, 129)(118, 128)(119, 131)(120, 132)(124, 130)(133, 143)(134, 145)(135, 144)(136, 146)(137, 147)(138, 148)(139, 150)(140, 149)(141, 151)(142, 152)(153, 161)(154, 162)(155, 163)(156, 164)(157, 165)(158, 166)(159, 167)(160, 168)(169, 177)(170, 178)(171, 179)(172, 180)(173, 181)(174, 182)(175, 183)(176, 184)(185, 191)(186, 192)(187, 189)(188, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 24, 24 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E15.1171 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.1168 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2^-1, (T2^-3 * T1)^2, T1^8, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 64, 80, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 88, 76, 60, 44, 22, 8)(4, 12, 29, 49, 65, 81, 91, 77, 61, 45, 23, 9)(6, 17, 36, 53, 69, 84, 94, 85, 70, 54, 38, 18)(11, 27, 37, 32, 51, 67, 83, 92, 78, 62, 46, 24)(13, 28, 43, 59, 75, 90, 95, 86, 71, 55, 39, 20)(14, 31, 50, 66, 82, 93, 79, 63, 47, 26, 35, 16)(21, 42, 58, 74, 89, 96, 87, 72, 56, 41, 30, 34)(97, 98, 102, 112, 130, 123, 109, 100)(99, 105, 113, 104, 117, 131, 124, 107)(101, 110, 114, 133, 126, 108, 116, 103)(106, 120, 132, 119, 138, 118, 139, 122)(111, 128, 134, 125, 137, 115, 135, 127)(121, 143, 149, 142, 154, 141, 155, 140)(129, 145, 150, 136, 152, 146, 151, 147)(144, 156, 165, 159, 170, 158, 171, 157)(148, 153, 166, 162, 168, 163, 167, 161)(160, 173, 180, 172, 185, 175, 186, 174)(164, 178, 181, 179, 183, 177, 182, 169)(176, 188, 190, 187, 192, 184, 191, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1172 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.1169 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2 * T1^-4)^2, (T1^-2 * T2)^4, T1^12 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 84)(68, 86)(71, 88)(74, 90)(77, 91)(82, 92)(83, 93)(85, 94)(87, 95)(89, 96)(97, 98, 101, 107, 119, 139, 162, 161, 138, 118, 106, 100)(99, 103, 111, 127, 151, 173, 183, 164, 140, 132, 114, 104)(102, 109, 123, 147, 137, 160, 179, 181, 163, 150, 126, 110)(105, 115, 133, 158, 177, 185, 167, 142, 120, 141, 134, 116)(108, 121, 143, 136, 117, 135, 159, 178, 180, 170, 146, 122)(112, 124, 144, 165, 157, 172, 186, 192, 187, 176, 154, 129)(113, 125, 145, 166, 182, 190, 188, 174, 152, 171, 155, 130)(128, 148, 168, 156, 131, 149, 169, 184, 191, 189, 175, 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) :: { ( 16, 16 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E15.1170 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 2^48, 12^8 ] E15.1170 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^8, (T2^-1 * T1)^12 ] Map:: R = (1, 97, 3, 99, 8, 104, 17, 113, 28, 124, 19, 115, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 22, 118, 34, 130, 24, 120, 14, 110, 6, 102)(7, 103, 15, 111, 26, 122, 39, 135, 30, 126, 18, 114, 9, 105, 16, 112)(11, 107, 20, 116, 32, 128, 44, 140, 36, 132, 23, 119, 13, 109, 21, 117)(25, 121, 37, 133, 48, 144, 41, 137, 29, 125, 40, 136, 27, 123, 38, 134)(31, 127, 42, 138, 53, 149, 46, 142, 35, 131, 45, 141, 33, 129, 43, 139)(47, 143, 57, 153, 51, 147, 60, 156, 50, 146, 59, 155, 49, 145, 58, 154)(52, 148, 61, 157, 56, 152, 64, 160, 55, 151, 63, 159, 54, 150, 62, 158)(65, 161, 73, 169, 68, 164, 76, 172, 67, 163, 75, 171, 66, 162, 74, 170)(69, 165, 77, 173, 72, 168, 80, 176, 71, 167, 79, 175, 70, 166, 78, 174)(81, 177, 89, 185, 84, 180, 92, 188, 83, 179, 91, 187, 82, 178, 90, 186)(85, 181, 93, 189, 88, 184, 96, 192, 87, 183, 95, 191, 86, 182, 94, 190) 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, 121)(16, 123)(17, 122)(18, 125)(19, 126)(20, 127)(21, 129)(22, 128)(23, 131)(24, 132)(25, 111)(26, 113)(27, 112)(28, 130)(29, 114)(30, 115)(31, 116)(32, 118)(33, 117)(34, 124)(35, 119)(36, 120)(37, 143)(38, 145)(39, 144)(40, 146)(41, 147)(42, 148)(43, 150)(44, 149)(45, 151)(46, 152)(47, 133)(48, 135)(49, 134)(50, 136)(51, 137)(52, 138)(53, 140)(54, 139)(55, 141)(56, 142)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)(89, 191)(90, 192)(91, 189)(92, 190)(93, 187)(94, 188)(95, 185)(96, 186) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E15.1169 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1171 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2^-1, (T2^-3 * T1)^2, T1^8, T2^12 ] Map:: R = (1, 97, 3, 99, 10, 106, 25, 121, 48, 144, 64, 160, 80, 176, 68, 164, 52, 148, 33, 129, 15, 111, 5, 101)(2, 98, 7, 103, 19, 115, 40, 136, 57, 153, 73, 169, 88, 184, 76, 172, 60, 156, 44, 140, 22, 118, 8, 104)(4, 100, 12, 108, 29, 125, 49, 145, 65, 161, 81, 177, 91, 187, 77, 173, 61, 157, 45, 141, 23, 119, 9, 105)(6, 102, 17, 113, 36, 132, 53, 149, 69, 165, 84, 180, 94, 190, 85, 181, 70, 166, 54, 150, 38, 134, 18, 114)(11, 107, 27, 123, 37, 133, 32, 128, 51, 147, 67, 163, 83, 179, 92, 188, 78, 174, 62, 158, 46, 142, 24, 120)(13, 109, 28, 124, 43, 139, 59, 155, 75, 171, 90, 186, 95, 191, 86, 182, 71, 167, 55, 151, 39, 135, 20, 116)(14, 110, 31, 127, 50, 146, 66, 162, 82, 178, 93, 189, 79, 175, 63, 159, 47, 143, 26, 122, 35, 131, 16, 112)(21, 117, 42, 138, 58, 154, 74, 170, 89, 185, 96, 192, 87, 183, 72, 168, 56, 152, 41, 137, 30, 126, 34, 130) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 101)(8, 117)(9, 113)(10, 120)(11, 99)(12, 116)(13, 100)(14, 114)(15, 128)(16, 130)(17, 104)(18, 133)(19, 135)(20, 103)(21, 131)(22, 139)(23, 138)(24, 132)(25, 143)(26, 106)(27, 109)(28, 107)(29, 137)(30, 108)(31, 111)(32, 134)(33, 145)(34, 123)(35, 124)(36, 119)(37, 126)(38, 125)(39, 127)(40, 152)(41, 115)(42, 118)(43, 122)(44, 121)(45, 155)(46, 154)(47, 149)(48, 156)(49, 150)(50, 151)(51, 129)(52, 153)(53, 142)(54, 136)(55, 147)(56, 146)(57, 166)(58, 141)(59, 140)(60, 165)(61, 144)(62, 171)(63, 170)(64, 173)(65, 148)(66, 168)(67, 167)(68, 178)(69, 159)(70, 162)(71, 161)(72, 163)(73, 164)(74, 158)(75, 157)(76, 185)(77, 180)(78, 160)(79, 186)(80, 188)(81, 182)(82, 181)(83, 183)(84, 172)(85, 179)(86, 169)(87, 177)(88, 191)(89, 175)(90, 174)(91, 192)(92, 190)(93, 176)(94, 187)(95, 189)(96, 184) 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 ) } Outer automorphisms :: reflexible Dual of E15.1167 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 24^8 ] E15.1172 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2 * T1^-4)^2, (T1^-2 * T2)^4, T1^12 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 21, 117)(11, 107, 24, 120)(13, 109, 28, 124)(14, 110, 29, 125)(15, 111, 32, 128)(18, 114, 35, 131)(19, 115, 33, 129)(20, 116, 34, 130)(22, 118, 41, 137)(23, 119, 44, 140)(25, 121, 48, 144)(26, 122, 49, 145)(27, 123, 52, 148)(30, 126, 53, 149)(31, 127, 56, 152)(36, 132, 61, 157)(37, 133, 57, 153)(38, 134, 60, 156)(39, 135, 58, 154)(40, 136, 59, 155)(42, 138, 55, 151)(43, 139, 67, 163)(45, 141, 69, 165)(46, 142, 70, 166)(47, 143, 72, 168)(50, 146, 73, 169)(51, 147, 75, 171)(54, 150, 76, 172)(62, 158, 78, 174)(63, 159, 79, 175)(64, 160, 80, 176)(65, 161, 81, 177)(66, 162, 84, 180)(68, 164, 86, 182)(71, 167, 88, 184)(74, 170, 90, 186)(77, 173, 91, 187)(82, 178, 92, 188)(83, 179, 93, 189)(85, 181, 94, 190)(87, 183, 95, 191)(89, 185, 96, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 115)(10, 100)(11, 119)(12, 121)(13, 123)(14, 102)(15, 127)(16, 124)(17, 125)(18, 104)(19, 133)(20, 105)(21, 135)(22, 106)(23, 139)(24, 141)(25, 143)(26, 108)(27, 147)(28, 144)(29, 145)(30, 110)(31, 151)(32, 148)(33, 112)(34, 113)(35, 149)(36, 114)(37, 158)(38, 116)(39, 159)(40, 117)(41, 160)(42, 118)(43, 162)(44, 132)(45, 134)(46, 120)(47, 136)(48, 165)(49, 166)(50, 122)(51, 137)(52, 168)(53, 169)(54, 126)(55, 173)(56, 171)(57, 128)(58, 129)(59, 130)(60, 131)(61, 172)(62, 177)(63, 178)(64, 179)(65, 138)(66, 161)(67, 150)(68, 140)(69, 157)(70, 182)(71, 142)(72, 156)(73, 184)(74, 146)(75, 155)(76, 186)(77, 183)(78, 152)(79, 153)(80, 154)(81, 185)(82, 180)(83, 181)(84, 170)(85, 163)(86, 190)(87, 164)(88, 191)(89, 167)(90, 192)(91, 176)(92, 174)(93, 175)(94, 188)(95, 189)(96, 187) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.1168 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.1173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^8, (Y3 * Y2^-1)^12 ] 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, 25, 121)(16, 112, 27, 123)(17, 113, 26, 122)(18, 114, 29, 125)(19, 115, 30, 126)(20, 116, 31, 127)(21, 117, 33, 129)(22, 118, 32, 128)(23, 119, 35, 131)(24, 120, 36, 132)(28, 124, 34, 130)(37, 133, 47, 143)(38, 134, 49, 145)(39, 135, 48, 144)(40, 136, 50, 146)(41, 137, 51, 147)(42, 138, 52, 148)(43, 139, 54, 150)(44, 140, 53, 149)(45, 141, 55, 151)(46, 142, 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, 95, 191)(90, 186, 96, 192)(91, 187, 93, 189)(92, 188, 94, 190)(193, 289, 195, 291, 200, 296, 209, 305, 220, 316, 211, 307, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 214, 310, 226, 322, 216, 312, 206, 302, 198, 294)(199, 295, 207, 303, 218, 314, 231, 327, 222, 318, 210, 306, 201, 297, 208, 304)(203, 299, 212, 308, 224, 320, 236, 332, 228, 324, 215, 311, 205, 301, 213, 309)(217, 313, 229, 325, 240, 336, 233, 329, 221, 317, 232, 328, 219, 315, 230, 326)(223, 319, 234, 330, 245, 341, 238, 334, 227, 323, 237, 333, 225, 321, 235, 331)(239, 335, 249, 345, 243, 339, 252, 348, 242, 338, 251, 347, 241, 337, 250, 346)(244, 340, 253, 349, 248, 344, 256, 352, 247, 343, 255, 351, 246, 342, 254, 350)(257, 353, 265, 361, 260, 356, 268, 364, 259, 355, 267, 363, 258, 354, 266, 362)(261, 357, 269, 365, 264, 360, 272, 368, 263, 359, 271, 367, 262, 358, 270, 366)(273, 369, 281, 377, 276, 372, 284, 380, 275, 371, 283, 379, 274, 370, 282, 378)(277, 373, 285, 381, 280, 376, 288, 384, 279, 375, 287, 383, 278, 374, 286, 382) 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, 217)(16, 219)(17, 218)(18, 221)(19, 222)(20, 223)(21, 225)(22, 224)(23, 227)(24, 228)(25, 207)(26, 209)(27, 208)(28, 226)(29, 210)(30, 211)(31, 212)(32, 214)(33, 213)(34, 220)(35, 215)(36, 216)(37, 239)(38, 241)(39, 240)(40, 242)(41, 243)(42, 244)(43, 246)(44, 245)(45, 247)(46, 248)(47, 229)(48, 231)(49, 230)(50, 232)(51, 233)(52, 234)(53, 236)(54, 235)(55, 237)(56, 238)(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, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 265)(82, 266)(83, 267)(84, 268)(85, 269)(86, 270)(87, 271)(88, 272)(89, 287)(90, 288)(91, 285)(92, 286)(93, 283)(94, 284)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E15.1176 Graph:: bipartite v = 60 e = 192 f = 104 degree seq :: [ 4^48, 16^12 ] E15.1174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y1^-1 * Y2^-1)^2, (Y2 * Y1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y1^-2 * Y2 * Y1^2 * Y2^-1, (Y2^-3 * Y1)^2, Y1^8, Y2^12 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 34, 130, 27, 123, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 8, 104, 21, 117, 35, 131, 28, 124, 11, 107)(5, 101, 14, 110, 18, 114, 37, 133, 30, 126, 12, 108, 20, 116, 7, 103)(10, 106, 24, 120, 36, 132, 23, 119, 42, 138, 22, 118, 43, 139, 26, 122)(15, 111, 32, 128, 38, 134, 29, 125, 41, 137, 19, 115, 39, 135, 31, 127)(25, 121, 47, 143, 53, 149, 46, 142, 58, 154, 45, 141, 59, 155, 44, 140)(33, 129, 49, 145, 54, 150, 40, 136, 56, 152, 50, 146, 55, 151, 51, 147)(48, 144, 60, 156, 69, 165, 63, 159, 74, 170, 62, 158, 75, 171, 61, 157)(52, 148, 57, 153, 70, 166, 66, 162, 72, 168, 67, 163, 71, 167, 65, 161)(64, 160, 77, 173, 84, 180, 76, 172, 89, 185, 79, 175, 90, 186, 78, 174)(68, 164, 82, 178, 85, 181, 83, 179, 87, 183, 81, 177, 86, 182, 73, 169)(80, 176, 92, 188, 94, 190, 91, 187, 96, 192, 88, 184, 95, 191, 93, 189)(193, 289, 195, 291, 202, 298, 217, 313, 240, 336, 256, 352, 272, 368, 260, 356, 244, 340, 225, 321, 207, 303, 197, 293)(194, 290, 199, 295, 211, 307, 232, 328, 249, 345, 265, 361, 280, 376, 268, 364, 252, 348, 236, 332, 214, 310, 200, 296)(196, 292, 204, 300, 221, 317, 241, 337, 257, 353, 273, 369, 283, 379, 269, 365, 253, 349, 237, 333, 215, 311, 201, 297)(198, 294, 209, 305, 228, 324, 245, 341, 261, 357, 276, 372, 286, 382, 277, 373, 262, 358, 246, 342, 230, 326, 210, 306)(203, 299, 219, 315, 229, 325, 224, 320, 243, 339, 259, 355, 275, 371, 284, 380, 270, 366, 254, 350, 238, 334, 216, 312)(205, 301, 220, 316, 235, 331, 251, 347, 267, 363, 282, 378, 287, 383, 278, 374, 263, 359, 247, 343, 231, 327, 212, 308)(206, 302, 223, 319, 242, 338, 258, 354, 274, 370, 285, 381, 271, 367, 255, 351, 239, 335, 218, 314, 227, 323, 208, 304)(213, 309, 234, 330, 250, 346, 266, 362, 281, 377, 288, 384, 279, 375, 264, 360, 248, 344, 233, 329, 222, 318, 226, 322) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 217)(11, 219)(12, 221)(13, 220)(14, 223)(15, 197)(16, 206)(17, 228)(18, 198)(19, 232)(20, 205)(21, 234)(22, 200)(23, 201)(24, 203)(25, 240)(26, 227)(27, 229)(28, 235)(29, 241)(30, 226)(31, 242)(32, 243)(33, 207)(34, 213)(35, 208)(36, 245)(37, 224)(38, 210)(39, 212)(40, 249)(41, 222)(42, 250)(43, 251)(44, 214)(45, 215)(46, 216)(47, 218)(48, 256)(49, 257)(50, 258)(51, 259)(52, 225)(53, 261)(54, 230)(55, 231)(56, 233)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 248)(73, 280)(74, 281)(75, 282)(76, 252)(77, 253)(78, 254)(79, 255)(80, 260)(81, 283)(82, 285)(83, 284)(84, 286)(85, 262)(86, 263)(87, 264)(88, 268)(89, 288)(90, 287)(91, 269)(92, 270)(93, 271)(94, 277)(95, 278)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 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 E15.1175 Graph:: bipartite v = 20 e = 192 f = 144 degree seq :: [ 16^12, 24^8 ] E15.1175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-4 * Y2)^2, (Y3^-2 * Y2)^4, Y3^4 * Y2 * Y3^-2 * Y2 * Y3^3 * Y2 * Y3^-2 * Y2 * Y3, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 209, 305)(202, 298, 213, 309)(204, 300, 217, 313)(206, 302, 221, 317)(207, 303, 215, 311)(208, 304, 219, 315)(210, 306, 227, 323)(211, 307, 216, 312)(212, 308, 220, 316)(214, 310, 233, 329)(218, 314, 239, 335)(222, 318, 245, 341)(223, 319, 237, 333)(224, 320, 243, 339)(225, 321, 235, 331)(226, 322, 241, 337)(228, 324, 246, 342)(229, 325, 238, 334)(230, 326, 244, 340)(231, 327, 236, 332)(232, 328, 242, 338)(234, 330, 240, 336)(247, 343, 262, 358)(248, 344, 267, 363)(249, 345, 260, 356)(250, 346, 266, 362)(251, 347, 258, 354)(252, 348, 265, 361)(253, 349, 269, 365)(254, 350, 263, 359)(255, 351, 261, 357)(256, 352, 259, 355)(257, 353, 273, 369)(264, 360, 276, 372)(268, 364, 280, 376)(270, 366, 282, 378)(271, 367, 281, 377)(272, 368, 284, 380)(274, 370, 278, 374)(275, 371, 277, 373)(279, 375, 287, 383)(283, 379, 288, 384)(285, 381, 286, 382) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 210)(9, 211)(10, 196)(11, 215)(12, 218)(13, 219)(14, 198)(15, 223)(16, 199)(17, 225)(18, 228)(19, 229)(20, 201)(21, 231)(22, 202)(23, 235)(24, 203)(25, 237)(26, 240)(27, 241)(28, 205)(29, 243)(30, 206)(31, 247)(32, 208)(33, 249)(34, 209)(35, 251)(36, 253)(37, 254)(38, 212)(39, 255)(40, 213)(41, 256)(42, 214)(43, 258)(44, 216)(45, 260)(46, 217)(47, 262)(48, 264)(49, 265)(50, 220)(51, 266)(52, 221)(53, 267)(54, 222)(55, 233)(56, 224)(57, 232)(58, 226)(59, 230)(60, 227)(61, 272)(62, 273)(63, 274)(64, 275)(65, 234)(66, 245)(67, 236)(68, 244)(69, 238)(70, 242)(71, 239)(72, 279)(73, 280)(74, 281)(75, 282)(76, 246)(77, 248)(78, 250)(79, 252)(80, 257)(81, 285)(82, 284)(83, 283)(84, 259)(85, 261)(86, 263)(87, 268)(88, 288)(89, 287)(90, 286)(91, 269)(92, 270)(93, 271)(94, 276)(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) :: { ( 16, 24 ), ( 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E15.1174 Graph:: simple bipartite v = 144 e = 192 f = 20 degree seq :: [ 2^96, 4^48 ] E15.1176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-2 * Y1^-1 * Y3, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3, Y3 * Y1^-4 * Y3^-1 * Y1^-4, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1, Y1^12, Y1 * Y3^-4 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 97, 2, 98, 5, 101, 11, 107, 23, 119, 43, 139, 66, 162, 65, 161, 42, 138, 22, 118, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 31, 127, 55, 151, 77, 173, 87, 183, 68, 164, 44, 140, 36, 132, 18, 114, 8, 104)(6, 102, 13, 109, 27, 123, 51, 147, 41, 137, 64, 160, 83, 179, 85, 181, 67, 163, 54, 150, 30, 126, 14, 110)(9, 105, 19, 115, 37, 133, 62, 158, 81, 177, 89, 185, 71, 167, 46, 142, 24, 120, 45, 141, 38, 134, 20, 116)(12, 108, 25, 121, 47, 143, 40, 136, 21, 117, 39, 135, 63, 159, 82, 178, 84, 180, 74, 170, 50, 146, 26, 122)(16, 112, 28, 124, 48, 144, 69, 165, 61, 157, 76, 172, 90, 186, 96, 192, 91, 187, 80, 176, 58, 154, 33, 129)(17, 113, 29, 125, 49, 145, 70, 166, 86, 182, 94, 190, 92, 188, 78, 174, 56, 152, 75, 171, 59, 155, 34, 130)(32, 128, 52, 148, 72, 168, 60, 156, 35, 131, 53, 149, 73, 169, 88, 184, 95, 191, 93, 189, 79, 175, 57, 153)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 213)(11, 216)(12, 197)(13, 220)(14, 221)(15, 224)(16, 199)(17, 200)(18, 227)(19, 225)(20, 226)(21, 202)(22, 233)(23, 236)(24, 203)(25, 240)(26, 241)(27, 244)(28, 205)(29, 206)(30, 245)(31, 248)(32, 207)(33, 211)(34, 212)(35, 210)(36, 253)(37, 249)(38, 252)(39, 250)(40, 251)(41, 214)(42, 247)(43, 259)(44, 215)(45, 261)(46, 262)(47, 264)(48, 217)(49, 218)(50, 265)(51, 267)(52, 219)(53, 222)(54, 268)(55, 234)(56, 223)(57, 229)(58, 231)(59, 232)(60, 230)(61, 228)(62, 270)(63, 271)(64, 272)(65, 273)(66, 276)(67, 235)(68, 278)(69, 237)(70, 238)(71, 280)(72, 239)(73, 242)(74, 282)(75, 243)(76, 246)(77, 283)(78, 254)(79, 255)(80, 256)(81, 257)(82, 284)(83, 285)(84, 258)(85, 286)(86, 260)(87, 287)(88, 263)(89, 288)(90, 266)(91, 269)(92, 274)(93, 275)(94, 277)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1173 Graph:: simple bipartite v = 104 e = 192 f = 60 degree seq :: [ 2^96, 24^8 ] E15.1177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ Y1^2, 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, Y2^12, Y2^4 * Y1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1 * Y2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 17, 113)(10, 106, 21, 117)(12, 108, 25, 121)(14, 110, 29, 125)(15, 111, 23, 119)(16, 112, 27, 123)(18, 114, 35, 131)(19, 115, 24, 120)(20, 116, 28, 124)(22, 118, 41, 137)(26, 122, 47, 143)(30, 126, 53, 149)(31, 127, 45, 141)(32, 128, 51, 147)(33, 129, 43, 139)(34, 130, 49, 145)(36, 132, 54, 150)(37, 133, 46, 142)(38, 134, 52, 148)(39, 135, 44, 140)(40, 136, 50, 146)(42, 138, 48, 144)(55, 151, 70, 166)(56, 152, 75, 171)(57, 153, 68, 164)(58, 154, 74, 170)(59, 155, 66, 162)(60, 156, 73, 169)(61, 157, 77, 173)(62, 158, 71, 167)(63, 159, 69, 165)(64, 160, 67, 163)(65, 161, 81, 177)(72, 168, 84, 180)(76, 172, 88, 184)(78, 174, 90, 186)(79, 175, 89, 185)(80, 176, 92, 188)(82, 178, 86, 182)(83, 179, 85, 181)(87, 183, 95, 191)(91, 187, 96, 192)(93, 189, 94, 190)(193, 289, 195, 291, 200, 296, 210, 306, 228, 324, 253, 349, 272, 368, 257, 353, 234, 330, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 240, 336, 264, 360, 279, 375, 268, 364, 246, 342, 222, 318, 206, 302, 198, 294)(199, 295, 207, 303, 223, 319, 247, 343, 233, 329, 256, 352, 275, 371, 283, 379, 269, 365, 248, 344, 224, 320, 208, 304)(201, 297, 211, 307, 229, 325, 254, 350, 273, 369, 285, 381, 271, 367, 252, 348, 227, 323, 251, 347, 230, 326, 212, 308)(203, 299, 215, 311, 235, 331, 258, 354, 245, 341, 267, 363, 282, 378, 286, 382, 276, 372, 259, 355, 236, 332, 216, 312)(205, 301, 219, 315, 241, 337, 265, 361, 280, 376, 288, 384, 278, 374, 263, 359, 239, 335, 262, 358, 242, 338, 220, 316)(209, 305, 225, 321, 249, 345, 232, 328, 213, 309, 231, 327, 255, 351, 274, 370, 284, 380, 270, 366, 250, 346, 226, 322)(217, 313, 237, 333, 260, 356, 244, 340, 221, 317, 243, 339, 266, 362, 281, 377, 287, 383, 277, 373, 261, 357, 238, 334) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 209)(9, 196)(10, 213)(11, 197)(12, 217)(13, 198)(14, 221)(15, 215)(16, 219)(17, 200)(18, 227)(19, 216)(20, 220)(21, 202)(22, 233)(23, 207)(24, 211)(25, 204)(26, 239)(27, 208)(28, 212)(29, 206)(30, 245)(31, 237)(32, 243)(33, 235)(34, 241)(35, 210)(36, 246)(37, 238)(38, 244)(39, 236)(40, 242)(41, 214)(42, 240)(43, 225)(44, 231)(45, 223)(46, 229)(47, 218)(48, 234)(49, 226)(50, 232)(51, 224)(52, 230)(53, 222)(54, 228)(55, 262)(56, 267)(57, 260)(58, 266)(59, 258)(60, 265)(61, 269)(62, 263)(63, 261)(64, 259)(65, 273)(66, 251)(67, 256)(68, 249)(69, 255)(70, 247)(71, 254)(72, 276)(73, 252)(74, 250)(75, 248)(76, 280)(77, 253)(78, 282)(79, 281)(80, 284)(81, 257)(82, 278)(83, 277)(84, 264)(85, 275)(86, 274)(87, 287)(88, 268)(89, 271)(90, 270)(91, 288)(92, 272)(93, 286)(94, 285)(95, 279)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E15.1178 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 4^48, 24^8 ] E15.1178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C12 x C4) : C2 (small group id <96, 12>) Aut = $<192, 381>$ (small group id <192, 381>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1^-1 * Y3^-1)^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^2 * Y3^-1, (Y3^-3 * Y1)^2, Y1^8, (Y3 * Y2^-1)^12 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 16, 112, 34, 130, 27, 123, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 8, 104, 21, 117, 35, 131, 28, 124, 11, 107)(5, 101, 14, 110, 18, 114, 37, 133, 30, 126, 12, 108, 20, 116, 7, 103)(10, 106, 24, 120, 36, 132, 23, 119, 42, 138, 22, 118, 43, 139, 26, 122)(15, 111, 32, 128, 38, 134, 29, 125, 41, 137, 19, 115, 39, 135, 31, 127)(25, 121, 47, 143, 53, 149, 46, 142, 58, 154, 45, 141, 59, 155, 44, 140)(33, 129, 49, 145, 54, 150, 40, 136, 56, 152, 50, 146, 55, 151, 51, 147)(48, 144, 60, 156, 69, 165, 63, 159, 74, 170, 62, 158, 75, 171, 61, 157)(52, 148, 57, 153, 70, 166, 66, 162, 72, 168, 67, 163, 71, 167, 65, 161)(64, 160, 77, 173, 84, 180, 76, 172, 89, 185, 79, 175, 90, 186, 78, 174)(68, 164, 82, 178, 85, 181, 83, 179, 87, 183, 81, 177, 86, 182, 73, 169)(80, 176, 92, 188, 94, 190, 91, 187, 96, 192, 88, 184, 95, 191, 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, 209)(7, 211)(8, 194)(9, 196)(10, 217)(11, 219)(12, 221)(13, 220)(14, 223)(15, 197)(16, 206)(17, 228)(18, 198)(19, 232)(20, 205)(21, 234)(22, 200)(23, 201)(24, 203)(25, 240)(26, 227)(27, 229)(28, 235)(29, 241)(30, 226)(31, 242)(32, 243)(33, 207)(34, 213)(35, 208)(36, 245)(37, 224)(38, 210)(39, 212)(40, 249)(41, 222)(42, 250)(43, 251)(44, 214)(45, 215)(46, 216)(47, 218)(48, 256)(49, 257)(50, 258)(51, 259)(52, 225)(53, 261)(54, 230)(55, 231)(56, 233)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 248)(73, 280)(74, 281)(75, 282)(76, 252)(77, 253)(78, 254)(79, 255)(80, 260)(81, 283)(82, 285)(83, 284)(84, 286)(85, 262)(86, 263)(87, 264)(88, 268)(89, 288)(90, 287)(91, 269)(92, 270)(93, 271)(94, 277)(95, 278)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.1177 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1179 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^12, (T1 * T2)^8 ] Map:: polytopal 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, 92, 84, 68, 60, 43, 58)(52, 69, 53, 71, 63, 80, 91, 93, 83, 72, 54, 70)(75, 85, 76, 86, 78, 88, 94, 96, 95, 90, 77, 87) 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, 91)(80, 90)(82, 92)(84, 94)(89, 95)(93, 96) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.1180 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.1180 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, T1^8, T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 15, 25, 31, 22, 12, 8)(6, 13, 9, 18, 29, 32, 21, 14)(16, 26, 17, 28, 33, 43, 37, 27)(23, 34, 24, 36, 42, 41, 30, 35)(38, 47, 39, 49, 52, 50, 40, 48)(44, 53, 45, 55, 51, 56, 46, 54)(57, 65, 58, 67, 60, 68, 59, 66)(61, 69, 62, 71, 64, 72, 63, 70)(73, 81, 74, 83, 76, 84, 75, 82)(77, 85, 78, 87, 80, 88, 79, 86)(89, 93, 90, 94, 92, 96, 91, 95) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 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) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.1179 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.1181 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, (T2^-1 * T1)^12 ] Map:: polytopal R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 9, 18, 30, 40, 27, 16)(11, 20, 13, 23, 36, 45, 33, 21)(25, 37, 26, 39, 50, 41, 29, 38)(31, 42, 32, 44, 55, 46, 35, 43)(47, 57, 48, 59, 51, 60, 49, 58)(52, 61, 53, 63, 56, 64, 54, 62)(65, 73, 66, 75, 68, 76, 67, 74)(69, 77, 70, 79, 72, 80, 71, 78)(81, 89, 82, 91, 84, 92, 83, 90)(85, 93, 86, 95, 88, 96, 87, 94)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 110)(106, 108)(111, 121)(112, 122)(113, 123)(114, 125)(115, 126)(116, 127)(117, 128)(118, 129)(119, 131)(120, 132)(124, 130)(133, 143)(134, 144)(135, 145)(136, 146)(137, 147)(138, 148)(139, 149)(140, 150)(141, 151)(142, 152)(153, 161)(154, 162)(155, 163)(156, 164)(157, 165)(158, 166)(159, 167)(160, 168)(169, 177)(170, 178)(171, 179)(172, 180)(173, 181)(174, 182)(175, 183)(176, 184)(185, 189)(186, 191)(187, 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) :: { ( 24, 24 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E15.1185 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.1182 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^8, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 52, 68, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 63, 78, 64, 48, 32, 18, 8)(4, 11, 23, 39, 55, 71, 81, 67, 51, 35, 20, 9)(6, 15, 29, 45, 61, 76, 88, 77, 62, 46, 30, 16)(12, 19, 34, 50, 66, 80, 90, 83, 70, 54, 38, 22)(14, 27, 43, 59, 74, 86, 94, 87, 75, 60, 44, 28)(24, 37, 53, 69, 82, 91, 95, 89, 79, 65, 49, 33)(26, 41, 57, 72, 84, 92, 96, 93, 85, 73, 58, 42)(97, 98, 102, 110, 122, 120, 108, 100)(99, 105, 115, 129, 137, 124, 111, 104)(101, 107, 118, 133, 138, 123, 112, 103)(106, 114, 125, 140, 153, 145, 130, 116)(109, 113, 126, 139, 154, 149, 134, 119)(117, 131, 146, 161, 168, 156, 141, 128)(121, 135, 150, 165, 169, 155, 142, 127)(132, 144, 157, 171, 180, 175, 162, 147)(136, 143, 158, 170, 181, 178, 166, 151)(148, 163, 176, 185, 188, 183, 172, 160)(152, 167, 179, 187, 189, 182, 173, 159)(164, 174, 184, 190, 192, 191, 186, 177) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1186 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.1183 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^12, (T2 * T1)^8 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 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, 91)(80, 90)(82, 92)(84, 94)(89, 95)(93, 96)(97, 98, 101, 107, 116, 128, 143, 142, 127, 115, 106, 100)(99, 103, 111, 121, 135, 151, 160, 145, 129, 118, 108, 104)(102, 109, 105, 114, 125, 140, 157, 161, 144, 130, 117, 110)(112, 122, 113, 124, 131, 147, 162, 178, 169, 152, 136, 123)(119, 132, 120, 134, 146, 163, 177, 175, 158, 141, 126, 133)(137, 153, 138, 155, 170, 185, 188, 180, 164, 156, 139, 154)(148, 165, 149, 167, 159, 176, 187, 189, 179, 168, 150, 166)(171, 181, 172, 182, 174, 184, 190, 192, 191, 186, 173, 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) :: { ( 16, 16 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E15.1184 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 2^48, 12^8 ] E15.1184 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, (T2^-1 * T1)^12 ] Map:: R = (1, 97, 3, 99, 8, 104, 17, 113, 28, 124, 19, 115, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 22, 118, 34, 130, 24, 120, 14, 110, 6, 102)(7, 103, 15, 111, 9, 105, 18, 114, 30, 126, 40, 136, 27, 123, 16, 112)(11, 107, 20, 116, 13, 109, 23, 119, 36, 132, 45, 141, 33, 129, 21, 117)(25, 121, 37, 133, 26, 122, 39, 135, 50, 146, 41, 137, 29, 125, 38, 134)(31, 127, 42, 138, 32, 128, 44, 140, 55, 151, 46, 142, 35, 131, 43, 139)(47, 143, 57, 153, 48, 144, 59, 155, 51, 147, 60, 156, 49, 145, 58, 154)(52, 148, 61, 157, 53, 149, 63, 159, 56, 152, 64, 160, 54, 150, 62, 158)(65, 161, 73, 169, 66, 162, 75, 171, 68, 164, 76, 172, 67, 163, 74, 170)(69, 165, 77, 173, 70, 166, 79, 175, 72, 168, 80, 176, 71, 167, 78, 174)(81, 177, 89, 185, 82, 178, 91, 187, 84, 180, 92, 188, 83, 179, 90, 186)(85, 181, 93, 189, 86, 182, 95, 191, 88, 184, 96, 192, 87, 183, 94, 190) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 110)(9, 100)(10, 108)(11, 101)(12, 106)(13, 102)(14, 104)(15, 121)(16, 122)(17, 123)(18, 125)(19, 126)(20, 127)(21, 128)(22, 129)(23, 131)(24, 132)(25, 111)(26, 112)(27, 113)(28, 130)(29, 114)(30, 115)(31, 116)(32, 117)(33, 118)(34, 124)(35, 119)(36, 120)(37, 143)(38, 144)(39, 145)(40, 146)(41, 147)(42, 148)(43, 149)(44, 150)(45, 151)(46, 152)(47, 133)(48, 134)(49, 135)(50, 136)(51, 137)(52, 138)(53, 139)(54, 140)(55, 141)(56, 142)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)(89, 189)(90, 191)(91, 190)(92, 192)(93, 185)(94, 187)(95, 186)(96, 188) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E15.1183 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1185 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^8, T2^12 ] Map:: R = (1, 97, 3, 99, 10, 106, 21, 117, 36, 132, 52, 148, 68, 164, 56, 152, 40, 136, 25, 121, 13, 109, 5, 101)(2, 98, 7, 103, 17, 113, 31, 127, 47, 143, 63, 159, 78, 174, 64, 160, 48, 144, 32, 128, 18, 114, 8, 104)(4, 100, 11, 107, 23, 119, 39, 135, 55, 151, 71, 167, 81, 177, 67, 163, 51, 147, 35, 131, 20, 116, 9, 105)(6, 102, 15, 111, 29, 125, 45, 141, 61, 157, 76, 172, 88, 184, 77, 173, 62, 158, 46, 142, 30, 126, 16, 112)(12, 108, 19, 115, 34, 130, 50, 146, 66, 162, 80, 176, 90, 186, 83, 179, 70, 166, 54, 150, 38, 134, 22, 118)(14, 110, 27, 123, 43, 139, 59, 155, 74, 170, 86, 182, 94, 190, 87, 183, 75, 171, 60, 156, 44, 140, 28, 124)(24, 120, 37, 133, 53, 149, 69, 165, 82, 178, 91, 187, 95, 191, 89, 185, 79, 175, 65, 161, 49, 145, 33, 129)(26, 122, 41, 137, 57, 153, 72, 168, 84, 180, 92, 188, 96, 192, 93, 189, 85, 181, 73, 169, 58, 154, 42, 138) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 110)(7, 101)(8, 99)(9, 115)(10, 114)(11, 118)(12, 100)(13, 113)(14, 122)(15, 104)(16, 103)(17, 126)(18, 125)(19, 129)(20, 106)(21, 131)(22, 133)(23, 109)(24, 108)(25, 135)(26, 120)(27, 112)(28, 111)(29, 140)(30, 139)(31, 121)(32, 117)(33, 137)(34, 116)(35, 146)(36, 144)(37, 138)(38, 119)(39, 150)(40, 143)(41, 124)(42, 123)(43, 154)(44, 153)(45, 128)(46, 127)(47, 158)(48, 157)(49, 130)(50, 161)(51, 132)(52, 163)(53, 134)(54, 165)(55, 136)(56, 167)(57, 145)(58, 149)(59, 142)(60, 141)(61, 171)(62, 170)(63, 152)(64, 148)(65, 168)(66, 147)(67, 176)(68, 174)(69, 169)(70, 151)(71, 179)(72, 156)(73, 155)(74, 181)(75, 180)(76, 160)(77, 159)(78, 184)(79, 162)(80, 185)(81, 164)(82, 166)(83, 187)(84, 175)(85, 178)(86, 173)(87, 172)(88, 190)(89, 188)(90, 177)(91, 189)(92, 183)(93, 182)(94, 192)(95, 186)(96, 191) 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 ) } Outer automorphisms :: reflexible Dual of E15.1181 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 24^8 ] E15.1186 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^12, (T2 * T1)^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 15, 111)(11, 107, 21, 117)(13, 109, 23, 119)(14, 110, 24, 120)(18, 114, 30, 126)(19, 115, 29, 125)(20, 116, 33, 129)(22, 118, 35, 131)(25, 121, 40, 136)(26, 122, 41, 137)(27, 123, 42, 138)(28, 124, 43, 139)(31, 127, 39, 135)(32, 128, 48, 144)(34, 130, 50, 146)(36, 132, 52, 148)(37, 133, 53, 149)(38, 134, 54, 150)(44, 140, 62, 158)(45, 141, 63, 159)(46, 142, 61, 157)(47, 143, 64, 160)(49, 145, 66, 162)(51, 147, 68, 164)(55, 151, 73, 169)(56, 152, 74, 170)(57, 153, 75, 171)(58, 154, 76, 172)(59, 155, 77, 173)(60, 156, 78, 174)(65, 161, 81, 177)(67, 163, 83, 179)(69, 165, 85, 181)(70, 166, 86, 182)(71, 167, 87, 183)(72, 168, 88, 184)(79, 175, 91, 187)(80, 176, 90, 186)(82, 178, 92, 188)(84, 180, 94, 190)(89, 185, 95, 191)(93, 189, 96, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 114)(10, 100)(11, 116)(12, 104)(13, 105)(14, 102)(15, 121)(16, 122)(17, 124)(18, 125)(19, 106)(20, 128)(21, 110)(22, 108)(23, 132)(24, 134)(25, 135)(26, 113)(27, 112)(28, 131)(29, 140)(30, 133)(31, 115)(32, 143)(33, 118)(34, 117)(35, 147)(36, 120)(37, 119)(38, 146)(39, 151)(40, 123)(41, 153)(42, 155)(43, 154)(44, 157)(45, 126)(46, 127)(47, 142)(48, 130)(49, 129)(50, 163)(51, 162)(52, 165)(53, 167)(54, 166)(55, 160)(56, 136)(57, 138)(58, 137)(59, 170)(60, 139)(61, 161)(62, 141)(63, 176)(64, 145)(65, 144)(66, 178)(67, 177)(68, 156)(69, 149)(70, 148)(71, 159)(72, 150)(73, 152)(74, 185)(75, 181)(76, 182)(77, 183)(78, 184)(79, 158)(80, 187)(81, 175)(82, 169)(83, 168)(84, 164)(85, 172)(86, 174)(87, 171)(88, 190)(89, 188)(90, 173)(91, 189)(92, 180)(93, 179)(94, 192)(95, 186)(96, 191) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.1182 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.1187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y2^8, (Y3 * Y2^-1)^12 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 14, 110)(10, 106, 12, 108)(15, 111, 25, 121)(16, 112, 26, 122)(17, 113, 27, 123)(18, 114, 29, 125)(19, 115, 30, 126)(20, 116, 31, 127)(21, 117, 32, 128)(22, 118, 33, 129)(23, 119, 35, 131)(24, 120, 36, 132)(28, 124, 34, 130)(37, 133, 47, 143)(38, 134, 48, 144)(39, 135, 49, 145)(40, 136, 50, 146)(41, 137, 51, 147)(42, 138, 52, 148)(43, 139, 53, 149)(44, 140, 54, 150)(45, 141, 55, 151)(46, 142, 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, 93, 189)(90, 186, 95, 191)(91, 187, 94, 190)(92, 188, 96, 192)(193, 289, 195, 291, 200, 296, 209, 305, 220, 316, 211, 307, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 214, 310, 226, 322, 216, 312, 206, 302, 198, 294)(199, 295, 207, 303, 201, 297, 210, 306, 222, 318, 232, 328, 219, 315, 208, 304)(203, 299, 212, 308, 205, 301, 215, 311, 228, 324, 237, 333, 225, 321, 213, 309)(217, 313, 229, 325, 218, 314, 231, 327, 242, 338, 233, 329, 221, 317, 230, 326)(223, 319, 234, 330, 224, 320, 236, 332, 247, 343, 238, 334, 227, 323, 235, 331)(239, 335, 249, 345, 240, 336, 251, 347, 243, 339, 252, 348, 241, 337, 250, 346)(244, 340, 253, 349, 245, 341, 255, 351, 248, 344, 256, 352, 246, 342, 254, 350)(257, 353, 265, 361, 258, 354, 267, 363, 260, 356, 268, 364, 259, 355, 266, 362)(261, 357, 269, 365, 262, 358, 271, 367, 264, 360, 272, 368, 263, 359, 270, 366)(273, 369, 281, 377, 274, 370, 283, 379, 276, 372, 284, 380, 275, 371, 282, 378)(277, 373, 285, 381, 278, 374, 287, 383, 280, 376, 288, 384, 279, 375, 286, 382) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 206)(9, 196)(10, 204)(11, 197)(12, 202)(13, 198)(14, 200)(15, 217)(16, 218)(17, 219)(18, 221)(19, 222)(20, 223)(21, 224)(22, 225)(23, 227)(24, 228)(25, 207)(26, 208)(27, 209)(28, 226)(29, 210)(30, 211)(31, 212)(32, 213)(33, 214)(34, 220)(35, 215)(36, 216)(37, 239)(38, 240)(39, 241)(40, 242)(41, 243)(42, 244)(43, 245)(44, 246)(45, 247)(46, 248)(47, 229)(48, 230)(49, 231)(50, 232)(51, 233)(52, 234)(53, 235)(54, 236)(55, 237)(56, 238)(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, 273)(74, 274)(75, 275)(76, 276)(77, 277)(78, 278)(79, 279)(80, 280)(81, 265)(82, 266)(83, 267)(84, 268)(85, 269)(86, 270)(87, 271)(88, 272)(89, 285)(90, 287)(91, 286)(92, 288)(93, 281)(94, 283)(95, 282)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E15.1190 Graph:: bipartite v = 60 e = 192 f = 104 degree seq :: [ 4^48, 16^12 ] E15.1188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2^-1)^2, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^8, Y2^12 ] Map:: R = (1, 97, 2, 98, 6, 102, 14, 110, 26, 122, 24, 120, 12, 108, 4, 100)(3, 99, 9, 105, 19, 115, 33, 129, 41, 137, 28, 124, 15, 111, 8, 104)(5, 101, 11, 107, 22, 118, 37, 133, 42, 138, 27, 123, 16, 112, 7, 103)(10, 106, 18, 114, 29, 125, 44, 140, 57, 153, 49, 145, 34, 130, 20, 116)(13, 109, 17, 113, 30, 126, 43, 139, 58, 154, 53, 149, 38, 134, 23, 119)(21, 117, 35, 131, 50, 146, 65, 161, 72, 168, 60, 156, 45, 141, 32, 128)(25, 121, 39, 135, 54, 150, 69, 165, 73, 169, 59, 155, 46, 142, 31, 127)(36, 132, 48, 144, 61, 157, 75, 171, 84, 180, 79, 175, 66, 162, 51, 147)(40, 136, 47, 143, 62, 158, 74, 170, 85, 181, 82, 178, 70, 166, 55, 151)(52, 148, 67, 163, 80, 176, 89, 185, 92, 188, 87, 183, 76, 172, 64, 160)(56, 152, 71, 167, 83, 179, 91, 187, 93, 189, 86, 182, 77, 173, 63, 159)(68, 164, 78, 174, 88, 184, 94, 190, 96, 192, 95, 191, 90, 186, 81, 177)(193, 289, 195, 291, 202, 298, 213, 309, 228, 324, 244, 340, 260, 356, 248, 344, 232, 328, 217, 313, 205, 301, 197, 293)(194, 290, 199, 295, 209, 305, 223, 319, 239, 335, 255, 351, 270, 366, 256, 352, 240, 336, 224, 320, 210, 306, 200, 296)(196, 292, 203, 299, 215, 311, 231, 327, 247, 343, 263, 359, 273, 369, 259, 355, 243, 339, 227, 323, 212, 308, 201, 297)(198, 294, 207, 303, 221, 317, 237, 333, 253, 349, 268, 364, 280, 376, 269, 365, 254, 350, 238, 334, 222, 318, 208, 304)(204, 300, 211, 307, 226, 322, 242, 338, 258, 354, 272, 368, 282, 378, 275, 371, 262, 358, 246, 342, 230, 326, 214, 310)(206, 302, 219, 315, 235, 331, 251, 347, 266, 362, 278, 374, 286, 382, 279, 375, 267, 363, 252, 348, 236, 332, 220, 316)(216, 312, 229, 325, 245, 341, 261, 357, 274, 370, 283, 379, 287, 383, 281, 377, 271, 367, 257, 353, 241, 337, 225, 321)(218, 314, 233, 329, 249, 345, 264, 360, 276, 372, 284, 380, 288, 384, 285, 381, 277, 373, 265, 361, 250, 346, 234, 330) L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 207)(7, 209)(8, 194)(9, 196)(10, 213)(11, 215)(12, 211)(13, 197)(14, 219)(15, 221)(16, 198)(17, 223)(18, 200)(19, 226)(20, 201)(21, 228)(22, 204)(23, 231)(24, 229)(25, 205)(26, 233)(27, 235)(28, 206)(29, 237)(30, 208)(31, 239)(32, 210)(33, 216)(34, 242)(35, 212)(36, 244)(37, 245)(38, 214)(39, 247)(40, 217)(41, 249)(42, 218)(43, 251)(44, 220)(45, 253)(46, 222)(47, 255)(48, 224)(49, 225)(50, 258)(51, 227)(52, 260)(53, 261)(54, 230)(55, 263)(56, 232)(57, 264)(58, 234)(59, 266)(60, 236)(61, 268)(62, 238)(63, 270)(64, 240)(65, 241)(66, 272)(67, 243)(68, 248)(69, 274)(70, 246)(71, 273)(72, 276)(73, 250)(74, 278)(75, 252)(76, 280)(77, 254)(78, 256)(79, 257)(80, 282)(81, 259)(82, 283)(83, 262)(84, 284)(85, 265)(86, 286)(87, 267)(88, 269)(89, 271)(90, 275)(91, 287)(92, 288)(93, 277)(94, 279)(95, 281)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 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 E15.1189 Graph:: bipartite v = 20 e = 192 f = 144 degree seq :: [ 16^12, 24^8 ] E15.1189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^4 * Y2 * Y3^-8 * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 206, 302)(202, 298, 204, 300)(207, 303, 217, 313)(208, 304, 218, 314)(209, 305, 219, 315)(210, 306, 221, 317)(211, 307, 222, 318)(212, 308, 224, 320)(213, 309, 225, 321)(214, 310, 226, 322)(215, 311, 228, 324)(216, 312, 229, 325)(220, 316, 230, 326)(223, 319, 227, 323)(231, 327, 247, 343)(232, 328, 248, 344)(233, 329, 249, 345)(234, 330, 250, 346)(235, 331, 251, 347)(236, 332, 253, 349)(237, 333, 254, 350)(238, 334, 255, 351)(239, 335, 256, 352)(240, 336, 257, 353)(241, 337, 258, 354)(242, 338, 259, 355)(243, 339, 260, 356)(244, 340, 262, 358)(245, 341, 263, 359)(246, 342, 264, 360)(252, 348, 261, 357)(265, 361, 273, 369)(266, 362, 275, 371)(267, 363, 274, 370)(268, 364, 279, 375)(269, 365, 281, 377)(270, 366, 282, 378)(271, 367, 276, 372)(272, 368, 283, 379)(277, 373, 284, 380)(278, 374, 285, 381)(280, 376, 286, 382)(287, 383, 288, 384) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 209)(9, 210)(10, 196)(11, 212)(12, 214)(13, 215)(14, 198)(15, 201)(16, 199)(17, 220)(18, 222)(19, 202)(20, 205)(21, 203)(22, 227)(23, 229)(24, 206)(25, 231)(26, 233)(27, 208)(28, 235)(29, 232)(30, 237)(31, 211)(32, 239)(33, 241)(34, 213)(35, 243)(36, 240)(37, 245)(38, 216)(39, 218)(40, 217)(41, 250)(42, 219)(43, 252)(44, 221)(45, 255)(46, 223)(47, 225)(48, 224)(49, 259)(50, 226)(51, 261)(52, 228)(53, 264)(54, 230)(55, 265)(56, 267)(57, 266)(58, 269)(59, 234)(60, 238)(61, 271)(62, 236)(63, 270)(64, 273)(65, 275)(66, 274)(67, 277)(68, 242)(69, 246)(70, 279)(71, 244)(72, 278)(73, 248)(74, 247)(75, 253)(76, 249)(77, 282)(78, 251)(79, 283)(80, 254)(81, 257)(82, 256)(83, 262)(84, 258)(85, 285)(86, 260)(87, 286)(88, 263)(89, 268)(90, 272)(91, 287)(92, 276)(93, 280)(94, 288)(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) :: { ( 16, 24 ), ( 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E15.1188 Graph:: simple bipartite v = 144 e = 192 f = 20 degree seq :: [ 2^96, 4^48 ] E15.1190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |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, Y1^12, (Y3^-1 * Y1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 5, 101, 11, 107, 20, 116, 32, 128, 47, 143, 46, 142, 31, 127, 19, 115, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 25, 121, 39, 135, 55, 151, 64, 160, 49, 145, 33, 129, 22, 118, 12, 108, 8, 104)(6, 102, 13, 109, 9, 105, 18, 114, 29, 125, 44, 140, 61, 157, 65, 161, 48, 144, 34, 130, 21, 117, 14, 110)(16, 112, 26, 122, 17, 113, 28, 124, 35, 131, 51, 147, 66, 162, 82, 178, 73, 169, 56, 152, 40, 136, 27, 123)(23, 119, 36, 132, 24, 120, 38, 134, 50, 146, 67, 163, 81, 177, 79, 175, 62, 158, 45, 141, 30, 126, 37, 133)(41, 137, 57, 153, 42, 138, 59, 155, 74, 170, 89, 185, 92, 188, 84, 180, 68, 164, 60, 156, 43, 139, 58, 154)(52, 148, 69, 165, 53, 149, 71, 167, 63, 159, 80, 176, 91, 187, 93, 189, 83, 179, 72, 168, 54, 150, 70, 166)(75, 171, 85, 181, 76, 172, 86, 182, 78, 174, 88, 184, 94, 190, 96, 192, 95, 191, 90, 186, 77, 173, 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, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 207)(11, 213)(12, 197)(13, 215)(14, 216)(15, 202)(16, 199)(17, 200)(18, 222)(19, 221)(20, 225)(21, 203)(22, 227)(23, 205)(24, 206)(25, 232)(26, 233)(27, 234)(28, 235)(29, 211)(30, 210)(31, 231)(32, 240)(33, 212)(34, 242)(35, 214)(36, 244)(37, 245)(38, 246)(39, 223)(40, 217)(41, 218)(42, 219)(43, 220)(44, 254)(45, 255)(46, 253)(47, 256)(48, 224)(49, 258)(50, 226)(51, 260)(52, 228)(53, 229)(54, 230)(55, 265)(56, 266)(57, 267)(58, 268)(59, 269)(60, 270)(61, 238)(62, 236)(63, 237)(64, 239)(65, 273)(66, 241)(67, 275)(68, 243)(69, 277)(70, 278)(71, 279)(72, 280)(73, 247)(74, 248)(75, 249)(76, 250)(77, 251)(78, 252)(79, 283)(80, 282)(81, 257)(82, 284)(83, 259)(84, 286)(85, 261)(86, 262)(87, 263)(88, 264)(89, 287)(90, 272)(91, 271)(92, 274)(93, 288)(94, 276)(95, 281)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1187 Graph:: simple bipartite v = 104 e = 192 f = 60 degree seq :: [ 2^96, 24^8 ] E15.1191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |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, Y2^12, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 14, 110)(10, 106, 12, 108)(15, 111, 25, 121)(16, 112, 26, 122)(17, 113, 27, 123)(18, 114, 29, 125)(19, 115, 30, 126)(20, 116, 32, 128)(21, 117, 33, 129)(22, 118, 34, 130)(23, 119, 36, 132)(24, 120, 37, 133)(28, 124, 38, 134)(31, 127, 35, 131)(39, 135, 55, 151)(40, 136, 56, 152)(41, 137, 57, 153)(42, 138, 58, 154)(43, 139, 59, 155)(44, 140, 61, 157)(45, 141, 62, 158)(46, 142, 63, 159)(47, 143, 64, 160)(48, 144, 65, 161)(49, 145, 66, 162)(50, 146, 67, 163)(51, 147, 68, 164)(52, 148, 70, 166)(53, 149, 71, 167)(54, 150, 72, 168)(60, 156, 69, 165)(73, 169, 81, 177)(74, 170, 83, 179)(75, 171, 82, 178)(76, 172, 87, 183)(77, 173, 89, 185)(78, 174, 90, 186)(79, 175, 84, 180)(80, 176, 91, 187)(85, 181, 92, 188)(86, 182, 93, 189)(88, 184, 94, 190)(95, 191, 96, 192)(193, 289, 195, 291, 200, 296, 209, 305, 220, 316, 235, 331, 252, 348, 238, 334, 223, 319, 211, 307, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 214, 310, 227, 323, 243, 339, 261, 357, 246, 342, 230, 326, 216, 312, 206, 302, 198, 294)(199, 295, 207, 303, 201, 297, 210, 306, 222, 318, 237, 333, 255, 351, 270, 366, 251, 347, 234, 330, 219, 315, 208, 304)(203, 299, 212, 308, 205, 301, 215, 311, 229, 325, 245, 341, 264, 360, 278, 374, 260, 356, 242, 338, 226, 322, 213, 309)(217, 313, 231, 327, 218, 314, 233, 329, 250, 346, 269, 365, 282, 378, 272, 368, 254, 350, 236, 332, 221, 317, 232, 328)(224, 320, 239, 335, 225, 321, 241, 337, 259, 355, 277, 373, 285, 381, 280, 376, 263, 359, 244, 340, 228, 324, 240, 336)(247, 343, 265, 361, 248, 344, 267, 363, 253, 349, 271, 367, 283, 379, 287, 383, 281, 377, 268, 364, 249, 345, 266, 362)(256, 352, 273, 369, 257, 353, 275, 371, 262, 358, 279, 375, 286, 382, 288, 384, 284, 380, 276, 372, 258, 354, 274, 370) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 206)(9, 196)(10, 204)(11, 197)(12, 202)(13, 198)(14, 200)(15, 217)(16, 218)(17, 219)(18, 221)(19, 222)(20, 224)(21, 225)(22, 226)(23, 228)(24, 229)(25, 207)(26, 208)(27, 209)(28, 230)(29, 210)(30, 211)(31, 227)(32, 212)(33, 213)(34, 214)(35, 223)(36, 215)(37, 216)(38, 220)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 253)(45, 254)(46, 255)(47, 256)(48, 257)(49, 258)(50, 259)(51, 260)(52, 262)(53, 263)(54, 264)(55, 231)(56, 232)(57, 233)(58, 234)(59, 235)(60, 261)(61, 236)(62, 237)(63, 238)(64, 239)(65, 240)(66, 241)(67, 242)(68, 243)(69, 252)(70, 244)(71, 245)(72, 246)(73, 273)(74, 275)(75, 274)(76, 279)(77, 281)(78, 282)(79, 276)(80, 283)(81, 265)(82, 267)(83, 266)(84, 271)(85, 284)(86, 285)(87, 268)(88, 286)(89, 269)(90, 270)(91, 272)(92, 277)(93, 278)(94, 280)(95, 288)(96, 287)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E15.1192 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 4^48, 24^8 ] E15.1192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 16>) Aut = $<192, 332>$ (small group id <192, 332>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3 * Y2^-1)^12 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 14, 110, 26, 122, 24, 120, 12, 108, 4, 100)(3, 99, 9, 105, 19, 115, 33, 129, 41, 137, 28, 124, 15, 111, 8, 104)(5, 101, 11, 107, 22, 118, 37, 133, 42, 138, 27, 123, 16, 112, 7, 103)(10, 106, 18, 114, 29, 125, 44, 140, 57, 153, 49, 145, 34, 130, 20, 116)(13, 109, 17, 113, 30, 126, 43, 139, 58, 154, 53, 149, 38, 134, 23, 119)(21, 117, 35, 131, 50, 146, 65, 161, 72, 168, 60, 156, 45, 141, 32, 128)(25, 121, 39, 135, 54, 150, 69, 165, 73, 169, 59, 155, 46, 142, 31, 127)(36, 132, 48, 144, 61, 157, 75, 171, 84, 180, 79, 175, 66, 162, 51, 147)(40, 136, 47, 143, 62, 158, 74, 170, 85, 181, 82, 178, 70, 166, 55, 151)(52, 148, 67, 163, 80, 176, 89, 185, 92, 188, 87, 183, 76, 172, 64, 160)(56, 152, 71, 167, 83, 179, 91, 187, 93, 189, 86, 182, 77, 173, 63, 159)(68, 164, 78, 174, 88, 184, 94, 190, 96, 192, 95, 191, 90, 186, 81, 177)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 207)(7, 209)(8, 194)(9, 196)(10, 213)(11, 215)(12, 211)(13, 197)(14, 219)(15, 221)(16, 198)(17, 223)(18, 200)(19, 226)(20, 201)(21, 228)(22, 204)(23, 231)(24, 229)(25, 205)(26, 233)(27, 235)(28, 206)(29, 237)(30, 208)(31, 239)(32, 210)(33, 216)(34, 242)(35, 212)(36, 244)(37, 245)(38, 214)(39, 247)(40, 217)(41, 249)(42, 218)(43, 251)(44, 220)(45, 253)(46, 222)(47, 255)(48, 224)(49, 225)(50, 258)(51, 227)(52, 260)(53, 261)(54, 230)(55, 263)(56, 232)(57, 264)(58, 234)(59, 266)(60, 236)(61, 268)(62, 238)(63, 270)(64, 240)(65, 241)(66, 272)(67, 243)(68, 248)(69, 274)(70, 246)(71, 273)(72, 276)(73, 250)(74, 278)(75, 252)(76, 280)(77, 254)(78, 256)(79, 257)(80, 282)(81, 259)(82, 283)(83, 262)(84, 284)(85, 265)(86, 286)(87, 267)(88, 269)(89, 271)(90, 275)(91, 287)(92, 288)(93, 277)(94, 279)(95, 281)(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, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.1191 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1193 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^3 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1, T1^12, T1^-7 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 66, 65, 42, 22, 10, 4)(3, 7, 15, 24, 45, 69, 87, 83, 61, 37, 18, 8)(6, 13, 27, 44, 68, 89, 80, 58, 41, 21, 30, 14)(9, 19, 26, 12, 25, 46, 67, 88, 85, 63, 40, 20)(16, 32, 55, 70, 91, 84, 62, 39, 60, 36, 48, 33)(17, 34, 54, 31, 51, 28, 50, 73, 90, 81, 59, 35)(29, 52, 38, 49, 72, 47, 71, 92, 86, 64, 76, 53)(56, 78, 57, 77, 96, 74, 95, 75, 94, 82, 93, 79) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 44)(25, 47)(26, 48)(27, 49)(30, 54)(32, 46)(33, 56)(34, 57)(35, 58)(40, 53)(41, 64)(42, 63)(43, 67)(45, 70)(50, 69)(51, 74)(52, 75)(55, 77)(59, 79)(60, 82)(61, 81)(62, 83)(65, 80)(66, 87)(68, 90)(71, 89)(72, 93)(73, 94)(76, 96)(78, 92)(84, 95)(85, 91)(86, 88) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.1194 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.1194 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^8, T1^-3 * T2 * T1^4 * T2 * T1^-1, T1^-2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 * T2, (T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^2, (T2 * T1 * T2 * T1^-3)^3 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 46, 38, 18, 8)(6, 13, 27, 53, 45, 60, 30, 14)(9, 19, 39, 48, 24, 47, 42, 20)(12, 25, 49, 44, 21, 43, 52, 26)(16, 33, 51, 77, 70, 87, 65, 34)(17, 35, 50, 76, 61, 85, 68, 36)(28, 55, 74, 90, 84, 72, 41, 56)(29, 57, 73, 89, 79, 71, 40, 58)(32, 62, 78, 59, 37, 69, 75, 54)(63, 80, 91, 95, 94, 88, 67, 83)(64, 86, 93, 96, 92, 82, 66, 81) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 46)(25, 50)(26, 51)(27, 54)(30, 59)(31, 61)(33, 63)(34, 64)(35, 66)(36, 67)(38, 70)(39, 62)(42, 69)(43, 68)(44, 65)(47, 73)(48, 74)(49, 75)(52, 78)(53, 79)(55, 80)(56, 81)(57, 82)(58, 83)(60, 84)(71, 86)(72, 88)(76, 91)(77, 92)(85, 93)(87, 94)(89, 95)(90, 96) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.1193 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.1195 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-1 * T1 * T2^-3)^2, T2^-1 * T1 * T2 * T1 * T2^2 * T1 * T2 * T1 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 ] Map:: R = (1, 3, 8, 18, 38, 22, 10, 4)(2, 5, 12, 26, 53, 30, 14, 6)(7, 15, 32, 63, 45, 66, 34, 16)(9, 19, 40, 70, 37, 69, 42, 20)(11, 23, 47, 75, 60, 78, 49, 24)(13, 27, 55, 82, 52, 81, 57, 28)(17, 35, 67, 44, 21, 43, 68, 36)(25, 50, 79, 59, 29, 58, 80, 51)(31, 61, 85, 93, 88, 72, 41, 62)(33, 64, 87, 94, 86, 71, 39, 65)(46, 73, 89, 95, 92, 84, 56, 74)(48, 76, 91, 96, 90, 83, 54, 77)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 117)(108, 121)(110, 125)(111, 127)(112, 129)(114, 133)(115, 135)(116, 137)(118, 141)(119, 142)(120, 144)(122, 148)(123, 150)(124, 152)(126, 156)(128, 147)(130, 155)(131, 151)(132, 143)(134, 149)(136, 146)(138, 154)(139, 153)(140, 145)(157, 169)(158, 173)(159, 182)(160, 179)(161, 170)(162, 184)(163, 176)(164, 175)(165, 183)(166, 181)(167, 172)(168, 180)(171, 186)(174, 188)(177, 187)(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) :: { ( 24, 24 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E15.1199 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.1196 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-1 * T2^-2 * T1 * T2^-2 * T1^-2, T2^2 * T1^-1 * T2^-4 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T1^8, T1^-4 * T2^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 62, 75, 40, 74, 55, 39, 15, 5)(2, 7, 19, 48, 27, 64, 34, 71, 84, 56, 22, 8)(4, 12, 31, 63, 77, 42, 16, 41, 38, 60, 24, 9)(6, 17, 43, 79, 49, 30, 13, 33, 70, 85, 46, 18)(11, 28, 51, 88, 96, 90, 57, 37, 14, 36, 61, 25)(20, 50, 81, 65, 92, 72, 35, 54, 21, 53, 86, 47)(23, 58, 91, 69, 32, 66, 29, 67, 93, 73, 76, 59)(44, 80, 68, 87, 95, 89, 52, 83, 45, 82, 94, 78)(97, 98, 102, 112, 136, 130, 109, 100)(99, 105, 119, 153, 170, 138, 125, 107)(101, 110, 131, 167, 171, 147, 116, 103)(104, 117, 148, 129, 160, 177, 140, 113)(106, 121, 149, 118, 151, 186, 161, 123)(108, 126, 164, 172, 137, 114, 141, 128)(111, 134, 169, 184, 158, 127, 165, 132)(115, 143, 178, 142, 180, 168, 183, 145)(120, 139, 174, 163, 173, 166, 185, 154)(122, 144, 175, 156, 135, 152, 181, 159)(124, 162, 179, 150, 133, 155, 176, 146)(157, 187, 191, 188, 192, 189, 190, 182) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1200 Transitivity :: ET+ Graph:: bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.1197 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^3 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1, T1^12, T1^-6 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 44)(25, 47)(26, 48)(27, 49)(30, 54)(32, 46)(33, 56)(34, 57)(35, 58)(40, 53)(41, 64)(42, 63)(43, 67)(45, 70)(50, 69)(51, 74)(52, 75)(55, 77)(59, 79)(60, 82)(61, 81)(62, 83)(65, 80)(66, 87)(68, 90)(71, 89)(72, 93)(73, 94)(76, 96)(78, 92)(84, 95)(85, 91)(86, 88)(97, 98, 101, 107, 119, 139, 162, 161, 138, 118, 106, 100)(99, 103, 111, 120, 141, 165, 183, 179, 157, 133, 114, 104)(102, 109, 123, 140, 164, 185, 176, 154, 137, 117, 126, 110)(105, 115, 122, 108, 121, 142, 163, 184, 181, 159, 136, 116)(112, 128, 151, 166, 187, 180, 158, 135, 156, 132, 144, 129)(113, 130, 150, 127, 147, 124, 146, 169, 186, 177, 155, 131)(125, 148, 134, 145, 168, 143, 167, 188, 182, 160, 172, 149)(152, 174, 153, 173, 192, 170, 191, 171, 190, 178, 189, 175) 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, 16 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E15.1198 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 2^48, 12^8 ] E15.1198 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-1 * T1 * T2^-3)^2, T2^-1 * T1 * T2 * T1 * T2^2 * T1 * T2 * T1 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 ] Map:: R = (1, 97, 3, 99, 8, 104, 18, 114, 38, 134, 22, 118, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 26, 122, 53, 149, 30, 126, 14, 110, 6, 102)(7, 103, 15, 111, 32, 128, 63, 159, 45, 141, 66, 162, 34, 130, 16, 112)(9, 105, 19, 115, 40, 136, 70, 166, 37, 133, 69, 165, 42, 138, 20, 116)(11, 107, 23, 119, 47, 143, 75, 171, 60, 156, 78, 174, 49, 145, 24, 120)(13, 109, 27, 123, 55, 151, 82, 178, 52, 148, 81, 177, 57, 153, 28, 124)(17, 113, 35, 131, 67, 163, 44, 140, 21, 117, 43, 139, 68, 164, 36, 132)(25, 121, 50, 146, 79, 175, 59, 155, 29, 125, 58, 154, 80, 176, 51, 147)(31, 127, 61, 157, 85, 181, 93, 189, 88, 184, 72, 168, 41, 137, 62, 158)(33, 129, 64, 160, 87, 183, 94, 190, 86, 182, 71, 167, 39, 135, 65, 161)(46, 142, 73, 169, 89, 185, 95, 191, 92, 188, 84, 180, 56, 152, 74, 170)(48, 144, 76, 172, 91, 187, 96, 192, 90, 186, 83, 179, 54, 150, 77, 173) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 121)(13, 102)(14, 125)(15, 127)(16, 129)(17, 104)(18, 133)(19, 135)(20, 137)(21, 106)(22, 141)(23, 142)(24, 144)(25, 108)(26, 148)(27, 150)(28, 152)(29, 110)(30, 156)(31, 111)(32, 147)(33, 112)(34, 155)(35, 151)(36, 143)(37, 114)(38, 149)(39, 115)(40, 146)(41, 116)(42, 154)(43, 153)(44, 145)(45, 118)(46, 119)(47, 132)(48, 120)(49, 140)(50, 136)(51, 128)(52, 122)(53, 134)(54, 123)(55, 131)(56, 124)(57, 139)(58, 138)(59, 130)(60, 126)(61, 169)(62, 173)(63, 182)(64, 179)(65, 170)(66, 184)(67, 176)(68, 175)(69, 183)(70, 181)(71, 172)(72, 180)(73, 157)(74, 161)(75, 186)(76, 167)(77, 158)(78, 188)(79, 164)(80, 163)(81, 187)(82, 185)(83, 160)(84, 168)(85, 166)(86, 159)(87, 165)(88, 162)(89, 178)(90, 171)(91, 177)(92, 174)(93, 192)(94, 191)(95, 190)(96, 189) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E15.1197 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1199 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-1 * T2^-2 * T1 * T2^-2 * T1^-2, T2^2 * T1^-1 * T2^-4 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T1^8, T1^-4 * T2^6 ] Map:: R = (1, 97, 3, 99, 10, 106, 26, 122, 62, 158, 75, 171, 40, 136, 74, 170, 55, 151, 39, 135, 15, 111, 5, 101)(2, 98, 7, 103, 19, 115, 48, 144, 27, 123, 64, 160, 34, 130, 71, 167, 84, 180, 56, 152, 22, 118, 8, 104)(4, 100, 12, 108, 31, 127, 63, 159, 77, 173, 42, 138, 16, 112, 41, 137, 38, 134, 60, 156, 24, 120, 9, 105)(6, 102, 17, 113, 43, 139, 79, 175, 49, 145, 30, 126, 13, 109, 33, 129, 70, 166, 85, 181, 46, 142, 18, 114)(11, 107, 28, 124, 51, 147, 88, 184, 96, 192, 90, 186, 57, 153, 37, 133, 14, 110, 36, 132, 61, 157, 25, 121)(20, 116, 50, 146, 81, 177, 65, 161, 92, 188, 72, 168, 35, 131, 54, 150, 21, 117, 53, 149, 86, 182, 47, 143)(23, 119, 58, 154, 91, 187, 69, 165, 32, 128, 66, 162, 29, 125, 67, 163, 93, 189, 73, 169, 76, 172, 59, 155)(44, 140, 80, 176, 68, 164, 87, 183, 95, 191, 89, 185, 52, 148, 83, 179, 45, 141, 82, 178, 94, 190, 78, 174) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 101)(8, 117)(9, 119)(10, 121)(11, 99)(12, 126)(13, 100)(14, 131)(15, 134)(16, 136)(17, 104)(18, 141)(19, 143)(20, 103)(21, 148)(22, 151)(23, 153)(24, 139)(25, 149)(26, 144)(27, 106)(28, 162)(29, 107)(30, 164)(31, 165)(32, 108)(33, 160)(34, 109)(35, 167)(36, 111)(37, 155)(38, 169)(39, 152)(40, 130)(41, 114)(42, 125)(43, 174)(44, 113)(45, 128)(46, 180)(47, 178)(48, 175)(49, 115)(50, 124)(51, 116)(52, 129)(53, 118)(54, 133)(55, 186)(56, 181)(57, 170)(58, 120)(59, 176)(60, 135)(61, 187)(62, 127)(63, 122)(64, 177)(65, 123)(66, 179)(67, 173)(68, 172)(69, 132)(70, 185)(71, 171)(72, 183)(73, 184)(74, 138)(75, 147)(76, 137)(77, 166)(78, 163)(79, 156)(80, 146)(81, 140)(82, 142)(83, 150)(84, 168)(85, 159)(86, 157)(87, 145)(88, 158)(89, 154)(90, 161)(91, 191)(92, 192)(93, 190)(94, 182)(95, 188)(96, 189) 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 ) } Outer automorphisms :: reflexible Dual of E15.1195 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 24^8 ] E15.1200 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^3 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1, T1^12, T1^-6 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 21, 117)(11, 107, 24, 120)(13, 109, 28, 124)(14, 110, 29, 125)(15, 111, 31, 127)(18, 114, 36, 132)(19, 115, 38, 134)(20, 116, 39, 135)(22, 118, 37, 133)(23, 119, 44, 140)(25, 121, 47, 143)(26, 122, 48, 144)(27, 123, 49, 145)(30, 126, 54, 150)(32, 128, 46, 142)(33, 129, 56, 152)(34, 130, 57, 153)(35, 131, 58, 154)(40, 136, 53, 149)(41, 137, 64, 160)(42, 138, 63, 159)(43, 139, 67, 163)(45, 141, 70, 166)(50, 146, 69, 165)(51, 147, 74, 170)(52, 148, 75, 171)(55, 151, 77, 173)(59, 155, 79, 175)(60, 156, 82, 178)(61, 157, 81, 177)(62, 158, 83, 179)(65, 161, 80, 176)(66, 162, 87, 183)(68, 164, 90, 186)(71, 167, 89, 185)(72, 168, 93, 189)(73, 169, 94, 190)(76, 172, 96, 192)(78, 174, 92, 188)(84, 180, 95, 191)(85, 181, 91, 187)(86, 182, 88, 184) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 115)(10, 100)(11, 119)(12, 121)(13, 123)(14, 102)(15, 120)(16, 128)(17, 130)(18, 104)(19, 122)(20, 105)(21, 126)(22, 106)(23, 139)(24, 141)(25, 142)(26, 108)(27, 140)(28, 146)(29, 148)(30, 110)(31, 147)(32, 151)(33, 112)(34, 150)(35, 113)(36, 144)(37, 114)(38, 145)(39, 156)(40, 116)(41, 117)(42, 118)(43, 162)(44, 164)(45, 165)(46, 163)(47, 167)(48, 129)(49, 168)(50, 169)(51, 124)(52, 134)(53, 125)(54, 127)(55, 166)(56, 174)(57, 173)(58, 137)(59, 131)(60, 132)(61, 133)(62, 135)(63, 136)(64, 172)(65, 138)(66, 161)(67, 184)(68, 185)(69, 183)(70, 187)(71, 188)(72, 143)(73, 186)(74, 191)(75, 190)(76, 149)(77, 192)(78, 153)(79, 152)(80, 154)(81, 155)(82, 189)(83, 157)(84, 158)(85, 159)(86, 160)(87, 179)(88, 181)(89, 176)(90, 177)(91, 180)(92, 182)(93, 175)(94, 178)(95, 171)(96, 170) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.1196 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.1201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2 * R)^2, Y2^8, (Y2^-2 * R * Y2^-2)^2, (Y2^-3 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2 * R * Y2^-2 * R * Y2 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 17, 113)(10, 106, 21, 117)(12, 108, 25, 121)(14, 110, 29, 125)(15, 111, 31, 127)(16, 112, 33, 129)(18, 114, 37, 133)(19, 115, 39, 135)(20, 116, 41, 137)(22, 118, 45, 141)(23, 119, 46, 142)(24, 120, 48, 144)(26, 122, 52, 148)(27, 123, 54, 150)(28, 124, 56, 152)(30, 126, 60, 156)(32, 128, 51, 147)(34, 130, 59, 155)(35, 131, 55, 151)(36, 132, 47, 143)(38, 134, 53, 149)(40, 136, 50, 146)(42, 138, 58, 154)(43, 139, 57, 153)(44, 140, 49, 145)(61, 157, 73, 169)(62, 158, 77, 173)(63, 159, 86, 182)(64, 160, 83, 179)(65, 161, 74, 170)(66, 162, 88, 184)(67, 163, 80, 176)(68, 164, 79, 175)(69, 165, 87, 183)(70, 166, 85, 181)(71, 167, 76, 172)(72, 168, 84, 180)(75, 171, 90, 186)(78, 174, 92, 188)(81, 177, 91, 187)(82, 178, 89, 185)(93, 189, 96, 192)(94, 190, 95, 191)(193, 289, 195, 291, 200, 296, 210, 306, 230, 326, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 245, 341, 222, 318, 206, 302, 198, 294)(199, 295, 207, 303, 224, 320, 255, 351, 237, 333, 258, 354, 226, 322, 208, 304)(201, 297, 211, 307, 232, 328, 262, 358, 229, 325, 261, 357, 234, 330, 212, 308)(203, 299, 215, 311, 239, 335, 267, 363, 252, 348, 270, 366, 241, 337, 216, 312)(205, 301, 219, 315, 247, 343, 274, 370, 244, 340, 273, 369, 249, 345, 220, 316)(209, 305, 227, 323, 259, 355, 236, 332, 213, 309, 235, 331, 260, 356, 228, 324)(217, 313, 242, 338, 271, 367, 251, 347, 221, 317, 250, 346, 272, 368, 243, 339)(223, 319, 253, 349, 277, 373, 285, 381, 280, 376, 264, 360, 233, 329, 254, 350)(225, 321, 256, 352, 279, 375, 286, 382, 278, 374, 263, 359, 231, 327, 257, 353)(238, 334, 265, 361, 281, 377, 287, 383, 284, 380, 276, 372, 248, 344, 266, 362)(240, 336, 268, 364, 283, 379, 288, 384, 282, 378, 275, 371, 246, 342, 269, 365) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 209)(9, 196)(10, 213)(11, 197)(12, 217)(13, 198)(14, 221)(15, 223)(16, 225)(17, 200)(18, 229)(19, 231)(20, 233)(21, 202)(22, 237)(23, 238)(24, 240)(25, 204)(26, 244)(27, 246)(28, 248)(29, 206)(30, 252)(31, 207)(32, 243)(33, 208)(34, 251)(35, 247)(36, 239)(37, 210)(38, 245)(39, 211)(40, 242)(41, 212)(42, 250)(43, 249)(44, 241)(45, 214)(46, 215)(47, 228)(48, 216)(49, 236)(50, 232)(51, 224)(52, 218)(53, 230)(54, 219)(55, 227)(56, 220)(57, 235)(58, 234)(59, 226)(60, 222)(61, 265)(62, 269)(63, 278)(64, 275)(65, 266)(66, 280)(67, 272)(68, 271)(69, 279)(70, 277)(71, 268)(72, 276)(73, 253)(74, 257)(75, 282)(76, 263)(77, 254)(78, 284)(79, 260)(80, 259)(81, 283)(82, 281)(83, 256)(84, 264)(85, 262)(86, 255)(87, 261)(88, 258)(89, 274)(90, 267)(91, 273)(92, 270)(93, 288)(94, 287)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E15.1204 Graph:: bipartite v = 60 e = 192 f = 104 degree seq :: [ 4^48, 16^12 ] E15.1202 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, Y1^8, Y2^2 * Y1^-1 * Y2^-4 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-2 * Y1 * Y2^-2 * Y1^-2, (Y2 * Y1^-3)^2, Y1^-4 * Y2^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 40, 136, 34, 130, 13, 109, 4, 100)(3, 99, 9, 105, 23, 119, 57, 153, 74, 170, 42, 138, 29, 125, 11, 107)(5, 101, 14, 110, 35, 131, 71, 167, 75, 171, 51, 147, 20, 116, 7, 103)(8, 104, 21, 117, 52, 148, 33, 129, 64, 160, 81, 177, 44, 140, 17, 113)(10, 106, 25, 121, 53, 149, 22, 118, 55, 151, 90, 186, 65, 161, 27, 123)(12, 108, 30, 126, 68, 164, 76, 172, 41, 137, 18, 114, 45, 141, 32, 128)(15, 111, 38, 134, 73, 169, 88, 184, 62, 158, 31, 127, 69, 165, 36, 132)(19, 115, 47, 143, 82, 178, 46, 142, 84, 180, 72, 168, 87, 183, 49, 145)(24, 120, 43, 139, 78, 174, 67, 163, 77, 173, 70, 166, 89, 185, 58, 154)(26, 122, 48, 144, 79, 175, 60, 156, 39, 135, 56, 152, 85, 181, 63, 159)(28, 124, 66, 162, 83, 179, 54, 150, 37, 133, 59, 155, 80, 176, 50, 146)(61, 157, 91, 187, 95, 191, 92, 188, 96, 192, 93, 189, 94, 190, 86, 182)(193, 289, 195, 291, 202, 298, 218, 314, 254, 350, 267, 363, 232, 328, 266, 362, 247, 343, 231, 327, 207, 303, 197, 293)(194, 290, 199, 295, 211, 307, 240, 336, 219, 315, 256, 352, 226, 322, 263, 359, 276, 372, 248, 344, 214, 310, 200, 296)(196, 292, 204, 300, 223, 319, 255, 351, 269, 365, 234, 330, 208, 304, 233, 329, 230, 326, 252, 348, 216, 312, 201, 297)(198, 294, 209, 305, 235, 331, 271, 367, 241, 337, 222, 318, 205, 301, 225, 321, 262, 358, 277, 373, 238, 334, 210, 306)(203, 299, 220, 316, 243, 339, 280, 376, 288, 384, 282, 378, 249, 345, 229, 325, 206, 302, 228, 324, 253, 349, 217, 313)(212, 308, 242, 338, 273, 369, 257, 353, 284, 380, 264, 360, 227, 323, 246, 342, 213, 309, 245, 341, 278, 374, 239, 335)(215, 311, 250, 346, 283, 379, 261, 357, 224, 320, 258, 354, 221, 317, 259, 355, 285, 381, 265, 361, 268, 364, 251, 347)(236, 332, 272, 368, 260, 356, 279, 375, 287, 383, 281, 377, 244, 340, 275, 371, 237, 333, 274, 370, 286, 382, 270, 366) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 218)(11, 220)(12, 223)(13, 225)(14, 228)(15, 197)(16, 233)(17, 235)(18, 198)(19, 240)(20, 242)(21, 245)(22, 200)(23, 250)(24, 201)(25, 203)(26, 254)(27, 256)(28, 243)(29, 259)(30, 205)(31, 255)(32, 258)(33, 262)(34, 263)(35, 246)(36, 253)(37, 206)(38, 252)(39, 207)(40, 266)(41, 230)(42, 208)(43, 271)(44, 272)(45, 274)(46, 210)(47, 212)(48, 219)(49, 222)(50, 273)(51, 280)(52, 275)(53, 278)(54, 213)(55, 231)(56, 214)(57, 229)(58, 283)(59, 215)(60, 216)(61, 217)(62, 267)(63, 269)(64, 226)(65, 284)(66, 221)(67, 285)(68, 279)(69, 224)(70, 277)(71, 276)(72, 227)(73, 268)(74, 247)(75, 232)(76, 251)(77, 234)(78, 236)(79, 241)(80, 260)(81, 257)(82, 286)(83, 237)(84, 248)(85, 238)(86, 239)(87, 287)(88, 288)(89, 244)(90, 249)(91, 261)(92, 264)(93, 265)(94, 270)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 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 E15.1203 Graph:: bipartite v = 20 e = 192 f = 144 degree seq :: [ 16^12, 24^8 ] E15.1203 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^-3 * Y2, Y3^-1 * Y2 * Y3^-2 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1, Y3^12, (Y3 * Y2 * Y3 * Y2 * Y3^2 * Y2)^2, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 209, 305)(202, 298, 213, 309)(204, 300, 217, 313)(206, 302, 221, 317)(207, 303, 223, 319)(208, 304, 225, 321)(210, 306, 218, 314)(211, 307, 230, 326)(212, 308, 231, 327)(214, 310, 222, 318)(215, 311, 235, 331)(216, 312, 237, 333)(219, 315, 242, 338)(220, 316, 243, 339)(224, 320, 248, 344)(226, 322, 240, 336)(227, 323, 252, 348)(228, 324, 238, 334)(229, 325, 249, 345)(232, 328, 251, 347)(233, 329, 256, 352)(234, 330, 255, 351)(236, 332, 259, 355)(239, 335, 263, 359)(241, 337, 260, 356)(244, 340, 262, 358)(245, 341, 267, 363)(246, 342, 266, 362)(247, 343, 264, 360)(250, 346, 272, 368)(253, 349, 258, 354)(254, 350, 268, 364)(257, 353, 265, 361)(261, 357, 282, 378)(269, 365, 288, 384)(270, 366, 283, 379)(271, 367, 287, 383)(273, 369, 280, 376)(274, 370, 286, 382)(275, 371, 285, 381)(276, 372, 284, 380)(277, 373, 281, 377)(278, 374, 279, 375) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 210)(9, 211)(10, 196)(11, 215)(12, 218)(13, 219)(14, 198)(15, 224)(16, 199)(17, 227)(18, 229)(19, 228)(20, 201)(21, 226)(22, 202)(23, 236)(24, 203)(25, 239)(26, 241)(27, 240)(28, 205)(29, 238)(30, 206)(31, 247)(32, 249)(33, 250)(34, 208)(35, 235)(36, 209)(37, 253)(38, 248)(39, 245)(40, 212)(41, 213)(42, 214)(43, 258)(44, 260)(45, 261)(46, 216)(47, 223)(48, 217)(49, 264)(50, 259)(51, 233)(52, 220)(53, 221)(54, 222)(55, 269)(56, 270)(57, 271)(58, 230)(59, 225)(60, 274)(61, 275)(62, 231)(63, 232)(64, 273)(65, 234)(66, 279)(67, 280)(68, 281)(69, 242)(70, 237)(71, 284)(72, 285)(73, 243)(74, 244)(75, 283)(76, 246)(77, 287)(78, 252)(79, 286)(80, 288)(81, 251)(82, 282)(83, 257)(84, 254)(85, 255)(86, 256)(87, 277)(88, 263)(89, 276)(90, 278)(91, 262)(92, 272)(93, 268)(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) :: { ( 16, 24 ), ( 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E15.1202 Graph:: simple bipartite v = 144 e = 192 f = 20 degree seq :: [ 2^96, 4^48 ] E15.1204 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-3 * Y3 * Y1^3 * Y3, (Y3 * Y1^-1 * Y3 * Y1^2)^2, Y1^12, (Y3 * Y1^-1)^8 ] Map:: R = (1, 97, 2, 98, 5, 101, 11, 107, 23, 119, 43, 139, 66, 162, 65, 161, 42, 138, 22, 118, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 24, 120, 45, 141, 69, 165, 87, 183, 83, 179, 61, 157, 37, 133, 18, 114, 8, 104)(6, 102, 13, 109, 27, 123, 44, 140, 68, 164, 89, 185, 80, 176, 58, 154, 41, 137, 21, 117, 30, 126, 14, 110)(9, 105, 19, 115, 26, 122, 12, 108, 25, 121, 46, 142, 67, 163, 88, 184, 85, 181, 63, 159, 40, 136, 20, 116)(16, 112, 32, 128, 55, 151, 70, 166, 91, 187, 84, 180, 62, 158, 39, 135, 60, 156, 36, 132, 48, 144, 33, 129)(17, 113, 34, 130, 54, 150, 31, 127, 51, 147, 28, 124, 50, 146, 73, 169, 90, 186, 81, 177, 59, 155, 35, 131)(29, 125, 52, 148, 38, 134, 49, 145, 72, 168, 47, 143, 71, 167, 92, 188, 86, 182, 64, 160, 76, 172, 53, 149)(56, 152, 78, 174, 57, 153, 77, 173, 96, 192, 74, 170, 95, 191, 75, 171, 94, 190, 82, 178, 93, 189, 79, 175)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 213)(11, 216)(12, 197)(13, 220)(14, 221)(15, 223)(16, 199)(17, 200)(18, 228)(19, 230)(20, 231)(21, 202)(22, 229)(23, 236)(24, 203)(25, 239)(26, 240)(27, 241)(28, 205)(29, 206)(30, 246)(31, 207)(32, 238)(33, 248)(34, 249)(35, 250)(36, 210)(37, 214)(38, 211)(39, 212)(40, 245)(41, 256)(42, 255)(43, 259)(44, 215)(45, 262)(46, 224)(47, 217)(48, 218)(49, 219)(50, 261)(51, 266)(52, 267)(53, 232)(54, 222)(55, 269)(56, 225)(57, 226)(58, 227)(59, 271)(60, 274)(61, 273)(62, 275)(63, 234)(64, 233)(65, 272)(66, 279)(67, 235)(68, 282)(69, 242)(70, 237)(71, 281)(72, 285)(73, 286)(74, 243)(75, 244)(76, 288)(77, 247)(78, 284)(79, 251)(80, 257)(81, 253)(82, 252)(83, 254)(84, 287)(85, 283)(86, 280)(87, 258)(88, 278)(89, 263)(90, 260)(91, 277)(92, 270)(93, 264)(94, 265)(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) :: { ( 4, 16 ), ( 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 E15.1201 Graph:: simple bipartite v = 104 e = 192 f = 60 degree seq :: [ 2^96, 24^8 ] E15.1205 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-3 * Y1 * Y2^3 * Y1, (Y2^-2 * R * Y2^-1)^2, (R * Y2^2 * Y1)^2, Y2^-1 * Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, Y2^12, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 17, 113)(10, 106, 21, 117)(12, 108, 25, 121)(14, 110, 29, 125)(15, 111, 31, 127)(16, 112, 33, 129)(18, 114, 26, 122)(19, 115, 38, 134)(20, 116, 39, 135)(22, 118, 30, 126)(23, 119, 43, 139)(24, 120, 45, 141)(27, 123, 50, 146)(28, 124, 51, 147)(32, 128, 56, 152)(34, 130, 48, 144)(35, 131, 60, 156)(36, 132, 46, 142)(37, 133, 57, 153)(40, 136, 59, 155)(41, 137, 64, 160)(42, 138, 63, 159)(44, 140, 67, 163)(47, 143, 71, 167)(49, 145, 68, 164)(52, 148, 70, 166)(53, 149, 75, 171)(54, 150, 74, 170)(55, 151, 72, 168)(58, 154, 80, 176)(61, 157, 66, 162)(62, 158, 76, 172)(65, 161, 73, 169)(69, 165, 90, 186)(77, 173, 96, 192)(78, 174, 91, 187)(79, 175, 95, 191)(81, 177, 88, 184)(82, 178, 94, 190)(83, 179, 93, 189)(84, 180, 92, 188)(85, 181, 89, 185)(86, 182, 87, 183)(193, 289, 195, 291, 200, 296, 210, 306, 229, 325, 253, 349, 275, 371, 257, 353, 234, 330, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 241, 337, 264, 360, 285, 381, 268, 364, 246, 342, 222, 318, 206, 302, 198, 294)(199, 295, 207, 303, 224, 320, 249, 345, 271, 367, 286, 382, 265, 361, 243, 339, 233, 329, 213, 309, 226, 322, 208, 304)(201, 297, 211, 307, 228, 324, 209, 305, 227, 323, 235, 331, 258, 354, 279, 375, 277, 373, 255, 351, 232, 328, 212, 308)(203, 299, 215, 311, 236, 332, 260, 356, 281, 377, 276, 372, 254, 350, 231, 327, 245, 341, 221, 317, 238, 334, 216, 312)(205, 301, 219, 315, 240, 336, 217, 313, 239, 335, 223, 319, 247, 343, 269, 365, 287, 383, 266, 362, 244, 340, 220, 316)(225, 321, 250, 346, 230, 326, 248, 344, 270, 366, 252, 348, 274, 370, 282, 378, 278, 374, 256, 352, 273, 369, 251, 347)(237, 333, 261, 357, 242, 338, 259, 355, 280, 376, 263, 359, 284, 380, 272, 368, 288, 384, 267, 363, 283, 379, 262, 358) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 209)(9, 196)(10, 213)(11, 197)(12, 217)(13, 198)(14, 221)(15, 223)(16, 225)(17, 200)(18, 218)(19, 230)(20, 231)(21, 202)(22, 222)(23, 235)(24, 237)(25, 204)(26, 210)(27, 242)(28, 243)(29, 206)(30, 214)(31, 207)(32, 248)(33, 208)(34, 240)(35, 252)(36, 238)(37, 249)(38, 211)(39, 212)(40, 251)(41, 256)(42, 255)(43, 215)(44, 259)(45, 216)(46, 228)(47, 263)(48, 226)(49, 260)(50, 219)(51, 220)(52, 262)(53, 267)(54, 266)(55, 264)(56, 224)(57, 229)(58, 272)(59, 232)(60, 227)(61, 258)(62, 268)(63, 234)(64, 233)(65, 265)(66, 253)(67, 236)(68, 241)(69, 282)(70, 244)(71, 239)(72, 247)(73, 257)(74, 246)(75, 245)(76, 254)(77, 288)(78, 283)(79, 287)(80, 250)(81, 280)(82, 286)(83, 285)(84, 284)(85, 281)(86, 279)(87, 278)(88, 273)(89, 277)(90, 261)(91, 270)(92, 276)(93, 275)(94, 274)(95, 271)(96, 269)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16 ), ( 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 E15.1206 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 4^48, 24^8 ] E15.1206 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) Aut = $<192, 1484>$ (small group id <192, 1484>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y3^-2 * Y1 * Y3^-2 * Y1^-2, Y3^2 * Y1^-1 * Y3^-4 * Y1^-1, (Y3 * Y1^-3)^2, Y1^8, (Y3 * Y2^-1)^12 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 40, 136, 34, 130, 13, 109, 4, 100)(3, 99, 9, 105, 23, 119, 57, 153, 74, 170, 42, 138, 29, 125, 11, 107)(5, 101, 14, 110, 35, 131, 71, 167, 75, 171, 51, 147, 20, 116, 7, 103)(8, 104, 21, 117, 52, 148, 33, 129, 64, 160, 81, 177, 44, 140, 17, 113)(10, 106, 25, 121, 53, 149, 22, 118, 55, 151, 90, 186, 65, 161, 27, 123)(12, 108, 30, 126, 68, 164, 76, 172, 41, 137, 18, 114, 45, 141, 32, 128)(15, 111, 38, 134, 73, 169, 88, 184, 62, 158, 31, 127, 69, 165, 36, 132)(19, 115, 47, 143, 82, 178, 46, 142, 84, 180, 72, 168, 87, 183, 49, 145)(24, 120, 43, 139, 78, 174, 67, 163, 77, 173, 70, 166, 89, 185, 58, 154)(26, 122, 48, 144, 79, 175, 60, 156, 39, 135, 56, 152, 85, 181, 63, 159)(28, 124, 66, 162, 83, 179, 54, 150, 37, 133, 59, 155, 80, 176, 50, 146)(61, 157, 91, 187, 95, 191, 92, 188, 96, 192, 93, 189, 94, 190, 86, 182)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 218)(11, 220)(12, 223)(13, 225)(14, 228)(15, 197)(16, 233)(17, 235)(18, 198)(19, 240)(20, 242)(21, 245)(22, 200)(23, 250)(24, 201)(25, 203)(26, 254)(27, 256)(28, 243)(29, 259)(30, 205)(31, 255)(32, 258)(33, 262)(34, 263)(35, 246)(36, 253)(37, 206)(38, 252)(39, 207)(40, 266)(41, 230)(42, 208)(43, 271)(44, 272)(45, 274)(46, 210)(47, 212)(48, 219)(49, 222)(50, 273)(51, 280)(52, 275)(53, 278)(54, 213)(55, 231)(56, 214)(57, 229)(58, 283)(59, 215)(60, 216)(61, 217)(62, 267)(63, 269)(64, 226)(65, 284)(66, 221)(67, 285)(68, 279)(69, 224)(70, 277)(71, 276)(72, 227)(73, 268)(74, 247)(75, 232)(76, 251)(77, 234)(78, 236)(79, 241)(80, 260)(81, 257)(82, 286)(83, 237)(84, 248)(85, 238)(86, 239)(87, 287)(88, 288)(89, 244)(90, 249)(91, 261)(92, 264)(93, 265)(94, 270)(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) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.1205 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1207 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1^2)^2, (T2 * T1 * T2 * T1^-2)^2, (T2 * T1^-1 * T2 * T1 * T2 * T1^-1)^2, T1^12 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 70, 69, 42, 22, 10, 4)(3, 7, 15, 31, 55, 81, 90, 74, 45, 24, 18, 8)(6, 13, 27, 21, 41, 68, 88, 62, 72, 44, 30, 14)(9, 19, 38, 64, 84, 58, 71, 48, 26, 12, 25, 20)(16, 33, 57, 37, 63, 89, 67, 40, 66, 77, 47, 34)(17, 35, 60, 73, 51, 28, 50, 80, 54, 32, 56, 36)(29, 52, 39, 65, 76, 46, 75, 91, 78, 49, 79, 53)(59, 83, 61, 87, 93, 85, 95, 96, 94, 86, 92, 82) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 39)(20, 40)(22, 31)(23, 44)(25, 46)(26, 47)(27, 49)(30, 54)(33, 58)(34, 59)(35, 61)(36, 62)(38, 63)(41, 60)(42, 64)(43, 71)(45, 73)(48, 78)(50, 81)(51, 82)(52, 83)(53, 84)(55, 77)(56, 85)(57, 86)(65, 72)(66, 87)(67, 74)(68, 75)(69, 88)(70, 90)(76, 92)(79, 93)(80, 94)(89, 95)(91, 96) local type(s) :: { ( 8^12 ) } Outer automorphisms :: reflexible Dual of E15.1208 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 48 f = 12 degree seq :: [ 12^8 ] E15.1208 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 12}) Quotient :: regular Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^8, (T2 * T1^-4)^2, (T2 * T1^2 * T2 * T1^-1)^2, (T1^-1 * T2 * T1^-1 * T2 * T1^-1)^2, (T2 * T1 * T2 * T1^-1)^3, (T1 * T2)^12 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 46, 38, 18, 8)(6, 13, 27, 53, 45, 60, 30, 14)(9, 19, 39, 48, 24, 47, 42, 20)(12, 25, 49, 44, 21, 43, 52, 26)(16, 33, 63, 86, 70, 77, 51, 34)(17, 35, 66, 85, 61, 76, 50, 36)(28, 55, 41, 72, 84, 91, 74, 56)(29, 57, 40, 71, 79, 90, 73, 58)(32, 62, 78, 54, 37, 69, 75, 59)(64, 87, 68, 89, 93, 80, 94, 83)(65, 82, 67, 88, 95, 96, 92, 81) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 46)(25, 50)(26, 51)(27, 54)(30, 59)(31, 61)(33, 64)(34, 65)(35, 67)(36, 68)(38, 70)(39, 69)(42, 62)(43, 66)(44, 63)(47, 73)(48, 74)(49, 75)(52, 78)(53, 79)(55, 80)(56, 81)(57, 82)(58, 83)(60, 84)(71, 89)(72, 88)(76, 92)(77, 93)(85, 94)(86, 95)(87, 91)(90, 96) local type(s) :: { ( 12^8 ) } Outer automorphisms :: reflexible Dual of E15.1207 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 12 e = 48 f = 8 degree seq :: [ 8^12 ] E15.1209 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-1 * T1 * T2^-3)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2^-1 * T1 * T2 * T1 * T2^-1)^2, (T2 * T1 * T2 * T1 * T2^-1 * T1)^2, (T2 * T1)^12 ] Map:: R = (1, 3, 8, 18, 38, 22, 10, 4)(2, 5, 12, 26, 53, 30, 14, 6)(7, 15, 32, 63, 45, 66, 34, 16)(9, 19, 40, 70, 37, 69, 42, 20)(11, 23, 47, 75, 60, 78, 49, 24)(13, 27, 55, 82, 52, 81, 57, 28)(17, 35, 67, 44, 21, 43, 68, 36)(25, 50, 79, 59, 29, 58, 80, 51)(31, 61, 41, 72, 89, 90, 86, 62)(33, 64, 39, 71, 87, 95, 88, 65)(46, 73, 56, 84, 94, 85, 91, 74)(48, 76, 54, 83, 92, 96, 93, 77)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 117)(108, 121)(110, 125)(111, 127)(112, 129)(114, 133)(115, 135)(116, 137)(118, 141)(119, 142)(120, 144)(122, 148)(123, 150)(124, 152)(126, 156)(128, 155)(130, 147)(131, 153)(132, 145)(134, 149)(136, 154)(138, 146)(139, 151)(140, 143)(157, 181)(158, 173)(159, 183)(160, 172)(161, 170)(162, 185)(163, 176)(164, 175)(165, 184)(166, 182)(167, 180)(168, 179)(169, 186)(171, 188)(174, 190)(177, 189)(178, 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) :: { ( 24, 24 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E15.1213 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 96 f = 8 degree seq :: [ 2^48, 8^12 ] E15.1210 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^2, (T2 * T1^-1 * T2)^2, (T2^2 * T1^-1)^2, T1^8, (T2^-1 * T1^3)^2, T1^-1 * T2^-1 * T1 * T2 * T1^-2 * T2^-2 * T1^-2, T1 * T2^-1 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2^-1, T1^-3 * T2^4 * T1 * T2^-2, T2 * T1^-1 * T2^-1 * T1^2 * T2^-4 * T1^-1, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 58, 73, 37, 72, 71, 36, 15, 5)(2, 7, 19, 45, 85, 66, 33, 67, 92, 50, 22, 8)(4, 12, 30, 65, 76, 39, 16, 38, 74, 55, 24, 9)(6, 17, 40, 78, 63, 29, 13, 32, 54, 82, 43, 18)(11, 27, 14, 35, 69, 91, 51, 86, 47, 88, 57, 25)(20, 46, 21, 49, 90, 68, 34, 60, 80, 56, 84, 44)(23, 52, 93, 70, 75, 59, 28, 61, 94, 64, 31, 53)(41, 79, 42, 81, 96, 89, 48, 87, 62, 83, 95, 77)(97, 98, 102, 112, 133, 129, 109, 100)(99, 105, 119, 147, 168, 135, 124, 107)(101, 110, 130, 163, 169, 143, 116, 103)(104, 117, 144, 128, 162, 176, 137, 113)(106, 121, 152, 181, 167, 187, 145, 118)(108, 125, 158, 171, 134, 114, 138, 127)(111, 126, 160, 184, 154, 170, 166, 131)(115, 140, 179, 159, 188, 164, 177, 139)(120, 150, 185, 157, 172, 136, 173, 148)(122, 146, 174, 161, 132, 141, 178, 151)(123, 155, 183, 142, 182, 149, 175, 156)(153, 190, 192, 186, 165, 189, 191, 180) 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) :: { ( 4^8 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E15.1214 Transitivity :: ET+ Graph:: bipartite v = 20 e = 96 f = 48 degree seq :: [ 8^12, 12^8 ] E15.1211 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 12}) Quotient :: edge Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1^2)^2, (T2 * T1 * T2 * T1^-2)^2, (T2 * T1^-1 * T2 * T1 * T2 * T1^-1)^2, T1^12 ] 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, 37)(19, 39)(20, 40)(22, 31)(23, 44)(25, 46)(26, 47)(27, 49)(30, 54)(33, 58)(34, 59)(35, 61)(36, 62)(38, 63)(41, 60)(42, 64)(43, 71)(45, 73)(48, 78)(50, 81)(51, 82)(52, 83)(53, 84)(55, 77)(56, 85)(57, 86)(65, 72)(66, 87)(67, 74)(68, 75)(69, 88)(70, 90)(76, 92)(79, 93)(80, 94)(89, 95)(91, 96)(97, 98, 101, 107, 119, 139, 166, 165, 138, 118, 106, 100)(99, 103, 111, 127, 151, 177, 186, 170, 141, 120, 114, 104)(102, 109, 123, 117, 137, 164, 184, 158, 168, 140, 126, 110)(105, 115, 134, 160, 180, 154, 167, 144, 122, 108, 121, 116)(112, 129, 153, 133, 159, 185, 163, 136, 162, 173, 143, 130)(113, 131, 156, 169, 147, 124, 146, 176, 150, 128, 152, 132)(125, 148, 135, 161, 172, 142, 171, 187, 174, 145, 175, 149)(155, 179, 157, 183, 189, 181, 191, 192, 190, 182, 188, 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) :: { ( 16, 16 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E15.1212 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 12 degree seq :: [ 2^48, 12^8 ] E15.1212 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-1 * T1 * T2^-3)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2^-1 * T1 * T2 * T1 * T2^-1)^2, (T2 * T1 * T2 * T1 * T2^-1 * T1)^2, (T2 * T1)^12 ] Map:: R = (1, 97, 3, 99, 8, 104, 18, 114, 38, 134, 22, 118, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 26, 122, 53, 149, 30, 126, 14, 110, 6, 102)(7, 103, 15, 111, 32, 128, 63, 159, 45, 141, 66, 162, 34, 130, 16, 112)(9, 105, 19, 115, 40, 136, 70, 166, 37, 133, 69, 165, 42, 138, 20, 116)(11, 107, 23, 119, 47, 143, 75, 171, 60, 156, 78, 174, 49, 145, 24, 120)(13, 109, 27, 123, 55, 151, 82, 178, 52, 148, 81, 177, 57, 153, 28, 124)(17, 113, 35, 131, 67, 163, 44, 140, 21, 117, 43, 139, 68, 164, 36, 132)(25, 121, 50, 146, 79, 175, 59, 155, 29, 125, 58, 154, 80, 176, 51, 147)(31, 127, 61, 157, 41, 137, 72, 168, 89, 185, 90, 186, 86, 182, 62, 158)(33, 129, 64, 160, 39, 135, 71, 167, 87, 183, 95, 191, 88, 184, 65, 161)(46, 142, 73, 169, 56, 152, 84, 180, 94, 190, 85, 181, 91, 187, 74, 170)(48, 144, 76, 172, 54, 150, 83, 179, 92, 188, 96, 192, 93, 189, 77, 173) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 121)(13, 102)(14, 125)(15, 127)(16, 129)(17, 104)(18, 133)(19, 135)(20, 137)(21, 106)(22, 141)(23, 142)(24, 144)(25, 108)(26, 148)(27, 150)(28, 152)(29, 110)(30, 156)(31, 111)(32, 155)(33, 112)(34, 147)(35, 153)(36, 145)(37, 114)(38, 149)(39, 115)(40, 154)(41, 116)(42, 146)(43, 151)(44, 143)(45, 118)(46, 119)(47, 140)(48, 120)(49, 132)(50, 138)(51, 130)(52, 122)(53, 134)(54, 123)(55, 139)(56, 124)(57, 131)(58, 136)(59, 128)(60, 126)(61, 181)(62, 173)(63, 183)(64, 172)(65, 170)(66, 185)(67, 176)(68, 175)(69, 184)(70, 182)(71, 180)(72, 179)(73, 186)(74, 161)(75, 188)(76, 160)(77, 158)(78, 190)(79, 164)(80, 163)(81, 189)(82, 187)(83, 168)(84, 167)(85, 157)(86, 166)(87, 159)(88, 165)(89, 162)(90, 169)(91, 178)(92, 171)(93, 177)(94, 174)(95, 192)(96, 191) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E15.1211 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 56 degree seq :: [ 16^12 ] E15.1213 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^2, (T2 * T1^-1 * T2)^2, (T2^2 * T1^-1)^2, T1^8, (T2^-1 * T1^3)^2, T1^-1 * T2^-1 * T1 * T2 * T1^-2 * T2^-2 * T1^-2, T1 * T2^-1 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2^-1, T1^-3 * T2^4 * T1 * T2^-2, T2 * T1^-1 * T2^-1 * T1^2 * T2^-4 * T1^-1, T2^12 ] Map:: R = (1, 97, 3, 99, 10, 106, 26, 122, 58, 154, 73, 169, 37, 133, 72, 168, 71, 167, 36, 132, 15, 111, 5, 101)(2, 98, 7, 103, 19, 115, 45, 141, 85, 181, 66, 162, 33, 129, 67, 163, 92, 188, 50, 146, 22, 118, 8, 104)(4, 100, 12, 108, 30, 126, 65, 161, 76, 172, 39, 135, 16, 112, 38, 134, 74, 170, 55, 151, 24, 120, 9, 105)(6, 102, 17, 113, 40, 136, 78, 174, 63, 159, 29, 125, 13, 109, 32, 128, 54, 150, 82, 178, 43, 139, 18, 114)(11, 107, 27, 123, 14, 110, 35, 131, 69, 165, 91, 187, 51, 147, 86, 182, 47, 143, 88, 184, 57, 153, 25, 121)(20, 116, 46, 142, 21, 117, 49, 145, 90, 186, 68, 164, 34, 130, 60, 156, 80, 176, 56, 152, 84, 180, 44, 140)(23, 119, 52, 148, 93, 189, 70, 166, 75, 171, 59, 155, 28, 124, 61, 157, 94, 190, 64, 160, 31, 127, 53, 149)(41, 137, 79, 175, 42, 138, 81, 177, 96, 192, 89, 185, 48, 144, 87, 183, 62, 158, 83, 179, 95, 191, 77, 173) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 112)(7, 101)(8, 117)(9, 119)(10, 121)(11, 99)(12, 125)(13, 100)(14, 130)(15, 126)(16, 133)(17, 104)(18, 138)(19, 140)(20, 103)(21, 144)(22, 106)(23, 147)(24, 150)(25, 152)(26, 146)(27, 155)(28, 107)(29, 158)(30, 160)(31, 108)(32, 162)(33, 109)(34, 163)(35, 111)(36, 141)(37, 129)(38, 114)(39, 124)(40, 173)(41, 113)(42, 127)(43, 115)(44, 179)(45, 178)(46, 182)(47, 116)(48, 128)(49, 118)(50, 174)(51, 168)(52, 120)(53, 175)(54, 185)(55, 122)(56, 181)(57, 190)(58, 170)(59, 183)(60, 123)(61, 172)(62, 171)(63, 188)(64, 184)(65, 132)(66, 176)(67, 169)(68, 177)(69, 189)(70, 131)(71, 187)(72, 135)(73, 143)(74, 166)(75, 134)(76, 136)(77, 148)(78, 161)(79, 156)(80, 137)(81, 139)(82, 151)(83, 159)(84, 153)(85, 167)(86, 149)(87, 142)(88, 154)(89, 157)(90, 165)(91, 145)(92, 164)(93, 191)(94, 192)(95, 180)(96, 186) 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 ) } Outer automorphisms :: reflexible Dual of E15.1209 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 96 f = 60 degree seq :: [ 24^8 ] E15.1214 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 12}) Quotient :: loop Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1^2)^2, (T2 * T1 * T2 * T1^-2)^2, (T2 * T1^-1 * T2 * T1 * T2 * T1^-1)^2, T1^12 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 21, 117)(11, 107, 24, 120)(13, 109, 28, 124)(14, 110, 29, 125)(15, 111, 32, 128)(18, 114, 37, 133)(19, 115, 39, 135)(20, 116, 40, 136)(22, 118, 31, 127)(23, 119, 44, 140)(25, 121, 46, 142)(26, 122, 47, 143)(27, 123, 49, 145)(30, 126, 54, 150)(33, 129, 58, 154)(34, 130, 59, 155)(35, 131, 61, 157)(36, 132, 62, 158)(38, 134, 63, 159)(41, 137, 60, 156)(42, 138, 64, 160)(43, 139, 71, 167)(45, 141, 73, 169)(48, 144, 78, 174)(50, 146, 81, 177)(51, 147, 82, 178)(52, 148, 83, 179)(53, 149, 84, 180)(55, 151, 77, 173)(56, 152, 85, 181)(57, 153, 86, 182)(65, 161, 72, 168)(66, 162, 87, 183)(67, 163, 74, 170)(68, 164, 75, 171)(69, 165, 88, 184)(70, 166, 90, 186)(76, 172, 92, 188)(79, 175, 93, 189)(80, 176, 94, 190)(89, 185, 95, 191)(91, 187, 96, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 115)(10, 100)(11, 119)(12, 121)(13, 123)(14, 102)(15, 127)(16, 129)(17, 131)(18, 104)(19, 134)(20, 105)(21, 137)(22, 106)(23, 139)(24, 114)(25, 116)(26, 108)(27, 117)(28, 146)(29, 148)(30, 110)(31, 151)(32, 152)(33, 153)(34, 112)(35, 156)(36, 113)(37, 159)(38, 160)(39, 161)(40, 162)(41, 164)(42, 118)(43, 166)(44, 126)(45, 120)(46, 171)(47, 130)(48, 122)(49, 175)(50, 176)(51, 124)(52, 135)(53, 125)(54, 128)(55, 177)(56, 132)(57, 133)(58, 167)(59, 179)(60, 169)(61, 183)(62, 168)(63, 185)(64, 180)(65, 172)(66, 173)(67, 136)(68, 184)(69, 138)(70, 165)(71, 144)(72, 140)(73, 147)(74, 141)(75, 187)(76, 142)(77, 143)(78, 145)(79, 149)(80, 150)(81, 186)(82, 155)(83, 157)(84, 154)(85, 191)(86, 188)(87, 189)(88, 158)(89, 163)(90, 170)(91, 174)(92, 178)(93, 181)(94, 182)(95, 192)(96, 190) local type(s) :: { ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.1210 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 20 degree seq :: [ 4^48 ] E15.1215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2 * R)^2, Y2^8, (Y2^-2 * R * Y2^-2)^2, Y2^-3 * Y1 * Y2^4 * Y1 * Y2^-1, (Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2 * R * Y2^2 * R * Y2 * Y1 * Y2^-1, (Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1)^2, (Y3 * Y2^-1)^12 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 17, 113)(10, 106, 21, 117)(12, 108, 25, 121)(14, 110, 29, 125)(15, 111, 31, 127)(16, 112, 33, 129)(18, 114, 37, 133)(19, 115, 39, 135)(20, 116, 41, 137)(22, 118, 45, 141)(23, 119, 46, 142)(24, 120, 48, 144)(26, 122, 52, 148)(27, 123, 54, 150)(28, 124, 56, 152)(30, 126, 60, 156)(32, 128, 59, 155)(34, 130, 51, 147)(35, 131, 57, 153)(36, 132, 49, 145)(38, 134, 53, 149)(40, 136, 58, 154)(42, 138, 50, 146)(43, 139, 55, 151)(44, 140, 47, 143)(61, 157, 85, 181)(62, 158, 77, 173)(63, 159, 87, 183)(64, 160, 76, 172)(65, 161, 74, 170)(66, 162, 89, 185)(67, 163, 80, 176)(68, 164, 79, 175)(69, 165, 88, 184)(70, 166, 86, 182)(71, 167, 84, 180)(72, 168, 83, 179)(73, 169, 90, 186)(75, 171, 92, 188)(78, 174, 94, 190)(81, 177, 93, 189)(82, 178, 91, 187)(95, 191, 96, 192)(193, 289, 195, 291, 200, 296, 210, 306, 230, 326, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 245, 341, 222, 318, 206, 302, 198, 294)(199, 295, 207, 303, 224, 320, 255, 351, 237, 333, 258, 354, 226, 322, 208, 304)(201, 297, 211, 307, 232, 328, 262, 358, 229, 325, 261, 357, 234, 330, 212, 308)(203, 299, 215, 311, 239, 335, 267, 363, 252, 348, 270, 366, 241, 337, 216, 312)(205, 301, 219, 315, 247, 343, 274, 370, 244, 340, 273, 369, 249, 345, 220, 316)(209, 305, 227, 323, 259, 355, 236, 332, 213, 309, 235, 331, 260, 356, 228, 324)(217, 313, 242, 338, 271, 367, 251, 347, 221, 317, 250, 346, 272, 368, 243, 339)(223, 319, 253, 349, 233, 329, 264, 360, 281, 377, 282, 378, 278, 374, 254, 350)(225, 321, 256, 352, 231, 327, 263, 359, 279, 375, 287, 383, 280, 376, 257, 353)(238, 334, 265, 361, 248, 344, 276, 372, 286, 382, 277, 373, 283, 379, 266, 362)(240, 336, 268, 364, 246, 342, 275, 371, 284, 380, 288, 384, 285, 381, 269, 365) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 209)(9, 196)(10, 213)(11, 197)(12, 217)(13, 198)(14, 221)(15, 223)(16, 225)(17, 200)(18, 229)(19, 231)(20, 233)(21, 202)(22, 237)(23, 238)(24, 240)(25, 204)(26, 244)(27, 246)(28, 248)(29, 206)(30, 252)(31, 207)(32, 251)(33, 208)(34, 243)(35, 249)(36, 241)(37, 210)(38, 245)(39, 211)(40, 250)(41, 212)(42, 242)(43, 247)(44, 239)(45, 214)(46, 215)(47, 236)(48, 216)(49, 228)(50, 234)(51, 226)(52, 218)(53, 230)(54, 219)(55, 235)(56, 220)(57, 227)(58, 232)(59, 224)(60, 222)(61, 277)(62, 269)(63, 279)(64, 268)(65, 266)(66, 281)(67, 272)(68, 271)(69, 280)(70, 278)(71, 276)(72, 275)(73, 282)(74, 257)(75, 284)(76, 256)(77, 254)(78, 286)(79, 260)(80, 259)(81, 285)(82, 283)(83, 264)(84, 263)(85, 253)(86, 262)(87, 255)(88, 261)(89, 258)(90, 265)(91, 274)(92, 267)(93, 273)(94, 270)(95, 288)(96, 287)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E15.1218 Graph:: bipartite v = 60 e = 192 f = 104 degree seq :: [ 4^48, 16^12 ] E15.1216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y1^-1 * Y2^-1)^2, (Y2 * Y1^-1 * Y2)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y1^-1 * Y2 * Y1^-2)^2, Y1^8, Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-2 * Y2^-2 * Y1^-2, Y1^-3 * Y2^4 * Y1 * Y2^-2, Y2 * Y1^-1 * Y2^-1 * Y1^2 * Y2^-4 * Y1^-1, Y1 * Y2^-1 * Y1^2 * Y2 * Y1^-1 * Y2 * Y1^2 * Y2^-1, Y2^12 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 37, 133, 33, 129, 13, 109, 4, 100)(3, 99, 9, 105, 23, 119, 51, 147, 72, 168, 39, 135, 28, 124, 11, 107)(5, 101, 14, 110, 34, 130, 67, 163, 73, 169, 47, 143, 20, 116, 7, 103)(8, 104, 21, 117, 48, 144, 32, 128, 66, 162, 80, 176, 41, 137, 17, 113)(10, 106, 25, 121, 56, 152, 85, 181, 71, 167, 91, 187, 49, 145, 22, 118)(12, 108, 29, 125, 62, 158, 75, 171, 38, 134, 18, 114, 42, 138, 31, 127)(15, 111, 30, 126, 64, 160, 88, 184, 58, 154, 74, 170, 70, 166, 35, 131)(19, 115, 44, 140, 83, 179, 63, 159, 92, 188, 68, 164, 81, 177, 43, 139)(24, 120, 54, 150, 89, 185, 61, 157, 76, 172, 40, 136, 77, 173, 52, 148)(26, 122, 50, 146, 78, 174, 65, 161, 36, 132, 45, 141, 82, 178, 55, 151)(27, 123, 59, 155, 87, 183, 46, 142, 86, 182, 53, 149, 79, 175, 60, 156)(57, 153, 94, 190, 96, 192, 90, 186, 69, 165, 93, 189, 95, 191, 84, 180)(193, 289, 195, 291, 202, 298, 218, 314, 250, 346, 265, 361, 229, 325, 264, 360, 263, 359, 228, 324, 207, 303, 197, 293)(194, 290, 199, 295, 211, 307, 237, 333, 277, 373, 258, 354, 225, 321, 259, 355, 284, 380, 242, 338, 214, 310, 200, 296)(196, 292, 204, 300, 222, 318, 257, 353, 268, 364, 231, 327, 208, 304, 230, 326, 266, 362, 247, 343, 216, 312, 201, 297)(198, 294, 209, 305, 232, 328, 270, 366, 255, 351, 221, 317, 205, 301, 224, 320, 246, 342, 274, 370, 235, 331, 210, 306)(203, 299, 219, 315, 206, 302, 227, 323, 261, 357, 283, 379, 243, 339, 278, 374, 239, 335, 280, 376, 249, 345, 217, 313)(212, 308, 238, 334, 213, 309, 241, 337, 282, 378, 260, 356, 226, 322, 252, 348, 272, 368, 248, 344, 276, 372, 236, 332)(215, 311, 244, 340, 285, 381, 262, 358, 267, 363, 251, 347, 220, 316, 253, 349, 286, 382, 256, 352, 223, 319, 245, 341)(233, 329, 271, 367, 234, 330, 273, 369, 288, 384, 281, 377, 240, 336, 279, 375, 254, 350, 275, 371, 287, 383, 269, 365) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 218)(11, 219)(12, 222)(13, 224)(14, 227)(15, 197)(16, 230)(17, 232)(18, 198)(19, 237)(20, 238)(21, 241)(22, 200)(23, 244)(24, 201)(25, 203)(26, 250)(27, 206)(28, 253)(29, 205)(30, 257)(31, 245)(32, 246)(33, 259)(34, 252)(35, 261)(36, 207)(37, 264)(38, 266)(39, 208)(40, 270)(41, 271)(42, 273)(43, 210)(44, 212)(45, 277)(46, 213)(47, 280)(48, 279)(49, 282)(50, 214)(51, 278)(52, 285)(53, 215)(54, 274)(55, 216)(56, 276)(57, 217)(58, 265)(59, 220)(60, 272)(61, 286)(62, 275)(63, 221)(64, 223)(65, 268)(66, 225)(67, 284)(68, 226)(69, 283)(70, 267)(71, 228)(72, 263)(73, 229)(74, 247)(75, 251)(76, 231)(77, 233)(78, 255)(79, 234)(80, 248)(81, 288)(82, 235)(83, 287)(84, 236)(85, 258)(86, 239)(87, 254)(88, 249)(89, 240)(90, 260)(91, 243)(92, 242)(93, 262)(94, 256)(95, 269)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 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 E15.1217 Graph:: bipartite v = 20 e = 192 f = 144 degree seq :: [ 16^12, 24^8 ] E15.1217 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-3 * Y2)^2, (Y3^2 * Y2 * Y3^-1 * Y2)^2, (Y3 * Y2 * Y3^-1 * Y2)^3, Y3^12, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 209, 305)(202, 298, 213, 309)(204, 300, 217, 313)(206, 302, 221, 317)(207, 303, 223, 319)(208, 304, 225, 321)(210, 306, 222, 318)(211, 307, 230, 326)(212, 308, 232, 328)(214, 310, 218, 314)(215, 311, 235, 331)(216, 312, 237, 333)(219, 315, 242, 338)(220, 316, 244, 340)(224, 320, 249, 345)(226, 322, 240, 336)(227, 323, 253, 349)(228, 324, 238, 334)(229, 325, 252, 348)(231, 327, 245, 341)(233, 329, 243, 339)(234, 330, 257, 353)(236, 332, 264, 360)(239, 335, 268, 364)(241, 337, 267, 363)(246, 342, 272, 368)(247, 343, 270, 366)(248, 344, 266, 362)(250, 346, 265, 361)(251, 347, 263, 359)(254, 350, 278, 374)(255, 351, 262, 358)(256, 352, 273, 369)(258, 354, 271, 367)(259, 355, 276, 372)(260, 356, 279, 375)(261, 357, 274, 370)(269, 365, 283, 379)(275, 371, 284, 380)(277, 373, 285, 381)(280, 376, 282, 378)(281, 377, 286, 382)(287, 383, 288, 384) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 210)(9, 211)(10, 196)(11, 215)(12, 218)(13, 219)(14, 198)(15, 224)(16, 199)(17, 227)(18, 229)(19, 231)(20, 201)(21, 233)(22, 202)(23, 236)(24, 203)(25, 239)(26, 241)(27, 243)(28, 205)(29, 245)(30, 206)(31, 247)(32, 213)(33, 250)(34, 208)(35, 212)(36, 209)(37, 255)(38, 256)(39, 257)(40, 258)(41, 260)(42, 214)(43, 262)(44, 221)(45, 265)(46, 216)(47, 220)(48, 217)(49, 270)(50, 271)(51, 272)(52, 273)(53, 275)(54, 222)(55, 269)(56, 223)(57, 277)(58, 230)(59, 225)(60, 226)(61, 279)(62, 228)(63, 281)(64, 280)(65, 263)(66, 267)(67, 232)(68, 274)(69, 234)(70, 254)(71, 235)(72, 282)(73, 242)(74, 237)(75, 238)(76, 284)(77, 240)(78, 286)(79, 285)(80, 248)(81, 252)(82, 244)(83, 259)(84, 246)(85, 251)(86, 249)(87, 287)(88, 253)(89, 261)(90, 266)(91, 264)(92, 288)(93, 268)(94, 276)(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) :: { ( 16, 24 ), ( 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E15.1216 Graph:: simple bipartite v = 144 e = 192 f = 20 degree seq :: [ 2^96, 4^48 ] E15.1218 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, (Y1 * Y3 * Y1^2)^2, (Y3 * Y1^-1 * Y3 * Y1^2)^2, (Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1)^2, Y1^12 ] Map:: R = (1, 97, 2, 98, 5, 101, 11, 107, 23, 119, 43, 139, 70, 166, 69, 165, 42, 138, 22, 118, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 31, 127, 55, 151, 81, 177, 90, 186, 74, 170, 45, 141, 24, 120, 18, 114, 8, 104)(6, 102, 13, 109, 27, 123, 21, 117, 41, 137, 68, 164, 88, 184, 62, 158, 72, 168, 44, 140, 30, 126, 14, 110)(9, 105, 19, 115, 38, 134, 64, 160, 84, 180, 58, 154, 71, 167, 48, 144, 26, 122, 12, 108, 25, 121, 20, 116)(16, 112, 33, 129, 57, 153, 37, 133, 63, 159, 89, 185, 67, 163, 40, 136, 66, 162, 77, 173, 47, 143, 34, 130)(17, 113, 35, 131, 60, 156, 73, 169, 51, 147, 28, 124, 50, 146, 80, 176, 54, 150, 32, 128, 56, 152, 36, 132)(29, 125, 52, 148, 39, 135, 65, 161, 76, 172, 46, 142, 75, 171, 91, 187, 78, 174, 49, 145, 79, 175, 53, 149)(59, 155, 83, 179, 61, 157, 87, 183, 93, 189, 85, 181, 95, 191, 96, 192, 94, 190, 86, 182, 92, 188, 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, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 213)(11, 216)(12, 197)(13, 220)(14, 221)(15, 224)(16, 199)(17, 200)(18, 229)(19, 231)(20, 232)(21, 202)(22, 223)(23, 236)(24, 203)(25, 238)(26, 239)(27, 241)(28, 205)(29, 206)(30, 246)(31, 214)(32, 207)(33, 250)(34, 251)(35, 253)(36, 254)(37, 210)(38, 255)(39, 211)(40, 212)(41, 252)(42, 256)(43, 263)(44, 215)(45, 265)(46, 217)(47, 218)(48, 270)(49, 219)(50, 273)(51, 274)(52, 275)(53, 276)(54, 222)(55, 269)(56, 277)(57, 278)(58, 225)(59, 226)(60, 233)(61, 227)(62, 228)(63, 230)(64, 234)(65, 264)(66, 279)(67, 266)(68, 267)(69, 280)(70, 282)(71, 235)(72, 257)(73, 237)(74, 259)(75, 260)(76, 284)(77, 247)(78, 240)(79, 285)(80, 286)(81, 242)(82, 243)(83, 244)(84, 245)(85, 248)(86, 249)(87, 258)(88, 261)(89, 287)(90, 262)(91, 288)(92, 268)(93, 271)(94, 272)(95, 281)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E15.1215 Graph:: simple bipartite v = 104 e = 192 f = 60 degree seq :: [ 2^96, 24^8 ] E15.1219 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (R * Y2^2 * Y1)^2, (Y2 * Y1 * Y2^2)^2, Y2 * R * Y2^-3 * R * Y2^2, (Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2, Y2^12, (Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 17, 113)(10, 106, 21, 117)(12, 108, 25, 121)(14, 110, 29, 125)(15, 111, 31, 127)(16, 112, 33, 129)(18, 114, 30, 126)(19, 115, 38, 134)(20, 116, 40, 136)(22, 118, 26, 122)(23, 119, 43, 139)(24, 120, 45, 141)(27, 123, 50, 146)(28, 124, 52, 148)(32, 128, 57, 153)(34, 130, 48, 144)(35, 131, 61, 157)(36, 132, 46, 142)(37, 133, 60, 156)(39, 135, 53, 149)(41, 137, 51, 147)(42, 138, 65, 161)(44, 140, 72, 168)(47, 143, 76, 172)(49, 145, 75, 171)(54, 150, 80, 176)(55, 151, 78, 174)(56, 152, 74, 170)(58, 154, 73, 169)(59, 155, 71, 167)(62, 158, 86, 182)(63, 159, 70, 166)(64, 160, 81, 177)(66, 162, 79, 175)(67, 163, 84, 180)(68, 164, 87, 183)(69, 165, 82, 178)(77, 173, 91, 187)(83, 179, 92, 188)(85, 181, 93, 189)(88, 184, 90, 186)(89, 185, 94, 190)(95, 191, 96, 192)(193, 289, 195, 291, 200, 296, 210, 306, 229, 325, 255, 351, 281, 377, 261, 357, 234, 330, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 241, 337, 270, 366, 286, 382, 276, 372, 246, 342, 222, 318, 206, 302, 198, 294)(199, 295, 207, 303, 224, 320, 213, 309, 233, 329, 260, 356, 274, 370, 244, 340, 273, 369, 252, 348, 226, 322, 208, 304)(201, 297, 211, 307, 231, 327, 257, 353, 263, 359, 235, 331, 262, 358, 254, 350, 228, 324, 209, 305, 227, 323, 212, 308)(203, 299, 215, 311, 236, 332, 221, 317, 245, 341, 275, 371, 259, 355, 232, 328, 258, 354, 267, 363, 238, 334, 216, 312)(205, 301, 219, 315, 243, 339, 272, 368, 248, 344, 223, 319, 247, 343, 269, 365, 240, 336, 217, 313, 239, 335, 220, 316)(225, 321, 250, 346, 230, 326, 256, 352, 280, 376, 253, 349, 279, 375, 287, 383, 278, 374, 249, 345, 277, 373, 251, 347)(237, 333, 265, 361, 242, 338, 271, 367, 285, 381, 268, 364, 284, 380, 288, 384, 283, 379, 264, 360, 282, 378, 266, 362) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 209)(9, 196)(10, 213)(11, 197)(12, 217)(13, 198)(14, 221)(15, 223)(16, 225)(17, 200)(18, 222)(19, 230)(20, 232)(21, 202)(22, 218)(23, 235)(24, 237)(25, 204)(26, 214)(27, 242)(28, 244)(29, 206)(30, 210)(31, 207)(32, 249)(33, 208)(34, 240)(35, 253)(36, 238)(37, 252)(38, 211)(39, 245)(40, 212)(41, 243)(42, 257)(43, 215)(44, 264)(45, 216)(46, 228)(47, 268)(48, 226)(49, 267)(50, 219)(51, 233)(52, 220)(53, 231)(54, 272)(55, 270)(56, 266)(57, 224)(58, 265)(59, 263)(60, 229)(61, 227)(62, 278)(63, 262)(64, 273)(65, 234)(66, 271)(67, 276)(68, 279)(69, 274)(70, 255)(71, 251)(72, 236)(73, 250)(74, 248)(75, 241)(76, 239)(77, 283)(78, 247)(79, 258)(80, 246)(81, 256)(82, 261)(83, 284)(84, 259)(85, 285)(86, 254)(87, 260)(88, 282)(89, 286)(90, 280)(91, 269)(92, 275)(93, 277)(94, 281)(95, 288)(96, 287)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E15.1220 Graph:: bipartite v = 56 e = 192 f = 108 degree seq :: [ 4^48, 24^8 ] E15.1220 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 12}) Quotient :: dipole Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>) Aut = $<192, 1481>$ (small group id <192, 1481>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y1^-1 * Y3)^2, (Y1^-1 * Y3^2)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-3)^2, Y1^8, Y3^-1 * Y1^-1 * Y3^5 * Y1^3, Y1 * Y3^-1 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3^-1, Y1^-1 * Y3^4 * Y1 * Y3^-2 * Y1^-2, Y3 * Y1^-1 * Y3^-1 * Y1^2 * Y3^-4 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 37, 133, 33, 129, 13, 109, 4, 100)(3, 99, 9, 105, 23, 119, 51, 147, 72, 168, 39, 135, 28, 124, 11, 107)(5, 101, 14, 110, 34, 130, 67, 163, 73, 169, 47, 143, 20, 116, 7, 103)(8, 104, 21, 117, 48, 144, 32, 128, 66, 162, 80, 176, 41, 137, 17, 113)(10, 106, 25, 121, 56, 152, 85, 181, 71, 167, 91, 187, 49, 145, 22, 118)(12, 108, 29, 125, 62, 158, 75, 171, 38, 134, 18, 114, 42, 138, 31, 127)(15, 111, 30, 126, 64, 160, 88, 184, 58, 154, 74, 170, 70, 166, 35, 131)(19, 115, 44, 140, 83, 179, 63, 159, 92, 188, 68, 164, 81, 177, 43, 139)(24, 120, 54, 150, 89, 185, 61, 157, 76, 172, 40, 136, 77, 173, 52, 148)(26, 122, 50, 146, 78, 174, 65, 161, 36, 132, 45, 141, 82, 178, 55, 151)(27, 123, 59, 155, 87, 183, 46, 142, 86, 182, 53, 149, 79, 175, 60, 156)(57, 153, 94, 190, 96, 192, 90, 186, 69, 165, 93, 189, 95, 191, 84, 180)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 211)(8, 194)(9, 196)(10, 218)(11, 219)(12, 222)(13, 224)(14, 227)(15, 197)(16, 230)(17, 232)(18, 198)(19, 237)(20, 238)(21, 241)(22, 200)(23, 244)(24, 201)(25, 203)(26, 250)(27, 206)(28, 253)(29, 205)(30, 257)(31, 245)(32, 246)(33, 259)(34, 252)(35, 261)(36, 207)(37, 264)(38, 266)(39, 208)(40, 270)(41, 271)(42, 273)(43, 210)(44, 212)(45, 277)(46, 213)(47, 280)(48, 279)(49, 282)(50, 214)(51, 278)(52, 285)(53, 215)(54, 274)(55, 216)(56, 276)(57, 217)(58, 265)(59, 220)(60, 272)(61, 286)(62, 275)(63, 221)(64, 223)(65, 268)(66, 225)(67, 284)(68, 226)(69, 283)(70, 267)(71, 228)(72, 263)(73, 229)(74, 247)(75, 251)(76, 231)(77, 233)(78, 255)(79, 234)(80, 248)(81, 288)(82, 235)(83, 287)(84, 236)(85, 258)(86, 239)(87, 254)(88, 249)(89, 240)(90, 260)(91, 243)(92, 242)(93, 262)(94, 256)(95, 269)(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, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E15.1219 Graph:: simple bipartite v = 108 e = 192 f = 56 degree seq :: [ 2^96, 16^12 ] E15.1221 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 7, 14}) Quotient :: regular Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, (T1^-1 * T2)^7, T1^14 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 65, 64, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 66, 84, 80, 60, 43, 28, 17, 8)(6, 13, 21, 34, 48, 67, 83, 82, 63, 45, 30, 18, 9, 14)(15, 25, 35, 51, 68, 86, 95, 93, 79, 59, 42, 27, 16, 26)(23, 36, 50, 69, 85, 96, 94, 81, 62, 44, 29, 38, 24, 37)(39, 55, 70, 88, 97, 90, 98, 89, 78, 58, 41, 57, 40, 56)(52, 71, 87, 77, 92, 76, 91, 75, 61, 74, 54, 73, 53, 72) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 61)(45, 62)(46, 63)(47, 66)(49, 68)(51, 70)(55, 75)(56, 76)(57, 77)(58, 71)(59, 78)(60, 79)(64, 80)(65, 83)(67, 85)(69, 87)(72, 89)(73, 90)(74, 88)(81, 91)(82, 94)(84, 95)(86, 97)(92, 96)(93, 98) local type(s) :: { ( 7^14 ) } Outer automorphisms :: reflexible Dual of E15.1222 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 7 e = 49 f = 14 degree seq :: [ 14^7 ] E15.1222 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 7, 14}) Quotient :: regular Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^7, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2, T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1^2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 22, 10, 4)(3, 7, 15, 30, 35, 18, 8)(6, 13, 26, 47, 50, 29, 14)(9, 19, 36, 57, 58, 37, 20)(12, 24, 43, 67, 70, 46, 25)(16, 27, 44, 64, 75, 53, 32)(17, 28, 45, 65, 76, 54, 33)(21, 38, 59, 79, 80, 60, 39)(23, 41, 63, 83, 86, 66, 42)(31, 48, 68, 84, 90, 74, 52)(34, 49, 69, 85, 91, 77, 55)(40, 61, 81, 93, 94, 82, 62)(51, 71, 87, 95, 97, 89, 73)(56, 72, 88, 96, 98, 92, 78) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 23)(13, 27)(14, 28)(15, 31)(18, 34)(19, 32)(20, 33)(22, 40)(24, 44)(25, 45)(26, 48)(29, 49)(30, 51)(35, 56)(36, 52)(37, 55)(38, 53)(39, 54)(41, 64)(42, 65)(43, 68)(46, 69)(47, 71)(50, 72)(57, 73)(58, 78)(59, 74)(60, 77)(61, 75)(62, 76)(63, 84)(66, 85)(67, 87)(70, 88)(79, 89)(80, 92)(81, 90)(82, 91)(83, 95)(86, 96)(93, 97)(94, 98) local type(s) :: { ( 14^7 ) } Outer automorphisms :: reflexible Dual of E15.1221 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 14 e = 49 f = 7 degree seq :: [ 7^14 ] E15.1223 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 7, 14}) Quotient :: edge Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^7, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1, T2^3 * T1 * T2^3 * T1 * T2^-3 * T1 * T2^-3 * T1 ] Map:: polytopal R = (1, 3, 8, 18, 22, 10, 4)(2, 5, 12, 26, 30, 14, 6)(7, 15, 31, 51, 52, 32, 16)(9, 19, 36, 57, 58, 37, 20)(11, 23, 41, 63, 64, 42, 24)(13, 27, 46, 69, 70, 47, 28)(17, 33, 53, 75, 76, 54, 34)(21, 38, 59, 79, 80, 60, 39)(25, 43, 65, 83, 84, 66, 44)(29, 48, 71, 87, 88, 72, 49)(35, 55, 77, 91, 92, 78, 56)(40, 61, 81, 93, 94, 82, 62)(45, 67, 85, 95, 96, 86, 68)(50, 73, 89, 97, 98, 90, 74)(99, 100)(101, 105)(102, 107)(103, 109)(104, 111)(106, 115)(108, 119)(110, 123)(112, 127)(113, 121)(114, 125)(116, 133)(117, 122)(118, 126)(120, 138)(124, 143)(128, 148)(129, 141)(130, 146)(131, 139)(132, 144)(134, 142)(135, 147)(136, 140)(137, 145)(149, 165)(150, 171)(151, 163)(152, 169)(153, 161)(154, 167)(155, 166)(156, 172)(157, 164)(158, 170)(159, 162)(160, 168)(173, 183)(174, 187)(175, 181)(176, 185)(177, 184)(178, 188)(179, 182)(180, 186)(189, 193)(190, 195)(191, 194)(192, 196) L = (1, 99)(2, 100)(3, 101)(4, 102)(5, 103)(6, 104)(7, 105)(8, 106)(9, 107)(10, 108)(11, 109)(12, 110)(13, 111)(14, 112)(15, 113)(16, 114)(17, 115)(18, 116)(19, 117)(20, 118)(21, 119)(22, 120)(23, 121)(24, 122)(25, 123)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 130)(33, 131)(34, 132)(35, 133)(36, 134)(37, 135)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 146)(49, 147)(50, 148)(51, 149)(52, 150)(53, 151)(54, 152)(55, 153)(56, 154)(57, 155)(58, 156)(59, 157)(60, 158)(61, 159)(62, 160)(63, 161)(64, 162)(65, 163)(66, 164)(67, 165)(68, 166)(69, 167)(70, 168)(71, 169)(72, 170)(73, 171)(74, 172)(75, 173)(76, 174)(77, 175)(78, 176)(79, 177)(80, 178)(81, 179)(82, 180)(83, 181)(84, 182)(85, 183)(86, 184)(87, 185)(88, 186)(89, 187)(90, 188)(91, 189)(92, 190)(93, 191)(94, 192)(95, 193)(96, 194)(97, 195)(98, 196) local type(s) :: { ( 28, 28 ), ( 28^7 ) } Outer automorphisms :: reflexible Dual of E15.1227 Transitivity :: ET+ Graph:: simple bipartite v = 63 e = 98 f = 7 degree seq :: [ 2^49, 7^14 ] E15.1224 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 7, 14}) Quotient :: edge Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-1 * T2^-3 * T1^-1 * T2, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1, T1^7, T2 * T1^-3 * T2^2 * T1^-2 * T2 * T1^2, T1^-1 * T2 * T1^-1 * T2^11 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 47, 72, 90, 96, 87, 64, 43, 21, 15, 5)(2, 7, 19, 11, 27, 48, 74, 91, 97, 84, 65, 38, 22, 8)(4, 12, 26, 49, 73, 92, 98, 86, 68, 42, 33, 14, 24, 9)(6, 17, 36, 20, 40, 28, 51, 75, 94, 95, 85, 60, 39, 18)(13, 30, 50, 76, 93, 83, 88, 67, 57, 32, 46, 23, 45, 29)(16, 34, 58, 37, 62, 41, 66, 52, 78, 79, 89, 80, 61, 35)(31, 55, 77, 59, 82, 63, 81, 56, 70, 44, 69, 53, 71, 54)(99, 100, 104, 114, 129, 111, 102)(101, 107, 121, 142, 150, 126, 109)(103, 112, 130, 154, 139, 118, 105)(106, 119, 140, 165, 161, 135, 115)(108, 117, 134, 156, 175, 148, 124)(110, 127, 151, 177, 173, 146, 123)(113, 120, 137, 159, 169, 143, 122)(116, 136, 162, 184, 181, 157, 132)(125, 138, 160, 180, 191, 171, 145)(128, 152, 178, 193, 189, 170, 147)(131, 141, 163, 183, 187, 167, 144)(133, 158, 182, 194, 190, 174, 153)(149, 164, 179, 186, 196, 188, 172)(155, 166, 185, 195, 192, 176, 168) L = (1, 99)(2, 100)(3, 101)(4, 102)(5, 103)(6, 104)(7, 105)(8, 106)(9, 107)(10, 108)(11, 109)(12, 110)(13, 111)(14, 112)(15, 113)(16, 114)(17, 115)(18, 116)(19, 117)(20, 118)(21, 119)(22, 120)(23, 121)(24, 122)(25, 123)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 130)(33, 131)(34, 132)(35, 133)(36, 134)(37, 135)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 146)(49, 147)(50, 148)(51, 149)(52, 150)(53, 151)(54, 152)(55, 153)(56, 154)(57, 155)(58, 156)(59, 157)(60, 158)(61, 159)(62, 160)(63, 161)(64, 162)(65, 163)(66, 164)(67, 165)(68, 166)(69, 167)(70, 168)(71, 169)(72, 170)(73, 171)(74, 172)(75, 173)(76, 174)(77, 175)(78, 176)(79, 177)(80, 178)(81, 179)(82, 180)(83, 181)(84, 182)(85, 183)(86, 184)(87, 185)(88, 186)(89, 187)(90, 188)(91, 189)(92, 190)(93, 191)(94, 192)(95, 193)(96, 194)(97, 195)(98, 196) local type(s) :: { ( 4^7 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E15.1228 Transitivity :: ET+ Graph:: simple bipartite v = 21 e = 98 f = 49 degree seq :: [ 7^14, 14^7 ] E15.1225 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 7, 14}) Quotient :: edge Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, T1^14, (T2 * T1^-1)^7 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 61)(45, 62)(46, 63)(47, 66)(49, 68)(51, 70)(55, 75)(56, 76)(57, 77)(58, 71)(59, 78)(60, 79)(64, 80)(65, 83)(67, 85)(69, 87)(72, 89)(73, 90)(74, 88)(81, 91)(82, 94)(84, 95)(86, 97)(92, 96)(93, 98)(99, 100, 103, 109, 118, 130, 145, 163, 162, 144, 129, 117, 108, 102)(101, 105, 110, 120, 131, 147, 164, 182, 178, 158, 141, 126, 115, 106)(104, 111, 119, 132, 146, 165, 181, 180, 161, 143, 128, 116, 107, 112)(113, 123, 133, 149, 166, 184, 193, 191, 177, 157, 140, 125, 114, 124)(121, 134, 148, 167, 183, 194, 192, 179, 160, 142, 127, 136, 122, 135)(137, 153, 168, 186, 195, 188, 196, 187, 176, 156, 139, 155, 138, 154)(150, 169, 185, 175, 190, 174, 189, 173, 159, 172, 152, 171, 151, 170) L = (1, 99)(2, 100)(3, 101)(4, 102)(5, 103)(6, 104)(7, 105)(8, 106)(9, 107)(10, 108)(11, 109)(12, 110)(13, 111)(14, 112)(15, 113)(16, 114)(17, 115)(18, 116)(19, 117)(20, 118)(21, 119)(22, 120)(23, 121)(24, 122)(25, 123)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 130)(33, 131)(34, 132)(35, 133)(36, 134)(37, 135)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 146)(49, 147)(50, 148)(51, 149)(52, 150)(53, 151)(54, 152)(55, 153)(56, 154)(57, 155)(58, 156)(59, 157)(60, 158)(61, 159)(62, 160)(63, 161)(64, 162)(65, 163)(66, 164)(67, 165)(68, 166)(69, 167)(70, 168)(71, 169)(72, 170)(73, 171)(74, 172)(75, 173)(76, 174)(77, 175)(78, 176)(79, 177)(80, 178)(81, 179)(82, 180)(83, 181)(84, 182)(85, 183)(86, 184)(87, 185)(88, 186)(89, 187)(90, 188)(91, 189)(92, 190)(93, 191)(94, 192)(95, 193)(96, 194)(97, 195)(98, 196) local type(s) :: { ( 14, 14 ), ( 14^14 ) } Outer automorphisms :: reflexible Dual of E15.1226 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 98 f = 14 degree seq :: [ 2^49, 14^7 ] E15.1226 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 7, 14}) Quotient :: loop Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^7, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1, T2^3 * T1 * T2^3 * T1 * T2^-3 * T1 * T2^-3 * T1 ] Map:: R = (1, 99, 3, 101, 8, 106, 18, 116, 22, 120, 10, 108, 4, 102)(2, 100, 5, 103, 12, 110, 26, 124, 30, 128, 14, 112, 6, 104)(7, 105, 15, 113, 31, 129, 51, 149, 52, 150, 32, 130, 16, 114)(9, 107, 19, 117, 36, 134, 57, 155, 58, 156, 37, 135, 20, 118)(11, 109, 23, 121, 41, 139, 63, 161, 64, 162, 42, 140, 24, 122)(13, 111, 27, 125, 46, 144, 69, 167, 70, 168, 47, 145, 28, 126)(17, 115, 33, 131, 53, 151, 75, 173, 76, 174, 54, 152, 34, 132)(21, 119, 38, 136, 59, 157, 79, 177, 80, 178, 60, 158, 39, 137)(25, 123, 43, 141, 65, 163, 83, 181, 84, 182, 66, 164, 44, 142)(29, 127, 48, 146, 71, 169, 87, 185, 88, 186, 72, 170, 49, 147)(35, 133, 55, 153, 77, 175, 91, 189, 92, 190, 78, 176, 56, 154)(40, 138, 61, 159, 81, 179, 93, 191, 94, 192, 82, 180, 62, 160)(45, 143, 67, 165, 85, 183, 95, 193, 96, 194, 86, 184, 68, 166)(50, 148, 73, 171, 89, 187, 97, 195, 98, 196, 90, 188, 74, 172) L = (1, 100)(2, 99)(3, 105)(4, 107)(5, 109)(6, 111)(7, 101)(8, 115)(9, 102)(10, 119)(11, 103)(12, 123)(13, 104)(14, 127)(15, 121)(16, 125)(17, 106)(18, 133)(19, 122)(20, 126)(21, 108)(22, 138)(23, 113)(24, 117)(25, 110)(26, 143)(27, 114)(28, 118)(29, 112)(30, 148)(31, 141)(32, 146)(33, 139)(34, 144)(35, 116)(36, 142)(37, 147)(38, 140)(39, 145)(40, 120)(41, 131)(42, 136)(43, 129)(44, 134)(45, 124)(46, 132)(47, 137)(48, 130)(49, 135)(50, 128)(51, 165)(52, 171)(53, 163)(54, 169)(55, 161)(56, 167)(57, 166)(58, 172)(59, 164)(60, 170)(61, 162)(62, 168)(63, 153)(64, 159)(65, 151)(66, 157)(67, 149)(68, 155)(69, 154)(70, 160)(71, 152)(72, 158)(73, 150)(74, 156)(75, 183)(76, 187)(77, 181)(78, 185)(79, 184)(80, 188)(81, 182)(82, 186)(83, 175)(84, 179)(85, 173)(86, 177)(87, 176)(88, 180)(89, 174)(90, 178)(91, 193)(92, 195)(93, 194)(94, 196)(95, 189)(96, 191)(97, 190)(98, 192) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.1225 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 14 e = 98 f = 56 degree seq :: [ 14^14 ] E15.1227 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 7, 14}) Quotient :: loop Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-1 * T2^-3 * T1^-1 * T2, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1, T1^7, T2 * T1^-3 * T2^2 * T1^-2 * T2 * T1^2, T1^-1 * T2 * T1^-1 * T2^11 ] Map:: R = (1, 99, 3, 101, 10, 108, 25, 123, 47, 145, 72, 170, 90, 188, 96, 194, 87, 185, 64, 162, 43, 141, 21, 119, 15, 113, 5, 103)(2, 100, 7, 105, 19, 117, 11, 109, 27, 125, 48, 146, 74, 172, 91, 189, 97, 195, 84, 182, 65, 163, 38, 136, 22, 120, 8, 106)(4, 102, 12, 110, 26, 124, 49, 147, 73, 171, 92, 190, 98, 196, 86, 184, 68, 166, 42, 140, 33, 131, 14, 112, 24, 122, 9, 107)(6, 104, 17, 115, 36, 134, 20, 118, 40, 138, 28, 126, 51, 149, 75, 173, 94, 192, 95, 193, 85, 183, 60, 158, 39, 137, 18, 116)(13, 111, 30, 128, 50, 148, 76, 174, 93, 191, 83, 181, 88, 186, 67, 165, 57, 155, 32, 130, 46, 144, 23, 121, 45, 143, 29, 127)(16, 114, 34, 132, 58, 156, 37, 135, 62, 160, 41, 139, 66, 164, 52, 150, 78, 176, 79, 177, 89, 187, 80, 178, 61, 159, 35, 133)(31, 129, 55, 153, 77, 175, 59, 157, 82, 180, 63, 161, 81, 179, 56, 154, 70, 168, 44, 142, 69, 167, 53, 151, 71, 169, 54, 152) L = (1, 100)(2, 104)(3, 107)(4, 99)(5, 112)(6, 114)(7, 103)(8, 119)(9, 121)(10, 117)(11, 101)(12, 127)(13, 102)(14, 130)(15, 120)(16, 129)(17, 106)(18, 136)(19, 134)(20, 105)(21, 140)(22, 137)(23, 142)(24, 113)(25, 110)(26, 108)(27, 138)(28, 109)(29, 151)(30, 152)(31, 111)(32, 154)(33, 141)(34, 116)(35, 158)(36, 156)(37, 115)(38, 162)(39, 159)(40, 160)(41, 118)(42, 165)(43, 163)(44, 150)(45, 122)(46, 131)(47, 125)(48, 123)(49, 128)(50, 124)(51, 164)(52, 126)(53, 177)(54, 178)(55, 133)(56, 139)(57, 166)(58, 175)(59, 132)(60, 182)(61, 169)(62, 180)(63, 135)(64, 184)(65, 183)(66, 179)(67, 161)(68, 185)(69, 144)(70, 155)(71, 143)(72, 147)(73, 145)(74, 149)(75, 146)(76, 153)(77, 148)(78, 168)(79, 173)(80, 193)(81, 186)(82, 191)(83, 157)(84, 194)(85, 187)(86, 181)(87, 195)(88, 196)(89, 167)(90, 172)(91, 170)(92, 174)(93, 171)(94, 176)(95, 189)(96, 190)(97, 192)(98, 188) local type(s) :: { ( 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E15.1223 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 98 f = 63 degree seq :: [ 28^7 ] E15.1228 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 7, 14}) Quotient :: loop Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, T1^14, (T2 * T1^-1)^7 ] Map:: polytopal non-degenerate R = (1, 99, 3, 101)(2, 100, 6, 104)(4, 102, 9, 107)(5, 103, 12, 110)(7, 105, 15, 113)(8, 106, 16, 114)(10, 108, 17, 115)(11, 109, 21, 119)(13, 111, 23, 121)(14, 112, 24, 122)(18, 116, 29, 127)(19, 117, 30, 128)(20, 118, 33, 131)(22, 120, 35, 133)(25, 123, 39, 137)(26, 124, 40, 138)(27, 125, 41, 139)(28, 126, 42, 140)(31, 129, 43, 141)(32, 130, 48, 146)(34, 132, 50, 148)(36, 134, 52, 150)(37, 135, 53, 151)(38, 136, 54, 152)(44, 142, 61, 159)(45, 143, 62, 160)(46, 144, 63, 161)(47, 145, 66, 164)(49, 147, 68, 166)(51, 149, 70, 168)(55, 153, 75, 173)(56, 154, 76, 174)(57, 155, 77, 175)(58, 156, 71, 169)(59, 157, 78, 176)(60, 158, 79, 177)(64, 162, 80, 178)(65, 163, 83, 181)(67, 165, 85, 183)(69, 167, 87, 185)(72, 170, 89, 187)(73, 171, 90, 188)(74, 172, 88, 186)(81, 179, 91, 189)(82, 180, 94, 192)(84, 182, 95, 193)(86, 184, 97, 195)(92, 190, 96, 194)(93, 191, 98, 196) L = (1, 100)(2, 103)(3, 105)(4, 99)(5, 109)(6, 111)(7, 110)(8, 101)(9, 112)(10, 102)(11, 118)(12, 120)(13, 119)(14, 104)(15, 123)(16, 124)(17, 106)(18, 107)(19, 108)(20, 130)(21, 132)(22, 131)(23, 134)(24, 135)(25, 133)(26, 113)(27, 114)(28, 115)(29, 136)(30, 116)(31, 117)(32, 145)(33, 147)(34, 146)(35, 149)(36, 148)(37, 121)(38, 122)(39, 153)(40, 154)(41, 155)(42, 125)(43, 126)(44, 127)(45, 128)(46, 129)(47, 163)(48, 165)(49, 164)(50, 167)(51, 166)(52, 169)(53, 170)(54, 171)(55, 168)(56, 137)(57, 138)(58, 139)(59, 140)(60, 141)(61, 172)(62, 142)(63, 143)(64, 144)(65, 162)(66, 182)(67, 181)(68, 184)(69, 183)(70, 186)(71, 185)(72, 150)(73, 151)(74, 152)(75, 159)(76, 189)(77, 190)(78, 156)(79, 157)(80, 158)(81, 160)(82, 161)(83, 180)(84, 178)(85, 194)(86, 193)(87, 175)(88, 195)(89, 176)(90, 196)(91, 173)(92, 174)(93, 177)(94, 179)(95, 191)(96, 192)(97, 188)(98, 187) local type(s) :: { ( 7, 14, 7, 14 ) } Outer automorphisms :: reflexible Dual of E15.1224 Transitivity :: ET+ VT+ AT Graph:: simple v = 49 e = 98 f = 21 degree seq :: [ 4^49 ] E15.1229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^7, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1, Y2^3 * Y1 * Y2^3 * Y1 * Y2^-3 * Y1 * Y2^-3 * Y1, (Y3 * Y2^-1)^14 ] Map:: R = (1, 99, 2, 100)(3, 101, 7, 105)(4, 102, 9, 107)(5, 103, 11, 109)(6, 104, 13, 111)(8, 106, 17, 115)(10, 108, 21, 119)(12, 110, 25, 123)(14, 112, 29, 127)(15, 113, 23, 121)(16, 114, 27, 125)(18, 116, 35, 133)(19, 117, 24, 122)(20, 118, 28, 126)(22, 120, 40, 138)(26, 124, 45, 143)(30, 128, 50, 148)(31, 129, 43, 141)(32, 130, 48, 146)(33, 131, 41, 139)(34, 132, 46, 144)(36, 134, 44, 142)(37, 135, 49, 147)(38, 136, 42, 140)(39, 137, 47, 145)(51, 149, 67, 165)(52, 150, 73, 171)(53, 151, 65, 163)(54, 152, 71, 169)(55, 153, 63, 161)(56, 154, 69, 167)(57, 155, 68, 166)(58, 156, 74, 172)(59, 157, 66, 164)(60, 158, 72, 170)(61, 159, 64, 162)(62, 160, 70, 168)(75, 173, 85, 183)(76, 174, 89, 187)(77, 175, 83, 181)(78, 176, 87, 185)(79, 177, 86, 184)(80, 178, 90, 188)(81, 179, 84, 182)(82, 180, 88, 186)(91, 189, 95, 193)(92, 190, 97, 195)(93, 191, 96, 194)(94, 192, 98, 196)(197, 295, 199, 297, 204, 302, 214, 312, 218, 316, 206, 304, 200, 298)(198, 296, 201, 299, 208, 306, 222, 320, 226, 324, 210, 308, 202, 300)(203, 301, 211, 309, 227, 325, 247, 345, 248, 346, 228, 326, 212, 310)(205, 303, 215, 313, 232, 330, 253, 351, 254, 352, 233, 331, 216, 314)(207, 305, 219, 317, 237, 335, 259, 357, 260, 358, 238, 336, 220, 318)(209, 307, 223, 321, 242, 340, 265, 363, 266, 364, 243, 341, 224, 322)(213, 311, 229, 327, 249, 347, 271, 369, 272, 370, 250, 348, 230, 328)(217, 315, 234, 332, 255, 353, 275, 373, 276, 374, 256, 354, 235, 333)(221, 319, 239, 337, 261, 359, 279, 377, 280, 378, 262, 360, 240, 338)(225, 323, 244, 342, 267, 365, 283, 381, 284, 382, 268, 366, 245, 343)(231, 329, 251, 349, 273, 371, 287, 385, 288, 386, 274, 372, 252, 350)(236, 334, 257, 355, 277, 375, 289, 387, 290, 388, 278, 376, 258, 356)(241, 339, 263, 361, 281, 379, 291, 389, 292, 390, 282, 380, 264, 362)(246, 344, 269, 367, 285, 383, 293, 391, 294, 392, 286, 384, 270, 368) L = (1, 198)(2, 197)(3, 203)(4, 205)(5, 207)(6, 209)(7, 199)(8, 213)(9, 200)(10, 217)(11, 201)(12, 221)(13, 202)(14, 225)(15, 219)(16, 223)(17, 204)(18, 231)(19, 220)(20, 224)(21, 206)(22, 236)(23, 211)(24, 215)(25, 208)(26, 241)(27, 212)(28, 216)(29, 210)(30, 246)(31, 239)(32, 244)(33, 237)(34, 242)(35, 214)(36, 240)(37, 245)(38, 238)(39, 243)(40, 218)(41, 229)(42, 234)(43, 227)(44, 232)(45, 222)(46, 230)(47, 235)(48, 228)(49, 233)(50, 226)(51, 263)(52, 269)(53, 261)(54, 267)(55, 259)(56, 265)(57, 264)(58, 270)(59, 262)(60, 268)(61, 260)(62, 266)(63, 251)(64, 257)(65, 249)(66, 255)(67, 247)(68, 253)(69, 252)(70, 258)(71, 250)(72, 256)(73, 248)(74, 254)(75, 281)(76, 285)(77, 279)(78, 283)(79, 282)(80, 286)(81, 280)(82, 284)(83, 273)(84, 277)(85, 271)(86, 275)(87, 274)(88, 278)(89, 272)(90, 276)(91, 291)(92, 293)(93, 292)(94, 294)(95, 287)(96, 289)(97, 288)(98, 290)(99, 295)(100, 296)(101, 297)(102, 298)(103, 299)(104, 300)(105, 301)(106, 302)(107, 303)(108, 304)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 311)(116, 312)(117, 313)(118, 314)(119, 315)(120, 316)(121, 317)(122, 318)(123, 319)(124, 320)(125, 321)(126, 322)(127, 323)(128, 324)(129, 325)(130, 326)(131, 327)(132, 328)(133, 329)(134, 330)(135, 331)(136, 332)(137, 333)(138, 334)(139, 335)(140, 336)(141, 337)(142, 338)(143, 339)(144, 340)(145, 341)(146, 342)(147, 343)(148, 344)(149, 345)(150, 346)(151, 347)(152, 348)(153, 349)(154, 350)(155, 351)(156, 352)(157, 353)(158, 354)(159, 355)(160, 356)(161, 357)(162, 358)(163, 359)(164, 360)(165, 361)(166, 362)(167, 363)(168, 364)(169, 365)(170, 366)(171, 367)(172, 368)(173, 369)(174, 370)(175, 371)(176, 372)(177, 373)(178, 374)(179, 375)(180, 376)(181, 377)(182, 378)(183, 379)(184, 380)(185, 381)(186, 382)(187, 383)(188, 384)(189, 385)(190, 386)(191, 387)(192, 388)(193, 389)(194, 390)(195, 391)(196, 392) local type(s) :: { ( 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E15.1232 Graph:: bipartite v = 63 e = 196 f = 105 degree seq :: [ 4^49, 14^14 ] E15.1230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y1^7, Y2 * Y1^-3 * Y2^2 * Y1^-2 * Y2 * Y1^2, Y1^-1 * Y2 * Y1^-1 * Y2^11 ] Map:: R = (1, 99, 2, 100, 6, 104, 16, 114, 31, 129, 13, 111, 4, 102)(3, 101, 9, 107, 23, 121, 44, 142, 52, 150, 28, 126, 11, 109)(5, 103, 14, 112, 32, 130, 56, 154, 41, 139, 20, 118, 7, 105)(8, 106, 21, 119, 42, 140, 67, 165, 63, 161, 37, 135, 17, 115)(10, 108, 19, 117, 36, 134, 58, 156, 77, 175, 50, 148, 26, 124)(12, 110, 29, 127, 53, 151, 79, 177, 75, 173, 48, 146, 25, 123)(15, 113, 22, 120, 39, 137, 61, 159, 71, 169, 45, 143, 24, 122)(18, 116, 38, 136, 64, 162, 86, 184, 83, 181, 59, 157, 34, 132)(27, 125, 40, 138, 62, 160, 82, 180, 93, 191, 73, 171, 47, 145)(30, 128, 54, 152, 80, 178, 95, 193, 91, 189, 72, 170, 49, 147)(33, 131, 43, 141, 65, 163, 85, 183, 89, 187, 69, 167, 46, 144)(35, 133, 60, 158, 84, 182, 96, 194, 92, 190, 76, 174, 55, 153)(51, 149, 66, 164, 81, 179, 88, 186, 98, 196, 90, 188, 74, 172)(57, 155, 68, 166, 87, 185, 97, 195, 94, 192, 78, 176, 70, 168)(197, 295, 199, 297, 206, 304, 221, 319, 243, 341, 268, 366, 286, 384, 292, 390, 283, 381, 260, 358, 239, 337, 217, 315, 211, 309, 201, 299)(198, 296, 203, 301, 215, 313, 207, 305, 223, 321, 244, 342, 270, 368, 287, 385, 293, 391, 280, 378, 261, 359, 234, 332, 218, 316, 204, 302)(200, 298, 208, 306, 222, 320, 245, 343, 269, 367, 288, 386, 294, 392, 282, 380, 264, 362, 238, 336, 229, 327, 210, 308, 220, 318, 205, 303)(202, 300, 213, 311, 232, 330, 216, 314, 236, 334, 224, 322, 247, 345, 271, 369, 290, 388, 291, 389, 281, 379, 256, 354, 235, 333, 214, 312)(209, 307, 226, 324, 246, 344, 272, 370, 289, 387, 279, 377, 284, 382, 263, 361, 253, 351, 228, 326, 242, 340, 219, 317, 241, 339, 225, 323)(212, 310, 230, 328, 254, 352, 233, 331, 258, 356, 237, 335, 262, 360, 248, 346, 274, 372, 275, 373, 285, 383, 276, 374, 257, 355, 231, 329)(227, 325, 251, 349, 273, 371, 255, 353, 278, 376, 259, 357, 277, 375, 252, 350, 266, 364, 240, 338, 265, 363, 249, 347, 267, 365, 250, 348) L = (1, 199)(2, 203)(3, 206)(4, 208)(5, 197)(6, 213)(7, 215)(8, 198)(9, 200)(10, 221)(11, 223)(12, 222)(13, 226)(14, 220)(15, 201)(16, 230)(17, 232)(18, 202)(19, 207)(20, 236)(21, 211)(22, 204)(23, 241)(24, 205)(25, 243)(26, 245)(27, 244)(28, 247)(29, 209)(30, 246)(31, 251)(32, 242)(33, 210)(34, 254)(35, 212)(36, 216)(37, 258)(38, 218)(39, 214)(40, 224)(41, 262)(42, 229)(43, 217)(44, 265)(45, 225)(46, 219)(47, 268)(48, 270)(49, 269)(50, 272)(51, 271)(52, 274)(53, 267)(54, 227)(55, 273)(56, 266)(57, 228)(58, 233)(59, 278)(60, 235)(61, 231)(62, 237)(63, 277)(64, 239)(65, 234)(66, 248)(67, 253)(68, 238)(69, 249)(70, 240)(71, 250)(72, 286)(73, 288)(74, 287)(75, 290)(76, 289)(77, 255)(78, 275)(79, 285)(80, 257)(81, 252)(82, 259)(83, 284)(84, 261)(85, 256)(86, 264)(87, 260)(88, 263)(89, 276)(90, 292)(91, 293)(92, 294)(93, 279)(94, 291)(95, 281)(96, 283)(97, 280)(98, 282)(99, 295)(100, 296)(101, 297)(102, 298)(103, 299)(104, 300)(105, 301)(106, 302)(107, 303)(108, 304)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 311)(116, 312)(117, 313)(118, 314)(119, 315)(120, 316)(121, 317)(122, 318)(123, 319)(124, 320)(125, 321)(126, 322)(127, 323)(128, 324)(129, 325)(130, 326)(131, 327)(132, 328)(133, 329)(134, 330)(135, 331)(136, 332)(137, 333)(138, 334)(139, 335)(140, 336)(141, 337)(142, 338)(143, 339)(144, 340)(145, 341)(146, 342)(147, 343)(148, 344)(149, 345)(150, 346)(151, 347)(152, 348)(153, 349)(154, 350)(155, 351)(156, 352)(157, 353)(158, 354)(159, 355)(160, 356)(161, 357)(162, 358)(163, 359)(164, 360)(165, 361)(166, 362)(167, 363)(168, 364)(169, 365)(170, 366)(171, 367)(172, 368)(173, 369)(174, 370)(175, 371)(176, 372)(177, 373)(178, 374)(179, 375)(180, 376)(181, 377)(182, 378)(183, 379)(184, 380)(185, 381)(186, 382)(187, 383)(188, 384)(189, 385)(190, 386)(191, 387)(192, 388)(193, 389)(194, 390)(195, 391)(196, 392) 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 ) } Outer automorphisms :: reflexible Dual of E15.1231 Graph:: bipartite v = 21 e = 196 f = 147 degree seq :: [ 14^14, 28^7 ] E15.1231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^2 * Y2, (Y3 * Y2)^7, (Y3^-1 * Y1^-1)^14 ] Map:: polytopal R = (1, 99)(2, 100)(3, 101)(4, 102)(5, 103)(6, 104)(7, 105)(8, 106)(9, 107)(10, 108)(11, 109)(12, 110)(13, 111)(14, 112)(15, 113)(16, 114)(17, 115)(18, 116)(19, 117)(20, 118)(21, 119)(22, 120)(23, 121)(24, 122)(25, 123)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 130)(33, 131)(34, 132)(35, 133)(36, 134)(37, 135)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 146)(49, 147)(50, 148)(51, 149)(52, 150)(53, 151)(54, 152)(55, 153)(56, 154)(57, 155)(58, 156)(59, 157)(60, 158)(61, 159)(62, 160)(63, 161)(64, 162)(65, 163)(66, 164)(67, 165)(68, 166)(69, 167)(70, 168)(71, 169)(72, 170)(73, 171)(74, 172)(75, 173)(76, 174)(77, 175)(78, 176)(79, 177)(80, 178)(81, 179)(82, 180)(83, 181)(84, 182)(85, 183)(86, 184)(87, 185)(88, 186)(89, 187)(90, 188)(91, 189)(92, 190)(93, 191)(94, 192)(95, 193)(96, 194)(97, 195)(98, 196)(197, 295, 198, 296)(199, 297, 203, 301)(200, 298, 205, 303)(201, 299, 207, 305)(202, 300, 209, 307)(204, 302, 208, 306)(206, 304, 210, 308)(211, 309, 221, 319)(212, 310, 223, 321)(213, 311, 222, 320)(214, 312, 225, 323)(215, 313, 226, 324)(216, 314, 228, 326)(217, 315, 230, 328)(218, 316, 229, 327)(219, 317, 232, 330)(220, 318, 233, 331)(224, 322, 231, 329)(227, 325, 234, 332)(235, 333, 251, 349)(236, 334, 253, 351)(237, 335, 252, 350)(238, 336, 255, 353)(239, 337, 254, 352)(240, 338, 257, 355)(241, 339, 258, 356)(242, 340, 259, 357)(243, 341, 261, 359)(244, 342, 263, 361)(245, 343, 262, 360)(246, 344, 265, 363)(247, 345, 264, 362)(248, 346, 267, 365)(249, 347, 268, 366)(250, 348, 269, 367)(256, 354, 266, 364)(260, 358, 270, 368)(271, 369, 285, 383)(272, 370, 283, 381)(273, 371, 288, 386)(274, 372, 287, 385)(275, 373, 280, 378)(276, 374, 289, 387)(277, 375, 279, 377)(278, 376, 290, 388)(281, 379, 292, 390)(282, 380, 291, 389)(284, 382, 293, 391)(286, 384, 294, 392) L = (1, 199)(2, 201)(3, 204)(4, 197)(5, 208)(6, 198)(7, 211)(8, 213)(9, 212)(10, 200)(11, 216)(12, 218)(13, 217)(14, 202)(15, 222)(16, 203)(17, 224)(18, 205)(19, 206)(20, 229)(21, 207)(22, 231)(23, 209)(24, 210)(25, 235)(26, 237)(27, 236)(28, 239)(29, 238)(30, 214)(31, 215)(32, 243)(33, 245)(34, 244)(35, 247)(36, 246)(37, 219)(38, 220)(39, 252)(40, 221)(41, 254)(42, 223)(43, 256)(44, 225)(45, 226)(46, 227)(47, 262)(48, 228)(49, 264)(50, 230)(51, 266)(52, 232)(53, 233)(54, 234)(55, 267)(56, 272)(57, 271)(58, 274)(59, 273)(60, 276)(61, 275)(62, 240)(63, 241)(64, 242)(65, 257)(66, 280)(67, 279)(68, 282)(69, 281)(70, 284)(71, 283)(72, 248)(73, 249)(74, 250)(75, 251)(76, 287)(77, 253)(78, 289)(79, 255)(80, 260)(81, 258)(82, 259)(83, 261)(84, 291)(85, 263)(86, 293)(87, 265)(88, 270)(89, 268)(90, 269)(91, 292)(92, 294)(93, 278)(94, 277)(95, 288)(96, 290)(97, 286)(98, 285)(99, 295)(100, 296)(101, 297)(102, 298)(103, 299)(104, 300)(105, 301)(106, 302)(107, 303)(108, 304)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 311)(116, 312)(117, 313)(118, 314)(119, 315)(120, 316)(121, 317)(122, 318)(123, 319)(124, 320)(125, 321)(126, 322)(127, 323)(128, 324)(129, 325)(130, 326)(131, 327)(132, 328)(133, 329)(134, 330)(135, 331)(136, 332)(137, 333)(138, 334)(139, 335)(140, 336)(141, 337)(142, 338)(143, 339)(144, 340)(145, 341)(146, 342)(147, 343)(148, 344)(149, 345)(150, 346)(151, 347)(152, 348)(153, 349)(154, 350)(155, 351)(156, 352)(157, 353)(158, 354)(159, 355)(160, 356)(161, 357)(162, 358)(163, 359)(164, 360)(165, 361)(166, 362)(167, 363)(168, 364)(169, 365)(170, 366)(171, 367)(172, 368)(173, 369)(174, 370)(175, 371)(176, 372)(177, 373)(178, 374)(179, 375)(180, 376)(181, 377)(182, 378)(183, 379)(184, 380)(185, 381)(186, 382)(187, 383)(188, 384)(189, 385)(190, 386)(191, 387)(192, 388)(193, 389)(194, 390)(195, 391)(196, 392) local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28 ) } Outer automorphisms :: reflexible Dual of E15.1230 Graph:: simple bipartite v = 147 e = 196 f = 21 degree seq :: [ 2^98, 4^49 ] E15.1232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |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^-1)^7, Y1^14 ] Map:: polytopal R = (1, 99, 2, 100, 5, 103, 11, 109, 20, 118, 32, 130, 47, 145, 65, 163, 64, 162, 46, 144, 31, 129, 19, 117, 10, 108, 4, 102)(3, 101, 7, 105, 12, 110, 22, 120, 33, 131, 49, 147, 66, 164, 84, 182, 80, 178, 60, 158, 43, 141, 28, 126, 17, 115, 8, 106)(6, 104, 13, 111, 21, 119, 34, 132, 48, 146, 67, 165, 83, 181, 82, 180, 63, 161, 45, 143, 30, 128, 18, 116, 9, 107, 14, 112)(15, 113, 25, 123, 35, 133, 51, 149, 68, 166, 86, 184, 95, 193, 93, 191, 79, 177, 59, 157, 42, 140, 27, 125, 16, 114, 26, 124)(23, 121, 36, 134, 50, 148, 69, 167, 85, 183, 96, 194, 94, 192, 81, 179, 62, 160, 44, 142, 29, 127, 38, 136, 24, 122, 37, 135)(39, 137, 55, 153, 70, 168, 88, 186, 97, 195, 90, 188, 98, 196, 89, 187, 78, 176, 58, 156, 41, 139, 57, 155, 40, 138, 56, 154)(52, 150, 71, 169, 87, 185, 77, 175, 92, 190, 76, 174, 91, 189, 75, 173, 61, 159, 74, 172, 54, 152, 73, 171, 53, 151, 72, 170)(197, 295)(198, 296)(199, 297)(200, 298)(201, 299)(202, 300)(203, 301)(204, 302)(205, 303)(206, 304)(207, 305)(208, 306)(209, 307)(210, 308)(211, 309)(212, 310)(213, 311)(214, 312)(215, 313)(216, 314)(217, 315)(218, 316)(219, 317)(220, 318)(221, 319)(222, 320)(223, 321)(224, 322)(225, 323)(226, 324)(227, 325)(228, 326)(229, 327)(230, 328)(231, 329)(232, 330)(233, 331)(234, 332)(235, 333)(236, 334)(237, 335)(238, 336)(239, 337)(240, 338)(241, 339)(242, 340)(243, 341)(244, 342)(245, 343)(246, 344)(247, 345)(248, 346)(249, 347)(250, 348)(251, 349)(252, 350)(253, 351)(254, 352)(255, 353)(256, 354)(257, 355)(258, 356)(259, 357)(260, 358)(261, 359)(262, 360)(263, 361)(264, 362)(265, 363)(266, 364)(267, 365)(268, 366)(269, 367)(270, 368)(271, 369)(272, 370)(273, 371)(274, 372)(275, 373)(276, 374)(277, 375)(278, 376)(279, 377)(280, 378)(281, 379)(282, 380)(283, 381)(284, 382)(285, 383)(286, 384)(287, 385)(288, 386)(289, 387)(290, 388)(291, 389)(292, 390)(293, 391)(294, 392) L = (1, 199)(2, 202)(3, 197)(4, 205)(5, 208)(6, 198)(7, 211)(8, 212)(9, 200)(10, 213)(11, 217)(12, 201)(13, 219)(14, 220)(15, 203)(16, 204)(17, 206)(18, 225)(19, 226)(20, 229)(21, 207)(22, 231)(23, 209)(24, 210)(25, 235)(26, 236)(27, 237)(28, 238)(29, 214)(30, 215)(31, 239)(32, 244)(33, 216)(34, 246)(35, 218)(36, 248)(37, 249)(38, 250)(39, 221)(40, 222)(41, 223)(42, 224)(43, 227)(44, 257)(45, 258)(46, 259)(47, 262)(48, 228)(49, 264)(50, 230)(51, 266)(52, 232)(53, 233)(54, 234)(55, 271)(56, 272)(57, 273)(58, 267)(59, 274)(60, 275)(61, 240)(62, 241)(63, 242)(64, 276)(65, 279)(66, 243)(67, 281)(68, 245)(69, 283)(70, 247)(71, 254)(72, 285)(73, 286)(74, 284)(75, 251)(76, 252)(77, 253)(78, 255)(79, 256)(80, 260)(81, 287)(82, 290)(83, 261)(84, 291)(85, 263)(86, 293)(87, 265)(88, 270)(89, 268)(90, 269)(91, 277)(92, 292)(93, 294)(94, 278)(95, 280)(96, 288)(97, 282)(98, 289)(99, 295)(100, 296)(101, 297)(102, 298)(103, 299)(104, 300)(105, 301)(106, 302)(107, 303)(108, 304)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 311)(116, 312)(117, 313)(118, 314)(119, 315)(120, 316)(121, 317)(122, 318)(123, 319)(124, 320)(125, 321)(126, 322)(127, 323)(128, 324)(129, 325)(130, 326)(131, 327)(132, 328)(133, 329)(134, 330)(135, 331)(136, 332)(137, 333)(138, 334)(139, 335)(140, 336)(141, 337)(142, 338)(143, 339)(144, 340)(145, 341)(146, 342)(147, 343)(148, 344)(149, 345)(150, 346)(151, 347)(152, 348)(153, 349)(154, 350)(155, 351)(156, 352)(157, 353)(158, 354)(159, 355)(160, 356)(161, 357)(162, 358)(163, 359)(164, 360)(165, 361)(166, 362)(167, 363)(168, 364)(169, 365)(170, 366)(171, 367)(172, 368)(173, 369)(174, 370)(175, 371)(176, 372)(177, 373)(178, 374)(179, 375)(180, 376)(181, 377)(182, 378)(183, 379)(184, 380)(185, 381)(186, 382)(187, 383)(188, 384)(189, 385)(190, 386)(191, 387)(192, 388)(193, 389)(194, 390)(195, 391)(196, 392) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E15.1229 Graph:: simple bipartite v = 105 e = 196 f = 63 degree seq :: [ 2^98, 28^7 ] E15.1233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |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, (Y3 * Y2^-1)^7, Y2^14 ] Map:: R = (1, 99, 2, 100)(3, 101, 7, 105)(4, 102, 9, 107)(5, 103, 11, 109)(6, 104, 13, 111)(8, 106, 12, 110)(10, 108, 14, 112)(15, 113, 25, 123)(16, 114, 27, 125)(17, 115, 26, 124)(18, 116, 29, 127)(19, 117, 30, 128)(20, 118, 32, 130)(21, 119, 34, 132)(22, 120, 33, 131)(23, 121, 36, 134)(24, 122, 37, 135)(28, 126, 35, 133)(31, 129, 38, 136)(39, 137, 55, 153)(40, 138, 57, 155)(41, 139, 56, 154)(42, 140, 59, 157)(43, 141, 58, 156)(44, 142, 61, 159)(45, 143, 62, 160)(46, 144, 63, 161)(47, 145, 65, 163)(48, 146, 67, 165)(49, 147, 66, 164)(50, 148, 69, 167)(51, 149, 68, 166)(52, 150, 71, 169)(53, 151, 72, 170)(54, 152, 73, 171)(60, 158, 70, 168)(64, 162, 74, 172)(75, 173, 89, 187)(76, 174, 87, 185)(77, 175, 92, 190)(78, 176, 91, 189)(79, 177, 84, 182)(80, 178, 93, 191)(81, 179, 83, 181)(82, 180, 94, 192)(85, 183, 96, 194)(86, 184, 95, 193)(88, 186, 97, 195)(90, 188, 98, 196)(197, 295, 199, 297, 204, 302, 213, 311, 224, 322, 239, 337, 256, 354, 276, 374, 260, 358, 242, 340, 227, 325, 215, 313, 206, 304, 200, 298)(198, 296, 201, 299, 208, 306, 218, 316, 231, 329, 247, 345, 266, 364, 284, 382, 270, 368, 250, 348, 234, 332, 220, 318, 210, 308, 202, 300)(203, 301, 211, 309, 222, 320, 237, 335, 254, 352, 274, 372, 289, 387, 278, 376, 259, 357, 241, 339, 226, 324, 214, 312, 205, 303, 212, 310)(207, 305, 216, 314, 229, 327, 245, 343, 264, 362, 282, 380, 293, 391, 286, 384, 269, 367, 249, 347, 233, 331, 219, 317, 209, 307, 217, 315)(221, 319, 235, 333, 252, 350, 272, 370, 287, 385, 292, 390, 290, 388, 277, 375, 258, 356, 240, 338, 225, 323, 238, 336, 223, 321, 236, 334)(228, 326, 243, 341, 262, 360, 280, 378, 291, 389, 288, 386, 294, 392, 285, 383, 268, 366, 248, 346, 232, 330, 246, 344, 230, 328, 244, 342)(251, 349, 267, 365, 283, 381, 265, 363, 281, 379, 263, 361, 279, 377, 261, 359, 257, 355, 275, 373, 255, 353, 273, 371, 253, 351, 271, 369) L = (1, 198)(2, 197)(3, 203)(4, 205)(5, 207)(6, 209)(7, 199)(8, 208)(9, 200)(10, 210)(11, 201)(12, 204)(13, 202)(14, 206)(15, 221)(16, 223)(17, 222)(18, 225)(19, 226)(20, 228)(21, 230)(22, 229)(23, 232)(24, 233)(25, 211)(26, 213)(27, 212)(28, 231)(29, 214)(30, 215)(31, 234)(32, 216)(33, 218)(34, 217)(35, 224)(36, 219)(37, 220)(38, 227)(39, 251)(40, 253)(41, 252)(42, 255)(43, 254)(44, 257)(45, 258)(46, 259)(47, 261)(48, 263)(49, 262)(50, 265)(51, 264)(52, 267)(53, 268)(54, 269)(55, 235)(56, 237)(57, 236)(58, 239)(59, 238)(60, 266)(61, 240)(62, 241)(63, 242)(64, 270)(65, 243)(66, 245)(67, 244)(68, 247)(69, 246)(70, 256)(71, 248)(72, 249)(73, 250)(74, 260)(75, 285)(76, 283)(77, 288)(78, 287)(79, 280)(80, 289)(81, 279)(82, 290)(83, 277)(84, 275)(85, 292)(86, 291)(87, 272)(88, 293)(89, 271)(90, 294)(91, 274)(92, 273)(93, 276)(94, 278)(95, 282)(96, 281)(97, 284)(98, 286)(99, 295)(100, 296)(101, 297)(102, 298)(103, 299)(104, 300)(105, 301)(106, 302)(107, 303)(108, 304)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 311)(116, 312)(117, 313)(118, 314)(119, 315)(120, 316)(121, 317)(122, 318)(123, 319)(124, 320)(125, 321)(126, 322)(127, 323)(128, 324)(129, 325)(130, 326)(131, 327)(132, 328)(133, 329)(134, 330)(135, 331)(136, 332)(137, 333)(138, 334)(139, 335)(140, 336)(141, 337)(142, 338)(143, 339)(144, 340)(145, 341)(146, 342)(147, 343)(148, 344)(149, 345)(150, 346)(151, 347)(152, 348)(153, 349)(154, 350)(155, 351)(156, 352)(157, 353)(158, 354)(159, 355)(160, 356)(161, 357)(162, 358)(163, 359)(164, 360)(165, 361)(166, 362)(167, 363)(168, 364)(169, 365)(170, 366)(171, 367)(172, 368)(173, 369)(174, 370)(175, 371)(176, 372)(177, 373)(178, 374)(179, 375)(180, 376)(181, 377)(182, 378)(183, 379)(184, 380)(185, 381)(186, 382)(187, 383)(188, 384)(189, 385)(190, 386)(191, 387)(192, 388)(193, 389)(194, 390)(195, 391)(196, 392) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.1234 Graph:: bipartite v = 56 e = 196 f = 112 degree seq :: [ 4^49, 28^7 ] E15.1234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C7 x D14 (small group id <98, 3>) Aut = D14 x D14 (small group id <196, 9>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y3^-3 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1^7, Y3 * Y1^-3 * Y3^2 * Y1^-2 * Y3 * Y1^2, (Y3 * Y2^-1)^14 ] Map:: polytopal R = (1, 99, 2, 100, 6, 104, 16, 114, 31, 129, 13, 111, 4, 102)(3, 101, 9, 107, 23, 121, 44, 142, 52, 150, 28, 126, 11, 109)(5, 103, 14, 112, 32, 130, 56, 154, 41, 139, 20, 118, 7, 105)(8, 106, 21, 119, 42, 140, 67, 165, 63, 161, 37, 135, 17, 115)(10, 108, 19, 117, 36, 134, 58, 156, 77, 175, 50, 148, 26, 124)(12, 110, 29, 127, 53, 151, 79, 177, 75, 173, 48, 146, 25, 123)(15, 113, 22, 120, 39, 137, 61, 159, 71, 169, 45, 143, 24, 122)(18, 116, 38, 136, 64, 162, 86, 184, 83, 181, 59, 157, 34, 132)(27, 125, 40, 138, 62, 160, 82, 180, 93, 191, 73, 171, 47, 145)(30, 128, 54, 152, 80, 178, 95, 193, 91, 189, 72, 170, 49, 147)(33, 131, 43, 141, 65, 163, 85, 183, 89, 187, 69, 167, 46, 144)(35, 133, 60, 158, 84, 182, 96, 194, 92, 190, 76, 174, 55, 153)(51, 149, 66, 164, 81, 179, 88, 186, 98, 196, 90, 188, 74, 172)(57, 155, 68, 166, 87, 185, 97, 195, 94, 192, 78, 176, 70, 168)(197, 295)(198, 296)(199, 297)(200, 298)(201, 299)(202, 300)(203, 301)(204, 302)(205, 303)(206, 304)(207, 305)(208, 306)(209, 307)(210, 308)(211, 309)(212, 310)(213, 311)(214, 312)(215, 313)(216, 314)(217, 315)(218, 316)(219, 317)(220, 318)(221, 319)(222, 320)(223, 321)(224, 322)(225, 323)(226, 324)(227, 325)(228, 326)(229, 327)(230, 328)(231, 329)(232, 330)(233, 331)(234, 332)(235, 333)(236, 334)(237, 335)(238, 336)(239, 337)(240, 338)(241, 339)(242, 340)(243, 341)(244, 342)(245, 343)(246, 344)(247, 345)(248, 346)(249, 347)(250, 348)(251, 349)(252, 350)(253, 351)(254, 352)(255, 353)(256, 354)(257, 355)(258, 356)(259, 357)(260, 358)(261, 359)(262, 360)(263, 361)(264, 362)(265, 363)(266, 364)(267, 365)(268, 366)(269, 367)(270, 368)(271, 369)(272, 370)(273, 371)(274, 372)(275, 373)(276, 374)(277, 375)(278, 376)(279, 377)(280, 378)(281, 379)(282, 380)(283, 381)(284, 382)(285, 383)(286, 384)(287, 385)(288, 386)(289, 387)(290, 388)(291, 389)(292, 390)(293, 391)(294, 392) L = (1, 199)(2, 203)(3, 206)(4, 208)(5, 197)(6, 213)(7, 215)(8, 198)(9, 200)(10, 221)(11, 223)(12, 222)(13, 226)(14, 220)(15, 201)(16, 230)(17, 232)(18, 202)(19, 207)(20, 236)(21, 211)(22, 204)(23, 241)(24, 205)(25, 243)(26, 245)(27, 244)(28, 247)(29, 209)(30, 246)(31, 251)(32, 242)(33, 210)(34, 254)(35, 212)(36, 216)(37, 258)(38, 218)(39, 214)(40, 224)(41, 262)(42, 229)(43, 217)(44, 265)(45, 225)(46, 219)(47, 268)(48, 270)(49, 269)(50, 272)(51, 271)(52, 274)(53, 267)(54, 227)(55, 273)(56, 266)(57, 228)(58, 233)(59, 278)(60, 235)(61, 231)(62, 237)(63, 277)(64, 239)(65, 234)(66, 248)(67, 253)(68, 238)(69, 249)(70, 240)(71, 250)(72, 286)(73, 288)(74, 287)(75, 290)(76, 289)(77, 255)(78, 275)(79, 285)(80, 257)(81, 252)(82, 259)(83, 284)(84, 261)(85, 256)(86, 264)(87, 260)(88, 263)(89, 276)(90, 292)(91, 293)(92, 294)(93, 279)(94, 291)(95, 281)(96, 283)(97, 280)(98, 282)(99, 295)(100, 296)(101, 297)(102, 298)(103, 299)(104, 300)(105, 301)(106, 302)(107, 303)(108, 304)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 311)(116, 312)(117, 313)(118, 314)(119, 315)(120, 316)(121, 317)(122, 318)(123, 319)(124, 320)(125, 321)(126, 322)(127, 323)(128, 324)(129, 325)(130, 326)(131, 327)(132, 328)(133, 329)(134, 330)(135, 331)(136, 332)(137, 333)(138, 334)(139, 335)(140, 336)(141, 337)(142, 338)(143, 339)(144, 340)(145, 341)(146, 342)(147, 343)(148, 344)(149, 345)(150, 346)(151, 347)(152, 348)(153, 349)(154, 350)(155, 351)(156, 352)(157, 353)(158, 354)(159, 355)(160, 356)(161, 357)(162, 358)(163, 359)(164, 360)(165, 361)(166, 362)(167, 363)(168, 364)(169, 365)(170, 366)(171, 367)(172, 368)(173, 369)(174, 370)(175, 371)(176, 372)(177, 373)(178, 374)(179, 375)(180, 376)(181, 377)(182, 378)(183, 379)(184, 380)(185, 381)(186, 382)(187, 383)(188, 384)(189, 385)(190, 386)(191, 387)(192, 388)(193, 389)(194, 390)(195, 391)(196, 392) local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E15.1233 Graph:: simple bipartite v = 112 e = 196 f = 56 degree seq :: [ 2^98, 14^14 ] E15.1235 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = D8 x D14 (small group id <112, 31>) Aut = D16 x D14 (small group id <224, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1, (Y2 * Y3)^4, (Y3 * Y1)^14 ] Map:: polytopal non-degenerate R = (1, 114, 2, 113)(3, 119, 7, 115)(4, 121, 9, 116)(5, 123, 11, 117)(6, 125, 13, 118)(8, 124, 12, 120)(10, 126, 14, 122)(15, 137, 25, 127)(16, 138, 26, 128)(17, 139, 27, 129)(18, 141, 29, 130)(19, 142, 30, 131)(20, 143, 31, 132)(21, 144, 32, 133)(22, 145, 33, 134)(23, 147, 35, 135)(24, 148, 36, 136)(28, 146, 34, 140)(37, 159, 47, 149)(38, 160, 48, 150)(39, 161, 49, 151)(40, 162, 50, 152)(41, 163, 51, 153)(42, 164, 52, 154)(43, 165, 53, 155)(44, 166, 54, 156)(45, 167, 55, 157)(46, 168, 56, 158)(57, 177, 65, 169)(58, 178, 66, 170)(59, 179, 67, 171)(60, 180, 68, 172)(61, 181, 69, 173)(62, 182, 70, 174)(63, 183, 71, 175)(64, 184, 72, 176)(73, 193, 81, 185)(74, 194, 82, 186)(75, 195, 83, 187)(76, 196, 84, 188)(77, 197, 85, 189)(78, 198, 86, 190)(79, 199, 87, 191)(80, 200, 88, 192)(89, 209, 97, 201)(90, 210, 98, 202)(91, 211, 99, 203)(92, 212, 100, 204)(93, 213, 101, 205)(94, 214, 102, 206)(95, 215, 103, 207)(96, 216, 104, 208)(105, 221, 109, 217)(106, 222, 110, 218)(107, 223, 111, 219)(108, 224, 112, 220) 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, 79)(71, 78)(72, 80)(81, 89)(82, 91)(83, 90)(84, 92)(85, 93)(86, 95)(87, 94)(88, 96)(97, 105)(98, 107)(99, 106)(100, 108)(101, 109)(102, 111)(103, 110)(104, 112)(113, 116)(114, 118)(115, 120)(117, 124)(119, 128)(121, 127)(122, 131)(123, 133)(125, 132)(126, 136)(129, 140)(130, 142)(134, 146)(135, 148)(137, 150)(138, 149)(139, 152)(141, 153)(143, 155)(144, 154)(145, 157)(147, 158)(151, 162)(156, 167)(159, 170)(160, 169)(161, 172)(163, 171)(164, 174)(165, 173)(166, 176)(168, 175)(177, 186)(178, 185)(179, 188)(180, 187)(181, 190)(182, 189)(183, 192)(184, 191)(193, 202)(194, 201)(195, 204)(196, 203)(197, 206)(198, 205)(199, 208)(200, 207)(209, 218)(210, 217)(211, 220)(212, 219)(213, 222)(214, 221)(215, 224)(216, 223) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.1237 Transitivity :: VT+ AT Graph:: simple bipartite v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.1236 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1, (Y2 * Y3)^4, 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 ] Map:: polytopal non-degenerate R = (1, 114, 2, 113)(3, 119, 7, 115)(4, 121, 9, 116)(5, 123, 11, 117)(6, 125, 13, 118)(8, 124, 12, 120)(10, 126, 14, 122)(15, 137, 25, 127)(16, 138, 26, 128)(17, 139, 27, 129)(18, 141, 29, 130)(19, 142, 30, 131)(20, 143, 31, 132)(21, 144, 32, 133)(22, 145, 33, 134)(23, 147, 35, 135)(24, 148, 36, 136)(28, 146, 34, 140)(37, 159, 47, 149)(38, 160, 48, 150)(39, 161, 49, 151)(40, 162, 50, 152)(41, 163, 51, 153)(42, 164, 52, 154)(43, 165, 53, 155)(44, 166, 54, 156)(45, 167, 55, 157)(46, 168, 56, 158)(57, 177, 65, 169)(58, 178, 66, 170)(59, 179, 67, 171)(60, 180, 68, 172)(61, 181, 69, 173)(62, 182, 70, 174)(63, 183, 71, 175)(64, 184, 72, 176)(73, 193, 81, 185)(74, 194, 82, 186)(75, 195, 83, 187)(76, 196, 84, 188)(77, 197, 85, 189)(78, 198, 86, 190)(79, 199, 87, 191)(80, 200, 88, 192)(89, 209, 97, 201)(90, 210, 98, 202)(91, 211, 99, 203)(92, 212, 100, 204)(93, 213, 101, 205)(94, 214, 102, 206)(95, 215, 103, 207)(96, 216, 104, 208)(105, 224, 112, 217)(106, 223, 111, 218)(107, 222, 110, 219)(108, 221, 109, 220) 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, 79)(71, 78)(72, 80)(81, 89)(82, 91)(83, 90)(84, 92)(85, 93)(86, 95)(87, 94)(88, 96)(97, 105)(98, 107)(99, 106)(100, 108)(101, 109)(102, 111)(103, 110)(104, 112)(113, 116)(114, 118)(115, 120)(117, 124)(119, 128)(121, 127)(122, 131)(123, 133)(125, 132)(126, 136)(129, 140)(130, 142)(134, 146)(135, 148)(137, 150)(138, 149)(139, 152)(141, 153)(143, 155)(144, 154)(145, 157)(147, 158)(151, 162)(156, 167)(159, 170)(160, 169)(161, 172)(163, 171)(164, 174)(165, 173)(166, 176)(168, 175)(177, 186)(178, 185)(179, 188)(180, 187)(181, 190)(182, 189)(183, 192)(184, 191)(193, 202)(194, 201)(195, 204)(196, 203)(197, 206)(198, 205)(199, 208)(200, 207)(209, 218)(210, 217)(211, 220)(212, 219)(213, 222)(214, 221)(215, 224)(216, 223) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.1238 Transitivity :: VT+ AT Graph:: simple bipartite v = 56 e = 112 f = 28 degree seq :: [ 4^56 ] E15.1237 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = D8 x D14 (small group id <112, 31>) Aut = D16 x D14 (small group id <224, 105>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, (R * Y1)^2, R * Y3 * R * Y2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y3 * Y2 * Y3 * Y1^-2 * Y2, (Y1^-1 * Y2 * Y3)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * 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 ] Map:: polytopal non-degenerate R = (1, 114, 2, 118, 6, 117, 5, 113)(3, 121, 9, 129, 17, 123, 11, 115)(4, 124, 12, 130, 18, 126, 14, 116)(7, 131, 19, 127, 15, 133, 21, 119)(8, 134, 22, 128, 16, 136, 24, 120)(10, 132, 20, 125, 13, 135, 23, 122)(25, 145, 33, 139, 27, 146, 34, 137)(26, 147, 35, 140, 28, 148, 36, 138)(29, 149, 37, 143, 31, 150, 38, 141)(30, 151, 39, 144, 32, 152, 40, 142)(41, 161, 49, 155, 43, 162, 50, 153)(42, 163, 51, 156, 44, 164, 52, 154)(45, 165, 53, 159, 47, 166, 54, 157)(46, 167, 55, 160, 48, 168, 56, 158)(57, 177, 65, 171, 59, 178, 66, 169)(58, 179, 67, 172, 60, 180, 68, 170)(61, 181, 69, 175, 63, 182, 70, 173)(62, 183, 71, 176, 64, 184, 72, 174)(73, 193, 81, 187, 75, 194, 82, 185)(74, 195, 83, 188, 76, 196, 84, 186)(77, 197, 85, 191, 79, 198, 86, 189)(78, 199, 87, 192, 80, 200, 88, 190)(89, 209, 97, 203, 91, 210, 98, 201)(90, 211, 99, 204, 92, 212, 100, 202)(93, 213, 101, 207, 95, 214, 102, 205)(94, 215, 103, 208, 96, 216, 104, 206)(105, 223, 111, 219, 107, 221, 109, 217)(106, 224, 112, 220, 108, 222, 110, 218) 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, 77)(70, 79)(71, 80)(72, 78)(81, 89)(82, 91)(83, 92)(84, 90)(85, 93)(86, 95)(87, 96)(88, 94)(97, 105)(98, 107)(99, 108)(100, 106)(101, 109)(102, 111)(103, 112)(104, 110)(113, 116)(114, 120)(115, 122)(117, 128)(118, 130)(119, 132)(121, 138)(123, 140)(124, 137)(125, 129)(126, 139)(127, 135)(131, 142)(133, 144)(134, 141)(136, 143)(145, 154)(146, 156)(147, 153)(148, 155)(149, 158)(150, 160)(151, 157)(152, 159)(161, 170)(162, 172)(163, 169)(164, 171)(165, 174)(166, 176)(167, 173)(168, 175)(177, 186)(178, 188)(179, 185)(180, 187)(181, 190)(182, 192)(183, 189)(184, 191)(193, 202)(194, 204)(195, 201)(196, 203)(197, 206)(198, 208)(199, 205)(200, 207)(209, 218)(210, 220)(211, 217)(212, 219)(213, 222)(214, 224)(215, 221)(216, 223) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.1235 Transitivity :: VT+ AT Graph:: bipartite v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.1238 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^4, (Y1^-1 * Y2 * Y1^-1)^2, (Y1^-1 * Y3 * 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^-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, 114, 2, 118, 6, 117, 5, 113)(3, 121, 9, 129, 17, 123, 11, 115)(4, 124, 12, 130, 18, 126, 14, 116)(7, 131, 19, 127, 15, 133, 21, 119)(8, 134, 22, 128, 16, 136, 24, 120)(10, 132, 20, 125, 13, 135, 23, 122)(25, 145, 33, 139, 27, 146, 34, 137)(26, 147, 35, 140, 28, 148, 36, 138)(29, 149, 37, 143, 31, 150, 38, 141)(30, 151, 39, 144, 32, 152, 40, 142)(41, 161, 49, 155, 43, 162, 50, 153)(42, 163, 51, 156, 44, 164, 52, 154)(45, 165, 53, 159, 47, 166, 54, 157)(46, 167, 55, 160, 48, 168, 56, 158)(57, 177, 65, 171, 59, 178, 66, 169)(58, 179, 67, 172, 60, 180, 68, 170)(61, 181, 69, 175, 63, 182, 70, 173)(62, 183, 71, 176, 64, 184, 72, 174)(73, 193, 81, 187, 75, 194, 82, 185)(74, 195, 83, 188, 76, 196, 84, 186)(77, 197, 85, 191, 79, 198, 86, 189)(78, 199, 87, 192, 80, 200, 88, 190)(89, 209, 97, 203, 91, 210, 98, 201)(90, 211, 99, 204, 92, 212, 100, 202)(93, 213, 101, 207, 95, 214, 102, 205)(94, 215, 103, 208, 96, 216, 104, 206)(105, 221, 109, 219, 107, 223, 111, 217)(106, 222, 110, 220, 108, 224, 112, 218) 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, 77)(70, 79)(71, 80)(72, 78)(81, 89)(82, 91)(83, 92)(84, 90)(85, 93)(86, 95)(87, 96)(88, 94)(97, 105)(98, 107)(99, 108)(100, 106)(101, 109)(102, 111)(103, 112)(104, 110)(113, 116)(114, 120)(115, 122)(117, 128)(118, 130)(119, 132)(121, 138)(123, 140)(124, 137)(125, 129)(126, 139)(127, 135)(131, 142)(133, 144)(134, 141)(136, 143)(145, 154)(146, 156)(147, 153)(148, 155)(149, 158)(150, 160)(151, 157)(152, 159)(161, 170)(162, 172)(163, 169)(164, 171)(165, 174)(166, 176)(167, 173)(168, 175)(177, 186)(178, 188)(179, 185)(180, 187)(181, 190)(182, 192)(183, 189)(184, 191)(193, 202)(194, 204)(195, 201)(196, 203)(197, 206)(198, 208)(199, 205)(200, 207)(209, 218)(210, 220)(211, 217)(212, 219)(213, 222)(214, 224)(215, 221)(216, 223) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.1236 Transitivity :: VT+ AT Graph:: bipartite v = 28 e = 112 f = 56 degree seq :: [ 8^28 ] E15.1239 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = D8 x D14 (small group id <112, 31>) Aut = D16 x D14 (small group id <224, 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)^14 ] Map:: polytopal R = (1, 113, 4, 116)(2, 114, 6, 118)(3, 115, 8, 120)(5, 117, 12, 124)(7, 119, 16, 128)(9, 121, 18, 130)(10, 122, 19, 131)(11, 123, 21, 133)(13, 125, 23, 135)(14, 126, 24, 136)(15, 127, 25, 137)(17, 129, 27, 139)(20, 132, 31, 143)(22, 134, 33, 145)(26, 138, 37, 149)(28, 140, 39, 151)(29, 141, 40, 152)(30, 142, 41, 153)(32, 144, 42, 154)(34, 146, 44, 156)(35, 147, 45, 157)(36, 148, 46, 158)(38, 150, 47, 159)(43, 155, 52, 164)(48, 160, 57, 169)(49, 161, 58, 170)(50, 162, 59, 171)(51, 163, 60, 172)(53, 165, 61, 173)(54, 166, 62, 174)(55, 167, 63, 175)(56, 168, 64, 176)(65, 177, 73, 185)(66, 178, 74, 186)(67, 179, 75, 187)(68, 180, 76, 188)(69, 181, 77, 189)(70, 182, 78, 190)(71, 183, 79, 191)(72, 184, 80, 192)(81, 193, 89, 201)(82, 194, 90, 202)(83, 195, 91, 203)(84, 196, 92, 204)(85, 197, 93, 205)(86, 198, 94, 206)(87, 199, 95, 207)(88, 200, 96, 208)(97, 209, 105, 217)(98, 210, 106, 218)(99, 211, 107, 219)(100, 212, 108, 220)(101, 213, 109, 221)(102, 214, 110, 222)(103, 215, 111, 223)(104, 216, 112, 224)(225, 226)(227, 231)(228, 233)(229, 235)(230, 237)(232, 241)(234, 240)(236, 246)(238, 245)(239, 244)(242, 252)(243, 254)(247, 258)(248, 260)(249, 256)(250, 255)(251, 259)(253, 257)(261, 267)(262, 266)(263, 272)(264, 274)(265, 273)(268, 277)(269, 279)(270, 278)(271, 280)(275, 276)(281, 289)(282, 291)(283, 290)(284, 292)(285, 293)(286, 295)(287, 294)(288, 296)(297, 305)(298, 307)(299, 306)(300, 308)(301, 309)(302, 311)(303, 310)(304, 312)(313, 321)(314, 323)(315, 322)(316, 324)(317, 325)(318, 327)(319, 326)(320, 328)(329, 333)(330, 335)(331, 334)(332, 336)(337, 339)(338, 341)(340, 346)(342, 350)(343, 351)(344, 349)(345, 348)(347, 356)(352, 362)(353, 361)(354, 365)(355, 364)(357, 368)(358, 367)(359, 371)(360, 370)(363, 374)(366, 373)(369, 379)(372, 378)(375, 385)(376, 384)(377, 387)(380, 390)(381, 389)(382, 392)(383, 391)(386, 388)(393, 402)(394, 401)(395, 404)(396, 403)(397, 406)(398, 405)(399, 408)(400, 407)(409, 418)(410, 417)(411, 420)(412, 419)(413, 422)(414, 421)(415, 424)(416, 423)(425, 434)(426, 433)(427, 436)(428, 435)(429, 438)(430, 437)(431, 440)(432, 439)(441, 446)(442, 445)(443, 448)(444, 447) L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E15.1245 Graph:: simple bipartite v = 168 e = 224 f = 28 degree seq :: [ 2^112, 4^56 ] E15.1240 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 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 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: polytopal R = (1, 113, 4, 116)(2, 114, 6, 118)(3, 115, 8, 120)(5, 117, 12, 124)(7, 119, 16, 128)(9, 121, 18, 130)(10, 122, 19, 131)(11, 123, 21, 133)(13, 125, 23, 135)(14, 126, 24, 136)(15, 127, 25, 137)(17, 129, 27, 139)(20, 132, 31, 143)(22, 134, 33, 145)(26, 138, 37, 149)(28, 140, 39, 151)(29, 141, 40, 152)(30, 142, 41, 153)(32, 144, 42, 154)(34, 146, 44, 156)(35, 147, 45, 157)(36, 148, 46, 158)(38, 150, 47, 159)(43, 155, 52, 164)(48, 160, 57, 169)(49, 161, 58, 170)(50, 162, 59, 171)(51, 163, 60, 172)(53, 165, 61, 173)(54, 166, 62, 174)(55, 167, 63, 175)(56, 168, 64, 176)(65, 177, 73, 185)(66, 178, 74, 186)(67, 179, 75, 187)(68, 180, 76, 188)(69, 181, 77, 189)(70, 182, 78, 190)(71, 183, 79, 191)(72, 184, 80, 192)(81, 193, 89, 201)(82, 194, 90, 202)(83, 195, 91, 203)(84, 196, 92, 204)(85, 197, 93, 205)(86, 198, 94, 206)(87, 199, 95, 207)(88, 200, 96, 208)(97, 209, 105, 217)(98, 210, 106, 218)(99, 211, 107, 219)(100, 212, 108, 220)(101, 213, 109, 221)(102, 214, 110, 222)(103, 215, 111, 223)(104, 216, 112, 224)(225, 226)(227, 231)(228, 233)(229, 235)(230, 237)(232, 241)(234, 240)(236, 246)(238, 245)(239, 244)(242, 252)(243, 254)(247, 258)(248, 260)(249, 256)(250, 255)(251, 259)(253, 257)(261, 267)(262, 266)(263, 272)(264, 274)(265, 273)(268, 277)(269, 279)(270, 278)(271, 280)(275, 276)(281, 289)(282, 291)(283, 290)(284, 292)(285, 293)(286, 295)(287, 294)(288, 296)(297, 305)(298, 307)(299, 306)(300, 308)(301, 309)(302, 311)(303, 310)(304, 312)(313, 321)(314, 323)(315, 322)(316, 324)(317, 325)(318, 327)(319, 326)(320, 328)(329, 336)(330, 334)(331, 335)(332, 333)(337, 339)(338, 341)(340, 346)(342, 350)(343, 351)(344, 349)(345, 348)(347, 356)(352, 362)(353, 361)(354, 365)(355, 364)(357, 368)(358, 367)(359, 371)(360, 370)(363, 374)(366, 373)(369, 379)(372, 378)(375, 385)(376, 384)(377, 387)(380, 390)(381, 389)(382, 392)(383, 391)(386, 388)(393, 402)(394, 401)(395, 404)(396, 403)(397, 406)(398, 405)(399, 408)(400, 407)(409, 418)(410, 417)(411, 420)(412, 419)(413, 422)(414, 421)(415, 424)(416, 423)(425, 434)(426, 433)(427, 436)(428, 435)(429, 438)(430, 437)(431, 440)(432, 439)(441, 447)(442, 448)(443, 445)(444, 446) L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E15.1246 Graph:: simple bipartite v = 168 e = 224 f = 28 degree seq :: [ 2^112, 4^56 ] E15.1241 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = D8 x D14 (small group id <112, 31>) Aut = D16 x D14 (small group id <224, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 113, 4, 116, 14, 126, 5, 117)(2, 114, 7, 119, 22, 134, 8, 120)(3, 115, 10, 122, 17, 129, 11, 123)(6, 118, 18, 130, 9, 121, 19, 131)(12, 124, 25, 137, 15, 127, 26, 138)(13, 125, 27, 139, 16, 128, 28, 140)(20, 132, 29, 141, 23, 135, 30, 142)(21, 133, 31, 143, 24, 136, 32, 144)(33, 145, 41, 153, 35, 147, 42, 154)(34, 146, 43, 155, 36, 148, 44, 156)(37, 149, 45, 157, 39, 151, 46, 158)(38, 150, 47, 159, 40, 152, 48, 160)(49, 161, 57, 169, 51, 163, 58, 170)(50, 162, 59, 171, 52, 164, 60, 172)(53, 165, 61, 173, 55, 167, 62, 174)(54, 166, 63, 175, 56, 168, 64, 176)(65, 177, 73, 185, 67, 179, 74, 186)(66, 178, 75, 187, 68, 180, 76, 188)(69, 181, 77, 189, 71, 183, 78, 190)(70, 182, 79, 191, 72, 184, 80, 192)(81, 193, 89, 201, 83, 195, 90, 202)(82, 194, 91, 203, 84, 196, 92, 204)(85, 197, 93, 205, 87, 199, 94, 206)(86, 198, 95, 207, 88, 200, 96, 208)(97, 209, 105, 217, 99, 211, 106, 218)(98, 210, 107, 219, 100, 212, 108, 220)(101, 213, 109, 221, 103, 215, 110, 222)(102, 214, 111, 223, 104, 216, 112, 224)(225, 226)(227, 233)(228, 236)(229, 239)(230, 241)(231, 244)(232, 247)(234, 248)(235, 245)(237, 243)(238, 246)(240, 242)(249, 257)(250, 259)(251, 260)(252, 258)(253, 261)(254, 263)(255, 264)(256, 262)(265, 273)(266, 275)(267, 276)(268, 274)(269, 277)(270, 279)(271, 280)(272, 278)(281, 289)(282, 291)(283, 292)(284, 290)(285, 293)(286, 295)(287, 296)(288, 294)(297, 305)(298, 307)(299, 308)(300, 306)(301, 309)(302, 311)(303, 312)(304, 310)(313, 321)(314, 323)(315, 324)(316, 322)(317, 325)(318, 327)(319, 328)(320, 326)(329, 334)(330, 333)(331, 335)(332, 336)(337, 339)(338, 342)(340, 349)(341, 352)(343, 357)(344, 360)(345, 358)(346, 356)(347, 359)(348, 354)(350, 353)(351, 355)(361, 370)(362, 372)(363, 369)(364, 371)(365, 374)(366, 376)(367, 373)(368, 375)(377, 386)(378, 388)(379, 385)(380, 387)(381, 390)(382, 392)(383, 389)(384, 391)(393, 402)(394, 404)(395, 401)(396, 403)(397, 406)(398, 408)(399, 405)(400, 407)(409, 418)(410, 420)(411, 417)(412, 419)(413, 422)(414, 424)(415, 421)(416, 423)(425, 434)(426, 436)(427, 433)(428, 435)(429, 438)(430, 440)(431, 437)(432, 439)(441, 448)(442, 447)(443, 446)(444, 445) L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E15.1243 Graph:: simple bipartite v = 140 e = 224 f = 56 degree seq :: [ 2^112, 8^28 ] E15.1242 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 113, 4, 116, 14, 126, 5, 117)(2, 114, 7, 119, 22, 134, 8, 120)(3, 115, 10, 122, 17, 129, 11, 123)(6, 118, 18, 130, 9, 121, 19, 131)(12, 124, 25, 137, 15, 127, 26, 138)(13, 125, 27, 139, 16, 128, 28, 140)(20, 132, 29, 141, 23, 135, 30, 142)(21, 133, 31, 143, 24, 136, 32, 144)(33, 145, 41, 153, 35, 147, 42, 154)(34, 146, 43, 155, 36, 148, 44, 156)(37, 149, 45, 157, 39, 151, 46, 158)(38, 150, 47, 159, 40, 152, 48, 160)(49, 161, 57, 169, 51, 163, 58, 170)(50, 162, 59, 171, 52, 164, 60, 172)(53, 165, 61, 173, 55, 167, 62, 174)(54, 166, 63, 175, 56, 168, 64, 176)(65, 177, 73, 185, 67, 179, 74, 186)(66, 178, 75, 187, 68, 180, 76, 188)(69, 181, 77, 189, 71, 183, 78, 190)(70, 182, 79, 191, 72, 184, 80, 192)(81, 193, 89, 201, 83, 195, 90, 202)(82, 194, 91, 203, 84, 196, 92, 204)(85, 197, 93, 205, 87, 199, 94, 206)(86, 198, 95, 207, 88, 200, 96, 208)(97, 209, 105, 217, 99, 211, 106, 218)(98, 210, 107, 219, 100, 212, 108, 220)(101, 213, 109, 221, 103, 215, 110, 222)(102, 214, 111, 223, 104, 216, 112, 224)(225, 226)(227, 233)(228, 236)(229, 239)(230, 241)(231, 244)(232, 247)(234, 248)(235, 245)(237, 243)(238, 246)(240, 242)(249, 257)(250, 259)(251, 260)(252, 258)(253, 261)(254, 263)(255, 264)(256, 262)(265, 273)(266, 275)(267, 276)(268, 274)(269, 277)(270, 279)(271, 280)(272, 278)(281, 289)(282, 291)(283, 292)(284, 290)(285, 293)(286, 295)(287, 296)(288, 294)(297, 305)(298, 307)(299, 308)(300, 306)(301, 309)(302, 311)(303, 312)(304, 310)(313, 321)(314, 323)(315, 324)(316, 322)(317, 325)(318, 327)(319, 328)(320, 326)(329, 333)(330, 334)(331, 336)(332, 335)(337, 339)(338, 342)(340, 349)(341, 352)(343, 357)(344, 360)(345, 358)(346, 356)(347, 359)(348, 354)(350, 353)(351, 355)(361, 370)(362, 372)(363, 369)(364, 371)(365, 374)(366, 376)(367, 373)(368, 375)(377, 386)(378, 388)(379, 385)(380, 387)(381, 390)(382, 392)(383, 389)(384, 391)(393, 402)(394, 404)(395, 401)(396, 403)(397, 406)(398, 408)(399, 405)(400, 407)(409, 418)(410, 420)(411, 417)(412, 419)(413, 422)(414, 424)(415, 421)(416, 423)(425, 434)(426, 436)(427, 433)(428, 435)(429, 438)(430, 440)(431, 437)(432, 439)(441, 447)(442, 448)(443, 445)(444, 446) L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E15.1244 Graph:: simple bipartite v = 140 e = 224 f = 56 degree seq :: [ 2^112, 8^28 ] E15.1243 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = D8 x D14 (small group id <112, 31>) Aut = D16 x D14 (small group id <224, 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)^14 ] Map:: R = (1, 113, 225, 337, 4, 116, 228, 340)(2, 114, 226, 338, 6, 118, 230, 342)(3, 115, 227, 339, 8, 120, 232, 344)(5, 117, 229, 341, 12, 124, 236, 348)(7, 119, 231, 343, 16, 128, 240, 352)(9, 121, 233, 345, 18, 130, 242, 354)(10, 122, 234, 346, 19, 131, 243, 355)(11, 123, 235, 347, 21, 133, 245, 357)(13, 125, 237, 349, 23, 135, 247, 359)(14, 126, 238, 350, 24, 136, 248, 360)(15, 127, 239, 351, 25, 137, 249, 361)(17, 129, 241, 353, 27, 139, 251, 363)(20, 132, 244, 356, 31, 143, 255, 367)(22, 134, 246, 358, 33, 145, 257, 369)(26, 138, 250, 362, 37, 149, 261, 373)(28, 140, 252, 364, 39, 151, 263, 375)(29, 141, 253, 365, 40, 152, 264, 376)(30, 142, 254, 366, 41, 153, 265, 377)(32, 144, 256, 368, 42, 154, 266, 378)(34, 146, 258, 370, 44, 156, 268, 380)(35, 147, 259, 371, 45, 157, 269, 381)(36, 148, 260, 372, 46, 158, 270, 382)(38, 150, 262, 374, 47, 159, 271, 383)(43, 155, 267, 379, 52, 164, 276, 388)(48, 160, 272, 384, 57, 169, 281, 393)(49, 161, 273, 385, 58, 170, 282, 394)(50, 162, 274, 386, 59, 171, 283, 395)(51, 163, 275, 387, 60, 172, 284, 396)(53, 165, 277, 389, 61, 173, 285, 397)(54, 166, 278, 390, 62, 174, 286, 398)(55, 167, 279, 391, 63, 175, 287, 399)(56, 168, 280, 392, 64, 176, 288, 400)(65, 177, 289, 401, 73, 185, 297, 409)(66, 178, 290, 402, 74, 186, 298, 410)(67, 179, 291, 403, 75, 187, 299, 411)(68, 180, 292, 404, 76, 188, 300, 412)(69, 181, 293, 405, 77, 189, 301, 413)(70, 182, 294, 406, 78, 190, 302, 414)(71, 183, 295, 407, 79, 191, 303, 415)(72, 184, 296, 408, 80, 192, 304, 416)(81, 193, 305, 417, 89, 201, 313, 425)(82, 194, 306, 418, 90, 202, 314, 426)(83, 195, 307, 419, 91, 203, 315, 427)(84, 196, 308, 420, 92, 204, 316, 428)(85, 197, 309, 421, 93, 205, 317, 429)(86, 198, 310, 422, 94, 206, 318, 430)(87, 199, 311, 423, 95, 207, 319, 431)(88, 200, 312, 424, 96, 208, 320, 432)(97, 209, 321, 433, 105, 217, 329, 441)(98, 210, 322, 434, 106, 218, 330, 442)(99, 211, 323, 435, 107, 219, 331, 443)(100, 212, 324, 436, 108, 220, 332, 444)(101, 213, 325, 437, 109, 221, 333, 445)(102, 214, 326, 438, 110, 222, 334, 446)(103, 215, 327, 439, 111, 223, 335, 447)(104, 216, 328, 440, 112, 224, 336, 448) L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 123)(6, 125)(7, 115)(8, 129)(9, 116)(10, 128)(11, 117)(12, 134)(13, 118)(14, 133)(15, 132)(16, 122)(17, 120)(18, 140)(19, 142)(20, 127)(21, 126)(22, 124)(23, 146)(24, 148)(25, 144)(26, 143)(27, 147)(28, 130)(29, 145)(30, 131)(31, 138)(32, 137)(33, 141)(34, 135)(35, 139)(36, 136)(37, 155)(38, 154)(39, 160)(40, 162)(41, 161)(42, 150)(43, 149)(44, 165)(45, 167)(46, 166)(47, 168)(48, 151)(49, 153)(50, 152)(51, 164)(52, 163)(53, 156)(54, 158)(55, 157)(56, 159)(57, 177)(58, 179)(59, 178)(60, 180)(61, 181)(62, 183)(63, 182)(64, 184)(65, 169)(66, 171)(67, 170)(68, 172)(69, 173)(70, 175)(71, 174)(72, 176)(73, 193)(74, 195)(75, 194)(76, 196)(77, 197)(78, 199)(79, 198)(80, 200)(81, 185)(82, 187)(83, 186)(84, 188)(85, 189)(86, 191)(87, 190)(88, 192)(89, 209)(90, 211)(91, 210)(92, 212)(93, 213)(94, 215)(95, 214)(96, 216)(97, 201)(98, 203)(99, 202)(100, 204)(101, 205)(102, 207)(103, 206)(104, 208)(105, 221)(106, 223)(107, 222)(108, 224)(109, 217)(110, 219)(111, 218)(112, 220)(225, 339)(226, 341)(227, 337)(228, 346)(229, 338)(230, 350)(231, 351)(232, 349)(233, 348)(234, 340)(235, 356)(236, 345)(237, 344)(238, 342)(239, 343)(240, 362)(241, 361)(242, 365)(243, 364)(244, 347)(245, 368)(246, 367)(247, 371)(248, 370)(249, 353)(250, 352)(251, 374)(252, 355)(253, 354)(254, 373)(255, 358)(256, 357)(257, 379)(258, 360)(259, 359)(260, 378)(261, 366)(262, 363)(263, 385)(264, 384)(265, 387)(266, 372)(267, 369)(268, 390)(269, 389)(270, 392)(271, 391)(272, 376)(273, 375)(274, 388)(275, 377)(276, 386)(277, 381)(278, 380)(279, 383)(280, 382)(281, 402)(282, 401)(283, 404)(284, 403)(285, 406)(286, 405)(287, 408)(288, 407)(289, 394)(290, 393)(291, 396)(292, 395)(293, 398)(294, 397)(295, 400)(296, 399)(297, 418)(298, 417)(299, 420)(300, 419)(301, 422)(302, 421)(303, 424)(304, 423)(305, 410)(306, 409)(307, 412)(308, 411)(309, 414)(310, 413)(311, 416)(312, 415)(313, 434)(314, 433)(315, 436)(316, 435)(317, 438)(318, 437)(319, 440)(320, 439)(321, 426)(322, 425)(323, 428)(324, 427)(325, 430)(326, 429)(327, 432)(328, 431)(329, 446)(330, 445)(331, 448)(332, 447)(333, 442)(334, 441)(335, 444)(336, 443) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.1241 Transitivity :: VT+ Graph:: bipartite v = 56 e = 224 f = 140 degree seq :: [ 8^56 ] E15.1244 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 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 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: R = (1, 113, 225, 337, 4, 116, 228, 340)(2, 114, 226, 338, 6, 118, 230, 342)(3, 115, 227, 339, 8, 120, 232, 344)(5, 117, 229, 341, 12, 124, 236, 348)(7, 119, 231, 343, 16, 128, 240, 352)(9, 121, 233, 345, 18, 130, 242, 354)(10, 122, 234, 346, 19, 131, 243, 355)(11, 123, 235, 347, 21, 133, 245, 357)(13, 125, 237, 349, 23, 135, 247, 359)(14, 126, 238, 350, 24, 136, 248, 360)(15, 127, 239, 351, 25, 137, 249, 361)(17, 129, 241, 353, 27, 139, 251, 363)(20, 132, 244, 356, 31, 143, 255, 367)(22, 134, 246, 358, 33, 145, 257, 369)(26, 138, 250, 362, 37, 149, 261, 373)(28, 140, 252, 364, 39, 151, 263, 375)(29, 141, 253, 365, 40, 152, 264, 376)(30, 142, 254, 366, 41, 153, 265, 377)(32, 144, 256, 368, 42, 154, 266, 378)(34, 146, 258, 370, 44, 156, 268, 380)(35, 147, 259, 371, 45, 157, 269, 381)(36, 148, 260, 372, 46, 158, 270, 382)(38, 150, 262, 374, 47, 159, 271, 383)(43, 155, 267, 379, 52, 164, 276, 388)(48, 160, 272, 384, 57, 169, 281, 393)(49, 161, 273, 385, 58, 170, 282, 394)(50, 162, 274, 386, 59, 171, 283, 395)(51, 163, 275, 387, 60, 172, 284, 396)(53, 165, 277, 389, 61, 173, 285, 397)(54, 166, 278, 390, 62, 174, 286, 398)(55, 167, 279, 391, 63, 175, 287, 399)(56, 168, 280, 392, 64, 176, 288, 400)(65, 177, 289, 401, 73, 185, 297, 409)(66, 178, 290, 402, 74, 186, 298, 410)(67, 179, 291, 403, 75, 187, 299, 411)(68, 180, 292, 404, 76, 188, 300, 412)(69, 181, 293, 405, 77, 189, 301, 413)(70, 182, 294, 406, 78, 190, 302, 414)(71, 183, 295, 407, 79, 191, 303, 415)(72, 184, 296, 408, 80, 192, 304, 416)(81, 193, 305, 417, 89, 201, 313, 425)(82, 194, 306, 418, 90, 202, 314, 426)(83, 195, 307, 419, 91, 203, 315, 427)(84, 196, 308, 420, 92, 204, 316, 428)(85, 197, 309, 421, 93, 205, 317, 429)(86, 198, 310, 422, 94, 206, 318, 430)(87, 199, 311, 423, 95, 207, 319, 431)(88, 200, 312, 424, 96, 208, 320, 432)(97, 209, 321, 433, 105, 217, 329, 441)(98, 210, 322, 434, 106, 218, 330, 442)(99, 211, 323, 435, 107, 219, 331, 443)(100, 212, 324, 436, 108, 220, 332, 444)(101, 213, 325, 437, 109, 221, 333, 445)(102, 214, 326, 438, 110, 222, 334, 446)(103, 215, 327, 439, 111, 223, 335, 447)(104, 216, 328, 440, 112, 224, 336, 448) L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 123)(6, 125)(7, 115)(8, 129)(9, 116)(10, 128)(11, 117)(12, 134)(13, 118)(14, 133)(15, 132)(16, 122)(17, 120)(18, 140)(19, 142)(20, 127)(21, 126)(22, 124)(23, 146)(24, 148)(25, 144)(26, 143)(27, 147)(28, 130)(29, 145)(30, 131)(31, 138)(32, 137)(33, 141)(34, 135)(35, 139)(36, 136)(37, 155)(38, 154)(39, 160)(40, 162)(41, 161)(42, 150)(43, 149)(44, 165)(45, 167)(46, 166)(47, 168)(48, 151)(49, 153)(50, 152)(51, 164)(52, 163)(53, 156)(54, 158)(55, 157)(56, 159)(57, 177)(58, 179)(59, 178)(60, 180)(61, 181)(62, 183)(63, 182)(64, 184)(65, 169)(66, 171)(67, 170)(68, 172)(69, 173)(70, 175)(71, 174)(72, 176)(73, 193)(74, 195)(75, 194)(76, 196)(77, 197)(78, 199)(79, 198)(80, 200)(81, 185)(82, 187)(83, 186)(84, 188)(85, 189)(86, 191)(87, 190)(88, 192)(89, 209)(90, 211)(91, 210)(92, 212)(93, 213)(94, 215)(95, 214)(96, 216)(97, 201)(98, 203)(99, 202)(100, 204)(101, 205)(102, 207)(103, 206)(104, 208)(105, 224)(106, 222)(107, 223)(108, 221)(109, 220)(110, 218)(111, 219)(112, 217)(225, 339)(226, 341)(227, 337)(228, 346)(229, 338)(230, 350)(231, 351)(232, 349)(233, 348)(234, 340)(235, 356)(236, 345)(237, 344)(238, 342)(239, 343)(240, 362)(241, 361)(242, 365)(243, 364)(244, 347)(245, 368)(246, 367)(247, 371)(248, 370)(249, 353)(250, 352)(251, 374)(252, 355)(253, 354)(254, 373)(255, 358)(256, 357)(257, 379)(258, 360)(259, 359)(260, 378)(261, 366)(262, 363)(263, 385)(264, 384)(265, 387)(266, 372)(267, 369)(268, 390)(269, 389)(270, 392)(271, 391)(272, 376)(273, 375)(274, 388)(275, 377)(276, 386)(277, 381)(278, 380)(279, 383)(280, 382)(281, 402)(282, 401)(283, 404)(284, 403)(285, 406)(286, 405)(287, 408)(288, 407)(289, 394)(290, 393)(291, 396)(292, 395)(293, 398)(294, 397)(295, 400)(296, 399)(297, 418)(298, 417)(299, 420)(300, 419)(301, 422)(302, 421)(303, 424)(304, 423)(305, 410)(306, 409)(307, 412)(308, 411)(309, 414)(310, 413)(311, 416)(312, 415)(313, 434)(314, 433)(315, 436)(316, 435)(317, 438)(318, 437)(319, 440)(320, 439)(321, 426)(322, 425)(323, 428)(324, 427)(325, 430)(326, 429)(327, 432)(328, 431)(329, 447)(330, 448)(331, 445)(332, 446)(333, 443)(334, 444)(335, 441)(336, 442) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.1242 Transitivity :: VT+ Graph:: bipartite v = 56 e = 224 f = 140 degree seq :: [ 8^56 ] E15.1245 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = D8 x D14 (small group id <112, 31>) Aut = D16 x D14 (small group id <224, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 113, 225, 337, 4, 116, 228, 340, 14, 126, 238, 350, 5, 117, 229, 341)(2, 114, 226, 338, 7, 119, 231, 343, 22, 134, 246, 358, 8, 120, 232, 344)(3, 115, 227, 339, 10, 122, 234, 346, 17, 129, 241, 353, 11, 123, 235, 347)(6, 118, 230, 342, 18, 130, 242, 354, 9, 121, 233, 345, 19, 131, 243, 355)(12, 124, 236, 348, 25, 137, 249, 361, 15, 127, 239, 351, 26, 138, 250, 362)(13, 125, 237, 349, 27, 139, 251, 363, 16, 128, 240, 352, 28, 140, 252, 364)(20, 132, 244, 356, 29, 141, 253, 365, 23, 135, 247, 359, 30, 142, 254, 366)(21, 133, 245, 357, 31, 143, 255, 367, 24, 136, 248, 360, 32, 144, 256, 368)(33, 145, 257, 369, 41, 153, 265, 377, 35, 147, 259, 371, 42, 154, 266, 378)(34, 146, 258, 370, 43, 155, 267, 379, 36, 148, 260, 372, 44, 156, 268, 380)(37, 149, 261, 373, 45, 157, 269, 381, 39, 151, 263, 375, 46, 158, 270, 382)(38, 150, 262, 374, 47, 159, 271, 383, 40, 152, 264, 376, 48, 160, 272, 384)(49, 161, 273, 385, 57, 169, 281, 393, 51, 163, 275, 387, 58, 170, 282, 394)(50, 162, 274, 386, 59, 171, 283, 395, 52, 164, 276, 388, 60, 172, 284, 396)(53, 165, 277, 389, 61, 173, 285, 397, 55, 167, 279, 391, 62, 174, 286, 398)(54, 166, 278, 390, 63, 175, 287, 399, 56, 168, 280, 392, 64, 176, 288, 400)(65, 177, 289, 401, 73, 185, 297, 409, 67, 179, 291, 403, 74, 186, 298, 410)(66, 178, 290, 402, 75, 187, 299, 411, 68, 180, 292, 404, 76, 188, 300, 412)(69, 181, 293, 405, 77, 189, 301, 413, 71, 183, 295, 407, 78, 190, 302, 414)(70, 182, 294, 406, 79, 191, 303, 415, 72, 184, 296, 408, 80, 192, 304, 416)(81, 193, 305, 417, 89, 201, 313, 425, 83, 195, 307, 419, 90, 202, 314, 426)(82, 194, 306, 418, 91, 203, 315, 427, 84, 196, 308, 420, 92, 204, 316, 428)(85, 197, 309, 421, 93, 205, 317, 429, 87, 199, 311, 423, 94, 206, 318, 430)(86, 198, 310, 422, 95, 207, 319, 431, 88, 200, 312, 424, 96, 208, 320, 432)(97, 209, 321, 433, 105, 217, 329, 441, 99, 211, 323, 435, 106, 218, 330, 442)(98, 210, 322, 434, 107, 219, 331, 443, 100, 212, 324, 436, 108, 220, 332, 444)(101, 213, 325, 437, 109, 221, 333, 445, 103, 215, 327, 439, 110, 222, 334, 446)(102, 214, 326, 438, 111, 223, 335, 447, 104, 216, 328, 440, 112, 224, 336, 448) L = (1, 114)(2, 113)(3, 121)(4, 124)(5, 127)(6, 129)(7, 132)(8, 135)(9, 115)(10, 136)(11, 133)(12, 116)(13, 131)(14, 134)(15, 117)(16, 130)(17, 118)(18, 128)(19, 125)(20, 119)(21, 123)(22, 126)(23, 120)(24, 122)(25, 145)(26, 147)(27, 148)(28, 146)(29, 149)(30, 151)(31, 152)(32, 150)(33, 137)(34, 140)(35, 138)(36, 139)(37, 141)(38, 144)(39, 142)(40, 143)(41, 161)(42, 163)(43, 164)(44, 162)(45, 165)(46, 167)(47, 168)(48, 166)(49, 153)(50, 156)(51, 154)(52, 155)(53, 157)(54, 160)(55, 158)(56, 159)(57, 177)(58, 179)(59, 180)(60, 178)(61, 181)(62, 183)(63, 184)(64, 182)(65, 169)(66, 172)(67, 170)(68, 171)(69, 173)(70, 176)(71, 174)(72, 175)(73, 193)(74, 195)(75, 196)(76, 194)(77, 197)(78, 199)(79, 200)(80, 198)(81, 185)(82, 188)(83, 186)(84, 187)(85, 189)(86, 192)(87, 190)(88, 191)(89, 209)(90, 211)(91, 212)(92, 210)(93, 213)(94, 215)(95, 216)(96, 214)(97, 201)(98, 204)(99, 202)(100, 203)(101, 205)(102, 208)(103, 206)(104, 207)(105, 222)(106, 221)(107, 223)(108, 224)(109, 218)(110, 217)(111, 219)(112, 220)(225, 339)(226, 342)(227, 337)(228, 349)(229, 352)(230, 338)(231, 357)(232, 360)(233, 358)(234, 356)(235, 359)(236, 354)(237, 340)(238, 353)(239, 355)(240, 341)(241, 350)(242, 348)(243, 351)(244, 346)(245, 343)(246, 345)(247, 347)(248, 344)(249, 370)(250, 372)(251, 369)(252, 371)(253, 374)(254, 376)(255, 373)(256, 375)(257, 363)(258, 361)(259, 364)(260, 362)(261, 367)(262, 365)(263, 368)(264, 366)(265, 386)(266, 388)(267, 385)(268, 387)(269, 390)(270, 392)(271, 389)(272, 391)(273, 379)(274, 377)(275, 380)(276, 378)(277, 383)(278, 381)(279, 384)(280, 382)(281, 402)(282, 404)(283, 401)(284, 403)(285, 406)(286, 408)(287, 405)(288, 407)(289, 395)(290, 393)(291, 396)(292, 394)(293, 399)(294, 397)(295, 400)(296, 398)(297, 418)(298, 420)(299, 417)(300, 419)(301, 422)(302, 424)(303, 421)(304, 423)(305, 411)(306, 409)(307, 412)(308, 410)(309, 415)(310, 413)(311, 416)(312, 414)(313, 434)(314, 436)(315, 433)(316, 435)(317, 438)(318, 440)(319, 437)(320, 439)(321, 427)(322, 425)(323, 428)(324, 426)(325, 431)(326, 429)(327, 432)(328, 430)(329, 448)(330, 447)(331, 446)(332, 445)(333, 444)(334, 443)(335, 442)(336, 441) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1239 Transitivity :: VT+ Graph:: bipartite v = 28 e = 224 f = 168 degree seq :: [ 16^28 ] E15.1246 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 113, 225, 337, 4, 116, 228, 340, 14, 126, 238, 350, 5, 117, 229, 341)(2, 114, 226, 338, 7, 119, 231, 343, 22, 134, 246, 358, 8, 120, 232, 344)(3, 115, 227, 339, 10, 122, 234, 346, 17, 129, 241, 353, 11, 123, 235, 347)(6, 118, 230, 342, 18, 130, 242, 354, 9, 121, 233, 345, 19, 131, 243, 355)(12, 124, 236, 348, 25, 137, 249, 361, 15, 127, 239, 351, 26, 138, 250, 362)(13, 125, 237, 349, 27, 139, 251, 363, 16, 128, 240, 352, 28, 140, 252, 364)(20, 132, 244, 356, 29, 141, 253, 365, 23, 135, 247, 359, 30, 142, 254, 366)(21, 133, 245, 357, 31, 143, 255, 367, 24, 136, 248, 360, 32, 144, 256, 368)(33, 145, 257, 369, 41, 153, 265, 377, 35, 147, 259, 371, 42, 154, 266, 378)(34, 146, 258, 370, 43, 155, 267, 379, 36, 148, 260, 372, 44, 156, 268, 380)(37, 149, 261, 373, 45, 157, 269, 381, 39, 151, 263, 375, 46, 158, 270, 382)(38, 150, 262, 374, 47, 159, 271, 383, 40, 152, 264, 376, 48, 160, 272, 384)(49, 161, 273, 385, 57, 169, 281, 393, 51, 163, 275, 387, 58, 170, 282, 394)(50, 162, 274, 386, 59, 171, 283, 395, 52, 164, 276, 388, 60, 172, 284, 396)(53, 165, 277, 389, 61, 173, 285, 397, 55, 167, 279, 391, 62, 174, 286, 398)(54, 166, 278, 390, 63, 175, 287, 399, 56, 168, 280, 392, 64, 176, 288, 400)(65, 177, 289, 401, 73, 185, 297, 409, 67, 179, 291, 403, 74, 186, 298, 410)(66, 178, 290, 402, 75, 187, 299, 411, 68, 180, 292, 404, 76, 188, 300, 412)(69, 181, 293, 405, 77, 189, 301, 413, 71, 183, 295, 407, 78, 190, 302, 414)(70, 182, 294, 406, 79, 191, 303, 415, 72, 184, 296, 408, 80, 192, 304, 416)(81, 193, 305, 417, 89, 201, 313, 425, 83, 195, 307, 419, 90, 202, 314, 426)(82, 194, 306, 418, 91, 203, 315, 427, 84, 196, 308, 420, 92, 204, 316, 428)(85, 197, 309, 421, 93, 205, 317, 429, 87, 199, 311, 423, 94, 206, 318, 430)(86, 198, 310, 422, 95, 207, 319, 431, 88, 200, 312, 424, 96, 208, 320, 432)(97, 209, 321, 433, 105, 217, 329, 441, 99, 211, 323, 435, 106, 218, 330, 442)(98, 210, 322, 434, 107, 219, 331, 443, 100, 212, 324, 436, 108, 220, 332, 444)(101, 213, 325, 437, 109, 221, 333, 445, 103, 215, 327, 439, 110, 222, 334, 446)(102, 214, 326, 438, 111, 223, 335, 447, 104, 216, 328, 440, 112, 224, 336, 448) L = (1, 114)(2, 113)(3, 121)(4, 124)(5, 127)(6, 129)(7, 132)(8, 135)(9, 115)(10, 136)(11, 133)(12, 116)(13, 131)(14, 134)(15, 117)(16, 130)(17, 118)(18, 128)(19, 125)(20, 119)(21, 123)(22, 126)(23, 120)(24, 122)(25, 145)(26, 147)(27, 148)(28, 146)(29, 149)(30, 151)(31, 152)(32, 150)(33, 137)(34, 140)(35, 138)(36, 139)(37, 141)(38, 144)(39, 142)(40, 143)(41, 161)(42, 163)(43, 164)(44, 162)(45, 165)(46, 167)(47, 168)(48, 166)(49, 153)(50, 156)(51, 154)(52, 155)(53, 157)(54, 160)(55, 158)(56, 159)(57, 177)(58, 179)(59, 180)(60, 178)(61, 181)(62, 183)(63, 184)(64, 182)(65, 169)(66, 172)(67, 170)(68, 171)(69, 173)(70, 176)(71, 174)(72, 175)(73, 193)(74, 195)(75, 196)(76, 194)(77, 197)(78, 199)(79, 200)(80, 198)(81, 185)(82, 188)(83, 186)(84, 187)(85, 189)(86, 192)(87, 190)(88, 191)(89, 209)(90, 211)(91, 212)(92, 210)(93, 213)(94, 215)(95, 216)(96, 214)(97, 201)(98, 204)(99, 202)(100, 203)(101, 205)(102, 208)(103, 206)(104, 207)(105, 221)(106, 222)(107, 224)(108, 223)(109, 217)(110, 218)(111, 220)(112, 219)(225, 339)(226, 342)(227, 337)(228, 349)(229, 352)(230, 338)(231, 357)(232, 360)(233, 358)(234, 356)(235, 359)(236, 354)(237, 340)(238, 353)(239, 355)(240, 341)(241, 350)(242, 348)(243, 351)(244, 346)(245, 343)(246, 345)(247, 347)(248, 344)(249, 370)(250, 372)(251, 369)(252, 371)(253, 374)(254, 376)(255, 373)(256, 375)(257, 363)(258, 361)(259, 364)(260, 362)(261, 367)(262, 365)(263, 368)(264, 366)(265, 386)(266, 388)(267, 385)(268, 387)(269, 390)(270, 392)(271, 389)(272, 391)(273, 379)(274, 377)(275, 380)(276, 378)(277, 383)(278, 381)(279, 384)(280, 382)(281, 402)(282, 404)(283, 401)(284, 403)(285, 406)(286, 408)(287, 405)(288, 407)(289, 395)(290, 393)(291, 396)(292, 394)(293, 399)(294, 397)(295, 400)(296, 398)(297, 418)(298, 420)(299, 417)(300, 419)(301, 422)(302, 424)(303, 421)(304, 423)(305, 411)(306, 409)(307, 412)(308, 410)(309, 415)(310, 413)(311, 416)(312, 414)(313, 434)(314, 436)(315, 433)(316, 435)(317, 438)(318, 440)(319, 437)(320, 439)(321, 427)(322, 425)(323, 428)(324, 426)(325, 431)(326, 429)(327, 432)(328, 430)(329, 447)(330, 448)(331, 445)(332, 446)(333, 443)(334, 444)(335, 441)(336, 442) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1240 Transitivity :: VT+ Graph:: bipartite v = 28 e = 224 f = 168 degree seq :: [ 16^28 ] E15.1247 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D14 (small group id <112, 31>) Aut = C2 x D8 x D14 (small group id <224, 178>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^4, (Y3 * Y1 * Y2 * Y1)^2, (Y2 * Y1)^14 ] Map:: polytopal non-degenerate R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 10, 122)(6, 118, 12, 124)(8, 120, 15, 127)(11, 123, 20, 132)(13, 125, 23, 135)(14, 126, 21, 133)(16, 128, 19, 131)(17, 129, 22, 134)(18, 130, 28, 140)(24, 136, 35, 147)(25, 137, 34, 146)(26, 138, 32, 144)(27, 139, 31, 143)(29, 141, 39, 151)(30, 142, 38, 150)(33, 145, 41, 153)(36, 148, 44, 156)(37, 149, 45, 157)(40, 152, 48, 160)(42, 154, 51, 163)(43, 155, 50, 162)(46, 158, 55, 167)(47, 159, 54, 166)(49, 161, 57, 169)(52, 164, 60, 172)(53, 165, 61, 173)(56, 168, 64, 176)(58, 170, 67, 179)(59, 171, 66, 178)(62, 174, 71, 183)(63, 175, 70, 182)(65, 177, 73, 185)(68, 180, 76, 188)(69, 181, 77, 189)(72, 184, 80, 192)(74, 186, 83, 195)(75, 187, 82, 194)(78, 190, 87, 199)(79, 191, 86, 198)(81, 193, 89, 201)(84, 196, 92, 204)(85, 197, 93, 205)(88, 200, 96, 208)(90, 202, 99, 211)(91, 203, 98, 210)(94, 206, 103, 215)(95, 207, 102, 214)(97, 209, 101, 213)(100, 212, 107, 219)(104, 216, 110, 222)(105, 217, 109, 221)(106, 218, 108, 220)(111, 223, 112, 224)(225, 337, 227, 339)(226, 338, 229, 341)(228, 340, 232, 344)(230, 342, 235, 347)(231, 343, 237, 349)(233, 345, 240, 352)(234, 346, 242, 354)(236, 348, 245, 357)(238, 350, 248, 360)(239, 351, 249, 361)(241, 353, 251, 363)(243, 355, 253, 365)(244, 356, 254, 366)(246, 358, 256, 368)(247, 359, 257, 369)(250, 362, 260, 372)(252, 364, 261, 373)(255, 367, 264, 376)(258, 370, 266, 378)(259, 371, 267, 379)(262, 374, 270, 382)(263, 375, 271, 383)(265, 377, 273, 385)(268, 380, 276, 388)(269, 381, 277, 389)(272, 384, 280, 392)(274, 386, 282, 394)(275, 387, 283, 395)(278, 390, 286, 398)(279, 391, 287, 399)(281, 393, 289, 401)(284, 396, 292, 404)(285, 397, 293, 405)(288, 400, 296, 408)(290, 402, 298, 410)(291, 403, 299, 411)(294, 406, 302, 414)(295, 407, 303, 415)(297, 409, 305, 417)(300, 412, 308, 420)(301, 413, 309, 421)(304, 416, 312, 424)(306, 418, 314, 426)(307, 419, 315, 427)(310, 422, 318, 430)(311, 423, 319, 431)(313, 425, 321, 433)(316, 428, 324, 436)(317, 429, 325, 437)(320, 432, 328, 440)(322, 434, 329, 441)(323, 435, 330, 442)(326, 438, 332, 444)(327, 439, 333, 445)(331, 443, 335, 447)(334, 446, 336, 448) L = (1, 228)(2, 230)(3, 232)(4, 225)(5, 235)(6, 226)(7, 238)(8, 227)(9, 241)(10, 243)(11, 229)(12, 246)(13, 248)(14, 231)(15, 250)(16, 251)(17, 233)(18, 253)(19, 234)(20, 255)(21, 256)(22, 236)(23, 258)(24, 237)(25, 260)(26, 239)(27, 240)(28, 262)(29, 242)(30, 264)(31, 244)(32, 245)(33, 266)(34, 247)(35, 268)(36, 249)(37, 270)(38, 252)(39, 272)(40, 254)(41, 274)(42, 257)(43, 276)(44, 259)(45, 278)(46, 261)(47, 280)(48, 263)(49, 282)(50, 265)(51, 284)(52, 267)(53, 286)(54, 269)(55, 288)(56, 271)(57, 290)(58, 273)(59, 292)(60, 275)(61, 294)(62, 277)(63, 296)(64, 279)(65, 298)(66, 281)(67, 300)(68, 283)(69, 302)(70, 285)(71, 304)(72, 287)(73, 306)(74, 289)(75, 308)(76, 291)(77, 310)(78, 293)(79, 312)(80, 295)(81, 314)(82, 297)(83, 316)(84, 299)(85, 318)(86, 301)(87, 320)(88, 303)(89, 322)(90, 305)(91, 324)(92, 307)(93, 326)(94, 309)(95, 328)(96, 311)(97, 329)(98, 313)(99, 331)(100, 315)(101, 332)(102, 317)(103, 334)(104, 319)(105, 321)(106, 335)(107, 323)(108, 325)(109, 336)(110, 327)(111, 330)(112, 333)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1252 Graph:: simple bipartite v = 112 e = 224 f = 84 degree seq :: [ 4^112 ] E15.1248 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D14 (small group id <112, 31>) Aut = C2 x D8 x D14 (small group id <224, 178>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * 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, Y3^14, Y3^-6 * Y2 * Y3^2 * Y1 * Y3^-4 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 113, 2, 114)(3, 115, 9, 121)(4, 116, 12, 124)(5, 117, 14, 126)(6, 118, 16, 128)(7, 119, 19, 131)(8, 120, 21, 133)(10, 122, 24, 136)(11, 123, 26, 138)(13, 125, 22, 134)(15, 127, 20, 132)(17, 129, 34, 146)(18, 130, 36, 148)(23, 135, 37, 149)(25, 137, 43, 155)(27, 139, 33, 145)(28, 140, 38, 150)(29, 141, 41, 153)(30, 142, 50, 162)(31, 143, 39, 151)(32, 144, 44, 156)(35, 147, 53, 165)(40, 152, 60, 172)(42, 154, 54, 166)(45, 157, 58, 170)(46, 158, 59, 171)(47, 159, 65, 177)(48, 160, 55, 167)(49, 161, 56, 168)(51, 163, 62, 174)(52, 164, 61, 173)(57, 169, 73, 185)(63, 175, 75, 187)(64, 176, 76, 188)(66, 178, 79, 191)(67, 179, 71, 183)(68, 180, 72, 184)(69, 181, 84, 196)(70, 182, 80, 192)(74, 186, 87, 199)(77, 189, 92, 204)(78, 190, 88, 200)(81, 193, 91, 203)(82, 194, 97, 209)(83, 195, 89, 201)(85, 197, 94, 206)(86, 198, 93, 205)(90, 202, 104, 216)(95, 207, 106, 218)(96, 208, 107, 219)(98, 210, 105, 217)(99, 211, 102, 214)(100, 212, 103, 215)(101, 213, 109, 221)(108, 220, 111, 223)(110, 222, 112, 224)(225, 337, 227, 339)(226, 338, 230, 342)(228, 340, 235, 347)(229, 341, 234, 346)(231, 343, 242, 354)(232, 344, 241, 353)(233, 345, 244, 356)(236, 348, 251, 363)(237, 349, 240, 352)(238, 350, 250, 362)(239, 351, 249, 361)(243, 355, 261, 373)(245, 357, 260, 372)(246, 358, 259, 371)(247, 359, 264, 376)(248, 360, 268, 380)(252, 364, 272, 384)(253, 365, 273, 385)(254, 366, 257, 369)(255, 367, 269, 381)(256, 368, 271, 383)(258, 370, 278, 390)(262, 374, 282, 394)(263, 375, 283, 395)(265, 377, 279, 391)(266, 378, 281, 393)(267, 379, 285, 397)(270, 382, 288, 400)(274, 386, 291, 403)(275, 387, 277, 389)(276, 388, 290, 402)(280, 392, 296, 408)(284, 396, 299, 411)(286, 398, 298, 410)(287, 399, 301, 413)(289, 401, 304, 416)(292, 404, 307, 419)(293, 405, 295, 407)(294, 406, 306, 418)(297, 409, 312, 424)(300, 412, 315, 427)(302, 414, 314, 426)(303, 415, 317, 429)(305, 417, 320, 432)(308, 420, 323, 435)(309, 421, 311, 423)(310, 422, 322, 434)(313, 425, 327, 439)(316, 428, 330, 442)(318, 430, 329, 441)(319, 431, 332, 444)(321, 433, 333, 445)(324, 436, 334, 446)(325, 437, 326, 438)(328, 440, 335, 447)(331, 443, 336, 448) L = (1, 228)(2, 231)(3, 234)(4, 237)(5, 225)(6, 241)(7, 244)(8, 226)(9, 242)(10, 249)(11, 227)(12, 252)(13, 254)(14, 255)(15, 229)(16, 235)(17, 259)(18, 230)(19, 262)(20, 264)(21, 265)(22, 232)(23, 233)(24, 269)(25, 271)(26, 272)(27, 273)(28, 238)(29, 236)(30, 275)(31, 268)(32, 239)(33, 240)(34, 279)(35, 281)(36, 282)(37, 283)(38, 245)(39, 243)(40, 285)(41, 278)(42, 246)(43, 247)(44, 288)(45, 250)(46, 248)(47, 290)(48, 251)(49, 291)(50, 253)(51, 293)(52, 256)(53, 257)(54, 296)(55, 260)(56, 258)(57, 298)(58, 261)(59, 299)(60, 263)(61, 301)(62, 266)(63, 267)(64, 304)(65, 270)(66, 306)(67, 307)(68, 274)(69, 309)(70, 276)(71, 277)(72, 312)(73, 280)(74, 314)(75, 315)(76, 284)(77, 317)(78, 286)(79, 287)(80, 320)(81, 289)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 327)(89, 297)(90, 329)(91, 330)(92, 300)(93, 332)(94, 302)(95, 303)(96, 333)(97, 305)(98, 326)(99, 334)(100, 308)(101, 310)(102, 311)(103, 335)(104, 313)(105, 319)(106, 336)(107, 316)(108, 318)(109, 324)(110, 321)(111, 331)(112, 328)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1253 Graph:: simple bipartite v = 112 e = 224 f = 84 degree seq :: [ 4^112 ] E15.1249 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D14 (small group id <112, 31>) Aut = C2 x D8 x D14 (small group id <224, 178>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (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 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 10, 122)(6, 118, 12, 124)(8, 120, 15, 127)(11, 123, 20, 132)(13, 125, 23, 135)(14, 126, 21, 133)(16, 128, 19, 131)(17, 129, 22, 134)(18, 130, 28, 140)(24, 136, 35, 147)(25, 137, 34, 146)(26, 138, 32, 144)(27, 139, 31, 143)(29, 141, 39, 151)(30, 142, 38, 150)(33, 145, 41, 153)(36, 148, 44, 156)(37, 149, 45, 157)(40, 152, 48, 160)(42, 154, 51, 163)(43, 155, 50, 162)(46, 158, 55, 167)(47, 159, 54, 166)(49, 161, 57, 169)(52, 164, 60, 172)(53, 165, 61, 173)(56, 168, 64, 176)(58, 170, 67, 179)(59, 171, 66, 178)(62, 174, 71, 183)(63, 175, 70, 182)(65, 177, 73, 185)(68, 180, 76, 188)(69, 181, 77, 189)(72, 184, 80, 192)(74, 186, 83, 195)(75, 187, 82, 194)(78, 190, 87, 199)(79, 191, 86, 198)(81, 193, 89, 201)(84, 196, 92, 204)(85, 197, 93, 205)(88, 200, 96, 208)(90, 202, 99, 211)(91, 203, 98, 210)(94, 206, 103, 215)(95, 207, 102, 214)(97, 209, 105, 217)(100, 212, 108, 220)(101, 213, 109, 221)(104, 216, 112, 224)(106, 218, 110, 222)(107, 219, 111, 223)(225, 337, 227, 339)(226, 338, 229, 341)(228, 340, 232, 344)(230, 342, 235, 347)(231, 343, 237, 349)(233, 345, 240, 352)(234, 346, 242, 354)(236, 348, 245, 357)(238, 350, 248, 360)(239, 351, 249, 361)(241, 353, 251, 363)(243, 355, 253, 365)(244, 356, 254, 366)(246, 358, 256, 368)(247, 359, 257, 369)(250, 362, 260, 372)(252, 364, 261, 373)(255, 367, 264, 376)(258, 370, 266, 378)(259, 371, 267, 379)(262, 374, 270, 382)(263, 375, 271, 383)(265, 377, 273, 385)(268, 380, 276, 388)(269, 381, 277, 389)(272, 384, 280, 392)(274, 386, 282, 394)(275, 387, 283, 395)(278, 390, 286, 398)(279, 391, 287, 399)(281, 393, 289, 401)(284, 396, 292, 404)(285, 397, 293, 405)(288, 400, 296, 408)(290, 402, 298, 410)(291, 403, 299, 411)(294, 406, 302, 414)(295, 407, 303, 415)(297, 409, 305, 417)(300, 412, 308, 420)(301, 413, 309, 421)(304, 416, 312, 424)(306, 418, 314, 426)(307, 419, 315, 427)(310, 422, 318, 430)(311, 423, 319, 431)(313, 425, 321, 433)(316, 428, 324, 436)(317, 429, 325, 437)(320, 432, 328, 440)(322, 434, 330, 442)(323, 435, 331, 443)(326, 438, 334, 446)(327, 439, 335, 447)(329, 441, 336, 448)(332, 444, 333, 445) L = (1, 228)(2, 230)(3, 232)(4, 225)(5, 235)(6, 226)(7, 238)(8, 227)(9, 241)(10, 243)(11, 229)(12, 246)(13, 248)(14, 231)(15, 250)(16, 251)(17, 233)(18, 253)(19, 234)(20, 255)(21, 256)(22, 236)(23, 258)(24, 237)(25, 260)(26, 239)(27, 240)(28, 262)(29, 242)(30, 264)(31, 244)(32, 245)(33, 266)(34, 247)(35, 268)(36, 249)(37, 270)(38, 252)(39, 272)(40, 254)(41, 274)(42, 257)(43, 276)(44, 259)(45, 278)(46, 261)(47, 280)(48, 263)(49, 282)(50, 265)(51, 284)(52, 267)(53, 286)(54, 269)(55, 288)(56, 271)(57, 290)(58, 273)(59, 292)(60, 275)(61, 294)(62, 277)(63, 296)(64, 279)(65, 298)(66, 281)(67, 300)(68, 283)(69, 302)(70, 285)(71, 304)(72, 287)(73, 306)(74, 289)(75, 308)(76, 291)(77, 310)(78, 293)(79, 312)(80, 295)(81, 314)(82, 297)(83, 316)(84, 299)(85, 318)(86, 301)(87, 320)(88, 303)(89, 322)(90, 305)(91, 324)(92, 307)(93, 326)(94, 309)(95, 328)(96, 311)(97, 330)(98, 313)(99, 332)(100, 315)(101, 334)(102, 317)(103, 336)(104, 319)(105, 335)(106, 321)(107, 333)(108, 323)(109, 331)(110, 325)(111, 329)(112, 327)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1251 Graph:: simple bipartite v = 112 e = 224 f = 84 degree seq :: [ 4^112 ] E15.1250 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 185>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, 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 ] Map:: polytopal non-degenerate R = (1, 113, 2, 114)(3, 115, 9, 121)(4, 116, 7, 119)(5, 117, 8, 120)(6, 118, 13, 125)(10, 122, 18, 130)(11, 123, 19, 131)(12, 124, 16, 128)(14, 126, 22, 134)(15, 127, 23, 135)(17, 129, 25, 137)(20, 132, 28, 140)(21, 133, 29, 141)(24, 136, 32, 144)(26, 138, 34, 146)(27, 139, 35, 147)(30, 142, 38, 150)(31, 143, 39, 151)(33, 145, 41, 153)(36, 148, 44, 156)(37, 149, 45, 157)(40, 152, 48, 160)(42, 154, 50, 162)(43, 155, 51, 163)(46, 158, 54, 166)(47, 159, 55, 167)(49, 161, 57, 169)(52, 164, 60, 172)(53, 165, 61, 173)(56, 168, 64, 176)(58, 170, 66, 178)(59, 171, 67, 179)(62, 174, 70, 182)(63, 175, 71, 183)(65, 177, 73, 185)(68, 180, 76, 188)(69, 181, 77, 189)(72, 184, 80, 192)(74, 186, 82, 194)(75, 187, 83, 195)(78, 190, 86, 198)(79, 191, 87, 199)(81, 193, 89, 201)(84, 196, 92, 204)(85, 197, 93, 205)(88, 200, 96, 208)(90, 202, 98, 210)(91, 203, 99, 211)(94, 206, 102, 214)(95, 207, 103, 215)(97, 209, 105, 217)(100, 212, 108, 220)(101, 213, 109, 221)(104, 216, 112, 224)(106, 218, 111, 223)(107, 219, 110, 222)(225, 337, 227, 339)(226, 338, 230, 342)(228, 340, 235, 347)(229, 341, 234, 346)(231, 343, 239, 351)(232, 344, 238, 350)(233, 345, 241, 353)(236, 348, 244, 356)(237, 349, 245, 357)(240, 352, 248, 360)(242, 354, 251, 363)(243, 355, 250, 362)(246, 358, 255, 367)(247, 359, 254, 366)(249, 361, 257, 369)(252, 364, 260, 372)(253, 365, 261, 373)(256, 368, 264, 376)(258, 370, 267, 379)(259, 371, 266, 378)(262, 374, 271, 383)(263, 375, 270, 382)(265, 377, 273, 385)(268, 380, 276, 388)(269, 381, 277, 389)(272, 384, 280, 392)(274, 386, 283, 395)(275, 387, 282, 394)(278, 390, 287, 399)(279, 391, 286, 398)(281, 393, 289, 401)(284, 396, 292, 404)(285, 397, 293, 405)(288, 400, 296, 408)(290, 402, 299, 411)(291, 403, 298, 410)(294, 406, 303, 415)(295, 407, 302, 414)(297, 409, 305, 417)(300, 412, 308, 420)(301, 413, 309, 421)(304, 416, 312, 424)(306, 418, 315, 427)(307, 419, 314, 426)(310, 422, 319, 431)(311, 423, 318, 430)(313, 425, 321, 433)(316, 428, 324, 436)(317, 429, 325, 437)(320, 432, 328, 440)(322, 434, 331, 443)(323, 435, 330, 442)(326, 438, 335, 447)(327, 439, 334, 446)(329, 441, 336, 448)(332, 444, 333, 445) L = (1, 228)(2, 231)(3, 234)(4, 236)(5, 225)(6, 238)(7, 240)(8, 226)(9, 242)(10, 244)(11, 227)(12, 229)(13, 246)(14, 248)(15, 230)(16, 232)(17, 250)(18, 252)(19, 233)(20, 235)(21, 254)(22, 256)(23, 237)(24, 239)(25, 258)(26, 260)(27, 241)(28, 243)(29, 262)(30, 264)(31, 245)(32, 247)(33, 266)(34, 268)(35, 249)(36, 251)(37, 270)(38, 272)(39, 253)(40, 255)(41, 274)(42, 276)(43, 257)(44, 259)(45, 278)(46, 280)(47, 261)(48, 263)(49, 282)(50, 284)(51, 265)(52, 267)(53, 286)(54, 288)(55, 269)(56, 271)(57, 290)(58, 292)(59, 273)(60, 275)(61, 294)(62, 296)(63, 277)(64, 279)(65, 298)(66, 300)(67, 281)(68, 283)(69, 302)(70, 304)(71, 285)(72, 287)(73, 306)(74, 308)(75, 289)(76, 291)(77, 310)(78, 312)(79, 293)(80, 295)(81, 314)(82, 316)(83, 297)(84, 299)(85, 318)(86, 320)(87, 301)(88, 303)(89, 322)(90, 324)(91, 305)(92, 307)(93, 326)(94, 328)(95, 309)(96, 311)(97, 330)(98, 332)(99, 313)(100, 315)(101, 334)(102, 336)(103, 317)(104, 319)(105, 335)(106, 333)(107, 321)(108, 323)(109, 331)(110, 329)(111, 325)(112, 327)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1254 Graph:: simple bipartite v = 112 e = 224 f = 84 degree seq :: [ 4^112 ] E15.1251 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D14 (small group id <112, 31>) Aut = C2 x D8 x D14 (small group id <224, 178>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y1^4, (Y3 * Y2)^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^-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, 113, 2, 114, 6, 118, 5, 117)(3, 115, 9, 121, 14, 126, 11, 123)(4, 116, 12, 124, 15, 127, 8, 120)(7, 119, 16, 128, 13, 125, 18, 130)(10, 122, 21, 133, 24, 136, 20, 132)(17, 129, 27, 139, 23, 135, 26, 138)(19, 131, 29, 141, 22, 134, 31, 143)(25, 137, 33, 145, 28, 140, 35, 147)(30, 142, 39, 151, 32, 144, 38, 150)(34, 146, 43, 155, 36, 148, 42, 154)(37, 149, 45, 157, 40, 152, 47, 159)(41, 153, 49, 161, 44, 156, 51, 163)(46, 158, 55, 167, 48, 160, 54, 166)(50, 162, 59, 171, 52, 164, 58, 170)(53, 165, 61, 173, 56, 168, 63, 175)(57, 169, 65, 177, 60, 172, 67, 179)(62, 174, 71, 183, 64, 176, 70, 182)(66, 178, 75, 187, 68, 180, 74, 186)(69, 181, 77, 189, 72, 184, 79, 191)(73, 185, 81, 193, 76, 188, 83, 195)(78, 190, 87, 199, 80, 192, 86, 198)(82, 194, 91, 203, 84, 196, 90, 202)(85, 197, 93, 205, 88, 200, 95, 207)(89, 201, 97, 209, 92, 204, 99, 211)(94, 206, 103, 215, 96, 208, 102, 214)(98, 210, 107, 219, 100, 212, 106, 218)(101, 213, 105, 217, 104, 216, 108, 220)(109, 221, 112, 224, 110, 222, 111, 223)(225, 337, 227, 339)(226, 338, 231, 343)(228, 340, 234, 346)(229, 341, 237, 349)(230, 342, 238, 350)(232, 344, 241, 353)(233, 345, 243, 355)(235, 347, 246, 358)(236, 348, 247, 359)(239, 351, 248, 360)(240, 352, 249, 361)(242, 354, 252, 364)(244, 356, 254, 366)(245, 357, 256, 368)(250, 362, 258, 370)(251, 363, 260, 372)(253, 365, 261, 373)(255, 367, 264, 376)(257, 369, 265, 377)(259, 371, 268, 380)(262, 374, 270, 382)(263, 375, 272, 384)(266, 378, 274, 386)(267, 379, 276, 388)(269, 381, 277, 389)(271, 383, 280, 392)(273, 385, 281, 393)(275, 387, 284, 396)(278, 390, 286, 398)(279, 391, 288, 400)(282, 394, 290, 402)(283, 395, 292, 404)(285, 397, 293, 405)(287, 399, 296, 408)(289, 401, 297, 409)(291, 403, 300, 412)(294, 406, 302, 414)(295, 407, 304, 416)(298, 410, 306, 418)(299, 411, 308, 420)(301, 413, 309, 421)(303, 415, 312, 424)(305, 417, 313, 425)(307, 419, 316, 428)(310, 422, 318, 430)(311, 423, 320, 432)(314, 426, 322, 434)(315, 427, 324, 436)(317, 429, 325, 437)(319, 431, 328, 440)(321, 433, 329, 441)(323, 435, 332, 444)(326, 438, 333, 445)(327, 439, 334, 446)(330, 442, 335, 447)(331, 443, 336, 448) L = (1, 228)(2, 232)(3, 234)(4, 225)(5, 236)(6, 239)(7, 241)(8, 226)(9, 244)(10, 227)(11, 245)(12, 229)(13, 247)(14, 248)(15, 230)(16, 250)(17, 231)(18, 251)(19, 254)(20, 233)(21, 235)(22, 256)(23, 237)(24, 238)(25, 258)(26, 240)(27, 242)(28, 260)(29, 262)(30, 243)(31, 263)(32, 246)(33, 266)(34, 249)(35, 267)(36, 252)(37, 270)(38, 253)(39, 255)(40, 272)(41, 274)(42, 257)(43, 259)(44, 276)(45, 278)(46, 261)(47, 279)(48, 264)(49, 282)(50, 265)(51, 283)(52, 268)(53, 286)(54, 269)(55, 271)(56, 288)(57, 290)(58, 273)(59, 275)(60, 292)(61, 294)(62, 277)(63, 295)(64, 280)(65, 298)(66, 281)(67, 299)(68, 284)(69, 302)(70, 285)(71, 287)(72, 304)(73, 306)(74, 289)(75, 291)(76, 308)(77, 310)(78, 293)(79, 311)(80, 296)(81, 314)(82, 297)(83, 315)(84, 300)(85, 318)(86, 301)(87, 303)(88, 320)(89, 322)(90, 305)(91, 307)(92, 324)(93, 326)(94, 309)(95, 327)(96, 312)(97, 330)(98, 313)(99, 331)(100, 316)(101, 333)(102, 317)(103, 319)(104, 334)(105, 335)(106, 321)(107, 323)(108, 336)(109, 325)(110, 328)(111, 329)(112, 332)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.1249 Graph:: simple bipartite v = 84 e = 224 f = 112 degree seq :: [ 4^56, 8^28 ] E15.1252 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D14 (small group id <112, 31>) Aut = C2 x D8 x D14 (small group id <224, 178>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1^-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^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 113, 2, 114, 6, 118, 5, 117)(3, 115, 9, 121, 14, 126, 11, 123)(4, 116, 12, 124, 15, 127, 8, 120)(7, 119, 16, 128, 13, 125, 18, 130)(10, 122, 21, 133, 24, 136, 20, 132)(17, 129, 27, 139, 23, 135, 26, 138)(19, 131, 29, 141, 22, 134, 31, 143)(25, 137, 33, 145, 28, 140, 35, 147)(30, 142, 39, 151, 32, 144, 38, 150)(34, 146, 43, 155, 36, 148, 42, 154)(37, 149, 45, 157, 40, 152, 47, 159)(41, 153, 49, 161, 44, 156, 51, 163)(46, 158, 55, 167, 48, 160, 54, 166)(50, 162, 59, 171, 52, 164, 58, 170)(53, 165, 61, 173, 56, 168, 63, 175)(57, 169, 65, 177, 60, 172, 67, 179)(62, 174, 71, 183, 64, 176, 70, 182)(66, 178, 75, 187, 68, 180, 74, 186)(69, 181, 77, 189, 72, 184, 79, 191)(73, 185, 81, 193, 76, 188, 83, 195)(78, 190, 87, 199, 80, 192, 86, 198)(82, 194, 91, 203, 84, 196, 90, 202)(85, 197, 93, 205, 88, 200, 95, 207)(89, 201, 97, 209, 92, 204, 99, 211)(94, 206, 103, 215, 96, 208, 102, 214)(98, 210, 107, 219, 100, 212, 106, 218)(101, 213, 108, 220, 104, 216, 105, 217)(109, 221, 111, 223, 110, 222, 112, 224)(225, 337, 227, 339)(226, 338, 231, 343)(228, 340, 234, 346)(229, 341, 237, 349)(230, 342, 238, 350)(232, 344, 241, 353)(233, 345, 243, 355)(235, 347, 246, 358)(236, 348, 247, 359)(239, 351, 248, 360)(240, 352, 249, 361)(242, 354, 252, 364)(244, 356, 254, 366)(245, 357, 256, 368)(250, 362, 258, 370)(251, 363, 260, 372)(253, 365, 261, 373)(255, 367, 264, 376)(257, 369, 265, 377)(259, 371, 268, 380)(262, 374, 270, 382)(263, 375, 272, 384)(266, 378, 274, 386)(267, 379, 276, 388)(269, 381, 277, 389)(271, 383, 280, 392)(273, 385, 281, 393)(275, 387, 284, 396)(278, 390, 286, 398)(279, 391, 288, 400)(282, 394, 290, 402)(283, 395, 292, 404)(285, 397, 293, 405)(287, 399, 296, 408)(289, 401, 297, 409)(291, 403, 300, 412)(294, 406, 302, 414)(295, 407, 304, 416)(298, 410, 306, 418)(299, 411, 308, 420)(301, 413, 309, 421)(303, 415, 312, 424)(305, 417, 313, 425)(307, 419, 316, 428)(310, 422, 318, 430)(311, 423, 320, 432)(314, 426, 322, 434)(315, 427, 324, 436)(317, 429, 325, 437)(319, 431, 328, 440)(321, 433, 329, 441)(323, 435, 332, 444)(326, 438, 333, 445)(327, 439, 334, 446)(330, 442, 335, 447)(331, 443, 336, 448) L = (1, 228)(2, 232)(3, 234)(4, 225)(5, 236)(6, 239)(7, 241)(8, 226)(9, 244)(10, 227)(11, 245)(12, 229)(13, 247)(14, 248)(15, 230)(16, 250)(17, 231)(18, 251)(19, 254)(20, 233)(21, 235)(22, 256)(23, 237)(24, 238)(25, 258)(26, 240)(27, 242)(28, 260)(29, 262)(30, 243)(31, 263)(32, 246)(33, 266)(34, 249)(35, 267)(36, 252)(37, 270)(38, 253)(39, 255)(40, 272)(41, 274)(42, 257)(43, 259)(44, 276)(45, 278)(46, 261)(47, 279)(48, 264)(49, 282)(50, 265)(51, 283)(52, 268)(53, 286)(54, 269)(55, 271)(56, 288)(57, 290)(58, 273)(59, 275)(60, 292)(61, 294)(62, 277)(63, 295)(64, 280)(65, 298)(66, 281)(67, 299)(68, 284)(69, 302)(70, 285)(71, 287)(72, 304)(73, 306)(74, 289)(75, 291)(76, 308)(77, 310)(78, 293)(79, 311)(80, 296)(81, 314)(82, 297)(83, 315)(84, 300)(85, 318)(86, 301)(87, 303)(88, 320)(89, 322)(90, 305)(91, 307)(92, 324)(93, 326)(94, 309)(95, 327)(96, 312)(97, 330)(98, 313)(99, 331)(100, 316)(101, 333)(102, 317)(103, 319)(104, 334)(105, 335)(106, 321)(107, 323)(108, 336)(109, 325)(110, 328)(111, 329)(112, 332)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.1247 Graph:: simple bipartite v = 84 e = 224 f = 112 degree seq :: [ 4^56, 8^28 ] E15.1253 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D14 (small group id <112, 31>) Aut = C2 x D8 x D14 (small group id <224, 178>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, Y1^4, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 113, 2, 114, 7, 119, 5, 117)(3, 115, 11, 123, 16, 128, 13, 125)(4, 116, 9, 121, 6, 118, 10, 122)(8, 120, 17, 129, 15, 127, 19, 131)(12, 124, 22, 134, 14, 126, 23, 135)(18, 130, 26, 138, 20, 132, 27, 139)(21, 133, 29, 141, 24, 136, 31, 143)(25, 137, 33, 145, 28, 140, 35, 147)(30, 142, 38, 150, 32, 144, 39, 151)(34, 146, 42, 154, 36, 148, 43, 155)(37, 149, 45, 157, 40, 152, 47, 159)(41, 153, 49, 161, 44, 156, 51, 163)(46, 158, 54, 166, 48, 160, 55, 167)(50, 162, 58, 170, 52, 164, 59, 171)(53, 165, 61, 173, 56, 168, 63, 175)(57, 169, 65, 177, 60, 172, 67, 179)(62, 174, 70, 182, 64, 176, 71, 183)(66, 178, 74, 186, 68, 180, 75, 187)(69, 181, 77, 189, 72, 184, 79, 191)(73, 185, 81, 193, 76, 188, 83, 195)(78, 190, 86, 198, 80, 192, 87, 199)(82, 194, 90, 202, 84, 196, 91, 203)(85, 197, 93, 205, 88, 200, 95, 207)(89, 201, 97, 209, 92, 204, 99, 211)(94, 206, 102, 214, 96, 208, 103, 215)(98, 210, 106, 218, 100, 212, 107, 219)(101, 213, 108, 220, 104, 216, 105, 217)(109, 221, 112, 224, 110, 222, 111, 223)(225, 337, 227, 339)(226, 338, 232, 344)(228, 340, 238, 350)(229, 341, 239, 351)(230, 342, 236, 348)(231, 343, 240, 352)(233, 345, 244, 356)(234, 346, 242, 354)(235, 347, 245, 357)(237, 349, 248, 360)(241, 353, 249, 361)(243, 355, 252, 364)(246, 358, 256, 368)(247, 359, 254, 366)(250, 362, 260, 372)(251, 363, 258, 370)(253, 365, 261, 373)(255, 367, 264, 376)(257, 369, 265, 377)(259, 371, 268, 380)(262, 374, 272, 384)(263, 375, 270, 382)(266, 378, 276, 388)(267, 379, 274, 386)(269, 381, 277, 389)(271, 383, 280, 392)(273, 385, 281, 393)(275, 387, 284, 396)(278, 390, 288, 400)(279, 391, 286, 398)(282, 394, 292, 404)(283, 395, 290, 402)(285, 397, 293, 405)(287, 399, 296, 408)(289, 401, 297, 409)(291, 403, 300, 412)(294, 406, 304, 416)(295, 407, 302, 414)(298, 410, 308, 420)(299, 411, 306, 418)(301, 413, 309, 421)(303, 415, 312, 424)(305, 417, 313, 425)(307, 419, 316, 428)(310, 422, 320, 432)(311, 423, 318, 430)(314, 426, 324, 436)(315, 427, 322, 434)(317, 429, 325, 437)(319, 431, 328, 440)(321, 433, 329, 441)(323, 435, 332, 444)(326, 438, 334, 446)(327, 439, 333, 445)(330, 442, 336, 448)(331, 443, 335, 447) L = (1, 228)(2, 233)(3, 236)(4, 231)(5, 234)(6, 225)(7, 230)(8, 242)(9, 229)(10, 226)(11, 246)(12, 240)(13, 247)(14, 227)(15, 244)(16, 238)(17, 250)(18, 239)(19, 251)(20, 232)(21, 254)(22, 237)(23, 235)(24, 256)(25, 258)(26, 243)(27, 241)(28, 260)(29, 262)(30, 248)(31, 263)(32, 245)(33, 266)(34, 252)(35, 267)(36, 249)(37, 270)(38, 255)(39, 253)(40, 272)(41, 274)(42, 259)(43, 257)(44, 276)(45, 278)(46, 264)(47, 279)(48, 261)(49, 282)(50, 268)(51, 283)(52, 265)(53, 286)(54, 271)(55, 269)(56, 288)(57, 290)(58, 275)(59, 273)(60, 292)(61, 294)(62, 280)(63, 295)(64, 277)(65, 298)(66, 284)(67, 299)(68, 281)(69, 302)(70, 287)(71, 285)(72, 304)(73, 306)(74, 291)(75, 289)(76, 308)(77, 310)(78, 296)(79, 311)(80, 293)(81, 314)(82, 300)(83, 315)(84, 297)(85, 318)(86, 303)(87, 301)(88, 320)(89, 322)(90, 307)(91, 305)(92, 324)(93, 326)(94, 312)(95, 327)(96, 309)(97, 330)(98, 316)(99, 331)(100, 313)(101, 333)(102, 319)(103, 317)(104, 334)(105, 335)(106, 323)(107, 321)(108, 336)(109, 328)(110, 325)(111, 332)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.1248 Graph:: simple bipartite v = 84 e = 224 f = 112 degree seq :: [ 4^56, 8^28 ] E15.1254 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C4 x D14) : C2 (small group id <112, 34>) Aut = (D8 x D14) : C2 (small group id <224, 185>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2 * Y1^2, Y3^-2 * Y1^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y1^4, (Y1^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-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, 113, 2, 114, 7, 119, 5, 117)(3, 115, 11, 123, 16, 128, 13, 125)(4, 116, 9, 121, 6, 118, 10, 122)(8, 120, 17, 129, 15, 127, 19, 131)(12, 124, 22, 134, 14, 126, 23, 135)(18, 130, 26, 138, 20, 132, 27, 139)(21, 133, 29, 141, 24, 136, 31, 143)(25, 137, 33, 145, 28, 140, 35, 147)(30, 142, 38, 150, 32, 144, 39, 151)(34, 146, 42, 154, 36, 148, 43, 155)(37, 149, 45, 157, 40, 152, 47, 159)(41, 153, 49, 161, 44, 156, 51, 163)(46, 158, 54, 166, 48, 160, 55, 167)(50, 162, 58, 170, 52, 164, 59, 171)(53, 165, 61, 173, 56, 168, 63, 175)(57, 169, 65, 177, 60, 172, 67, 179)(62, 174, 70, 182, 64, 176, 71, 183)(66, 178, 74, 186, 68, 180, 75, 187)(69, 181, 77, 189, 72, 184, 79, 191)(73, 185, 81, 193, 76, 188, 83, 195)(78, 190, 86, 198, 80, 192, 87, 199)(82, 194, 90, 202, 84, 196, 91, 203)(85, 197, 93, 205, 88, 200, 95, 207)(89, 201, 97, 209, 92, 204, 99, 211)(94, 206, 102, 214, 96, 208, 103, 215)(98, 210, 106, 218, 100, 212, 107, 219)(101, 213, 105, 217, 104, 216, 108, 220)(109, 221, 111, 223, 110, 222, 112, 224)(225, 337, 227, 339)(226, 338, 232, 344)(228, 340, 238, 350)(229, 341, 239, 351)(230, 342, 236, 348)(231, 343, 240, 352)(233, 345, 244, 356)(234, 346, 242, 354)(235, 347, 245, 357)(237, 349, 248, 360)(241, 353, 249, 361)(243, 355, 252, 364)(246, 358, 256, 368)(247, 359, 254, 366)(250, 362, 260, 372)(251, 363, 258, 370)(253, 365, 261, 373)(255, 367, 264, 376)(257, 369, 265, 377)(259, 371, 268, 380)(262, 374, 272, 384)(263, 375, 270, 382)(266, 378, 276, 388)(267, 379, 274, 386)(269, 381, 277, 389)(271, 383, 280, 392)(273, 385, 281, 393)(275, 387, 284, 396)(278, 390, 288, 400)(279, 391, 286, 398)(282, 394, 292, 404)(283, 395, 290, 402)(285, 397, 293, 405)(287, 399, 296, 408)(289, 401, 297, 409)(291, 403, 300, 412)(294, 406, 304, 416)(295, 407, 302, 414)(298, 410, 308, 420)(299, 411, 306, 418)(301, 413, 309, 421)(303, 415, 312, 424)(305, 417, 313, 425)(307, 419, 316, 428)(310, 422, 320, 432)(311, 423, 318, 430)(314, 426, 324, 436)(315, 427, 322, 434)(317, 429, 325, 437)(319, 431, 328, 440)(321, 433, 329, 441)(323, 435, 332, 444)(326, 438, 334, 446)(327, 439, 333, 445)(330, 442, 336, 448)(331, 443, 335, 447) L = (1, 228)(2, 233)(3, 236)(4, 231)(5, 234)(6, 225)(7, 230)(8, 242)(9, 229)(10, 226)(11, 246)(12, 240)(13, 247)(14, 227)(15, 244)(16, 238)(17, 250)(18, 239)(19, 251)(20, 232)(21, 254)(22, 237)(23, 235)(24, 256)(25, 258)(26, 243)(27, 241)(28, 260)(29, 262)(30, 248)(31, 263)(32, 245)(33, 266)(34, 252)(35, 267)(36, 249)(37, 270)(38, 255)(39, 253)(40, 272)(41, 274)(42, 259)(43, 257)(44, 276)(45, 278)(46, 264)(47, 279)(48, 261)(49, 282)(50, 268)(51, 283)(52, 265)(53, 286)(54, 271)(55, 269)(56, 288)(57, 290)(58, 275)(59, 273)(60, 292)(61, 294)(62, 280)(63, 295)(64, 277)(65, 298)(66, 284)(67, 299)(68, 281)(69, 302)(70, 287)(71, 285)(72, 304)(73, 306)(74, 291)(75, 289)(76, 308)(77, 310)(78, 296)(79, 311)(80, 293)(81, 314)(82, 300)(83, 315)(84, 297)(85, 318)(86, 303)(87, 301)(88, 320)(89, 322)(90, 307)(91, 305)(92, 324)(93, 326)(94, 312)(95, 327)(96, 309)(97, 330)(98, 316)(99, 331)(100, 313)(101, 333)(102, 319)(103, 317)(104, 334)(105, 335)(106, 323)(107, 321)(108, 336)(109, 328)(110, 325)(111, 332)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E15.1250 Graph:: simple bipartite v = 84 e = 224 f = 112 degree seq :: [ 4^56, 8^28 ] E15.1255 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 3, 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, (T1 * T2)^3, (T2^-1 * T1^-1)^3, T2^-2 * T1 * T2^3 * T1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^10 ] Map:: polytopal non-degenerate R = (1, 3, 9, 25, 54, 97, 75, 39, 15, 5)(2, 6, 17, 26, 56, 100, 91, 49, 21, 7)(4, 11, 30, 42, 79, 118, 74, 37, 33, 12)(8, 22, 50, 55, 99, 115, 113, 67, 38, 23)(10, 27, 58, 93, 76, 71, 35, 13, 34, 28)(14, 36, 24, 53, 96, 98, 84, 48, 40, 16)(18, 43, 81, 73, 104, 88, 46, 19, 45, 44)(20, 47, 41, 78, 117, 101, 109, 66, 61, 29)(31, 62, 107, 90, 51, 94, 65, 32, 64, 63)(52, 95, 92, 112, 69, 108, 114, 68, 102, 57)(59, 80, 77, 116, 72, 70, 86, 60, 103, 85)(82, 106, 105, 120, 89, 87, 111, 83, 119, 110)(121, 122, 124)(123, 128, 130)(125, 133, 134)(126, 136, 138)(127, 139, 140)(129, 144, 146)(131, 149, 151)(132, 152, 142)(135, 157, 158)(137, 161, 162)(141, 159, 168)(143, 171, 172)(145, 150, 175)(147, 177, 179)(148, 180, 173)(153, 169, 186)(154, 187, 188)(155, 189, 190)(156, 192, 193)(160, 196, 197)(163, 200, 202)(164, 203, 198)(165, 204, 205)(166, 206, 207)(167, 209, 210)(170, 212, 213)(174, 178, 218)(176, 201, 221)(181, 224, 225)(182, 226, 222)(183, 228, 219)(184, 229, 230)(185, 231, 232)(191, 195, 235)(194, 237, 214)(199, 227, 233)(208, 211, 216)(215, 240, 236)(217, 220, 238)(223, 234, 239) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6^3 ), ( 6^10 ) } Outer automorphisms :: reflexible Dual of E15.1256 Transitivity :: ET+ Graph:: simple bipartite v = 52 e = 120 f = 40 degree seq :: [ 3^40, 10^12 ] E15.1256 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 3, 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, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2^-1 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 5, 125)(2, 122, 6, 126, 7, 127)(4, 124, 10, 130, 11, 131)(8, 128, 18, 138, 19, 139)(9, 129, 20, 140, 21, 141)(12, 132, 26, 146, 27, 147)(13, 133, 28, 148, 29, 149)(14, 134, 30, 150, 31, 151)(15, 135, 32, 152, 33, 153)(16, 136, 34, 154, 35, 155)(17, 137, 36, 156, 37, 157)(22, 142, 46, 166, 47, 167)(23, 143, 48, 168, 49, 169)(24, 144, 50, 170, 51, 171)(25, 145, 52, 172, 53, 173)(38, 158, 62, 182, 78, 198)(39, 159, 79, 199, 80, 200)(40, 160, 81, 201, 73, 193)(41, 161, 82, 202, 83, 203)(42, 162, 84, 204, 75, 195)(43, 163, 85, 205, 67, 187)(44, 164, 86, 206, 71, 191)(45, 165, 87, 207, 88, 208)(54, 174, 63, 183, 100, 220)(55, 175, 93, 213, 101, 221)(56, 176, 96, 216, 72, 192)(57, 177, 90, 210, 102, 222)(58, 178, 65, 185, 103, 223)(59, 179, 92, 212, 104, 224)(60, 180, 69, 189, 105, 225)(61, 181, 77, 197, 99, 219)(64, 184, 106, 226, 97, 217)(66, 186, 107, 227, 98, 218)(68, 188, 108, 228, 95, 215)(70, 190, 89, 209, 109, 229)(74, 194, 91, 211, 110, 230)(76, 196, 94, 214, 111, 231)(112, 232, 118, 238, 115, 235)(113, 233, 114, 234, 119, 239)(116, 236, 117, 237, 120, 240) L = (1, 122)(2, 124)(3, 128)(4, 121)(5, 132)(6, 134)(7, 136)(8, 129)(9, 123)(10, 142)(11, 144)(12, 133)(13, 125)(14, 135)(15, 126)(16, 137)(17, 127)(18, 158)(19, 160)(20, 162)(21, 164)(22, 143)(23, 130)(24, 145)(25, 131)(26, 174)(27, 176)(28, 178)(29, 180)(30, 182)(31, 184)(32, 186)(33, 188)(34, 190)(35, 192)(36, 194)(37, 196)(38, 159)(39, 138)(40, 161)(41, 139)(42, 163)(43, 140)(44, 165)(45, 141)(46, 198)(47, 210)(48, 212)(49, 213)(50, 200)(51, 216)(52, 203)(53, 208)(54, 175)(55, 146)(56, 177)(57, 147)(58, 179)(59, 148)(60, 181)(61, 149)(62, 183)(63, 150)(64, 185)(65, 151)(66, 187)(67, 152)(68, 189)(69, 153)(70, 191)(71, 154)(72, 193)(73, 155)(74, 195)(75, 156)(76, 197)(77, 157)(78, 209)(79, 232)(80, 215)(81, 233)(82, 230)(83, 218)(84, 220)(85, 168)(86, 221)(87, 222)(88, 219)(89, 166)(90, 211)(91, 167)(92, 205)(93, 214)(94, 169)(95, 170)(96, 217)(97, 171)(98, 172)(99, 173)(100, 234)(101, 228)(102, 235)(103, 202)(104, 199)(105, 201)(106, 236)(107, 229)(108, 206)(109, 237)(110, 223)(111, 226)(112, 224)(113, 225)(114, 204)(115, 207)(116, 231)(117, 227)(118, 239)(119, 240)(120, 238) local type(s) :: { ( 3, 10, 3, 10, 3, 10 ) } Outer automorphisms :: reflexible Dual of E15.1255 Transitivity :: ET+ VT+ AT Graph:: simple v = 40 e = 120 f = 52 degree seq :: [ 6^40 ] E15.1257 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^3, (Y1^-1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, Y2^-2 * Y1 * Y2^3 * Y1, Y2^10, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 ] 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, 22, 142)(15, 135, 37, 157, 38, 158)(17, 137, 41, 161, 42, 162)(21, 141, 39, 159, 48, 168)(23, 143, 51, 171, 52, 172)(25, 145, 30, 150, 55, 175)(27, 147, 57, 177, 59, 179)(28, 148, 60, 180, 53, 173)(33, 153, 49, 169, 66, 186)(34, 154, 67, 187, 68, 188)(35, 155, 69, 189, 70, 190)(36, 156, 72, 192, 73, 193)(40, 160, 76, 196, 77, 197)(43, 163, 80, 200, 82, 202)(44, 164, 83, 203, 78, 198)(45, 165, 84, 204, 85, 205)(46, 166, 86, 206, 87, 207)(47, 167, 89, 209, 90, 210)(50, 170, 92, 212, 93, 213)(54, 174, 58, 178, 98, 218)(56, 176, 81, 201, 101, 221)(61, 181, 104, 224, 105, 225)(62, 182, 106, 226, 102, 222)(63, 183, 108, 228, 99, 219)(64, 184, 109, 229, 110, 230)(65, 185, 111, 231, 112, 232)(71, 191, 75, 195, 115, 235)(74, 194, 117, 237, 94, 214)(79, 199, 107, 227, 113, 233)(88, 208, 91, 211, 96, 216)(95, 215, 120, 240, 116, 236)(97, 217, 100, 220, 118, 238)(103, 223, 114, 234, 119, 239)(241, 361, 243, 363, 249, 369, 265, 385, 294, 414, 337, 457, 315, 435, 279, 399, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 266, 386, 296, 416, 340, 460, 331, 451, 289, 409, 261, 381, 247, 367)(244, 364, 251, 371, 270, 390, 282, 402, 319, 439, 358, 478, 314, 434, 277, 397, 273, 393, 252, 372)(248, 368, 262, 382, 290, 410, 295, 415, 339, 459, 355, 475, 353, 473, 307, 427, 278, 398, 263, 383)(250, 370, 267, 387, 298, 418, 333, 453, 316, 436, 311, 431, 275, 395, 253, 373, 274, 394, 268, 388)(254, 374, 276, 396, 264, 384, 293, 413, 336, 456, 338, 458, 324, 444, 288, 408, 280, 400, 256, 376)(258, 378, 283, 403, 321, 441, 313, 433, 344, 464, 328, 448, 286, 406, 259, 379, 285, 405, 284, 404)(260, 380, 287, 407, 281, 401, 318, 438, 357, 477, 341, 461, 349, 469, 306, 426, 301, 421, 269, 389)(271, 391, 302, 422, 347, 467, 330, 450, 291, 411, 334, 454, 305, 425, 272, 392, 304, 424, 303, 423)(292, 412, 335, 455, 332, 452, 352, 472, 309, 429, 348, 468, 354, 474, 308, 428, 342, 462, 297, 417)(299, 419, 320, 440, 317, 437, 356, 476, 312, 432, 310, 430, 326, 446, 300, 420, 343, 463, 325, 445)(322, 442, 346, 466, 345, 465, 360, 480, 329, 449, 327, 447, 351, 471, 323, 443, 359, 479, 350, 470) 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, 274)(14, 276)(15, 245)(16, 254)(17, 266)(18, 283)(19, 285)(20, 287)(21, 247)(22, 290)(23, 248)(24, 293)(25, 294)(26, 296)(27, 298)(28, 250)(29, 260)(30, 282)(31, 302)(32, 304)(33, 252)(34, 268)(35, 253)(36, 264)(37, 273)(38, 263)(39, 255)(40, 256)(41, 318)(42, 319)(43, 321)(44, 258)(45, 284)(46, 259)(47, 281)(48, 280)(49, 261)(50, 295)(51, 334)(52, 335)(53, 336)(54, 337)(55, 339)(56, 340)(57, 292)(58, 333)(59, 320)(60, 343)(61, 269)(62, 347)(63, 271)(64, 303)(65, 272)(66, 301)(67, 278)(68, 342)(69, 348)(70, 326)(71, 275)(72, 310)(73, 344)(74, 277)(75, 279)(76, 311)(77, 356)(78, 357)(79, 358)(80, 317)(81, 313)(82, 346)(83, 359)(84, 288)(85, 299)(86, 300)(87, 351)(88, 286)(89, 327)(90, 291)(91, 289)(92, 352)(93, 316)(94, 305)(95, 332)(96, 338)(97, 315)(98, 324)(99, 355)(100, 331)(101, 349)(102, 297)(103, 325)(104, 328)(105, 360)(106, 345)(107, 330)(108, 354)(109, 306)(110, 322)(111, 323)(112, 309)(113, 307)(114, 308)(115, 353)(116, 312)(117, 341)(118, 314)(119, 350)(120, 329)(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 ) } Outer automorphisms :: reflexible Dual of E15.1258 Graph:: bipartite v = 52 e = 240 f = 160 degree seq :: [ 6^40, 20^12 ] E15.1258 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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^-1)^3, Y3^2 * Y2 * Y3^-3 * Y2, Y3^-1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (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, 268, 388, 270, 390)(252, 372, 271, 391, 272, 392)(255, 375, 277, 397, 278, 398)(257, 377, 265, 385, 283, 403)(261, 381, 288, 408, 289, 409)(262, 382, 290, 410, 292, 412)(263, 383, 293, 413, 294, 414)(267, 387, 297, 417, 298, 418)(269, 389, 282, 402, 301, 421)(273, 393, 306, 426, 279, 399)(274, 394, 307, 427, 308, 428)(275, 395, 309, 429, 310, 430)(276, 396, 311, 431, 312, 432)(280, 400, 316, 436, 318, 438)(281, 401, 319, 439, 320, 440)(284, 404, 322, 442, 323, 443)(285, 405, 324, 444, 325, 445)(286, 406, 326, 446, 327, 447)(287, 407, 328, 448, 329, 449)(291, 411, 296, 416, 334, 454)(295, 415, 338, 458, 340, 460)(299, 419, 344, 464, 332, 452)(300, 420, 345, 465, 346, 466)(302, 422, 347, 467, 348, 468)(303, 423, 343, 463, 349, 469)(304, 424, 333, 453, 350, 470)(305, 425, 351, 471, 337, 457)(313, 433, 356, 476, 315, 435)(314, 434, 330, 450, 357, 477)(317, 437, 321, 441, 355, 475)(331, 451, 352, 472, 335, 455)(336, 456, 360, 480, 354, 474)(339, 459, 341, 461, 358, 478)(342, 462, 353, 473, 359, 479) L = (1, 243)(2, 246)(3, 249)(4, 251)(5, 241)(6, 257)(7, 242)(8, 262)(9, 265)(10, 259)(11, 269)(12, 244)(13, 274)(14, 275)(15, 245)(16, 280)(17, 282)(18, 271)(19, 285)(20, 286)(21, 247)(22, 291)(23, 248)(24, 295)(25, 296)(26, 293)(27, 250)(28, 299)(29, 264)(30, 253)(31, 303)(32, 304)(33, 252)(34, 266)(35, 263)(36, 254)(37, 267)(38, 261)(39, 255)(40, 317)(41, 256)(42, 321)(43, 319)(44, 258)(45, 283)(46, 281)(47, 260)(48, 284)(49, 273)(50, 332)(51, 324)(52, 297)(53, 335)(54, 336)(55, 339)(56, 341)(57, 342)(58, 330)(59, 340)(60, 268)(61, 345)(62, 270)(63, 301)(64, 300)(65, 272)(66, 302)(67, 323)(68, 311)(69, 316)(70, 277)(71, 337)(72, 320)(73, 276)(74, 278)(75, 279)(76, 292)(77, 343)(78, 322)(79, 356)(80, 354)(81, 358)(82, 359)(83, 352)(84, 348)(85, 328)(86, 344)(87, 288)(88, 312)(89, 346)(90, 287)(91, 289)(92, 347)(93, 290)(94, 350)(95, 334)(96, 333)(97, 294)(98, 327)(99, 331)(100, 307)(101, 315)(102, 325)(103, 298)(104, 318)(105, 357)(106, 360)(107, 353)(108, 313)(109, 351)(110, 306)(111, 329)(112, 305)(113, 308)(114, 309)(115, 310)(116, 355)(117, 338)(118, 314)(119, 349)(120, 326)(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 ) } Outer automorphisms :: reflexible Dual of E15.1257 Graph:: simple bipartite v = 160 e = 240 f = 52 degree seq :: [ 2^120, 6^40 ] E15.1259 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 10}) Quotient :: regular Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2, T1^10, (T1^-2 * T2 * T1^-1 * T2)^2, (T2 * T1^2 * T2 * T1^-2)^3 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 47, 46, 22, 10, 4)(3, 7, 15, 31, 28, 54, 41, 38, 18, 8)(6, 13, 27, 52, 50, 36, 17, 35, 30, 14)(9, 19, 39, 34, 16, 33, 60, 67, 42, 20)(12, 25, 49, 72, 70, 45, 29, 55, 51, 26)(21, 43, 68, 66, 40, 24, 48, 71, 69, 44)(32, 58, 80, 99, 85, 64, 61, 82, 81, 59)(37, 63, 84, 83, 62, 57, 79, 96, 76, 53)(56, 78, 98, 97, 77, 75, 95, 109, 93, 73)(65, 86, 103, 115, 101, 89, 88, 105, 104, 87)(74, 94, 110, 106, 90, 92, 108, 116, 107, 91)(100, 114, 118, 112, 102, 113, 119, 120, 117, 111) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 33)(25, 50)(26, 43)(27, 53)(30, 56)(31, 57)(34, 61)(35, 62)(36, 46)(38, 64)(39, 65)(42, 58)(44, 60)(47, 54)(48, 70)(49, 73)(51, 74)(52, 75)(55, 77)(59, 63)(66, 88)(67, 89)(68, 90)(69, 86)(71, 91)(72, 92)(76, 78)(79, 85)(80, 87)(81, 100)(82, 101)(83, 95)(84, 102)(93, 94)(96, 111)(97, 108)(98, 112)(99, 113)(103, 106)(104, 114)(105, 107)(109, 117)(110, 118)(115, 119)(116, 120) local type(s) :: { ( 6^10 ) } Outer automorphisms :: reflexible Dual of E15.1260 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 12 e = 60 f = 20 degree seq :: [ 10^12 ] E15.1260 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 10}) Quotient :: regular Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T1^-1 * T2 * T1^-2)^2, T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, (T2 * T1 * T2 * T1^-1)^5 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 22, 18, 8)(6, 13, 25, 21, 28, 14)(9, 19, 24, 12, 23, 20)(16, 30, 47, 34, 50, 31)(17, 32, 46, 29, 45, 33)(26, 40, 62, 44, 52, 41)(27, 42, 61, 39, 60, 43)(35, 53, 58, 37, 57, 54)(36, 55, 48, 38, 59, 56)(49, 67, 84, 66, 83, 68)(51, 69, 82, 65, 81, 70)(63, 77, 98, 76, 97, 78)(64, 79, 96, 75, 95, 80)(71, 87, 92, 73, 91, 88)(72, 89, 94, 74, 93, 90)(85, 103, 113, 102, 108, 104)(86, 105, 110, 101, 111, 99)(100, 112, 106, 109, 116, 107)(114, 118, 115, 119, 120, 117) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 29)(18, 34)(19, 35)(20, 36)(23, 37)(24, 38)(25, 39)(28, 44)(30, 48)(31, 49)(32, 51)(33, 52)(40, 46)(41, 63)(42, 64)(43, 53)(45, 65)(47, 66)(50, 56)(54, 71)(55, 72)(57, 61)(58, 73)(59, 74)(60, 75)(62, 76)(67, 85)(68, 69)(70, 86)(77, 99)(78, 79)(80, 100)(81, 84)(82, 101)(83, 102)(87, 106)(88, 89)(90, 103)(91, 107)(92, 93)(94, 108)(95, 98)(96, 109)(97, 110)(104, 114)(105, 115)(111, 117)(112, 118)(113, 119)(116, 120) local type(s) :: { ( 10^6 ) } Outer automorphisms :: reflexible Dual of E15.1259 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 20 e = 60 f = 12 degree seq :: [ 6^20 ] E15.1261 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 10}) Quotient :: edge Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, (T2^-2 * T1 * T2^-1)^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2, (T2 * T1 * T2^-1 * T1)^5 ] Map:: R = (1, 3, 8, 18, 10, 4)(2, 5, 12, 25, 14, 6)(7, 15, 30, 21, 32, 16)(9, 19, 34, 17, 33, 20)(11, 22, 38, 28, 40, 23)(13, 26, 42, 24, 41, 27)(29, 45, 63, 50, 44, 46)(31, 48, 66, 47, 65, 49)(35, 53, 69, 51, 68, 54)(36, 55, 37, 52, 70, 56)(39, 58, 74, 57, 73, 59)(43, 61, 77, 60, 76, 62)(64, 80, 98, 79, 97, 81)(67, 83, 100, 82, 99, 84)(71, 87, 103, 85, 102, 88)(72, 89, 105, 86, 104, 90)(75, 92, 108, 91, 107, 93)(78, 95, 111, 94, 110, 96)(101, 114, 106, 113, 119, 115)(109, 117, 112, 116, 120, 118)(121, 122)(123, 127)(124, 129)(125, 131)(126, 133)(128, 137)(130, 141)(132, 144)(134, 148)(135, 149)(136, 151)(138, 145)(139, 155)(140, 156)(142, 157)(143, 159)(146, 163)(147, 164)(150, 167)(152, 170)(153, 171)(154, 172)(158, 177)(160, 176)(161, 180)(162, 165)(166, 184)(168, 187)(169, 173)(174, 191)(175, 192)(178, 195)(179, 181)(182, 198)(183, 199)(185, 202)(186, 188)(189, 205)(190, 206)(193, 211)(194, 196)(197, 214)(200, 216)(201, 203)(204, 221)(207, 226)(208, 209)(210, 212)(213, 229)(215, 232)(217, 231)(218, 219)(220, 233)(222, 235)(223, 224)(225, 227)(228, 236)(230, 238)(234, 237)(239, 240) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 20, 20 ), ( 20^6 ) } Outer automorphisms :: reflexible Dual of E15.1265 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 120 f = 12 degree seq :: [ 2^60, 6^20 ] E15.1262 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 10}) Quotient :: edge Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^2)^2, T1^6, T1^-1 * T2^5 * T1^-2, T2^-3 * T1^-2 * T2^2 * T1 * T2^-3 * T1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 37, 16, 36, 35, 15, 5)(2, 7, 19, 42, 29, 13, 31, 48, 22, 8)(4, 12, 30, 40, 18, 6, 17, 38, 24, 9)(11, 28, 56, 74, 50, 23, 49, 73, 53, 25)(14, 32, 58, 66, 41, 20, 44, 69, 59, 33)(21, 45, 70, 84, 61, 39, 63, 86, 71, 46)(27, 55, 79, 60, 34, 52, 76, 98, 78, 54)(43, 68, 91, 72, 47, 65, 88, 106, 90, 67)(51, 62, 85, 104, 87, 64, 57, 81, 97, 75)(77, 95, 111, 119, 112, 96, 80, 101, 113, 99)(82, 100, 114, 102, 83, 92, 109, 117, 107, 89)(93, 108, 118, 110, 94, 105, 116, 120, 115, 103)(121, 122, 126, 136, 133, 124)(123, 129, 143, 156, 138, 131)(125, 134, 151, 157, 140, 127)(128, 141, 132, 149, 159, 137)(130, 145, 172, 155, 170, 147)(135, 154, 164, 146, 174, 152)(139, 161, 185, 168, 153, 163)(142, 167, 183, 162, 187, 165)(144, 171, 148, 160, 184, 169)(150, 166, 182, 158, 181, 177)(173, 197, 175, 194, 216, 196)(176, 195, 215, 193, 207, 200)(178, 198, 212, 189, 180, 202)(179, 203, 208, 186, 209, 188)(190, 210, 225, 206, 192, 213)(191, 214, 201, 204, 223, 205)(199, 219, 229, 218, 232, 220)(211, 227, 236, 226, 222, 228)(217, 230, 221, 224, 235, 231)(233, 238, 234, 239, 240, 237) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^6 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E15.1266 Transitivity :: ET+ Graph:: bipartite v = 32 e = 120 f = 60 degree seq :: [ 6^20, 10^12 ] E15.1263 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 10}) Quotient :: edge Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2, T1^10, (T2 * T1^2 * T2 * T1)^2, (T2 * T1^2 * T2 * T1^-2)^3 ] 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, 37)(19, 40)(20, 41)(22, 45)(23, 33)(25, 50)(26, 43)(27, 53)(30, 56)(31, 57)(34, 61)(35, 62)(36, 46)(38, 64)(39, 65)(42, 58)(44, 60)(47, 54)(48, 70)(49, 73)(51, 74)(52, 75)(55, 77)(59, 63)(66, 88)(67, 89)(68, 90)(69, 86)(71, 91)(72, 92)(76, 78)(79, 85)(80, 87)(81, 100)(82, 101)(83, 95)(84, 102)(93, 94)(96, 111)(97, 108)(98, 112)(99, 113)(103, 106)(104, 114)(105, 107)(109, 117)(110, 118)(115, 119)(116, 120)(121, 122, 125, 131, 143, 167, 166, 142, 130, 124)(123, 127, 135, 151, 148, 174, 161, 158, 138, 128)(126, 133, 147, 172, 170, 156, 137, 155, 150, 134)(129, 139, 159, 154, 136, 153, 180, 187, 162, 140)(132, 145, 169, 192, 190, 165, 149, 175, 171, 146)(141, 163, 188, 186, 160, 144, 168, 191, 189, 164)(152, 178, 200, 219, 205, 184, 181, 202, 201, 179)(157, 183, 204, 203, 182, 177, 199, 216, 196, 173)(176, 198, 218, 217, 197, 195, 215, 229, 213, 193)(185, 206, 223, 235, 221, 209, 208, 225, 224, 207)(194, 214, 230, 226, 210, 212, 228, 236, 227, 211)(220, 234, 238, 232, 222, 233, 239, 240, 237, 231) 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) :: { ( 12, 12 ), ( 12^10 ) } Outer automorphisms :: reflexible Dual of E15.1264 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 120 f = 20 degree seq :: [ 2^60, 10^12 ] E15.1264 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 10}) Quotient :: loop Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, (T2^-2 * T1 * T2^-1)^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2, (T2 * T1 * T2^-1 * T1)^5 ] Map:: R = (1, 121, 3, 123, 8, 128, 18, 138, 10, 130, 4, 124)(2, 122, 5, 125, 12, 132, 25, 145, 14, 134, 6, 126)(7, 127, 15, 135, 30, 150, 21, 141, 32, 152, 16, 136)(9, 129, 19, 139, 34, 154, 17, 137, 33, 153, 20, 140)(11, 131, 22, 142, 38, 158, 28, 148, 40, 160, 23, 143)(13, 133, 26, 146, 42, 162, 24, 144, 41, 161, 27, 147)(29, 149, 45, 165, 63, 183, 50, 170, 44, 164, 46, 166)(31, 151, 48, 168, 66, 186, 47, 167, 65, 185, 49, 169)(35, 155, 53, 173, 69, 189, 51, 171, 68, 188, 54, 174)(36, 156, 55, 175, 37, 157, 52, 172, 70, 190, 56, 176)(39, 159, 58, 178, 74, 194, 57, 177, 73, 193, 59, 179)(43, 163, 61, 181, 77, 197, 60, 180, 76, 196, 62, 182)(64, 184, 80, 200, 98, 218, 79, 199, 97, 217, 81, 201)(67, 187, 83, 203, 100, 220, 82, 202, 99, 219, 84, 204)(71, 191, 87, 207, 103, 223, 85, 205, 102, 222, 88, 208)(72, 192, 89, 209, 105, 225, 86, 206, 104, 224, 90, 210)(75, 195, 92, 212, 108, 228, 91, 211, 107, 227, 93, 213)(78, 198, 95, 215, 111, 231, 94, 214, 110, 230, 96, 216)(101, 221, 114, 234, 106, 226, 113, 233, 119, 239, 115, 235)(109, 229, 117, 237, 112, 232, 116, 236, 120, 240, 118, 238) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 137)(9, 124)(10, 141)(11, 125)(12, 144)(13, 126)(14, 148)(15, 149)(16, 151)(17, 128)(18, 145)(19, 155)(20, 156)(21, 130)(22, 157)(23, 159)(24, 132)(25, 138)(26, 163)(27, 164)(28, 134)(29, 135)(30, 167)(31, 136)(32, 170)(33, 171)(34, 172)(35, 139)(36, 140)(37, 142)(38, 177)(39, 143)(40, 176)(41, 180)(42, 165)(43, 146)(44, 147)(45, 162)(46, 184)(47, 150)(48, 187)(49, 173)(50, 152)(51, 153)(52, 154)(53, 169)(54, 191)(55, 192)(56, 160)(57, 158)(58, 195)(59, 181)(60, 161)(61, 179)(62, 198)(63, 199)(64, 166)(65, 202)(66, 188)(67, 168)(68, 186)(69, 205)(70, 206)(71, 174)(72, 175)(73, 211)(74, 196)(75, 178)(76, 194)(77, 214)(78, 182)(79, 183)(80, 216)(81, 203)(82, 185)(83, 201)(84, 221)(85, 189)(86, 190)(87, 226)(88, 209)(89, 208)(90, 212)(91, 193)(92, 210)(93, 229)(94, 197)(95, 232)(96, 200)(97, 231)(98, 219)(99, 218)(100, 233)(101, 204)(102, 235)(103, 224)(104, 223)(105, 227)(106, 207)(107, 225)(108, 236)(109, 213)(110, 238)(111, 217)(112, 215)(113, 220)(114, 237)(115, 222)(116, 228)(117, 234)(118, 230)(119, 240)(120, 239) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E15.1263 Transitivity :: ET+ VT+ AT Graph:: v = 20 e = 120 f = 72 degree seq :: [ 12^20 ] E15.1265 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 10}) Quotient :: loop Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^2)^2, T1^6, T1^-1 * T2^5 * T1^-2, T2^-3 * T1^-2 * T2^2 * T1 * T2^-3 * T1 ] Map:: R = (1, 121, 3, 123, 10, 130, 26, 146, 37, 157, 16, 136, 36, 156, 35, 155, 15, 135, 5, 125)(2, 122, 7, 127, 19, 139, 42, 162, 29, 149, 13, 133, 31, 151, 48, 168, 22, 142, 8, 128)(4, 124, 12, 132, 30, 150, 40, 160, 18, 138, 6, 126, 17, 137, 38, 158, 24, 144, 9, 129)(11, 131, 28, 148, 56, 176, 74, 194, 50, 170, 23, 143, 49, 169, 73, 193, 53, 173, 25, 145)(14, 134, 32, 152, 58, 178, 66, 186, 41, 161, 20, 140, 44, 164, 69, 189, 59, 179, 33, 153)(21, 141, 45, 165, 70, 190, 84, 204, 61, 181, 39, 159, 63, 183, 86, 206, 71, 191, 46, 166)(27, 147, 55, 175, 79, 199, 60, 180, 34, 154, 52, 172, 76, 196, 98, 218, 78, 198, 54, 174)(43, 163, 68, 188, 91, 211, 72, 192, 47, 167, 65, 185, 88, 208, 106, 226, 90, 210, 67, 187)(51, 171, 62, 182, 85, 205, 104, 224, 87, 207, 64, 184, 57, 177, 81, 201, 97, 217, 75, 195)(77, 197, 95, 215, 111, 231, 119, 239, 112, 232, 96, 216, 80, 200, 101, 221, 113, 233, 99, 219)(82, 202, 100, 220, 114, 234, 102, 222, 83, 203, 92, 212, 109, 229, 117, 237, 107, 227, 89, 209)(93, 213, 108, 228, 118, 238, 110, 230, 94, 214, 105, 225, 116, 236, 120, 240, 115, 235, 103, 223) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 125)(8, 141)(9, 143)(10, 145)(11, 123)(12, 149)(13, 124)(14, 151)(15, 154)(16, 133)(17, 128)(18, 131)(19, 161)(20, 127)(21, 132)(22, 167)(23, 156)(24, 171)(25, 172)(26, 174)(27, 130)(28, 160)(29, 159)(30, 166)(31, 157)(32, 135)(33, 163)(34, 164)(35, 170)(36, 138)(37, 140)(38, 181)(39, 137)(40, 184)(41, 185)(42, 187)(43, 139)(44, 146)(45, 142)(46, 182)(47, 183)(48, 153)(49, 144)(50, 147)(51, 148)(52, 155)(53, 197)(54, 152)(55, 194)(56, 195)(57, 150)(58, 198)(59, 203)(60, 202)(61, 177)(62, 158)(63, 162)(64, 169)(65, 168)(66, 209)(67, 165)(68, 179)(69, 180)(70, 210)(71, 214)(72, 213)(73, 207)(74, 216)(75, 215)(76, 173)(77, 175)(78, 212)(79, 219)(80, 176)(81, 204)(82, 178)(83, 208)(84, 223)(85, 191)(86, 192)(87, 200)(88, 186)(89, 188)(90, 225)(91, 227)(92, 189)(93, 190)(94, 201)(95, 193)(96, 196)(97, 230)(98, 232)(99, 229)(100, 199)(101, 224)(102, 228)(103, 205)(104, 235)(105, 206)(106, 222)(107, 236)(108, 211)(109, 218)(110, 221)(111, 217)(112, 220)(113, 238)(114, 239)(115, 231)(116, 226)(117, 233)(118, 234)(119, 240)(120, 237) local type(s) :: { ( 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 E15.1261 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 120 f = 80 degree seq :: [ 20^12 ] E15.1266 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 10}) Quotient :: loop Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2, T1^10, (T2 * T1^2 * T2 * T1)^2, (T2 * T1^2 * T2 * T1^-2)^3 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 12, 132)(7, 127, 16, 136)(8, 128, 17, 137)(10, 130, 21, 141)(11, 131, 24, 144)(13, 133, 28, 148)(14, 134, 29, 149)(15, 135, 32, 152)(18, 138, 37, 157)(19, 139, 40, 160)(20, 140, 41, 161)(22, 142, 45, 165)(23, 143, 33, 153)(25, 145, 50, 170)(26, 146, 43, 163)(27, 147, 53, 173)(30, 150, 56, 176)(31, 151, 57, 177)(34, 154, 61, 181)(35, 155, 62, 182)(36, 156, 46, 166)(38, 158, 64, 184)(39, 159, 65, 185)(42, 162, 58, 178)(44, 164, 60, 180)(47, 167, 54, 174)(48, 168, 70, 190)(49, 169, 73, 193)(51, 171, 74, 194)(52, 172, 75, 195)(55, 175, 77, 197)(59, 179, 63, 183)(66, 186, 88, 208)(67, 187, 89, 209)(68, 188, 90, 210)(69, 189, 86, 206)(71, 191, 91, 211)(72, 192, 92, 212)(76, 196, 78, 198)(79, 199, 85, 205)(80, 200, 87, 207)(81, 201, 100, 220)(82, 202, 101, 221)(83, 203, 95, 215)(84, 204, 102, 222)(93, 213, 94, 214)(96, 216, 111, 231)(97, 217, 108, 228)(98, 218, 112, 232)(99, 219, 113, 233)(103, 223, 106, 226)(104, 224, 114, 234)(105, 225, 107, 227)(109, 229, 117, 237)(110, 230, 118, 238)(115, 235, 119, 239)(116, 236, 120, 240) L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 131)(6, 133)(7, 135)(8, 123)(9, 139)(10, 124)(11, 143)(12, 145)(13, 147)(14, 126)(15, 151)(16, 153)(17, 155)(18, 128)(19, 159)(20, 129)(21, 163)(22, 130)(23, 167)(24, 168)(25, 169)(26, 132)(27, 172)(28, 174)(29, 175)(30, 134)(31, 148)(32, 178)(33, 180)(34, 136)(35, 150)(36, 137)(37, 183)(38, 138)(39, 154)(40, 144)(41, 158)(42, 140)(43, 188)(44, 141)(45, 149)(46, 142)(47, 166)(48, 191)(49, 192)(50, 156)(51, 146)(52, 170)(53, 157)(54, 161)(55, 171)(56, 198)(57, 199)(58, 200)(59, 152)(60, 187)(61, 202)(62, 177)(63, 204)(64, 181)(65, 206)(66, 160)(67, 162)(68, 186)(69, 164)(70, 165)(71, 189)(72, 190)(73, 176)(74, 214)(75, 215)(76, 173)(77, 195)(78, 218)(79, 216)(80, 219)(81, 179)(82, 201)(83, 182)(84, 203)(85, 184)(86, 223)(87, 185)(88, 225)(89, 208)(90, 212)(91, 194)(92, 228)(93, 193)(94, 230)(95, 229)(96, 196)(97, 197)(98, 217)(99, 205)(100, 234)(101, 209)(102, 233)(103, 235)(104, 207)(105, 224)(106, 210)(107, 211)(108, 236)(109, 213)(110, 226)(111, 220)(112, 222)(113, 239)(114, 238)(115, 221)(116, 227)(117, 231)(118, 232)(119, 240)(120, 237) local type(s) :: { ( 6, 10, 6, 10 ) } Outer automorphisms :: reflexible Dual of E15.1262 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 60 e = 120 f = 32 degree seq :: [ 4^60 ] E15.1267 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 10}) Quotient :: dipole Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y2^-2 * Y1 * Y2^-1)^2, Y2^2 * R * Y2^2 * R * Y1 * Y2^-1 * Y1 * Y2, Y1 * Y2 * R * Y2^2 * R * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y2^-1)^10, (Y2 * Y1 * Y2^-1 * Y1)^5 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 17, 137)(10, 130, 21, 141)(12, 132, 24, 144)(14, 134, 28, 148)(15, 135, 29, 149)(16, 136, 31, 151)(18, 138, 25, 145)(19, 139, 35, 155)(20, 140, 36, 156)(22, 142, 37, 157)(23, 143, 39, 159)(26, 146, 43, 163)(27, 147, 44, 164)(30, 150, 47, 167)(32, 152, 50, 170)(33, 153, 51, 171)(34, 154, 52, 172)(38, 158, 57, 177)(40, 160, 56, 176)(41, 161, 60, 180)(42, 162, 45, 165)(46, 166, 64, 184)(48, 168, 67, 187)(49, 169, 53, 173)(54, 174, 71, 191)(55, 175, 72, 192)(58, 178, 75, 195)(59, 179, 61, 181)(62, 182, 78, 198)(63, 183, 79, 199)(65, 185, 82, 202)(66, 186, 68, 188)(69, 189, 85, 205)(70, 190, 86, 206)(73, 193, 91, 211)(74, 194, 76, 196)(77, 197, 94, 214)(80, 200, 96, 216)(81, 201, 83, 203)(84, 204, 101, 221)(87, 207, 106, 226)(88, 208, 89, 209)(90, 210, 92, 212)(93, 213, 109, 229)(95, 215, 112, 232)(97, 217, 111, 231)(98, 218, 99, 219)(100, 220, 113, 233)(102, 222, 115, 235)(103, 223, 104, 224)(105, 225, 107, 227)(108, 228, 116, 236)(110, 230, 118, 238)(114, 234, 117, 237)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 265, 385, 254, 374, 246, 366)(247, 367, 255, 375, 270, 390, 261, 381, 272, 392, 256, 376)(249, 369, 259, 379, 274, 394, 257, 377, 273, 393, 260, 380)(251, 371, 262, 382, 278, 398, 268, 388, 280, 400, 263, 383)(253, 373, 266, 386, 282, 402, 264, 384, 281, 401, 267, 387)(269, 389, 285, 405, 303, 423, 290, 410, 284, 404, 286, 406)(271, 391, 288, 408, 306, 426, 287, 407, 305, 425, 289, 409)(275, 395, 293, 413, 309, 429, 291, 411, 308, 428, 294, 414)(276, 396, 295, 415, 277, 397, 292, 412, 310, 430, 296, 416)(279, 399, 298, 418, 314, 434, 297, 417, 313, 433, 299, 419)(283, 403, 301, 421, 317, 437, 300, 420, 316, 436, 302, 422)(304, 424, 320, 440, 338, 458, 319, 439, 337, 457, 321, 441)(307, 427, 323, 443, 340, 460, 322, 442, 339, 459, 324, 444)(311, 431, 327, 447, 343, 463, 325, 445, 342, 462, 328, 448)(312, 432, 329, 449, 345, 465, 326, 446, 344, 464, 330, 450)(315, 435, 332, 452, 348, 468, 331, 451, 347, 467, 333, 453)(318, 438, 335, 455, 351, 471, 334, 454, 350, 470, 336, 456)(341, 461, 354, 474, 346, 466, 353, 473, 359, 479, 355, 475)(349, 469, 357, 477, 352, 472, 356, 476, 360, 480, 358, 478) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 261)(11, 245)(12, 264)(13, 246)(14, 268)(15, 269)(16, 271)(17, 248)(18, 265)(19, 275)(20, 276)(21, 250)(22, 277)(23, 279)(24, 252)(25, 258)(26, 283)(27, 284)(28, 254)(29, 255)(30, 287)(31, 256)(32, 290)(33, 291)(34, 292)(35, 259)(36, 260)(37, 262)(38, 297)(39, 263)(40, 296)(41, 300)(42, 285)(43, 266)(44, 267)(45, 282)(46, 304)(47, 270)(48, 307)(49, 293)(50, 272)(51, 273)(52, 274)(53, 289)(54, 311)(55, 312)(56, 280)(57, 278)(58, 315)(59, 301)(60, 281)(61, 299)(62, 318)(63, 319)(64, 286)(65, 322)(66, 308)(67, 288)(68, 306)(69, 325)(70, 326)(71, 294)(72, 295)(73, 331)(74, 316)(75, 298)(76, 314)(77, 334)(78, 302)(79, 303)(80, 336)(81, 323)(82, 305)(83, 321)(84, 341)(85, 309)(86, 310)(87, 346)(88, 329)(89, 328)(90, 332)(91, 313)(92, 330)(93, 349)(94, 317)(95, 352)(96, 320)(97, 351)(98, 339)(99, 338)(100, 353)(101, 324)(102, 355)(103, 344)(104, 343)(105, 347)(106, 327)(107, 345)(108, 356)(109, 333)(110, 358)(111, 337)(112, 335)(113, 340)(114, 357)(115, 342)(116, 348)(117, 354)(118, 350)(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, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E15.1270 Graph:: bipartite v = 80 e = 240 f = 132 degree seq :: [ 4^60, 12^20 ] E15.1268 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 10}) Quotient :: dipole Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1^-1)^2, Y1^6, (Y1 * Y2^-1 * Y1)^2, Y1^-1 * Y2^3 * Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2^-5 * Y1^2, Y2^-1 * Y1 * Y2^-2 * Y1^-2 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 ] Map:: R = (1, 121, 2, 122, 6, 126, 16, 136, 13, 133, 4, 124)(3, 123, 9, 129, 23, 143, 36, 156, 18, 138, 11, 131)(5, 125, 14, 134, 31, 151, 37, 157, 20, 140, 7, 127)(8, 128, 21, 141, 12, 132, 29, 149, 39, 159, 17, 137)(10, 130, 25, 145, 52, 172, 35, 155, 50, 170, 27, 147)(15, 135, 34, 154, 44, 164, 26, 146, 54, 174, 32, 152)(19, 139, 41, 161, 65, 185, 48, 168, 33, 153, 43, 163)(22, 142, 47, 167, 63, 183, 42, 162, 67, 187, 45, 165)(24, 144, 51, 171, 28, 148, 40, 160, 64, 184, 49, 169)(30, 150, 46, 166, 62, 182, 38, 158, 61, 181, 57, 177)(53, 173, 77, 197, 55, 175, 74, 194, 96, 216, 76, 196)(56, 176, 75, 195, 95, 215, 73, 193, 87, 207, 80, 200)(58, 178, 78, 198, 92, 212, 69, 189, 60, 180, 82, 202)(59, 179, 83, 203, 88, 208, 66, 186, 89, 209, 68, 188)(70, 190, 90, 210, 105, 225, 86, 206, 72, 192, 93, 213)(71, 191, 94, 214, 81, 201, 84, 204, 103, 223, 85, 205)(79, 199, 99, 219, 109, 229, 98, 218, 112, 232, 100, 220)(91, 211, 107, 227, 116, 236, 106, 226, 102, 222, 108, 228)(97, 217, 110, 230, 101, 221, 104, 224, 115, 235, 111, 231)(113, 233, 118, 238, 114, 234, 119, 239, 120, 240, 117, 237)(241, 361, 243, 363, 250, 370, 266, 386, 277, 397, 256, 376, 276, 396, 275, 395, 255, 375, 245, 365)(242, 362, 247, 367, 259, 379, 282, 402, 269, 389, 253, 373, 271, 391, 288, 408, 262, 382, 248, 368)(244, 364, 252, 372, 270, 390, 280, 400, 258, 378, 246, 366, 257, 377, 278, 398, 264, 384, 249, 369)(251, 371, 268, 388, 296, 416, 314, 434, 290, 410, 263, 383, 289, 409, 313, 433, 293, 413, 265, 385)(254, 374, 272, 392, 298, 418, 306, 426, 281, 401, 260, 380, 284, 404, 309, 429, 299, 419, 273, 393)(261, 381, 285, 405, 310, 430, 324, 444, 301, 421, 279, 399, 303, 423, 326, 446, 311, 431, 286, 406)(267, 387, 295, 415, 319, 439, 300, 420, 274, 394, 292, 412, 316, 436, 338, 458, 318, 438, 294, 414)(283, 403, 308, 428, 331, 451, 312, 432, 287, 407, 305, 425, 328, 448, 346, 466, 330, 450, 307, 427)(291, 411, 302, 422, 325, 445, 344, 464, 327, 447, 304, 424, 297, 417, 321, 441, 337, 457, 315, 435)(317, 437, 335, 455, 351, 471, 359, 479, 352, 472, 336, 456, 320, 440, 341, 461, 353, 473, 339, 459)(322, 442, 340, 460, 354, 474, 342, 462, 323, 443, 332, 452, 349, 469, 357, 477, 347, 467, 329, 449)(333, 453, 348, 468, 358, 478, 350, 470, 334, 454, 345, 465, 356, 476, 360, 480, 355, 475, 343, 463) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 259)(8, 242)(9, 244)(10, 266)(11, 268)(12, 270)(13, 271)(14, 272)(15, 245)(16, 276)(17, 278)(18, 246)(19, 282)(20, 284)(21, 285)(22, 248)(23, 289)(24, 249)(25, 251)(26, 277)(27, 295)(28, 296)(29, 253)(30, 280)(31, 288)(32, 298)(33, 254)(34, 292)(35, 255)(36, 275)(37, 256)(38, 264)(39, 303)(40, 258)(41, 260)(42, 269)(43, 308)(44, 309)(45, 310)(46, 261)(47, 305)(48, 262)(49, 313)(50, 263)(51, 302)(52, 316)(53, 265)(54, 267)(55, 319)(56, 314)(57, 321)(58, 306)(59, 273)(60, 274)(61, 279)(62, 325)(63, 326)(64, 297)(65, 328)(66, 281)(67, 283)(68, 331)(69, 299)(70, 324)(71, 286)(72, 287)(73, 293)(74, 290)(75, 291)(76, 338)(77, 335)(78, 294)(79, 300)(80, 341)(81, 337)(82, 340)(83, 332)(84, 301)(85, 344)(86, 311)(87, 304)(88, 346)(89, 322)(90, 307)(91, 312)(92, 349)(93, 348)(94, 345)(95, 351)(96, 320)(97, 315)(98, 318)(99, 317)(100, 354)(101, 353)(102, 323)(103, 333)(104, 327)(105, 356)(106, 330)(107, 329)(108, 358)(109, 357)(110, 334)(111, 359)(112, 336)(113, 339)(114, 342)(115, 343)(116, 360)(117, 347)(118, 350)(119, 352)(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, 4, 2, 4, 2, 4, 2, 4, 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 E15.1269 Graph:: bipartite v = 32 e = 240 f = 180 degree seq :: [ 12^20, 20^12 ] E15.1269 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 10}) Quotient :: dipole Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y3^4 * Y2 * Y3^-1, (Y3^2 * Y2 * Y3 * Y2)^2, (Y3^2 * Y2 * Y3^-2 * Y2)^3, (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)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 257, 377)(250, 370, 261, 381)(252, 372, 265, 385)(254, 374, 269, 389)(255, 375, 271, 391)(256, 376, 273, 393)(258, 378, 277, 397)(259, 379, 279, 399)(260, 380, 281, 401)(262, 382, 285, 405)(263, 383, 278, 398)(264, 384, 288, 408)(266, 386, 291, 411)(267, 387, 292, 412)(268, 388, 286, 406)(270, 390, 296, 416)(272, 392, 295, 415)(274, 394, 300, 420)(275, 395, 293, 413)(276, 396, 283, 403)(280, 400, 306, 426)(282, 402, 289, 409)(284, 404, 287, 407)(290, 410, 294, 414)(297, 417, 304, 424)(298, 418, 319, 439)(299, 419, 320, 440)(301, 421, 322, 442)(302, 422, 324, 444)(303, 423, 310, 430)(305, 425, 326, 446)(307, 427, 329, 449)(308, 428, 330, 450)(309, 429, 327, 447)(311, 431, 331, 451)(312, 432, 328, 448)(313, 433, 333, 453)(314, 434, 318, 438)(315, 435, 335, 455)(316, 436, 336, 456)(317, 437, 321, 441)(323, 443, 340, 460)(325, 445, 342, 462)(332, 452, 348, 468)(334, 454, 350, 470)(337, 457, 353, 473)(338, 458, 352, 472)(339, 459, 341, 461)(343, 463, 355, 475)(344, 464, 346, 466)(345, 465, 349, 469)(347, 467, 356, 476)(351, 471, 358, 478)(354, 474, 357, 477)(359, 479, 360, 480) L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 258)(9, 259)(10, 244)(11, 263)(12, 266)(13, 267)(14, 246)(15, 272)(16, 247)(17, 275)(18, 278)(19, 280)(20, 249)(21, 283)(22, 250)(23, 287)(24, 251)(25, 289)(26, 271)(27, 274)(28, 253)(29, 294)(30, 254)(31, 297)(32, 298)(33, 299)(34, 256)(35, 301)(36, 257)(37, 303)(38, 304)(39, 277)(40, 264)(41, 270)(42, 260)(43, 308)(44, 261)(45, 273)(46, 262)(47, 307)(48, 311)(49, 312)(50, 265)(51, 314)(52, 291)(53, 268)(54, 316)(55, 269)(56, 288)(57, 281)(58, 293)(59, 302)(60, 321)(61, 323)(62, 276)(63, 325)(64, 286)(65, 279)(66, 327)(67, 282)(68, 305)(69, 284)(70, 285)(71, 313)(72, 332)(73, 290)(74, 334)(75, 292)(76, 315)(77, 295)(78, 296)(79, 335)(80, 319)(81, 338)(82, 300)(83, 310)(84, 341)(85, 309)(86, 343)(87, 344)(88, 306)(89, 326)(90, 340)(91, 329)(92, 318)(93, 349)(94, 317)(95, 351)(96, 348)(97, 320)(98, 337)(99, 322)(100, 353)(101, 354)(102, 324)(103, 345)(104, 347)(105, 328)(106, 330)(107, 331)(108, 356)(109, 357)(110, 333)(111, 339)(112, 336)(113, 359)(114, 346)(115, 342)(116, 360)(117, 352)(118, 350)(119, 355)(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) :: { ( 12, 20 ), ( 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E15.1268 Graph:: simple bipartite v = 180 e = 240 f = 32 degree seq :: [ 2^120, 4^60 ] E15.1270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 10}) Quotient :: dipole Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^4 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, (Y3 * Y1^-2 * Y3 * Y1^-1)^2, Y1^10, (Y3 * Y1^2 * Y3 * Y1^-2)^3 ] Map:: R = (1, 121, 2, 122, 5, 125, 11, 131, 23, 143, 47, 167, 46, 166, 22, 142, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 31, 151, 28, 148, 54, 174, 41, 161, 38, 158, 18, 138, 8, 128)(6, 126, 13, 133, 27, 147, 52, 172, 50, 170, 36, 156, 17, 137, 35, 155, 30, 150, 14, 134)(9, 129, 19, 139, 39, 159, 34, 154, 16, 136, 33, 153, 60, 180, 67, 187, 42, 162, 20, 140)(12, 132, 25, 145, 49, 169, 72, 192, 70, 190, 45, 165, 29, 149, 55, 175, 51, 171, 26, 146)(21, 141, 43, 163, 68, 188, 66, 186, 40, 160, 24, 144, 48, 168, 71, 191, 69, 189, 44, 164)(32, 152, 58, 178, 80, 200, 99, 219, 85, 205, 64, 184, 61, 181, 82, 202, 81, 201, 59, 179)(37, 157, 63, 183, 84, 204, 83, 203, 62, 182, 57, 177, 79, 199, 96, 216, 76, 196, 53, 173)(56, 176, 78, 198, 98, 218, 97, 217, 77, 197, 75, 195, 95, 215, 109, 229, 93, 213, 73, 193)(65, 185, 86, 206, 103, 223, 115, 235, 101, 221, 89, 209, 88, 208, 105, 225, 104, 224, 87, 207)(74, 194, 94, 214, 110, 230, 106, 226, 90, 210, 92, 212, 108, 228, 116, 236, 107, 227, 91, 211)(100, 220, 114, 234, 118, 238, 112, 232, 102, 222, 113, 233, 119, 239, 120, 240, 117, 237, 111, 231)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 261)(11, 264)(12, 245)(13, 268)(14, 269)(15, 272)(16, 247)(17, 248)(18, 277)(19, 280)(20, 281)(21, 250)(22, 285)(23, 273)(24, 251)(25, 290)(26, 283)(27, 293)(28, 253)(29, 254)(30, 296)(31, 297)(32, 255)(33, 263)(34, 301)(35, 302)(36, 286)(37, 258)(38, 304)(39, 305)(40, 259)(41, 260)(42, 298)(43, 266)(44, 300)(45, 262)(46, 276)(47, 294)(48, 310)(49, 313)(50, 265)(51, 314)(52, 315)(53, 267)(54, 287)(55, 317)(56, 270)(57, 271)(58, 282)(59, 303)(60, 284)(61, 274)(62, 275)(63, 299)(64, 278)(65, 279)(66, 328)(67, 329)(68, 330)(69, 326)(70, 288)(71, 331)(72, 332)(73, 289)(74, 291)(75, 292)(76, 318)(77, 295)(78, 316)(79, 325)(80, 327)(81, 340)(82, 341)(83, 335)(84, 342)(85, 319)(86, 309)(87, 320)(88, 306)(89, 307)(90, 308)(91, 311)(92, 312)(93, 334)(94, 333)(95, 323)(96, 351)(97, 348)(98, 352)(99, 353)(100, 321)(101, 322)(102, 324)(103, 346)(104, 354)(105, 347)(106, 343)(107, 345)(108, 337)(109, 357)(110, 358)(111, 336)(112, 338)(113, 339)(114, 344)(115, 359)(116, 360)(117, 349)(118, 350)(119, 355)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 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 E15.1267 Graph:: simple bipartite v = 132 e = 240 f = 80 degree seq :: [ 2^120, 20^12 ] E15.1271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 10}) Quotient :: dipole Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1 * Y2^4 * Y1 * Y2^-1, Y2 * R * Y2^4 * R * Y2 * Y1, Y2^10, (Y2 * Y1 * Y2^2 * Y1)^2, (Y3 * Y2^-1)^6, (Y2^2 * Y1 * Y2^-2 * Y1)^3 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 17, 137)(10, 130, 21, 141)(12, 132, 25, 145)(14, 134, 29, 149)(15, 135, 31, 151)(16, 136, 33, 153)(18, 138, 37, 157)(19, 139, 39, 159)(20, 140, 41, 161)(22, 142, 45, 165)(23, 143, 38, 158)(24, 144, 48, 168)(26, 146, 51, 171)(27, 147, 52, 172)(28, 148, 46, 166)(30, 150, 56, 176)(32, 152, 55, 175)(34, 154, 60, 180)(35, 155, 53, 173)(36, 156, 43, 163)(40, 160, 66, 186)(42, 162, 49, 169)(44, 164, 47, 167)(50, 170, 54, 174)(57, 177, 64, 184)(58, 178, 79, 199)(59, 179, 80, 200)(61, 181, 82, 202)(62, 182, 84, 204)(63, 183, 70, 190)(65, 185, 86, 206)(67, 187, 89, 209)(68, 188, 90, 210)(69, 189, 87, 207)(71, 191, 91, 211)(72, 192, 88, 208)(73, 193, 93, 213)(74, 194, 78, 198)(75, 195, 95, 215)(76, 196, 96, 216)(77, 197, 81, 201)(83, 203, 100, 220)(85, 205, 102, 222)(92, 212, 108, 228)(94, 214, 110, 230)(97, 217, 113, 233)(98, 218, 112, 232)(99, 219, 101, 221)(103, 223, 115, 235)(104, 224, 106, 226)(105, 225, 109, 229)(107, 227, 116, 236)(111, 231, 118, 238)(114, 234, 117, 237)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 278, 398, 304, 424, 286, 406, 262, 382, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 266, 386, 271, 391, 297, 417, 281, 401, 270, 390, 254, 374, 246, 366)(247, 367, 255, 375, 272, 392, 298, 418, 293, 413, 268, 388, 253, 373, 267, 387, 274, 394, 256, 376)(249, 369, 259, 379, 280, 400, 264, 384, 251, 371, 263, 383, 287, 407, 307, 427, 282, 402, 260, 380)(257, 377, 275, 395, 301, 421, 323, 443, 310, 430, 285, 405, 273, 393, 299, 419, 302, 422, 276, 396)(261, 381, 283, 403, 308, 428, 305, 425, 279, 399, 277, 397, 303, 423, 325, 445, 309, 429, 284, 404)(265, 385, 289, 409, 312, 432, 332, 452, 318, 438, 296, 416, 288, 408, 311, 431, 313, 433, 290, 410)(269, 389, 294, 414, 316, 436, 315, 435, 292, 412, 291, 411, 314, 434, 334, 454, 317, 437, 295, 415)(300, 420, 321, 441, 338, 458, 337, 457, 320, 440, 319, 439, 335, 455, 351, 471, 339, 459, 322, 442)(306, 426, 327, 447, 344, 464, 347, 467, 331, 451, 329, 449, 326, 446, 343, 463, 345, 465, 328, 448)(324, 444, 341, 461, 354, 474, 346, 466, 330, 450, 340, 460, 353, 473, 359, 479, 355, 475, 342, 462)(333, 453, 349, 469, 357, 477, 352, 472, 336, 456, 348, 468, 356, 476, 360, 480, 358, 478, 350, 470) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 261)(11, 245)(12, 265)(13, 246)(14, 269)(15, 271)(16, 273)(17, 248)(18, 277)(19, 279)(20, 281)(21, 250)(22, 285)(23, 278)(24, 288)(25, 252)(26, 291)(27, 292)(28, 286)(29, 254)(30, 296)(31, 255)(32, 295)(33, 256)(34, 300)(35, 293)(36, 283)(37, 258)(38, 263)(39, 259)(40, 306)(41, 260)(42, 289)(43, 276)(44, 287)(45, 262)(46, 268)(47, 284)(48, 264)(49, 282)(50, 294)(51, 266)(52, 267)(53, 275)(54, 290)(55, 272)(56, 270)(57, 304)(58, 319)(59, 320)(60, 274)(61, 322)(62, 324)(63, 310)(64, 297)(65, 326)(66, 280)(67, 329)(68, 330)(69, 327)(70, 303)(71, 331)(72, 328)(73, 333)(74, 318)(75, 335)(76, 336)(77, 321)(78, 314)(79, 298)(80, 299)(81, 317)(82, 301)(83, 340)(84, 302)(85, 342)(86, 305)(87, 309)(88, 312)(89, 307)(90, 308)(91, 311)(92, 348)(93, 313)(94, 350)(95, 315)(96, 316)(97, 353)(98, 352)(99, 341)(100, 323)(101, 339)(102, 325)(103, 355)(104, 346)(105, 349)(106, 344)(107, 356)(108, 332)(109, 345)(110, 334)(111, 358)(112, 338)(113, 337)(114, 357)(115, 343)(116, 347)(117, 354)(118, 351)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 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 E15.1272 Graph:: bipartite v = 72 e = 240 f = 140 degree seq :: [ 4^60, 20^12 ] E15.1272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 10}) Quotient :: dipole Aut^+ = C2 x A5 (small group id <120, 35>) Aut = C2 x C2 x A5 (small group id <240, 190>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^2)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1 * Y1)^2, Y1^6, Y3^-1 * Y1^-1 * Y3^3 * Y1^-1 * Y3^-1 * Y1, Y3^-3 * Y1^3 * Y3^-2, (Y3 * Y2^-1)^10 ] Map:: R = (1, 121, 2, 122, 6, 126, 16, 136, 13, 133, 4, 124)(3, 123, 9, 129, 23, 143, 36, 156, 18, 138, 11, 131)(5, 125, 14, 134, 31, 151, 37, 157, 20, 140, 7, 127)(8, 128, 21, 141, 12, 132, 29, 149, 39, 159, 17, 137)(10, 130, 25, 145, 52, 172, 35, 155, 50, 170, 27, 147)(15, 135, 34, 154, 44, 164, 26, 146, 54, 174, 32, 152)(19, 139, 41, 161, 65, 185, 48, 168, 33, 153, 43, 163)(22, 142, 47, 167, 63, 183, 42, 162, 67, 187, 45, 165)(24, 144, 51, 171, 28, 148, 40, 160, 64, 184, 49, 169)(30, 150, 46, 166, 62, 182, 38, 158, 61, 181, 57, 177)(53, 173, 77, 197, 55, 175, 74, 194, 96, 216, 76, 196)(56, 176, 75, 195, 95, 215, 73, 193, 87, 207, 80, 200)(58, 178, 78, 198, 92, 212, 69, 189, 60, 180, 82, 202)(59, 179, 83, 203, 88, 208, 66, 186, 89, 209, 68, 188)(70, 190, 90, 210, 105, 225, 86, 206, 72, 192, 93, 213)(71, 191, 94, 214, 81, 201, 84, 204, 103, 223, 85, 205)(79, 199, 99, 219, 109, 229, 98, 218, 112, 232, 100, 220)(91, 211, 107, 227, 116, 236, 106, 226, 102, 222, 108, 228)(97, 217, 110, 230, 101, 221, 104, 224, 115, 235, 111, 231)(113, 233, 118, 238, 114, 234, 119, 239, 120, 240, 117, 237)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 259)(8, 242)(9, 244)(10, 266)(11, 268)(12, 270)(13, 271)(14, 272)(15, 245)(16, 276)(17, 278)(18, 246)(19, 282)(20, 284)(21, 285)(22, 248)(23, 289)(24, 249)(25, 251)(26, 277)(27, 295)(28, 296)(29, 253)(30, 280)(31, 288)(32, 298)(33, 254)(34, 292)(35, 255)(36, 275)(37, 256)(38, 264)(39, 303)(40, 258)(41, 260)(42, 269)(43, 308)(44, 309)(45, 310)(46, 261)(47, 305)(48, 262)(49, 313)(50, 263)(51, 302)(52, 316)(53, 265)(54, 267)(55, 319)(56, 314)(57, 321)(58, 306)(59, 273)(60, 274)(61, 279)(62, 325)(63, 326)(64, 297)(65, 328)(66, 281)(67, 283)(68, 331)(69, 299)(70, 324)(71, 286)(72, 287)(73, 293)(74, 290)(75, 291)(76, 338)(77, 335)(78, 294)(79, 300)(80, 341)(81, 337)(82, 340)(83, 332)(84, 301)(85, 344)(86, 311)(87, 304)(88, 346)(89, 322)(90, 307)(91, 312)(92, 349)(93, 348)(94, 345)(95, 351)(96, 320)(97, 315)(98, 318)(99, 317)(100, 354)(101, 353)(102, 323)(103, 333)(104, 327)(105, 356)(106, 330)(107, 329)(108, 358)(109, 357)(110, 334)(111, 359)(112, 336)(113, 339)(114, 342)(115, 343)(116, 360)(117, 347)(118, 350)(119, 352)(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, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E15.1271 Graph:: simple bipartite v = 140 e = 240 f = 72 degree seq :: [ 2^120, 12^20 ] E15.1273 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 60}) Quotient :: regular Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^-2 * T2 * T1^13 * T2 * T1^-15 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 93, 111, 114, 117, 120, 98, 92, 87, 84, 79, 75, 66, 70, 67, 71, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 95, 104, 101, 102, 105, 108, 113, 100, 91, 88, 83, 80, 72, 68, 63, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 97, 109, 107, 112, 116, 118, 89, 96, 81, 86, 69, 78, 62, 77, 64, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 99, 103, 106, 110, 115, 94, 119, 85, 90, 76, 82, 65, 74, 61, 73, 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, 73)(55, 95)(57, 71)(60, 97)(61, 101)(62, 102)(63, 103)(64, 104)(65, 105)(66, 106)(67, 99)(68, 107)(69, 108)(70, 109)(72, 110)(74, 111)(75, 112)(76, 113)(77, 93)(78, 114)(79, 115)(80, 116)(81, 100)(82, 117)(83, 94)(84, 118)(85, 91)(86, 120)(87, 119)(88, 89)(90, 98)(92, 96) local type(s) :: { ( 4^60 ) } Outer automorphisms :: reflexible Dual of E15.1274 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 60 f = 30 degree seq :: [ 60^2 ] E15.1274 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 60}) Quotient :: regular Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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^-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, 37, 32, 42)(35, 55, 39, 53)(36, 59, 38, 62)(40, 66, 41, 57)(43, 64, 44, 60)(45, 70, 46, 68)(47, 75, 48, 73)(49, 79, 50, 77)(51, 83, 52, 81)(54, 87, 56, 85)(58, 93, 67, 94)(61, 102, 65, 100)(63, 91, 72, 89)(69, 97, 71, 98)(74, 101, 76, 103)(78, 108, 80, 109)(82, 113, 84, 114)(86, 117, 88, 118)(90, 120, 92, 119)(95, 116, 96, 115)(99, 104, 107, 106)(105, 110, 112, 111) 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, 89)(52, 91)(54, 94)(56, 93)(58, 98)(61, 103)(63, 100)(65, 101)(67, 97)(69, 109)(71, 108)(72, 102)(74, 114)(76, 113)(78, 118)(80, 117)(82, 119)(84, 120)(86, 115)(88, 116)(90, 111)(92, 110)(95, 106)(96, 104)(99, 105)(107, 112) local type(s) :: { ( 60^4 ) } Outer automorphisms :: reflexible Dual of E15.1273 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 30 e = 60 f = 2 degree seq :: [ 4^30 ] E15.1275 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 60}) Quotient :: edge Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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^-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, 57, 34, 59)(35, 62, 42, 64)(36, 66, 45, 68)(37, 70, 38, 65)(39, 74, 40, 61)(41, 77, 43, 79)(44, 82, 46, 84)(47, 72, 48, 69)(49, 89, 50, 91)(51, 93, 52, 95)(53, 97, 54, 99)(55, 101, 56, 103)(58, 105, 60, 107)(63, 110, 80, 112)(67, 113, 85, 114)(71, 116, 73, 111)(75, 118, 76, 109)(78, 119, 81, 120)(83, 108, 86, 106)(87, 117, 88, 115)(90, 102, 92, 104)(94, 98, 96, 100)(121, 122)(123, 127)(124, 129)(125, 130)(126, 132)(128, 131)(133, 137)(134, 138)(135, 139)(136, 140)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 168)(152, 167)(155, 181)(156, 185)(157, 189)(158, 192)(159, 177)(160, 179)(161, 182)(162, 194)(163, 184)(164, 186)(165, 190)(166, 188)(169, 197)(170, 199)(171, 202)(172, 204)(173, 209)(174, 211)(175, 213)(176, 215)(178, 217)(180, 219)(183, 229)(187, 231)(191, 235)(193, 237)(195, 225)(196, 227)(198, 230)(200, 238)(201, 232)(203, 233)(205, 236)(206, 234)(207, 223)(208, 221)(210, 239)(212, 240)(214, 228)(216, 226)(218, 222)(220, 224) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 120, 120 ), ( 120^4 ) } Outer automorphisms :: reflexible Dual of E15.1279 Transitivity :: ET+ Graph:: simple bipartite v = 90 e = 120 f = 2 degree seq :: [ 2^60, 4^30 ] E15.1276 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 60}) Quotient :: edge Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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^-30 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 80, 72, 65, 61, 63, 70, 78, 86, 93, 98, 103, 108, 118, 113, 109, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 101, 96, 89, 82, 74, 66, 73, 81, 88, 95, 100, 105, 111, 116, 120, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 91, 84, 76, 68, 62, 67, 75, 83, 90, 97, 102, 106, 114, 117, 115, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 92, 85, 77, 69, 64, 71, 79, 87, 94, 99, 104, 110, 112, 119, 107, 56, 48, 40, 32, 24, 16, 8)(121, 122, 126, 124)(123, 129, 133, 128)(125, 131, 134, 127)(130, 136, 141, 137)(132, 135, 142, 139)(138, 145, 149, 144)(140, 147, 150, 143)(146, 152, 157, 153)(148, 151, 158, 155)(154, 161, 165, 160)(156, 163, 166, 159)(162, 168, 173, 169)(164, 167, 174, 171)(170, 177, 221, 176)(172, 179, 229, 175)(178, 227, 216, 235)(180, 211, 233, 212)(181, 224, 186, 222)(182, 218, 184, 225)(183, 217, 193, 219)(185, 226, 194, 230)(187, 220, 191, 213)(188, 231, 189, 223)(190, 214, 201, 210)(192, 232, 202, 234)(195, 206, 199, 215)(196, 228, 197, 236)(198, 203, 208, 207)(200, 237, 209, 239)(204, 240, 205, 238) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^4 ), ( 4^60 ) } Outer automorphisms :: reflexible Dual of E15.1280 Transitivity :: ET+ Graph:: bipartite v = 32 e = 120 f = 60 degree seq :: [ 4^30, 60^2 ] E15.1277 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 60}) Quotient :: edge Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^-2 * T2 * T1^13 * T2 * T1^-15 ] 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, 63)(55, 87)(57, 61)(60, 89)(62, 91)(64, 96)(65, 98)(66, 85)(67, 101)(68, 103)(69, 105)(70, 107)(71, 109)(72, 111)(73, 113)(74, 115)(75, 117)(76, 114)(77, 119)(78, 112)(79, 120)(80, 106)(81, 118)(82, 104)(83, 116)(84, 100)(86, 110)(88, 99)(90, 108)(92, 95)(93, 102)(94, 97)(121, 122, 125, 131, 140, 149, 157, 165, 173, 205, 225, 233, 239, 238, 230, 212, 204, 200, 196, 192, 188, 185, 182, 181, 178, 170, 162, 154, 146, 136, 143, 137, 144, 152, 160, 168, 176, 207, 216, 221, 227, 235, 232, 224, 219, 214, 213, 210, 203, 199, 195, 191, 180, 172, 164, 156, 148, 139, 130, 124)(123, 127, 135, 145, 153, 161, 169, 177, 209, 218, 237, 231, 236, 226, 222, 215, 208, 201, 198, 193, 190, 186, 184, 174, 167, 158, 151, 141, 134, 126, 133, 129, 138, 147, 155, 163, 171, 179, 211, 229, 223, 240, 234, 228, 220, 217, 206, 202, 197, 194, 189, 187, 183, 175, 166, 159, 150, 142, 132, 128) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8, 8 ), ( 8^60 ) } Outer automorphisms :: reflexible Dual of E15.1278 Transitivity :: ET+ Graph:: simple bipartite v = 62 e = 120 f = 30 degree seq :: [ 2^60, 60^2 ] E15.1278 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 60}) Quotient :: loop Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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^-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, 121, 3, 123, 8, 128, 4, 124)(2, 122, 5, 125, 11, 131, 6, 126)(7, 127, 13, 133, 9, 129, 14, 134)(10, 130, 15, 135, 12, 132, 16, 136)(17, 137, 21, 141, 18, 138, 22, 142)(19, 139, 23, 143, 20, 140, 24, 144)(25, 145, 29, 149, 26, 146, 30, 150)(27, 147, 31, 151, 28, 148, 32, 152)(33, 153, 39, 159, 34, 154, 40, 160)(35, 155, 60, 180, 42, 162, 61, 181)(36, 156, 63, 183, 45, 165, 64, 184)(37, 157, 56, 176, 38, 158, 55, 175)(41, 161, 66, 186, 43, 163, 59, 179)(44, 164, 69, 189, 46, 166, 62, 182)(47, 167, 67, 187, 48, 168, 65, 185)(49, 169, 70, 190, 50, 170, 68, 188)(51, 171, 72, 192, 52, 172, 71, 191)(53, 173, 74, 194, 54, 174, 73, 193)(57, 177, 76, 196, 58, 178, 75, 195)(77, 197, 79, 199, 78, 198, 80, 200)(81, 201, 84, 204, 82, 202, 85, 205)(83, 203, 108, 228, 90, 210, 109, 229)(86, 206, 111, 231, 93, 213, 112, 232)(87, 207, 104, 224, 88, 208, 103, 223)(89, 209, 114, 234, 91, 211, 107, 227)(92, 212, 117, 237, 94, 214, 110, 230)(95, 215, 115, 235, 96, 216, 113, 233)(97, 217, 118, 238, 98, 218, 116, 236)(99, 219, 120, 240, 100, 220, 119, 239)(101, 221, 105, 225, 102, 222, 106, 226) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 130)(6, 132)(7, 123)(8, 131)(9, 124)(10, 125)(11, 128)(12, 126)(13, 137)(14, 138)(15, 139)(16, 140)(17, 133)(18, 134)(19, 135)(20, 136)(21, 145)(22, 146)(23, 147)(24, 148)(25, 141)(26, 142)(27, 143)(28, 144)(29, 153)(30, 154)(31, 175)(32, 176)(33, 149)(34, 150)(35, 179)(36, 182)(37, 183)(38, 184)(39, 180)(40, 181)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 151)(56, 152)(57, 201)(58, 202)(59, 155)(60, 159)(61, 160)(62, 156)(63, 157)(64, 158)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 223)(80, 224)(81, 177)(82, 178)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 226)(98, 225)(99, 221)(100, 222)(101, 219)(102, 220)(103, 199)(104, 200)(105, 218)(106, 217)(107, 203)(108, 204)(109, 205)(110, 206)(111, 207)(112, 208)(113, 209)(114, 210)(115, 211)(116, 212)(117, 213)(118, 214)(119, 215)(120, 216) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E15.1277 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 30 e = 120 f = 62 degree seq :: [ 8^30 ] E15.1279 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 60}) Quotient :: loop Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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^-30 * T1^-1 ] Map:: R = (1, 121, 3, 123, 10, 130, 18, 138, 26, 146, 34, 154, 42, 162, 50, 170, 58, 178, 69, 189, 73, 193, 77, 197, 81, 201, 85, 205, 89, 209, 103, 223, 96, 216, 100, 220, 108, 228, 116, 236, 114, 234, 104, 224, 98, 218, 93, 213, 54, 174, 46, 166, 38, 158, 30, 150, 22, 142, 14, 134, 6, 126, 13, 133, 21, 141, 29, 149, 37, 157, 45, 165, 53, 173, 65, 185, 61, 181, 63, 183, 67, 187, 71, 191, 75, 195, 79, 199, 83, 203, 87, 207, 92, 212, 111, 231, 119, 239, 120, 240, 112, 232, 106, 226, 60, 180, 52, 172, 44, 164, 36, 156, 28, 148, 20, 140, 12, 132, 5, 125)(2, 122, 7, 127, 15, 135, 23, 143, 31, 151, 39, 159, 47, 167, 55, 175, 64, 184, 68, 188, 72, 192, 76, 196, 80, 200, 84, 204, 88, 208, 94, 214, 97, 217, 105, 225, 113, 233, 117, 237, 107, 227, 101, 221, 95, 215, 57, 177, 49, 169, 41, 161, 33, 153, 25, 145, 17, 137, 9, 129, 4, 124, 11, 131, 19, 139, 27, 147, 35, 155, 43, 163, 51, 171, 59, 179, 62, 182, 66, 186, 70, 190, 74, 194, 78, 198, 82, 202, 86, 206, 90, 210, 102, 222, 110, 230, 118, 238, 115, 235, 109, 229, 99, 219, 91, 211, 56, 176, 48, 168, 40, 160, 32, 152, 24, 144, 16, 136, 8, 128) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 131)(6, 124)(7, 125)(8, 123)(9, 133)(10, 136)(11, 134)(12, 135)(13, 128)(14, 127)(15, 142)(16, 141)(17, 130)(18, 145)(19, 132)(20, 147)(21, 137)(22, 139)(23, 140)(24, 138)(25, 149)(26, 152)(27, 150)(28, 151)(29, 144)(30, 143)(31, 158)(32, 157)(33, 146)(34, 161)(35, 148)(36, 163)(37, 153)(38, 155)(39, 156)(40, 154)(41, 165)(42, 168)(43, 166)(44, 167)(45, 160)(46, 159)(47, 174)(48, 173)(49, 162)(50, 177)(51, 164)(52, 179)(53, 169)(54, 171)(55, 172)(56, 170)(57, 185)(58, 211)(59, 213)(60, 184)(61, 215)(62, 180)(63, 219)(64, 218)(65, 176)(66, 224)(67, 227)(68, 226)(69, 221)(70, 232)(71, 235)(72, 234)(73, 229)(74, 236)(75, 233)(76, 240)(77, 237)(78, 239)(79, 230)(80, 228)(81, 238)(82, 220)(83, 217)(84, 231)(85, 225)(86, 212)(87, 210)(88, 216)(89, 222)(90, 223)(91, 181)(92, 208)(93, 175)(94, 207)(95, 178)(96, 206)(97, 209)(98, 182)(99, 189)(100, 204)(101, 183)(102, 203)(103, 214)(104, 188)(105, 199)(106, 186)(107, 193)(108, 198)(109, 187)(110, 205)(111, 202)(112, 192)(113, 201)(114, 190)(115, 197)(116, 196)(117, 191)(118, 195)(119, 200)(120, 194) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1275 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 120 f = 90 degree seq :: [ 120^2 ] E15.1280 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 60}) Quotient :: loop Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^-2 * T2 * T1^13 * T2 * T1^-15 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 12, 132)(7, 127, 16, 136)(8, 128, 17, 137)(10, 130, 15, 135)(11, 131, 21, 141)(13, 133, 23, 143)(14, 134, 24, 144)(18, 138, 26, 146)(19, 139, 27, 147)(20, 140, 30, 150)(22, 142, 32, 152)(25, 145, 34, 154)(28, 148, 33, 153)(29, 149, 38, 158)(31, 151, 40, 160)(35, 155, 42, 162)(36, 156, 43, 163)(37, 157, 46, 166)(39, 159, 48, 168)(41, 161, 50, 170)(44, 164, 49, 169)(45, 165, 54, 174)(47, 167, 56, 176)(51, 171, 58, 178)(52, 172, 59, 179)(53, 173, 91, 211)(55, 175, 107, 227)(57, 177, 102, 222)(60, 180, 109, 229)(61, 181, 101, 221)(62, 182, 108, 228)(63, 183, 110, 230)(64, 184, 96, 216)(65, 185, 113, 233)(66, 186, 103, 223)(67, 187, 104, 224)(68, 188, 94, 214)(69, 189, 115, 235)(70, 190, 89, 209)(71, 191, 116, 236)(72, 192, 98, 218)(73, 193, 99, 219)(74, 194, 87, 207)(75, 195, 118, 238)(76, 196, 95, 215)(77, 197, 106, 226)(78, 198, 112, 232)(79, 199, 81, 201)(80, 200, 92, 212)(82, 202, 100, 220)(83, 203, 119, 239)(84, 204, 117, 237)(85, 205, 88, 208)(86, 206, 105, 225)(90, 210, 120, 240)(93, 213, 114, 234)(97, 217, 111, 231) 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, 143)(17, 144)(18, 147)(19, 130)(20, 149)(21, 134)(22, 132)(23, 137)(24, 152)(25, 153)(26, 136)(27, 155)(28, 139)(29, 157)(30, 142)(31, 141)(32, 160)(33, 161)(34, 146)(35, 163)(36, 148)(37, 165)(38, 151)(39, 150)(40, 168)(41, 169)(42, 154)(43, 171)(44, 156)(45, 173)(46, 159)(47, 158)(48, 176)(49, 177)(50, 162)(51, 179)(52, 164)(53, 225)(54, 167)(55, 166)(56, 227)(57, 229)(58, 170)(59, 231)(60, 172)(61, 182)(62, 185)(63, 187)(64, 181)(65, 191)(66, 193)(67, 195)(68, 183)(69, 198)(70, 184)(71, 180)(72, 188)(73, 189)(74, 186)(75, 204)(76, 202)(77, 203)(78, 206)(79, 190)(80, 194)(81, 192)(82, 197)(83, 210)(84, 211)(85, 196)(86, 213)(87, 199)(88, 201)(89, 200)(90, 217)(91, 175)(92, 205)(93, 174)(94, 207)(95, 209)(96, 208)(97, 222)(98, 212)(99, 214)(100, 216)(101, 215)(102, 178)(103, 218)(104, 219)(105, 238)(106, 221)(107, 234)(108, 220)(109, 240)(110, 223)(111, 236)(112, 224)(113, 226)(114, 237)(115, 230)(116, 239)(117, 232)(118, 235)(119, 228)(120, 233) local type(s) :: { ( 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E15.1276 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 60 e = 120 f = 32 degree seq :: [ 4^60 ] E15.1281 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 60}) Quotient :: dipole Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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^-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)^60 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 11, 131)(13, 133, 17, 137)(14, 134, 18, 138)(15, 135, 19, 139)(16, 136, 20, 140)(21, 141, 25, 145)(22, 142, 26, 146)(23, 143, 27, 147)(24, 144, 28, 148)(29, 149, 33, 153)(30, 150, 34, 154)(31, 151, 38, 158)(32, 152, 37, 157)(35, 155, 53, 173)(36, 156, 60, 180)(39, 159, 57, 177)(40, 160, 55, 175)(41, 161, 59, 179)(42, 162, 61, 181)(43, 163, 64, 184)(44, 164, 63, 183)(45, 165, 67, 187)(46, 166, 69, 189)(47, 167, 72, 192)(48, 168, 74, 194)(49, 169, 77, 197)(50, 170, 79, 199)(51, 171, 81, 201)(52, 172, 83, 203)(54, 174, 85, 205)(56, 176, 87, 207)(58, 178, 94, 214)(62, 182, 102, 222)(65, 185, 91, 211)(66, 186, 89, 209)(68, 188, 98, 218)(70, 190, 93, 213)(71, 191, 97, 217)(73, 193, 103, 223)(75, 195, 100, 220)(76, 196, 101, 221)(78, 198, 108, 228)(80, 200, 107, 227)(82, 202, 113, 233)(84, 204, 112, 232)(86, 206, 118, 238)(88, 208, 117, 237)(90, 210, 119, 239)(92, 212, 120, 240)(95, 215, 116, 236)(96, 216, 114, 234)(99, 219, 104, 224)(105, 225, 109, 229)(106, 226, 111, 231)(110, 230, 115, 235)(241, 361, 243, 363, 248, 368, 244, 364)(242, 362, 245, 365, 251, 371, 246, 366)(247, 367, 253, 373, 249, 369, 254, 374)(250, 370, 255, 375, 252, 372, 256, 376)(257, 377, 261, 381, 258, 378, 262, 382)(259, 379, 263, 383, 260, 380, 264, 384)(265, 385, 269, 389, 266, 386, 270, 390)(267, 387, 271, 391, 268, 388, 272, 392)(273, 393, 293, 413, 274, 394, 295, 415)(275, 395, 297, 417, 280, 400, 299, 419)(276, 396, 301, 421, 283, 403, 303, 423)(277, 397, 304, 424, 278, 398, 300, 420)(279, 399, 307, 427, 281, 401, 309, 429)(282, 402, 312, 432, 284, 404, 314, 434)(285, 405, 317, 437, 286, 406, 319, 439)(287, 407, 321, 441, 288, 408, 323, 443)(289, 409, 325, 445, 290, 410, 327, 447)(291, 411, 329, 449, 292, 412, 331, 451)(294, 414, 334, 454, 296, 416, 333, 453)(298, 418, 338, 458, 310, 430, 337, 457)(302, 422, 343, 463, 315, 435, 341, 461)(305, 425, 340, 460, 306, 426, 342, 462)(308, 428, 348, 468, 311, 431, 347, 467)(313, 433, 353, 473, 316, 436, 352, 472)(318, 438, 358, 478, 320, 440, 357, 477)(322, 442, 359, 479, 324, 444, 360, 480)(326, 446, 356, 476, 328, 448, 354, 474)(330, 450, 351, 471, 332, 452, 349, 469)(335, 455, 344, 464, 336, 456, 355, 475)(339, 459, 345, 465, 350, 470, 346, 466) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 250)(6, 252)(7, 243)(8, 251)(9, 244)(10, 245)(11, 248)(12, 246)(13, 257)(14, 258)(15, 259)(16, 260)(17, 253)(18, 254)(19, 255)(20, 256)(21, 265)(22, 266)(23, 267)(24, 268)(25, 261)(26, 262)(27, 263)(28, 264)(29, 273)(30, 274)(31, 278)(32, 277)(33, 269)(34, 270)(35, 293)(36, 300)(37, 272)(38, 271)(39, 297)(40, 295)(41, 299)(42, 301)(43, 304)(44, 303)(45, 307)(46, 309)(47, 312)(48, 314)(49, 317)(50, 319)(51, 321)(52, 323)(53, 275)(54, 325)(55, 280)(56, 327)(57, 279)(58, 334)(59, 281)(60, 276)(61, 282)(62, 342)(63, 284)(64, 283)(65, 331)(66, 329)(67, 285)(68, 338)(69, 286)(70, 333)(71, 337)(72, 287)(73, 343)(74, 288)(75, 340)(76, 341)(77, 289)(78, 348)(79, 290)(80, 347)(81, 291)(82, 353)(83, 292)(84, 352)(85, 294)(86, 358)(87, 296)(88, 357)(89, 306)(90, 359)(91, 305)(92, 360)(93, 310)(94, 298)(95, 356)(96, 354)(97, 311)(98, 308)(99, 344)(100, 315)(101, 316)(102, 302)(103, 313)(104, 339)(105, 349)(106, 351)(107, 320)(108, 318)(109, 345)(110, 355)(111, 346)(112, 324)(113, 322)(114, 336)(115, 350)(116, 335)(117, 328)(118, 326)(119, 330)(120, 332)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120 ) } Outer automorphisms :: reflexible Dual of E15.1284 Graph:: bipartite v = 90 e = 240 f = 122 degree seq :: [ 4^60, 8^30 ] E15.1282 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 60}) Quotient :: dipole Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, Y2^29 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 13, 133, 8, 128)(5, 125, 11, 131, 14, 134, 7, 127)(10, 130, 16, 136, 21, 141, 17, 137)(12, 132, 15, 135, 22, 142, 19, 139)(18, 138, 25, 145, 29, 149, 24, 144)(20, 140, 27, 147, 30, 150, 23, 143)(26, 146, 32, 152, 37, 157, 33, 153)(28, 148, 31, 151, 38, 158, 35, 155)(34, 154, 41, 161, 45, 165, 40, 160)(36, 156, 43, 163, 46, 166, 39, 159)(42, 162, 48, 168, 53, 173, 49, 169)(44, 164, 47, 167, 54, 174, 51, 171)(50, 170, 57, 177, 97, 217, 56, 176)(52, 172, 59, 179, 78, 198, 55, 175)(58, 178, 79, 199, 118, 238, 75, 195)(60, 180, 99, 219, 70, 190, 103, 223)(61, 181, 105, 225, 66, 186, 107, 227)(62, 182, 108, 228, 64, 184, 106, 226)(63, 183, 109, 229, 73, 193, 111, 231)(65, 185, 112, 232, 74, 194, 114, 234)(67, 187, 113, 233, 71, 191, 102, 222)(68, 188, 110, 230, 69, 189, 115, 235)(72, 192, 117, 237, 81, 201, 119, 239)(76, 196, 104, 224, 77, 197, 116, 236)(80, 200, 100, 220, 85, 205, 101, 221)(82, 202, 120, 240, 83, 203, 96, 216)(84, 204, 95, 215, 89, 209, 94, 214)(86, 206, 92, 212, 87, 207, 98, 218)(88, 208, 90, 210, 93, 213, 91, 211)(241, 361, 243, 363, 250, 370, 258, 378, 266, 386, 274, 394, 282, 402, 290, 410, 298, 418, 342, 462, 348, 468, 355, 475, 344, 464, 336, 456, 332, 452, 328, 448, 324, 444, 320, 440, 312, 432, 305, 425, 301, 421, 303, 423, 310, 430, 318, 438, 294, 414, 286, 406, 278, 398, 270, 390, 262, 382, 254, 374, 246, 366, 253, 373, 261, 381, 269, 389, 277, 397, 285, 405, 293, 413, 337, 457, 358, 478, 353, 473, 346, 466, 350, 470, 356, 476, 360, 480, 338, 458, 333, 453, 329, 449, 325, 445, 321, 441, 314, 434, 306, 426, 313, 433, 300, 420, 292, 412, 284, 404, 276, 396, 268, 388, 260, 380, 252, 372, 245, 365)(242, 362, 247, 367, 255, 375, 263, 383, 271, 391, 279, 399, 287, 407, 295, 415, 339, 459, 349, 469, 347, 467, 352, 472, 359, 479, 340, 460, 334, 454, 330, 450, 326, 446, 322, 442, 316, 436, 308, 428, 302, 422, 307, 427, 315, 435, 297, 417, 289, 409, 281, 401, 273, 393, 265, 385, 257, 377, 249, 369, 244, 364, 251, 371, 259, 379, 267, 387, 275, 395, 283, 403, 291, 411, 299, 419, 343, 463, 351, 471, 345, 465, 354, 474, 357, 477, 341, 461, 335, 455, 331, 451, 327, 447, 323, 443, 317, 437, 309, 429, 304, 424, 311, 431, 319, 439, 296, 416, 288, 408, 280, 400, 272, 392, 264, 384, 256, 376, 248, 368) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 253)(7, 255)(8, 242)(9, 244)(10, 258)(11, 259)(12, 245)(13, 261)(14, 246)(15, 263)(16, 248)(17, 249)(18, 266)(19, 267)(20, 252)(21, 269)(22, 254)(23, 271)(24, 256)(25, 257)(26, 274)(27, 275)(28, 260)(29, 277)(30, 262)(31, 279)(32, 264)(33, 265)(34, 282)(35, 283)(36, 268)(37, 285)(38, 270)(39, 287)(40, 272)(41, 273)(42, 290)(43, 291)(44, 276)(45, 293)(46, 278)(47, 295)(48, 280)(49, 281)(50, 298)(51, 299)(52, 284)(53, 337)(54, 286)(55, 339)(56, 288)(57, 289)(58, 342)(59, 343)(60, 292)(61, 303)(62, 307)(63, 310)(64, 311)(65, 301)(66, 313)(67, 315)(68, 302)(69, 304)(70, 318)(71, 319)(72, 305)(73, 300)(74, 306)(75, 297)(76, 308)(77, 309)(78, 294)(79, 296)(80, 312)(81, 314)(82, 316)(83, 317)(84, 320)(85, 321)(86, 322)(87, 323)(88, 324)(89, 325)(90, 326)(91, 327)(92, 328)(93, 329)(94, 330)(95, 331)(96, 332)(97, 358)(98, 333)(99, 349)(100, 334)(101, 335)(102, 348)(103, 351)(104, 336)(105, 354)(106, 350)(107, 352)(108, 355)(109, 347)(110, 356)(111, 345)(112, 359)(113, 346)(114, 357)(115, 344)(116, 360)(117, 341)(118, 353)(119, 340)(120, 338)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1283 Graph:: bipartite v = 32 e = 240 f = 180 degree seq :: [ 8^30, 120^2 ] E15.1283 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 60}) Quotient :: dipole Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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, Y3^27 * Y2 * Y3^-1 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^60 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 254, 374)(250, 370, 252, 372)(255, 375, 260, 380)(256, 376, 263, 383)(257, 377, 265, 385)(258, 378, 261, 381)(259, 379, 267, 387)(262, 382, 269, 389)(264, 384, 271, 391)(266, 386, 272, 392)(268, 388, 270, 390)(273, 393, 279, 399)(274, 394, 281, 401)(275, 395, 277, 397)(276, 396, 283, 403)(278, 398, 285, 405)(280, 400, 287, 407)(282, 402, 288, 408)(284, 404, 286, 406)(289, 409, 295, 415)(290, 410, 297, 417)(291, 411, 293, 413)(292, 412, 299, 419)(294, 414, 337, 457)(296, 416, 319, 439)(298, 418, 340, 460)(300, 420, 316, 436)(301, 421, 343, 463)(302, 422, 344, 464)(303, 423, 345, 465)(304, 424, 347, 467)(305, 425, 349, 469)(306, 426, 351, 471)(307, 427, 346, 466)(308, 428, 353, 473)(309, 429, 348, 468)(310, 430, 355, 475)(311, 431, 350, 470)(312, 432, 356, 476)(313, 433, 352, 472)(314, 434, 354, 474)(315, 435, 357, 477)(317, 437, 338, 458)(318, 438, 341, 461)(320, 440, 358, 478)(321, 441, 335, 455)(322, 442, 359, 479)(323, 443, 336, 456)(324, 444, 360, 480)(325, 445, 339, 459)(326, 446, 342, 462)(327, 447, 329, 449)(328, 448, 331, 451)(330, 450, 333, 453)(332, 452, 334, 454) 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, 266)(18, 267)(19, 250)(20, 253)(21, 251)(22, 270)(23, 271)(24, 254)(25, 256)(26, 274)(27, 275)(28, 259)(29, 261)(30, 278)(31, 279)(32, 264)(33, 265)(34, 282)(35, 283)(36, 268)(37, 269)(38, 286)(39, 287)(40, 272)(41, 273)(42, 290)(43, 291)(44, 276)(45, 277)(46, 294)(47, 295)(48, 280)(49, 281)(50, 298)(51, 299)(52, 284)(53, 285)(54, 316)(55, 319)(56, 288)(57, 289)(58, 311)(59, 314)(60, 292)(61, 303)(62, 305)(63, 308)(64, 301)(65, 312)(66, 302)(67, 315)(68, 317)(69, 318)(70, 304)(71, 320)(72, 321)(73, 322)(74, 306)(75, 309)(76, 307)(77, 323)(78, 324)(79, 310)(80, 313)(81, 325)(82, 326)(83, 327)(84, 328)(85, 329)(86, 330)(87, 331)(88, 332)(89, 333)(90, 334)(91, 335)(92, 336)(93, 338)(94, 339)(95, 341)(96, 342)(97, 293)(98, 359)(99, 360)(100, 296)(101, 349)(102, 353)(103, 350)(104, 346)(105, 358)(106, 354)(107, 340)(108, 344)(109, 357)(110, 355)(111, 300)(112, 343)(113, 352)(114, 337)(115, 297)(116, 348)(117, 351)(118, 347)(119, 345)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 120 ), ( 8, 120, 8, 120 ) } Outer automorphisms :: reflexible Dual of E15.1282 Graph:: simple bipartite v = 180 e = 240 f = 32 degree seq :: [ 2^120, 4^60 ] E15.1284 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 60}) Quotient :: dipole Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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 * Y1^13 * Y3 * Y1^-15 ] Map:: R = (1, 121, 2, 122, 5, 125, 11, 131, 20, 140, 29, 149, 37, 157, 45, 165, 53, 173, 70, 190, 74, 194, 78, 198, 82, 202, 87, 207, 91, 211, 93, 213, 95, 215, 100, 220, 106, 226, 114, 234, 109, 229, 103, 223, 96, 216, 88, 208, 58, 178, 50, 170, 42, 162, 34, 154, 26, 146, 16, 136, 23, 143, 17, 137, 24, 144, 32, 152, 40, 160, 48, 168, 56, 176, 61, 181, 62, 182, 63, 183, 66, 186, 69, 189, 73, 193, 77, 197, 81, 201, 86, 206, 108, 228, 116, 236, 120, 240, 117, 237, 111, 231, 101, 221, 60, 180, 52, 172, 44, 164, 36, 156, 28, 148, 19, 139, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 25, 145, 33, 153, 41, 161, 49, 169, 57, 177, 65, 185, 68, 188, 72, 192, 76, 196, 80, 200, 84, 204, 90, 210, 97, 217, 102, 222, 110, 230, 113, 233, 119, 239, 99, 219, 107, 227, 92, 212, 54, 174, 47, 167, 38, 158, 31, 151, 21, 141, 14, 134, 6, 126, 13, 133, 9, 129, 18, 138, 27, 147, 35, 155, 43, 163, 51, 171, 59, 179, 64, 184, 67, 187, 71, 191, 75, 195, 79, 199, 83, 203, 89, 209, 98, 218, 104, 224, 112, 232, 118, 238, 105, 225, 115, 235, 94, 214, 85, 205, 55, 175, 46, 166, 39, 159, 30, 150, 22, 142, 12, 132, 8, 128)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 255)(11, 261)(12, 245)(13, 263)(14, 264)(15, 250)(16, 247)(17, 248)(18, 266)(19, 267)(20, 270)(21, 251)(22, 272)(23, 253)(24, 254)(25, 274)(26, 258)(27, 259)(28, 273)(29, 278)(30, 260)(31, 280)(32, 262)(33, 268)(34, 265)(35, 282)(36, 283)(37, 286)(38, 269)(39, 288)(40, 271)(41, 290)(42, 275)(43, 276)(44, 289)(45, 294)(46, 277)(47, 296)(48, 279)(49, 284)(50, 281)(51, 298)(52, 299)(53, 325)(54, 285)(55, 301)(56, 287)(57, 328)(58, 291)(59, 292)(60, 305)(61, 295)(62, 332)(63, 334)(64, 336)(65, 300)(66, 339)(67, 341)(68, 343)(69, 345)(70, 347)(71, 349)(72, 351)(73, 353)(74, 355)(75, 357)(76, 354)(77, 352)(78, 359)(79, 346)(80, 360)(81, 342)(82, 358)(83, 356)(84, 340)(85, 293)(86, 338)(87, 350)(88, 297)(89, 335)(90, 348)(91, 344)(92, 302)(93, 337)(94, 303)(95, 329)(96, 304)(97, 333)(98, 326)(99, 306)(100, 324)(101, 307)(102, 321)(103, 308)(104, 331)(105, 309)(106, 319)(107, 310)(108, 330)(109, 311)(110, 327)(111, 312)(112, 317)(113, 313)(114, 316)(115, 314)(116, 323)(117, 315)(118, 322)(119, 318)(120, 320)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.1281 Graph:: simple bipartite v = 122 e = 240 f = 90 degree seq :: [ 2^120, 120^2 ] E15.1285 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 60}) Quotient :: dipole Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |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, Y2^25 * Y1 * Y2^-5 * Y1 ] 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, 20, 140)(16, 136, 23, 143)(17, 137, 25, 145)(18, 138, 21, 141)(19, 139, 27, 147)(22, 142, 29, 149)(24, 144, 31, 151)(26, 146, 32, 152)(28, 148, 30, 150)(33, 153, 39, 159)(34, 154, 41, 161)(35, 155, 37, 157)(36, 156, 43, 163)(38, 158, 45, 165)(40, 160, 47, 167)(42, 162, 48, 168)(44, 164, 46, 166)(49, 169, 55, 175)(50, 170, 57, 177)(51, 171, 53, 173)(52, 172, 59, 179)(54, 174, 101, 221)(56, 176, 88, 208)(58, 178, 104, 224)(60, 180, 85, 205)(61, 181, 107, 227)(62, 182, 105, 225)(63, 183, 106, 226)(64, 184, 110, 230)(65, 185, 112, 232)(66, 186, 113, 233)(67, 187, 115, 235)(68, 188, 97, 217)(69, 189, 99, 219)(70, 190, 116, 236)(71, 191, 117, 237)(72, 192, 95, 215)(73, 193, 102, 222)(74, 194, 118, 238)(75, 195, 119, 239)(76, 196, 111, 231)(77, 197, 96, 216)(78, 198, 103, 223)(79, 199, 109, 229)(80, 200, 120, 240)(81, 201, 114, 234)(82, 202, 98, 218)(83, 203, 100, 220)(84, 204, 108, 228)(86, 206, 89, 209)(87, 207, 91, 211)(90, 210, 93, 213)(92, 212, 94, 214)(241, 361, 243, 363, 248, 368, 257, 377, 266, 386, 274, 394, 282, 402, 290, 410, 298, 418, 321, 441, 311, 431, 320, 440, 313, 433, 323, 443, 330, 450, 334, 454, 338, 458, 343, 463, 352, 472, 359, 479, 353, 473, 351, 471, 348, 468, 341, 461, 293, 413, 285, 405, 277, 397, 269, 389, 261, 381, 251, 371, 260, 380, 253, 373, 263, 383, 271, 391, 279, 399, 287, 407, 295, 415, 328, 448, 319, 439, 310, 430, 304, 424, 301, 421, 303, 423, 308, 428, 317, 437, 326, 446, 331, 451, 335, 455, 339, 459, 345, 465, 355, 475, 358, 478, 300, 420, 292, 412, 284, 404, 276, 396, 268, 388, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 270, 390, 278, 398, 286, 406, 294, 414, 325, 445, 316, 436, 307, 427, 315, 435, 309, 429, 318, 438, 327, 447, 332, 452, 336, 456, 340, 460, 346, 466, 360, 480, 350, 470, 354, 474, 349, 469, 297, 417, 289, 409, 281, 401, 273, 393, 265, 385, 256, 376, 247, 367, 255, 375, 249, 369, 258, 378, 267, 387, 275, 395, 283, 403, 291, 411, 299, 419, 324, 444, 314, 434, 306, 426, 302, 422, 305, 425, 312, 432, 322, 442, 329, 449, 333, 453, 337, 457, 342, 462, 347, 467, 357, 477, 356, 476, 344, 464, 296, 416, 288, 408, 280, 400, 272, 392, 264, 384, 254, 374, 246, 366) 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, 260)(16, 263)(17, 265)(18, 261)(19, 267)(20, 255)(21, 258)(22, 269)(23, 256)(24, 271)(25, 257)(26, 272)(27, 259)(28, 270)(29, 262)(30, 268)(31, 264)(32, 266)(33, 279)(34, 281)(35, 277)(36, 283)(37, 275)(38, 285)(39, 273)(40, 287)(41, 274)(42, 288)(43, 276)(44, 286)(45, 278)(46, 284)(47, 280)(48, 282)(49, 295)(50, 297)(51, 293)(52, 299)(53, 291)(54, 341)(55, 289)(56, 328)(57, 290)(58, 344)(59, 292)(60, 325)(61, 347)(62, 345)(63, 346)(64, 350)(65, 352)(66, 353)(67, 355)(68, 337)(69, 339)(70, 356)(71, 357)(72, 335)(73, 342)(74, 358)(75, 359)(76, 351)(77, 336)(78, 343)(79, 349)(80, 360)(81, 354)(82, 338)(83, 340)(84, 348)(85, 300)(86, 329)(87, 331)(88, 296)(89, 326)(90, 333)(91, 327)(92, 334)(93, 330)(94, 332)(95, 312)(96, 317)(97, 308)(98, 322)(99, 309)(100, 323)(101, 294)(102, 313)(103, 318)(104, 298)(105, 302)(106, 303)(107, 301)(108, 324)(109, 319)(110, 304)(111, 316)(112, 305)(113, 306)(114, 321)(115, 307)(116, 310)(117, 311)(118, 314)(119, 315)(120, 320)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1286 Graph:: bipartite v = 62 e = 240 f = 150 degree seq :: [ 4^60, 120^2 ] E15.1286 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 60}) Quotient :: dipole Aut^+ = C4 x D30 (small group id <120, 27>) Aut = D8 x D30 (small group id <240, 179>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-30 * Y1^-1, (Y3 * Y2^-1)^60 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 13, 133, 8, 128)(5, 125, 11, 131, 14, 134, 7, 127)(10, 130, 16, 136, 21, 141, 17, 137)(12, 132, 15, 135, 22, 142, 19, 139)(18, 138, 25, 145, 29, 149, 24, 144)(20, 140, 27, 147, 30, 150, 23, 143)(26, 146, 32, 152, 37, 157, 33, 153)(28, 148, 31, 151, 38, 158, 35, 155)(34, 154, 41, 161, 45, 165, 40, 160)(36, 156, 43, 163, 46, 166, 39, 159)(42, 162, 48, 168, 53, 173, 49, 169)(44, 164, 47, 167, 54, 174, 51, 171)(50, 170, 57, 177, 101, 221, 56, 176)(52, 172, 59, 179, 90, 210, 55, 175)(58, 178, 88, 208, 120, 240, 80, 200)(60, 180, 103, 223, 84, 204, 107, 227)(61, 181, 109, 229, 66, 186, 110, 230)(62, 182, 111, 231, 64, 184, 106, 226)(63, 183, 108, 228, 73, 193, 104, 224)(65, 185, 112, 232, 74, 194, 113, 233)(67, 187, 99, 219, 71, 191, 114, 234)(68, 188, 115, 235, 69, 189, 116, 236)(70, 190, 98, 218, 81, 201, 100, 220)(72, 192, 105, 225, 82, 202, 117, 237)(75, 195, 102, 222, 79, 199, 95, 215)(76, 196, 118, 238, 77, 197, 119, 239)(78, 198, 96, 216, 87, 207, 94, 214)(83, 203, 91, 211, 86, 206, 97, 217)(85, 205, 89, 209, 93, 213, 92, 212)(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, 253)(7, 255)(8, 242)(9, 244)(10, 258)(11, 259)(12, 245)(13, 261)(14, 246)(15, 263)(16, 248)(17, 249)(18, 266)(19, 267)(20, 252)(21, 269)(22, 254)(23, 271)(24, 256)(25, 257)(26, 274)(27, 275)(28, 260)(29, 277)(30, 262)(31, 279)(32, 264)(33, 265)(34, 282)(35, 283)(36, 268)(37, 285)(38, 270)(39, 287)(40, 272)(41, 273)(42, 290)(43, 291)(44, 276)(45, 293)(46, 278)(47, 295)(48, 280)(49, 281)(50, 298)(51, 299)(52, 284)(53, 341)(54, 286)(55, 343)(56, 288)(57, 289)(58, 345)(59, 347)(60, 292)(61, 314)(62, 309)(63, 306)(64, 308)(65, 322)(66, 305)(67, 304)(68, 317)(69, 316)(70, 313)(71, 302)(72, 328)(73, 301)(74, 312)(75, 311)(76, 324)(77, 300)(78, 321)(79, 307)(80, 297)(81, 303)(82, 320)(83, 319)(84, 330)(85, 327)(86, 315)(87, 310)(88, 296)(89, 326)(90, 294)(91, 333)(92, 323)(93, 318)(94, 332)(95, 337)(96, 329)(97, 325)(98, 336)(99, 342)(100, 334)(101, 360)(102, 331)(103, 358)(104, 340)(105, 352)(106, 354)(107, 359)(108, 338)(109, 348)(110, 344)(111, 339)(112, 349)(113, 350)(114, 335)(115, 351)(116, 346)(117, 353)(118, 355)(119, 356)(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) :: { ( 4, 120 ), ( 4, 120, 4, 120, 4, 120, 4, 120 ) } Outer automorphisms :: reflexible Dual of E15.1285 Graph:: simple bipartite v = 150 e = 240 f = 62 degree seq :: [ 2^120, 8^30 ] E15.1287 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 32}) Quotient :: regular Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^4, (T2 * T1^4)^2, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^3 * T2, T1^6 * T2 * T1^-10 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 45, 68, 85, 101, 117, 110, 96, 79, 61, 32, 54, 73, 63, 36, 57, 75, 91, 107, 123, 116, 100, 84, 67, 44, 22, 10, 4)(3, 7, 15, 31, 59, 77, 93, 109, 121, 103, 86, 76, 52, 26, 12, 25, 49, 42, 21, 41, 65, 82, 98, 114, 118, 108, 89, 70, 46, 37, 18, 8)(6, 13, 27, 53, 43, 66, 83, 99, 115, 119, 102, 92, 72, 48, 24, 47, 40, 20, 9, 19, 38, 64, 81, 97, 113, 124, 105, 87, 69, 58, 30, 14)(16, 33, 50, 29, 56, 71, 90, 104, 122, 127, 125, 112, 95, 78, 60, 39, 55, 28, 17, 35, 51, 74, 88, 106, 120, 128, 126, 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, 125)(113, 117)(114, 126)(116, 121)(119, 127)(124, 128) local type(s) :: { ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.1288 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 64 f = 32 degree seq :: [ 32^4 ] E15.1288 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 32}) Quotient :: regular Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * 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, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 32, 25)(15, 26, 33, 27)(21, 35, 29, 36)(22, 37, 30, 38)(23, 34, 44, 39)(40, 49, 42, 50)(41, 51, 43, 52)(45, 53, 47, 54)(46, 55, 48, 56)(57, 65, 59, 66)(58, 67, 60, 68)(61, 69, 63, 70)(62, 71, 64, 72)(73, 81, 75, 82)(74, 83, 76, 84)(77, 85, 79, 86)(78, 87, 80, 88)(89, 97, 91, 98)(90, 99, 92, 100)(93, 101, 95, 102)(94, 103, 96, 104)(105, 113, 107, 114)(106, 115, 108, 116)(109, 117, 111, 118)(110, 119, 112, 120)(121, 128, 123, 126)(122, 127, 124, 125) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128) local type(s) :: { ( 32^4 ) } Outer automorphisms :: reflexible Dual of E15.1287 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 32 e = 64 f = 4 degree seq :: [ 4^32 ] E15.1289 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 32}) Quotient :: edge Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^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^-1 * T1 * T2^-1 * T1 * T2, T2^-1 * T1 * T2 * T1 * T2^-1 * 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 ] 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, 77, 71, 78)(70, 79, 72, 80)(81, 89, 83, 90)(82, 91, 84, 92)(85, 93, 87, 94)(86, 95, 88, 96)(97, 105, 99, 106)(98, 107, 100, 108)(101, 109, 103, 110)(102, 111, 104, 112)(113, 121, 115, 122)(114, 123, 116, 124)(117, 125, 119, 126)(118, 127, 120, 128)(129, 130)(131, 135)(132, 137)(133, 138)(134, 140)(136, 143)(139, 148)(141, 151)(142, 153)(144, 156)(145, 158)(146, 159)(147, 161)(149, 164)(150, 166)(152, 162)(154, 160)(155, 165)(157, 163)(167, 177)(168, 178)(169, 179)(170, 180)(171, 176)(172, 181)(173, 182)(174, 183)(175, 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 ), ( 64^4 ) } Outer automorphisms :: reflexible Dual of E15.1293 Transitivity :: ET+ Graph:: simple bipartite v = 96 e = 128 f = 4 degree seq :: [ 2^64, 4^32 ] E15.1290 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 32}) Quotient :: edge Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2 * T1^-1 * T2^2 * T1^2, T2^2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1, (T2^-1 * T1)^4, T2 * T1 * T2^-14 * T1^-1 * T2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 48, 64, 80, 96, 112, 120, 104, 88, 72, 56, 39, 28, 42, 19, 41, 58, 74, 90, 106, 122, 116, 100, 84, 68, 52, 32, 14, 5)(2, 7, 17, 38, 57, 73, 89, 105, 121, 110, 94, 78, 62, 46, 23, 11, 26, 35, 31, 51, 67, 83, 99, 115, 124, 108, 92, 76, 60, 44, 20, 8)(4, 12, 27, 49, 65, 81, 97, 113, 126, 111, 95, 79, 63, 47, 25, 34, 30, 13, 29, 50, 66, 82, 98, 114, 125, 109, 93, 77, 61, 45, 22, 9)(6, 15, 33, 53, 69, 85, 101, 117, 127, 119, 103, 87, 71, 55, 37, 18, 40, 21, 43, 59, 75, 91, 107, 123, 128, 118, 102, 86, 70, 54, 36, 16)(129, 130, 134, 132)(131, 137, 149, 139)(133, 141, 146, 135)(136, 147, 162, 143)(138, 151, 161, 153)(140, 144, 163, 156)(142, 159, 164, 157)(145, 165, 155, 167)(148, 171, 150, 169)(152, 175, 187, 172)(154, 168, 158, 170)(160, 177, 183, 179)(166, 184, 178, 182)(173, 181, 174, 186)(176, 188, 197, 189)(180, 185, 198, 193)(190, 203, 191, 202)(192, 205, 219, 206)(194, 200, 195, 199)(196, 210, 215, 201)(204, 218, 207, 213)(208, 222, 229, 223)(209, 214, 211, 216)(212, 227, 230, 226)(217, 231, 225, 232)(220, 235, 221, 234)(224, 239, 251, 236)(228, 241, 247, 243)(233, 248, 242, 246)(237, 245, 238, 250)(240, 252, 255, 253)(244, 249, 256, 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) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.1294 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.1291 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 32}) Quotient :: edge Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |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, T1^6 * T2 * T1^-10 * 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, 125)(113, 117)(114, 126)(116, 121)(119, 127)(124, 128)(129, 130, 133, 139, 151, 173, 196, 213, 229, 245, 238, 224, 207, 189, 160, 182, 201, 191, 164, 185, 203, 219, 235, 251, 244, 228, 212, 195, 172, 150, 138, 132)(131, 135, 143, 159, 187, 205, 221, 237, 249, 231, 214, 204, 180, 154, 140, 153, 177, 170, 149, 169, 193, 210, 226, 242, 246, 236, 217, 198, 174, 165, 146, 136)(134, 141, 155, 181, 171, 194, 211, 227, 243, 247, 230, 220, 200, 176, 152, 175, 168, 148, 137, 147, 166, 192, 209, 225, 241, 252, 233, 215, 197, 186, 158, 142)(144, 161, 178, 157, 184, 199, 218, 232, 250, 255, 253, 240, 223, 206, 188, 167, 183, 156, 145, 163, 179, 202, 216, 234, 248, 256, 254, 239, 222, 208, 190, 162) 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) :: { ( 8, 8 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E15.1292 Transitivity :: ET+ Graph:: simple bipartite v = 68 e = 128 f = 32 degree seq :: [ 2^64, 32^4 ] E15.1292 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 32}) Quotient :: loop Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T2)^2, (F * T1)^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^-1 * T1 * T2^-1 * T1 * T2, T2^-1 * T1 * T2 * T1 * T2^-1 * 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 ] Map:: R = (1, 129, 3, 131, 8, 136, 4, 132)(2, 130, 5, 133, 11, 139, 6, 134)(7, 135, 13, 141, 24, 152, 14, 142)(9, 137, 16, 144, 29, 157, 17, 145)(10, 138, 18, 146, 32, 160, 19, 147)(12, 140, 21, 149, 37, 165, 22, 150)(15, 143, 26, 154, 43, 171, 27, 155)(20, 148, 34, 162, 48, 176, 35, 163)(23, 151, 39, 167, 28, 156, 40, 168)(25, 153, 41, 169, 30, 158, 42, 170)(31, 159, 44, 172, 36, 164, 45, 173)(33, 161, 46, 174, 38, 166, 47, 175)(49, 177, 57, 185, 51, 179, 58, 186)(50, 178, 59, 187, 52, 180, 60, 188)(53, 181, 61, 189, 55, 183, 62, 190)(54, 182, 63, 191, 56, 184, 64, 192)(65, 193, 73, 201, 67, 195, 74, 202)(66, 194, 75, 203, 68, 196, 76, 204)(69, 197, 77, 205, 71, 199, 78, 206)(70, 198, 79, 207, 72, 200, 80, 208)(81, 209, 89, 217, 83, 211, 90, 218)(82, 210, 91, 219, 84, 212, 92, 220)(85, 213, 93, 221, 87, 215, 94, 222)(86, 214, 95, 223, 88, 216, 96, 224)(97, 225, 105, 233, 99, 227, 106, 234)(98, 226, 107, 235, 100, 228, 108, 236)(101, 229, 109, 237, 103, 231, 110, 238)(102, 230, 111, 239, 104, 232, 112, 240)(113, 241, 121, 249, 115, 243, 122, 250)(114, 242, 123, 251, 116, 244, 124, 252)(117, 245, 125, 253, 119, 247, 126, 254)(118, 246, 127, 255, 120, 248, 128, 256) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 138)(6, 140)(7, 131)(8, 143)(9, 132)(10, 133)(11, 148)(12, 134)(13, 151)(14, 153)(15, 136)(16, 156)(17, 158)(18, 159)(19, 161)(20, 139)(21, 164)(22, 166)(23, 141)(24, 162)(25, 142)(26, 160)(27, 165)(28, 144)(29, 163)(30, 145)(31, 146)(32, 154)(33, 147)(34, 152)(35, 157)(36, 149)(37, 155)(38, 150)(39, 177)(40, 178)(41, 179)(42, 180)(43, 176)(44, 181)(45, 182)(46, 183)(47, 184)(48, 171)(49, 167)(50, 168)(51, 169)(52, 170)(53, 172)(54, 173)(55, 174)(56, 175)(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 ) } Outer automorphisms :: reflexible Dual of E15.1291 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 32 e = 128 f = 68 degree seq :: [ 8^32 ] E15.1293 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 32}) Quotient :: loop Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2 * T1^-1 * T2^2 * T1^2, T2^2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1, (T2^-1 * T1)^4, T2 * T1 * T2^-14 * T1^-1 * T2 ] Map:: R = (1, 129, 3, 131, 10, 138, 24, 152, 48, 176, 64, 192, 80, 208, 96, 224, 112, 240, 120, 248, 104, 232, 88, 216, 72, 200, 56, 184, 39, 167, 28, 156, 42, 170, 19, 147, 41, 169, 58, 186, 74, 202, 90, 218, 106, 234, 122, 250, 116, 244, 100, 228, 84, 212, 68, 196, 52, 180, 32, 160, 14, 142, 5, 133)(2, 130, 7, 135, 17, 145, 38, 166, 57, 185, 73, 201, 89, 217, 105, 233, 121, 249, 110, 238, 94, 222, 78, 206, 62, 190, 46, 174, 23, 151, 11, 139, 26, 154, 35, 163, 31, 159, 51, 179, 67, 195, 83, 211, 99, 227, 115, 243, 124, 252, 108, 236, 92, 220, 76, 204, 60, 188, 44, 172, 20, 148, 8, 136)(4, 132, 12, 140, 27, 155, 49, 177, 65, 193, 81, 209, 97, 225, 113, 241, 126, 254, 111, 239, 95, 223, 79, 207, 63, 191, 47, 175, 25, 153, 34, 162, 30, 158, 13, 141, 29, 157, 50, 178, 66, 194, 82, 210, 98, 226, 114, 242, 125, 253, 109, 237, 93, 221, 77, 205, 61, 189, 45, 173, 22, 150, 9, 137)(6, 134, 15, 143, 33, 161, 53, 181, 69, 197, 85, 213, 101, 229, 117, 245, 127, 255, 119, 247, 103, 231, 87, 215, 71, 199, 55, 183, 37, 165, 18, 146, 40, 168, 21, 149, 43, 171, 59, 187, 75, 203, 91, 219, 107, 235, 123, 251, 128, 256, 118, 246, 102, 230, 86, 214, 70, 198, 54, 182, 36, 164, 16, 144) L = (1, 130)(2, 134)(3, 137)(4, 129)(5, 141)(6, 132)(7, 133)(8, 147)(9, 149)(10, 151)(11, 131)(12, 144)(13, 146)(14, 159)(15, 136)(16, 163)(17, 165)(18, 135)(19, 162)(20, 171)(21, 139)(22, 169)(23, 161)(24, 175)(25, 138)(26, 168)(27, 167)(28, 140)(29, 142)(30, 170)(31, 164)(32, 177)(33, 153)(34, 143)(35, 156)(36, 157)(37, 155)(38, 184)(39, 145)(40, 158)(41, 148)(42, 154)(43, 150)(44, 152)(45, 181)(46, 186)(47, 187)(48, 188)(49, 183)(50, 182)(51, 160)(52, 185)(53, 174)(54, 166)(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, 189)(70, 193)(71, 194)(72, 195)(73, 196)(74, 190)(75, 191)(76, 218)(77, 219)(78, 192)(79, 213)(80, 222)(81, 214)(82, 215)(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, 223)(102, 226)(103, 225)(104, 217)(105, 248)(106, 220)(107, 221)(108, 224)(109, 245)(110, 250)(111, 251)(112, 252)(113, 247)(114, 246)(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, 253)(128, 254) 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 E15.1289 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 128 f = 96 degree seq :: [ 64^4 ] E15.1294 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 32}) Quotient :: loop Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |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, T1^6 * T2 * T1^-10 * 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, 36, 164)(19, 147, 39, 167)(20, 148, 33, 161)(22, 150, 43, 171)(23, 151, 46, 174)(25, 153, 50, 178)(26, 154, 51, 179)(27, 155, 54, 182)(30, 158, 57, 185)(31, 159, 60, 188)(34, 162, 53, 181)(35, 163, 47, 175)(37, 165, 56, 184)(38, 166, 61, 189)(40, 168, 63, 191)(41, 169, 62, 190)(42, 170, 55, 183)(44, 172, 59, 187)(45, 173, 69, 197)(48, 176, 71, 199)(49, 177, 73, 201)(52, 180, 75, 203)(58, 186, 74, 202)(64, 192, 80, 208)(65, 193, 79, 207)(66, 194, 78, 206)(67, 195, 81, 209)(68, 196, 86, 214)(70, 198, 88, 216)(72, 200, 91, 219)(76, 204, 90, 218)(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, 107, 235)(92, 220, 106, 234)(93, 221, 110, 238)(97, 225, 112, 240)(99, 227, 111, 239)(100, 228, 115, 243)(101, 229, 118, 246)(103, 231, 120, 248)(105, 233, 123, 251)(108, 236, 122, 250)(109, 237, 125, 253)(113, 241, 117, 245)(114, 242, 126, 254)(116, 244, 121, 249)(119, 247, 127, 255)(124, 252, 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, 161)(17, 163)(18, 136)(19, 166)(20, 137)(21, 169)(22, 138)(23, 173)(24, 175)(25, 177)(26, 140)(27, 181)(28, 145)(29, 184)(30, 142)(31, 187)(32, 182)(33, 178)(34, 144)(35, 179)(36, 185)(37, 146)(38, 192)(39, 183)(40, 148)(41, 193)(42, 149)(43, 194)(44, 150)(45, 196)(46, 165)(47, 168)(48, 152)(49, 170)(50, 157)(51, 202)(52, 154)(53, 171)(54, 201)(55, 156)(56, 199)(57, 203)(58, 158)(59, 205)(60, 167)(61, 160)(62, 162)(63, 164)(64, 209)(65, 210)(66, 211)(67, 172)(68, 213)(69, 186)(70, 174)(71, 218)(72, 176)(73, 191)(74, 216)(75, 219)(76, 180)(77, 221)(78, 188)(79, 189)(80, 190)(81, 225)(82, 226)(83, 227)(84, 195)(85, 229)(86, 204)(87, 197)(88, 234)(89, 198)(90, 232)(91, 235)(92, 200)(93, 237)(94, 208)(95, 206)(96, 207)(97, 241)(98, 242)(99, 243)(100, 212)(101, 245)(102, 220)(103, 214)(104, 250)(105, 215)(106, 248)(107, 251)(108, 217)(109, 249)(110, 224)(111, 222)(112, 223)(113, 252)(114, 246)(115, 247)(116, 228)(117, 238)(118, 236)(119, 230)(120, 256)(121, 231)(122, 255)(123, 244)(124, 233)(125, 240)(126, 239)(127, 253)(128, 254) local type(s) :: { ( 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.1290 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.1295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |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^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^32 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 10, 138)(6, 134, 12, 140)(8, 136, 15, 143)(11, 139, 20, 148)(13, 141, 23, 151)(14, 142, 25, 153)(16, 144, 28, 156)(17, 145, 30, 158)(18, 146, 31, 159)(19, 147, 33, 161)(21, 149, 36, 164)(22, 150, 38, 166)(24, 152, 34, 162)(26, 154, 32, 160)(27, 155, 37, 165)(29, 157, 35, 163)(39, 167, 49, 177)(40, 168, 50, 178)(41, 169, 51, 179)(42, 170, 52, 180)(43, 171, 48, 176)(44, 172, 53, 181)(45, 173, 54, 182)(46, 174, 55, 183)(47, 175, 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, 260, 388)(258, 386, 261, 389, 267, 395, 262, 390)(263, 391, 269, 397, 280, 408, 270, 398)(265, 393, 272, 400, 285, 413, 273, 401)(266, 394, 274, 402, 288, 416, 275, 403)(268, 396, 277, 405, 293, 421, 278, 406)(271, 399, 282, 410, 299, 427, 283, 411)(276, 404, 290, 418, 304, 432, 291, 419)(279, 407, 295, 423, 284, 412, 296, 424)(281, 409, 297, 425, 286, 414, 298, 426)(287, 415, 300, 428, 292, 420, 301, 429)(289, 417, 302, 430, 294, 422, 303, 431)(305, 433, 313, 441, 307, 435, 314, 442)(306, 434, 315, 443, 308, 436, 316, 444)(309, 437, 317, 445, 311, 439, 318, 446)(310, 438, 319, 447, 312, 440, 320, 448)(321, 449, 329, 457, 323, 451, 330, 458)(322, 450, 331, 459, 324, 452, 332, 460)(325, 453, 333, 461, 327, 455, 334, 462)(326, 454, 335, 463, 328, 456, 336, 464)(337, 465, 345, 473, 339, 467, 346, 474)(338, 466, 347, 475, 340, 468, 348, 476)(341, 469, 349, 477, 343, 471, 350, 478)(342, 470, 351, 479, 344, 472, 352, 480)(353, 481, 361, 489, 355, 483, 362, 490)(354, 482, 363, 491, 356, 484, 364, 492)(357, 485, 365, 493, 359, 487, 366, 494)(358, 486, 367, 495, 360, 488, 368, 496)(369, 497, 377, 505, 371, 499, 378, 506)(370, 498, 379, 507, 372, 500, 380, 508)(373, 501, 381, 509, 375, 503, 382, 510)(374, 502, 383, 511, 376, 504, 384, 512) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 266)(6, 268)(7, 259)(8, 271)(9, 260)(10, 261)(11, 276)(12, 262)(13, 279)(14, 281)(15, 264)(16, 284)(17, 286)(18, 287)(19, 289)(20, 267)(21, 292)(22, 294)(23, 269)(24, 290)(25, 270)(26, 288)(27, 293)(28, 272)(29, 291)(30, 273)(31, 274)(32, 282)(33, 275)(34, 280)(35, 285)(36, 277)(37, 283)(38, 278)(39, 305)(40, 306)(41, 307)(42, 308)(43, 304)(44, 309)(45, 310)(46, 311)(47, 312)(48, 299)(49, 295)(50, 296)(51, 297)(52, 298)(53, 300)(54, 301)(55, 302)(56, 303)(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 ) } Outer automorphisms :: reflexible Dual of E15.1298 Graph:: bipartite v = 96 e = 256 f = 132 degree seq :: [ 4^64, 8^32 ] E15.1296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y1^-1 * Y2^-1)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^2 * Y1^-1, (Y2^-1 * Y1)^4, Y2^2 * Y1^-1 * Y2^-14 * Y1 ] Map:: R = (1, 129, 2, 130, 6, 134, 4, 132)(3, 131, 9, 137, 21, 149, 11, 139)(5, 133, 13, 141, 18, 146, 7, 135)(8, 136, 19, 147, 34, 162, 15, 143)(10, 138, 23, 151, 33, 161, 25, 153)(12, 140, 16, 144, 35, 163, 28, 156)(14, 142, 31, 159, 36, 164, 29, 157)(17, 145, 37, 165, 27, 155, 39, 167)(20, 148, 43, 171, 22, 150, 41, 169)(24, 152, 47, 175, 59, 187, 44, 172)(26, 154, 40, 168, 30, 158, 42, 170)(32, 160, 49, 177, 55, 183, 51, 179)(38, 166, 56, 184, 50, 178, 54, 182)(45, 173, 53, 181, 46, 174, 58, 186)(48, 176, 60, 188, 69, 197, 61, 189)(52, 180, 57, 185, 70, 198, 65, 193)(62, 190, 75, 203, 63, 191, 74, 202)(64, 192, 77, 205, 91, 219, 78, 206)(66, 194, 72, 200, 67, 195, 71, 199)(68, 196, 82, 210, 87, 215, 73, 201)(76, 204, 90, 218, 79, 207, 85, 213)(80, 208, 94, 222, 101, 229, 95, 223)(81, 209, 86, 214, 83, 211, 88, 216)(84, 212, 99, 227, 102, 230, 98, 226)(89, 217, 103, 231, 97, 225, 104, 232)(92, 220, 107, 235, 93, 221, 106, 234)(96, 224, 111, 239, 123, 251, 108, 236)(100, 228, 113, 241, 119, 247, 115, 243)(105, 233, 120, 248, 114, 242, 118, 246)(109, 237, 117, 245, 110, 238, 122, 250)(112, 240, 124, 252, 127, 255, 125, 253)(116, 244, 121, 249, 128, 256, 126, 254)(257, 385, 259, 387, 266, 394, 280, 408, 304, 432, 320, 448, 336, 464, 352, 480, 368, 496, 376, 504, 360, 488, 344, 472, 328, 456, 312, 440, 295, 423, 284, 412, 298, 426, 275, 403, 297, 425, 314, 442, 330, 458, 346, 474, 362, 490, 378, 506, 372, 500, 356, 484, 340, 468, 324, 452, 308, 436, 288, 416, 270, 398, 261, 389)(258, 386, 263, 391, 273, 401, 294, 422, 313, 441, 329, 457, 345, 473, 361, 489, 377, 505, 366, 494, 350, 478, 334, 462, 318, 446, 302, 430, 279, 407, 267, 395, 282, 410, 291, 419, 287, 415, 307, 435, 323, 451, 339, 467, 355, 483, 371, 499, 380, 508, 364, 492, 348, 476, 332, 460, 316, 444, 300, 428, 276, 404, 264, 392)(260, 388, 268, 396, 283, 411, 305, 433, 321, 449, 337, 465, 353, 481, 369, 497, 382, 510, 367, 495, 351, 479, 335, 463, 319, 447, 303, 431, 281, 409, 290, 418, 286, 414, 269, 397, 285, 413, 306, 434, 322, 450, 338, 466, 354, 482, 370, 498, 381, 509, 365, 493, 349, 477, 333, 461, 317, 445, 301, 429, 278, 406, 265, 393)(262, 390, 271, 399, 289, 417, 309, 437, 325, 453, 341, 469, 357, 485, 373, 501, 383, 511, 375, 503, 359, 487, 343, 471, 327, 455, 311, 439, 293, 421, 274, 402, 296, 424, 277, 405, 299, 427, 315, 443, 331, 459, 347, 475, 363, 491, 379, 507, 384, 512, 374, 502, 358, 486, 342, 470, 326, 454, 310, 438, 292, 420, 272, 400) L = (1, 259)(2, 263)(3, 266)(4, 268)(5, 257)(6, 271)(7, 273)(8, 258)(9, 260)(10, 280)(11, 282)(12, 283)(13, 285)(14, 261)(15, 289)(16, 262)(17, 294)(18, 296)(19, 297)(20, 264)(21, 299)(22, 265)(23, 267)(24, 304)(25, 290)(26, 291)(27, 305)(28, 298)(29, 306)(30, 269)(31, 307)(32, 270)(33, 309)(34, 286)(35, 287)(36, 272)(37, 274)(38, 313)(39, 284)(40, 277)(41, 314)(42, 275)(43, 315)(44, 276)(45, 278)(46, 279)(47, 281)(48, 320)(49, 321)(50, 322)(51, 323)(52, 288)(53, 325)(54, 292)(55, 293)(56, 295)(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 ) } Outer automorphisms :: reflexible Dual of E15.1297 Graph:: bipartite v = 36 e = 256 f = 192 degree seq :: [ 8^32, 64^4 ] E15.1297 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, Y3^-1 * Y2 * Y3^-3 * Y2 * Y3^-1 * Y2 * Y3 * Y2, (Y3^4 * Y2)^2, Y3^6 * Y2 * Y3^-10 * 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, 273, 401)(266, 394, 277, 405)(268, 396, 281, 409)(270, 398, 285, 413)(271, 399, 284, 412)(272, 400, 288, 416)(274, 402, 292, 420)(275, 403, 294, 422)(276, 404, 279, 407)(278, 406, 299, 427)(280, 408, 302, 430)(282, 410, 306, 434)(283, 411, 308, 436)(286, 414, 313, 441)(287, 415, 304, 432)(289, 417, 311, 439)(290, 418, 301, 429)(291, 419, 309, 437)(293, 421, 314, 442)(295, 423, 305, 433)(296, 424, 312, 440)(297, 425, 303, 431)(298, 426, 310, 438)(300, 428, 307, 435)(315, 443, 329, 457)(316, 444, 325, 453)(317, 445, 330, 458)(318, 446, 331, 459)(319, 447, 333, 461)(320, 448, 324, 452)(321, 449, 326, 454)(322, 450, 327, 455)(323, 451, 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, 363, 491)(351, 479, 361, 489)(352, 480, 367, 495)(353, 481, 359, 487)(355, 483, 357, 485)(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, 383, 511)(382, 510, 384, 512) 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, 290)(18, 293)(19, 295)(20, 265)(21, 297)(22, 266)(23, 301)(24, 267)(25, 304)(26, 307)(27, 309)(28, 269)(29, 311)(30, 270)(31, 302)(32, 313)(33, 272)(34, 316)(35, 273)(36, 308)(37, 319)(38, 310)(39, 320)(40, 276)(41, 321)(42, 277)(43, 322)(44, 278)(45, 288)(46, 299)(47, 280)(48, 325)(49, 281)(50, 294)(51, 328)(52, 296)(53, 329)(54, 284)(55, 330)(56, 285)(57, 331)(58, 286)(59, 289)(60, 298)(61, 291)(62, 292)(63, 336)(64, 337)(65, 338)(66, 339)(67, 300)(68, 303)(69, 312)(70, 305)(71, 306)(72, 344)(73, 345)(74, 346)(75, 347)(76, 314)(77, 315)(78, 317)(79, 318)(80, 352)(81, 353)(82, 354)(83, 355)(84, 323)(85, 324)(86, 326)(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) :: { ( 8, 64 ), ( 8, 64, 8, 64 ) } Outer automorphisms :: reflexible Dual of E15.1296 Graph:: simple bipartite v = 192 e = 256 f = 36 degree seq :: [ 2^128, 4^64 ] E15.1298 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |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^-5 * Y3 * Y1^6 * Y3 * Y1^-5 ] Map:: polytopal R = (1, 129, 2, 130, 5, 133, 11, 139, 23, 151, 45, 173, 68, 196, 85, 213, 101, 229, 117, 245, 110, 238, 96, 224, 79, 207, 61, 189, 32, 160, 54, 182, 73, 201, 63, 191, 36, 164, 57, 185, 75, 203, 91, 219, 107, 235, 123, 251, 116, 244, 100, 228, 84, 212, 67, 195, 44, 172, 22, 150, 10, 138, 4, 132)(3, 131, 7, 135, 15, 143, 31, 159, 59, 187, 77, 205, 93, 221, 109, 237, 121, 249, 103, 231, 86, 214, 76, 204, 52, 180, 26, 154, 12, 140, 25, 153, 49, 177, 42, 170, 21, 149, 41, 169, 65, 193, 82, 210, 98, 226, 114, 242, 118, 246, 108, 236, 89, 217, 70, 198, 46, 174, 37, 165, 18, 146, 8, 136)(6, 134, 13, 141, 27, 155, 53, 181, 43, 171, 66, 194, 83, 211, 99, 227, 115, 243, 119, 247, 102, 230, 92, 220, 72, 200, 48, 176, 24, 152, 47, 175, 40, 168, 20, 148, 9, 137, 19, 147, 38, 166, 64, 192, 81, 209, 97, 225, 113, 241, 124, 252, 105, 233, 87, 215, 69, 197, 58, 186, 30, 158, 14, 142)(16, 144, 33, 161, 50, 178, 29, 157, 56, 184, 71, 199, 90, 218, 104, 232, 122, 250, 127, 255, 125, 253, 112, 240, 95, 223, 78, 206, 60, 188, 39, 167, 55, 183, 28, 156, 17, 145, 35, 163, 51, 179, 74, 202, 88, 216, 106, 234, 120, 248, 128, 256, 126, 254, 111, 239, 94, 222, 80, 208, 62, 190, 34, 162)(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, 292)(19, 295)(20, 289)(21, 266)(22, 299)(23, 302)(24, 267)(25, 306)(26, 307)(27, 310)(28, 269)(29, 270)(30, 313)(31, 316)(32, 271)(33, 276)(34, 309)(35, 303)(36, 274)(37, 312)(38, 317)(39, 275)(40, 319)(41, 318)(42, 311)(43, 278)(44, 315)(45, 325)(46, 279)(47, 291)(48, 327)(49, 329)(50, 281)(51, 282)(52, 331)(53, 290)(54, 283)(55, 298)(56, 293)(57, 286)(58, 330)(59, 300)(60, 287)(61, 294)(62, 297)(63, 296)(64, 336)(65, 335)(66, 334)(67, 337)(68, 342)(69, 301)(70, 344)(71, 304)(72, 347)(73, 305)(74, 314)(75, 308)(76, 346)(77, 350)(78, 322)(79, 321)(80, 320)(81, 323)(82, 351)(83, 352)(84, 354)(85, 358)(86, 324)(87, 360)(88, 326)(89, 363)(90, 332)(91, 328)(92, 362)(93, 366)(94, 333)(95, 338)(96, 339)(97, 368)(98, 340)(99, 367)(100, 371)(101, 374)(102, 341)(103, 376)(104, 343)(105, 379)(106, 348)(107, 345)(108, 378)(109, 381)(110, 349)(111, 355)(112, 353)(113, 373)(114, 382)(115, 356)(116, 377)(117, 369)(118, 357)(119, 383)(120, 359)(121, 372)(122, 364)(123, 361)(124, 384)(125, 365)(126, 370)(127, 375)(128, 380)(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, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.1295 Graph:: simple bipartite v = 132 e = 256 f = 96 degree seq :: [ 2^128, 64^4 ] E15.1299 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^4, (Y3 * Y2^-1)^4, Y2^2 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1, (Y2^-4 * Y1)^2, Y2^14 * Y1 * Y2^-2 * Y1 ] 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, 28, 156)(16, 144, 32, 160)(18, 146, 36, 164)(19, 147, 38, 166)(20, 148, 23, 151)(22, 150, 43, 171)(24, 152, 46, 174)(26, 154, 50, 178)(27, 155, 52, 180)(30, 158, 57, 185)(31, 159, 48, 176)(33, 161, 55, 183)(34, 162, 45, 173)(35, 163, 53, 181)(37, 165, 58, 186)(39, 167, 49, 177)(40, 168, 56, 184)(41, 169, 47, 175)(42, 170, 54, 182)(44, 172, 51, 179)(59, 187, 73, 201)(60, 188, 69, 197)(61, 189, 74, 202)(62, 190, 75, 203)(63, 191, 77, 205)(64, 192, 68, 196)(65, 193, 70, 198)(66, 194, 71, 199)(67, 195, 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, 107, 235)(95, 223, 105, 233)(96, 224, 111, 239)(97, 225, 103, 231)(99, 227, 101, 229)(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, 127, 255)(126, 254, 128, 256)(257, 385, 259, 387, 264, 392, 274, 402, 293, 421, 319, 447, 336, 464, 352, 480, 368, 496, 374, 502, 358, 486, 342, 470, 326, 454, 305, 433, 281, 409, 304, 432, 325, 453, 312, 440, 285, 413, 311, 439, 330, 458, 346, 474, 362, 490, 378, 506, 372, 500, 356, 484, 340, 468, 323, 451, 300, 428, 278, 406, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 282, 410, 307, 435, 328, 456, 344, 472, 360, 488, 376, 504, 366, 494, 350, 478, 334, 462, 317, 445, 291, 419, 273, 401, 290, 418, 316, 444, 298, 426, 277, 405, 297, 425, 321, 449, 338, 466, 354, 482, 370, 498, 380, 508, 364, 492, 348, 476, 332, 460, 314, 442, 286, 414, 270, 398, 262, 390)(263, 391, 271, 399, 287, 415, 302, 430, 299, 427, 322, 450, 339, 467, 355, 483, 371, 499, 382, 510, 367, 495, 351, 479, 335, 463, 318, 446, 292, 420, 308, 436, 296, 424, 276, 404, 265, 393, 275, 403, 295, 423, 320, 448, 337, 465, 353, 481, 369, 497, 381, 509, 365, 493, 349, 477, 333, 461, 315, 443, 289, 417, 272, 400)(267, 395, 279, 407, 301, 429, 288, 416, 313, 441, 331, 459, 347, 475, 363, 491, 379, 507, 384, 512, 375, 503, 359, 487, 343, 471, 327, 455, 306, 434, 294, 422, 310, 438, 284, 412, 269, 397, 283, 411, 309, 437, 329, 457, 345, 473, 361, 489, 377, 505, 383, 511, 373, 501, 357, 485, 341, 469, 324, 452, 303, 431, 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, 284)(16, 288)(17, 264)(18, 292)(19, 294)(20, 279)(21, 266)(22, 299)(23, 276)(24, 302)(25, 268)(26, 306)(27, 308)(28, 271)(29, 270)(30, 313)(31, 304)(32, 272)(33, 311)(34, 301)(35, 309)(36, 274)(37, 314)(38, 275)(39, 305)(40, 312)(41, 303)(42, 310)(43, 278)(44, 307)(45, 290)(46, 280)(47, 297)(48, 287)(49, 295)(50, 282)(51, 300)(52, 283)(53, 291)(54, 298)(55, 289)(56, 296)(57, 286)(58, 293)(59, 329)(60, 325)(61, 330)(62, 331)(63, 333)(64, 324)(65, 326)(66, 327)(67, 337)(68, 320)(69, 316)(70, 321)(71, 322)(72, 341)(73, 315)(74, 317)(75, 318)(76, 345)(77, 319)(78, 347)(79, 346)(80, 350)(81, 323)(82, 343)(83, 342)(84, 354)(85, 328)(86, 339)(87, 338)(88, 358)(89, 332)(90, 335)(91, 334)(92, 362)(93, 363)(94, 336)(95, 361)(96, 367)(97, 359)(98, 340)(99, 357)(100, 371)(101, 355)(102, 344)(103, 353)(104, 375)(105, 351)(106, 348)(107, 349)(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, 383)(126, 384)(127, 381)(128, 382)(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, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1300 Graph:: bipartite v = 68 e = 256 f = 160 degree seq :: [ 4^64, 64^4 ] E15.1300 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 : C2) : C2 (small group id <128, 150>) Aut = $<256, 6655>$ (small group id <256, 6655>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^2 * Y1^2, Y3^-1 * Y1^2 * Y3^-1 * Y1 * Y3^-2 * Y1, Y3 * Y1 * Y3^-14 * Y1^-1 * Y3, (Y3 * Y2^-1)^32 ] Map:: polytopal R = (1, 129, 2, 130, 6, 134, 4, 132)(3, 131, 9, 137, 21, 149, 11, 139)(5, 133, 13, 141, 18, 146, 7, 135)(8, 136, 19, 147, 34, 162, 15, 143)(10, 138, 23, 151, 33, 161, 25, 153)(12, 140, 16, 144, 35, 163, 28, 156)(14, 142, 31, 159, 36, 164, 29, 157)(17, 145, 37, 165, 27, 155, 39, 167)(20, 148, 43, 171, 22, 150, 41, 169)(24, 152, 47, 175, 59, 187, 44, 172)(26, 154, 40, 168, 30, 158, 42, 170)(32, 160, 49, 177, 55, 183, 51, 179)(38, 166, 56, 184, 50, 178, 54, 182)(45, 173, 53, 181, 46, 174, 58, 186)(48, 176, 60, 188, 69, 197, 61, 189)(52, 180, 57, 185, 70, 198, 65, 193)(62, 190, 75, 203, 63, 191, 74, 202)(64, 192, 77, 205, 91, 219, 78, 206)(66, 194, 72, 200, 67, 195, 71, 199)(68, 196, 82, 210, 87, 215, 73, 201)(76, 204, 90, 218, 79, 207, 85, 213)(80, 208, 94, 222, 101, 229, 95, 223)(81, 209, 86, 214, 83, 211, 88, 216)(84, 212, 99, 227, 102, 230, 98, 226)(89, 217, 103, 231, 97, 225, 104, 232)(92, 220, 107, 235, 93, 221, 106, 234)(96, 224, 111, 239, 123, 251, 108, 236)(100, 228, 113, 241, 119, 247, 115, 243)(105, 233, 120, 248, 114, 242, 118, 246)(109, 237, 117, 245, 110, 238, 122, 250)(112, 240, 124, 252, 127, 255, 125, 253)(116, 244, 121, 249, 128, 256, 126, 254)(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, 271)(7, 273)(8, 258)(9, 260)(10, 280)(11, 282)(12, 283)(13, 285)(14, 261)(15, 289)(16, 262)(17, 294)(18, 296)(19, 297)(20, 264)(21, 299)(22, 265)(23, 267)(24, 304)(25, 290)(26, 291)(27, 305)(28, 298)(29, 306)(30, 269)(31, 307)(32, 270)(33, 309)(34, 286)(35, 287)(36, 272)(37, 274)(38, 313)(39, 284)(40, 277)(41, 314)(42, 275)(43, 315)(44, 276)(45, 278)(46, 279)(47, 281)(48, 320)(49, 321)(50, 322)(51, 323)(52, 288)(53, 325)(54, 292)(55, 293)(56, 295)(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 ) } Outer automorphisms :: reflexible Dual of E15.1299 Graph:: simple bipartite v = 160 e = 256 f = 68 degree seq :: [ 2^128, 8^32 ] E15.1301 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 32}) Quotient :: regular Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^32 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 116, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 121, 124, 119, 110, 103, 94, 87, 78, 71, 62, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 123, 125, 118, 111, 102, 95, 86, 79, 70, 63, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 126, 128, 127, 122, 114, 106, 98, 90, 82, 74, 66, 58, 50, 42, 34, 26) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 102)(95, 104)(99, 106)(100, 107)(101, 110)(103, 112)(105, 114)(108, 113)(109, 118)(111, 120)(115, 122)(116, 123)(117, 124)(119, 126)(121, 127)(125, 128) local type(s) :: { ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.1302 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 64 f = 32 degree seq :: [ 32^4 ] E15.1302 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 32}) Quotient :: regular Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^32 ] 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, 65, 38, 66)(39, 67, 43, 69)(40, 70, 42, 72)(41, 71, 48, 74)(44, 75, 47, 68)(45, 76, 46, 77)(49, 79, 50, 80)(51, 78, 52, 73)(53, 81, 54, 82)(55, 83, 56, 84)(57, 85, 58, 86)(59, 87, 60, 88)(61, 89, 62, 90)(63, 91, 64, 92)(93, 121, 94, 122)(95, 119, 97, 120)(96, 123, 103, 124)(98, 118, 100, 117)(99, 125, 102, 127)(101, 126, 106, 128)(104, 116, 105, 115)(107, 113, 108, 114)(109, 111, 110, 112) 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, 52)(36, 51)(39, 68)(40, 71)(41, 73)(42, 74)(43, 75)(44, 66)(45, 67)(46, 69)(47, 65)(48, 78)(49, 70)(50, 72)(53, 76)(54, 77)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(89, 93)(90, 94)(91, 101)(92, 106)(95, 123)(96, 121)(97, 124)(98, 125)(99, 126)(100, 127)(102, 128)(103, 122)(104, 119)(105, 120)(107, 118)(108, 117)(109, 116)(110, 115)(111, 113)(112, 114) local type(s) :: { ( 32^4 ) } Outer automorphisms :: reflexible Dual of E15.1301 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 32 e = 64 f = 4 degree seq :: [ 4^32 ] E15.1303 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 32}) Quotient :: edge Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^32 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 57, 36, 59)(39, 61, 42, 63)(40, 64, 45, 66)(41, 67, 43, 69)(44, 72, 46, 74)(47, 77, 48, 79)(49, 81, 50, 83)(51, 85, 52, 87)(53, 89, 54, 91)(55, 93, 56, 95)(58, 98, 60, 97)(62, 102, 70, 101)(65, 105, 75, 104)(68, 108, 71, 107)(73, 113, 76, 112)(78, 118, 80, 117)(82, 122, 84, 121)(86, 126, 88, 125)(90, 128, 92, 127)(94, 123, 96, 124)(99, 119, 100, 120)(103, 114, 110, 116)(106, 109, 115, 111)(129, 130)(131, 135)(132, 137)(133, 138)(134, 140)(136, 139)(141, 145)(142, 146)(143, 147)(144, 148)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164)(165, 170)(166, 167)(168, 187)(169, 189)(171, 191)(172, 192)(173, 185)(174, 194)(175, 195)(176, 197)(177, 200)(178, 202)(179, 205)(180, 207)(181, 209)(182, 211)(183, 213)(184, 215)(186, 217)(188, 219)(190, 223)(193, 225)(196, 230)(198, 221)(199, 229)(201, 233)(203, 226)(204, 232)(206, 236)(208, 235)(210, 241)(212, 240)(214, 246)(216, 245)(218, 250)(220, 249)(222, 254)(224, 253)(227, 256)(228, 255)(231, 252)(234, 248)(237, 242)(238, 251)(239, 244)(243, 247) 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 ), ( 64^4 ) } Outer automorphisms :: reflexible Dual of E15.1307 Transitivity :: ET+ Graph:: simple bipartite v = 96 e = 128 f = 4 degree seq :: [ 2^64, 4^32 ] E15.1304 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 32}) Quotient :: edge Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^32 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122, 116, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 126, 120, 112, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 123, 127, 121, 113, 105, 97, 89, 81, 73, 65, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 124, 128, 125, 118, 110, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14)(129, 130, 134, 132)(131, 137, 141, 136)(133, 139, 142, 135)(138, 144, 149, 145)(140, 143, 150, 147)(146, 153, 157, 152)(148, 155, 158, 151)(154, 160, 165, 161)(156, 159, 166, 163)(162, 169, 173, 168)(164, 171, 174, 167)(170, 176, 181, 177)(172, 175, 182, 179)(178, 185, 189, 184)(180, 187, 190, 183)(186, 192, 197, 193)(188, 191, 198, 195)(194, 201, 205, 200)(196, 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, 252, 248)(244, 251, 253, 247)(250, 254, 256, 255) 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) :: { ( 4^4 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E15.1308 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 128 f = 64 degree seq :: [ 4^32, 32^4 ] E15.1305 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 32}) Quotient :: edge Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^32 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 102)(95, 104)(99, 106)(100, 107)(101, 110)(103, 112)(105, 114)(108, 113)(109, 118)(111, 120)(115, 122)(116, 123)(117, 124)(119, 126)(121, 127)(125, 128)(129, 130, 133, 139, 148, 157, 165, 173, 181, 189, 197, 205, 213, 221, 229, 237, 245, 244, 236, 228, 220, 212, 204, 196, 188, 180, 172, 164, 156, 147, 138, 132)(131, 135, 143, 153, 161, 169, 177, 185, 193, 201, 209, 217, 225, 233, 241, 249, 252, 247, 238, 231, 222, 215, 206, 199, 190, 183, 174, 167, 158, 150, 140, 136)(134, 141, 137, 146, 155, 163, 171, 179, 187, 195, 203, 211, 219, 227, 235, 243, 251, 253, 246, 239, 230, 223, 214, 207, 198, 191, 182, 175, 166, 159, 149, 142)(144, 151, 145, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 254, 256, 255, 250, 242, 234, 226, 218, 210, 202, 194, 186, 178, 170, 162, 154) 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) :: { ( 8, 8 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E15.1306 Transitivity :: ET+ Graph:: simple bipartite v = 68 e = 128 f = 32 degree seq :: [ 2^64, 32^4 ] E15.1306 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 32}) Quotient :: loop Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^32 ] Map:: R = (1, 129, 3, 131, 8, 136, 4, 132)(2, 130, 5, 133, 11, 139, 6, 134)(7, 135, 13, 141, 9, 137, 14, 142)(10, 138, 15, 143, 12, 140, 16, 144)(17, 145, 21, 149, 18, 146, 22, 150)(19, 147, 23, 151, 20, 148, 24, 152)(25, 153, 29, 157, 26, 154, 30, 158)(27, 155, 31, 159, 28, 156, 32, 160)(33, 161, 37, 165, 34, 162, 38, 166)(35, 163, 60, 188, 36, 164, 59, 187)(39, 167, 72, 200, 46, 174, 73, 201)(40, 168, 75, 203, 49, 177, 76, 204)(41, 169, 77, 205, 42, 170, 78, 206)(43, 171, 79, 207, 44, 172, 80, 208)(45, 173, 82, 210, 47, 175, 71, 199)(48, 176, 85, 213, 50, 178, 74, 202)(51, 179, 87, 215, 52, 180, 88, 216)(53, 181, 70, 198, 54, 182, 69, 197)(55, 183, 83, 211, 56, 184, 81, 209)(57, 185, 86, 214, 58, 186, 84, 212)(61, 189, 90, 218, 62, 190, 89, 217)(63, 191, 92, 220, 64, 192, 91, 219)(65, 193, 94, 222, 66, 194, 93, 221)(67, 195, 96, 224, 68, 196, 95, 223)(97, 225, 101, 229, 98, 226, 102, 230)(99, 227, 120, 248, 100, 228, 119, 247)(103, 231, 116, 244, 114, 242, 118, 246)(104, 232, 123, 251, 105, 233, 124, 252)(106, 234, 113, 241, 117, 245, 115, 243)(107, 235, 121, 249, 108, 236, 122, 250)(109, 237, 125, 253, 110, 238, 126, 254)(111, 239, 127, 255, 112, 240, 128, 256) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 138)(6, 140)(7, 131)(8, 139)(9, 132)(10, 133)(11, 136)(12, 134)(13, 145)(14, 146)(15, 147)(16, 148)(17, 141)(18, 142)(19, 143)(20, 144)(21, 153)(22, 154)(23, 155)(24, 156)(25, 149)(26, 150)(27, 151)(28, 152)(29, 161)(30, 162)(31, 163)(32, 164)(33, 157)(34, 158)(35, 159)(36, 160)(37, 197)(38, 198)(39, 199)(40, 202)(41, 203)(42, 204)(43, 200)(44, 201)(45, 209)(46, 210)(47, 211)(48, 212)(49, 213)(50, 214)(51, 205)(52, 206)(53, 207)(54, 208)(55, 217)(56, 218)(57, 219)(58, 220)(59, 215)(60, 216)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 165)(70, 166)(71, 167)(72, 171)(73, 172)(74, 168)(75, 169)(76, 170)(77, 179)(78, 180)(79, 181)(80, 182)(81, 173)(82, 174)(83, 175)(84, 176)(85, 177)(86, 178)(87, 187)(88, 188)(89, 183)(90, 184)(91, 185)(92, 186)(93, 189)(94, 190)(95, 191)(96, 192)(97, 193)(98, 194)(99, 195)(100, 196)(101, 256)(102, 255)(103, 234)(104, 244)(105, 246)(106, 231)(107, 241)(108, 243)(109, 249)(110, 250)(111, 251)(112, 252)(113, 235)(114, 245)(115, 236)(116, 232)(117, 242)(118, 233)(119, 253)(120, 254)(121, 237)(122, 238)(123, 239)(124, 240)(125, 247)(126, 248)(127, 230)(128, 229) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E15.1305 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 32 e = 128 f = 68 degree seq :: [ 8^32 ] E15.1307 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 32}) Quotient :: loop Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^32 ] Map:: R = (1, 129, 3, 131, 10, 138, 18, 146, 26, 154, 34, 162, 42, 170, 50, 178, 58, 186, 66, 194, 74, 202, 82, 210, 90, 218, 98, 226, 106, 234, 114, 242, 122, 250, 116, 244, 108, 236, 100, 228, 92, 220, 84, 212, 76, 204, 68, 196, 60, 188, 52, 180, 44, 172, 36, 164, 28, 156, 20, 148, 12, 140, 5, 133)(2, 130, 7, 135, 15, 143, 23, 151, 31, 159, 39, 167, 47, 175, 55, 183, 63, 191, 71, 199, 79, 207, 87, 215, 95, 223, 103, 231, 111, 239, 119, 247, 126, 254, 120, 248, 112, 240, 104, 232, 96, 224, 88, 216, 80, 208, 72, 200, 64, 192, 56, 184, 48, 176, 40, 168, 32, 160, 24, 152, 16, 144, 8, 136)(4, 132, 11, 139, 19, 147, 27, 155, 35, 163, 43, 171, 51, 179, 59, 187, 67, 195, 75, 203, 83, 211, 91, 219, 99, 227, 107, 235, 115, 243, 123, 251, 127, 255, 121, 249, 113, 241, 105, 233, 97, 225, 89, 217, 81, 209, 73, 201, 65, 193, 57, 185, 49, 177, 41, 169, 33, 161, 25, 153, 17, 145, 9, 137)(6, 134, 13, 141, 21, 149, 29, 157, 37, 165, 45, 173, 53, 181, 61, 189, 69, 197, 77, 205, 85, 213, 93, 221, 101, 229, 109, 237, 117, 245, 124, 252, 128, 256, 125, 253, 118, 246, 110, 238, 102, 230, 94, 222, 86, 214, 78, 206, 70, 198, 62, 190, 54, 182, 46, 174, 38, 166, 30, 158, 22, 150, 14, 142) 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, 189)(58, 192)(59, 190)(60, 191)(61, 184)(62, 183)(63, 198)(64, 197)(65, 186)(66, 201)(67, 188)(68, 203)(69, 193)(70, 195)(71, 196)(72, 194)(73, 205)(74, 208)(75, 206)(76, 207)(77, 200)(78, 199)(79, 214)(80, 213)(81, 202)(82, 217)(83, 204)(84, 219)(85, 209)(86, 211)(87, 212)(88, 210)(89, 221)(90, 224)(91, 222)(92, 223)(93, 216)(94, 215)(95, 230)(96, 229)(97, 218)(98, 233)(99, 220)(100, 235)(101, 225)(102, 227)(103, 228)(104, 226)(105, 237)(106, 240)(107, 238)(108, 239)(109, 232)(110, 231)(111, 246)(112, 245)(113, 234)(114, 249)(115, 236)(116, 251)(117, 241)(118, 243)(119, 244)(120, 242)(121, 252)(122, 254)(123, 253)(124, 248)(125, 247)(126, 256)(127, 250)(128, 255) 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 E15.1303 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 128 f = 96 degree seq :: [ 64^4 ] E15.1308 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 32}) Quotient :: loop Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^32 ] 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, 26, 154)(19, 147, 27, 155)(20, 148, 30, 158)(22, 150, 32, 160)(25, 153, 34, 162)(28, 156, 33, 161)(29, 157, 38, 166)(31, 159, 40, 168)(35, 163, 42, 170)(36, 164, 43, 171)(37, 165, 46, 174)(39, 167, 48, 176)(41, 169, 50, 178)(44, 172, 49, 177)(45, 173, 54, 182)(47, 175, 56, 184)(51, 179, 58, 186)(52, 180, 59, 187)(53, 181, 62, 190)(55, 183, 64, 192)(57, 185, 66, 194)(60, 188, 65, 193)(61, 189, 70, 198)(63, 191, 72, 200)(67, 195, 74, 202)(68, 196, 75, 203)(69, 197, 78, 206)(71, 199, 80, 208)(73, 201, 82, 210)(76, 204, 81, 209)(77, 205, 86, 214)(79, 207, 88, 216)(83, 211, 90, 218)(84, 212, 91, 219)(85, 213, 94, 222)(87, 215, 96, 224)(89, 217, 98, 226)(92, 220, 97, 225)(93, 221, 102, 230)(95, 223, 104, 232)(99, 227, 106, 234)(100, 228, 107, 235)(101, 229, 110, 238)(103, 231, 112, 240)(105, 233, 114, 242)(108, 236, 113, 241)(109, 237, 118, 246)(111, 239, 120, 248)(115, 243, 122, 250)(116, 244, 123, 251)(117, 245, 124, 252)(119, 247, 126, 254)(121, 249, 127, 255)(125, 253, 128, 256) 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, 151)(17, 152)(18, 155)(19, 138)(20, 157)(21, 142)(22, 140)(23, 145)(24, 160)(25, 161)(26, 144)(27, 163)(28, 147)(29, 165)(30, 150)(31, 149)(32, 168)(33, 169)(34, 154)(35, 171)(36, 156)(37, 173)(38, 159)(39, 158)(40, 176)(41, 177)(42, 162)(43, 179)(44, 164)(45, 181)(46, 167)(47, 166)(48, 184)(49, 185)(50, 170)(51, 187)(52, 172)(53, 189)(54, 175)(55, 174)(56, 192)(57, 193)(58, 178)(59, 195)(60, 180)(61, 197)(62, 183)(63, 182)(64, 200)(65, 201)(66, 186)(67, 203)(68, 188)(69, 205)(70, 191)(71, 190)(72, 208)(73, 209)(74, 194)(75, 211)(76, 196)(77, 213)(78, 199)(79, 198)(80, 216)(81, 217)(82, 202)(83, 219)(84, 204)(85, 221)(86, 207)(87, 206)(88, 224)(89, 225)(90, 210)(91, 227)(92, 212)(93, 229)(94, 215)(95, 214)(96, 232)(97, 233)(98, 218)(99, 235)(100, 220)(101, 237)(102, 223)(103, 222)(104, 240)(105, 241)(106, 226)(107, 243)(108, 228)(109, 245)(110, 231)(111, 230)(112, 248)(113, 249)(114, 234)(115, 251)(116, 236)(117, 244)(118, 239)(119, 238)(120, 254)(121, 252)(122, 242)(123, 253)(124, 247)(125, 246)(126, 256)(127, 250)(128, 255) local type(s) :: { ( 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E15.1304 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 64 e = 128 f = 36 degree seq :: [ 4^64 ] E15.1309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |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)^32 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 10, 138)(6, 134, 12, 140)(8, 136, 11, 139)(13, 141, 17, 145)(14, 142, 18, 146)(15, 143, 19, 147)(16, 144, 20, 148)(21, 149, 25, 153)(22, 150, 26, 154)(23, 151, 27, 155)(24, 152, 28, 156)(29, 157, 33, 161)(30, 158, 34, 162)(31, 159, 35, 163)(32, 160, 36, 164)(37, 165, 61, 189)(38, 166, 63, 191)(39, 167, 65, 193)(40, 168, 69, 197)(41, 169, 71, 199)(42, 170, 74, 202)(43, 171, 76, 204)(44, 172, 79, 207)(45, 173, 66, 194)(46, 174, 77, 205)(47, 175, 68, 196)(48, 176, 72, 200)(49, 177, 85, 213)(50, 178, 87, 215)(51, 179, 89, 217)(52, 180, 91, 219)(53, 181, 93, 221)(54, 182, 95, 223)(55, 183, 97, 225)(56, 184, 99, 227)(57, 185, 101, 229)(58, 186, 103, 231)(59, 187, 105, 233)(60, 188, 107, 235)(62, 190, 109, 237)(64, 192, 111, 239)(67, 195, 113, 241)(70, 198, 117, 245)(73, 201, 119, 247)(75, 203, 122, 250)(78, 206, 123, 251)(80, 208, 121, 249)(81, 209, 114, 242)(82, 210, 124, 252)(83, 211, 116, 244)(84, 212, 120, 248)(86, 214, 115, 243)(88, 216, 126, 254)(90, 218, 118, 246)(92, 220, 128, 256)(94, 222, 125, 253)(96, 224, 127, 255)(98, 226, 112, 240)(100, 228, 110, 238)(102, 230, 106, 234)(104, 232, 108, 236)(257, 385, 259, 387, 264, 392, 260, 388)(258, 386, 261, 389, 267, 395, 262, 390)(263, 391, 269, 397, 265, 393, 270, 398)(266, 394, 271, 399, 268, 396, 272, 400)(273, 401, 277, 405, 274, 402, 278, 406)(275, 403, 279, 407, 276, 404, 280, 408)(281, 409, 285, 413, 282, 410, 286, 414)(283, 411, 287, 415, 284, 412, 288, 416)(289, 417, 293, 421, 290, 418, 294, 422)(291, 419, 303, 431, 292, 420, 301, 429)(295, 423, 322, 450, 302, 430, 324, 452)(296, 424, 319, 447, 304, 432, 317, 445)(297, 425, 328, 456, 298, 426, 325, 453)(299, 427, 333, 461, 300, 428, 321, 449)(305, 433, 330, 458, 306, 434, 327, 455)(307, 435, 335, 463, 308, 436, 332, 460)(309, 437, 343, 471, 310, 438, 341, 469)(311, 439, 347, 475, 312, 440, 345, 473)(313, 441, 351, 479, 314, 442, 349, 477)(315, 443, 355, 483, 316, 444, 353, 481)(318, 446, 359, 487, 320, 448, 357, 485)(323, 451, 370, 498, 338, 466, 372, 500)(326, 454, 367, 495, 340, 468, 365, 493)(329, 457, 376, 504, 331, 459, 373, 501)(334, 462, 380, 508, 336, 464, 369, 497)(337, 465, 361, 489, 339, 467, 363, 491)(342, 470, 378, 506, 344, 472, 375, 503)(346, 474, 377, 505, 348, 476, 379, 507)(350, 478, 382, 510, 352, 480, 371, 499)(354, 482, 384, 512, 356, 484, 374, 502)(358, 486, 383, 511, 360, 488, 381, 509)(362, 490, 366, 494, 364, 492, 368, 496) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 266)(6, 268)(7, 259)(8, 267)(9, 260)(10, 261)(11, 264)(12, 262)(13, 273)(14, 274)(15, 275)(16, 276)(17, 269)(18, 270)(19, 271)(20, 272)(21, 281)(22, 282)(23, 283)(24, 284)(25, 277)(26, 278)(27, 279)(28, 280)(29, 289)(30, 290)(31, 291)(32, 292)(33, 285)(34, 286)(35, 287)(36, 288)(37, 317)(38, 319)(39, 321)(40, 325)(41, 327)(42, 330)(43, 332)(44, 335)(45, 322)(46, 333)(47, 324)(48, 328)(49, 341)(50, 343)(51, 345)(52, 347)(53, 349)(54, 351)(55, 353)(56, 355)(57, 357)(58, 359)(59, 361)(60, 363)(61, 293)(62, 365)(63, 294)(64, 367)(65, 295)(66, 301)(67, 369)(68, 303)(69, 296)(70, 373)(71, 297)(72, 304)(73, 375)(74, 298)(75, 378)(76, 299)(77, 302)(78, 379)(79, 300)(80, 377)(81, 370)(82, 380)(83, 372)(84, 376)(85, 305)(86, 371)(87, 306)(88, 382)(89, 307)(90, 374)(91, 308)(92, 384)(93, 309)(94, 381)(95, 310)(96, 383)(97, 311)(98, 368)(99, 312)(100, 366)(101, 313)(102, 362)(103, 314)(104, 364)(105, 315)(106, 358)(107, 316)(108, 360)(109, 318)(110, 356)(111, 320)(112, 354)(113, 323)(114, 337)(115, 342)(116, 339)(117, 326)(118, 346)(119, 329)(120, 340)(121, 336)(122, 331)(123, 334)(124, 338)(125, 350)(126, 344)(127, 352)(128, 348)(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 ) } Outer automorphisms :: reflexible Dual of E15.1312 Graph:: bipartite v = 96 e = 256 f = 132 degree seq :: [ 4^64, 8^32 ] E15.1310 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |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, Y2^32 ] Map:: R = (1, 129, 2, 130, 6, 134, 4, 132)(3, 131, 9, 137, 13, 141, 8, 136)(5, 133, 11, 139, 14, 142, 7, 135)(10, 138, 16, 144, 21, 149, 17, 145)(12, 140, 15, 143, 22, 150, 19, 147)(18, 146, 25, 153, 29, 157, 24, 152)(20, 148, 27, 155, 30, 158, 23, 151)(26, 154, 32, 160, 37, 165, 33, 161)(28, 156, 31, 159, 38, 166, 35, 163)(34, 162, 41, 169, 45, 173, 40, 168)(36, 164, 43, 171, 46, 174, 39, 167)(42, 170, 48, 176, 53, 181, 49, 177)(44, 172, 47, 175, 54, 182, 51, 179)(50, 178, 57, 185, 61, 189, 56, 184)(52, 180, 59, 187, 62, 190, 55, 183)(58, 186, 64, 192, 69, 197, 65, 193)(60, 188, 63, 191, 70, 198, 67, 195)(66, 194, 73, 201, 77, 205, 72, 200)(68, 196, 75, 203, 78, 206, 71, 199)(74, 202, 80, 208, 85, 213, 81, 209)(76, 204, 79, 207, 86, 214, 83, 211)(82, 210, 89, 217, 93, 221, 88, 216)(84, 212, 91, 219, 94, 222, 87, 215)(90, 218, 96, 224, 101, 229, 97, 225)(92, 220, 95, 223, 102, 230, 99, 227)(98, 226, 105, 233, 109, 237, 104, 232)(100, 228, 107, 235, 110, 238, 103, 231)(106, 234, 112, 240, 117, 245, 113, 241)(108, 236, 111, 239, 118, 246, 115, 243)(114, 242, 121, 249, 124, 252, 120, 248)(116, 244, 123, 251, 125, 253, 119, 247)(122, 250, 126, 254, 128, 256, 127, 255)(257, 385, 259, 387, 266, 394, 274, 402, 282, 410, 290, 418, 298, 426, 306, 434, 314, 442, 322, 450, 330, 458, 338, 466, 346, 474, 354, 482, 362, 490, 370, 498, 378, 506, 372, 500, 364, 492, 356, 484, 348, 476, 340, 468, 332, 460, 324, 452, 316, 444, 308, 436, 300, 428, 292, 420, 284, 412, 276, 404, 268, 396, 261, 389)(258, 386, 263, 391, 271, 399, 279, 407, 287, 415, 295, 423, 303, 431, 311, 439, 319, 447, 327, 455, 335, 463, 343, 471, 351, 479, 359, 487, 367, 495, 375, 503, 382, 510, 376, 504, 368, 496, 360, 488, 352, 480, 344, 472, 336, 464, 328, 456, 320, 448, 312, 440, 304, 432, 296, 424, 288, 416, 280, 408, 272, 400, 264, 392)(260, 388, 267, 395, 275, 403, 283, 411, 291, 419, 299, 427, 307, 435, 315, 443, 323, 451, 331, 459, 339, 467, 347, 475, 355, 483, 363, 491, 371, 499, 379, 507, 383, 511, 377, 505, 369, 497, 361, 489, 353, 481, 345, 473, 337, 465, 329, 457, 321, 449, 313, 441, 305, 433, 297, 425, 289, 417, 281, 409, 273, 401, 265, 393)(262, 390, 269, 397, 277, 405, 285, 413, 293, 421, 301, 429, 309, 437, 317, 445, 325, 453, 333, 461, 341, 469, 349, 477, 357, 485, 365, 493, 373, 501, 380, 508, 384, 512, 381, 509, 374, 502, 366, 494, 358, 486, 350, 478, 342, 470, 334, 462, 326, 454, 318, 446, 310, 438, 302, 430, 294, 422, 286, 414, 278, 406, 270, 398) L = (1, 259)(2, 263)(3, 266)(4, 267)(5, 257)(6, 269)(7, 271)(8, 258)(9, 260)(10, 274)(11, 275)(12, 261)(13, 277)(14, 262)(15, 279)(16, 264)(17, 265)(18, 282)(19, 283)(20, 268)(21, 285)(22, 270)(23, 287)(24, 272)(25, 273)(26, 290)(27, 291)(28, 276)(29, 293)(30, 278)(31, 295)(32, 280)(33, 281)(34, 298)(35, 299)(36, 284)(37, 301)(38, 286)(39, 303)(40, 288)(41, 289)(42, 306)(43, 307)(44, 292)(45, 309)(46, 294)(47, 311)(48, 296)(49, 297)(50, 314)(51, 315)(52, 300)(53, 317)(54, 302)(55, 319)(56, 304)(57, 305)(58, 322)(59, 323)(60, 308)(61, 325)(62, 310)(63, 327)(64, 312)(65, 313)(66, 330)(67, 331)(68, 316)(69, 333)(70, 318)(71, 335)(72, 320)(73, 321)(74, 338)(75, 339)(76, 324)(77, 341)(78, 326)(79, 343)(80, 328)(81, 329)(82, 346)(83, 347)(84, 332)(85, 349)(86, 334)(87, 351)(88, 336)(89, 337)(90, 354)(91, 355)(92, 340)(93, 357)(94, 342)(95, 359)(96, 344)(97, 345)(98, 362)(99, 363)(100, 348)(101, 365)(102, 350)(103, 367)(104, 352)(105, 353)(106, 370)(107, 371)(108, 356)(109, 373)(110, 358)(111, 375)(112, 360)(113, 361)(114, 378)(115, 379)(116, 364)(117, 380)(118, 366)(119, 382)(120, 368)(121, 369)(122, 372)(123, 383)(124, 384)(125, 374)(126, 376)(127, 377)(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, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E15.1311 Graph:: bipartite v = 36 e = 256 f = 192 degree seq :: [ 8^32, 64^4 ] E15.1311 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |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, Y3^14 * Y2 * Y3^-18 * 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, 276, 404)(272, 400, 279, 407)(273, 401, 281, 409)(274, 402, 277, 405)(275, 403, 283, 411)(278, 406, 285, 413)(280, 408, 287, 415)(282, 410, 288, 416)(284, 412, 286, 414)(289, 417, 295, 423)(290, 418, 297, 425)(291, 419, 293, 421)(292, 420, 299, 427)(294, 422, 301, 429)(296, 424, 303, 431)(298, 426, 304, 432)(300, 428, 302, 430)(305, 433, 311, 439)(306, 434, 313, 441)(307, 435, 309, 437)(308, 436, 315, 443)(310, 438, 317, 445)(312, 440, 319, 447)(314, 442, 320, 448)(316, 444, 318, 446)(321, 449, 327, 455)(322, 450, 329, 457)(323, 451, 325, 453)(324, 452, 331, 459)(326, 454, 333, 461)(328, 456, 335, 463)(330, 458, 336, 464)(332, 460, 334, 462)(337, 465, 343, 471)(338, 466, 345, 473)(339, 467, 341, 469)(340, 468, 347, 475)(342, 470, 349, 477)(344, 472, 351, 479)(346, 474, 352, 480)(348, 476, 350, 478)(353, 481, 359, 487)(354, 482, 361, 489)(355, 483, 357, 485)(356, 484, 363, 491)(358, 486, 365, 493)(360, 488, 367, 495)(362, 490, 368, 496)(364, 492, 366, 494)(369, 497, 375, 503)(370, 498, 377, 505)(371, 499, 373, 501)(372, 500, 379, 507)(374, 502, 380, 508)(376, 504, 382, 510)(378, 506, 381, 509)(383, 511, 384, 512) 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, 282)(18, 283)(19, 266)(20, 269)(21, 267)(22, 286)(23, 287)(24, 270)(25, 272)(26, 290)(27, 291)(28, 275)(29, 277)(30, 294)(31, 295)(32, 280)(33, 281)(34, 298)(35, 299)(36, 284)(37, 285)(38, 302)(39, 303)(40, 288)(41, 289)(42, 306)(43, 307)(44, 292)(45, 293)(46, 310)(47, 311)(48, 296)(49, 297)(50, 314)(51, 315)(52, 300)(53, 301)(54, 318)(55, 319)(56, 304)(57, 305)(58, 322)(59, 323)(60, 308)(61, 309)(62, 326)(63, 327)(64, 312)(65, 313)(66, 330)(67, 331)(68, 316)(69, 317)(70, 334)(71, 335)(72, 320)(73, 321)(74, 338)(75, 339)(76, 324)(77, 325)(78, 342)(79, 343)(80, 328)(81, 329)(82, 346)(83, 347)(84, 332)(85, 333)(86, 350)(87, 351)(88, 336)(89, 337)(90, 354)(91, 355)(92, 340)(93, 341)(94, 358)(95, 359)(96, 344)(97, 345)(98, 362)(99, 363)(100, 348)(101, 349)(102, 366)(103, 367)(104, 352)(105, 353)(106, 370)(107, 371)(108, 356)(109, 357)(110, 374)(111, 375)(112, 360)(113, 361)(114, 378)(115, 379)(116, 364)(117, 365)(118, 381)(119, 382)(120, 368)(121, 369)(122, 372)(123, 383)(124, 373)(125, 376)(126, 384)(127, 377)(128, 380)(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) :: { ( 8, 64 ), ( 8, 64, 8, 64 ) } Outer automorphisms :: reflexible Dual of E15.1310 Graph:: simple bipartite v = 192 e = 256 f = 36 degree seq :: [ 2^128, 4^64 ] E15.1312 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |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, Y1^32 ] Map:: polytopal R = (1, 129, 2, 130, 5, 133, 11, 139, 20, 148, 29, 157, 37, 165, 45, 173, 53, 181, 61, 189, 69, 197, 77, 205, 85, 213, 93, 221, 101, 229, 109, 237, 117, 245, 116, 244, 108, 236, 100, 228, 92, 220, 84, 212, 76, 204, 68, 196, 60, 188, 52, 180, 44, 172, 36, 164, 28, 156, 19, 147, 10, 138, 4, 132)(3, 131, 7, 135, 15, 143, 25, 153, 33, 161, 41, 169, 49, 177, 57, 185, 65, 193, 73, 201, 81, 209, 89, 217, 97, 225, 105, 233, 113, 241, 121, 249, 124, 252, 119, 247, 110, 238, 103, 231, 94, 222, 87, 215, 78, 206, 71, 199, 62, 190, 55, 183, 46, 174, 39, 167, 30, 158, 22, 150, 12, 140, 8, 136)(6, 134, 13, 141, 9, 137, 18, 146, 27, 155, 35, 163, 43, 171, 51, 179, 59, 187, 67, 195, 75, 203, 83, 211, 91, 219, 99, 227, 107, 235, 115, 243, 123, 251, 125, 253, 118, 246, 111, 239, 102, 230, 95, 223, 86, 214, 79, 207, 70, 198, 63, 191, 54, 182, 47, 175, 38, 166, 31, 159, 21, 149, 14, 142)(16, 144, 23, 151, 17, 145, 24, 152, 32, 160, 40, 168, 48, 176, 56, 184, 64, 192, 72, 200, 80, 208, 88, 216, 96, 224, 104, 232, 112, 240, 120, 248, 126, 254, 128, 256, 127, 255, 122, 250, 114, 242, 106, 234, 98, 226, 90, 218, 82, 210, 74, 202, 66, 194, 58, 186, 50, 178, 42, 170, 34, 162, 26, 154)(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, 282)(19, 283)(20, 286)(21, 267)(22, 288)(23, 269)(24, 270)(25, 290)(26, 274)(27, 275)(28, 289)(29, 294)(30, 276)(31, 296)(32, 278)(33, 284)(34, 281)(35, 298)(36, 299)(37, 302)(38, 285)(39, 304)(40, 287)(41, 306)(42, 291)(43, 292)(44, 305)(45, 310)(46, 293)(47, 312)(48, 295)(49, 300)(50, 297)(51, 314)(52, 315)(53, 318)(54, 301)(55, 320)(56, 303)(57, 322)(58, 307)(59, 308)(60, 321)(61, 326)(62, 309)(63, 328)(64, 311)(65, 316)(66, 313)(67, 330)(68, 331)(69, 334)(70, 317)(71, 336)(72, 319)(73, 338)(74, 323)(75, 324)(76, 337)(77, 342)(78, 325)(79, 344)(80, 327)(81, 332)(82, 329)(83, 346)(84, 347)(85, 350)(86, 333)(87, 352)(88, 335)(89, 354)(90, 339)(91, 340)(92, 353)(93, 358)(94, 341)(95, 360)(96, 343)(97, 348)(98, 345)(99, 362)(100, 363)(101, 366)(102, 349)(103, 368)(104, 351)(105, 370)(106, 355)(107, 356)(108, 369)(109, 374)(110, 357)(111, 376)(112, 359)(113, 364)(114, 361)(115, 378)(116, 379)(117, 380)(118, 365)(119, 382)(120, 367)(121, 383)(122, 371)(123, 372)(124, 373)(125, 384)(126, 375)(127, 377)(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) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.1309 Graph:: simple bipartite v = 132 e = 256 f = 96 degree seq :: [ 2^128, 64^4 ] E15.1313 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |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, Y2^32 ] 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, 20, 148)(16, 144, 23, 151)(17, 145, 25, 153)(18, 146, 21, 149)(19, 147, 27, 155)(22, 150, 29, 157)(24, 152, 31, 159)(26, 154, 32, 160)(28, 156, 30, 158)(33, 161, 39, 167)(34, 162, 41, 169)(35, 163, 37, 165)(36, 164, 43, 171)(38, 166, 45, 173)(40, 168, 47, 175)(42, 170, 48, 176)(44, 172, 46, 174)(49, 177, 55, 183)(50, 178, 57, 185)(51, 179, 53, 181)(52, 180, 59, 187)(54, 182, 61, 189)(56, 184, 63, 191)(58, 186, 64, 192)(60, 188, 62, 190)(65, 193, 71, 199)(66, 194, 73, 201)(67, 195, 69, 197)(68, 196, 75, 203)(70, 198, 77, 205)(72, 200, 79, 207)(74, 202, 80, 208)(76, 204, 78, 206)(81, 209, 87, 215)(82, 210, 89, 217)(83, 211, 85, 213)(84, 212, 91, 219)(86, 214, 93, 221)(88, 216, 95, 223)(90, 218, 96, 224)(92, 220, 94, 222)(97, 225, 103, 231)(98, 226, 105, 233)(99, 227, 101, 229)(100, 228, 107, 235)(102, 230, 109, 237)(104, 232, 111, 239)(106, 234, 112, 240)(108, 236, 110, 238)(113, 241, 119, 247)(114, 242, 121, 249)(115, 243, 117, 245)(116, 244, 123, 251)(118, 246, 124, 252)(120, 248, 126, 254)(122, 250, 125, 253)(127, 255, 128, 256)(257, 385, 259, 387, 264, 392, 273, 401, 282, 410, 290, 418, 298, 426, 306, 434, 314, 442, 322, 450, 330, 458, 338, 466, 346, 474, 354, 482, 362, 490, 370, 498, 378, 506, 372, 500, 364, 492, 356, 484, 348, 476, 340, 468, 332, 460, 324, 452, 316, 444, 308, 436, 300, 428, 292, 420, 284, 412, 275, 403, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 278, 406, 286, 414, 294, 422, 302, 430, 310, 438, 318, 446, 326, 454, 334, 462, 342, 470, 350, 478, 358, 486, 366, 494, 374, 502, 381, 509, 376, 504, 368, 496, 360, 488, 352, 480, 344, 472, 336, 464, 328, 456, 320, 448, 312, 440, 304, 432, 296, 424, 288, 416, 280, 408, 270, 398, 262, 390)(263, 391, 271, 399, 265, 393, 274, 402, 283, 411, 291, 419, 299, 427, 307, 435, 315, 443, 323, 451, 331, 459, 339, 467, 347, 475, 355, 483, 363, 491, 371, 499, 379, 507, 383, 511, 377, 505, 369, 497, 361, 489, 353, 481, 345, 473, 337, 465, 329, 457, 321, 449, 313, 441, 305, 433, 297, 425, 289, 417, 281, 409, 272, 400)(267, 395, 276, 404, 269, 397, 279, 407, 287, 415, 295, 423, 303, 431, 311, 439, 319, 447, 327, 455, 335, 463, 343, 471, 351, 479, 359, 487, 367, 495, 375, 503, 382, 510, 384, 512, 380, 508, 373, 501, 365, 493, 357, 485, 349, 477, 341, 469, 333, 461, 325, 453, 317, 445, 309, 437, 301, 429, 293, 421, 285, 413, 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, 276)(16, 279)(17, 281)(18, 277)(19, 283)(20, 271)(21, 274)(22, 285)(23, 272)(24, 287)(25, 273)(26, 288)(27, 275)(28, 286)(29, 278)(30, 284)(31, 280)(32, 282)(33, 295)(34, 297)(35, 293)(36, 299)(37, 291)(38, 301)(39, 289)(40, 303)(41, 290)(42, 304)(43, 292)(44, 302)(45, 294)(46, 300)(47, 296)(48, 298)(49, 311)(50, 313)(51, 309)(52, 315)(53, 307)(54, 317)(55, 305)(56, 319)(57, 306)(58, 320)(59, 308)(60, 318)(61, 310)(62, 316)(63, 312)(64, 314)(65, 327)(66, 329)(67, 325)(68, 331)(69, 323)(70, 333)(71, 321)(72, 335)(73, 322)(74, 336)(75, 324)(76, 334)(77, 326)(78, 332)(79, 328)(80, 330)(81, 343)(82, 345)(83, 341)(84, 347)(85, 339)(86, 349)(87, 337)(88, 351)(89, 338)(90, 352)(91, 340)(92, 350)(93, 342)(94, 348)(95, 344)(96, 346)(97, 359)(98, 361)(99, 357)(100, 363)(101, 355)(102, 365)(103, 353)(104, 367)(105, 354)(106, 368)(107, 356)(108, 366)(109, 358)(110, 364)(111, 360)(112, 362)(113, 375)(114, 377)(115, 373)(116, 379)(117, 371)(118, 380)(119, 369)(120, 382)(121, 370)(122, 381)(123, 372)(124, 374)(125, 378)(126, 376)(127, 384)(128, 383)(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, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1314 Graph:: bipartite v = 68 e = 256 f = 160 degree seq :: [ 4^64, 64^4 ] E15.1314 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32}) Quotient :: dipole Aut^+ = (C32 x C2) : C2 (small group id <128, 147>) Aut = $<256, 6649>$ (small group id <256, 6649>) |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)^32 ] Map:: polytopal R = (1, 129, 2, 130, 6, 134, 4, 132)(3, 131, 9, 137, 13, 141, 8, 136)(5, 133, 11, 139, 14, 142, 7, 135)(10, 138, 16, 144, 21, 149, 17, 145)(12, 140, 15, 143, 22, 150, 19, 147)(18, 146, 25, 153, 29, 157, 24, 152)(20, 148, 27, 155, 30, 158, 23, 151)(26, 154, 32, 160, 37, 165, 33, 161)(28, 156, 31, 159, 38, 166, 35, 163)(34, 162, 41, 169, 45, 173, 40, 168)(36, 164, 43, 171, 46, 174, 39, 167)(42, 170, 48, 176, 53, 181, 49, 177)(44, 172, 47, 175, 54, 182, 51, 179)(50, 178, 57, 185, 61, 189, 56, 184)(52, 180, 59, 187, 62, 190, 55, 183)(58, 186, 64, 192, 69, 197, 65, 193)(60, 188, 63, 191, 70, 198, 67, 195)(66, 194, 73, 201, 77, 205, 72, 200)(68, 196, 75, 203, 78, 206, 71, 199)(74, 202, 80, 208, 85, 213, 81, 209)(76, 204, 79, 207, 86, 214, 83, 211)(82, 210, 89, 217, 93, 221, 88, 216)(84, 212, 91, 219, 94, 222, 87, 215)(90, 218, 96, 224, 101, 229, 97, 225)(92, 220, 95, 223, 102, 230, 99, 227)(98, 226, 105, 233, 109, 237, 104, 232)(100, 228, 107, 235, 110, 238, 103, 231)(106, 234, 112, 240, 117, 245, 113, 241)(108, 236, 111, 239, 118, 246, 115, 243)(114, 242, 121, 249, 124, 252, 120, 248)(116, 244, 123, 251, 125, 253, 119, 247)(122, 250, 126, 254, 128, 256, 127, 255)(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, 269)(7, 271)(8, 258)(9, 260)(10, 274)(11, 275)(12, 261)(13, 277)(14, 262)(15, 279)(16, 264)(17, 265)(18, 282)(19, 283)(20, 268)(21, 285)(22, 270)(23, 287)(24, 272)(25, 273)(26, 290)(27, 291)(28, 276)(29, 293)(30, 278)(31, 295)(32, 280)(33, 281)(34, 298)(35, 299)(36, 284)(37, 301)(38, 286)(39, 303)(40, 288)(41, 289)(42, 306)(43, 307)(44, 292)(45, 309)(46, 294)(47, 311)(48, 296)(49, 297)(50, 314)(51, 315)(52, 300)(53, 317)(54, 302)(55, 319)(56, 304)(57, 305)(58, 322)(59, 323)(60, 308)(61, 325)(62, 310)(63, 327)(64, 312)(65, 313)(66, 330)(67, 331)(68, 316)(69, 333)(70, 318)(71, 335)(72, 320)(73, 321)(74, 338)(75, 339)(76, 324)(77, 341)(78, 326)(79, 343)(80, 328)(81, 329)(82, 346)(83, 347)(84, 332)(85, 349)(86, 334)(87, 351)(88, 336)(89, 337)(90, 354)(91, 355)(92, 340)(93, 357)(94, 342)(95, 359)(96, 344)(97, 345)(98, 362)(99, 363)(100, 348)(101, 365)(102, 350)(103, 367)(104, 352)(105, 353)(106, 370)(107, 371)(108, 356)(109, 373)(110, 358)(111, 375)(112, 360)(113, 361)(114, 378)(115, 379)(116, 364)(117, 380)(118, 366)(119, 382)(120, 368)(121, 369)(122, 372)(123, 383)(124, 384)(125, 374)(126, 376)(127, 377)(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) :: { ( 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E15.1313 Graph:: simple bipartite v = 160 e = 256 f = 68 degree seq :: [ 2^128, 8^32 ] E15.1315 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 18}) Quotient :: regular Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2 * T1^-1)^2, (T1^-1 * T2)^4, T1^18 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 41, 61, 80, 97, 113, 112, 96, 79, 60, 40, 22, 10, 4)(3, 7, 15, 31, 51, 71, 89, 105, 121, 128, 117, 99, 81, 65, 43, 24, 18, 8)(6, 13, 27, 21, 39, 59, 78, 95, 111, 127, 131, 115, 98, 84, 63, 42, 30, 14)(9, 19, 37, 57, 76, 93, 109, 125, 129, 114, 101, 82, 62, 46, 26, 12, 25, 20)(16, 33, 53, 36, 45, 67, 86, 100, 118, 133, 139, 136, 122, 108, 91, 72, 55, 34)(17, 35, 50, 64, 85, 103, 116, 132, 141, 135, 123, 106, 90, 73, 52, 32, 48, 28)(29, 49, 68, 83, 102, 119, 130, 140, 138, 126, 110, 94, 77, 58, 38, 47, 66, 44)(54, 75, 92, 107, 124, 137, 143, 144, 142, 134, 120, 104, 88, 70, 56, 74, 87, 69) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 38)(20, 33)(22, 31)(23, 42)(25, 44)(26, 45)(27, 47)(30, 50)(34, 54)(35, 56)(37, 55)(39, 52)(40, 57)(41, 62)(43, 64)(46, 68)(48, 69)(49, 70)(51, 72)(53, 74)(58, 75)(59, 77)(60, 78)(61, 81)(63, 83)(65, 86)(66, 87)(67, 88)(71, 90)(73, 92)(76, 94)(79, 89)(80, 98)(82, 100)(84, 103)(85, 104)(91, 107)(93, 108)(95, 106)(96, 109)(97, 114)(99, 116)(101, 119)(102, 120)(105, 122)(110, 124)(111, 126)(112, 127)(113, 128)(115, 130)(117, 133)(118, 134)(121, 135)(123, 137)(125, 138)(129, 139)(131, 141)(132, 142)(136, 143)(140, 144) local type(s) :: { ( 4^18 ) } Outer automorphisms :: reflexible Dual of E15.1316 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 72 f = 36 degree seq :: [ 18^8 ] E15.1316 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 18}) Quotient :: regular Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1 * T2 * T1^-1)^2, (T1^-1 * T2)^18 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 33, 25)(15, 26, 32, 27)(21, 35, 30, 36)(22, 37, 29, 38)(23, 39, 44, 34)(40, 49, 43, 50)(41, 51, 42, 52)(45, 53, 48, 54)(46, 55, 47, 56)(57, 65, 60, 66)(58, 67, 59, 68)(61, 69, 64, 70)(62, 71, 63, 72)(73, 81, 76, 82)(74, 83, 75, 84)(77, 85, 80, 86)(78, 87, 79, 88)(89, 97, 92, 98)(90, 99, 91, 100)(93, 101, 96, 102)(94, 103, 95, 104)(105, 113, 108, 114)(106, 115, 107, 116)(109, 117, 112, 118)(110, 119, 111, 120)(121, 129, 124, 130)(122, 131, 123, 132)(125, 133, 128, 134)(126, 135, 127, 136)(137, 141, 140, 144)(138, 143, 139, 142) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128)(129, 137)(130, 138)(131, 139)(132, 140)(133, 141)(134, 142)(135, 143)(136, 144) local type(s) :: { ( 18^4 ) } Outer automorphisms :: reflexible Dual of E15.1315 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 36 e = 72 f = 8 degree seq :: [ 4^36 ] E15.1317 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 18}) Quotient :: edge Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^18 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 30, 40)(25, 41, 28, 42)(31, 44, 38, 45)(33, 46, 36, 47)(49, 57, 52, 58)(50, 59, 51, 60)(53, 61, 56, 62)(54, 63, 55, 64)(65, 73, 68, 74)(66, 75, 67, 76)(69, 77, 72, 78)(70, 79, 71, 80)(81, 89, 84, 90)(82, 91, 83, 92)(85, 93, 88, 94)(86, 95, 87, 96)(97, 105, 100, 106)(98, 107, 99, 108)(101, 109, 104, 110)(102, 111, 103, 112)(113, 121, 116, 122)(114, 123, 115, 124)(117, 125, 120, 126)(118, 127, 119, 128)(129, 137, 132, 138)(130, 139, 131, 140)(133, 141, 136, 142)(134, 143, 135, 144)(145, 146)(147, 151)(148, 153)(149, 154)(150, 156)(152, 159)(155, 164)(157, 167)(158, 169)(160, 172)(161, 174)(162, 175)(163, 177)(165, 180)(166, 182)(168, 179)(170, 181)(171, 176)(173, 178)(183, 193)(184, 194)(185, 195)(186, 196)(187, 192)(188, 197)(189, 198)(190, 199)(191, 200)(201, 209)(202, 210)(203, 211)(204, 212)(205, 213)(206, 214)(207, 215)(208, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 241)(234, 242)(235, 243)(236, 244)(237, 245)(238, 246)(239, 247)(240, 248)(249, 257)(250, 258)(251, 259)(252, 260)(253, 261)(254, 262)(255, 263)(256, 264)(265, 273)(266, 274)(267, 275)(268, 276)(269, 277)(270, 278)(271, 279)(272, 280)(281, 285)(282, 288)(283, 287)(284, 286) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 36, 36 ), ( 36^4 ) } Outer automorphisms :: reflexible Dual of E15.1321 Transitivity :: ET+ Graph:: simple bipartite v = 108 e = 144 f = 8 degree seq :: [ 2^72, 4^36 ] E15.1318 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 18}) Quotient :: edge Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, T1^4, (F * T2)^2, (T2^-2 * T1)^2, T2^18 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 43, 60, 76, 92, 108, 124, 112, 96, 80, 64, 47, 29, 14, 5)(2, 7, 17, 35, 54, 70, 86, 102, 118, 133, 120, 104, 88, 72, 56, 38, 20, 8)(4, 12, 26, 45, 62, 78, 94, 110, 126, 136, 122, 106, 90, 74, 58, 41, 22, 9)(6, 15, 30, 49, 66, 82, 98, 114, 129, 140, 131, 116, 100, 84, 68, 52, 33, 16)(11, 25, 13, 28, 46, 63, 79, 95, 111, 127, 137, 123, 107, 91, 75, 59, 42, 23)(18, 36, 19, 37, 55, 71, 87, 103, 119, 134, 142, 132, 117, 101, 85, 69, 53, 34)(21, 39, 57, 73, 89, 105, 121, 135, 143, 138, 125, 109, 93, 77, 61, 44, 27, 40)(31, 50, 32, 51, 67, 83, 99, 115, 130, 141, 144, 139, 128, 113, 97, 81, 65, 48)(145, 146, 150, 148)(147, 153, 165, 155)(149, 157, 162, 151)(152, 163, 175, 159)(154, 167, 181, 164)(156, 160, 176, 171)(158, 170, 188, 172)(161, 178, 195, 177)(166, 174, 192, 183)(168, 182, 193, 185)(169, 184, 194, 180)(173, 179, 196, 189)(186, 201, 209, 199)(187, 202, 217, 203)(190, 205, 211, 197)(191, 207, 213, 198)(200, 215, 225, 210)(204, 219, 231, 216)(206, 212, 227, 221)(208, 222, 237, 223)(214, 229, 243, 228)(218, 226, 241, 233)(220, 232, 242, 234)(224, 230, 244, 238)(235, 249, 257, 247)(236, 250, 265, 251)(239, 253, 259, 245)(240, 255, 261, 246)(248, 263, 272, 258)(252, 267, 278, 264)(254, 260, 274, 269)(256, 270, 282, 271)(262, 276, 285, 275)(266, 273, 283, 279)(268, 277, 284, 280)(281, 287, 288, 286) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^4 ), ( 4^18 ) } Outer automorphisms :: reflexible Dual of E15.1322 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 144 f = 72 degree seq :: [ 4^36, 18^8 ] E15.1319 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 18}) Quotient :: edge Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T2 * T1^-3)^2, T1^18 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 38)(20, 33)(22, 31)(23, 42)(25, 44)(26, 45)(27, 47)(30, 50)(34, 54)(35, 56)(37, 55)(39, 52)(40, 57)(41, 62)(43, 64)(46, 68)(48, 69)(49, 70)(51, 72)(53, 74)(58, 75)(59, 77)(60, 78)(61, 81)(63, 83)(65, 86)(66, 87)(67, 88)(71, 90)(73, 92)(76, 94)(79, 89)(80, 98)(82, 100)(84, 103)(85, 104)(91, 107)(93, 108)(95, 106)(96, 109)(97, 114)(99, 116)(101, 119)(102, 120)(105, 122)(110, 124)(111, 126)(112, 127)(113, 128)(115, 130)(117, 133)(118, 134)(121, 135)(123, 137)(125, 138)(129, 139)(131, 141)(132, 142)(136, 143)(140, 144)(145, 146, 149, 155, 167, 185, 205, 224, 241, 257, 256, 240, 223, 204, 184, 166, 154, 148)(147, 151, 159, 175, 195, 215, 233, 249, 265, 272, 261, 243, 225, 209, 187, 168, 162, 152)(150, 157, 171, 165, 183, 203, 222, 239, 255, 271, 275, 259, 242, 228, 207, 186, 174, 158)(153, 163, 181, 201, 220, 237, 253, 269, 273, 258, 245, 226, 206, 190, 170, 156, 169, 164)(160, 177, 197, 180, 189, 211, 230, 244, 262, 277, 283, 280, 266, 252, 235, 216, 199, 178)(161, 179, 194, 208, 229, 247, 260, 276, 285, 279, 267, 250, 234, 217, 196, 176, 192, 172)(173, 193, 212, 227, 246, 263, 274, 284, 282, 270, 254, 238, 221, 202, 182, 191, 210, 188)(198, 219, 236, 251, 268, 281, 287, 288, 286, 278, 264, 248, 232, 214, 200, 218, 231, 213) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 8 ), ( 8^18 ) } Outer automorphisms :: reflexible Dual of E15.1320 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 144 f = 36 degree seq :: [ 2^72, 18^8 ] E15.1320 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 18}) Quotient :: loop Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^18 ] Map:: R = (1, 145, 3, 147, 8, 152, 4, 148)(2, 146, 5, 149, 11, 155, 6, 150)(7, 151, 13, 157, 24, 168, 14, 158)(9, 153, 16, 160, 29, 173, 17, 161)(10, 154, 18, 162, 32, 176, 19, 163)(12, 156, 21, 165, 37, 181, 22, 166)(15, 159, 26, 170, 43, 187, 27, 171)(20, 164, 34, 178, 48, 192, 35, 179)(23, 167, 39, 183, 30, 174, 40, 184)(25, 169, 41, 185, 28, 172, 42, 186)(31, 175, 44, 188, 38, 182, 45, 189)(33, 177, 46, 190, 36, 180, 47, 191)(49, 193, 57, 201, 52, 196, 58, 202)(50, 194, 59, 203, 51, 195, 60, 204)(53, 197, 61, 205, 56, 200, 62, 206)(54, 198, 63, 207, 55, 199, 64, 208)(65, 209, 73, 217, 68, 212, 74, 218)(66, 210, 75, 219, 67, 211, 76, 220)(69, 213, 77, 221, 72, 216, 78, 222)(70, 214, 79, 223, 71, 215, 80, 224)(81, 225, 89, 233, 84, 228, 90, 234)(82, 226, 91, 235, 83, 227, 92, 236)(85, 229, 93, 237, 88, 232, 94, 238)(86, 230, 95, 239, 87, 231, 96, 240)(97, 241, 105, 249, 100, 244, 106, 250)(98, 242, 107, 251, 99, 243, 108, 252)(101, 245, 109, 253, 104, 248, 110, 254)(102, 246, 111, 255, 103, 247, 112, 256)(113, 257, 121, 265, 116, 260, 122, 266)(114, 258, 123, 267, 115, 259, 124, 268)(117, 261, 125, 269, 120, 264, 126, 270)(118, 262, 127, 271, 119, 263, 128, 272)(129, 273, 137, 281, 132, 276, 138, 282)(130, 274, 139, 283, 131, 275, 140, 284)(133, 277, 141, 285, 136, 280, 142, 286)(134, 278, 143, 287, 135, 279, 144, 288) L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 154)(6, 156)(7, 147)(8, 159)(9, 148)(10, 149)(11, 164)(12, 150)(13, 167)(14, 169)(15, 152)(16, 172)(17, 174)(18, 175)(19, 177)(20, 155)(21, 180)(22, 182)(23, 157)(24, 179)(25, 158)(26, 181)(27, 176)(28, 160)(29, 178)(30, 161)(31, 162)(32, 171)(33, 163)(34, 173)(35, 168)(36, 165)(37, 170)(38, 166)(39, 193)(40, 194)(41, 195)(42, 196)(43, 192)(44, 197)(45, 198)(46, 199)(47, 200)(48, 187)(49, 183)(50, 184)(51, 185)(52, 186)(53, 188)(54, 189)(55, 190)(56, 191)(57, 209)(58, 210)(59, 211)(60, 212)(61, 213)(62, 214)(63, 215)(64, 216)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 225)(74, 226)(75, 227)(76, 228)(77, 229)(78, 230)(79, 231)(80, 232)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272)(137, 285)(138, 288)(139, 287)(140, 286)(141, 281)(142, 284)(143, 283)(144, 282) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E15.1319 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 36 e = 144 f = 80 degree seq :: [ 8^36 ] E15.1321 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 18}) Quotient :: loop Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, T1^4, (F * T2)^2, (T2^-2 * T1)^2, T2^18 ] Map:: R = (1, 145, 3, 147, 10, 154, 24, 168, 43, 187, 60, 204, 76, 220, 92, 236, 108, 252, 124, 268, 112, 256, 96, 240, 80, 224, 64, 208, 47, 191, 29, 173, 14, 158, 5, 149)(2, 146, 7, 151, 17, 161, 35, 179, 54, 198, 70, 214, 86, 230, 102, 246, 118, 262, 133, 277, 120, 264, 104, 248, 88, 232, 72, 216, 56, 200, 38, 182, 20, 164, 8, 152)(4, 148, 12, 156, 26, 170, 45, 189, 62, 206, 78, 222, 94, 238, 110, 254, 126, 270, 136, 280, 122, 266, 106, 250, 90, 234, 74, 218, 58, 202, 41, 185, 22, 166, 9, 153)(6, 150, 15, 159, 30, 174, 49, 193, 66, 210, 82, 226, 98, 242, 114, 258, 129, 273, 140, 284, 131, 275, 116, 260, 100, 244, 84, 228, 68, 212, 52, 196, 33, 177, 16, 160)(11, 155, 25, 169, 13, 157, 28, 172, 46, 190, 63, 207, 79, 223, 95, 239, 111, 255, 127, 271, 137, 281, 123, 267, 107, 251, 91, 235, 75, 219, 59, 203, 42, 186, 23, 167)(18, 162, 36, 180, 19, 163, 37, 181, 55, 199, 71, 215, 87, 231, 103, 247, 119, 263, 134, 278, 142, 286, 132, 276, 117, 261, 101, 245, 85, 229, 69, 213, 53, 197, 34, 178)(21, 165, 39, 183, 57, 201, 73, 217, 89, 233, 105, 249, 121, 265, 135, 279, 143, 287, 138, 282, 125, 269, 109, 253, 93, 237, 77, 221, 61, 205, 44, 188, 27, 171, 40, 184)(31, 175, 50, 194, 32, 176, 51, 195, 67, 211, 83, 227, 99, 243, 115, 259, 130, 274, 141, 285, 144, 288, 139, 283, 128, 272, 113, 257, 97, 241, 81, 225, 65, 209, 48, 192) L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 157)(6, 148)(7, 149)(8, 163)(9, 165)(10, 167)(11, 147)(12, 160)(13, 162)(14, 170)(15, 152)(16, 176)(17, 178)(18, 151)(19, 175)(20, 154)(21, 155)(22, 174)(23, 181)(24, 182)(25, 184)(26, 188)(27, 156)(28, 158)(29, 179)(30, 192)(31, 159)(32, 171)(33, 161)(34, 195)(35, 196)(36, 169)(37, 164)(38, 193)(39, 166)(40, 194)(41, 168)(42, 201)(43, 202)(44, 172)(45, 173)(46, 205)(47, 207)(48, 183)(49, 185)(50, 180)(51, 177)(52, 189)(53, 190)(54, 191)(55, 186)(56, 215)(57, 209)(58, 217)(59, 187)(60, 219)(61, 211)(62, 212)(63, 213)(64, 222)(65, 199)(66, 200)(67, 197)(68, 227)(69, 198)(70, 229)(71, 225)(72, 204)(73, 203)(74, 226)(75, 231)(76, 232)(77, 206)(78, 237)(79, 208)(80, 230)(81, 210)(82, 241)(83, 221)(84, 214)(85, 243)(86, 244)(87, 216)(88, 242)(89, 218)(90, 220)(91, 249)(92, 250)(93, 223)(94, 224)(95, 253)(96, 255)(97, 233)(98, 234)(99, 228)(100, 238)(101, 239)(102, 240)(103, 235)(104, 263)(105, 257)(106, 265)(107, 236)(108, 267)(109, 259)(110, 260)(111, 261)(112, 270)(113, 247)(114, 248)(115, 245)(116, 274)(117, 246)(118, 276)(119, 272)(120, 252)(121, 251)(122, 273)(123, 278)(124, 277)(125, 254)(126, 282)(127, 256)(128, 258)(129, 283)(130, 269)(131, 262)(132, 285)(133, 284)(134, 264)(135, 266)(136, 268)(137, 287)(138, 271)(139, 279)(140, 280)(141, 275)(142, 281)(143, 288)(144, 286) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1317 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 144 f = 108 degree seq :: [ 36^8 ] E15.1322 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 18}) Quotient :: loop Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T2 * T1^-3)^2, T1^18 ] Map:: polytopal non-degenerate R = (1, 145, 3, 147)(2, 146, 6, 150)(4, 148, 9, 153)(5, 149, 12, 156)(7, 151, 16, 160)(8, 152, 17, 161)(10, 154, 21, 165)(11, 155, 24, 168)(13, 157, 28, 172)(14, 158, 29, 173)(15, 159, 32, 176)(18, 162, 36, 180)(19, 163, 38, 182)(20, 164, 33, 177)(22, 166, 31, 175)(23, 167, 42, 186)(25, 169, 44, 188)(26, 170, 45, 189)(27, 171, 47, 191)(30, 174, 50, 194)(34, 178, 54, 198)(35, 179, 56, 200)(37, 181, 55, 199)(39, 183, 52, 196)(40, 184, 57, 201)(41, 185, 62, 206)(43, 187, 64, 208)(46, 190, 68, 212)(48, 192, 69, 213)(49, 193, 70, 214)(51, 195, 72, 216)(53, 197, 74, 218)(58, 202, 75, 219)(59, 203, 77, 221)(60, 204, 78, 222)(61, 205, 81, 225)(63, 207, 83, 227)(65, 209, 86, 230)(66, 210, 87, 231)(67, 211, 88, 232)(71, 215, 90, 234)(73, 217, 92, 236)(76, 220, 94, 238)(79, 223, 89, 233)(80, 224, 98, 242)(82, 226, 100, 244)(84, 228, 103, 247)(85, 229, 104, 248)(91, 235, 107, 251)(93, 237, 108, 252)(95, 239, 106, 250)(96, 240, 109, 253)(97, 241, 114, 258)(99, 243, 116, 260)(101, 245, 119, 263)(102, 246, 120, 264)(105, 249, 122, 266)(110, 254, 124, 268)(111, 255, 126, 270)(112, 256, 127, 271)(113, 257, 128, 272)(115, 259, 130, 274)(117, 261, 133, 277)(118, 262, 134, 278)(121, 265, 135, 279)(123, 267, 137, 281)(125, 269, 138, 282)(129, 273, 139, 283)(131, 275, 141, 285)(132, 276, 142, 286)(136, 280, 143, 287)(140, 284, 144, 288) L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 163)(10, 148)(11, 167)(12, 169)(13, 171)(14, 150)(15, 175)(16, 177)(17, 179)(18, 152)(19, 181)(20, 153)(21, 183)(22, 154)(23, 185)(24, 162)(25, 164)(26, 156)(27, 165)(28, 161)(29, 193)(30, 158)(31, 195)(32, 192)(33, 197)(34, 160)(35, 194)(36, 189)(37, 201)(38, 191)(39, 203)(40, 166)(41, 205)(42, 174)(43, 168)(44, 173)(45, 211)(46, 170)(47, 210)(48, 172)(49, 212)(50, 208)(51, 215)(52, 176)(53, 180)(54, 219)(55, 178)(56, 218)(57, 220)(58, 182)(59, 222)(60, 184)(61, 224)(62, 190)(63, 186)(64, 229)(65, 187)(66, 188)(67, 230)(68, 227)(69, 198)(70, 200)(71, 233)(72, 199)(73, 196)(74, 231)(75, 236)(76, 237)(77, 202)(78, 239)(79, 204)(80, 241)(81, 209)(82, 206)(83, 246)(84, 207)(85, 247)(86, 244)(87, 213)(88, 214)(89, 249)(90, 217)(91, 216)(92, 251)(93, 253)(94, 221)(95, 255)(96, 223)(97, 257)(98, 228)(99, 225)(100, 262)(101, 226)(102, 263)(103, 260)(104, 232)(105, 265)(106, 234)(107, 268)(108, 235)(109, 269)(110, 238)(111, 271)(112, 240)(113, 256)(114, 245)(115, 242)(116, 276)(117, 243)(118, 277)(119, 274)(120, 248)(121, 272)(122, 252)(123, 250)(124, 281)(125, 273)(126, 254)(127, 275)(128, 261)(129, 258)(130, 284)(131, 259)(132, 285)(133, 283)(134, 264)(135, 267)(136, 266)(137, 287)(138, 270)(139, 280)(140, 282)(141, 279)(142, 278)(143, 288)(144, 286) local type(s) :: { ( 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E15.1318 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 72 e = 144 f = 44 degree seq :: [ 4^72 ] E15.1323 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 18}) Quotient :: dipole Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^18 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 10, 154)(6, 150, 12, 156)(8, 152, 15, 159)(11, 155, 20, 164)(13, 157, 23, 167)(14, 158, 25, 169)(16, 160, 28, 172)(17, 161, 30, 174)(18, 162, 31, 175)(19, 163, 33, 177)(21, 165, 36, 180)(22, 166, 38, 182)(24, 168, 35, 179)(26, 170, 37, 181)(27, 171, 32, 176)(29, 173, 34, 178)(39, 183, 49, 193)(40, 184, 50, 194)(41, 185, 51, 195)(42, 186, 52, 196)(43, 187, 48, 192)(44, 188, 53, 197)(45, 189, 54, 198)(46, 190, 55, 199)(47, 191, 56, 200)(57, 201, 65, 209)(58, 202, 66, 210)(59, 203, 67, 211)(60, 204, 68, 212)(61, 205, 69, 213)(62, 206, 70, 214)(63, 207, 71, 215)(64, 208, 72, 216)(73, 217, 81, 225)(74, 218, 82, 226)(75, 219, 83, 227)(76, 220, 84, 228)(77, 221, 85, 229)(78, 222, 86, 230)(79, 223, 87, 231)(80, 224, 88, 232)(89, 233, 97, 241)(90, 234, 98, 242)(91, 235, 99, 243)(92, 236, 100, 244)(93, 237, 101, 245)(94, 238, 102, 246)(95, 239, 103, 247)(96, 240, 104, 248)(105, 249, 113, 257)(106, 250, 114, 258)(107, 251, 115, 259)(108, 252, 116, 260)(109, 253, 117, 261)(110, 254, 118, 262)(111, 255, 119, 263)(112, 256, 120, 264)(121, 265, 129, 273)(122, 266, 130, 274)(123, 267, 131, 275)(124, 268, 132, 276)(125, 269, 133, 277)(126, 270, 134, 278)(127, 271, 135, 279)(128, 272, 136, 280)(137, 281, 141, 285)(138, 282, 144, 288)(139, 283, 143, 287)(140, 284, 142, 286)(289, 433, 291, 435, 296, 440, 292, 436)(290, 434, 293, 437, 299, 443, 294, 438)(295, 439, 301, 445, 312, 456, 302, 446)(297, 441, 304, 448, 317, 461, 305, 449)(298, 442, 306, 450, 320, 464, 307, 451)(300, 444, 309, 453, 325, 469, 310, 454)(303, 447, 314, 458, 331, 475, 315, 459)(308, 452, 322, 466, 336, 480, 323, 467)(311, 455, 327, 471, 318, 462, 328, 472)(313, 457, 329, 473, 316, 460, 330, 474)(319, 463, 332, 476, 326, 470, 333, 477)(321, 465, 334, 478, 324, 468, 335, 479)(337, 481, 345, 489, 340, 484, 346, 490)(338, 482, 347, 491, 339, 483, 348, 492)(341, 485, 349, 493, 344, 488, 350, 494)(342, 486, 351, 495, 343, 487, 352, 496)(353, 497, 361, 505, 356, 500, 362, 506)(354, 498, 363, 507, 355, 499, 364, 508)(357, 501, 365, 509, 360, 504, 366, 510)(358, 502, 367, 511, 359, 503, 368, 512)(369, 513, 377, 521, 372, 516, 378, 522)(370, 514, 379, 523, 371, 515, 380, 524)(373, 517, 381, 525, 376, 520, 382, 526)(374, 518, 383, 527, 375, 519, 384, 528)(385, 529, 393, 537, 388, 532, 394, 538)(386, 530, 395, 539, 387, 531, 396, 540)(389, 533, 397, 541, 392, 536, 398, 542)(390, 534, 399, 543, 391, 535, 400, 544)(401, 545, 409, 553, 404, 548, 410, 554)(402, 546, 411, 555, 403, 547, 412, 556)(405, 549, 413, 557, 408, 552, 414, 558)(406, 550, 415, 559, 407, 551, 416, 560)(417, 561, 425, 569, 420, 564, 426, 570)(418, 562, 427, 571, 419, 563, 428, 572)(421, 565, 429, 573, 424, 568, 430, 574)(422, 566, 431, 575, 423, 567, 432, 576) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 298)(6, 300)(7, 291)(8, 303)(9, 292)(10, 293)(11, 308)(12, 294)(13, 311)(14, 313)(15, 296)(16, 316)(17, 318)(18, 319)(19, 321)(20, 299)(21, 324)(22, 326)(23, 301)(24, 323)(25, 302)(26, 325)(27, 320)(28, 304)(29, 322)(30, 305)(31, 306)(32, 315)(33, 307)(34, 317)(35, 312)(36, 309)(37, 314)(38, 310)(39, 337)(40, 338)(41, 339)(42, 340)(43, 336)(44, 341)(45, 342)(46, 343)(47, 344)(48, 331)(49, 327)(50, 328)(51, 329)(52, 330)(53, 332)(54, 333)(55, 334)(56, 335)(57, 353)(58, 354)(59, 355)(60, 356)(61, 357)(62, 358)(63, 359)(64, 360)(65, 345)(66, 346)(67, 347)(68, 348)(69, 349)(70, 350)(71, 351)(72, 352)(73, 369)(74, 370)(75, 371)(76, 372)(77, 373)(78, 374)(79, 375)(80, 376)(81, 361)(82, 362)(83, 363)(84, 364)(85, 365)(86, 366)(87, 367)(88, 368)(89, 385)(90, 386)(91, 387)(92, 388)(93, 389)(94, 390)(95, 391)(96, 392)(97, 377)(98, 378)(99, 379)(100, 380)(101, 381)(102, 382)(103, 383)(104, 384)(105, 401)(106, 402)(107, 403)(108, 404)(109, 405)(110, 406)(111, 407)(112, 408)(113, 393)(114, 394)(115, 395)(116, 396)(117, 397)(118, 398)(119, 399)(120, 400)(121, 417)(122, 418)(123, 419)(124, 420)(125, 421)(126, 422)(127, 423)(128, 424)(129, 409)(130, 410)(131, 411)(132, 412)(133, 413)(134, 414)(135, 415)(136, 416)(137, 429)(138, 432)(139, 431)(140, 430)(141, 425)(142, 428)(143, 427)(144, 426)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E15.1326 Graph:: bipartite v = 108 e = 288 f = 152 degree seq :: [ 4^72, 8^36 ] E15.1324 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 18}) Quotient :: dipole Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y1^4, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-2 * Y1)^2, Y2^18 ] Map:: R = (1, 145, 2, 146, 6, 150, 4, 148)(3, 147, 9, 153, 21, 165, 11, 155)(5, 149, 13, 157, 18, 162, 7, 151)(8, 152, 19, 163, 31, 175, 15, 159)(10, 154, 23, 167, 37, 181, 20, 164)(12, 156, 16, 160, 32, 176, 27, 171)(14, 158, 26, 170, 44, 188, 28, 172)(17, 161, 34, 178, 51, 195, 33, 177)(22, 166, 30, 174, 48, 192, 39, 183)(24, 168, 38, 182, 49, 193, 41, 185)(25, 169, 40, 184, 50, 194, 36, 180)(29, 173, 35, 179, 52, 196, 45, 189)(42, 186, 57, 201, 65, 209, 55, 199)(43, 187, 58, 202, 73, 217, 59, 203)(46, 190, 61, 205, 67, 211, 53, 197)(47, 191, 63, 207, 69, 213, 54, 198)(56, 200, 71, 215, 81, 225, 66, 210)(60, 204, 75, 219, 87, 231, 72, 216)(62, 206, 68, 212, 83, 227, 77, 221)(64, 208, 78, 222, 93, 237, 79, 223)(70, 214, 85, 229, 99, 243, 84, 228)(74, 218, 82, 226, 97, 241, 89, 233)(76, 220, 88, 232, 98, 242, 90, 234)(80, 224, 86, 230, 100, 244, 94, 238)(91, 235, 105, 249, 113, 257, 103, 247)(92, 236, 106, 250, 121, 265, 107, 251)(95, 239, 109, 253, 115, 259, 101, 245)(96, 240, 111, 255, 117, 261, 102, 246)(104, 248, 119, 263, 128, 272, 114, 258)(108, 252, 123, 267, 134, 278, 120, 264)(110, 254, 116, 260, 130, 274, 125, 269)(112, 256, 126, 270, 138, 282, 127, 271)(118, 262, 132, 276, 141, 285, 131, 275)(122, 266, 129, 273, 139, 283, 135, 279)(124, 268, 133, 277, 140, 284, 136, 280)(137, 281, 143, 287, 144, 288, 142, 286)(289, 433, 291, 435, 298, 442, 312, 456, 331, 475, 348, 492, 364, 508, 380, 524, 396, 540, 412, 556, 400, 544, 384, 528, 368, 512, 352, 496, 335, 479, 317, 461, 302, 446, 293, 437)(290, 434, 295, 439, 305, 449, 323, 467, 342, 486, 358, 502, 374, 518, 390, 534, 406, 550, 421, 565, 408, 552, 392, 536, 376, 520, 360, 504, 344, 488, 326, 470, 308, 452, 296, 440)(292, 436, 300, 444, 314, 458, 333, 477, 350, 494, 366, 510, 382, 526, 398, 542, 414, 558, 424, 568, 410, 554, 394, 538, 378, 522, 362, 506, 346, 490, 329, 473, 310, 454, 297, 441)(294, 438, 303, 447, 318, 462, 337, 481, 354, 498, 370, 514, 386, 530, 402, 546, 417, 561, 428, 572, 419, 563, 404, 548, 388, 532, 372, 516, 356, 500, 340, 484, 321, 465, 304, 448)(299, 443, 313, 457, 301, 445, 316, 460, 334, 478, 351, 495, 367, 511, 383, 527, 399, 543, 415, 559, 425, 569, 411, 555, 395, 539, 379, 523, 363, 507, 347, 491, 330, 474, 311, 455)(306, 450, 324, 468, 307, 451, 325, 469, 343, 487, 359, 503, 375, 519, 391, 535, 407, 551, 422, 566, 430, 574, 420, 564, 405, 549, 389, 533, 373, 517, 357, 501, 341, 485, 322, 466)(309, 453, 327, 471, 345, 489, 361, 505, 377, 521, 393, 537, 409, 553, 423, 567, 431, 575, 426, 570, 413, 557, 397, 541, 381, 525, 365, 509, 349, 493, 332, 476, 315, 459, 328, 472)(319, 463, 338, 482, 320, 464, 339, 483, 355, 499, 371, 515, 387, 531, 403, 547, 418, 562, 429, 573, 432, 576, 427, 571, 416, 560, 401, 545, 385, 529, 369, 513, 353, 497, 336, 480) L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 303)(7, 305)(8, 290)(9, 292)(10, 312)(11, 313)(12, 314)(13, 316)(14, 293)(15, 318)(16, 294)(17, 323)(18, 324)(19, 325)(20, 296)(21, 327)(22, 297)(23, 299)(24, 331)(25, 301)(26, 333)(27, 328)(28, 334)(29, 302)(30, 337)(31, 338)(32, 339)(33, 304)(34, 306)(35, 342)(36, 307)(37, 343)(38, 308)(39, 345)(40, 309)(41, 310)(42, 311)(43, 348)(44, 315)(45, 350)(46, 351)(47, 317)(48, 319)(49, 354)(50, 320)(51, 355)(52, 321)(53, 322)(54, 358)(55, 359)(56, 326)(57, 361)(58, 329)(59, 330)(60, 364)(61, 332)(62, 366)(63, 367)(64, 335)(65, 336)(66, 370)(67, 371)(68, 340)(69, 341)(70, 374)(71, 375)(72, 344)(73, 377)(74, 346)(75, 347)(76, 380)(77, 349)(78, 382)(79, 383)(80, 352)(81, 353)(82, 386)(83, 387)(84, 356)(85, 357)(86, 390)(87, 391)(88, 360)(89, 393)(90, 362)(91, 363)(92, 396)(93, 365)(94, 398)(95, 399)(96, 368)(97, 369)(98, 402)(99, 403)(100, 372)(101, 373)(102, 406)(103, 407)(104, 376)(105, 409)(106, 378)(107, 379)(108, 412)(109, 381)(110, 414)(111, 415)(112, 384)(113, 385)(114, 417)(115, 418)(116, 388)(117, 389)(118, 421)(119, 422)(120, 392)(121, 423)(122, 394)(123, 395)(124, 400)(125, 397)(126, 424)(127, 425)(128, 401)(129, 428)(130, 429)(131, 404)(132, 405)(133, 408)(134, 430)(135, 431)(136, 410)(137, 411)(138, 413)(139, 416)(140, 419)(141, 432)(142, 420)(143, 426)(144, 427)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E15.1325 Graph:: bipartite v = 44 e = 288 f = 216 degree seq :: [ 8^36, 36^8 ] E15.1325 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 18}) Quotient :: dipole Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, (Y3^-1 * Y2 * Y3^-2)^2, Y3^6 * Y2 * Y3^-12 * Y2, (Y3^-1 * Y1^-1)^18 ] Map:: polytopal R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 305, 449)(298, 442, 309, 453)(300, 444, 313, 457)(302, 446, 317, 461)(303, 447, 316, 460)(304, 448, 320, 464)(306, 450, 318, 462)(307, 451, 325, 469)(308, 452, 311, 455)(310, 454, 314, 458)(312, 456, 330, 474)(315, 459, 335, 479)(319, 463, 339, 483)(321, 465, 336, 480)(322, 466, 341, 485)(323, 467, 337, 481)(324, 468, 342, 486)(326, 470, 331, 475)(327, 471, 333, 477)(328, 472, 346, 490)(329, 473, 349, 493)(332, 476, 351, 495)(334, 478, 352, 496)(338, 482, 356, 500)(340, 484, 355, 499)(343, 487, 360, 504)(344, 488, 362, 506)(345, 489, 350, 494)(347, 491, 364, 508)(348, 492, 366, 510)(353, 497, 369, 513)(354, 498, 371, 515)(357, 501, 373, 517)(358, 502, 375, 519)(359, 503, 368, 512)(361, 505, 377, 521)(363, 507, 376, 520)(365, 509, 381, 525)(367, 511, 372, 516)(370, 514, 385, 529)(374, 518, 389, 533)(378, 522, 390, 534)(379, 523, 391, 535)(380, 524, 394, 538)(382, 526, 386, 530)(383, 527, 387, 531)(384, 528, 398, 542)(388, 532, 402, 546)(392, 536, 406, 550)(393, 537, 405, 549)(395, 539, 409, 553)(396, 540, 411, 555)(397, 541, 401, 545)(399, 543, 413, 557)(400, 544, 415, 559)(403, 547, 416, 560)(404, 548, 418, 562)(407, 551, 420, 564)(408, 552, 422, 566)(410, 554, 423, 567)(412, 556, 419, 563)(414, 558, 426, 570)(417, 561, 427, 571)(421, 565, 430, 574)(424, 568, 429, 573)(425, 569, 428, 572)(431, 575, 432, 576) L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 303)(8, 306)(9, 307)(10, 292)(11, 311)(12, 314)(13, 315)(14, 294)(15, 319)(16, 295)(17, 322)(18, 324)(19, 326)(20, 297)(21, 327)(22, 298)(23, 329)(24, 299)(25, 332)(26, 334)(27, 336)(28, 301)(29, 337)(30, 302)(31, 309)(32, 340)(33, 304)(34, 308)(35, 305)(36, 344)(37, 339)(38, 346)(39, 347)(40, 310)(41, 317)(42, 350)(43, 312)(44, 316)(45, 313)(46, 354)(47, 349)(48, 356)(49, 357)(50, 318)(51, 359)(52, 360)(53, 320)(54, 321)(55, 323)(56, 363)(57, 325)(58, 365)(59, 366)(60, 328)(61, 368)(62, 369)(63, 330)(64, 331)(65, 333)(66, 372)(67, 335)(68, 374)(69, 375)(70, 338)(71, 341)(72, 377)(73, 342)(74, 343)(75, 380)(76, 345)(77, 382)(78, 383)(79, 348)(80, 351)(81, 385)(82, 352)(83, 353)(84, 388)(85, 355)(86, 390)(87, 391)(88, 358)(89, 393)(90, 361)(91, 362)(92, 396)(93, 364)(94, 398)(95, 399)(96, 367)(97, 401)(98, 370)(99, 371)(100, 404)(101, 373)(102, 406)(103, 407)(104, 376)(105, 409)(106, 378)(107, 379)(108, 412)(109, 381)(110, 414)(111, 415)(112, 384)(113, 416)(114, 386)(115, 387)(116, 419)(117, 389)(118, 421)(119, 422)(120, 392)(121, 423)(122, 394)(123, 395)(124, 400)(125, 397)(126, 425)(127, 424)(128, 427)(129, 402)(130, 403)(131, 408)(132, 405)(133, 429)(134, 428)(135, 431)(136, 410)(137, 411)(138, 413)(139, 432)(140, 417)(141, 418)(142, 420)(143, 426)(144, 430)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 8, 36 ), ( 8, 36, 8, 36 ) } Outer automorphisms :: reflexible Dual of E15.1324 Graph:: simple bipartite v = 216 e = 288 f = 44 degree seq :: [ 2^144, 4^72 ] E15.1326 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 18}) Quotient :: dipole Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^2 * Y1 * Y3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-3 * Y3^-1 * Y1^-3, Y1^18 ] Map:: polytopal R = (1, 145, 2, 146, 5, 149, 11, 155, 23, 167, 41, 185, 61, 205, 80, 224, 97, 241, 113, 257, 112, 256, 96, 240, 79, 223, 60, 204, 40, 184, 22, 166, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 31, 175, 51, 195, 71, 215, 89, 233, 105, 249, 121, 265, 128, 272, 117, 261, 99, 243, 81, 225, 65, 209, 43, 187, 24, 168, 18, 162, 8, 152)(6, 150, 13, 157, 27, 171, 21, 165, 39, 183, 59, 203, 78, 222, 95, 239, 111, 255, 127, 271, 131, 275, 115, 259, 98, 242, 84, 228, 63, 207, 42, 186, 30, 174, 14, 158)(9, 153, 19, 163, 37, 181, 57, 201, 76, 220, 93, 237, 109, 253, 125, 269, 129, 273, 114, 258, 101, 245, 82, 226, 62, 206, 46, 190, 26, 170, 12, 156, 25, 169, 20, 164)(16, 160, 33, 177, 53, 197, 36, 180, 45, 189, 67, 211, 86, 230, 100, 244, 118, 262, 133, 277, 139, 283, 136, 280, 122, 266, 108, 252, 91, 235, 72, 216, 55, 199, 34, 178)(17, 161, 35, 179, 50, 194, 64, 208, 85, 229, 103, 247, 116, 260, 132, 276, 141, 285, 135, 279, 123, 267, 106, 250, 90, 234, 73, 217, 52, 196, 32, 176, 48, 192, 28, 172)(29, 173, 49, 193, 68, 212, 83, 227, 102, 246, 119, 263, 130, 274, 140, 284, 138, 282, 126, 270, 110, 254, 94, 238, 77, 221, 58, 202, 38, 182, 47, 191, 66, 210, 44, 188)(54, 198, 75, 219, 92, 236, 107, 251, 124, 268, 137, 281, 143, 287, 144, 288, 142, 286, 134, 278, 120, 264, 104, 248, 88, 232, 70, 214, 56, 200, 74, 218, 87, 231, 69, 213)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 294)(3, 289)(4, 297)(5, 300)(6, 290)(7, 304)(8, 305)(9, 292)(10, 309)(11, 312)(12, 293)(13, 316)(14, 317)(15, 320)(16, 295)(17, 296)(18, 324)(19, 326)(20, 321)(21, 298)(22, 319)(23, 330)(24, 299)(25, 332)(26, 333)(27, 335)(28, 301)(29, 302)(30, 338)(31, 310)(32, 303)(33, 308)(34, 342)(35, 344)(36, 306)(37, 343)(38, 307)(39, 340)(40, 345)(41, 350)(42, 311)(43, 352)(44, 313)(45, 314)(46, 356)(47, 315)(48, 357)(49, 358)(50, 318)(51, 360)(52, 327)(53, 362)(54, 322)(55, 325)(56, 323)(57, 328)(58, 363)(59, 365)(60, 366)(61, 369)(62, 329)(63, 371)(64, 331)(65, 374)(66, 375)(67, 376)(68, 334)(69, 336)(70, 337)(71, 378)(72, 339)(73, 380)(74, 341)(75, 346)(76, 382)(77, 347)(78, 348)(79, 377)(80, 386)(81, 349)(82, 388)(83, 351)(84, 391)(85, 392)(86, 353)(87, 354)(88, 355)(89, 367)(90, 359)(91, 395)(92, 361)(93, 396)(94, 364)(95, 394)(96, 397)(97, 402)(98, 368)(99, 404)(100, 370)(101, 407)(102, 408)(103, 372)(104, 373)(105, 410)(106, 383)(107, 379)(108, 381)(109, 384)(110, 412)(111, 414)(112, 415)(113, 416)(114, 385)(115, 418)(116, 387)(117, 421)(118, 422)(119, 389)(120, 390)(121, 423)(122, 393)(123, 425)(124, 398)(125, 426)(126, 399)(127, 400)(128, 401)(129, 427)(130, 403)(131, 429)(132, 430)(133, 405)(134, 406)(135, 409)(136, 431)(137, 411)(138, 413)(139, 417)(140, 432)(141, 419)(142, 420)(143, 424)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E15.1323 Graph:: simple bipartite v = 152 e = 288 f = 108 degree seq :: [ 2^144, 36^8 ] E15.1327 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 18}) Quotient :: dipole Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^4, (Y2^-2 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^18 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 28, 172)(16, 160, 32, 176)(18, 162, 30, 174)(19, 163, 37, 181)(20, 164, 23, 167)(22, 166, 26, 170)(24, 168, 42, 186)(27, 171, 47, 191)(31, 175, 51, 195)(33, 177, 48, 192)(34, 178, 53, 197)(35, 179, 49, 193)(36, 180, 54, 198)(38, 182, 43, 187)(39, 183, 45, 189)(40, 184, 58, 202)(41, 185, 61, 205)(44, 188, 63, 207)(46, 190, 64, 208)(50, 194, 68, 212)(52, 196, 67, 211)(55, 199, 72, 216)(56, 200, 74, 218)(57, 201, 62, 206)(59, 203, 76, 220)(60, 204, 78, 222)(65, 209, 81, 225)(66, 210, 83, 227)(69, 213, 85, 229)(70, 214, 87, 231)(71, 215, 80, 224)(73, 217, 89, 233)(75, 219, 88, 232)(77, 221, 93, 237)(79, 223, 84, 228)(82, 226, 97, 241)(86, 230, 101, 245)(90, 234, 102, 246)(91, 235, 103, 247)(92, 236, 106, 250)(94, 238, 98, 242)(95, 239, 99, 243)(96, 240, 110, 254)(100, 244, 114, 258)(104, 248, 118, 262)(105, 249, 117, 261)(107, 251, 121, 265)(108, 252, 123, 267)(109, 253, 113, 257)(111, 255, 125, 269)(112, 256, 127, 271)(115, 259, 128, 272)(116, 260, 130, 274)(119, 263, 132, 276)(120, 264, 134, 278)(122, 266, 135, 279)(124, 268, 131, 275)(126, 270, 138, 282)(129, 273, 139, 283)(133, 277, 142, 286)(136, 280, 141, 285)(137, 281, 140, 284)(143, 287, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 324, 468, 344, 488, 363, 507, 380, 524, 396, 540, 412, 556, 400, 544, 384, 528, 367, 511, 348, 492, 328, 472, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 334, 478, 354, 498, 372, 516, 388, 532, 404, 548, 419, 563, 408, 552, 392, 536, 376, 520, 358, 502, 338, 482, 318, 462, 302, 446, 294, 438)(295, 439, 303, 447, 319, 463, 309, 453, 327, 471, 347, 491, 366, 510, 383, 527, 399, 543, 415, 559, 424, 568, 410, 554, 394, 538, 378, 522, 361, 505, 342, 486, 321, 465, 304, 448)(297, 441, 307, 451, 326, 470, 346, 490, 365, 509, 382, 526, 398, 542, 414, 558, 425, 569, 411, 555, 395, 539, 379, 523, 362, 506, 343, 487, 323, 467, 305, 449, 322, 466, 308, 452)(299, 443, 311, 455, 329, 473, 317, 461, 337, 481, 357, 501, 375, 519, 391, 535, 407, 551, 422, 566, 428, 572, 417, 561, 402, 546, 386, 530, 370, 514, 352, 496, 331, 475, 312, 456)(301, 445, 315, 459, 336, 480, 356, 500, 374, 518, 390, 534, 406, 550, 421, 565, 429, 573, 418, 562, 403, 547, 387, 531, 371, 515, 353, 497, 333, 477, 313, 457, 332, 476, 316, 460)(320, 464, 340, 484, 360, 504, 377, 521, 393, 537, 409, 553, 423, 567, 431, 575, 426, 570, 413, 557, 397, 541, 381, 525, 364, 508, 345, 489, 325, 469, 339, 483, 359, 503, 341, 485)(330, 474, 350, 494, 369, 513, 385, 529, 401, 545, 416, 560, 427, 571, 432, 576, 430, 574, 420, 564, 405, 549, 389, 533, 373, 517, 355, 499, 335, 479, 349, 493, 368, 512, 351, 495) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 316)(16, 320)(17, 296)(18, 318)(19, 325)(20, 311)(21, 298)(22, 314)(23, 308)(24, 330)(25, 300)(26, 310)(27, 335)(28, 303)(29, 302)(30, 306)(31, 339)(32, 304)(33, 336)(34, 341)(35, 337)(36, 342)(37, 307)(38, 331)(39, 333)(40, 346)(41, 349)(42, 312)(43, 326)(44, 351)(45, 327)(46, 352)(47, 315)(48, 321)(49, 323)(50, 356)(51, 319)(52, 355)(53, 322)(54, 324)(55, 360)(56, 362)(57, 350)(58, 328)(59, 364)(60, 366)(61, 329)(62, 345)(63, 332)(64, 334)(65, 369)(66, 371)(67, 340)(68, 338)(69, 373)(70, 375)(71, 368)(72, 343)(73, 377)(74, 344)(75, 376)(76, 347)(77, 381)(78, 348)(79, 372)(80, 359)(81, 353)(82, 385)(83, 354)(84, 367)(85, 357)(86, 389)(87, 358)(88, 363)(89, 361)(90, 390)(91, 391)(92, 394)(93, 365)(94, 386)(95, 387)(96, 398)(97, 370)(98, 382)(99, 383)(100, 402)(101, 374)(102, 378)(103, 379)(104, 406)(105, 405)(106, 380)(107, 409)(108, 411)(109, 401)(110, 384)(111, 413)(112, 415)(113, 397)(114, 388)(115, 416)(116, 418)(117, 393)(118, 392)(119, 420)(120, 422)(121, 395)(122, 423)(123, 396)(124, 419)(125, 399)(126, 426)(127, 400)(128, 403)(129, 427)(130, 404)(131, 412)(132, 407)(133, 430)(134, 408)(135, 410)(136, 429)(137, 428)(138, 414)(139, 417)(140, 425)(141, 424)(142, 421)(143, 432)(144, 431)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E15.1328 Graph:: bipartite v = 80 e = 288 f = 180 degree seq :: [ 4^72, 36^8 ] E15.1328 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 18}) Quotient :: dipole Aut^+ = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>) Aut = $<288, 835>$ (small group id <288, 835>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y1)^2, (Y3 * Y2^-1)^18 ] Map:: polytopal R = (1, 145, 2, 146, 6, 150, 4, 148)(3, 147, 9, 153, 21, 165, 11, 155)(5, 149, 13, 157, 18, 162, 7, 151)(8, 152, 19, 163, 31, 175, 15, 159)(10, 154, 23, 167, 37, 181, 20, 164)(12, 156, 16, 160, 32, 176, 27, 171)(14, 158, 26, 170, 44, 188, 28, 172)(17, 161, 34, 178, 51, 195, 33, 177)(22, 166, 30, 174, 48, 192, 39, 183)(24, 168, 38, 182, 49, 193, 41, 185)(25, 169, 40, 184, 50, 194, 36, 180)(29, 173, 35, 179, 52, 196, 45, 189)(42, 186, 57, 201, 65, 209, 55, 199)(43, 187, 58, 202, 73, 217, 59, 203)(46, 190, 61, 205, 67, 211, 53, 197)(47, 191, 63, 207, 69, 213, 54, 198)(56, 200, 71, 215, 81, 225, 66, 210)(60, 204, 75, 219, 87, 231, 72, 216)(62, 206, 68, 212, 83, 227, 77, 221)(64, 208, 78, 222, 93, 237, 79, 223)(70, 214, 85, 229, 99, 243, 84, 228)(74, 218, 82, 226, 97, 241, 89, 233)(76, 220, 88, 232, 98, 242, 90, 234)(80, 224, 86, 230, 100, 244, 94, 238)(91, 235, 105, 249, 113, 257, 103, 247)(92, 236, 106, 250, 121, 265, 107, 251)(95, 239, 109, 253, 115, 259, 101, 245)(96, 240, 111, 255, 117, 261, 102, 246)(104, 248, 119, 263, 128, 272, 114, 258)(108, 252, 123, 267, 134, 278, 120, 264)(110, 254, 116, 260, 130, 274, 125, 269)(112, 256, 126, 270, 138, 282, 127, 271)(118, 262, 132, 276, 141, 285, 131, 275)(122, 266, 129, 273, 139, 283, 135, 279)(124, 268, 133, 277, 140, 284, 136, 280)(137, 281, 143, 287, 144, 288, 142, 286)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 303)(7, 305)(8, 290)(9, 292)(10, 312)(11, 313)(12, 314)(13, 316)(14, 293)(15, 318)(16, 294)(17, 323)(18, 324)(19, 325)(20, 296)(21, 327)(22, 297)(23, 299)(24, 331)(25, 301)(26, 333)(27, 328)(28, 334)(29, 302)(30, 337)(31, 338)(32, 339)(33, 304)(34, 306)(35, 342)(36, 307)(37, 343)(38, 308)(39, 345)(40, 309)(41, 310)(42, 311)(43, 348)(44, 315)(45, 350)(46, 351)(47, 317)(48, 319)(49, 354)(50, 320)(51, 355)(52, 321)(53, 322)(54, 358)(55, 359)(56, 326)(57, 361)(58, 329)(59, 330)(60, 364)(61, 332)(62, 366)(63, 367)(64, 335)(65, 336)(66, 370)(67, 371)(68, 340)(69, 341)(70, 374)(71, 375)(72, 344)(73, 377)(74, 346)(75, 347)(76, 380)(77, 349)(78, 382)(79, 383)(80, 352)(81, 353)(82, 386)(83, 387)(84, 356)(85, 357)(86, 390)(87, 391)(88, 360)(89, 393)(90, 362)(91, 363)(92, 396)(93, 365)(94, 398)(95, 399)(96, 368)(97, 369)(98, 402)(99, 403)(100, 372)(101, 373)(102, 406)(103, 407)(104, 376)(105, 409)(106, 378)(107, 379)(108, 412)(109, 381)(110, 414)(111, 415)(112, 384)(113, 385)(114, 417)(115, 418)(116, 388)(117, 389)(118, 421)(119, 422)(120, 392)(121, 423)(122, 394)(123, 395)(124, 400)(125, 397)(126, 424)(127, 425)(128, 401)(129, 428)(130, 429)(131, 404)(132, 405)(133, 408)(134, 430)(135, 431)(136, 410)(137, 411)(138, 413)(139, 416)(140, 419)(141, 432)(142, 420)(143, 426)(144, 427)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E15.1327 Graph:: simple bipartite v = 180 e = 288 f = 80 degree seq :: [ 2^144, 8^36 ] E15.1329 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 3, 7}) Quotient :: edge Aut^+ = (C7 x C7) : C3 (small group id <147, 5>) Aut = ((C7 x C7) : C3) : C2 (small group id <294, 7>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^3, (T2^-1 * T1)^3, (T2^-1 * T1^-1)^3, T2^7, T1^-1 * T2 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^2, T2^3 * T1^-1 * T2^-1 * T1 * T2^3 * T1 * T2^-1 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 25, 37, 15, 5)(2, 6, 17, 40, 47, 21, 7)(4, 11, 29, 60, 65, 32, 12)(8, 22, 48, 88, 90, 50, 23)(10, 19, 43, 82, 100, 57, 27)(13, 33, 67, 111, 106, 62, 30)(14, 34, 68, 112, 75, 38, 16)(18, 31, 56, 96, 126, 80, 42)(20, 44, 83, 128, 101, 58, 28)(24, 51, 64, 107, 135, 92, 52)(26, 49, 45, 84, 130, 97, 55)(35, 70, 115, 144, 105, 61, 69)(36, 71, 116, 122, 76, 39, 66)(41, 74, 63, 98, 138, 125, 79)(46, 85, 131, 142, 102, 59, 81)(53, 93, 99, 109, 145, 136, 94)(54, 91, 89, 86, 132, 137, 95)(72, 118, 139, 141, 104, 113, 117)(73, 119, 134, 123, 77, 110, 114)(78, 121, 120, 108, 140, 147, 124)(87, 133, 146, 143, 103, 127, 129)(148, 149, 151)(150, 155, 157)(152, 160, 161)(153, 163, 165)(154, 166, 167)(156, 171, 173)(158, 175, 177)(159, 178, 169)(162, 182, 183)(164, 186, 188)(168, 192, 193)(170, 196, 191)(172, 200, 201)(174, 203, 198)(176, 206, 208)(179, 210, 211)(180, 213, 189)(181, 205, 216)(184, 219, 220)(185, 221, 195)(187, 224, 225)(190, 228, 209)(194, 233, 234)(197, 236, 232)(199, 238, 230)(202, 243, 240)(204, 245, 246)(207, 250, 251)(212, 255, 256)(214, 257, 226)(215, 249, 260)(217, 261, 227)(218, 248, 264)(222, 267, 254)(223, 268, 235)(229, 274, 252)(231, 276, 253)(237, 270, 280)(239, 281, 278)(241, 266, 275)(242, 273, 265)(244, 285, 286)(247, 287, 288)(258, 279, 271)(259, 290, 292)(262, 284, 272)(263, 289, 283)(269, 293, 282)(277, 294, 291) L = (1, 148)(2, 149)(3, 150)(4, 151)(5, 152)(6, 153)(7, 154)(8, 155)(9, 156)(10, 157)(11, 158)(12, 159)(13, 160)(14, 161)(15, 162)(16, 163)(17, 164)(18, 165)(19, 166)(20, 167)(21, 168)(22, 169)(23, 170)(24, 171)(25, 172)(26, 173)(27, 174)(28, 175)(29, 176)(30, 177)(31, 178)(32, 179)(33, 180)(34, 181)(35, 182)(36, 183)(37, 184)(38, 185)(39, 186)(40, 187)(41, 188)(42, 189)(43, 190)(44, 191)(45, 192)(46, 193)(47, 194)(48, 195)(49, 196)(50, 197)(51, 198)(52, 199)(53, 200)(54, 201)(55, 202)(56, 203)(57, 204)(58, 205)(59, 206)(60, 207)(61, 208)(62, 209)(63, 210)(64, 211)(65, 212)(66, 213)(67, 214)(68, 215)(69, 216)(70, 217)(71, 218)(72, 219)(73, 220)(74, 221)(75, 222)(76, 223)(77, 224)(78, 225)(79, 226)(80, 227)(81, 228)(82, 229)(83, 230)(84, 231)(85, 232)(86, 233)(87, 234)(88, 235)(89, 236)(90, 237)(91, 238)(92, 239)(93, 240)(94, 241)(95, 242)(96, 243)(97, 244)(98, 245)(99, 246)(100, 247)(101, 248)(102, 249)(103, 250)(104, 251)(105, 252)(106, 253)(107, 254)(108, 255)(109, 256)(110, 257)(111, 258)(112, 259)(113, 260)(114, 261)(115, 262)(116, 263)(117, 264)(118, 265)(119, 266)(120, 267)(121, 268)(122, 269)(123, 270)(124, 271)(125, 272)(126, 273)(127, 274)(128, 275)(129, 276)(130, 277)(131, 278)(132, 279)(133, 280)(134, 281)(135, 282)(136, 283)(137, 284)(138, 285)(139, 286)(140, 287)(141, 288)(142, 289)(143, 290)(144, 291)(145, 292)(146, 293)(147, 294) local type(s) :: { ( 6^3 ), ( 6^7 ) } Outer automorphisms :: reflexible Dual of E15.1330 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 147 f = 49 degree seq :: [ 3^49, 7^21 ] E15.1330 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 3, 7}) Quotient :: loop Aut^+ = (C7 x C7) : C3 (small group id <147, 5>) Aut = ((C7 x C7) : C3) : C2 (small group id <294, 7>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, (T2^-1 * T1^-1)^7 ] Map:: polyhedral non-degenerate R = (1, 148, 3, 150, 5, 152)(2, 149, 6, 153, 7, 154)(4, 151, 10, 157, 11, 158)(8, 155, 18, 165, 19, 166)(9, 156, 16, 163, 20, 167)(12, 159, 25, 172, 22, 169)(13, 160, 26, 173, 27, 174)(14, 161, 28, 175, 29, 176)(15, 162, 23, 170, 30, 177)(17, 164, 31, 178, 32, 179)(21, 168, 38, 185, 39, 186)(24, 171, 40, 187, 41, 188)(33, 180, 53, 200, 54, 201)(34, 181, 36, 183, 55, 202)(35, 182, 56, 203, 57, 204)(37, 184, 51, 198, 58, 205)(42, 189, 64, 211, 60, 207)(43, 190, 44, 191, 65, 212)(45, 192, 66, 213, 67, 214)(46, 193, 68, 215, 69, 216)(47, 194, 49, 196, 70, 217)(48, 195, 71, 218, 72, 219)(50, 197, 62, 209, 73, 220)(52, 199, 74, 221, 75, 222)(59, 206, 84, 231, 85, 232)(61, 208, 86, 233, 87, 234)(63, 210, 88, 235, 89, 236)(76, 223, 106, 253, 107, 254)(77, 224, 79, 226, 108, 255)(78, 225, 109, 256, 110, 257)(80, 227, 82, 229, 111, 258)(81, 228, 112, 259, 113, 260)(83, 230, 104, 251, 114, 261)(90, 237, 120, 267, 116, 263)(91, 238, 92, 239, 121, 268)(93, 240, 94, 241, 122, 269)(95, 242, 123, 270, 96, 243)(97, 244, 99, 246, 124, 271)(98, 245, 125, 272, 126, 273)(100, 247, 102, 249, 127, 274)(101, 248, 128, 275, 129, 276)(103, 250, 119, 266, 130, 277)(105, 252, 131, 278, 115, 262)(117, 264, 138, 285, 139, 286)(118, 265, 140, 287, 132, 279)(133, 280, 135, 282, 146, 293)(134, 281, 147, 294, 144, 291)(136, 283, 137, 284, 141, 288)(142, 289, 143, 290, 145, 292) L = (1, 149)(2, 151)(3, 155)(4, 148)(5, 159)(6, 161)(7, 163)(8, 156)(9, 150)(10, 168)(11, 170)(12, 160)(13, 152)(14, 162)(15, 153)(16, 164)(17, 154)(18, 180)(19, 173)(20, 183)(21, 169)(22, 157)(23, 171)(24, 158)(25, 189)(26, 182)(27, 191)(28, 193)(29, 178)(30, 196)(31, 195)(32, 198)(33, 181)(34, 165)(35, 166)(36, 184)(37, 167)(38, 206)(39, 187)(40, 208)(41, 209)(42, 190)(43, 172)(44, 192)(45, 174)(46, 194)(47, 175)(48, 176)(49, 197)(50, 177)(51, 199)(52, 179)(53, 223)(54, 203)(55, 226)(56, 225)(57, 213)(58, 229)(59, 207)(60, 185)(61, 186)(62, 210)(63, 188)(64, 237)(65, 239)(66, 228)(67, 241)(68, 243)(69, 218)(70, 246)(71, 245)(72, 221)(73, 249)(74, 248)(75, 251)(76, 224)(77, 200)(78, 201)(79, 227)(80, 202)(81, 204)(82, 230)(83, 205)(84, 262)(85, 233)(86, 264)(87, 235)(88, 265)(89, 266)(90, 238)(91, 211)(92, 240)(93, 212)(94, 242)(95, 214)(96, 244)(97, 215)(98, 216)(99, 247)(100, 217)(101, 219)(102, 250)(103, 220)(104, 252)(105, 222)(106, 236)(107, 256)(108, 277)(109, 279)(110, 259)(111, 282)(112, 281)(113, 270)(114, 284)(115, 263)(116, 231)(117, 232)(118, 234)(119, 253)(120, 261)(121, 288)(122, 290)(123, 272)(124, 269)(125, 260)(126, 275)(127, 292)(128, 291)(129, 278)(130, 280)(131, 285)(132, 254)(133, 255)(134, 257)(135, 283)(136, 258)(137, 267)(138, 276)(139, 287)(140, 294)(141, 289)(142, 268)(143, 271)(144, 273)(145, 293)(146, 274)(147, 286) local type(s) :: { ( 3, 7, 3, 7, 3, 7 ) } Outer automorphisms :: reflexible Dual of E15.1329 Transitivity :: ET+ VT+ AT Graph:: simple v = 49 e = 147 f = 70 degree seq :: [ 6^49 ] E15.1331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 7}) Quotient :: dipole Aut^+ = (C7 x C7) : C3 (small group id <147, 5>) Aut = ((C7 x C7) : C3) : C2 (small group id <294, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^3, (Y2^-1 * Y1)^3, (Y3^-1 * Y1^-1)^3, Y2^7, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^2, Y2^3 * Y1^-1 * Y2^-1 * Y1 * Y2^3 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 148, 2, 149, 4, 151)(3, 150, 8, 155, 10, 157)(5, 152, 13, 160, 14, 161)(6, 153, 16, 163, 18, 165)(7, 154, 19, 166, 20, 167)(9, 156, 24, 171, 26, 173)(11, 158, 28, 175, 30, 177)(12, 159, 31, 178, 22, 169)(15, 162, 35, 182, 36, 183)(17, 164, 39, 186, 41, 188)(21, 168, 45, 192, 46, 193)(23, 170, 49, 196, 44, 191)(25, 172, 53, 200, 54, 201)(27, 174, 56, 203, 51, 198)(29, 176, 59, 206, 61, 208)(32, 179, 63, 210, 64, 211)(33, 180, 66, 213, 42, 189)(34, 181, 58, 205, 69, 216)(37, 184, 72, 219, 73, 220)(38, 185, 74, 221, 48, 195)(40, 187, 77, 224, 78, 225)(43, 190, 81, 228, 62, 209)(47, 194, 86, 233, 87, 234)(50, 197, 89, 236, 85, 232)(52, 199, 91, 238, 83, 230)(55, 202, 96, 243, 93, 240)(57, 204, 98, 245, 99, 246)(60, 207, 103, 250, 104, 251)(65, 212, 108, 255, 109, 256)(67, 214, 110, 257, 79, 226)(68, 215, 102, 249, 113, 260)(70, 217, 114, 261, 80, 227)(71, 218, 101, 248, 117, 264)(75, 222, 120, 267, 107, 254)(76, 223, 121, 268, 88, 235)(82, 229, 127, 274, 105, 252)(84, 231, 129, 276, 106, 253)(90, 237, 123, 270, 133, 280)(92, 239, 134, 281, 131, 278)(94, 241, 119, 266, 128, 275)(95, 242, 126, 273, 118, 265)(97, 244, 138, 285, 139, 286)(100, 247, 140, 287, 141, 288)(111, 258, 132, 279, 124, 271)(112, 259, 143, 290, 145, 292)(115, 262, 137, 284, 125, 272)(116, 263, 142, 289, 136, 283)(122, 269, 146, 293, 135, 282)(130, 277, 147, 294, 144, 291)(295, 442, 297, 444, 303, 450, 319, 466, 331, 478, 309, 456, 299, 446)(296, 443, 300, 447, 311, 458, 334, 481, 341, 488, 315, 462, 301, 448)(298, 445, 305, 452, 323, 470, 354, 501, 359, 506, 326, 473, 306, 453)(302, 449, 316, 463, 342, 489, 382, 529, 384, 531, 344, 491, 317, 464)(304, 451, 313, 460, 337, 484, 376, 523, 394, 541, 351, 498, 321, 468)(307, 454, 327, 474, 361, 508, 405, 552, 400, 547, 356, 503, 324, 471)(308, 455, 328, 475, 362, 509, 406, 553, 369, 516, 332, 479, 310, 457)(312, 459, 325, 472, 350, 497, 390, 537, 420, 567, 374, 521, 336, 483)(314, 461, 338, 485, 377, 524, 422, 569, 395, 542, 352, 499, 322, 469)(318, 465, 345, 492, 358, 505, 401, 548, 429, 576, 386, 533, 346, 493)(320, 467, 343, 490, 339, 486, 378, 525, 424, 571, 391, 538, 349, 496)(329, 476, 364, 511, 409, 556, 438, 585, 399, 546, 355, 502, 363, 510)(330, 477, 365, 512, 410, 557, 416, 563, 370, 517, 333, 480, 360, 507)(335, 482, 368, 515, 357, 504, 392, 539, 432, 579, 419, 566, 373, 520)(340, 487, 379, 526, 425, 572, 436, 583, 396, 543, 353, 500, 375, 522)(347, 494, 387, 534, 393, 540, 403, 550, 439, 586, 430, 577, 388, 535)(348, 495, 385, 532, 383, 530, 380, 527, 426, 573, 431, 578, 389, 536)(366, 513, 412, 559, 433, 580, 435, 582, 398, 545, 407, 554, 411, 558)(367, 514, 413, 560, 428, 575, 417, 564, 371, 518, 404, 551, 408, 555)(372, 519, 415, 562, 414, 561, 402, 549, 434, 581, 441, 588, 418, 565)(381, 528, 427, 574, 440, 587, 437, 584, 397, 544, 421, 568, 423, 570) L = (1, 297)(2, 300)(3, 303)(4, 305)(5, 295)(6, 311)(7, 296)(8, 316)(9, 319)(10, 313)(11, 323)(12, 298)(13, 327)(14, 328)(15, 299)(16, 308)(17, 334)(18, 325)(19, 337)(20, 338)(21, 301)(22, 342)(23, 302)(24, 345)(25, 331)(26, 343)(27, 304)(28, 314)(29, 354)(30, 307)(31, 350)(32, 306)(33, 361)(34, 362)(35, 364)(36, 365)(37, 309)(38, 310)(39, 360)(40, 341)(41, 368)(42, 312)(43, 376)(44, 377)(45, 378)(46, 379)(47, 315)(48, 382)(49, 339)(50, 317)(51, 358)(52, 318)(53, 387)(54, 385)(55, 320)(56, 390)(57, 321)(58, 322)(59, 375)(60, 359)(61, 363)(62, 324)(63, 392)(64, 401)(65, 326)(66, 330)(67, 405)(68, 406)(69, 329)(70, 409)(71, 410)(72, 412)(73, 413)(74, 357)(75, 332)(76, 333)(77, 404)(78, 415)(79, 335)(80, 336)(81, 340)(82, 394)(83, 422)(84, 424)(85, 425)(86, 426)(87, 427)(88, 384)(89, 380)(90, 344)(91, 383)(92, 346)(93, 393)(94, 347)(95, 348)(96, 420)(97, 349)(98, 432)(99, 403)(100, 351)(101, 352)(102, 353)(103, 421)(104, 407)(105, 355)(106, 356)(107, 429)(108, 434)(109, 439)(110, 408)(111, 400)(112, 369)(113, 411)(114, 367)(115, 438)(116, 416)(117, 366)(118, 433)(119, 428)(120, 402)(121, 414)(122, 370)(123, 371)(124, 372)(125, 373)(126, 374)(127, 423)(128, 395)(129, 381)(130, 391)(131, 436)(132, 431)(133, 440)(134, 417)(135, 386)(136, 388)(137, 389)(138, 419)(139, 435)(140, 441)(141, 398)(142, 396)(143, 397)(144, 399)(145, 430)(146, 437)(147, 418)(148, 442)(149, 443)(150, 444)(151, 445)(152, 446)(153, 447)(154, 448)(155, 449)(156, 450)(157, 451)(158, 452)(159, 453)(160, 454)(161, 455)(162, 456)(163, 457)(164, 458)(165, 459)(166, 460)(167, 461)(168, 462)(169, 463)(170, 464)(171, 465)(172, 466)(173, 467)(174, 468)(175, 469)(176, 470)(177, 471)(178, 472)(179, 473)(180, 474)(181, 475)(182, 476)(183, 477)(184, 478)(185, 479)(186, 480)(187, 481)(188, 482)(189, 483)(190, 484)(191, 485)(192, 486)(193, 487)(194, 488)(195, 489)(196, 490)(197, 491)(198, 492)(199, 493)(200, 494)(201, 495)(202, 496)(203, 497)(204, 498)(205, 499)(206, 500)(207, 501)(208, 502)(209, 503)(210, 504)(211, 505)(212, 506)(213, 507)(214, 508)(215, 509)(216, 510)(217, 511)(218, 512)(219, 513)(220, 514)(221, 515)(222, 516)(223, 517)(224, 518)(225, 519)(226, 520)(227, 521)(228, 522)(229, 523)(230, 524)(231, 525)(232, 526)(233, 527)(234, 528)(235, 529)(236, 530)(237, 531)(238, 532)(239, 533)(240, 534)(241, 535)(242, 536)(243, 537)(244, 538)(245, 539)(246, 540)(247, 541)(248, 542)(249, 543)(250, 544)(251, 545)(252, 546)(253, 547)(254, 548)(255, 549)(256, 550)(257, 551)(258, 552)(259, 553)(260, 554)(261, 555)(262, 556)(263, 557)(264, 558)(265, 559)(266, 560)(267, 561)(268, 562)(269, 563)(270, 564)(271, 565)(272, 566)(273, 567)(274, 568)(275, 569)(276, 570)(277, 571)(278, 572)(279, 573)(280, 574)(281, 575)(282, 576)(283, 577)(284, 578)(285, 579)(286, 580)(287, 581)(288, 582)(289, 583)(290, 584)(291, 585)(292, 586)(293, 587)(294, 588) local type(s) :: { ( 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 E15.1332 Graph:: bipartite v = 70 e = 294 f = 196 degree seq :: [ 6^49, 14^21 ] E15.1332 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 7}) Quotient :: dipole Aut^+ = (C7 x C7) : C3 (small group id <147, 5>) Aut = ((C7 x C7) : C3) : C2 (small group id <294, 7>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^3, (Y3 * Y2^-1)^3, (Y3^-1 * Y2^-1)^3, (Y3 * Y2)^3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^7, Y3 * Y2 * Y3^-3 * Y2 * Y3 * Y2^-1 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^7 ] Map:: polytopal R = (1, 148)(2, 149)(3, 150)(4, 151)(5, 152)(6, 153)(7, 154)(8, 155)(9, 156)(10, 157)(11, 158)(12, 159)(13, 160)(14, 161)(15, 162)(16, 163)(17, 164)(18, 165)(19, 166)(20, 167)(21, 168)(22, 169)(23, 170)(24, 171)(25, 172)(26, 173)(27, 174)(28, 175)(29, 176)(30, 177)(31, 178)(32, 179)(33, 180)(34, 181)(35, 182)(36, 183)(37, 184)(38, 185)(39, 186)(40, 187)(41, 188)(42, 189)(43, 190)(44, 191)(45, 192)(46, 193)(47, 194)(48, 195)(49, 196)(50, 197)(51, 198)(52, 199)(53, 200)(54, 201)(55, 202)(56, 203)(57, 204)(58, 205)(59, 206)(60, 207)(61, 208)(62, 209)(63, 210)(64, 211)(65, 212)(66, 213)(67, 214)(68, 215)(69, 216)(70, 217)(71, 218)(72, 219)(73, 220)(74, 221)(75, 222)(76, 223)(77, 224)(78, 225)(79, 226)(80, 227)(81, 228)(82, 229)(83, 230)(84, 231)(85, 232)(86, 233)(87, 234)(88, 235)(89, 236)(90, 237)(91, 238)(92, 239)(93, 240)(94, 241)(95, 242)(96, 243)(97, 244)(98, 245)(99, 246)(100, 247)(101, 248)(102, 249)(103, 250)(104, 251)(105, 252)(106, 253)(107, 254)(108, 255)(109, 256)(110, 257)(111, 258)(112, 259)(113, 260)(114, 261)(115, 262)(116, 263)(117, 264)(118, 265)(119, 266)(120, 267)(121, 268)(122, 269)(123, 270)(124, 271)(125, 272)(126, 273)(127, 274)(128, 275)(129, 276)(130, 277)(131, 278)(132, 279)(133, 280)(134, 281)(135, 282)(136, 283)(137, 284)(138, 285)(139, 286)(140, 287)(141, 288)(142, 289)(143, 290)(144, 291)(145, 292)(146, 293)(147, 294)(295, 442, 296, 443, 298, 445)(297, 444, 302, 449, 304, 451)(299, 446, 307, 454, 308, 455)(300, 447, 310, 457, 312, 459)(301, 448, 313, 460, 314, 461)(303, 450, 318, 465, 320, 467)(305, 452, 322, 469, 324, 471)(306, 453, 325, 472, 316, 463)(309, 456, 329, 476, 330, 477)(311, 458, 333, 480, 335, 482)(315, 462, 339, 486, 340, 487)(317, 464, 343, 490, 338, 485)(319, 466, 347, 494, 348, 495)(321, 468, 350, 497, 345, 492)(323, 470, 353, 500, 355, 502)(326, 473, 357, 504, 358, 505)(327, 474, 360, 507, 336, 483)(328, 475, 352, 499, 363, 510)(331, 478, 366, 513, 367, 514)(332, 479, 368, 515, 342, 489)(334, 481, 371, 518, 372, 519)(337, 484, 375, 522, 356, 503)(341, 488, 380, 527, 381, 528)(344, 491, 383, 530, 379, 526)(346, 493, 385, 532, 377, 524)(349, 496, 390, 537, 387, 534)(351, 498, 392, 539, 393, 540)(354, 501, 397, 544, 398, 545)(359, 506, 402, 549, 403, 550)(361, 508, 404, 551, 373, 520)(362, 509, 396, 543, 407, 554)(364, 511, 408, 555, 374, 521)(365, 512, 395, 542, 411, 558)(369, 516, 414, 561, 401, 548)(370, 517, 415, 562, 382, 529)(376, 523, 421, 568, 399, 546)(378, 525, 423, 570, 400, 547)(384, 531, 417, 564, 427, 574)(386, 533, 428, 575, 425, 572)(388, 535, 413, 560, 422, 569)(389, 536, 420, 567, 412, 559)(391, 538, 432, 579, 433, 580)(394, 541, 434, 581, 435, 582)(405, 552, 426, 573, 418, 565)(406, 553, 437, 584, 439, 586)(409, 556, 431, 578, 419, 566)(410, 557, 436, 583, 430, 577)(416, 563, 440, 587, 429, 576)(424, 571, 441, 588, 438, 585) L = (1, 297)(2, 300)(3, 303)(4, 305)(5, 295)(6, 311)(7, 296)(8, 316)(9, 319)(10, 313)(11, 323)(12, 298)(13, 327)(14, 328)(15, 299)(16, 308)(17, 334)(18, 325)(19, 337)(20, 338)(21, 301)(22, 342)(23, 302)(24, 345)(25, 331)(26, 343)(27, 304)(28, 314)(29, 354)(30, 307)(31, 350)(32, 306)(33, 361)(34, 362)(35, 364)(36, 365)(37, 309)(38, 310)(39, 360)(40, 341)(41, 368)(42, 312)(43, 376)(44, 377)(45, 378)(46, 379)(47, 315)(48, 382)(49, 339)(50, 317)(51, 358)(52, 318)(53, 387)(54, 385)(55, 320)(56, 390)(57, 321)(58, 322)(59, 375)(60, 359)(61, 363)(62, 324)(63, 392)(64, 401)(65, 326)(66, 330)(67, 405)(68, 406)(69, 329)(70, 409)(71, 410)(72, 412)(73, 413)(74, 357)(75, 332)(76, 333)(77, 404)(78, 415)(79, 335)(80, 336)(81, 340)(82, 394)(83, 422)(84, 424)(85, 425)(86, 426)(87, 427)(88, 384)(89, 380)(90, 344)(91, 383)(92, 346)(93, 393)(94, 347)(95, 348)(96, 420)(97, 349)(98, 432)(99, 403)(100, 351)(101, 352)(102, 353)(103, 421)(104, 407)(105, 355)(106, 356)(107, 429)(108, 434)(109, 439)(110, 408)(111, 400)(112, 369)(113, 411)(114, 367)(115, 438)(116, 416)(117, 366)(118, 433)(119, 428)(120, 402)(121, 414)(122, 370)(123, 371)(124, 372)(125, 373)(126, 374)(127, 423)(128, 395)(129, 381)(130, 391)(131, 436)(132, 431)(133, 440)(134, 417)(135, 386)(136, 388)(137, 389)(138, 419)(139, 435)(140, 441)(141, 398)(142, 396)(143, 397)(144, 399)(145, 430)(146, 437)(147, 418)(148, 442)(149, 443)(150, 444)(151, 445)(152, 446)(153, 447)(154, 448)(155, 449)(156, 450)(157, 451)(158, 452)(159, 453)(160, 454)(161, 455)(162, 456)(163, 457)(164, 458)(165, 459)(166, 460)(167, 461)(168, 462)(169, 463)(170, 464)(171, 465)(172, 466)(173, 467)(174, 468)(175, 469)(176, 470)(177, 471)(178, 472)(179, 473)(180, 474)(181, 475)(182, 476)(183, 477)(184, 478)(185, 479)(186, 480)(187, 481)(188, 482)(189, 483)(190, 484)(191, 485)(192, 486)(193, 487)(194, 488)(195, 489)(196, 490)(197, 491)(198, 492)(199, 493)(200, 494)(201, 495)(202, 496)(203, 497)(204, 498)(205, 499)(206, 500)(207, 501)(208, 502)(209, 503)(210, 504)(211, 505)(212, 506)(213, 507)(214, 508)(215, 509)(216, 510)(217, 511)(218, 512)(219, 513)(220, 514)(221, 515)(222, 516)(223, 517)(224, 518)(225, 519)(226, 520)(227, 521)(228, 522)(229, 523)(230, 524)(231, 525)(232, 526)(233, 527)(234, 528)(235, 529)(236, 530)(237, 531)(238, 532)(239, 533)(240, 534)(241, 535)(242, 536)(243, 537)(244, 538)(245, 539)(246, 540)(247, 541)(248, 542)(249, 543)(250, 544)(251, 545)(252, 546)(253, 547)(254, 548)(255, 549)(256, 550)(257, 551)(258, 552)(259, 553)(260, 554)(261, 555)(262, 556)(263, 557)(264, 558)(265, 559)(266, 560)(267, 561)(268, 562)(269, 563)(270, 564)(271, 565)(272, 566)(273, 567)(274, 568)(275, 569)(276, 570)(277, 571)(278, 572)(279, 573)(280, 574)(281, 575)(282, 576)(283, 577)(284, 578)(285, 579)(286, 580)(287, 581)(288, 582)(289, 583)(290, 584)(291, 585)(292, 586)(293, 587)(294, 588) local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E15.1331 Graph:: simple bipartite v = 196 e = 294 f = 70 degree seq :: [ 2^147, 6^49 ] E15.1333 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 4}) Quotient :: edge Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = C2 x PSL(3,2) (small group id <336, 209>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, (T2^-1 * T1^-1)^4, (T2^2 * T1^-1)^4, T2^-2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 26, 12)(8, 20, 42, 21)(10, 18, 38, 24)(13, 30, 55, 27)(14, 31, 61, 32)(15, 33, 63, 34)(17, 28, 56, 37)(19, 39, 74, 40)(22, 46, 83, 47)(23, 44, 80, 48)(25, 51, 89, 52)(29, 57, 76, 41)(35, 66, 109, 67)(36, 64, 106, 68)(43, 49, 87, 79)(45, 81, 116, 73)(50, 88, 125, 82)(53, 92, 137, 93)(54, 90, 126, 94)(58, 86, 130, 99)(59, 62, 69, 100)(60, 91, 135, 101)(65, 107, 143, 98)(70, 113, 150, 108)(71, 112, 152, 114)(72, 75, 95, 115)(77, 121, 103, 122)(78, 119, 155, 123)(84, 85, 129, 128)(96, 141, 162, 136)(97, 140, 163, 142)(102, 146, 148, 105)(104, 144, 118, 147)(110, 111, 151, 145)(117, 154, 160, 134)(120, 156, 133, 132)(124, 157, 166, 158)(127, 159, 167, 161)(131, 153, 138, 139)(149, 164, 168, 165)(169, 170, 172)(171, 176, 178)(173, 181, 182)(174, 183, 185)(175, 186, 187)(177, 190, 191)(179, 193, 195)(180, 196, 197)(184, 203, 204)(188, 209, 211)(189, 212, 213)(192, 217, 218)(194, 221, 222)(198, 226, 227)(199, 228, 215)(200, 230, 201)(202, 232, 233)(205, 237, 238)(206, 239, 240)(207, 241, 235)(208, 243, 219)(210, 245, 246)(214, 250, 252)(216, 253, 254)(220, 258, 259)(223, 263, 264)(224, 265, 247)(225, 266, 261)(229, 270, 271)(231, 272, 273)(234, 276, 278)(236, 279, 280)(242, 285, 286)(244, 287, 288)(248, 292, 277)(249, 269, 290)(251, 294, 295)(255, 299, 296)(256, 300, 282)(257, 301, 302)(260, 304, 306)(262, 307, 308)(267, 309, 312)(268, 297, 313)(274, 317, 305)(275, 284, 315)(281, 289, 310)(283, 319, 321)(291, 318, 325)(293, 327, 328)(298, 322, 326)(303, 311, 324)(314, 329, 331)(316, 330, 332)(320, 323, 333)(334, 335, 336) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E15.1334 Transitivity :: ET+ Graph:: simple bipartite v = 98 e = 168 f = 42 degree seq :: [ 3^56, 4^42 ] E15.1334 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 4}) Quotient :: loop Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = C2 x PSL(3,2) (small group id <336, 209>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^4, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, (T2^-1 * T1^-1)^4, (T2^2 * T1^-1)^4, T2^-2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 ] Map:: polyhedral non-degenerate R = (1, 169, 3, 171, 9, 177, 5, 173)(2, 170, 6, 174, 16, 184, 7, 175)(4, 172, 11, 179, 26, 194, 12, 180)(8, 176, 20, 188, 42, 210, 21, 189)(10, 178, 18, 186, 38, 206, 24, 192)(13, 181, 30, 198, 55, 223, 27, 195)(14, 182, 31, 199, 61, 229, 32, 200)(15, 183, 33, 201, 63, 231, 34, 202)(17, 185, 28, 196, 56, 224, 37, 205)(19, 187, 39, 207, 74, 242, 40, 208)(22, 190, 46, 214, 83, 251, 47, 215)(23, 191, 44, 212, 80, 248, 48, 216)(25, 193, 51, 219, 89, 257, 52, 220)(29, 197, 57, 225, 76, 244, 41, 209)(35, 203, 66, 234, 109, 277, 67, 235)(36, 204, 64, 232, 106, 274, 68, 236)(43, 211, 49, 217, 87, 255, 79, 247)(45, 213, 81, 249, 116, 284, 73, 241)(50, 218, 88, 256, 125, 293, 82, 250)(53, 221, 92, 260, 137, 305, 93, 261)(54, 222, 90, 258, 126, 294, 94, 262)(58, 226, 86, 254, 130, 298, 99, 267)(59, 227, 62, 230, 69, 237, 100, 268)(60, 228, 91, 259, 135, 303, 101, 269)(65, 233, 107, 275, 143, 311, 98, 266)(70, 238, 113, 281, 150, 318, 108, 276)(71, 239, 112, 280, 152, 320, 114, 282)(72, 240, 75, 243, 95, 263, 115, 283)(77, 245, 121, 289, 103, 271, 122, 290)(78, 246, 119, 287, 155, 323, 123, 291)(84, 252, 85, 253, 129, 297, 128, 296)(96, 264, 141, 309, 162, 330, 136, 304)(97, 265, 140, 308, 163, 331, 142, 310)(102, 270, 146, 314, 148, 316, 105, 273)(104, 272, 144, 312, 118, 286, 147, 315)(110, 278, 111, 279, 151, 319, 145, 313)(117, 285, 154, 322, 160, 328, 134, 302)(120, 288, 156, 324, 133, 301, 132, 300)(124, 292, 157, 325, 166, 334, 158, 326)(127, 295, 159, 327, 167, 335, 161, 329)(131, 299, 153, 321, 138, 306, 139, 307)(149, 317, 164, 332, 168, 336, 165, 333) L = (1, 170)(2, 172)(3, 176)(4, 169)(5, 181)(6, 183)(7, 186)(8, 178)(9, 190)(10, 171)(11, 193)(12, 196)(13, 182)(14, 173)(15, 185)(16, 203)(17, 174)(18, 187)(19, 175)(20, 209)(21, 212)(22, 191)(23, 177)(24, 217)(25, 195)(26, 221)(27, 179)(28, 197)(29, 180)(30, 226)(31, 228)(32, 230)(33, 200)(34, 232)(35, 204)(36, 184)(37, 237)(38, 239)(39, 241)(40, 243)(41, 211)(42, 245)(43, 188)(44, 213)(45, 189)(46, 250)(47, 199)(48, 253)(49, 218)(50, 192)(51, 208)(52, 258)(53, 222)(54, 194)(55, 263)(56, 265)(57, 266)(58, 227)(59, 198)(60, 215)(61, 270)(62, 201)(63, 272)(64, 233)(65, 202)(66, 276)(67, 207)(68, 279)(69, 238)(70, 205)(71, 240)(72, 206)(73, 235)(74, 285)(75, 219)(76, 287)(77, 246)(78, 210)(79, 224)(80, 292)(81, 269)(82, 252)(83, 294)(84, 214)(85, 254)(86, 216)(87, 299)(88, 300)(89, 301)(90, 259)(91, 220)(92, 304)(93, 225)(94, 307)(95, 264)(96, 223)(97, 247)(98, 261)(99, 309)(100, 297)(101, 290)(102, 271)(103, 229)(104, 273)(105, 231)(106, 317)(107, 284)(108, 278)(109, 248)(110, 234)(111, 280)(112, 236)(113, 289)(114, 256)(115, 319)(116, 315)(117, 286)(118, 242)(119, 288)(120, 244)(121, 310)(122, 249)(123, 318)(124, 277)(125, 327)(126, 295)(127, 251)(128, 255)(129, 313)(130, 322)(131, 296)(132, 282)(133, 302)(134, 257)(135, 311)(136, 306)(137, 274)(138, 260)(139, 308)(140, 262)(141, 312)(142, 281)(143, 324)(144, 267)(145, 268)(146, 329)(147, 275)(148, 330)(149, 305)(150, 325)(151, 321)(152, 323)(153, 283)(154, 326)(155, 333)(156, 303)(157, 291)(158, 298)(159, 328)(160, 293)(161, 331)(162, 332)(163, 314)(164, 316)(165, 320)(166, 335)(167, 336)(168, 334) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E15.1333 Transitivity :: ET+ VT+ AT Graph:: simple v = 42 e = 168 f = 98 degree seq :: [ 8^42 ] E15.1335 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = C2 x PSL(3,2) (small group id <336, 209>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^2 * Y3^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2, (Y3 * Y2^-1)^4, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-2, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y3^2 * Y2^-2 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 ] Map:: R = (1, 169, 2, 170, 4, 172)(3, 171, 8, 176, 10, 178)(5, 173, 13, 181, 14, 182)(6, 174, 15, 183, 17, 185)(7, 175, 18, 186, 19, 187)(9, 177, 22, 190, 23, 191)(11, 179, 25, 193, 27, 195)(12, 180, 28, 196, 29, 197)(16, 184, 35, 203, 36, 204)(20, 188, 41, 209, 43, 211)(21, 189, 44, 212, 45, 213)(24, 192, 49, 217, 50, 218)(26, 194, 53, 221, 54, 222)(30, 198, 58, 226, 59, 227)(31, 199, 60, 228, 47, 215)(32, 200, 62, 230, 33, 201)(34, 202, 64, 232, 65, 233)(37, 205, 69, 237, 70, 238)(38, 206, 71, 239, 72, 240)(39, 207, 73, 241, 67, 235)(40, 208, 75, 243, 51, 219)(42, 210, 77, 245, 78, 246)(46, 214, 82, 250, 84, 252)(48, 216, 85, 253, 86, 254)(52, 220, 90, 258, 91, 259)(55, 223, 95, 263, 96, 264)(56, 224, 97, 265, 79, 247)(57, 225, 98, 266, 93, 261)(61, 229, 102, 270, 103, 271)(63, 231, 104, 272, 105, 273)(66, 234, 108, 276, 110, 278)(68, 236, 111, 279, 112, 280)(74, 242, 117, 285, 118, 286)(76, 244, 119, 287, 120, 288)(80, 248, 124, 292, 109, 277)(81, 249, 101, 269, 122, 290)(83, 251, 126, 294, 127, 295)(87, 255, 131, 299, 128, 296)(88, 256, 132, 300, 114, 282)(89, 257, 133, 301, 134, 302)(92, 260, 136, 304, 138, 306)(94, 262, 139, 307, 140, 308)(99, 267, 141, 309, 144, 312)(100, 268, 129, 297, 145, 313)(106, 274, 149, 317, 137, 305)(107, 275, 116, 284, 147, 315)(113, 281, 121, 289, 142, 310)(115, 283, 151, 319, 153, 321)(123, 291, 150, 318, 157, 325)(125, 293, 159, 327, 160, 328)(130, 298, 154, 322, 158, 326)(135, 303, 143, 311, 156, 324)(146, 314, 161, 329, 163, 331)(148, 316, 162, 330, 164, 332)(152, 320, 155, 323, 165, 333)(166, 334, 167, 335, 168, 336)(337, 505, 339, 507, 345, 513, 341, 509)(338, 506, 342, 510, 352, 520, 343, 511)(340, 508, 347, 515, 362, 530, 348, 516)(344, 512, 356, 524, 378, 546, 357, 525)(346, 514, 354, 522, 374, 542, 360, 528)(349, 517, 366, 534, 391, 559, 363, 531)(350, 518, 367, 535, 397, 565, 368, 536)(351, 519, 369, 537, 399, 567, 370, 538)(353, 521, 364, 532, 392, 560, 373, 541)(355, 523, 375, 543, 410, 578, 376, 544)(358, 526, 382, 550, 419, 587, 383, 551)(359, 527, 380, 548, 416, 584, 384, 552)(361, 529, 387, 555, 425, 593, 388, 556)(365, 533, 393, 561, 412, 580, 377, 545)(371, 539, 402, 570, 445, 613, 403, 571)(372, 540, 400, 568, 442, 610, 404, 572)(379, 547, 385, 553, 423, 591, 415, 583)(381, 549, 417, 585, 452, 620, 409, 577)(386, 554, 424, 592, 461, 629, 418, 586)(389, 557, 428, 596, 473, 641, 429, 597)(390, 558, 426, 594, 462, 630, 430, 598)(394, 562, 422, 590, 466, 634, 435, 603)(395, 563, 398, 566, 405, 573, 436, 604)(396, 564, 427, 595, 471, 639, 437, 605)(401, 569, 443, 611, 479, 647, 434, 602)(406, 574, 449, 617, 486, 654, 444, 612)(407, 575, 448, 616, 488, 656, 450, 618)(408, 576, 411, 579, 431, 599, 451, 619)(413, 581, 457, 625, 439, 607, 458, 626)(414, 582, 455, 623, 491, 659, 459, 627)(420, 588, 421, 589, 465, 633, 464, 632)(432, 600, 477, 645, 498, 666, 472, 640)(433, 601, 476, 644, 499, 667, 478, 646)(438, 606, 482, 650, 484, 652, 441, 609)(440, 608, 480, 648, 454, 622, 483, 651)(446, 614, 447, 615, 487, 655, 481, 649)(453, 621, 490, 658, 496, 664, 470, 638)(456, 624, 492, 660, 469, 637, 468, 636)(460, 628, 493, 661, 502, 670, 494, 662)(463, 631, 495, 663, 503, 671, 497, 665)(467, 635, 489, 657, 474, 642, 475, 643)(485, 653, 500, 668, 504, 672, 501, 669) L = (1, 340)(2, 337)(3, 346)(4, 338)(5, 350)(6, 353)(7, 355)(8, 339)(9, 359)(10, 344)(11, 363)(12, 365)(13, 341)(14, 349)(15, 342)(16, 372)(17, 351)(18, 343)(19, 354)(20, 379)(21, 381)(22, 345)(23, 358)(24, 386)(25, 347)(26, 390)(27, 361)(28, 348)(29, 364)(30, 395)(31, 383)(32, 369)(33, 398)(34, 401)(35, 352)(36, 371)(37, 406)(38, 408)(39, 403)(40, 387)(41, 356)(42, 414)(43, 377)(44, 357)(45, 380)(46, 420)(47, 396)(48, 422)(49, 360)(50, 385)(51, 411)(52, 427)(53, 362)(54, 389)(55, 432)(56, 415)(57, 429)(58, 366)(59, 394)(60, 367)(61, 439)(62, 368)(63, 441)(64, 370)(65, 400)(66, 446)(67, 409)(68, 448)(69, 373)(70, 405)(71, 374)(72, 407)(73, 375)(74, 454)(75, 376)(76, 456)(77, 378)(78, 413)(79, 433)(80, 445)(81, 458)(82, 382)(83, 463)(84, 418)(85, 384)(86, 421)(87, 464)(88, 450)(89, 470)(90, 388)(91, 426)(92, 474)(93, 434)(94, 476)(95, 391)(96, 431)(97, 392)(98, 393)(99, 480)(100, 481)(101, 417)(102, 397)(103, 438)(104, 399)(105, 440)(106, 473)(107, 483)(108, 402)(109, 460)(110, 444)(111, 404)(112, 447)(113, 478)(114, 468)(115, 489)(116, 443)(117, 410)(118, 453)(119, 412)(120, 455)(121, 449)(122, 437)(123, 493)(124, 416)(125, 496)(126, 419)(127, 462)(128, 467)(129, 436)(130, 494)(131, 423)(132, 424)(133, 425)(134, 469)(135, 492)(136, 428)(137, 485)(138, 472)(139, 430)(140, 475)(141, 435)(142, 457)(143, 471)(144, 477)(145, 465)(146, 499)(147, 452)(148, 500)(149, 442)(150, 459)(151, 451)(152, 501)(153, 487)(154, 466)(155, 488)(156, 479)(157, 486)(158, 490)(159, 461)(160, 495)(161, 482)(162, 484)(163, 497)(164, 498)(165, 491)(166, 504)(167, 502)(168, 503)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.1336 Graph:: bipartite v = 98 e = 336 f = 210 degree seq :: [ 6^56, 8^42 ] E15.1336 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = C2 x PSL(3,2) (small group id <336, 209>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1)^3, (Y3 * Y2^-1)^3, (Y1^-1 * Y3^-1)^4, (Y1^-1 * Y3^-1)^4, Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 ] Map:: polytopal R = (1, 169, 2, 170, 6, 174, 4, 172)(3, 171, 9, 177, 21, 189, 10, 178)(5, 173, 13, 181, 29, 197, 14, 182)(7, 175, 17, 185, 37, 205, 18, 186)(8, 176, 19, 187, 41, 209, 20, 188)(11, 179, 25, 193, 51, 219, 26, 194)(12, 180, 27, 195, 54, 222, 28, 196)(15, 183, 33, 201, 63, 231, 34, 202)(16, 184, 35, 203, 66, 234, 36, 204)(22, 190, 46, 214, 83, 251, 47, 215)(23, 191, 31, 199, 61, 229, 48, 216)(24, 192, 49, 217, 87, 255, 50, 218)(30, 198, 59, 227, 101, 269, 60, 228)(32, 200, 62, 230, 71, 239, 38, 206)(39, 207, 42, 210, 77, 245, 72, 240)(40, 208, 73, 241, 117, 285, 74, 242)(43, 211, 78, 246, 106, 274, 64, 232)(44, 212, 79, 247, 109, 277, 80, 248)(45, 213, 81, 249, 125, 293, 82, 250)(52, 220, 68, 236, 111, 279, 91, 259)(53, 221, 56, 224, 85, 253, 92, 260)(55, 223, 95, 263, 138, 306, 96, 264)(57, 225, 97, 265, 139, 307, 98, 266)(58, 226, 99, 267, 104, 272, 100, 268)(65, 233, 67, 235, 110, 278, 107, 275)(69, 237, 112, 280, 94, 262, 113, 281)(70, 238, 114, 282, 153, 321, 115, 283)(75, 243, 118, 286, 157, 325, 119, 287)(76, 244, 88, 256, 89, 257, 120, 288)(84, 252, 129, 297, 146, 314, 103, 271)(86, 254, 130, 298, 154, 322, 123, 291)(90, 258, 133, 301, 162, 330, 134, 302)(93, 261, 137, 305, 161, 329, 128, 296)(102, 270, 142, 310, 163, 331, 145, 313)(105, 273, 147, 315, 164, 332, 148, 316)(108, 276, 150, 318, 165, 333, 151, 319)(116, 284, 155, 323, 143, 311, 122, 290)(121, 289, 159, 327, 140, 308, 141, 309)(124, 292, 126, 294, 158, 326, 136, 304)(127, 295, 135, 303, 132, 300, 156, 324)(131, 299, 152, 320, 149, 317, 144, 312)(160, 328, 167, 335, 168, 336, 166, 334)(337, 505)(338, 506)(339, 507)(340, 508)(341, 509)(342, 510)(343, 511)(344, 512)(345, 513)(346, 514)(347, 515)(348, 516)(349, 517)(350, 518)(351, 519)(352, 520)(353, 521)(354, 522)(355, 523)(356, 524)(357, 525)(358, 526)(359, 527)(360, 528)(361, 529)(362, 530)(363, 531)(364, 532)(365, 533)(366, 534)(367, 535)(368, 536)(369, 537)(370, 538)(371, 539)(372, 540)(373, 541)(374, 542)(375, 543)(376, 544)(377, 545)(378, 546)(379, 547)(380, 548)(381, 549)(382, 550)(383, 551)(384, 552)(385, 553)(386, 554)(387, 555)(388, 556)(389, 557)(390, 558)(391, 559)(392, 560)(393, 561)(394, 562)(395, 563)(396, 564)(397, 565)(398, 566)(399, 567)(400, 568)(401, 569)(402, 570)(403, 571)(404, 572)(405, 573)(406, 574)(407, 575)(408, 576)(409, 577)(410, 578)(411, 579)(412, 580)(413, 581)(414, 582)(415, 583)(416, 584)(417, 585)(418, 586)(419, 587)(420, 588)(421, 589)(422, 590)(423, 591)(424, 592)(425, 593)(426, 594)(427, 595)(428, 596)(429, 597)(430, 598)(431, 599)(432, 600)(433, 601)(434, 602)(435, 603)(436, 604)(437, 605)(438, 606)(439, 607)(440, 608)(441, 609)(442, 610)(443, 611)(444, 612)(445, 613)(446, 614)(447, 615)(448, 616)(449, 617)(450, 618)(451, 619)(452, 620)(453, 621)(454, 622)(455, 623)(456, 624)(457, 625)(458, 626)(459, 627)(460, 628)(461, 629)(462, 630)(463, 631)(464, 632)(465, 633)(466, 634)(467, 635)(468, 636)(469, 637)(470, 638)(471, 639)(472, 640)(473, 641)(474, 642)(475, 643)(476, 644)(477, 645)(478, 646)(479, 647)(480, 648)(481, 649)(482, 650)(483, 651)(484, 652)(485, 653)(486, 654)(487, 655)(488, 656)(489, 657)(490, 658)(491, 659)(492, 660)(493, 661)(494, 662)(495, 663)(496, 664)(497, 665)(498, 666)(499, 667)(500, 668)(501, 669)(502, 670)(503, 671)(504, 672) L = (1, 339)(2, 343)(3, 341)(4, 347)(5, 337)(6, 351)(7, 344)(8, 338)(9, 358)(10, 355)(11, 348)(12, 340)(13, 366)(14, 367)(15, 352)(16, 342)(17, 374)(18, 371)(19, 360)(20, 378)(21, 380)(22, 359)(23, 345)(24, 346)(25, 388)(26, 349)(27, 391)(28, 392)(29, 393)(30, 362)(31, 368)(32, 350)(33, 400)(34, 363)(35, 376)(36, 403)(37, 405)(38, 375)(39, 353)(40, 354)(41, 411)(42, 379)(43, 356)(44, 381)(45, 357)(46, 364)(47, 417)(48, 421)(49, 410)(50, 424)(51, 425)(52, 389)(53, 361)(54, 429)(55, 370)(56, 382)(57, 394)(58, 365)(59, 386)(60, 435)(61, 438)(62, 439)(63, 440)(64, 401)(65, 369)(66, 444)(67, 404)(68, 372)(69, 406)(70, 373)(71, 450)(72, 397)(73, 432)(74, 416)(75, 412)(76, 377)(77, 457)(78, 458)(79, 459)(80, 385)(81, 420)(82, 462)(83, 463)(84, 383)(85, 422)(86, 384)(87, 467)(88, 395)(89, 426)(90, 387)(91, 469)(92, 446)(93, 430)(94, 390)(95, 396)(96, 449)(97, 470)(98, 398)(99, 431)(100, 477)(101, 479)(102, 408)(103, 434)(104, 441)(105, 399)(106, 483)(107, 413)(108, 445)(109, 402)(110, 472)(111, 488)(112, 481)(113, 409)(114, 452)(115, 490)(116, 407)(117, 492)(118, 418)(119, 414)(120, 494)(121, 443)(122, 455)(123, 460)(124, 415)(125, 496)(126, 454)(127, 464)(128, 419)(129, 453)(130, 448)(131, 468)(132, 423)(133, 471)(134, 476)(135, 427)(136, 428)(137, 484)(138, 482)(139, 461)(140, 433)(141, 478)(142, 436)(143, 480)(144, 437)(145, 466)(146, 491)(147, 485)(148, 499)(149, 442)(150, 451)(151, 447)(152, 487)(153, 502)(154, 486)(155, 474)(156, 465)(157, 489)(158, 495)(159, 456)(160, 475)(161, 498)(162, 503)(163, 473)(164, 504)(165, 500)(166, 493)(167, 497)(168, 501)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E15.1335 Graph:: simple bipartite v = 210 e = 336 f = 98 degree seq :: [ 2^168, 8^42 ] E15.1337 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 6}) Quotient :: edge Aut^+ = (C7 x Q8) : C3 (small group id <168, 23>) Aut = (C7 x Q8) : C3 (small group id <168, 23>) |r| :: 1 Presentation :: [ X1^3, X2^6, (X2^-1 * X1^-1)^3, X1^-1 * X2^-3 * X1 * X2^-3, X2 * X1 * X2^-1 * X1^-1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 29, 31)(12, 32, 22)(15, 37, 38)(17, 40, 42)(21, 48, 49)(23, 51, 52)(25, 41, 56)(27, 57, 59)(28, 60, 54)(30, 63, 53)(33, 68, 69)(34, 58, 70)(35, 71, 72)(36, 73, 74)(39, 75, 76)(43, 79, 81)(44, 82, 77)(45, 80, 84)(46, 85, 86)(47, 87, 88)(50, 89, 90)(55, 94, 95)(61, 101, 102)(62, 103, 104)(64, 107, 109)(65, 110, 105)(66, 108, 112)(67, 113, 114)(78, 124, 125)(83, 122, 130)(91, 106, 140)(92, 128, 141)(93, 126, 142)(96, 145, 146)(97, 147, 149)(98, 136, 115)(99, 148, 135)(100, 151, 117)(111, 138, 156)(116, 134, 143)(118, 161, 158)(119, 154, 162)(120, 157, 153)(121, 163, 164)(123, 152, 165)(127, 139, 131)(129, 167, 133)(132, 160, 166)(137, 150, 168)(144, 159, 155)(169, 171, 177, 193, 183, 173)(170, 174, 185, 209, 189, 175)(172, 179, 198, 224, 201, 180)(176, 190, 218, 205, 221, 191)(178, 195, 226, 206, 229, 196)(181, 202, 223, 192, 222, 203)(182, 204, 216, 194, 207, 184)(186, 211, 248, 217, 251, 212)(187, 213, 246, 208, 245, 214)(188, 215, 236, 210, 230, 197)(199, 232, 276, 237, 279, 233)(200, 234, 274, 231, 273, 235)(219, 259, 307, 257, 282, 260)(220, 261, 269, 258, 264, 225)(227, 265, 316, 270, 318, 266)(228, 267, 284, 238, 283, 268)(239, 285, 312, 262, 311, 286)(240, 287, 243, 263, 288, 241)(242, 289, 247, 244, 291, 290)(249, 294, 309, 298, 313, 295)(250, 296, 300, 252, 299, 297)(253, 301, 319, 292, 334, 302)(254, 303, 271, 293, 304, 255)(256, 305, 275, 272, 317, 306)(277, 320, 330, 324, 331, 321)(278, 322, 326, 280, 325, 323)(281, 327, 335, 308, 329, 328)(310, 332, 315, 314, 333, 336) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 6^3 ), ( 6^6 ) } Outer automorphisms :: chiral Dual of E15.1338 Transitivity :: ET+ Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 3^56, 6^28 ] E15.1338 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 6}) Quotient :: loop Aut^+ = (C7 x Q8) : C3 (small group id <168, 23>) Aut = (C7 x Q8) : C3 (small group id <168, 23>) |r| :: 1 Presentation :: [ X1^3, X2^3, X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1, (X2^-1 * X1^-1)^6, X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 169, 2, 170, 4, 172)(3, 171, 8, 176, 9, 177)(5, 173, 12, 180, 13, 181)(6, 174, 14, 182, 15, 183)(7, 175, 16, 184, 17, 185)(10, 178, 22, 190, 23, 191)(11, 179, 24, 192, 25, 193)(18, 186, 38, 206, 39, 207)(19, 187, 40, 208, 41, 209)(20, 188, 42, 210, 43, 211)(21, 189, 44, 212, 45, 213)(26, 194, 54, 222, 55, 223)(27, 195, 56, 224, 57, 225)(28, 196, 58, 226, 59, 227)(29, 197, 60, 228, 61, 229)(30, 198, 62, 230, 63, 231)(31, 199, 64, 232, 65, 233)(32, 200, 66, 234, 67, 235)(33, 201, 68, 236, 69, 237)(34, 202, 70, 238, 71, 239)(35, 203, 72, 240, 73, 241)(36, 204, 74, 242, 75, 243)(37, 205, 76, 244, 77, 245)(46, 214, 92, 260, 93, 261)(47, 215, 94, 262, 95, 263)(48, 216, 96, 264, 97, 265)(49, 217, 98, 266, 79, 247)(50, 218, 99, 267, 100, 268)(51, 219, 101, 269, 81, 249)(52, 220, 102, 270, 85, 253)(53, 221, 103, 271, 104, 272)(78, 246, 116, 284, 115, 283)(80, 248, 133, 301, 134, 302)(82, 250, 121, 289, 135, 303)(83, 251, 119, 287, 136, 304)(84, 252, 137, 305, 105, 273)(86, 254, 138, 306, 139, 307)(87, 255, 140, 308, 141, 309)(88, 256, 130, 298, 106, 274)(89, 257, 142, 310, 128, 296)(90, 258, 143, 311, 108, 276)(91, 259, 144, 312, 111, 279)(107, 275, 127, 295, 155, 323)(109, 277, 156, 324, 151, 319)(110, 278, 148, 316, 157, 325)(112, 280, 150, 318, 147, 315)(113, 281, 158, 326, 159, 327)(114, 282, 118, 286, 160, 328)(117, 285, 146, 314, 161, 329)(120, 288, 154, 322, 124, 292)(122, 290, 162, 330, 126, 294)(123, 291, 163, 331, 129, 297)(125, 293, 153, 321, 164, 332)(131, 299, 165, 333, 166, 334)(132, 300, 145, 313, 167, 335)(149, 317, 168, 336, 152, 320) L = (1, 171)(2, 174)(3, 173)(4, 178)(5, 169)(6, 175)(7, 170)(8, 186)(9, 188)(10, 179)(11, 172)(12, 194)(13, 196)(14, 198)(15, 200)(16, 202)(17, 204)(18, 187)(19, 176)(20, 189)(21, 177)(22, 214)(23, 216)(24, 218)(25, 220)(26, 195)(27, 180)(28, 197)(29, 181)(30, 199)(31, 182)(32, 201)(33, 183)(34, 203)(35, 184)(36, 205)(37, 185)(38, 246)(39, 247)(40, 249)(41, 251)(42, 253)(43, 255)(44, 257)(45, 259)(46, 215)(47, 190)(48, 217)(49, 191)(50, 219)(51, 192)(52, 221)(53, 193)(54, 271)(55, 274)(56, 276)(57, 278)(58, 279)(59, 281)(60, 282)(61, 260)(62, 284)(63, 213)(64, 225)(65, 285)(66, 227)(67, 287)(68, 289)(69, 291)(70, 228)(71, 292)(72, 294)(73, 296)(74, 297)(75, 299)(76, 300)(77, 206)(78, 245)(79, 248)(80, 207)(81, 250)(82, 208)(83, 252)(84, 209)(85, 254)(86, 210)(87, 256)(88, 211)(89, 258)(90, 212)(91, 231)(92, 283)(93, 237)(94, 241)(95, 309)(96, 243)(97, 314)(98, 316)(99, 244)(100, 318)(101, 320)(102, 302)(103, 273)(104, 230)(105, 222)(106, 275)(107, 223)(108, 277)(109, 224)(110, 232)(111, 280)(112, 226)(113, 234)(114, 238)(115, 229)(116, 272)(117, 286)(118, 233)(119, 288)(120, 235)(121, 290)(122, 236)(123, 261)(124, 293)(125, 239)(126, 295)(127, 240)(128, 262)(129, 298)(130, 242)(131, 264)(132, 267)(133, 324)(134, 322)(135, 328)(136, 329)(137, 333)(138, 303)(139, 327)(140, 304)(141, 313)(142, 305)(143, 331)(144, 323)(145, 263)(146, 315)(147, 265)(148, 317)(149, 266)(150, 319)(151, 268)(152, 321)(153, 269)(154, 270)(155, 336)(156, 330)(157, 335)(158, 325)(159, 334)(160, 306)(161, 308)(162, 301)(163, 332)(164, 311)(165, 310)(166, 307)(167, 326)(168, 312) local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E15.1337 Transitivity :: ET+ VT+ Graph:: simple v = 56 e = 168 f = 84 degree seq :: [ 6^56 ] E15.1339 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 6}) Quotient :: edge Aut^+ = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) Aut = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) |r| :: 1 Presentation :: [ X1^3, X2^3, X1 * X2 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1, X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2^-1, X2 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2 * X1 * X2 * X1^-1, (X2 * X1 * X2^-1 * X1 * X2^-1 * X1^-1)^2, (X2^-1 * X1^-1)^6, (X2 * X1^-1 * X2^-1 * X1^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 8, 9)(5, 12, 13)(6, 14, 15)(7, 16, 17)(10, 22, 23)(11, 24, 25)(18, 38, 39)(19, 40, 41)(20, 42, 43)(21, 44, 45)(26, 54, 55)(27, 56, 57)(28, 58, 59)(29, 60, 61)(30, 62, 63)(31, 64, 65)(32, 66, 67)(33, 68, 69)(34, 70, 71)(35, 72, 73)(36, 74, 75)(37, 76, 77)(46, 92, 80)(47, 93, 94)(48, 95, 96)(49, 97, 98)(50, 85, 99)(51, 100, 101)(52, 89, 102)(53, 103, 104)(78, 130, 106)(79, 134, 135)(81, 136, 120)(82, 137, 122)(83, 138, 123)(84, 133, 107)(86, 139, 140)(87, 141, 142)(88, 111, 131)(90, 114, 118)(91, 143, 121)(105, 152, 127)(108, 153, 154)(109, 155, 117)(110, 148, 144)(112, 156, 157)(113, 149, 125)(115, 126, 116)(119, 158, 147)(124, 159, 146)(128, 160, 161)(129, 162, 145)(132, 163, 164)(150, 166, 165)(151, 167, 168)(169, 171, 173)(170, 174, 175)(172, 178, 179)(176, 186, 187)(177, 188, 189)(180, 194, 195)(181, 196, 197)(182, 198, 199)(183, 200, 201)(184, 202, 203)(185, 204, 205)(190, 214, 215)(191, 216, 217)(192, 218, 219)(193, 220, 221)(206, 246, 247)(207, 231, 248)(208, 249, 250)(209, 251, 244)(210, 252, 253)(211, 254, 255)(212, 256, 257)(213, 258, 259)(222, 234, 273)(223, 274, 275)(224, 276, 277)(225, 278, 245)(226, 236, 279)(227, 280, 281)(228, 262, 282)(229, 269, 283)(230, 284, 285)(232, 286, 287)(233, 288, 271)(235, 289, 290)(237, 291, 292)(238, 263, 293)(239, 294, 295)(240, 296, 297)(241, 298, 272)(242, 265, 299)(243, 300, 301)(260, 312, 313)(261, 306, 309)(264, 314, 315)(266, 304, 307)(267, 316, 317)(268, 318, 302)(270, 319, 320)(303, 322, 311)(305, 328, 331)(308, 330, 333)(310, 321, 324)(323, 329, 327)(325, 332, 336)(326, 334, 335) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 12^3 ) } Outer automorphisms :: chiral Dual of E15.1344 Transitivity :: ET+ Graph:: simple bipartite v = 112 e = 168 f = 28 degree seq :: [ 3^112 ] E15.1340 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 6}) Quotient :: edge Aut^+ = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) Aut = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) |r| :: 1 Presentation :: [ X1^3, (X2 * X1)^3, X2^6, X2^-1 * X1 * X2^2 * X1^-1 * X2^-2 * X1, (X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1)^2 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 29, 31)(12, 32, 22)(15, 37, 38)(17, 40, 42)(21, 48, 49)(23, 51, 52)(25, 55, 56)(27, 59, 60)(28, 61, 54)(30, 64, 66)(33, 70, 71)(34, 72, 73)(35, 53, 74)(36, 76, 62)(39, 79, 80)(41, 83, 84)(43, 86, 87)(44, 88, 82)(45, 90, 91)(46, 81, 92)(47, 94, 89)(50, 97, 99)(57, 105, 106)(58, 107, 103)(63, 111, 112)(65, 115, 101)(67, 117, 114)(68, 118, 119)(69, 113, 120)(75, 126, 100)(77, 128, 129)(78, 104, 130)(85, 133, 134)(93, 139, 131)(95, 141, 142)(96, 132, 143)(98, 144, 145)(102, 147, 121)(108, 151, 152)(109, 127, 140)(110, 153, 154)(116, 124, 156)(122, 146, 159)(123, 149, 138)(125, 158, 160)(135, 162, 163)(136, 165, 148)(137, 164, 155)(150, 166, 167)(157, 168, 161)(169, 171, 177, 193, 183, 173)(170, 174, 185, 209, 189, 175)(172, 179, 198, 233, 201, 180)(176, 190, 218, 266, 221, 191)(178, 195, 210, 253, 230, 196)(181, 202, 232, 282, 243, 203)(182, 204, 245, 249, 207, 184)(186, 211, 234, 284, 257, 212)(187, 213, 192, 222, 261, 214)(188, 215, 263, 281, 231, 197)(194, 225, 267, 235, 199, 226)(200, 236, 208, 250, 289, 237)(205, 246, 296, 302, 258, 217)(206, 238, 290, 312, 274, 240)(216, 264, 309, 324, 286, 239)(219, 268, 223, 271, 314, 269)(220, 270, 316, 321, 276, 227)(224, 247, 299, 251, 228, 272)(229, 277, 265, 288, 323, 278)(241, 291, 297, 330, 328, 292)(242, 293, 304, 256, 295, 244)(248, 294, 329, 333, 303, 254)(252, 279, 315, 283, 255, 300)(259, 305, 310, 334, 317, 273)(260, 306, 325, 285, 308, 262)(275, 280, 307, 322, 336, 318)(287, 326, 313, 319, 332, 301)(298, 320, 327, 335, 311, 331) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 6^3 ), ( 6^6 ) } Outer automorphisms :: chiral Dual of E15.1343 Transitivity :: ET+ Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 3^56, 6^28 ] E15.1341 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 6}) Quotient :: edge Aut^+ = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) Aut = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) |r| :: 1 Presentation :: [ X1^3, (X2 * X1)^3, X2^6, X1^-1 * X2 * X1 * X2 * X1 * X2 * X1^-1, X2^-2 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2 * X1^-1, (X1 * X2^-2)^3, X1 * X2^2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 29, 31)(12, 32, 22)(15, 37, 38)(17, 40, 42)(21, 48, 49)(23, 51, 52)(25, 56, 57)(27, 60, 62)(28, 63, 54)(30, 66, 68)(33, 73, 74)(34, 75, 77)(35, 78, 79)(36, 81, 83)(39, 87, 64)(41, 90, 91)(43, 93, 95)(44, 96, 55)(45, 84, 99)(46, 100, 101)(47, 103, 104)(50, 107, 82)(53, 109, 76)(58, 113, 114)(59, 115, 110)(61, 117, 80)(65, 122, 97)(67, 124, 125)(69, 126, 127)(70, 128, 89)(71, 105, 130)(72, 131, 111)(85, 121, 136)(86, 137, 138)(88, 140, 98)(92, 142, 143)(94, 144, 102)(106, 150, 151)(108, 135, 146)(112, 154, 155)(116, 158, 132)(118, 159, 160)(119, 161, 152)(120, 139, 149)(123, 153, 129)(133, 165, 145)(134, 166, 141)(147, 157, 164)(148, 167, 163)(156, 168, 162)(169, 171, 177, 193, 183, 173)(170, 174, 185, 209, 189, 175)(172, 179, 198, 235, 201, 180)(176, 190, 218, 272, 221, 191)(178, 195, 229, 261, 232, 196)(181, 202, 244, 301, 248, 203)(182, 204, 250, 256, 207, 184)(186, 211, 262, 294, 265, 212)(187, 213, 266, 315, 270, 214)(188, 215, 251, 291, 233, 197)(192, 222, 234, 257, 208, 223)(194, 226, 216, 273, 242, 227)(199, 237, 284, 228, 220, 238)(200, 239, 297, 327, 300, 240)(205, 252, 217, 274, 236, 253)(206, 254, 210, 260, 241, 243)(219, 245, 293, 331, 321, 276)(224, 278, 285, 320, 275, 279)(225, 280, 277, 307, 255, 267)(230, 286, 324, 281, 264, 287)(231, 288, 295, 332, 330, 289)(246, 283, 311, 328, 335, 302)(247, 258, 306, 312, 303, 249)(259, 309, 308, 329, 290, 298)(263, 313, 336, 310, 296, 314)(268, 305, 304, 333, 323, 316)(269, 292, 319, 326, 317, 271)(282, 325, 334, 322, 299, 318) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 6^3 ), ( 6^6 ) } Outer automorphisms :: chiral Dual of E15.1342 Transitivity :: ET+ Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 3^56, 6^28 ] E15.1342 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 6}) Quotient :: loop Aut^+ = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) Aut = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) |r| :: 1 Presentation :: [ X1^3, X2^3, X1 * X2 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1, X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2^-1, X2 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2 * X1 * X2 * X1^-1, (X2 * X1 * X2^-1 * X1 * X2^-1 * X1^-1)^2, (X2^-1 * X1^-1)^6, (X2 * X1^-1 * X2^-1 * X1^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 169, 2, 170, 4, 172)(3, 171, 8, 176, 9, 177)(5, 173, 12, 180, 13, 181)(6, 174, 14, 182, 15, 183)(7, 175, 16, 184, 17, 185)(10, 178, 22, 190, 23, 191)(11, 179, 24, 192, 25, 193)(18, 186, 38, 206, 39, 207)(19, 187, 40, 208, 41, 209)(20, 188, 42, 210, 43, 211)(21, 189, 44, 212, 45, 213)(26, 194, 54, 222, 55, 223)(27, 195, 56, 224, 57, 225)(28, 196, 58, 226, 59, 227)(29, 197, 60, 228, 61, 229)(30, 198, 62, 230, 63, 231)(31, 199, 64, 232, 65, 233)(32, 200, 66, 234, 67, 235)(33, 201, 68, 236, 69, 237)(34, 202, 70, 238, 71, 239)(35, 203, 72, 240, 73, 241)(36, 204, 74, 242, 75, 243)(37, 205, 76, 244, 77, 245)(46, 214, 92, 260, 80, 248)(47, 215, 93, 261, 94, 262)(48, 216, 95, 263, 96, 264)(49, 217, 97, 265, 98, 266)(50, 218, 85, 253, 99, 267)(51, 219, 100, 268, 101, 269)(52, 220, 89, 257, 102, 270)(53, 221, 103, 271, 104, 272)(78, 246, 130, 298, 106, 274)(79, 247, 134, 302, 135, 303)(81, 249, 136, 304, 120, 288)(82, 250, 137, 305, 122, 290)(83, 251, 138, 306, 123, 291)(84, 252, 133, 301, 107, 275)(86, 254, 139, 307, 140, 308)(87, 255, 141, 309, 142, 310)(88, 256, 111, 279, 131, 299)(90, 258, 114, 282, 118, 286)(91, 259, 143, 311, 121, 289)(105, 273, 152, 320, 127, 295)(108, 276, 153, 321, 154, 322)(109, 277, 155, 323, 117, 285)(110, 278, 148, 316, 144, 312)(112, 280, 156, 324, 157, 325)(113, 281, 149, 317, 125, 293)(115, 283, 126, 294, 116, 284)(119, 287, 158, 326, 147, 315)(124, 292, 159, 327, 146, 314)(128, 296, 160, 328, 161, 329)(129, 297, 162, 330, 145, 313)(132, 300, 163, 331, 164, 332)(150, 318, 166, 334, 165, 333)(151, 319, 167, 335, 168, 336) L = (1, 171)(2, 174)(3, 173)(4, 178)(5, 169)(6, 175)(7, 170)(8, 186)(9, 188)(10, 179)(11, 172)(12, 194)(13, 196)(14, 198)(15, 200)(16, 202)(17, 204)(18, 187)(19, 176)(20, 189)(21, 177)(22, 214)(23, 216)(24, 218)(25, 220)(26, 195)(27, 180)(28, 197)(29, 181)(30, 199)(31, 182)(32, 201)(33, 183)(34, 203)(35, 184)(36, 205)(37, 185)(38, 246)(39, 231)(40, 249)(41, 251)(42, 252)(43, 254)(44, 256)(45, 258)(46, 215)(47, 190)(48, 217)(49, 191)(50, 219)(51, 192)(52, 221)(53, 193)(54, 234)(55, 274)(56, 276)(57, 278)(58, 236)(59, 280)(60, 262)(61, 269)(62, 284)(63, 248)(64, 286)(65, 288)(66, 273)(67, 289)(68, 279)(69, 291)(70, 263)(71, 294)(72, 296)(73, 298)(74, 265)(75, 300)(76, 209)(77, 225)(78, 247)(79, 206)(80, 207)(81, 250)(82, 208)(83, 244)(84, 253)(85, 210)(86, 255)(87, 211)(88, 257)(89, 212)(90, 259)(91, 213)(92, 312)(93, 306)(94, 282)(95, 293)(96, 314)(97, 299)(98, 304)(99, 316)(100, 318)(101, 283)(102, 319)(103, 233)(104, 241)(105, 222)(106, 275)(107, 223)(108, 277)(109, 224)(110, 245)(111, 226)(112, 281)(113, 227)(114, 228)(115, 229)(116, 285)(117, 230)(118, 287)(119, 232)(120, 271)(121, 290)(122, 235)(123, 292)(124, 237)(125, 238)(126, 295)(127, 239)(128, 297)(129, 240)(130, 272)(131, 242)(132, 301)(133, 243)(134, 268)(135, 322)(136, 307)(137, 328)(138, 309)(139, 266)(140, 330)(141, 261)(142, 321)(143, 303)(144, 313)(145, 260)(146, 315)(147, 264)(148, 317)(149, 267)(150, 302)(151, 320)(152, 270)(153, 324)(154, 311)(155, 329)(156, 310)(157, 332)(158, 334)(159, 323)(160, 331)(161, 327)(162, 333)(163, 305)(164, 336)(165, 308)(166, 335)(167, 326)(168, 325) local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E15.1341 Transitivity :: ET+ VT+ Graph:: simple v = 56 e = 168 f = 84 degree seq :: [ 6^56 ] E15.1343 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 6}) Quotient :: loop Aut^+ = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) Aut = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) |r| :: 1 Presentation :: [ X1^3, X2^3, X2 * X1 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2^-1 * X1^-1, X2 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1, X2 * X1^-1 * X2^-1 * X1^-1 * X2 * X1 * X2 * X1 * X2^-1 * X1^-1, (X2^-1 * X1^-1)^6, (X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1)^2, (X2 * X1 * X2 * X1^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 169, 2, 170, 4, 172)(3, 171, 8, 176, 9, 177)(5, 173, 12, 180, 13, 181)(6, 174, 14, 182, 15, 183)(7, 175, 16, 184, 17, 185)(10, 178, 22, 190, 23, 191)(11, 179, 24, 192, 25, 193)(18, 186, 38, 206, 39, 207)(19, 187, 40, 208, 41, 209)(20, 188, 42, 210, 43, 211)(21, 189, 44, 212, 45, 213)(26, 194, 54, 222, 55, 223)(27, 195, 56, 224, 57, 225)(28, 196, 58, 226, 59, 227)(29, 197, 60, 228, 61, 229)(30, 198, 62, 230, 63, 231)(31, 199, 64, 232, 65, 233)(32, 200, 66, 234, 67, 235)(33, 201, 68, 236, 69, 237)(34, 202, 70, 238, 71, 239)(35, 203, 72, 240, 73, 241)(36, 204, 74, 242, 75, 243)(37, 205, 76, 244, 77, 245)(46, 214, 81, 249, 92, 260)(47, 215, 93, 261, 94, 262)(48, 216, 95, 263, 96, 264)(49, 217, 97, 265, 91, 259)(50, 218, 83, 251, 98, 266)(51, 219, 99, 267, 100, 268)(52, 220, 101, 269, 102, 270)(53, 221, 103, 271, 104, 272)(78, 246, 134, 302, 135, 303)(79, 247, 131, 299, 136, 304)(80, 248, 120, 288, 114, 282)(82, 250, 133, 301, 122, 290)(84, 252, 124, 292, 137, 305)(85, 253, 107, 275, 138, 306)(86, 254, 139, 307, 140, 308)(87, 255, 141, 309, 142, 310)(88, 256, 116, 284, 115, 283)(89, 257, 109, 277, 130, 298)(90, 258, 143, 311, 125, 293)(105, 273, 149, 317, 153, 321)(106, 274, 123, 291, 128, 296)(108, 276, 154, 322, 155, 323)(110, 278, 119, 287, 126, 294)(111, 279, 148, 316, 152, 320)(112, 280, 156, 324, 117, 285)(113, 281, 157, 325, 144, 312)(118, 286, 146, 314, 132, 300)(121, 289, 158, 326, 159, 327)(127, 295, 160, 328, 161, 329)(129, 297, 145, 313, 150, 318)(147, 315, 164, 332, 163, 331)(151, 319, 165, 333, 166, 334)(162, 330, 167, 335, 168, 336) L = (1, 171)(2, 174)(3, 173)(4, 178)(5, 169)(6, 175)(7, 170)(8, 186)(9, 188)(10, 179)(11, 172)(12, 194)(13, 196)(14, 198)(15, 200)(16, 202)(17, 204)(18, 187)(19, 176)(20, 189)(21, 177)(22, 214)(23, 216)(24, 218)(25, 220)(26, 195)(27, 180)(28, 197)(29, 181)(30, 199)(31, 182)(32, 201)(33, 183)(34, 203)(35, 184)(36, 205)(37, 185)(38, 246)(39, 247)(40, 249)(41, 251)(42, 253)(43, 255)(44, 257)(45, 237)(46, 215)(47, 190)(48, 217)(49, 191)(50, 219)(51, 192)(52, 221)(53, 193)(54, 273)(55, 274)(56, 275)(57, 277)(58, 239)(59, 280)(60, 243)(61, 282)(62, 284)(63, 285)(64, 206)(65, 222)(66, 287)(67, 289)(68, 291)(69, 259)(70, 293)(71, 279)(72, 294)(73, 296)(74, 266)(75, 281)(76, 270)(77, 300)(78, 232)(79, 248)(80, 207)(81, 250)(82, 208)(83, 252)(84, 209)(85, 254)(86, 210)(87, 256)(88, 211)(89, 258)(90, 212)(91, 213)(92, 312)(93, 230)(94, 238)(95, 313)(96, 315)(97, 316)(98, 298)(99, 318)(100, 320)(101, 223)(102, 299)(103, 227)(104, 307)(105, 233)(106, 269)(107, 276)(108, 224)(109, 278)(110, 225)(111, 226)(112, 271)(113, 228)(114, 283)(115, 229)(116, 261)(117, 286)(118, 231)(119, 288)(120, 234)(121, 290)(122, 235)(123, 292)(124, 236)(125, 262)(126, 295)(127, 240)(128, 297)(129, 241)(130, 242)(131, 244)(132, 301)(133, 245)(134, 272)(135, 264)(136, 330)(137, 331)(138, 268)(139, 302)(140, 260)(141, 326)(142, 328)(143, 327)(144, 308)(145, 314)(146, 263)(147, 303)(148, 317)(149, 265)(150, 319)(151, 267)(152, 306)(153, 310)(154, 305)(155, 304)(156, 335)(157, 336)(158, 332)(159, 333)(160, 321)(161, 324)(162, 323)(163, 322)(164, 309)(165, 311)(166, 325)(167, 329)(168, 334) local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E15.1340 Transitivity :: ET+ VT+ Graph:: simple v = 56 e = 168 f = 84 degree seq :: [ 6^56 ] E15.1344 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 6}) Quotient :: loop Aut^+ = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) Aut = ((C2 x C2 x C2) : C7) : C3 (small group id <168, 43>) |r| :: 1 Presentation :: [ X2^3, (X1^-1 * X2^-1)^3, X1^6, X1^-1 * X2 * X1^2 * X2^-1 * X1^-2 * X2 ] Map:: polyhedral non-degenerate R = (1, 169, 2, 170, 6, 174, 16, 184, 12, 180, 4, 172)(3, 171, 9, 177, 23, 191, 54, 222, 27, 195, 10, 178)(5, 173, 14, 182, 34, 202, 72, 240, 38, 206, 15, 183)(7, 175, 19, 187, 45, 213, 90, 258, 47, 215, 20, 188)(8, 176, 21, 189, 49, 217, 94, 262, 53, 221, 22, 190)(11, 179, 29, 197, 63, 231, 111, 279, 66, 234, 30, 198)(13, 181, 33, 201, 70, 238, 101, 269, 56, 224, 24, 192)(17, 185, 41, 209, 83, 251, 59, 227, 26, 194, 42, 210)(18, 186, 43, 211, 86, 254, 75, 243, 36, 204, 44, 212)(25, 193, 57, 225, 73, 241, 122, 290, 106, 274, 58, 226)(28, 196, 62, 230, 109, 277, 124, 292, 74, 242, 35, 203)(31, 199, 68, 236, 116, 284, 134, 302, 84, 252, 61, 229)(32, 200, 69, 237, 118, 286, 137, 305, 88, 256, 64, 232)(37, 205, 76, 244, 55, 223, 100, 268, 129, 297, 77, 245)(39, 207, 79, 247, 131, 299, 92, 260, 46, 214, 80, 248)(40, 208, 81, 249, 132, 300, 96, 264, 51, 219, 82, 250)(48, 216, 93, 261, 140, 308, 144, 312, 95, 263, 50, 218)(52, 220, 97, 265, 91, 259, 130, 298, 147, 315, 98, 266)(60, 228, 108, 276, 153, 321, 156, 324, 127, 295, 78, 246)(65, 233, 112, 280, 119, 287, 162, 330, 157, 325, 113, 281)(67, 235, 115, 283, 151, 319, 105, 273, 120, 288, 71, 239)(85, 253, 135, 303, 155, 323, 165, 333, 136, 304, 87, 255)(89, 257, 125, 293, 133, 301, 148, 316, 166, 334, 138, 306)(99, 267, 123, 291, 141, 309, 121, 289, 104, 272, 149, 317)(102, 270, 114, 282, 158, 326, 168, 336, 150, 318, 103, 271)(107, 275, 152, 320, 163, 331, 126, 294, 146, 314, 110, 278)(117, 285, 145, 313, 161, 329, 167, 335, 154, 322, 160, 328)(128, 296, 159, 327, 139, 307, 143, 311, 164, 332, 142, 310) L = (1, 171)(2, 175)(3, 173)(4, 179)(5, 169)(6, 185)(7, 176)(8, 170)(9, 192)(10, 194)(11, 181)(12, 199)(13, 172)(14, 203)(15, 205)(16, 207)(17, 186)(18, 174)(19, 183)(20, 214)(21, 218)(22, 220)(23, 223)(24, 193)(25, 177)(26, 196)(27, 228)(28, 178)(29, 232)(30, 215)(31, 200)(32, 180)(33, 239)(34, 231)(35, 204)(36, 182)(37, 187)(38, 237)(39, 208)(40, 184)(41, 190)(42, 252)(43, 255)(44, 257)(45, 259)(46, 216)(47, 235)(48, 188)(49, 191)(50, 219)(51, 189)(52, 209)(53, 201)(54, 264)(55, 217)(56, 249)(57, 271)(58, 273)(59, 269)(60, 229)(61, 195)(62, 278)(63, 241)(64, 233)(65, 197)(66, 282)(67, 198)(68, 250)(69, 246)(70, 284)(71, 221)(72, 289)(73, 202)(74, 291)(75, 294)(76, 295)(77, 292)(78, 206)(79, 212)(80, 234)(81, 270)(82, 285)(83, 301)(84, 253)(85, 210)(86, 213)(87, 256)(88, 211)(89, 247)(90, 305)(91, 254)(92, 240)(93, 309)(94, 310)(95, 311)(96, 267)(97, 288)(98, 312)(99, 222)(100, 226)(101, 275)(102, 224)(103, 272)(104, 225)(105, 268)(106, 230)(107, 227)(108, 317)(109, 321)(110, 274)(111, 243)(112, 304)(113, 324)(114, 248)(115, 327)(116, 287)(117, 236)(118, 299)(119, 238)(120, 314)(121, 260)(122, 281)(123, 293)(124, 298)(125, 242)(126, 279)(127, 296)(128, 244)(129, 261)(130, 245)(131, 329)(132, 251)(133, 300)(134, 262)(135, 332)(136, 320)(137, 307)(138, 333)(139, 258)(140, 319)(141, 297)(142, 302)(143, 313)(144, 316)(145, 263)(146, 265)(147, 303)(148, 266)(149, 322)(150, 330)(151, 336)(152, 280)(153, 323)(154, 276)(155, 277)(156, 290)(157, 283)(158, 331)(159, 325)(160, 318)(161, 286)(162, 328)(163, 334)(164, 315)(165, 335)(166, 326)(167, 306)(168, 308) local type(s) :: { ( 3^12 ) } Outer automorphisms :: chiral Dual of E15.1339 Transitivity :: ET+ VT+ Graph:: simple v = 28 e = 168 f = 112 degree seq :: [ 12^28 ] E15.1345 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 20}) Quotient :: regular Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^3, T1^3 * T2 * T1^-5 * T2 * T1^2, T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-2, T2 * T1^-2 * T2 * T1^3 * T2 * T1^3 * T2 * T1^-2 * T2 * T1^3, (T2 * T1^-3 * T2 * T1^-4)^2, T1^20 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 21, 37, 63, 99, 143, 195, 231, 230, 194, 142, 98, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 64, 101, 145, 197, 233, 240, 235, 222, 166, 118, 90, 54, 31, 17, 8)(6, 13, 25, 43, 73, 100, 79, 119, 167, 223, 239, 229, 193, 141, 97, 61, 78, 46, 26, 14)(9, 18, 32, 55, 66, 38, 65, 102, 146, 198, 232, 201, 182, 131, 89, 128, 85, 51, 29, 16)(12, 23, 41, 69, 106, 144, 111, 159, 213, 188, 228, 192, 140, 96, 59, 35, 60, 72, 42, 24)(19, 34, 58, 68, 40, 22, 39, 67, 103, 148, 196, 152, 206, 177, 127, 178, 137, 94, 57, 33)(28, 49, 82, 122, 171, 133, 91, 132, 183, 218, 236, 199, 181, 130, 87, 53, 88, 125, 83, 50)(30, 52, 86, 121, 81, 48, 80, 120, 168, 225, 234, 221, 165, 116, 77, 117, 163, 114, 75, 44)(45, 76, 115, 161, 113, 74, 112, 160, 214, 191, 224, 170, 212, 157, 110, 158, 210, 155, 108, 70)(56, 92, 134, 184, 200, 147, 105, 151, 205, 175, 203, 149, 202, 173, 123, 84, 126, 176, 135, 93)(71, 109, 156, 208, 154, 107, 153, 207, 185, 136, 187, 216, 190, 139, 95, 138, 189, 204, 150, 104)(124, 174, 220, 164, 219, 172, 226, 237, 215, 162, 217, 186, 211, 180, 129, 179, 227, 238, 209, 169) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 79)(50, 80)(51, 84)(52, 87)(54, 89)(55, 91)(57, 92)(58, 95)(60, 97)(62, 90)(63, 100)(66, 101)(67, 104)(68, 105)(69, 107)(72, 110)(73, 111)(75, 112)(76, 116)(78, 118)(81, 119)(82, 123)(83, 124)(85, 127)(86, 129)(88, 131)(93, 132)(94, 136)(96, 138)(98, 128)(99, 144)(102, 147)(103, 149)(106, 152)(108, 153)(109, 157)(113, 159)(114, 162)(115, 164)(117, 166)(120, 169)(121, 170)(122, 172)(125, 175)(126, 177)(130, 179)(133, 145)(134, 185)(135, 186)(137, 188)(139, 151)(140, 191)(141, 158)(142, 178)(143, 196)(146, 199)(148, 201)(150, 202)(154, 206)(155, 209)(156, 211)(160, 215)(161, 216)(163, 218)(165, 219)(167, 224)(168, 210)(171, 221)(173, 226)(174, 205)(176, 208)(180, 212)(181, 200)(182, 203)(183, 217)(184, 227)(187, 213)(189, 214)(190, 220)(192, 223)(193, 225)(194, 228)(195, 232)(197, 234)(198, 235)(204, 237)(207, 238)(222, 236)(229, 233)(230, 239)(231, 240) local type(s) :: { ( 3^20 ) } Outer automorphisms :: reflexible Dual of E15.1346 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 12 e = 120 f = 80 degree seq :: [ 20^12 ] E15.1346 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 20}) Quotient :: regular Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(59, 83, 84)(60, 85, 86)(61, 87, 88)(62, 89, 90)(63, 91, 92)(64, 93, 94)(65, 95, 96)(66, 97, 98)(75, 107, 108)(76, 109, 110)(77, 111, 112)(78, 113, 114)(79, 115, 116)(80, 117, 118)(81, 119, 120)(82, 121, 122)(99, 139, 140)(100, 141, 142)(101, 143, 144)(102, 145, 146)(103, 147, 148)(104, 149, 150)(105, 151, 152)(106, 153, 154)(123, 155, 171)(124, 172, 173)(125, 174, 166)(126, 175, 176)(127, 177, 168)(128, 178, 160)(129, 179, 164)(130, 180, 181)(131, 156, 182)(132, 183, 184)(133, 185, 165)(134, 186, 187)(135, 158, 188)(136, 189, 190)(137, 162, 191)(138, 170, 192)(157, 199, 197)(159, 200, 198)(161, 201, 196)(163, 193, 202)(167, 194, 203)(169, 195, 204)(205, 223, 215)(206, 224, 216)(207, 221, 214)(208, 211, 225)(209, 212, 219)(210, 213, 226)(217, 227, 222)(218, 220, 228)(229, 235, 232)(230, 231, 236)(233, 234, 237)(238, 239, 240) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(139, 171)(140, 193)(141, 186)(142, 194)(143, 189)(144, 178)(145, 183)(146, 195)(147, 173)(148, 196)(149, 185)(150, 197)(151, 176)(152, 198)(153, 181)(154, 192)(172, 205)(174, 206)(175, 207)(177, 208)(179, 209)(180, 210)(182, 211)(184, 212)(187, 213)(188, 214)(190, 215)(191, 216)(199, 217)(200, 218)(201, 219)(202, 220)(203, 221)(204, 222)(223, 229)(224, 230)(225, 231)(226, 232)(227, 233)(228, 234)(235, 238)(236, 239)(237, 240) local type(s) :: { ( 20^3 ) } Outer automorphisms :: reflexible Dual of E15.1345 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 80 e = 120 f = 12 degree seq :: [ 3^80 ] E15.1347 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 20}) Quotient :: edge Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2)^2, T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 59, 60)(44, 61, 62)(45, 63, 64)(46, 65, 66)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(51, 75, 76)(52, 77, 78)(53, 79, 80)(54, 81, 82)(55, 83, 84)(56, 85, 86)(57, 87, 88)(58, 89, 90)(91, 123, 124)(92, 125, 126)(93, 127, 128)(94, 129, 130)(95, 131, 132)(96, 133, 134)(97, 135, 136)(98, 137, 138)(99, 139, 140)(100, 141, 142)(101, 143, 144)(102, 145, 146)(103, 147, 148)(104, 149, 150)(105, 151, 152)(106, 153, 154)(107, 155, 156)(108, 157, 158)(109, 159, 160)(110, 161, 162)(111, 163, 164)(112, 165, 166)(113, 167, 168)(114, 169, 170)(115, 171, 172)(116, 173, 174)(117, 175, 176)(118, 177, 178)(119, 179, 180)(120, 181, 182)(121, 183, 184)(122, 185, 186)(187, 211, 197)(188, 212, 198)(189, 213, 196)(190, 193, 214)(191, 194, 215)(192, 195, 216)(199, 217, 209)(200, 218, 210)(201, 219, 208)(202, 205, 220)(203, 206, 221)(204, 207, 222)(223, 231, 226)(224, 225, 232)(227, 233, 230)(228, 229, 234)(235, 236, 239)(237, 238, 240)(241, 242)(243, 247)(244, 248)(245, 249)(246, 250)(251, 259)(252, 260)(253, 261)(254, 262)(255, 263)(256, 264)(257, 265)(258, 266)(267, 283)(268, 284)(269, 285)(270, 286)(271, 287)(272, 288)(273, 289)(274, 290)(275, 291)(276, 292)(277, 293)(278, 294)(279, 295)(280, 296)(281, 297)(282, 298)(299, 331)(300, 332)(301, 333)(302, 334)(303, 335)(304, 336)(305, 337)(306, 338)(307, 339)(308, 340)(309, 341)(310, 342)(311, 343)(312, 344)(313, 345)(314, 346)(315, 347)(316, 348)(317, 349)(318, 350)(319, 351)(320, 352)(321, 353)(322, 354)(323, 355)(324, 356)(325, 357)(326, 358)(327, 359)(328, 360)(329, 361)(330, 362)(363, 395)(364, 411)(365, 427)(366, 419)(367, 428)(368, 406)(369, 429)(370, 423)(371, 430)(372, 408)(373, 416)(374, 400)(375, 431)(376, 404)(377, 432)(378, 425)(379, 396)(380, 433)(381, 417)(382, 434)(383, 421)(384, 405)(385, 413)(386, 435)(387, 398)(388, 436)(389, 415)(390, 437)(391, 402)(392, 438)(393, 410)(394, 426)(397, 439)(399, 440)(401, 441)(403, 442)(407, 443)(409, 444)(412, 445)(414, 446)(418, 447)(420, 448)(422, 449)(424, 450)(451, 463)(452, 464)(453, 461)(454, 465)(455, 459)(456, 466)(457, 467)(458, 468)(460, 469)(462, 470)(471, 475)(472, 476)(473, 477)(474, 478)(479, 480) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 40, 40 ), ( 40^3 ) } Outer automorphisms :: reflexible Dual of E15.1351 Transitivity :: ET+ Graph:: simple bipartite v = 200 e = 240 f = 12 degree seq :: [ 2^120, 3^80 ] E15.1348 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 20}) Quotient :: edge Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^2 * T1^-1 * T2^-6 * T1^-1 * T2^2, (T2^3 * T1^-1 * T2^2 * T1^-1)^2, T1^-1 * T2^4 * T1^-1 * T2^14 ] Map:: polytopal non-degenerate R = (1, 3, 9, 19, 37, 67, 116, 175, 223, 237, 240, 235, 214, 160, 101, 86, 48, 26, 13, 5)(2, 6, 14, 27, 50, 89, 68, 118, 176, 224, 238, 236, 219, 166, 107, 102, 58, 32, 16, 7)(4, 11, 22, 41, 74, 117, 90, 145, 203, 232, 239, 230, 198, 141, 85, 108, 62, 34, 17, 8)(10, 21, 40, 71, 123, 127, 75, 128, 186, 226, 229, 197, 140, 84, 47, 83, 112, 64, 35, 18)(12, 23, 43, 77, 115, 66, 38, 69, 119, 177, 225, 213, 159, 100, 57, 99, 136, 80, 44, 24)(15, 29, 53, 93, 144, 88, 51, 91, 146, 204, 233, 218, 165, 106, 61, 105, 155, 96, 54, 30)(20, 39, 70, 120, 179, 182, 124, 183, 135, 193, 196, 139, 82, 46, 25, 45, 81, 114, 65, 36)(28, 52, 92, 147, 206, 174, 131, 190, 154, 211, 212, 158, 98, 56, 31, 55, 97, 143, 87, 49)(33, 59, 103, 161, 126, 73, 42, 76, 129, 187, 227, 202, 150, 170, 111, 169, 217, 164, 104, 60)(63, 109, 167, 220, 181, 122, 72, 125, 184, 138, 195, 185, 216, 222, 173, 137, 194, 188, 168, 110)(78, 132, 191, 157, 172, 113, 171, 221, 201, 156, 178, 121, 180, 134, 79, 133, 192, 228, 189, 130)(94, 151, 209, 163, 200, 142, 199, 231, 215, 162, 205, 148, 207, 153, 95, 152, 210, 234, 208, 149)(241, 242, 244)(243, 248, 250)(245, 252, 246)(247, 255, 251)(249, 258, 260)(253, 265, 263)(254, 264, 268)(256, 271, 269)(257, 273, 261)(259, 276, 278)(262, 270, 282)(266, 287, 285)(267, 289, 291)(272, 297, 295)(274, 301, 299)(275, 303, 279)(277, 306, 308)(280, 300, 312)(281, 313, 315)(283, 286, 318)(284, 319, 292)(288, 325, 323)(290, 328, 330)(293, 296, 334)(294, 335, 316)(298, 341, 339)(302, 347, 345)(304, 351, 349)(305, 353, 309)(307, 329, 357)(310, 350, 361)(311, 362, 364)(314, 367, 356)(317, 370, 371)(320, 375, 373)(321, 324, 377)(322, 378, 372)(326, 342, 348)(327, 382, 331)(332, 374, 388)(333, 389, 390)(336, 394, 392)(337, 340, 396)(338, 397, 391)(343, 346, 402)(344, 403, 365)(352, 381, 409)(354, 413, 411)(355, 414, 358)(359, 412, 398)(360, 418, 399)(363, 422, 415)(366, 425, 368)(369, 393, 428)(376, 400, 433)(379, 426, 435)(380, 427, 434)(383, 441, 439)(384, 442, 385)(386, 440, 404)(387, 445, 405)(395, 406, 451)(401, 455, 456)(407, 410, 448)(408, 447, 420)(416, 446, 458)(417, 452, 459)(419, 453, 463)(421, 432, 423)(424, 449, 431)(429, 450, 430)(436, 454, 466)(437, 443, 467)(438, 444, 457)(460, 474, 468)(461, 462, 471)(464, 473, 470)(465, 476, 477)(469, 475, 472)(478, 479, 480) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4^3 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E15.1352 Transitivity :: ET+ Graph:: simple bipartite v = 92 e = 240 f = 120 degree seq :: [ 3^80, 20^12 ] E15.1349 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 20}) Quotient :: edge Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^-2 * T2 * T1^5 * T2 * T1^-3, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3, T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^3, T1^20 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 79)(50, 80)(51, 84)(52, 87)(54, 89)(55, 91)(57, 92)(58, 95)(60, 97)(62, 90)(63, 100)(66, 101)(67, 104)(68, 105)(69, 107)(72, 110)(73, 111)(75, 112)(76, 116)(78, 118)(81, 119)(82, 123)(83, 124)(85, 127)(86, 129)(88, 131)(93, 132)(94, 136)(96, 138)(98, 128)(99, 144)(102, 147)(103, 149)(106, 152)(108, 153)(109, 157)(113, 159)(114, 162)(115, 164)(117, 166)(120, 169)(121, 170)(122, 172)(125, 175)(126, 177)(130, 179)(133, 145)(134, 185)(135, 186)(137, 188)(139, 151)(140, 191)(141, 158)(142, 178)(143, 196)(146, 199)(148, 201)(150, 202)(154, 206)(155, 209)(156, 211)(160, 215)(161, 216)(163, 218)(165, 219)(167, 224)(168, 210)(171, 221)(173, 226)(174, 205)(176, 208)(180, 212)(181, 200)(182, 203)(183, 217)(184, 227)(187, 213)(189, 214)(190, 220)(192, 223)(193, 225)(194, 228)(195, 232)(197, 234)(198, 235)(204, 237)(207, 238)(222, 236)(229, 233)(230, 239)(231, 240)(241, 242, 245, 251, 261, 277, 303, 339, 383, 435, 471, 470, 434, 382, 338, 302, 276, 260, 250, 244)(243, 247, 255, 267, 287, 304, 341, 385, 437, 473, 480, 475, 462, 406, 358, 330, 294, 271, 257, 248)(246, 253, 265, 283, 313, 340, 319, 359, 407, 463, 479, 469, 433, 381, 337, 301, 318, 286, 266, 254)(249, 258, 272, 295, 306, 278, 305, 342, 386, 438, 472, 441, 422, 371, 329, 368, 325, 291, 269, 256)(252, 263, 281, 309, 346, 384, 351, 399, 453, 428, 468, 432, 380, 336, 299, 275, 300, 312, 282, 264)(259, 274, 298, 308, 280, 262, 279, 307, 343, 388, 436, 392, 446, 417, 367, 418, 377, 334, 297, 273)(268, 289, 322, 362, 411, 373, 331, 372, 423, 458, 476, 439, 421, 370, 327, 293, 328, 365, 323, 290)(270, 292, 326, 361, 321, 288, 320, 360, 408, 465, 474, 461, 405, 356, 317, 357, 403, 354, 315, 284)(285, 316, 355, 401, 353, 314, 352, 400, 454, 431, 464, 410, 452, 397, 350, 398, 450, 395, 348, 310)(296, 332, 374, 424, 440, 387, 345, 391, 445, 415, 443, 389, 442, 413, 363, 324, 366, 416, 375, 333)(311, 349, 396, 448, 394, 347, 393, 447, 425, 376, 427, 456, 430, 379, 335, 378, 429, 444, 390, 344)(364, 414, 460, 404, 459, 412, 466, 477, 455, 402, 457, 426, 451, 420, 369, 419, 467, 478, 449, 409) L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 6 ), ( 6^20 ) } Outer automorphisms :: reflexible Dual of E15.1350 Transitivity :: ET+ Graph:: simple bipartite v = 132 e = 240 f = 80 degree seq :: [ 2^120, 20^12 ] E15.1350 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 20}) Quotient :: loop Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2)^2, T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 ] Map:: R = (1, 241, 3, 243, 4, 244)(2, 242, 5, 245, 6, 246)(7, 247, 11, 251, 12, 252)(8, 248, 13, 253, 14, 254)(9, 249, 15, 255, 16, 256)(10, 250, 17, 257, 18, 258)(19, 259, 27, 267, 28, 268)(20, 260, 29, 269, 30, 270)(21, 261, 31, 271, 32, 272)(22, 262, 33, 273, 34, 274)(23, 263, 35, 275, 36, 276)(24, 264, 37, 277, 38, 278)(25, 265, 39, 279, 40, 280)(26, 266, 41, 281, 42, 282)(43, 283, 59, 299, 60, 300)(44, 284, 61, 301, 62, 302)(45, 285, 63, 303, 64, 304)(46, 286, 65, 305, 66, 306)(47, 287, 67, 307, 68, 308)(48, 288, 69, 309, 70, 310)(49, 289, 71, 311, 72, 312)(50, 290, 73, 313, 74, 314)(51, 291, 75, 315, 76, 316)(52, 292, 77, 317, 78, 318)(53, 293, 79, 319, 80, 320)(54, 294, 81, 321, 82, 322)(55, 295, 83, 323, 84, 324)(56, 296, 85, 325, 86, 326)(57, 297, 87, 327, 88, 328)(58, 298, 89, 329, 90, 330)(91, 331, 123, 363, 124, 364)(92, 332, 125, 365, 126, 366)(93, 333, 127, 367, 128, 368)(94, 334, 129, 369, 130, 370)(95, 335, 131, 371, 132, 372)(96, 336, 133, 373, 134, 374)(97, 337, 135, 375, 136, 376)(98, 338, 137, 377, 138, 378)(99, 339, 139, 379, 140, 380)(100, 340, 141, 381, 142, 382)(101, 341, 143, 383, 144, 384)(102, 342, 145, 385, 146, 386)(103, 343, 147, 387, 148, 388)(104, 344, 149, 389, 150, 390)(105, 345, 151, 391, 152, 392)(106, 346, 153, 393, 154, 394)(107, 347, 155, 395, 156, 396)(108, 348, 157, 397, 158, 398)(109, 349, 159, 399, 160, 400)(110, 350, 161, 401, 162, 402)(111, 351, 163, 403, 164, 404)(112, 352, 165, 405, 166, 406)(113, 353, 167, 407, 168, 408)(114, 354, 169, 409, 170, 410)(115, 355, 171, 411, 172, 412)(116, 356, 173, 413, 174, 414)(117, 357, 175, 415, 176, 416)(118, 358, 177, 417, 178, 418)(119, 359, 179, 419, 180, 420)(120, 360, 181, 421, 182, 422)(121, 361, 183, 423, 184, 424)(122, 362, 185, 425, 186, 426)(187, 427, 211, 451, 197, 437)(188, 428, 212, 452, 198, 438)(189, 429, 213, 453, 196, 436)(190, 430, 193, 433, 214, 454)(191, 431, 194, 434, 215, 455)(192, 432, 195, 435, 216, 456)(199, 439, 217, 457, 209, 449)(200, 440, 218, 458, 210, 450)(201, 441, 219, 459, 208, 448)(202, 442, 205, 445, 220, 460)(203, 443, 206, 446, 221, 461)(204, 444, 207, 447, 222, 462)(223, 463, 231, 471, 226, 466)(224, 464, 225, 465, 232, 472)(227, 467, 233, 473, 230, 470)(228, 468, 229, 469, 234, 474)(235, 475, 236, 476, 239, 479)(237, 477, 238, 478, 240, 480) L = (1, 242)(2, 241)(3, 247)(4, 248)(5, 249)(6, 250)(7, 243)(8, 244)(9, 245)(10, 246)(11, 259)(12, 260)(13, 261)(14, 262)(15, 263)(16, 264)(17, 265)(18, 266)(19, 251)(20, 252)(21, 253)(22, 254)(23, 255)(24, 256)(25, 257)(26, 258)(27, 283)(28, 284)(29, 285)(30, 286)(31, 287)(32, 288)(33, 289)(34, 290)(35, 291)(36, 292)(37, 293)(38, 294)(39, 295)(40, 296)(41, 297)(42, 298)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 331)(60, 332)(61, 333)(62, 334)(63, 335)(64, 336)(65, 337)(66, 338)(67, 339)(68, 340)(69, 341)(70, 342)(71, 343)(72, 344)(73, 345)(74, 346)(75, 347)(76, 348)(77, 349)(78, 350)(79, 351)(80, 352)(81, 353)(82, 354)(83, 355)(84, 356)(85, 357)(86, 358)(87, 359)(88, 360)(89, 361)(90, 362)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 395)(124, 411)(125, 427)(126, 419)(127, 428)(128, 406)(129, 429)(130, 423)(131, 430)(132, 408)(133, 416)(134, 400)(135, 431)(136, 404)(137, 432)(138, 425)(139, 396)(140, 433)(141, 417)(142, 434)(143, 421)(144, 405)(145, 413)(146, 435)(147, 398)(148, 436)(149, 415)(150, 437)(151, 402)(152, 438)(153, 410)(154, 426)(155, 363)(156, 379)(157, 439)(158, 387)(159, 440)(160, 374)(161, 441)(162, 391)(163, 442)(164, 376)(165, 384)(166, 368)(167, 443)(168, 372)(169, 444)(170, 393)(171, 364)(172, 445)(173, 385)(174, 446)(175, 389)(176, 373)(177, 381)(178, 447)(179, 366)(180, 448)(181, 383)(182, 449)(183, 370)(184, 450)(185, 378)(186, 394)(187, 365)(188, 367)(189, 369)(190, 371)(191, 375)(192, 377)(193, 380)(194, 382)(195, 386)(196, 388)(197, 390)(198, 392)(199, 397)(200, 399)(201, 401)(202, 403)(203, 407)(204, 409)(205, 412)(206, 414)(207, 418)(208, 420)(209, 422)(210, 424)(211, 463)(212, 464)(213, 461)(214, 465)(215, 459)(216, 466)(217, 467)(218, 468)(219, 455)(220, 469)(221, 453)(222, 470)(223, 451)(224, 452)(225, 454)(226, 456)(227, 457)(228, 458)(229, 460)(230, 462)(231, 475)(232, 476)(233, 477)(234, 478)(235, 471)(236, 472)(237, 473)(238, 474)(239, 480)(240, 479) local type(s) :: { ( 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E15.1349 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 80 e = 240 f = 132 degree seq :: [ 6^80 ] E15.1351 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 20}) Quotient :: loop Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T2^2 * T1^-1 * T2^-6 * T1^-1 * T2^2, (T2^3 * T1^-1 * T2^2 * T1^-1)^2, T1^-1 * T2^4 * T1^-1 * T2^14 ] Map:: R = (1, 241, 3, 243, 9, 249, 19, 259, 37, 277, 67, 307, 116, 356, 175, 415, 223, 463, 237, 477, 240, 480, 235, 475, 214, 454, 160, 400, 101, 341, 86, 326, 48, 288, 26, 266, 13, 253, 5, 245)(2, 242, 6, 246, 14, 254, 27, 267, 50, 290, 89, 329, 68, 308, 118, 358, 176, 416, 224, 464, 238, 478, 236, 476, 219, 459, 166, 406, 107, 347, 102, 342, 58, 298, 32, 272, 16, 256, 7, 247)(4, 244, 11, 251, 22, 262, 41, 281, 74, 314, 117, 357, 90, 330, 145, 385, 203, 443, 232, 472, 239, 479, 230, 470, 198, 438, 141, 381, 85, 325, 108, 348, 62, 302, 34, 274, 17, 257, 8, 248)(10, 250, 21, 261, 40, 280, 71, 311, 123, 363, 127, 367, 75, 315, 128, 368, 186, 426, 226, 466, 229, 469, 197, 437, 140, 380, 84, 324, 47, 287, 83, 323, 112, 352, 64, 304, 35, 275, 18, 258)(12, 252, 23, 263, 43, 283, 77, 317, 115, 355, 66, 306, 38, 278, 69, 309, 119, 359, 177, 417, 225, 465, 213, 453, 159, 399, 100, 340, 57, 297, 99, 339, 136, 376, 80, 320, 44, 284, 24, 264)(15, 255, 29, 269, 53, 293, 93, 333, 144, 384, 88, 328, 51, 291, 91, 331, 146, 386, 204, 444, 233, 473, 218, 458, 165, 405, 106, 346, 61, 301, 105, 345, 155, 395, 96, 336, 54, 294, 30, 270)(20, 260, 39, 279, 70, 310, 120, 360, 179, 419, 182, 422, 124, 364, 183, 423, 135, 375, 193, 433, 196, 436, 139, 379, 82, 322, 46, 286, 25, 265, 45, 285, 81, 321, 114, 354, 65, 305, 36, 276)(28, 268, 52, 292, 92, 332, 147, 387, 206, 446, 174, 414, 131, 371, 190, 430, 154, 394, 211, 451, 212, 452, 158, 398, 98, 338, 56, 296, 31, 271, 55, 295, 97, 337, 143, 383, 87, 327, 49, 289)(33, 273, 59, 299, 103, 343, 161, 401, 126, 366, 73, 313, 42, 282, 76, 316, 129, 369, 187, 427, 227, 467, 202, 442, 150, 390, 170, 410, 111, 351, 169, 409, 217, 457, 164, 404, 104, 344, 60, 300)(63, 303, 109, 349, 167, 407, 220, 460, 181, 421, 122, 362, 72, 312, 125, 365, 184, 424, 138, 378, 195, 435, 185, 425, 216, 456, 222, 462, 173, 413, 137, 377, 194, 434, 188, 428, 168, 408, 110, 350)(78, 318, 132, 372, 191, 431, 157, 397, 172, 412, 113, 353, 171, 411, 221, 461, 201, 441, 156, 396, 178, 418, 121, 361, 180, 420, 134, 374, 79, 319, 133, 373, 192, 432, 228, 468, 189, 429, 130, 370)(94, 334, 151, 391, 209, 449, 163, 403, 200, 440, 142, 382, 199, 439, 231, 471, 215, 455, 162, 402, 205, 445, 148, 388, 207, 447, 153, 393, 95, 335, 152, 392, 210, 450, 234, 474, 208, 448, 149, 389) L = (1, 242)(2, 244)(3, 248)(4, 241)(5, 252)(6, 245)(7, 255)(8, 250)(9, 258)(10, 243)(11, 247)(12, 246)(13, 265)(14, 264)(15, 251)(16, 271)(17, 273)(18, 260)(19, 276)(20, 249)(21, 257)(22, 270)(23, 253)(24, 268)(25, 263)(26, 287)(27, 289)(28, 254)(29, 256)(30, 282)(31, 269)(32, 297)(33, 261)(34, 301)(35, 303)(36, 278)(37, 306)(38, 259)(39, 275)(40, 300)(41, 313)(42, 262)(43, 286)(44, 319)(45, 266)(46, 318)(47, 285)(48, 325)(49, 291)(50, 328)(51, 267)(52, 284)(53, 296)(54, 335)(55, 272)(56, 334)(57, 295)(58, 341)(59, 274)(60, 312)(61, 299)(62, 347)(63, 279)(64, 351)(65, 353)(66, 308)(67, 329)(68, 277)(69, 305)(70, 350)(71, 362)(72, 280)(73, 315)(74, 367)(75, 281)(76, 294)(77, 370)(78, 283)(79, 292)(80, 375)(81, 324)(82, 378)(83, 288)(84, 377)(85, 323)(86, 342)(87, 382)(88, 330)(89, 357)(90, 290)(91, 327)(92, 374)(93, 389)(94, 293)(95, 316)(96, 394)(97, 340)(98, 397)(99, 298)(100, 396)(101, 339)(102, 348)(103, 346)(104, 403)(105, 302)(106, 402)(107, 345)(108, 326)(109, 304)(110, 361)(111, 349)(112, 381)(113, 309)(114, 413)(115, 414)(116, 314)(117, 307)(118, 355)(119, 412)(120, 418)(121, 310)(122, 364)(123, 422)(124, 311)(125, 344)(126, 425)(127, 356)(128, 366)(129, 393)(130, 371)(131, 317)(132, 322)(133, 320)(134, 388)(135, 373)(136, 400)(137, 321)(138, 372)(139, 426)(140, 427)(141, 409)(142, 331)(143, 441)(144, 442)(145, 384)(146, 440)(147, 445)(148, 332)(149, 390)(150, 333)(151, 338)(152, 336)(153, 428)(154, 392)(155, 406)(156, 337)(157, 391)(158, 359)(159, 360)(160, 433)(161, 455)(162, 343)(163, 365)(164, 386)(165, 387)(166, 451)(167, 410)(168, 447)(169, 352)(170, 448)(171, 354)(172, 398)(173, 411)(174, 358)(175, 363)(176, 446)(177, 452)(178, 399)(179, 453)(180, 408)(181, 432)(182, 415)(183, 421)(184, 449)(185, 368)(186, 435)(187, 434)(188, 369)(189, 450)(190, 429)(191, 424)(192, 423)(193, 376)(194, 380)(195, 379)(196, 454)(197, 443)(198, 444)(199, 383)(200, 404)(201, 439)(202, 385)(203, 467)(204, 457)(205, 405)(206, 458)(207, 420)(208, 407)(209, 431)(210, 430)(211, 395)(212, 459)(213, 463)(214, 466)(215, 456)(216, 401)(217, 438)(218, 416)(219, 417)(220, 474)(221, 462)(222, 471)(223, 419)(224, 473)(225, 476)(226, 436)(227, 437)(228, 460)(229, 475)(230, 464)(231, 461)(232, 469)(233, 470)(234, 468)(235, 472)(236, 477)(237, 465)(238, 479)(239, 480)(240, 478) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E15.1347 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 240 f = 200 degree seq :: [ 40^12 ] E15.1352 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 20}) Quotient :: loop Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^-2 * T2 * T1^5 * T2 * T1^-3, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3, T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^3, T1^20 ] Map:: polytopal non-degenerate R = (1, 241, 3, 243)(2, 242, 6, 246)(4, 244, 9, 249)(5, 245, 12, 252)(7, 247, 16, 256)(8, 248, 13, 253)(10, 250, 19, 259)(11, 251, 22, 262)(14, 254, 23, 263)(15, 255, 28, 268)(17, 257, 30, 270)(18, 258, 33, 273)(20, 260, 35, 275)(21, 261, 38, 278)(24, 264, 39, 279)(25, 265, 44, 284)(26, 266, 45, 285)(27, 267, 48, 288)(29, 269, 49, 289)(31, 271, 53, 293)(32, 272, 56, 296)(34, 274, 59, 299)(36, 276, 61, 301)(37, 277, 64, 304)(40, 280, 65, 305)(41, 281, 70, 310)(42, 282, 71, 311)(43, 283, 74, 314)(46, 286, 77, 317)(47, 287, 79, 319)(50, 290, 80, 320)(51, 291, 84, 324)(52, 292, 87, 327)(54, 294, 89, 329)(55, 295, 91, 331)(57, 297, 92, 332)(58, 298, 95, 335)(60, 300, 97, 337)(62, 302, 90, 330)(63, 303, 100, 340)(66, 306, 101, 341)(67, 307, 104, 344)(68, 308, 105, 345)(69, 309, 107, 347)(72, 312, 110, 350)(73, 313, 111, 351)(75, 315, 112, 352)(76, 316, 116, 356)(78, 318, 118, 358)(81, 321, 119, 359)(82, 322, 123, 363)(83, 323, 124, 364)(85, 325, 127, 367)(86, 326, 129, 369)(88, 328, 131, 371)(93, 333, 132, 372)(94, 334, 136, 376)(96, 336, 138, 378)(98, 338, 128, 368)(99, 339, 144, 384)(102, 342, 147, 387)(103, 343, 149, 389)(106, 346, 152, 392)(108, 348, 153, 393)(109, 349, 157, 397)(113, 353, 159, 399)(114, 354, 162, 402)(115, 355, 164, 404)(117, 357, 166, 406)(120, 360, 169, 409)(121, 361, 170, 410)(122, 362, 172, 412)(125, 365, 175, 415)(126, 366, 177, 417)(130, 370, 179, 419)(133, 373, 145, 385)(134, 374, 185, 425)(135, 375, 186, 426)(137, 377, 188, 428)(139, 379, 151, 391)(140, 380, 191, 431)(141, 381, 158, 398)(142, 382, 178, 418)(143, 383, 196, 436)(146, 386, 199, 439)(148, 388, 201, 441)(150, 390, 202, 442)(154, 394, 206, 446)(155, 395, 209, 449)(156, 396, 211, 451)(160, 400, 215, 455)(161, 401, 216, 456)(163, 403, 218, 458)(165, 405, 219, 459)(167, 407, 224, 464)(168, 408, 210, 450)(171, 411, 221, 461)(173, 413, 226, 466)(174, 414, 205, 445)(176, 416, 208, 448)(180, 420, 212, 452)(181, 421, 200, 440)(182, 422, 203, 443)(183, 423, 217, 457)(184, 424, 227, 467)(187, 427, 213, 453)(189, 429, 214, 454)(190, 430, 220, 460)(192, 432, 223, 463)(193, 433, 225, 465)(194, 434, 228, 468)(195, 435, 232, 472)(197, 437, 234, 474)(198, 438, 235, 475)(204, 444, 237, 477)(207, 447, 238, 478)(222, 462, 236, 476)(229, 469, 233, 473)(230, 470, 239, 479)(231, 471, 240, 480) L = (1, 242)(2, 245)(3, 247)(4, 241)(5, 251)(6, 253)(7, 255)(8, 243)(9, 258)(10, 244)(11, 261)(12, 263)(13, 265)(14, 246)(15, 267)(16, 249)(17, 248)(18, 272)(19, 274)(20, 250)(21, 277)(22, 279)(23, 281)(24, 252)(25, 283)(26, 254)(27, 287)(28, 289)(29, 256)(30, 292)(31, 257)(32, 295)(33, 259)(34, 298)(35, 300)(36, 260)(37, 303)(38, 305)(39, 307)(40, 262)(41, 309)(42, 264)(43, 313)(44, 270)(45, 316)(46, 266)(47, 304)(48, 320)(49, 322)(50, 268)(51, 269)(52, 326)(53, 328)(54, 271)(55, 306)(56, 332)(57, 273)(58, 308)(59, 275)(60, 312)(61, 318)(62, 276)(63, 339)(64, 341)(65, 342)(66, 278)(67, 343)(68, 280)(69, 346)(70, 285)(71, 349)(72, 282)(73, 340)(74, 352)(75, 284)(76, 355)(77, 357)(78, 286)(79, 359)(80, 360)(81, 288)(82, 362)(83, 290)(84, 366)(85, 291)(86, 361)(87, 293)(88, 365)(89, 368)(90, 294)(91, 372)(92, 374)(93, 296)(94, 297)(95, 378)(96, 299)(97, 301)(98, 302)(99, 383)(100, 319)(101, 385)(102, 386)(103, 388)(104, 311)(105, 391)(106, 384)(107, 393)(108, 310)(109, 396)(110, 398)(111, 399)(112, 400)(113, 314)(114, 315)(115, 401)(116, 317)(117, 403)(118, 330)(119, 407)(120, 408)(121, 321)(122, 411)(123, 324)(124, 414)(125, 323)(126, 416)(127, 418)(128, 325)(129, 419)(130, 327)(131, 329)(132, 423)(133, 331)(134, 424)(135, 333)(136, 427)(137, 334)(138, 429)(139, 335)(140, 336)(141, 337)(142, 338)(143, 435)(144, 351)(145, 437)(146, 438)(147, 345)(148, 436)(149, 442)(150, 344)(151, 445)(152, 446)(153, 447)(154, 347)(155, 348)(156, 448)(157, 350)(158, 450)(159, 453)(160, 454)(161, 353)(162, 457)(163, 354)(164, 459)(165, 356)(166, 358)(167, 463)(168, 465)(169, 364)(170, 452)(171, 373)(172, 466)(173, 363)(174, 460)(175, 443)(176, 375)(177, 367)(178, 377)(179, 467)(180, 369)(181, 370)(182, 371)(183, 458)(184, 440)(185, 376)(186, 451)(187, 456)(188, 468)(189, 444)(190, 379)(191, 464)(192, 380)(193, 381)(194, 382)(195, 471)(196, 392)(197, 473)(198, 472)(199, 421)(200, 387)(201, 422)(202, 413)(203, 389)(204, 390)(205, 415)(206, 417)(207, 425)(208, 394)(209, 409)(210, 395)(211, 420)(212, 397)(213, 428)(214, 431)(215, 402)(216, 430)(217, 426)(218, 476)(219, 412)(220, 404)(221, 405)(222, 406)(223, 479)(224, 410)(225, 474)(226, 477)(227, 478)(228, 432)(229, 433)(230, 434)(231, 470)(232, 441)(233, 480)(234, 461)(235, 462)(236, 439)(237, 455)(238, 449)(239, 469)(240, 475) local type(s) :: { ( 3, 20, 3, 20 ) } Outer automorphisms :: reflexible Dual of E15.1348 Transitivity :: ET+ VT+ AT Graph:: simple v = 120 e = 240 f = 92 degree seq :: [ 4^120 ] E15.1353 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 20}) Quotient :: dipole Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2, Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1, (Y3 * Y2^-1)^20 ] Map:: R = (1, 241, 2, 242)(3, 243, 7, 247)(4, 244, 8, 248)(5, 245, 9, 249)(6, 246, 10, 250)(11, 251, 19, 259)(12, 252, 20, 260)(13, 253, 21, 261)(14, 254, 22, 262)(15, 255, 23, 263)(16, 256, 24, 264)(17, 257, 25, 265)(18, 258, 26, 266)(27, 267, 43, 283)(28, 268, 44, 284)(29, 269, 45, 285)(30, 270, 46, 286)(31, 271, 47, 287)(32, 272, 48, 288)(33, 273, 49, 289)(34, 274, 50, 290)(35, 275, 51, 291)(36, 276, 52, 292)(37, 277, 53, 293)(38, 278, 54, 294)(39, 279, 55, 295)(40, 280, 56, 296)(41, 281, 57, 297)(42, 282, 58, 298)(59, 299, 91, 331)(60, 300, 92, 332)(61, 301, 93, 333)(62, 302, 94, 334)(63, 303, 95, 335)(64, 304, 96, 336)(65, 305, 97, 337)(66, 306, 98, 338)(67, 307, 99, 339)(68, 308, 100, 340)(69, 309, 101, 341)(70, 310, 102, 342)(71, 311, 103, 343)(72, 312, 104, 344)(73, 313, 105, 345)(74, 314, 106, 346)(75, 315, 107, 347)(76, 316, 108, 348)(77, 317, 109, 349)(78, 318, 110, 350)(79, 319, 111, 351)(80, 320, 112, 352)(81, 321, 113, 353)(82, 322, 114, 354)(83, 323, 115, 355)(84, 324, 116, 356)(85, 325, 117, 357)(86, 326, 118, 358)(87, 327, 119, 359)(88, 328, 120, 360)(89, 329, 121, 361)(90, 330, 122, 362)(123, 363, 155, 395)(124, 364, 171, 411)(125, 365, 187, 427)(126, 366, 179, 419)(127, 367, 188, 428)(128, 368, 166, 406)(129, 369, 189, 429)(130, 370, 183, 423)(131, 371, 190, 430)(132, 372, 168, 408)(133, 373, 176, 416)(134, 374, 160, 400)(135, 375, 191, 431)(136, 376, 164, 404)(137, 377, 192, 432)(138, 378, 185, 425)(139, 379, 156, 396)(140, 380, 193, 433)(141, 381, 177, 417)(142, 382, 194, 434)(143, 383, 181, 421)(144, 384, 165, 405)(145, 385, 173, 413)(146, 386, 195, 435)(147, 387, 158, 398)(148, 388, 196, 436)(149, 389, 175, 415)(150, 390, 197, 437)(151, 391, 162, 402)(152, 392, 198, 438)(153, 393, 170, 410)(154, 394, 186, 426)(157, 397, 199, 439)(159, 399, 200, 440)(161, 401, 201, 441)(163, 403, 202, 442)(167, 407, 203, 443)(169, 409, 204, 444)(172, 412, 205, 445)(174, 414, 206, 446)(178, 418, 207, 447)(180, 420, 208, 448)(182, 422, 209, 449)(184, 424, 210, 450)(211, 451, 223, 463)(212, 452, 224, 464)(213, 453, 221, 461)(214, 454, 225, 465)(215, 455, 219, 459)(216, 456, 226, 466)(217, 457, 227, 467)(218, 458, 228, 468)(220, 460, 229, 469)(222, 462, 230, 470)(231, 471, 235, 475)(232, 472, 236, 476)(233, 473, 237, 477)(234, 474, 238, 478)(239, 479, 240, 480)(481, 721, 483, 723, 484, 724)(482, 722, 485, 725, 486, 726)(487, 727, 491, 731, 492, 732)(488, 728, 493, 733, 494, 734)(489, 729, 495, 735, 496, 736)(490, 730, 497, 737, 498, 738)(499, 739, 507, 747, 508, 748)(500, 740, 509, 749, 510, 750)(501, 741, 511, 751, 512, 752)(502, 742, 513, 753, 514, 754)(503, 743, 515, 755, 516, 756)(504, 744, 517, 757, 518, 758)(505, 745, 519, 759, 520, 760)(506, 746, 521, 761, 522, 762)(523, 763, 539, 779, 540, 780)(524, 764, 541, 781, 542, 782)(525, 765, 543, 783, 544, 784)(526, 766, 545, 785, 546, 786)(527, 767, 547, 787, 548, 788)(528, 768, 549, 789, 550, 790)(529, 769, 551, 791, 552, 792)(530, 770, 553, 793, 554, 794)(531, 771, 555, 795, 556, 796)(532, 772, 557, 797, 558, 798)(533, 773, 559, 799, 560, 800)(534, 774, 561, 801, 562, 802)(535, 775, 563, 803, 564, 804)(536, 776, 565, 805, 566, 806)(537, 777, 567, 807, 568, 808)(538, 778, 569, 809, 570, 810)(571, 811, 603, 843, 604, 844)(572, 812, 605, 845, 606, 846)(573, 813, 607, 847, 608, 848)(574, 814, 609, 849, 610, 850)(575, 815, 611, 851, 612, 852)(576, 816, 613, 853, 614, 854)(577, 817, 615, 855, 616, 856)(578, 818, 617, 857, 618, 858)(579, 819, 619, 859, 620, 860)(580, 820, 621, 861, 622, 862)(581, 821, 623, 863, 624, 864)(582, 822, 625, 865, 626, 866)(583, 823, 627, 867, 628, 868)(584, 824, 629, 869, 630, 870)(585, 825, 631, 871, 632, 872)(586, 826, 633, 873, 634, 874)(587, 827, 635, 875, 636, 876)(588, 828, 637, 877, 638, 878)(589, 829, 639, 879, 640, 880)(590, 830, 641, 881, 642, 882)(591, 831, 643, 883, 644, 884)(592, 832, 645, 885, 646, 886)(593, 833, 647, 887, 648, 888)(594, 834, 649, 889, 650, 890)(595, 835, 651, 891, 652, 892)(596, 836, 653, 893, 654, 894)(597, 837, 655, 895, 656, 896)(598, 838, 657, 897, 658, 898)(599, 839, 659, 899, 660, 900)(600, 840, 661, 901, 662, 902)(601, 841, 663, 903, 664, 904)(602, 842, 665, 905, 666, 906)(667, 907, 691, 931, 677, 917)(668, 908, 692, 932, 678, 918)(669, 909, 693, 933, 676, 916)(670, 910, 673, 913, 694, 934)(671, 911, 674, 914, 695, 935)(672, 912, 675, 915, 696, 936)(679, 919, 697, 937, 689, 929)(680, 920, 698, 938, 690, 930)(681, 921, 699, 939, 688, 928)(682, 922, 685, 925, 700, 940)(683, 923, 686, 926, 701, 941)(684, 924, 687, 927, 702, 942)(703, 943, 711, 951, 706, 946)(704, 944, 705, 945, 712, 952)(707, 947, 713, 953, 710, 950)(708, 948, 709, 949, 714, 954)(715, 955, 716, 956, 719, 959)(717, 957, 718, 958, 720, 960) L = (1, 482)(2, 481)(3, 487)(4, 488)(5, 489)(6, 490)(7, 483)(8, 484)(9, 485)(10, 486)(11, 499)(12, 500)(13, 501)(14, 502)(15, 503)(16, 504)(17, 505)(18, 506)(19, 491)(20, 492)(21, 493)(22, 494)(23, 495)(24, 496)(25, 497)(26, 498)(27, 523)(28, 524)(29, 525)(30, 526)(31, 527)(32, 528)(33, 529)(34, 530)(35, 531)(36, 532)(37, 533)(38, 534)(39, 535)(40, 536)(41, 537)(42, 538)(43, 507)(44, 508)(45, 509)(46, 510)(47, 511)(48, 512)(49, 513)(50, 514)(51, 515)(52, 516)(53, 517)(54, 518)(55, 519)(56, 520)(57, 521)(58, 522)(59, 571)(60, 572)(61, 573)(62, 574)(63, 575)(64, 576)(65, 577)(66, 578)(67, 579)(68, 580)(69, 581)(70, 582)(71, 583)(72, 584)(73, 585)(74, 586)(75, 587)(76, 588)(77, 589)(78, 590)(79, 591)(80, 592)(81, 593)(82, 594)(83, 595)(84, 596)(85, 597)(86, 598)(87, 599)(88, 600)(89, 601)(90, 602)(91, 539)(92, 540)(93, 541)(94, 542)(95, 543)(96, 544)(97, 545)(98, 546)(99, 547)(100, 548)(101, 549)(102, 550)(103, 551)(104, 552)(105, 553)(106, 554)(107, 555)(108, 556)(109, 557)(110, 558)(111, 559)(112, 560)(113, 561)(114, 562)(115, 563)(116, 564)(117, 565)(118, 566)(119, 567)(120, 568)(121, 569)(122, 570)(123, 635)(124, 651)(125, 667)(126, 659)(127, 668)(128, 646)(129, 669)(130, 663)(131, 670)(132, 648)(133, 656)(134, 640)(135, 671)(136, 644)(137, 672)(138, 665)(139, 636)(140, 673)(141, 657)(142, 674)(143, 661)(144, 645)(145, 653)(146, 675)(147, 638)(148, 676)(149, 655)(150, 677)(151, 642)(152, 678)(153, 650)(154, 666)(155, 603)(156, 619)(157, 679)(158, 627)(159, 680)(160, 614)(161, 681)(162, 631)(163, 682)(164, 616)(165, 624)(166, 608)(167, 683)(168, 612)(169, 684)(170, 633)(171, 604)(172, 685)(173, 625)(174, 686)(175, 629)(176, 613)(177, 621)(178, 687)(179, 606)(180, 688)(181, 623)(182, 689)(183, 610)(184, 690)(185, 618)(186, 634)(187, 605)(188, 607)(189, 609)(190, 611)(191, 615)(192, 617)(193, 620)(194, 622)(195, 626)(196, 628)(197, 630)(198, 632)(199, 637)(200, 639)(201, 641)(202, 643)(203, 647)(204, 649)(205, 652)(206, 654)(207, 658)(208, 660)(209, 662)(210, 664)(211, 703)(212, 704)(213, 701)(214, 705)(215, 699)(216, 706)(217, 707)(218, 708)(219, 695)(220, 709)(221, 693)(222, 710)(223, 691)(224, 692)(225, 694)(226, 696)(227, 697)(228, 698)(229, 700)(230, 702)(231, 715)(232, 716)(233, 717)(234, 718)(235, 711)(236, 712)(237, 713)(238, 714)(239, 720)(240, 719)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960) local type(s) :: { ( 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E15.1356 Graph:: bipartite v = 200 e = 480 f = 252 degree seq :: [ 4^120, 6^80 ] E15.1354 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 20}) Quotient :: dipole Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^4 * Y1^-1 * Y2^-6, (Y2^3 * Y1^-1 * Y2^2 * Y1^-1)^2, Y1^-1 * Y2^4 * Y1^-1 * Y2^14 ] Map:: R = (1, 241, 2, 242, 4, 244)(3, 243, 8, 248, 10, 250)(5, 245, 12, 252, 6, 246)(7, 247, 15, 255, 11, 251)(9, 249, 18, 258, 20, 260)(13, 253, 25, 265, 23, 263)(14, 254, 24, 264, 28, 268)(16, 256, 31, 271, 29, 269)(17, 257, 33, 273, 21, 261)(19, 259, 36, 276, 38, 278)(22, 262, 30, 270, 42, 282)(26, 266, 47, 287, 45, 285)(27, 267, 49, 289, 51, 291)(32, 272, 57, 297, 55, 295)(34, 274, 61, 301, 59, 299)(35, 275, 63, 303, 39, 279)(37, 277, 66, 306, 68, 308)(40, 280, 60, 300, 72, 312)(41, 281, 73, 313, 75, 315)(43, 283, 46, 286, 78, 318)(44, 284, 79, 319, 52, 292)(48, 288, 85, 325, 83, 323)(50, 290, 88, 328, 90, 330)(53, 293, 56, 296, 94, 334)(54, 294, 95, 335, 76, 316)(58, 298, 101, 341, 99, 339)(62, 302, 107, 347, 105, 345)(64, 304, 111, 351, 109, 349)(65, 305, 113, 353, 69, 309)(67, 307, 89, 329, 117, 357)(70, 310, 110, 350, 121, 361)(71, 311, 122, 362, 124, 364)(74, 314, 127, 367, 116, 356)(77, 317, 130, 370, 131, 371)(80, 320, 135, 375, 133, 373)(81, 321, 84, 324, 137, 377)(82, 322, 138, 378, 132, 372)(86, 326, 102, 342, 108, 348)(87, 327, 142, 382, 91, 331)(92, 332, 134, 374, 148, 388)(93, 333, 149, 389, 150, 390)(96, 336, 154, 394, 152, 392)(97, 337, 100, 340, 156, 396)(98, 338, 157, 397, 151, 391)(103, 343, 106, 346, 162, 402)(104, 344, 163, 403, 125, 365)(112, 352, 141, 381, 169, 409)(114, 354, 173, 413, 171, 411)(115, 355, 174, 414, 118, 358)(119, 359, 172, 412, 158, 398)(120, 360, 178, 418, 159, 399)(123, 363, 182, 422, 175, 415)(126, 366, 185, 425, 128, 368)(129, 369, 153, 393, 188, 428)(136, 376, 160, 400, 193, 433)(139, 379, 186, 426, 195, 435)(140, 380, 187, 427, 194, 434)(143, 383, 201, 441, 199, 439)(144, 384, 202, 442, 145, 385)(146, 386, 200, 440, 164, 404)(147, 387, 205, 445, 165, 405)(155, 395, 166, 406, 211, 451)(161, 401, 215, 455, 216, 456)(167, 407, 170, 410, 208, 448)(168, 408, 207, 447, 180, 420)(176, 416, 206, 446, 218, 458)(177, 417, 212, 452, 219, 459)(179, 419, 213, 453, 223, 463)(181, 421, 192, 432, 183, 423)(184, 424, 209, 449, 191, 431)(189, 429, 210, 450, 190, 430)(196, 436, 214, 454, 226, 466)(197, 437, 203, 443, 227, 467)(198, 438, 204, 444, 217, 457)(220, 460, 234, 474, 228, 468)(221, 461, 222, 462, 231, 471)(224, 464, 233, 473, 230, 470)(225, 465, 236, 476, 237, 477)(229, 469, 235, 475, 232, 472)(238, 478, 239, 479, 240, 480)(481, 721, 483, 723, 489, 729, 499, 739, 517, 757, 547, 787, 596, 836, 655, 895, 703, 943, 717, 957, 720, 960, 715, 955, 694, 934, 640, 880, 581, 821, 566, 806, 528, 768, 506, 746, 493, 733, 485, 725)(482, 722, 486, 726, 494, 734, 507, 747, 530, 770, 569, 809, 548, 788, 598, 838, 656, 896, 704, 944, 718, 958, 716, 956, 699, 939, 646, 886, 587, 827, 582, 822, 538, 778, 512, 752, 496, 736, 487, 727)(484, 724, 491, 731, 502, 742, 521, 761, 554, 794, 597, 837, 570, 810, 625, 865, 683, 923, 712, 952, 719, 959, 710, 950, 678, 918, 621, 861, 565, 805, 588, 828, 542, 782, 514, 754, 497, 737, 488, 728)(490, 730, 501, 741, 520, 760, 551, 791, 603, 843, 607, 847, 555, 795, 608, 848, 666, 906, 706, 946, 709, 949, 677, 917, 620, 860, 564, 804, 527, 767, 563, 803, 592, 832, 544, 784, 515, 755, 498, 738)(492, 732, 503, 743, 523, 763, 557, 797, 595, 835, 546, 786, 518, 758, 549, 789, 599, 839, 657, 897, 705, 945, 693, 933, 639, 879, 580, 820, 537, 777, 579, 819, 616, 856, 560, 800, 524, 764, 504, 744)(495, 735, 509, 749, 533, 773, 573, 813, 624, 864, 568, 808, 531, 771, 571, 811, 626, 866, 684, 924, 713, 953, 698, 938, 645, 885, 586, 826, 541, 781, 585, 825, 635, 875, 576, 816, 534, 774, 510, 750)(500, 740, 519, 759, 550, 790, 600, 840, 659, 899, 662, 902, 604, 844, 663, 903, 615, 855, 673, 913, 676, 916, 619, 859, 562, 802, 526, 766, 505, 745, 525, 765, 561, 801, 594, 834, 545, 785, 516, 756)(508, 748, 532, 772, 572, 812, 627, 867, 686, 926, 654, 894, 611, 851, 670, 910, 634, 874, 691, 931, 692, 932, 638, 878, 578, 818, 536, 776, 511, 751, 535, 775, 577, 817, 623, 863, 567, 807, 529, 769)(513, 753, 539, 779, 583, 823, 641, 881, 606, 846, 553, 793, 522, 762, 556, 796, 609, 849, 667, 907, 707, 947, 682, 922, 630, 870, 650, 890, 591, 831, 649, 889, 697, 937, 644, 884, 584, 824, 540, 780)(543, 783, 589, 829, 647, 887, 700, 940, 661, 901, 602, 842, 552, 792, 605, 845, 664, 904, 618, 858, 675, 915, 665, 905, 696, 936, 702, 942, 653, 893, 617, 857, 674, 914, 668, 908, 648, 888, 590, 830)(558, 798, 612, 852, 671, 911, 637, 877, 652, 892, 593, 833, 651, 891, 701, 941, 681, 921, 636, 876, 658, 898, 601, 841, 660, 900, 614, 854, 559, 799, 613, 853, 672, 912, 708, 948, 669, 909, 610, 850)(574, 814, 631, 871, 689, 929, 643, 883, 680, 920, 622, 862, 679, 919, 711, 951, 695, 935, 642, 882, 685, 925, 628, 868, 687, 927, 633, 873, 575, 815, 632, 872, 690, 930, 714, 954, 688, 928, 629, 869) L = (1, 483)(2, 486)(3, 489)(4, 491)(5, 481)(6, 494)(7, 482)(8, 484)(9, 499)(10, 501)(11, 502)(12, 503)(13, 485)(14, 507)(15, 509)(16, 487)(17, 488)(18, 490)(19, 517)(20, 519)(21, 520)(22, 521)(23, 523)(24, 492)(25, 525)(26, 493)(27, 530)(28, 532)(29, 533)(30, 495)(31, 535)(32, 496)(33, 539)(34, 497)(35, 498)(36, 500)(37, 547)(38, 549)(39, 550)(40, 551)(41, 554)(42, 556)(43, 557)(44, 504)(45, 561)(46, 505)(47, 563)(48, 506)(49, 508)(50, 569)(51, 571)(52, 572)(53, 573)(54, 510)(55, 577)(56, 511)(57, 579)(58, 512)(59, 583)(60, 513)(61, 585)(62, 514)(63, 589)(64, 515)(65, 516)(66, 518)(67, 596)(68, 598)(69, 599)(70, 600)(71, 603)(72, 605)(73, 522)(74, 597)(75, 608)(76, 609)(77, 595)(78, 612)(79, 613)(80, 524)(81, 594)(82, 526)(83, 592)(84, 527)(85, 588)(86, 528)(87, 529)(88, 531)(89, 548)(90, 625)(91, 626)(92, 627)(93, 624)(94, 631)(95, 632)(96, 534)(97, 623)(98, 536)(99, 616)(100, 537)(101, 566)(102, 538)(103, 641)(104, 540)(105, 635)(106, 541)(107, 582)(108, 542)(109, 647)(110, 543)(111, 649)(112, 544)(113, 651)(114, 545)(115, 546)(116, 655)(117, 570)(118, 656)(119, 657)(120, 659)(121, 660)(122, 552)(123, 607)(124, 663)(125, 664)(126, 553)(127, 555)(128, 666)(129, 667)(130, 558)(131, 670)(132, 671)(133, 672)(134, 559)(135, 673)(136, 560)(137, 674)(138, 675)(139, 562)(140, 564)(141, 565)(142, 679)(143, 567)(144, 568)(145, 683)(146, 684)(147, 686)(148, 687)(149, 574)(150, 650)(151, 689)(152, 690)(153, 575)(154, 691)(155, 576)(156, 658)(157, 652)(158, 578)(159, 580)(160, 581)(161, 606)(162, 685)(163, 680)(164, 584)(165, 586)(166, 587)(167, 700)(168, 590)(169, 697)(170, 591)(171, 701)(172, 593)(173, 617)(174, 611)(175, 703)(176, 704)(177, 705)(178, 601)(179, 662)(180, 614)(181, 602)(182, 604)(183, 615)(184, 618)(185, 696)(186, 706)(187, 707)(188, 648)(189, 610)(190, 634)(191, 637)(192, 708)(193, 676)(194, 668)(195, 665)(196, 619)(197, 620)(198, 621)(199, 711)(200, 622)(201, 636)(202, 630)(203, 712)(204, 713)(205, 628)(206, 654)(207, 633)(208, 629)(209, 643)(210, 714)(211, 692)(212, 638)(213, 639)(214, 640)(215, 642)(216, 702)(217, 644)(218, 645)(219, 646)(220, 661)(221, 681)(222, 653)(223, 717)(224, 718)(225, 693)(226, 709)(227, 682)(228, 669)(229, 677)(230, 678)(231, 695)(232, 719)(233, 698)(234, 688)(235, 694)(236, 699)(237, 720)(238, 716)(239, 710)(240, 715)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1355 Graph:: bipartite v = 92 e = 480 f = 360 degree seq :: [ 6^80, 40^12 ] E15.1355 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 20}) Quotient :: dipole Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^-3 * Y2 * Y3^5 * Y2 * Y3^-2, Y2 * Y3^2 * Y2 * Y3^-3 * Y2 * Y3^2 * Y2 * Y3^-3 * Y2 * Y3^-3, Y3^2 * Y2 * Y3^3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^20 ] Map:: polytopal R = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)(481, 721, 482, 722)(483, 723, 487, 727)(484, 724, 489, 729)(485, 725, 491, 731)(486, 726, 493, 733)(488, 728, 496, 736)(490, 730, 499, 739)(492, 732, 502, 742)(494, 734, 505, 745)(495, 735, 507, 747)(497, 737, 510, 750)(498, 738, 512, 752)(500, 740, 515, 755)(501, 741, 517, 757)(503, 743, 520, 760)(504, 744, 522, 762)(506, 746, 525, 765)(508, 748, 528, 768)(509, 749, 530, 770)(511, 751, 533, 773)(513, 753, 536, 776)(514, 754, 538, 778)(516, 756, 541, 781)(518, 758, 544, 784)(519, 759, 546, 786)(521, 761, 549, 789)(523, 763, 552, 792)(524, 764, 554, 794)(526, 766, 557, 797)(527, 767, 559, 799)(529, 769, 562, 802)(531, 771, 565, 805)(532, 772, 567, 807)(534, 774, 550, 790)(535, 775, 571, 811)(537, 777, 574, 814)(539, 779, 576, 816)(540, 780, 577, 817)(542, 782, 558, 798)(543, 783, 579, 819)(545, 785, 582, 822)(547, 787, 585, 825)(548, 788, 587, 827)(551, 791, 591, 831)(553, 793, 594, 834)(555, 795, 596, 836)(556, 796, 597, 837)(560, 800, 600, 840)(561, 801, 602, 842)(563, 803, 598, 838)(564, 804, 605, 845)(566, 806, 608, 848)(568, 808, 610, 850)(569, 809, 590, 830)(570, 810, 589, 829)(572, 812, 613, 853)(573, 813, 615, 855)(575, 815, 618, 858)(578, 818, 583, 823)(580, 820, 624, 864)(581, 821, 626, 866)(584, 824, 629, 869)(586, 826, 632, 872)(588, 828, 634, 874)(592, 832, 637, 877)(593, 833, 639, 879)(595, 835, 642, 882)(599, 839, 647, 887)(601, 841, 650, 890)(603, 843, 652, 892)(604, 844, 646, 886)(606, 846, 654, 894)(607, 847, 656, 896)(609, 849, 659, 899)(611, 851, 641, 881)(612, 852, 663, 903)(614, 854, 666, 906)(616, 856, 668, 908)(617, 857, 635, 875)(619, 859, 670, 910)(620, 860, 661, 901)(621, 861, 658, 898)(622, 862, 628, 868)(623, 863, 675, 915)(625, 865, 678, 918)(627, 867, 680, 920)(630, 870, 682, 922)(631, 871, 684, 924)(633, 873, 687, 927)(636, 876, 691, 931)(638, 878, 694, 934)(640, 880, 696, 936)(643, 883, 698, 938)(644, 884, 689, 929)(645, 885, 686, 926)(648, 888, 681, 921)(649, 889, 679, 919)(651, 891, 677, 917)(653, 893, 676, 916)(655, 895, 701, 941)(657, 897, 700, 940)(660, 900, 699, 939)(662, 902, 704, 944)(664, 904, 697, 937)(665, 905, 695, 935)(667, 907, 693, 933)(669, 909, 692, 932)(671, 911, 688, 928)(672, 912, 685, 925)(673, 913, 683, 923)(674, 914, 708, 948)(690, 930, 712, 952)(702, 942, 716, 956)(703, 943, 713, 953)(705, 945, 711, 951)(706, 946, 718, 958)(707, 947, 717, 957)(709, 949, 715, 955)(710, 950, 714, 954)(719, 959, 720, 960) L = (1, 483)(2, 485)(3, 488)(4, 481)(5, 492)(6, 482)(7, 493)(8, 497)(9, 498)(10, 484)(11, 489)(12, 503)(13, 504)(14, 486)(15, 487)(16, 507)(17, 511)(18, 513)(19, 514)(20, 490)(21, 491)(22, 517)(23, 521)(24, 523)(25, 524)(26, 494)(27, 527)(28, 495)(29, 496)(30, 530)(31, 534)(32, 499)(33, 537)(34, 539)(35, 540)(36, 500)(37, 543)(38, 501)(39, 502)(40, 546)(41, 550)(42, 505)(43, 553)(44, 555)(45, 556)(46, 506)(47, 560)(48, 561)(49, 508)(50, 564)(51, 509)(52, 510)(53, 567)(54, 570)(55, 512)(56, 571)(57, 569)(58, 515)(59, 568)(60, 566)(61, 563)(62, 516)(63, 580)(64, 581)(65, 518)(66, 584)(67, 519)(68, 520)(69, 587)(70, 590)(71, 522)(72, 591)(73, 589)(74, 525)(75, 588)(76, 586)(77, 583)(78, 526)(79, 528)(80, 601)(81, 603)(82, 604)(83, 529)(84, 606)(85, 607)(86, 531)(87, 609)(88, 532)(89, 533)(90, 611)(91, 612)(92, 535)(93, 536)(94, 615)(95, 538)(96, 618)(97, 541)(98, 542)(99, 544)(100, 625)(101, 627)(102, 628)(103, 545)(104, 630)(105, 631)(106, 547)(107, 633)(108, 548)(109, 549)(110, 635)(111, 636)(112, 551)(113, 552)(114, 639)(115, 554)(116, 642)(117, 557)(118, 558)(119, 559)(120, 647)(121, 641)(122, 562)(123, 640)(124, 638)(125, 565)(126, 655)(127, 657)(128, 658)(129, 660)(130, 661)(131, 662)(132, 664)(133, 665)(134, 572)(135, 667)(136, 573)(137, 574)(138, 669)(139, 575)(140, 576)(141, 577)(142, 578)(143, 579)(144, 675)(145, 617)(146, 582)(147, 616)(148, 614)(149, 585)(150, 683)(151, 685)(152, 686)(153, 688)(154, 689)(155, 690)(156, 692)(157, 693)(158, 592)(159, 695)(160, 593)(161, 594)(162, 697)(163, 595)(164, 596)(165, 597)(166, 598)(167, 703)(168, 599)(169, 600)(170, 679)(171, 602)(172, 677)(173, 605)(174, 676)(175, 704)(176, 608)(177, 680)(178, 682)(179, 610)(180, 706)(181, 684)(182, 707)(183, 613)(184, 698)(185, 696)(186, 708)(187, 694)(188, 700)(189, 705)(190, 687)(191, 619)(192, 620)(193, 621)(194, 622)(195, 711)(196, 623)(197, 624)(198, 651)(199, 626)(200, 649)(201, 629)(202, 648)(203, 712)(204, 632)(205, 652)(206, 654)(207, 634)(208, 714)(209, 656)(210, 715)(211, 637)(212, 670)(213, 668)(214, 716)(215, 666)(216, 672)(217, 713)(218, 659)(219, 643)(220, 644)(221, 645)(222, 646)(223, 663)(224, 650)(225, 653)(226, 717)(227, 719)(228, 671)(229, 673)(230, 674)(231, 691)(232, 678)(233, 681)(234, 709)(235, 720)(236, 699)(237, 701)(238, 702)(239, 710)(240, 718)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960) local type(s) :: { ( 6, 40 ), ( 6, 40, 6, 40 ) } Outer automorphisms :: reflexible Dual of E15.1354 Graph:: simple bipartite v = 360 e = 480 f = 92 degree seq :: [ 2^240, 4^120 ] E15.1356 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 20}) Quotient :: dipole Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y1^-1 * Y3)^3, Y1^2 * Y3 * Y1^-5 * Y3 * Y1^3, Y1^-5 * Y3 * Y1^5 * Y3, Y3 * Y1^-2 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 * Y1^-2 * Y3 * Y1^3, Y1^20 ] Map:: polytopal R = (1, 241, 2, 242, 5, 245, 11, 251, 21, 261, 37, 277, 63, 303, 99, 339, 143, 383, 195, 435, 231, 471, 230, 470, 194, 434, 142, 382, 98, 338, 62, 302, 36, 276, 20, 260, 10, 250, 4, 244)(3, 243, 7, 247, 15, 255, 27, 267, 47, 287, 64, 304, 101, 341, 145, 385, 197, 437, 233, 473, 240, 480, 235, 475, 222, 462, 166, 406, 118, 358, 90, 330, 54, 294, 31, 271, 17, 257, 8, 248)(6, 246, 13, 253, 25, 265, 43, 283, 73, 313, 100, 340, 79, 319, 119, 359, 167, 407, 223, 463, 239, 479, 229, 469, 193, 433, 141, 381, 97, 337, 61, 301, 78, 318, 46, 286, 26, 266, 14, 254)(9, 249, 18, 258, 32, 272, 55, 295, 66, 306, 38, 278, 65, 305, 102, 342, 146, 386, 198, 438, 232, 472, 201, 441, 182, 422, 131, 371, 89, 329, 128, 368, 85, 325, 51, 291, 29, 269, 16, 256)(12, 252, 23, 263, 41, 281, 69, 309, 106, 346, 144, 384, 111, 351, 159, 399, 213, 453, 188, 428, 228, 468, 192, 432, 140, 380, 96, 336, 59, 299, 35, 275, 60, 300, 72, 312, 42, 282, 24, 264)(19, 259, 34, 274, 58, 298, 68, 308, 40, 280, 22, 262, 39, 279, 67, 307, 103, 343, 148, 388, 196, 436, 152, 392, 206, 446, 177, 417, 127, 367, 178, 418, 137, 377, 94, 334, 57, 297, 33, 273)(28, 268, 49, 289, 82, 322, 122, 362, 171, 411, 133, 373, 91, 331, 132, 372, 183, 423, 218, 458, 236, 476, 199, 439, 181, 421, 130, 370, 87, 327, 53, 293, 88, 328, 125, 365, 83, 323, 50, 290)(30, 270, 52, 292, 86, 326, 121, 361, 81, 321, 48, 288, 80, 320, 120, 360, 168, 408, 225, 465, 234, 474, 221, 461, 165, 405, 116, 356, 77, 317, 117, 357, 163, 403, 114, 354, 75, 315, 44, 284)(45, 285, 76, 316, 115, 355, 161, 401, 113, 353, 74, 314, 112, 352, 160, 400, 214, 454, 191, 431, 224, 464, 170, 410, 212, 452, 157, 397, 110, 350, 158, 398, 210, 450, 155, 395, 108, 348, 70, 310)(56, 296, 92, 332, 134, 374, 184, 424, 200, 440, 147, 387, 105, 345, 151, 391, 205, 445, 175, 415, 203, 443, 149, 389, 202, 442, 173, 413, 123, 363, 84, 324, 126, 366, 176, 416, 135, 375, 93, 333)(71, 311, 109, 349, 156, 396, 208, 448, 154, 394, 107, 347, 153, 393, 207, 447, 185, 425, 136, 376, 187, 427, 216, 456, 190, 430, 139, 379, 95, 335, 138, 378, 189, 429, 204, 444, 150, 390, 104, 344)(124, 364, 174, 414, 220, 460, 164, 404, 219, 459, 172, 412, 226, 466, 237, 477, 215, 455, 162, 402, 217, 457, 186, 426, 211, 451, 180, 420, 129, 369, 179, 419, 227, 467, 238, 478, 209, 449, 169, 409)(481, 721)(482, 722)(483, 723)(484, 724)(485, 725)(486, 726)(487, 727)(488, 728)(489, 729)(490, 730)(491, 731)(492, 732)(493, 733)(494, 734)(495, 735)(496, 736)(497, 737)(498, 738)(499, 739)(500, 740)(501, 741)(502, 742)(503, 743)(504, 744)(505, 745)(506, 746)(507, 747)(508, 748)(509, 749)(510, 750)(511, 751)(512, 752)(513, 753)(514, 754)(515, 755)(516, 756)(517, 757)(518, 758)(519, 759)(520, 760)(521, 761)(522, 762)(523, 763)(524, 764)(525, 765)(526, 766)(527, 767)(528, 768)(529, 769)(530, 770)(531, 771)(532, 772)(533, 773)(534, 774)(535, 775)(536, 776)(537, 777)(538, 778)(539, 779)(540, 780)(541, 781)(542, 782)(543, 783)(544, 784)(545, 785)(546, 786)(547, 787)(548, 788)(549, 789)(550, 790)(551, 791)(552, 792)(553, 793)(554, 794)(555, 795)(556, 796)(557, 797)(558, 798)(559, 799)(560, 800)(561, 801)(562, 802)(563, 803)(564, 804)(565, 805)(566, 806)(567, 807)(568, 808)(569, 809)(570, 810)(571, 811)(572, 812)(573, 813)(574, 814)(575, 815)(576, 816)(577, 817)(578, 818)(579, 819)(580, 820)(581, 821)(582, 822)(583, 823)(584, 824)(585, 825)(586, 826)(587, 827)(588, 828)(589, 829)(590, 830)(591, 831)(592, 832)(593, 833)(594, 834)(595, 835)(596, 836)(597, 837)(598, 838)(599, 839)(600, 840)(601, 841)(602, 842)(603, 843)(604, 844)(605, 845)(606, 846)(607, 847)(608, 848)(609, 849)(610, 850)(611, 851)(612, 852)(613, 853)(614, 854)(615, 855)(616, 856)(617, 857)(618, 858)(619, 859)(620, 860)(621, 861)(622, 862)(623, 863)(624, 864)(625, 865)(626, 866)(627, 867)(628, 868)(629, 869)(630, 870)(631, 871)(632, 872)(633, 873)(634, 874)(635, 875)(636, 876)(637, 877)(638, 878)(639, 879)(640, 880)(641, 881)(642, 882)(643, 883)(644, 884)(645, 885)(646, 886)(647, 887)(648, 888)(649, 889)(650, 890)(651, 891)(652, 892)(653, 893)(654, 894)(655, 895)(656, 896)(657, 897)(658, 898)(659, 899)(660, 900)(661, 901)(662, 902)(663, 903)(664, 904)(665, 905)(666, 906)(667, 907)(668, 908)(669, 909)(670, 910)(671, 911)(672, 912)(673, 913)(674, 914)(675, 915)(676, 916)(677, 917)(678, 918)(679, 919)(680, 920)(681, 921)(682, 922)(683, 923)(684, 924)(685, 925)(686, 926)(687, 927)(688, 928)(689, 929)(690, 930)(691, 931)(692, 932)(693, 933)(694, 934)(695, 935)(696, 936)(697, 937)(698, 938)(699, 939)(700, 940)(701, 941)(702, 942)(703, 943)(704, 944)(705, 945)(706, 946)(707, 947)(708, 948)(709, 949)(710, 950)(711, 951)(712, 952)(713, 953)(714, 954)(715, 955)(716, 956)(717, 957)(718, 958)(719, 959)(720, 960) L = (1, 483)(2, 486)(3, 481)(4, 489)(5, 492)(6, 482)(7, 496)(8, 493)(9, 484)(10, 499)(11, 502)(12, 485)(13, 488)(14, 503)(15, 508)(16, 487)(17, 510)(18, 513)(19, 490)(20, 515)(21, 518)(22, 491)(23, 494)(24, 519)(25, 524)(26, 525)(27, 528)(28, 495)(29, 529)(30, 497)(31, 533)(32, 536)(33, 498)(34, 539)(35, 500)(36, 541)(37, 544)(38, 501)(39, 504)(40, 545)(41, 550)(42, 551)(43, 554)(44, 505)(45, 506)(46, 557)(47, 559)(48, 507)(49, 509)(50, 560)(51, 564)(52, 567)(53, 511)(54, 569)(55, 571)(56, 512)(57, 572)(58, 575)(59, 514)(60, 577)(61, 516)(62, 570)(63, 580)(64, 517)(65, 520)(66, 581)(67, 584)(68, 585)(69, 587)(70, 521)(71, 522)(72, 590)(73, 591)(74, 523)(75, 592)(76, 596)(77, 526)(78, 598)(79, 527)(80, 530)(81, 599)(82, 603)(83, 604)(84, 531)(85, 607)(86, 609)(87, 532)(88, 611)(89, 534)(90, 542)(91, 535)(92, 537)(93, 612)(94, 616)(95, 538)(96, 618)(97, 540)(98, 608)(99, 624)(100, 543)(101, 546)(102, 627)(103, 629)(104, 547)(105, 548)(106, 632)(107, 549)(108, 633)(109, 637)(110, 552)(111, 553)(112, 555)(113, 639)(114, 642)(115, 644)(116, 556)(117, 646)(118, 558)(119, 561)(120, 649)(121, 650)(122, 652)(123, 562)(124, 563)(125, 655)(126, 657)(127, 565)(128, 578)(129, 566)(130, 659)(131, 568)(132, 573)(133, 625)(134, 665)(135, 666)(136, 574)(137, 668)(138, 576)(139, 631)(140, 671)(141, 638)(142, 658)(143, 676)(144, 579)(145, 613)(146, 679)(147, 582)(148, 681)(149, 583)(150, 682)(151, 619)(152, 586)(153, 588)(154, 686)(155, 689)(156, 691)(157, 589)(158, 621)(159, 593)(160, 695)(161, 696)(162, 594)(163, 698)(164, 595)(165, 699)(166, 597)(167, 704)(168, 690)(169, 600)(170, 601)(171, 701)(172, 602)(173, 706)(174, 685)(175, 605)(176, 688)(177, 606)(178, 622)(179, 610)(180, 692)(181, 680)(182, 683)(183, 697)(184, 707)(185, 614)(186, 615)(187, 693)(188, 617)(189, 694)(190, 700)(191, 620)(192, 703)(193, 705)(194, 708)(195, 712)(196, 623)(197, 714)(198, 715)(199, 626)(200, 661)(201, 628)(202, 630)(203, 662)(204, 717)(205, 654)(206, 634)(207, 718)(208, 656)(209, 635)(210, 648)(211, 636)(212, 660)(213, 667)(214, 669)(215, 640)(216, 641)(217, 663)(218, 643)(219, 645)(220, 670)(221, 651)(222, 716)(223, 672)(224, 647)(225, 673)(226, 653)(227, 664)(228, 674)(229, 713)(230, 719)(231, 720)(232, 675)(233, 709)(234, 677)(235, 678)(236, 702)(237, 684)(238, 687)(239, 710)(240, 711)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960) local type(s) :: { ( 4, 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 E15.1353 Graph:: simple bipartite v = 252 e = 480 f = 200 degree seq :: [ 2^240, 40^12 ] E15.1357 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 20}) Quotient :: dipole Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^3, (Y3 * Y2^-1)^3, (R * Y2^3 * Y1)^2, Y2^-2 * Y1 * Y2^5 * Y1 * Y2^-3, (Y2^2 * Y1 * Y2^4 * Y1 * Y2)^2, Y2^-2 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1 * Y2^3 * Y1, (Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1)^2, Y2^20 ] Map:: R = (1, 241, 2, 242)(3, 243, 7, 247)(4, 244, 9, 249)(5, 245, 11, 251)(6, 246, 13, 253)(8, 248, 16, 256)(10, 250, 19, 259)(12, 252, 22, 262)(14, 254, 25, 265)(15, 255, 27, 267)(17, 257, 30, 270)(18, 258, 32, 272)(20, 260, 35, 275)(21, 261, 37, 277)(23, 263, 40, 280)(24, 264, 42, 282)(26, 266, 45, 285)(28, 268, 48, 288)(29, 269, 50, 290)(31, 271, 53, 293)(33, 273, 56, 296)(34, 274, 58, 298)(36, 276, 61, 301)(38, 278, 64, 304)(39, 279, 66, 306)(41, 281, 69, 309)(43, 283, 72, 312)(44, 284, 74, 314)(46, 286, 77, 317)(47, 287, 79, 319)(49, 289, 82, 322)(51, 291, 85, 325)(52, 292, 87, 327)(54, 294, 70, 310)(55, 295, 91, 331)(57, 297, 94, 334)(59, 299, 96, 336)(60, 300, 97, 337)(62, 302, 78, 318)(63, 303, 99, 339)(65, 305, 102, 342)(67, 307, 105, 345)(68, 308, 107, 347)(71, 311, 111, 351)(73, 313, 114, 354)(75, 315, 116, 356)(76, 316, 117, 357)(80, 320, 120, 360)(81, 321, 122, 362)(83, 323, 118, 358)(84, 324, 125, 365)(86, 326, 128, 368)(88, 328, 130, 370)(89, 329, 110, 350)(90, 330, 109, 349)(92, 332, 133, 373)(93, 333, 135, 375)(95, 335, 138, 378)(98, 338, 103, 343)(100, 340, 144, 384)(101, 341, 146, 386)(104, 344, 149, 389)(106, 346, 152, 392)(108, 348, 154, 394)(112, 352, 157, 397)(113, 353, 159, 399)(115, 355, 162, 402)(119, 359, 167, 407)(121, 361, 170, 410)(123, 363, 172, 412)(124, 364, 166, 406)(126, 366, 174, 414)(127, 367, 176, 416)(129, 369, 179, 419)(131, 371, 161, 401)(132, 372, 183, 423)(134, 374, 186, 426)(136, 376, 188, 428)(137, 377, 155, 395)(139, 379, 190, 430)(140, 380, 181, 421)(141, 381, 178, 418)(142, 382, 148, 388)(143, 383, 195, 435)(145, 385, 198, 438)(147, 387, 200, 440)(150, 390, 202, 442)(151, 391, 204, 444)(153, 393, 207, 447)(156, 396, 211, 451)(158, 398, 214, 454)(160, 400, 216, 456)(163, 403, 218, 458)(164, 404, 209, 449)(165, 405, 206, 446)(168, 408, 201, 441)(169, 409, 199, 439)(171, 411, 197, 437)(173, 413, 196, 436)(175, 415, 221, 461)(177, 417, 220, 460)(180, 420, 219, 459)(182, 422, 224, 464)(184, 424, 217, 457)(185, 425, 215, 455)(187, 427, 213, 453)(189, 429, 212, 452)(191, 431, 208, 448)(192, 432, 205, 445)(193, 433, 203, 443)(194, 434, 228, 468)(210, 450, 232, 472)(222, 462, 236, 476)(223, 463, 233, 473)(225, 465, 231, 471)(226, 466, 238, 478)(227, 467, 237, 477)(229, 469, 235, 475)(230, 470, 234, 474)(239, 479, 240, 480)(481, 721, 483, 723, 488, 728, 497, 737, 511, 751, 534, 774, 570, 810, 611, 851, 662, 902, 707, 947, 719, 959, 710, 950, 674, 914, 622, 862, 578, 818, 542, 782, 516, 756, 500, 740, 490, 730, 484, 724)(482, 722, 485, 725, 492, 732, 503, 743, 521, 761, 550, 790, 590, 830, 635, 875, 690, 930, 715, 955, 720, 960, 718, 958, 702, 942, 646, 886, 598, 838, 558, 798, 526, 766, 506, 746, 494, 734, 486, 726)(487, 727, 493, 733, 504, 744, 523, 763, 553, 793, 589, 829, 549, 789, 587, 827, 633, 873, 688, 928, 714, 954, 709, 949, 673, 913, 621, 861, 577, 817, 541, 781, 563, 803, 529, 769, 508, 748, 495, 735)(489, 729, 498, 738, 513, 753, 537, 777, 569, 809, 533, 773, 567, 807, 609, 849, 660, 900, 706, 946, 717, 957, 701, 941, 645, 885, 597, 837, 557, 797, 583, 823, 545, 785, 518, 758, 501, 741, 491, 731)(496, 736, 507, 747, 527, 767, 560, 800, 601, 841, 641, 881, 594, 834, 639, 879, 695, 935, 666, 906, 708, 948, 671, 911, 619, 859, 575, 815, 538, 778, 515, 755, 540, 780, 566, 806, 531, 771, 509, 749)(499, 739, 514, 754, 539, 779, 568, 808, 532, 772, 510, 750, 530, 770, 564, 804, 606, 846, 655, 895, 704, 944, 650, 890, 679, 919, 626, 866, 582, 822, 628, 868, 614, 854, 572, 812, 535, 775, 512, 752)(502, 742, 517, 757, 543, 783, 580, 820, 625, 865, 617, 857, 574, 814, 615, 855, 667, 907, 694, 934, 716, 956, 699, 939, 643, 883, 595, 835, 554, 794, 525, 765, 556, 796, 586, 826, 547, 787, 519, 759)(505, 745, 524, 764, 555, 795, 588, 828, 548, 788, 520, 760, 546, 786, 584, 824, 630, 870, 683, 923, 712, 952, 678, 918, 651, 891, 602, 842, 562, 802, 604, 844, 638, 878, 592, 832, 551, 791, 522, 762)(528, 768, 561, 801, 603, 843, 640, 880, 593, 833, 552, 792, 591, 831, 636, 876, 692, 932, 670, 910, 687, 927, 634, 874, 689, 929, 656, 896, 608, 848, 658, 898, 682, 922, 648, 888, 599, 839, 559, 799)(536, 776, 571, 811, 612, 852, 664, 904, 698, 938, 659, 899, 610, 850, 661, 901, 684, 924, 632, 872, 686, 926, 654, 894, 676, 916, 623, 863, 579, 819, 544, 784, 581, 821, 627, 867, 616, 856, 573, 813)(565, 805, 607, 847, 657, 897, 680, 920, 649, 889, 600, 840, 647, 887, 703, 943, 663, 903, 613, 853, 665, 905, 696, 936, 672, 912, 620, 860, 576, 816, 618, 858, 669, 909, 705, 945, 653, 893, 605, 845)(585, 825, 631, 871, 685, 925, 652, 892, 677, 917, 624, 864, 675, 915, 711, 951, 691, 931, 637, 877, 693, 933, 668, 908, 700, 940, 644, 884, 596, 836, 642, 882, 697, 937, 713, 953, 681, 921, 629, 869) L = (1, 482)(2, 481)(3, 487)(4, 489)(5, 491)(6, 493)(7, 483)(8, 496)(9, 484)(10, 499)(11, 485)(12, 502)(13, 486)(14, 505)(15, 507)(16, 488)(17, 510)(18, 512)(19, 490)(20, 515)(21, 517)(22, 492)(23, 520)(24, 522)(25, 494)(26, 525)(27, 495)(28, 528)(29, 530)(30, 497)(31, 533)(32, 498)(33, 536)(34, 538)(35, 500)(36, 541)(37, 501)(38, 544)(39, 546)(40, 503)(41, 549)(42, 504)(43, 552)(44, 554)(45, 506)(46, 557)(47, 559)(48, 508)(49, 562)(50, 509)(51, 565)(52, 567)(53, 511)(54, 550)(55, 571)(56, 513)(57, 574)(58, 514)(59, 576)(60, 577)(61, 516)(62, 558)(63, 579)(64, 518)(65, 582)(66, 519)(67, 585)(68, 587)(69, 521)(70, 534)(71, 591)(72, 523)(73, 594)(74, 524)(75, 596)(76, 597)(77, 526)(78, 542)(79, 527)(80, 600)(81, 602)(82, 529)(83, 598)(84, 605)(85, 531)(86, 608)(87, 532)(88, 610)(89, 590)(90, 589)(91, 535)(92, 613)(93, 615)(94, 537)(95, 618)(96, 539)(97, 540)(98, 583)(99, 543)(100, 624)(101, 626)(102, 545)(103, 578)(104, 629)(105, 547)(106, 632)(107, 548)(108, 634)(109, 570)(110, 569)(111, 551)(112, 637)(113, 639)(114, 553)(115, 642)(116, 555)(117, 556)(118, 563)(119, 647)(120, 560)(121, 650)(122, 561)(123, 652)(124, 646)(125, 564)(126, 654)(127, 656)(128, 566)(129, 659)(130, 568)(131, 641)(132, 663)(133, 572)(134, 666)(135, 573)(136, 668)(137, 635)(138, 575)(139, 670)(140, 661)(141, 658)(142, 628)(143, 675)(144, 580)(145, 678)(146, 581)(147, 680)(148, 622)(149, 584)(150, 682)(151, 684)(152, 586)(153, 687)(154, 588)(155, 617)(156, 691)(157, 592)(158, 694)(159, 593)(160, 696)(161, 611)(162, 595)(163, 698)(164, 689)(165, 686)(166, 604)(167, 599)(168, 681)(169, 679)(170, 601)(171, 677)(172, 603)(173, 676)(174, 606)(175, 701)(176, 607)(177, 700)(178, 621)(179, 609)(180, 699)(181, 620)(182, 704)(183, 612)(184, 697)(185, 695)(186, 614)(187, 693)(188, 616)(189, 692)(190, 619)(191, 688)(192, 685)(193, 683)(194, 708)(195, 623)(196, 653)(197, 651)(198, 625)(199, 649)(200, 627)(201, 648)(202, 630)(203, 673)(204, 631)(205, 672)(206, 645)(207, 633)(208, 671)(209, 644)(210, 712)(211, 636)(212, 669)(213, 667)(214, 638)(215, 665)(216, 640)(217, 664)(218, 643)(219, 660)(220, 657)(221, 655)(222, 716)(223, 713)(224, 662)(225, 711)(226, 718)(227, 717)(228, 674)(229, 715)(230, 714)(231, 705)(232, 690)(233, 703)(234, 710)(235, 709)(236, 702)(237, 707)(238, 706)(239, 720)(240, 719)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960) local type(s) :: { ( 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 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 E15.1358 Graph:: bipartite v = 132 e = 480 f = 320 degree seq :: [ 4^120, 40^12 ] E15.1358 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 20}) Quotient :: dipole Aut^+ = SL(2,5) : C2 (small group id <240, 93>) Aut = $<480, 959>$ (small group id <480, 959>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3^-6 * Y1^-1 * Y3^2, (Y3^3 * Y1^-1 * Y3^2 * Y1^-1)^2, (Y3 * Y2^-1)^20 ] Map:: polytopal R = (1, 241, 2, 242, 4, 244)(3, 243, 8, 248, 10, 250)(5, 245, 12, 252, 6, 246)(7, 247, 15, 255, 11, 251)(9, 249, 18, 258, 20, 260)(13, 253, 25, 265, 23, 263)(14, 254, 24, 264, 28, 268)(16, 256, 31, 271, 29, 269)(17, 257, 33, 273, 21, 261)(19, 259, 36, 276, 38, 278)(22, 262, 30, 270, 42, 282)(26, 266, 47, 287, 45, 285)(27, 267, 49, 289, 51, 291)(32, 272, 57, 297, 55, 295)(34, 274, 61, 301, 59, 299)(35, 275, 63, 303, 39, 279)(37, 277, 66, 306, 68, 308)(40, 280, 60, 300, 72, 312)(41, 281, 73, 313, 75, 315)(43, 283, 46, 286, 78, 318)(44, 284, 79, 319, 52, 292)(48, 288, 85, 325, 83, 323)(50, 290, 88, 328, 90, 330)(53, 293, 56, 296, 94, 334)(54, 294, 95, 335, 76, 316)(58, 298, 101, 341, 99, 339)(62, 302, 107, 347, 105, 345)(64, 304, 111, 351, 109, 349)(65, 305, 113, 353, 69, 309)(67, 307, 89, 329, 117, 357)(70, 310, 110, 350, 121, 361)(71, 311, 122, 362, 124, 364)(74, 314, 127, 367, 116, 356)(77, 317, 130, 370, 131, 371)(80, 320, 135, 375, 133, 373)(81, 321, 84, 324, 137, 377)(82, 322, 138, 378, 132, 372)(86, 326, 102, 342, 108, 348)(87, 327, 142, 382, 91, 331)(92, 332, 134, 374, 148, 388)(93, 333, 149, 389, 150, 390)(96, 336, 154, 394, 152, 392)(97, 337, 100, 340, 156, 396)(98, 338, 157, 397, 151, 391)(103, 343, 106, 346, 162, 402)(104, 344, 163, 403, 125, 365)(112, 352, 141, 381, 169, 409)(114, 354, 173, 413, 171, 411)(115, 355, 174, 414, 118, 358)(119, 359, 172, 412, 158, 398)(120, 360, 178, 418, 159, 399)(123, 363, 182, 422, 175, 415)(126, 366, 185, 425, 128, 368)(129, 369, 153, 393, 188, 428)(136, 376, 160, 400, 193, 433)(139, 379, 186, 426, 195, 435)(140, 380, 187, 427, 194, 434)(143, 383, 201, 441, 199, 439)(144, 384, 202, 442, 145, 385)(146, 386, 200, 440, 164, 404)(147, 387, 205, 445, 165, 405)(155, 395, 166, 406, 211, 451)(161, 401, 215, 455, 216, 456)(167, 407, 170, 410, 208, 448)(168, 408, 207, 447, 180, 420)(176, 416, 206, 446, 218, 458)(177, 417, 212, 452, 219, 459)(179, 419, 213, 453, 223, 463)(181, 421, 192, 432, 183, 423)(184, 424, 209, 449, 191, 431)(189, 429, 210, 450, 190, 430)(196, 436, 214, 454, 226, 466)(197, 437, 203, 443, 227, 467)(198, 438, 204, 444, 217, 457)(220, 460, 234, 474, 228, 468)(221, 461, 222, 462, 231, 471)(224, 464, 233, 473, 230, 470)(225, 465, 236, 476, 237, 477)(229, 469, 235, 475, 232, 472)(238, 478, 239, 479, 240, 480)(481, 721)(482, 722)(483, 723)(484, 724)(485, 725)(486, 726)(487, 727)(488, 728)(489, 729)(490, 730)(491, 731)(492, 732)(493, 733)(494, 734)(495, 735)(496, 736)(497, 737)(498, 738)(499, 739)(500, 740)(501, 741)(502, 742)(503, 743)(504, 744)(505, 745)(506, 746)(507, 747)(508, 748)(509, 749)(510, 750)(511, 751)(512, 752)(513, 753)(514, 754)(515, 755)(516, 756)(517, 757)(518, 758)(519, 759)(520, 760)(521, 761)(522, 762)(523, 763)(524, 764)(525, 765)(526, 766)(527, 767)(528, 768)(529, 769)(530, 770)(531, 771)(532, 772)(533, 773)(534, 774)(535, 775)(536, 776)(537, 777)(538, 778)(539, 779)(540, 780)(541, 781)(542, 782)(543, 783)(544, 784)(545, 785)(546, 786)(547, 787)(548, 788)(549, 789)(550, 790)(551, 791)(552, 792)(553, 793)(554, 794)(555, 795)(556, 796)(557, 797)(558, 798)(559, 799)(560, 800)(561, 801)(562, 802)(563, 803)(564, 804)(565, 805)(566, 806)(567, 807)(568, 808)(569, 809)(570, 810)(571, 811)(572, 812)(573, 813)(574, 814)(575, 815)(576, 816)(577, 817)(578, 818)(579, 819)(580, 820)(581, 821)(582, 822)(583, 823)(584, 824)(585, 825)(586, 826)(587, 827)(588, 828)(589, 829)(590, 830)(591, 831)(592, 832)(593, 833)(594, 834)(595, 835)(596, 836)(597, 837)(598, 838)(599, 839)(600, 840)(601, 841)(602, 842)(603, 843)(604, 844)(605, 845)(606, 846)(607, 847)(608, 848)(609, 849)(610, 850)(611, 851)(612, 852)(613, 853)(614, 854)(615, 855)(616, 856)(617, 857)(618, 858)(619, 859)(620, 860)(621, 861)(622, 862)(623, 863)(624, 864)(625, 865)(626, 866)(627, 867)(628, 868)(629, 869)(630, 870)(631, 871)(632, 872)(633, 873)(634, 874)(635, 875)(636, 876)(637, 877)(638, 878)(639, 879)(640, 880)(641, 881)(642, 882)(643, 883)(644, 884)(645, 885)(646, 886)(647, 887)(648, 888)(649, 889)(650, 890)(651, 891)(652, 892)(653, 893)(654, 894)(655, 895)(656, 896)(657, 897)(658, 898)(659, 899)(660, 900)(661, 901)(662, 902)(663, 903)(664, 904)(665, 905)(666, 906)(667, 907)(668, 908)(669, 909)(670, 910)(671, 911)(672, 912)(673, 913)(674, 914)(675, 915)(676, 916)(677, 917)(678, 918)(679, 919)(680, 920)(681, 921)(682, 922)(683, 923)(684, 924)(685, 925)(686, 926)(687, 927)(688, 928)(689, 929)(690, 930)(691, 931)(692, 932)(693, 933)(694, 934)(695, 935)(696, 936)(697, 937)(698, 938)(699, 939)(700, 940)(701, 941)(702, 942)(703, 943)(704, 944)(705, 945)(706, 946)(707, 947)(708, 948)(709, 949)(710, 950)(711, 951)(712, 952)(713, 953)(714, 954)(715, 955)(716, 956)(717, 957)(718, 958)(719, 959)(720, 960) L = (1, 483)(2, 486)(3, 489)(4, 491)(5, 481)(6, 494)(7, 482)(8, 484)(9, 499)(10, 501)(11, 502)(12, 503)(13, 485)(14, 507)(15, 509)(16, 487)(17, 488)(18, 490)(19, 517)(20, 519)(21, 520)(22, 521)(23, 523)(24, 492)(25, 525)(26, 493)(27, 530)(28, 532)(29, 533)(30, 495)(31, 535)(32, 496)(33, 539)(34, 497)(35, 498)(36, 500)(37, 547)(38, 549)(39, 550)(40, 551)(41, 554)(42, 556)(43, 557)(44, 504)(45, 561)(46, 505)(47, 563)(48, 506)(49, 508)(50, 569)(51, 571)(52, 572)(53, 573)(54, 510)(55, 577)(56, 511)(57, 579)(58, 512)(59, 583)(60, 513)(61, 585)(62, 514)(63, 589)(64, 515)(65, 516)(66, 518)(67, 596)(68, 598)(69, 599)(70, 600)(71, 603)(72, 605)(73, 522)(74, 597)(75, 608)(76, 609)(77, 595)(78, 612)(79, 613)(80, 524)(81, 594)(82, 526)(83, 592)(84, 527)(85, 588)(86, 528)(87, 529)(88, 531)(89, 548)(90, 625)(91, 626)(92, 627)(93, 624)(94, 631)(95, 632)(96, 534)(97, 623)(98, 536)(99, 616)(100, 537)(101, 566)(102, 538)(103, 641)(104, 540)(105, 635)(106, 541)(107, 582)(108, 542)(109, 647)(110, 543)(111, 649)(112, 544)(113, 651)(114, 545)(115, 546)(116, 655)(117, 570)(118, 656)(119, 657)(120, 659)(121, 660)(122, 552)(123, 607)(124, 663)(125, 664)(126, 553)(127, 555)(128, 666)(129, 667)(130, 558)(131, 670)(132, 671)(133, 672)(134, 559)(135, 673)(136, 560)(137, 674)(138, 675)(139, 562)(140, 564)(141, 565)(142, 679)(143, 567)(144, 568)(145, 683)(146, 684)(147, 686)(148, 687)(149, 574)(150, 650)(151, 689)(152, 690)(153, 575)(154, 691)(155, 576)(156, 658)(157, 652)(158, 578)(159, 580)(160, 581)(161, 606)(162, 685)(163, 680)(164, 584)(165, 586)(166, 587)(167, 700)(168, 590)(169, 697)(170, 591)(171, 701)(172, 593)(173, 617)(174, 611)(175, 703)(176, 704)(177, 705)(178, 601)(179, 662)(180, 614)(181, 602)(182, 604)(183, 615)(184, 618)(185, 696)(186, 706)(187, 707)(188, 648)(189, 610)(190, 634)(191, 637)(192, 708)(193, 676)(194, 668)(195, 665)(196, 619)(197, 620)(198, 621)(199, 711)(200, 622)(201, 636)(202, 630)(203, 712)(204, 713)(205, 628)(206, 654)(207, 633)(208, 629)(209, 643)(210, 714)(211, 692)(212, 638)(213, 639)(214, 640)(215, 642)(216, 702)(217, 644)(218, 645)(219, 646)(220, 661)(221, 681)(222, 653)(223, 717)(224, 718)(225, 693)(226, 709)(227, 682)(228, 669)(229, 677)(230, 678)(231, 695)(232, 719)(233, 698)(234, 688)(235, 694)(236, 699)(237, 720)(238, 716)(239, 710)(240, 715)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960) local type(s) :: { ( 4, 40 ), ( 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E15.1357 Graph:: simple bipartite v = 320 e = 480 f = 132 degree seq :: [ 2^240, 6^80 ] E15.1359 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 14}) Quotient :: regular Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1, T1^14 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 21, 37, 63, 97, 96, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 79, 115, 165, 127, 87, 54, 31, 17, 8)(6, 13, 25, 43, 73, 109, 155, 204, 164, 114, 78, 46, 26, 14)(9, 18, 32, 55, 88, 128, 177, 220, 173, 122, 84, 51, 29, 16)(12, 23, 41, 69, 105, 150, 200, 252, 203, 154, 108, 72, 42, 24)(19, 34, 58, 91, 133, 181, 232, 261, 207, 159, 111, 74, 57, 33)(22, 39, 67, 53, 85, 123, 174, 221, 251, 199, 149, 104, 68, 40)(28, 49, 70, 45, 76, 103, 147, 192, 243, 218, 172, 120, 83, 50)(30, 52, 71, 106, 145, 194, 241, 231, 180, 132, 90, 56, 75, 44)(35, 60, 92, 135, 182, 234, 272, 217, 170, 119, 82, 48, 81, 59)(38, 65, 101, 77, 112, 160, 208, 262, 285, 248, 196, 146, 102, 66)(61, 94, 136, 184, 235, 277, 289, 259, 206, 156, 131, 89, 130, 93)(64, 99, 143, 107, 152, 126, 175, 223, 273, 282, 245, 193, 144, 100)(80, 117, 151, 121, 161, 113, 162, 198, 249, 281, 271, 215, 169, 118)(86, 125, 153, 201, 247, 283, 275, 229, 179, 129, 158, 110, 157, 124)(95, 138, 185, 237, 278, 284, 269, 214, 168, 116, 167, 134, 171, 137)(98, 141, 190, 148, 197, 163, 209, 264, 290, 276, 279, 242, 191, 142)(139, 187, 238, 244, 280, 250, 286, 256, 228, 178, 227, 183, 230, 186)(140, 188, 239, 195, 246, 202, 254, 211, 267, 233, 270, 236, 240, 189)(166, 212, 253, 216, 263, 219, 265, 210, 266, 287, 294, 291, 268, 213)(176, 225, 255, 288, 293, 292, 274, 226, 258, 205, 257, 222, 260, 224) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 80)(50, 81)(51, 69)(52, 67)(54, 86)(55, 89)(57, 75)(58, 83)(60, 93)(62, 95)(63, 98)(66, 99)(68, 103)(72, 107)(73, 110)(76, 101)(78, 113)(79, 116)(82, 117)(84, 121)(85, 124)(87, 126)(88, 129)(90, 130)(91, 134)(92, 132)(94, 137)(96, 139)(97, 140)(100, 141)(102, 145)(104, 148)(105, 151)(106, 143)(108, 153)(109, 156)(111, 157)(112, 161)(114, 163)(115, 166)(118, 167)(119, 150)(120, 171)(122, 160)(123, 159)(125, 152)(127, 176)(128, 178)(131, 158)(133, 169)(135, 183)(136, 172)(138, 186)(142, 188)(144, 192)(146, 195)(147, 190)(149, 198)(154, 202)(155, 205)(162, 197)(164, 210)(165, 211)(168, 212)(170, 216)(173, 219)(174, 222)(175, 224)(177, 226)(179, 227)(180, 230)(181, 233)(182, 229)(184, 236)(185, 231)(187, 189)(191, 241)(193, 244)(194, 239)(196, 247)(199, 250)(200, 253)(201, 246)(203, 255)(204, 256)(206, 257)(207, 260)(208, 263)(209, 265)(213, 267)(214, 252)(215, 270)(217, 262)(218, 240)(220, 264)(221, 259)(223, 261)(225, 254)(228, 258)(232, 268)(234, 276)(235, 271)(237, 242)(238, 243)(245, 281)(248, 284)(249, 280)(251, 287)(266, 286)(269, 288)(272, 292)(273, 291)(274, 290)(275, 279)(277, 282)(278, 283)(285, 293)(289, 294) local type(s) :: { ( 3^14 ) } Outer automorphisms :: reflexible Dual of E15.1360 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 21 e = 147 f = 98 degree seq :: [ 14^21 ] E15.1360 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 14}) Quotient :: regular Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1 * T2 * T1)^3, (T1^-1 * T2)^14 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 37, 41)(29, 42, 43)(30, 44, 45)(35, 49, 50)(36, 47, 51)(38, 52, 53)(46, 60, 61)(48, 62, 63)(54, 69, 70)(55, 58, 71)(56, 72, 73)(57, 74, 75)(59, 76, 77)(64, 82, 83)(65, 67, 84)(66, 85, 86)(68, 87, 88)(78, 98, 99)(79, 80, 100)(81, 101, 102)(89, 110, 111)(90, 92, 112)(91, 113, 114)(93, 108, 115)(94, 116, 117)(95, 96, 118)(97, 119, 120)(103, 195, 235)(104, 106, 198)(105, 197, 276)(107, 123, 174)(109, 201, 192)(121, 213, 241)(122, 215, 284)(124, 217, 175)(125, 218, 221)(126, 222, 225)(127, 226, 228)(128, 229, 227)(129, 204, 232)(130, 233, 199)(131, 236, 220)(132, 238, 202)(133, 239, 190)(134, 242, 224)(135, 184, 245)(136, 210, 189)(137, 247, 231)(138, 178, 250)(139, 251, 182)(140, 193, 173)(141, 255, 237)(142, 176, 258)(143, 259, 166)(144, 180, 183)(145, 263, 243)(146, 168, 265)(147, 164, 216)(148, 267, 172)(149, 186, 167)(150, 271, 248)(151, 153, 273)(152, 170, 191)(154, 230, 253)(155, 277, 196)(156, 279, 188)(157, 200, 160)(158, 268, 256)(159, 161, 205)(162, 219, 261)(163, 211, 214)(165, 252, 264)(169, 223, 269)(171, 260, 272)(177, 240, 278)(179, 234, 280)(181, 275, 282)(185, 246, 285)(187, 283, 266)(194, 287, 274)(203, 244, 290)(206, 254, 291)(207, 249, 209)(208, 289, 257)(212, 293, 262)(270, 294, 292)(281, 288, 286) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 46)(32, 43)(33, 47)(34, 48)(39, 54)(40, 55)(41, 56)(42, 57)(44, 58)(45, 59)(49, 64)(50, 65)(51, 66)(52, 67)(53, 68)(60, 78)(61, 79)(62, 80)(63, 81)(69, 89)(70, 90)(71, 91)(72, 92)(73, 93)(74, 94)(75, 95)(76, 96)(77, 97)(82, 103)(83, 104)(84, 105)(85, 106)(86, 107)(87, 108)(88, 109)(98, 121)(99, 117)(100, 122)(101, 123)(102, 124)(110, 134)(111, 202)(112, 162)(113, 132)(114, 205)(115, 207)(116, 154)(118, 203)(119, 159)(120, 211)(125, 219)(126, 223)(127, 197)(128, 230)(129, 215)(130, 234)(131, 213)(133, 240)(135, 244)(136, 246)(137, 195)(138, 249)(139, 252)(140, 254)(141, 242)(142, 257)(143, 260)(144, 262)(145, 247)(146, 201)(147, 266)(148, 268)(149, 270)(150, 236)(151, 217)(152, 274)(153, 275)(155, 255)(156, 271)(157, 281)(158, 229)(160, 282)(161, 283)(163, 263)(164, 286)(165, 218)(166, 214)(167, 272)(168, 287)(169, 198)(170, 288)(171, 222)(172, 188)(173, 256)(174, 289)(175, 277)(176, 292)(177, 226)(178, 293)(179, 238)(180, 294)(181, 233)(182, 196)(183, 264)(184, 206)(185, 204)(186, 291)(187, 239)(189, 248)(190, 243)(191, 278)(192, 279)(193, 212)(194, 210)(199, 237)(200, 285)(208, 251)(209, 267)(216, 280)(220, 227)(221, 224)(225, 231)(228, 235)(232, 241)(245, 253)(250, 261)(258, 269)(259, 290)(265, 276)(273, 284) local type(s) :: { ( 14^3 ) } Outer automorphisms :: reflexible Dual of E15.1359 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 98 e = 147 f = 21 degree seq :: [ 3^98 ] E15.1361 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 14}) Quotient :: edge Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1 * T1 * T2)^3, (T2^-1 * T1)^14 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 55, 56)(44, 47, 57)(45, 58, 59)(46, 60, 61)(48, 62, 63)(49, 64, 65)(50, 53, 66)(51, 67, 68)(52, 69, 70)(54, 71, 72)(73, 91, 92)(74, 76, 93)(75, 94, 95)(77, 96, 97)(78, 98, 99)(79, 80, 100)(81, 101, 102)(82, 103, 104)(83, 85, 105)(84, 106, 107)(86, 108, 109)(87, 110, 111)(88, 89, 112)(90, 113, 114)(115, 221, 196)(116, 118, 210)(117, 224, 279)(119, 123, 212)(120, 227, 294)(121, 228, 222)(122, 229, 289)(124, 202, 220)(125, 140, 144)(126, 136, 148)(127, 152, 146)(128, 156, 134)(129, 159, 150)(130, 163, 132)(131, 138, 166)(133, 142, 172)(135, 177, 167)(137, 180, 170)(139, 182, 173)(141, 185, 176)(143, 154, 188)(145, 158, 193)(147, 161, 197)(149, 164, 201)(151, 203, 189)(153, 184, 191)(155, 207, 174)(157, 205, 195)(160, 179, 199)(162, 216, 168)(165, 178, 223)(169, 181, 226)(171, 183, 274)(175, 186, 278)(187, 204, 277)(190, 206, 280)(192, 208, 276)(194, 209, 219)(198, 214, 273)(200, 218, 271)(211, 256, 272)(213, 249, 292)(215, 253, 270)(217, 247, 290)(225, 293, 262)(230, 282, 260)(231, 259, 263)(232, 286, 255)(233, 254, 266)(234, 284, 269)(235, 265, 264)(236, 268, 267)(237, 252, 251)(238, 288, 275)(239, 250, 248)(240, 291, 258)(241, 257, 281)(242, 287, 246)(243, 245, 283)(244, 261, 285)(295, 296)(297, 301)(298, 302)(299, 303)(300, 304)(305, 313)(306, 314)(307, 315)(308, 316)(309, 317)(310, 318)(311, 319)(312, 320)(321, 337)(322, 338)(323, 331)(324, 339)(325, 340)(326, 334)(327, 341)(328, 342)(329, 343)(330, 344)(332, 345)(333, 346)(335, 347)(336, 348)(349, 367)(350, 368)(351, 369)(352, 370)(353, 371)(354, 372)(355, 373)(356, 374)(357, 375)(358, 376)(359, 377)(360, 378)(361, 379)(362, 380)(363, 381)(364, 382)(365, 383)(366, 384)(385, 409)(386, 410)(387, 411)(388, 412)(389, 413)(390, 402)(391, 414)(392, 415)(393, 405)(394, 416)(395, 417)(396, 418)(397, 498)(398, 483)(399, 505)(400, 445)(401, 489)(403, 507)(404, 509)(406, 511)(407, 451)(408, 513)(419, 524)(420, 526)(421, 528)(422, 530)(423, 532)(424, 529)(425, 534)(426, 536)(427, 519)(428, 539)(429, 541)(430, 531)(431, 543)(432, 525)(433, 523)(434, 533)(435, 521)(436, 527)(437, 494)(438, 548)(439, 492)(440, 551)(441, 486)(442, 553)(443, 484)(444, 555)(446, 542)(447, 496)(448, 535)(449, 518)(450, 544)(452, 537)(453, 545)(454, 488)(455, 538)(456, 550)(457, 546)(458, 540)(459, 465)(460, 559)(461, 564)(462, 481)(463, 469)(464, 566)(466, 562)(467, 516)(468, 490)(470, 573)(471, 557)(472, 547)(473, 549)(474, 558)(475, 552)(476, 560)(477, 522)(478, 554)(479, 561)(480, 556)(482, 576)(485, 583)(487, 578)(491, 580)(493, 584)(495, 582)(497, 575)(499, 563)(500, 565)(501, 577)(502, 515)(503, 567)(504, 579)(506, 569)(508, 570)(510, 581)(512, 571)(514, 574)(517, 585)(520, 586)(568, 587)(572, 588) L = (1, 295)(2, 296)(3, 297)(4, 298)(5, 299)(6, 300)(7, 301)(8, 302)(9, 303)(10, 304)(11, 305)(12, 306)(13, 307)(14, 308)(15, 309)(16, 310)(17, 311)(18, 312)(19, 313)(20, 314)(21, 315)(22, 316)(23, 317)(24, 318)(25, 319)(26, 320)(27, 321)(28, 322)(29, 323)(30, 324)(31, 325)(32, 326)(33, 327)(34, 328)(35, 329)(36, 330)(37, 331)(38, 332)(39, 333)(40, 334)(41, 335)(42, 336)(43, 337)(44, 338)(45, 339)(46, 340)(47, 341)(48, 342)(49, 343)(50, 344)(51, 345)(52, 346)(53, 347)(54, 348)(55, 349)(56, 350)(57, 351)(58, 352)(59, 353)(60, 354)(61, 355)(62, 356)(63, 357)(64, 358)(65, 359)(66, 360)(67, 361)(68, 362)(69, 363)(70, 364)(71, 365)(72, 366)(73, 367)(74, 368)(75, 369)(76, 370)(77, 371)(78, 372)(79, 373)(80, 374)(81, 375)(82, 376)(83, 377)(84, 378)(85, 379)(86, 380)(87, 381)(88, 382)(89, 383)(90, 384)(91, 385)(92, 386)(93, 387)(94, 388)(95, 389)(96, 390)(97, 391)(98, 392)(99, 393)(100, 394)(101, 395)(102, 396)(103, 397)(104, 398)(105, 399)(106, 400)(107, 401)(108, 402)(109, 403)(110, 404)(111, 405)(112, 406)(113, 407)(114, 408)(115, 409)(116, 410)(117, 411)(118, 412)(119, 413)(120, 414)(121, 415)(122, 416)(123, 417)(124, 418)(125, 419)(126, 420)(127, 421)(128, 422)(129, 423)(130, 424)(131, 425)(132, 426)(133, 427)(134, 428)(135, 429)(136, 430)(137, 431)(138, 432)(139, 433)(140, 434)(141, 435)(142, 436)(143, 437)(144, 438)(145, 439)(146, 440)(147, 441)(148, 442)(149, 443)(150, 444)(151, 445)(152, 446)(153, 447)(154, 448)(155, 449)(156, 450)(157, 451)(158, 452)(159, 453)(160, 454)(161, 455)(162, 456)(163, 457)(164, 458)(165, 459)(166, 460)(167, 461)(168, 462)(169, 463)(170, 464)(171, 465)(172, 466)(173, 467)(174, 468)(175, 469)(176, 470)(177, 471)(178, 472)(179, 473)(180, 474)(181, 475)(182, 476)(183, 477)(184, 478)(185, 479)(186, 480)(187, 481)(188, 482)(189, 483)(190, 484)(191, 485)(192, 486)(193, 487)(194, 488)(195, 489)(196, 490)(197, 491)(198, 492)(199, 493)(200, 494)(201, 495)(202, 496)(203, 497)(204, 498)(205, 499)(206, 500)(207, 501)(208, 502)(209, 503)(210, 504)(211, 505)(212, 506)(213, 507)(214, 508)(215, 509)(216, 510)(217, 511)(218, 512)(219, 513)(220, 514)(221, 515)(222, 516)(223, 517)(224, 518)(225, 519)(226, 520)(227, 521)(228, 522)(229, 523)(230, 524)(231, 525)(232, 526)(233, 527)(234, 528)(235, 529)(236, 530)(237, 531)(238, 532)(239, 533)(240, 534)(241, 535)(242, 536)(243, 537)(244, 538)(245, 539)(246, 540)(247, 541)(248, 542)(249, 543)(250, 544)(251, 545)(252, 546)(253, 547)(254, 548)(255, 549)(256, 550)(257, 551)(258, 552)(259, 553)(260, 554)(261, 555)(262, 556)(263, 557)(264, 558)(265, 559)(266, 560)(267, 561)(268, 562)(269, 563)(270, 564)(271, 565)(272, 566)(273, 567)(274, 568)(275, 569)(276, 570)(277, 571)(278, 572)(279, 573)(280, 574)(281, 575)(282, 576)(283, 577)(284, 578)(285, 579)(286, 580)(287, 581)(288, 582)(289, 583)(290, 584)(291, 585)(292, 586)(293, 587)(294, 588) local type(s) :: { ( 28, 28 ), ( 28^3 ) } Outer automorphisms :: reflexible Dual of E15.1365 Transitivity :: ET+ Graph:: simple bipartite v = 245 e = 294 f = 21 degree seq :: [ 2^147, 3^98 ] E15.1362 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 14}) Quotient :: edge Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-1, (T2^2 * T1^-1)^3, T2^14, T2^3 * T1^-1 * T2^-5 * T1 * T2^4 * T1^-1 * T2^-6 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 37, 64, 98, 142, 115, 77, 48, 26, 13, 5)(2, 6, 14, 27, 50, 80, 119, 165, 129, 88, 57, 32, 16, 7)(4, 11, 22, 41, 69, 105, 149, 183, 135, 92, 60, 34, 17, 8)(10, 21, 40, 67, 101, 145, 194, 234, 185, 136, 94, 61, 35, 18)(12, 23, 43, 71, 107, 152, 202, 249, 205, 153, 109, 72, 44, 24)(15, 29, 53, 82, 122, 168, 219, 263, 220, 169, 123, 83, 54, 30)(20, 39, 31, 55, 84, 124, 170, 221, 236, 186, 138, 95, 62, 36)(25, 45, 73, 110, 154, 206, 251, 244, 196, 146, 103, 68, 42, 46)(28, 52, 33, 58, 89, 130, 177, 226, 257, 212, 161, 116, 78, 49)(38, 66, 59, 90, 131, 178, 227, 269, 276, 237, 188, 139, 96, 63)(47, 74, 111, 156, 207, 253, 283, 258, 213, 162, 117, 79, 51, 75)(56, 85, 125, 172, 222, 265, 291, 279, 245, 197, 147, 104, 70, 86)(65, 100, 93, 127, 87, 126, 173, 223, 266, 277, 239, 189, 140, 97)(76, 112, 157, 209, 254, 285, 280, 246, 198, 148, 106, 151, 108, 113)(81, 121, 102, 133, 91, 132, 179, 228, 270, 288, 259, 214, 163, 118)(99, 144, 137, 181, 134, 180, 229, 271, 293, 284, 278, 240, 190, 141)(114, 158, 210, 256, 286, 275, 289, 260, 215, 164, 120, 167, 155, 159)(128, 174, 224, 268, 292, 287, 294, 281, 247, 199, 150, 201, 171, 175)(143, 193, 187, 233, 184, 225, 176, 217, 262, 252, 282, 255, 241, 191)(160, 192, 242, 238, 274, 235, 273, 232, 200, 248, 203, 250, 208, 211)(166, 218, 195, 243, 204, 231, 182, 230, 272, 264, 290, 267, 261, 216)(295, 296, 298)(297, 302, 304)(299, 306, 300)(301, 309, 305)(303, 312, 314)(307, 319, 317)(308, 318, 322)(310, 325, 323)(311, 327, 315)(313, 330, 332)(316, 324, 336)(320, 341, 339)(321, 343, 345)(326, 350, 349)(328, 353, 352)(329, 347, 333)(331, 357, 359)(334, 346, 338)(335, 362, 364)(337, 340, 348)(342, 370, 368)(344, 373, 375)(351, 381, 379)(354, 385, 384)(355, 387, 376)(356, 383, 360)(358, 391, 393)(361, 366, 396)(363, 398, 400)(365, 377, 402)(367, 369, 372)(371, 408, 406)(374, 412, 414)(378, 380, 397)(382, 422, 420)(386, 428, 426)(388, 419, 421)(389, 431, 424)(390, 416, 394)(392, 435, 437)(395, 415, 411)(399, 442, 444)(401, 445, 441)(403, 425, 427)(404, 410, 449)(405, 407, 417)(409, 454, 452)(413, 458, 460)(418, 440, 465)(423, 470, 468)(429, 476, 474)(430, 478, 466)(432, 473, 475)(433, 481, 462)(434, 471, 438)(436, 485, 486)(439, 456, 489)(443, 493, 494)(446, 491, 497)(447, 498, 472)(448, 461, 457)(450, 463, 502)(451, 453, 455)(459, 510, 511)(464, 495, 492)(467, 469, 490)(477, 526, 524)(479, 518, 519)(480, 529, 522)(482, 516, 527)(483, 532, 520)(484, 513, 487)(488, 512, 509)(496, 542, 541)(499, 523, 525)(500, 508, 546)(501, 544, 539)(503, 506, 549)(504, 505, 514)(507, 521, 537)(515, 540, 558)(517, 538, 561)(528, 554, 562)(530, 566, 567)(531, 569, 559)(533, 564, 568)(534, 550, 557)(535, 551, 536)(543, 575, 565)(545, 556, 555)(547, 573, 578)(548, 576, 553)(552, 581, 563)(560, 584, 574)(570, 586, 583)(571, 579, 582)(572, 585, 580)(577, 587, 588) L = (1, 295)(2, 296)(3, 297)(4, 298)(5, 299)(6, 300)(7, 301)(8, 302)(9, 303)(10, 304)(11, 305)(12, 306)(13, 307)(14, 308)(15, 309)(16, 310)(17, 311)(18, 312)(19, 313)(20, 314)(21, 315)(22, 316)(23, 317)(24, 318)(25, 319)(26, 320)(27, 321)(28, 322)(29, 323)(30, 324)(31, 325)(32, 326)(33, 327)(34, 328)(35, 329)(36, 330)(37, 331)(38, 332)(39, 333)(40, 334)(41, 335)(42, 336)(43, 337)(44, 338)(45, 339)(46, 340)(47, 341)(48, 342)(49, 343)(50, 344)(51, 345)(52, 346)(53, 347)(54, 348)(55, 349)(56, 350)(57, 351)(58, 352)(59, 353)(60, 354)(61, 355)(62, 356)(63, 357)(64, 358)(65, 359)(66, 360)(67, 361)(68, 362)(69, 363)(70, 364)(71, 365)(72, 366)(73, 367)(74, 368)(75, 369)(76, 370)(77, 371)(78, 372)(79, 373)(80, 374)(81, 375)(82, 376)(83, 377)(84, 378)(85, 379)(86, 380)(87, 381)(88, 382)(89, 383)(90, 384)(91, 385)(92, 386)(93, 387)(94, 388)(95, 389)(96, 390)(97, 391)(98, 392)(99, 393)(100, 394)(101, 395)(102, 396)(103, 397)(104, 398)(105, 399)(106, 400)(107, 401)(108, 402)(109, 403)(110, 404)(111, 405)(112, 406)(113, 407)(114, 408)(115, 409)(116, 410)(117, 411)(118, 412)(119, 413)(120, 414)(121, 415)(122, 416)(123, 417)(124, 418)(125, 419)(126, 420)(127, 421)(128, 422)(129, 423)(130, 424)(131, 425)(132, 426)(133, 427)(134, 428)(135, 429)(136, 430)(137, 431)(138, 432)(139, 433)(140, 434)(141, 435)(142, 436)(143, 437)(144, 438)(145, 439)(146, 440)(147, 441)(148, 442)(149, 443)(150, 444)(151, 445)(152, 446)(153, 447)(154, 448)(155, 449)(156, 450)(157, 451)(158, 452)(159, 453)(160, 454)(161, 455)(162, 456)(163, 457)(164, 458)(165, 459)(166, 460)(167, 461)(168, 462)(169, 463)(170, 464)(171, 465)(172, 466)(173, 467)(174, 468)(175, 469)(176, 470)(177, 471)(178, 472)(179, 473)(180, 474)(181, 475)(182, 476)(183, 477)(184, 478)(185, 479)(186, 480)(187, 481)(188, 482)(189, 483)(190, 484)(191, 485)(192, 486)(193, 487)(194, 488)(195, 489)(196, 490)(197, 491)(198, 492)(199, 493)(200, 494)(201, 495)(202, 496)(203, 497)(204, 498)(205, 499)(206, 500)(207, 501)(208, 502)(209, 503)(210, 504)(211, 505)(212, 506)(213, 507)(214, 508)(215, 509)(216, 510)(217, 511)(218, 512)(219, 513)(220, 514)(221, 515)(222, 516)(223, 517)(224, 518)(225, 519)(226, 520)(227, 521)(228, 522)(229, 523)(230, 524)(231, 525)(232, 526)(233, 527)(234, 528)(235, 529)(236, 530)(237, 531)(238, 532)(239, 533)(240, 534)(241, 535)(242, 536)(243, 537)(244, 538)(245, 539)(246, 540)(247, 541)(248, 542)(249, 543)(250, 544)(251, 545)(252, 546)(253, 547)(254, 548)(255, 549)(256, 550)(257, 551)(258, 552)(259, 553)(260, 554)(261, 555)(262, 556)(263, 557)(264, 558)(265, 559)(266, 560)(267, 561)(268, 562)(269, 563)(270, 564)(271, 565)(272, 566)(273, 567)(274, 568)(275, 569)(276, 570)(277, 571)(278, 572)(279, 573)(280, 574)(281, 575)(282, 576)(283, 577)(284, 578)(285, 579)(286, 580)(287, 581)(288, 582)(289, 583)(290, 584)(291, 585)(292, 586)(293, 587)(294, 588) local type(s) :: { ( 4^3 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E15.1366 Transitivity :: ET+ Graph:: simple bipartite v = 119 e = 294 f = 147 degree seq :: [ 3^98, 14^21 ] E15.1363 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 14}) Quotient :: edge Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1, T1^14 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 80)(50, 81)(51, 69)(52, 67)(54, 86)(55, 89)(57, 75)(58, 83)(60, 93)(62, 95)(63, 98)(66, 99)(68, 103)(72, 107)(73, 110)(76, 101)(78, 113)(79, 116)(82, 117)(84, 121)(85, 124)(87, 126)(88, 129)(90, 130)(91, 134)(92, 132)(94, 137)(96, 139)(97, 140)(100, 141)(102, 145)(104, 148)(105, 151)(106, 143)(108, 153)(109, 156)(111, 157)(112, 161)(114, 163)(115, 166)(118, 167)(119, 150)(120, 171)(122, 160)(123, 159)(125, 152)(127, 176)(128, 178)(131, 158)(133, 169)(135, 183)(136, 172)(138, 186)(142, 188)(144, 192)(146, 195)(147, 190)(149, 198)(154, 202)(155, 205)(162, 197)(164, 210)(165, 211)(168, 212)(170, 216)(173, 219)(174, 222)(175, 224)(177, 226)(179, 227)(180, 230)(181, 233)(182, 229)(184, 236)(185, 231)(187, 189)(191, 241)(193, 244)(194, 239)(196, 247)(199, 250)(200, 253)(201, 246)(203, 255)(204, 256)(206, 257)(207, 260)(208, 263)(209, 265)(213, 267)(214, 252)(215, 270)(217, 262)(218, 240)(220, 264)(221, 259)(223, 261)(225, 254)(228, 258)(232, 268)(234, 276)(235, 271)(237, 242)(238, 243)(245, 281)(248, 284)(249, 280)(251, 287)(266, 286)(269, 288)(272, 292)(273, 291)(274, 290)(275, 279)(277, 282)(278, 283)(285, 293)(289, 294)(295, 296, 299, 305, 315, 331, 357, 391, 390, 356, 330, 314, 304, 298)(297, 301, 309, 321, 341, 373, 409, 459, 421, 381, 348, 325, 311, 302)(300, 307, 319, 337, 367, 403, 449, 498, 458, 408, 372, 340, 320, 308)(303, 312, 326, 349, 382, 422, 471, 514, 467, 416, 378, 345, 323, 310)(306, 317, 335, 363, 399, 444, 494, 546, 497, 448, 402, 366, 336, 318)(313, 328, 352, 385, 427, 475, 526, 555, 501, 453, 405, 368, 351, 327)(316, 333, 361, 347, 379, 417, 468, 515, 545, 493, 443, 398, 362, 334)(322, 343, 364, 339, 370, 397, 441, 486, 537, 512, 466, 414, 377, 344)(324, 346, 365, 400, 439, 488, 535, 525, 474, 426, 384, 350, 369, 338)(329, 354, 386, 429, 476, 528, 566, 511, 464, 413, 376, 342, 375, 353)(332, 359, 395, 371, 406, 454, 502, 556, 579, 542, 490, 440, 396, 360)(355, 388, 430, 478, 529, 571, 583, 553, 500, 450, 425, 383, 424, 387)(358, 393, 437, 401, 446, 420, 469, 517, 567, 576, 539, 487, 438, 394)(374, 411, 445, 415, 455, 407, 456, 492, 543, 575, 565, 509, 463, 412)(380, 419, 447, 495, 541, 577, 569, 523, 473, 423, 452, 404, 451, 418)(389, 432, 479, 531, 572, 578, 563, 508, 462, 410, 461, 428, 465, 431)(392, 435, 484, 442, 491, 457, 503, 558, 584, 570, 573, 536, 485, 436)(433, 481, 532, 538, 574, 544, 580, 550, 522, 472, 521, 477, 524, 480)(434, 482, 533, 489, 540, 496, 548, 505, 561, 527, 564, 530, 534, 483)(460, 506, 547, 510, 557, 513, 559, 504, 560, 581, 588, 585, 562, 507)(470, 519, 549, 582, 587, 586, 568, 520, 552, 499, 551, 516, 554, 518) L = (1, 295)(2, 296)(3, 297)(4, 298)(5, 299)(6, 300)(7, 301)(8, 302)(9, 303)(10, 304)(11, 305)(12, 306)(13, 307)(14, 308)(15, 309)(16, 310)(17, 311)(18, 312)(19, 313)(20, 314)(21, 315)(22, 316)(23, 317)(24, 318)(25, 319)(26, 320)(27, 321)(28, 322)(29, 323)(30, 324)(31, 325)(32, 326)(33, 327)(34, 328)(35, 329)(36, 330)(37, 331)(38, 332)(39, 333)(40, 334)(41, 335)(42, 336)(43, 337)(44, 338)(45, 339)(46, 340)(47, 341)(48, 342)(49, 343)(50, 344)(51, 345)(52, 346)(53, 347)(54, 348)(55, 349)(56, 350)(57, 351)(58, 352)(59, 353)(60, 354)(61, 355)(62, 356)(63, 357)(64, 358)(65, 359)(66, 360)(67, 361)(68, 362)(69, 363)(70, 364)(71, 365)(72, 366)(73, 367)(74, 368)(75, 369)(76, 370)(77, 371)(78, 372)(79, 373)(80, 374)(81, 375)(82, 376)(83, 377)(84, 378)(85, 379)(86, 380)(87, 381)(88, 382)(89, 383)(90, 384)(91, 385)(92, 386)(93, 387)(94, 388)(95, 389)(96, 390)(97, 391)(98, 392)(99, 393)(100, 394)(101, 395)(102, 396)(103, 397)(104, 398)(105, 399)(106, 400)(107, 401)(108, 402)(109, 403)(110, 404)(111, 405)(112, 406)(113, 407)(114, 408)(115, 409)(116, 410)(117, 411)(118, 412)(119, 413)(120, 414)(121, 415)(122, 416)(123, 417)(124, 418)(125, 419)(126, 420)(127, 421)(128, 422)(129, 423)(130, 424)(131, 425)(132, 426)(133, 427)(134, 428)(135, 429)(136, 430)(137, 431)(138, 432)(139, 433)(140, 434)(141, 435)(142, 436)(143, 437)(144, 438)(145, 439)(146, 440)(147, 441)(148, 442)(149, 443)(150, 444)(151, 445)(152, 446)(153, 447)(154, 448)(155, 449)(156, 450)(157, 451)(158, 452)(159, 453)(160, 454)(161, 455)(162, 456)(163, 457)(164, 458)(165, 459)(166, 460)(167, 461)(168, 462)(169, 463)(170, 464)(171, 465)(172, 466)(173, 467)(174, 468)(175, 469)(176, 470)(177, 471)(178, 472)(179, 473)(180, 474)(181, 475)(182, 476)(183, 477)(184, 478)(185, 479)(186, 480)(187, 481)(188, 482)(189, 483)(190, 484)(191, 485)(192, 486)(193, 487)(194, 488)(195, 489)(196, 490)(197, 491)(198, 492)(199, 493)(200, 494)(201, 495)(202, 496)(203, 497)(204, 498)(205, 499)(206, 500)(207, 501)(208, 502)(209, 503)(210, 504)(211, 505)(212, 506)(213, 507)(214, 508)(215, 509)(216, 510)(217, 511)(218, 512)(219, 513)(220, 514)(221, 515)(222, 516)(223, 517)(224, 518)(225, 519)(226, 520)(227, 521)(228, 522)(229, 523)(230, 524)(231, 525)(232, 526)(233, 527)(234, 528)(235, 529)(236, 530)(237, 531)(238, 532)(239, 533)(240, 534)(241, 535)(242, 536)(243, 537)(244, 538)(245, 539)(246, 540)(247, 541)(248, 542)(249, 543)(250, 544)(251, 545)(252, 546)(253, 547)(254, 548)(255, 549)(256, 550)(257, 551)(258, 552)(259, 553)(260, 554)(261, 555)(262, 556)(263, 557)(264, 558)(265, 559)(266, 560)(267, 561)(268, 562)(269, 563)(270, 564)(271, 565)(272, 566)(273, 567)(274, 568)(275, 569)(276, 570)(277, 571)(278, 572)(279, 573)(280, 574)(281, 575)(282, 576)(283, 577)(284, 578)(285, 579)(286, 580)(287, 581)(288, 582)(289, 583)(290, 584)(291, 585)(292, 586)(293, 587)(294, 588) local type(s) :: { ( 6, 6 ), ( 6^14 ) } Outer automorphisms :: reflexible Dual of E15.1364 Transitivity :: ET+ Graph:: simple bipartite v = 168 e = 294 f = 98 degree seq :: [ 2^147, 14^21 ] E15.1364 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 14}) Quotient :: loop Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1 * T1 * T2)^3, (T2^-1 * T1)^14 ] Map:: R = (1, 295, 3, 297, 4, 298)(2, 296, 5, 299, 6, 300)(7, 301, 11, 305, 12, 306)(8, 302, 13, 307, 14, 308)(9, 303, 15, 309, 16, 310)(10, 304, 17, 311, 18, 312)(19, 313, 27, 321, 28, 322)(20, 314, 29, 323, 30, 324)(21, 315, 31, 325, 32, 326)(22, 316, 33, 327, 34, 328)(23, 317, 35, 329, 36, 330)(24, 318, 37, 331, 38, 332)(25, 319, 39, 333, 40, 334)(26, 320, 41, 335, 42, 336)(43, 337, 55, 349, 56, 350)(44, 338, 47, 341, 57, 351)(45, 339, 58, 352, 59, 353)(46, 340, 60, 354, 61, 355)(48, 342, 62, 356, 63, 357)(49, 343, 64, 358, 65, 359)(50, 344, 53, 347, 66, 360)(51, 345, 67, 361, 68, 362)(52, 346, 69, 363, 70, 364)(54, 348, 71, 365, 72, 366)(73, 367, 91, 385, 92, 386)(74, 368, 76, 370, 93, 387)(75, 369, 94, 388, 95, 389)(77, 371, 96, 390, 97, 391)(78, 372, 98, 392, 99, 393)(79, 373, 80, 374, 100, 394)(81, 375, 101, 395, 102, 396)(82, 376, 103, 397, 104, 398)(83, 377, 85, 379, 105, 399)(84, 378, 106, 400, 107, 401)(86, 380, 108, 402, 109, 403)(87, 381, 110, 404, 111, 405)(88, 382, 89, 383, 112, 406)(90, 384, 113, 407, 114, 408)(115, 409, 209, 503, 289, 583)(116, 410, 118, 412, 212, 506)(117, 411, 211, 505, 191, 485)(119, 413, 123, 417, 217, 511)(120, 414, 214, 508, 176, 470)(121, 415, 215, 509, 291, 585)(122, 416, 216, 510, 171, 465)(124, 418, 219, 513, 174, 468)(125, 419, 188, 482, 187, 481)(126, 420, 200, 494, 198, 492)(127, 421, 177, 471, 193, 487)(128, 422, 175, 469, 173, 467)(129, 423, 168, 462, 205, 499)(130, 424, 166, 460, 164, 458)(131, 425, 225, 519, 226, 520)(132, 426, 227, 521, 203, 497)(133, 427, 152, 446, 202, 496)(134, 428, 170, 464, 155, 449)(135, 429, 163, 457, 231, 525)(136, 430, 158, 452, 154, 448)(137, 431, 144, 438, 190, 484)(138, 432, 179, 473, 147, 441)(139, 433, 172, 466, 236, 530)(140, 434, 150, 444, 146, 440)(141, 435, 238, 532, 162, 456)(142, 436, 239, 533, 240, 534)(143, 437, 148, 442, 195, 489)(145, 439, 186, 480, 242, 536)(149, 443, 192, 486, 246, 540)(151, 445, 156, 450, 208, 502)(153, 447, 197, 491, 249, 543)(157, 451, 204, 498, 252, 546)(159, 453, 254, 548, 167, 461)(160, 454, 235, 529, 255, 549)(161, 455, 230, 524, 256, 550)(165, 459, 182, 476, 259, 553)(169, 463, 210, 504, 262, 556)(178, 472, 261, 555, 266, 560)(180, 474, 223, 517, 269, 563)(181, 475, 228, 522, 271, 565)(183, 477, 221, 515, 273, 567)(184, 478, 220, 514, 196, 490)(185, 479, 233, 527, 276, 570)(189, 483, 248, 542, 278, 572)(194, 488, 257, 551, 275, 569)(199, 493, 206, 500, 245, 539)(201, 495, 241, 535, 285, 579)(207, 501, 264, 558, 270, 564)(213, 507, 222, 516, 290, 584)(218, 512, 244, 538, 292, 586)(224, 518, 293, 587, 274, 568)(229, 523, 284, 578, 272, 566)(232, 526, 283, 577, 288, 582)(234, 528, 280, 574, 268, 562)(237, 531, 277, 571, 282, 576)(243, 537, 281, 575, 267, 561)(247, 541, 265, 559, 279, 573)(250, 544, 287, 581, 263, 557)(251, 545, 294, 588, 260, 554)(253, 547, 258, 552, 286, 580) L = (1, 296)(2, 295)(3, 301)(4, 302)(5, 303)(6, 304)(7, 297)(8, 298)(9, 299)(10, 300)(11, 313)(12, 314)(13, 315)(14, 316)(15, 317)(16, 318)(17, 319)(18, 320)(19, 305)(20, 306)(21, 307)(22, 308)(23, 309)(24, 310)(25, 311)(26, 312)(27, 337)(28, 338)(29, 331)(30, 339)(31, 340)(32, 334)(33, 341)(34, 342)(35, 343)(36, 344)(37, 323)(38, 345)(39, 346)(40, 326)(41, 347)(42, 348)(43, 321)(44, 322)(45, 324)(46, 325)(47, 327)(48, 328)(49, 329)(50, 330)(51, 332)(52, 333)(53, 335)(54, 336)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 349)(74, 350)(75, 351)(76, 352)(77, 353)(78, 354)(79, 355)(80, 356)(81, 357)(82, 358)(83, 359)(84, 360)(85, 361)(86, 362)(87, 363)(88, 364)(89, 365)(90, 366)(91, 409)(92, 410)(93, 411)(94, 412)(95, 413)(96, 402)(97, 414)(98, 415)(99, 405)(100, 416)(101, 417)(102, 418)(103, 436)(104, 490)(105, 426)(106, 478)(107, 493)(108, 390)(109, 453)(110, 425)(111, 393)(112, 435)(113, 500)(114, 476)(115, 385)(116, 386)(117, 387)(118, 388)(119, 389)(120, 391)(121, 392)(122, 394)(123, 395)(124, 396)(125, 514)(126, 506)(127, 515)(128, 516)(129, 517)(130, 518)(131, 404)(132, 399)(133, 522)(134, 523)(135, 524)(136, 526)(137, 527)(138, 528)(139, 529)(140, 531)(141, 406)(142, 397)(143, 535)(144, 501)(145, 533)(146, 537)(147, 538)(148, 539)(149, 491)(150, 541)(151, 542)(152, 488)(153, 503)(154, 544)(155, 545)(156, 511)(157, 480)(158, 547)(159, 403)(160, 509)(161, 519)(162, 551)(163, 472)(164, 552)(165, 486)(166, 554)(167, 555)(168, 483)(169, 466)(170, 557)(171, 558)(172, 463)(173, 559)(174, 498)(175, 512)(176, 504)(177, 495)(178, 457)(179, 561)(180, 521)(181, 494)(182, 408)(183, 505)(184, 400)(185, 482)(186, 451)(187, 571)(188, 479)(189, 462)(190, 573)(191, 574)(192, 459)(193, 575)(194, 446)(195, 576)(196, 398)(197, 443)(198, 577)(199, 401)(200, 475)(201, 471)(202, 580)(203, 578)(204, 468)(205, 581)(206, 407)(207, 438)(208, 582)(209, 447)(210, 470)(211, 477)(212, 420)(213, 510)(214, 562)(215, 454)(216, 507)(217, 450)(218, 469)(219, 564)(220, 419)(221, 421)(222, 422)(223, 423)(224, 424)(225, 455)(226, 587)(227, 474)(228, 427)(229, 428)(230, 429)(231, 588)(232, 430)(233, 431)(234, 432)(235, 433)(236, 586)(237, 434)(238, 568)(239, 439)(240, 563)(241, 437)(242, 570)(243, 440)(244, 441)(245, 442)(246, 579)(247, 444)(248, 445)(249, 565)(250, 448)(251, 449)(252, 572)(253, 452)(254, 566)(255, 550)(256, 549)(257, 456)(258, 458)(259, 569)(260, 460)(261, 461)(262, 560)(263, 464)(264, 465)(265, 467)(266, 556)(267, 473)(268, 508)(269, 534)(270, 513)(271, 543)(272, 548)(273, 583)(274, 532)(275, 553)(276, 536)(277, 481)(278, 546)(279, 484)(280, 485)(281, 487)(282, 489)(283, 492)(284, 497)(285, 540)(286, 496)(287, 499)(288, 502)(289, 567)(290, 585)(291, 584)(292, 530)(293, 520)(294, 525) local type(s) :: { ( 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E15.1363 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 98 e = 294 f = 168 degree seq :: [ 6^98 ] E15.1365 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 14}) Quotient :: loop Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-1, (T2^2 * T1^-1)^3, T2^14, T2^3 * T1^-1 * T2^-5 * T1 * T2^4 * T1^-1 * T2^-6 * T1^-1 ] Map:: R = (1, 295, 3, 297, 9, 303, 19, 313, 37, 331, 64, 358, 98, 392, 142, 436, 115, 409, 77, 371, 48, 342, 26, 320, 13, 307, 5, 299)(2, 296, 6, 300, 14, 308, 27, 321, 50, 344, 80, 374, 119, 413, 165, 459, 129, 423, 88, 382, 57, 351, 32, 326, 16, 310, 7, 301)(4, 298, 11, 305, 22, 316, 41, 335, 69, 363, 105, 399, 149, 443, 183, 477, 135, 429, 92, 386, 60, 354, 34, 328, 17, 311, 8, 302)(10, 304, 21, 315, 40, 334, 67, 361, 101, 395, 145, 439, 194, 488, 234, 528, 185, 479, 136, 430, 94, 388, 61, 355, 35, 329, 18, 312)(12, 306, 23, 317, 43, 337, 71, 365, 107, 401, 152, 446, 202, 496, 249, 543, 205, 499, 153, 447, 109, 403, 72, 366, 44, 338, 24, 318)(15, 309, 29, 323, 53, 347, 82, 376, 122, 416, 168, 462, 219, 513, 263, 557, 220, 514, 169, 463, 123, 417, 83, 377, 54, 348, 30, 324)(20, 314, 39, 333, 31, 325, 55, 349, 84, 378, 124, 418, 170, 464, 221, 515, 236, 530, 186, 480, 138, 432, 95, 389, 62, 356, 36, 330)(25, 319, 45, 339, 73, 367, 110, 404, 154, 448, 206, 500, 251, 545, 244, 538, 196, 490, 146, 440, 103, 397, 68, 362, 42, 336, 46, 340)(28, 322, 52, 346, 33, 327, 58, 352, 89, 383, 130, 424, 177, 471, 226, 520, 257, 551, 212, 506, 161, 455, 116, 410, 78, 372, 49, 343)(38, 332, 66, 360, 59, 353, 90, 384, 131, 425, 178, 472, 227, 521, 269, 563, 276, 570, 237, 531, 188, 482, 139, 433, 96, 390, 63, 357)(47, 341, 74, 368, 111, 405, 156, 450, 207, 501, 253, 547, 283, 577, 258, 552, 213, 507, 162, 456, 117, 411, 79, 373, 51, 345, 75, 369)(56, 350, 85, 379, 125, 419, 172, 466, 222, 516, 265, 559, 291, 585, 279, 573, 245, 539, 197, 491, 147, 441, 104, 398, 70, 364, 86, 380)(65, 359, 100, 394, 93, 387, 127, 421, 87, 381, 126, 420, 173, 467, 223, 517, 266, 560, 277, 571, 239, 533, 189, 483, 140, 434, 97, 391)(76, 370, 112, 406, 157, 451, 209, 503, 254, 548, 285, 579, 280, 574, 246, 540, 198, 492, 148, 442, 106, 400, 151, 445, 108, 402, 113, 407)(81, 375, 121, 415, 102, 396, 133, 427, 91, 385, 132, 426, 179, 473, 228, 522, 270, 564, 288, 582, 259, 553, 214, 508, 163, 457, 118, 412)(99, 393, 144, 438, 137, 431, 181, 475, 134, 428, 180, 474, 229, 523, 271, 565, 293, 587, 284, 578, 278, 572, 240, 534, 190, 484, 141, 435)(114, 408, 158, 452, 210, 504, 256, 550, 286, 580, 275, 569, 289, 583, 260, 554, 215, 509, 164, 458, 120, 414, 167, 461, 155, 449, 159, 453)(128, 422, 174, 468, 224, 518, 268, 562, 292, 586, 287, 581, 294, 588, 281, 575, 247, 541, 199, 493, 150, 444, 201, 495, 171, 465, 175, 469)(143, 437, 193, 487, 187, 481, 233, 527, 184, 478, 225, 519, 176, 470, 217, 511, 262, 556, 252, 546, 282, 576, 255, 549, 241, 535, 191, 485)(160, 454, 192, 486, 242, 536, 238, 532, 274, 568, 235, 529, 273, 567, 232, 526, 200, 494, 248, 542, 203, 497, 250, 544, 208, 502, 211, 505)(166, 460, 218, 512, 195, 489, 243, 537, 204, 498, 231, 525, 182, 476, 230, 524, 272, 566, 264, 558, 290, 584, 267, 561, 261, 555, 216, 510) L = (1, 296)(2, 298)(3, 302)(4, 295)(5, 306)(6, 299)(7, 309)(8, 304)(9, 312)(10, 297)(11, 301)(12, 300)(13, 319)(14, 318)(15, 305)(16, 325)(17, 327)(18, 314)(19, 330)(20, 303)(21, 311)(22, 324)(23, 307)(24, 322)(25, 317)(26, 341)(27, 343)(28, 308)(29, 310)(30, 336)(31, 323)(32, 350)(33, 315)(34, 353)(35, 347)(36, 332)(37, 357)(38, 313)(39, 329)(40, 346)(41, 362)(42, 316)(43, 340)(44, 334)(45, 320)(46, 348)(47, 339)(48, 370)(49, 345)(50, 373)(51, 321)(52, 338)(53, 333)(54, 337)(55, 326)(56, 349)(57, 381)(58, 328)(59, 352)(60, 385)(61, 387)(62, 383)(63, 359)(64, 391)(65, 331)(66, 356)(67, 366)(68, 364)(69, 398)(70, 335)(71, 377)(72, 396)(73, 369)(74, 342)(75, 372)(76, 368)(77, 408)(78, 367)(79, 375)(80, 412)(81, 344)(82, 355)(83, 402)(84, 380)(85, 351)(86, 397)(87, 379)(88, 422)(89, 360)(90, 354)(91, 384)(92, 428)(93, 376)(94, 419)(95, 431)(96, 416)(97, 393)(98, 435)(99, 358)(100, 390)(101, 415)(102, 361)(103, 378)(104, 400)(105, 442)(106, 363)(107, 445)(108, 365)(109, 425)(110, 410)(111, 407)(112, 371)(113, 417)(114, 406)(115, 454)(116, 449)(117, 395)(118, 414)(119, 458)(120, 374)(121, 411)(122, 394)(123, 405)(124, 440)(125, 421)(126, 382)(127, 388)(128, 420)(129, 470)(130, 389)(131, 427)(132, 386)(133, 403)(134, 426)(135, 476)(136, 478)(137, 424)(138, 473)(139, 481)(140, 471)(141, 437)(142, 485)(143, 392)(144, 434)(145, 456)(146, 465)(147, 401)(148, 444)(149, 493)(150, 399)(151, 441)(152, 491)(153, 498)(154, 461)(155, 404)(156, 463)(157, 453)(158, 409)(159, 455)(160, 452)(161, 451)(162, 489)(163, 448)(164, 460)(165, 510)(166, 413)(167, 457)(168, 433)(169, 502)(170, 495)(171, 418)(172, 430)(173, 469)(174, 423)(175, 490)(176, 468)(177, 438)(178, 447)(179, 475)(180, 429)(181, 432)(182, 474)(183, 526)(184, 466)(185, 518)(186, 529)(187, 462)(188, 516)(189, 532)(190, 513)(191, 486)(192, 436)(193, 484)(194, 512)(195, 439)(196, 467)(197, 497)(198, 464)(199, 494)(200, 443)(201, 492)(202, 542)(203, 446)(204, 472)(205, 523)(206, 508)(207, 544)(208, 450)(209, 506)(210, 505)(211, 514)(212, 549)(213, 521)(214, 546)(215, 488)(216, 511)(217, 459)(218, 509)(219, 487)(220, 504)(221, 540)(222, 527)(223, 538)(224, 519)(225, 479)(226, 483)(227, 537)(228, 480)(229, 525)(230, 477)(231, 499)(232, 524)(233, 482)(234, 554)(235, 522)(236, 566)(237, 569)(238, 520)(239, 564)(240, 550)(241, 551)(242, 535)(243, 507)(244, 561)(245, 501)(246, 558)(247, 496)(248, 541)(249, 575)(250, 539)(251, 556)(252, 500)(253, 573)(254, 576)(255, 503)(256, 557)(257, 536)(258, 581)(259, 548)(260, 562)(261, 545)(262, 555)(263, 534)(264, 515)(265, 531)(266, 584)(267, 517)(268, 528)(269, 552)(270, 568)(271, 543)(272, 567)(273, 530)(274, 533)(275, 559)(276, 586)(277, 579)(278, 585)(279, 578)(280, 560)(281, 565)(282, 553)(283, 587)(284, 547)(285, 582)(286, 572)(287, 563)(288, 571)(289, 570)(290, 574)(291, 580)(292, 583)(293, 588)(294, 577) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E15.1361 Transitivity :: ET+ VT+ AT Graph:: v = 21 e = 294 f = 245 degree seq :: [ 28^21 ] E15.1366 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 14}) Quotient :: loop Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1, T1^14 ] Map:: polyhedral non-degenerate R = (1, 295, 3, 297)(2, 296, 6, 300)(4, 298, 9, 303)(5, 299, 12, 306)(7, 301, 16, 310)(8, 302, 13, 307)(10, 304, 19, 313)(11, 305, 22, 316)(14, 308, 23, 317)(15, 309, 28, 322)(17, 311, 30, 324)(18, 312, 33, 327)(20, 314, 35, 329)(21, 315, 38, 332)(24, 318, 39, 333)(25, 319, 44, 338)(26, 320, 45, 339)(27, 321, 48, 342)(29, 323, 49, 343)(31, 325, 53, 347)(32, 326, 56, 350)(34, 328, 59, 353)(36, 330, 61, 355)(37, 331, 64, 358)(40, 334, 65, 359)(41, 335, 70, 364)(42, 336, 71, 365)(43, 337, 74, 368)(46, 340, 77, 371)(47, 341, 80, 374)(50, 344, 81, 375)(51, 345, 69, 363)(52, 346, 67, 361)(54, 348, 86, 380)(55, 349, 89, 383)(57, 351, 75, 369)(58, 352, 83, 377)(60, 354, 93, 387)(62, 356, 95, 389)(63, 357, 98, 392)(66, 360, 99, 393)(68, 362, 103, 397)(72, 366, 107, 401)(73, 367, 110, 404)(76, 370, 101, 395)(78, 372, 113, 407)(79, 373, 116, 410)(82, 376, 117, 411)(84, 378, 121, 415)(85, 379, 124, 418)(87, 381, 126, 420)(88, 382, 129, 423)(90, 384, 130, 424)(91, 385, 134, 428)(92, 386, 132, 426)(94, 388, 137, 431)(96, 390, 139, 433)(97, 391, 140, 434)(100, 394, 141, 435)(102, 396, 145, 439)(104, 398, 148, 442)(105, 399, 151, 445)(106, 400, 143, 437)(108, 402, 153, 447)(109, 403, 156, 450)(111, 405, 157, 451)(112, 406, 161, 455)(114, 408, 163, 457)(115, 409, 166, 460)(118, 412, 167, 461)(119, 413, 150, 444)(120, 414, 171, 465)(122, 416, 160, 454)(123, 417, 159, 453)(125, 419, 152, 446)(127, 421, 176, 470)(128, 422, 178, 472)(131, 425, 158, 452)(133, 427, 169, 463)(135, 429, 183, 477)(136, 430, 172, 466)(138, 432, 186, 480)(142, 436, 188, 482)(144, 438, 192, 486)(146, 440, 195, 489)(147, 441, 190, 484)(149, 443, 198, 492)(154, 448, 202, 496)(155, 449, 205, 499)(162, 456, 197, 491)(164, 458, 210, 504)(165, 459, 211, 505)(168, 462, 212, 506)(170, 464, 216, 510)(173, 467, 219, 513)(174, 468, 222, 516)(175, 469, 224, 518)(177, 471, 226, 520)(179, 473, 227, 521)(180, 474, 230, 524)(181, 475, 233, 527)(182, 476, 229, 523)(184, 478, 236, 530)(185, 479, 231, 525)(187, 481, 189, 483)(191, 485, 241, 535)(193, 487, 244, 538)(194, 488, 239, 533)(196, 490, 247, 541)(199, 493, 250, 544)(200, 494, 253, 547)(201, 495, 246, 540)(203, 497, 255, 549)(204, 498, 256, 550)(206, 500, 257, 551)(207, 501, 260, 554)(208, 502, 263, 557)(209, 503, 265, 559)(213, 507, 267, 561)(214, 508, 252, 546)(215, 509, 270, 564)(217, 511, 262, 556)(218, 512, 240, 534)(220, 514, 264, 558)(221, 515, 259, 553)(223, 517, 261, 555)(225, 519, 254, 548)(228, 522, 258, 552)(232, 526, 268, 562)(234, 528, 276, 570)(235, 529, 271, 565)(237, 531, 242, 536)(238, 532, 243, 537)(245, 539, 281, 575)(248, 542, 284, 578)(249, 543, 280, 574)(251, 545, 287, 581)(266, 560, 286, 580)(269, 563, 288, 582)(272, 566, 292, 586)(273, 567, 291, 585)(274, 568, 290, 584)(275, 569, 279, 573)(277, 571, 282, 576)(278, 572, 283, 577)(285, 579, 293, 587)(289, 583, 294, 588) L = (1, 296)(2, 299)(3, 301)(4, 295)(5, 305)(6, 307)(7, 309)(8, 297)(9, 312)(10, 298)(11, 315)(12, 317)(13, 319)(14, 300)(15, 321)(16, 303)(17, 302)(18, 326)(19, 328)(20, 304)(21, 331)(22, 333)(23, 335)(24, 306)(25, 337)(26, 308)(27, 341)(28, 343)(29, 310)(30, 346)(31, 311)(32, 349)(33, 313)(34, 352)(35, 354)(36, 314)(37, 357)(38, 359)(39, 361)(40, 316)(41, 363)(42, 318)(43, 367)(44, 324)(45, 370)(46, 320)(47, 373)(48, 375)(49, 364)(50, 322)(51, 323)(52, 365)(53, 379)(54, 325)(55, 382)(56, 369)(57, 327)(58, 385)(59, 329)(60, 386)(61, 388)(62, 330)(63, 391)(64, 393)(65, 395)(66, 332)(67, 347)(68, 334)(69, 399)(70, 339)(71, 400)(72, 336)(73, 403)(74, 351)(75, 338)(76, 397)(77, 406)(78, 340)(79, 409)(80, 411)(81, 353)(82, 342)(83, 344)(84, 345)(85, 417)(86, 419)(87, 348)(88, 422)(89, 424)(90, 350)(91, 427)(92, 429)(93, 355)(94, 430)(95, 432)(96, 356)(97, 390)(98, 435)(99, 437)(100, 358)(101, 371)(102, 360)(103, 441)(104, 362)(105, 444)(106, 439)(107, 446)(108, 366)(109, 449)(110, 451)(111, 368)(112, 454)(113, 456)(114, 372)(115, 459)(116, 461)(117, 445)(118, 374)(119, 376)(120, 377)(121, 455)(122, 378)(123, 468)(124, 380)(125, 447)(126, 469)(127, 381)(128, 471)(129, 452)(130, 387)(131, 383)(132, 384)(133, 475)(134, 465)(135, 476)(136, 478)(137, 389)(138, 479)(139, 481)(140, 482)(141, 484)(142, 392)(143, 401)(144, 394)(145, 488)(146, 396)(147, 486)(148, 491)(149, 398)(150, 494)(151, 415)(152, 420)(153, 495)(154, 402)(155, 498)(156, 425)(157, 418)(158, 404)(159, 405)(160, 502)(161, 407)(162, 492)(163, 503)(164, 408)(165, 421)(166, 506)(167, 428)(168, 410)(169, 412)(170, 413)(171, 431)(172, 414)(173, 416)(174, 515)(175, 517)(176, 519)(177, 514)(178, 521)(179, 423)(180, 426)(181, 526)(182, 528)(183, 524)(184, 529)(185, 531)(186, 433)(187, 532)(188, 533)(189, 434)(190, 442)(191, 436)(192, 537)(193, 438)(194, 535)(195, 540)(196, 440)(197, 457)(198, 543)(199, 443)(200, 546)(201, 541)(202, 548)(203, 448)(204, 458)(205, 551)(206, 450)(207, 453)(208, 556)(209, 558)(210, 560)(211, 561)(212, 547)(213, 460)(214, 462)(215, 463)(216, 557)(217, 464)(218, 466)(219, 559)(220, 467)(221, 545)(222, 554)(223, 567)(224, 470)(225, 549)(226, 552)(227, 477)(228, 472)(229, 473)(230, 480)(231, 474)(232, 555)(233, 564)(234, 566)(235, 571)(236, 534)(237, 572)(238, 538)(239, 489)(240, 483)(241, 525)(242, 485)(243, 512)(244, 574)(245, 487)(246, 496)(247, 577)(248, 490)(249, 575)(250, 580)(251, 493)(252, 497)(253, 510)(254, 505)(255, 582)(256, 522)(257, 516)(258, 499)(259, 500)(260, 518)(261, 501)(262, 579)(263, 513)(264, 584)(265, 504)(266, 581)(267, 527)(268, 507)(269, 508)(270, 530)(271, 509)(272, 511)(273, 576)(274, 520)(275, 523)(276, 573)(277, 583)(278, 578)(279, 536)(280, 544)(281, 565)(282, 539)(283, 569)(284, 563)(285, 542)(286, 550)(287, 588)(288, 587)(289, 553)(290, 570)(291, 562)(292, 568)(293, 586)(294, 585) local type(s) :: { ( 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E15.1362 Transitivity :: ET+ VT+ AT Graph:: simple v = 147 e = 294 f = 119 degree seq :: [ 4^147 ] E15.1367 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14}) Quotient :: dipole Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1 * Y1 * Y2)^3, (Y3 * Y2^-1)^14 ] Map:: R = (1, 295, 2, 296)(3, 297, 7, 301)(4, 298, 8, 302)(5, 299, 9, 303)(6, 300, 10, 304)(11, 305, 19, 313)(12, 306, 20, 314)(13, 307, 21, 315)(14, 308, 22, 316)(15, 309, 23, 317)(16, 310, 24, 318)(17, 311, 25, 319)(18, 312, 26, 320)(27, 321, 43, 337)(28, 322, 44, 338)(29, 323, 37, 331)(30, 324, 45, 339)(31, 325, 46, 340)(32, 326, 40, 334)(33, 327, 47, 341)(34, 328, 48, 342)(35, 329, 49, 343)(36, 330, 50, 344)(38, 332, 51, 345)(39, 333, 52, 346)(41, 335, 53, 347)(42, 336, 54, 348)(55, 349, 73, 367)(56, 350, 74, 368)(57, 351, 75, 369)(58, 352, 76, 370)(59, 353, 77, 371)(60, 354, 78, 372)(61, 355, 79, 373)(62, 356, 80, 374)(63, 357, 81, 375)(64, 358, 82, 376)(65, 359, 83, 377)(66, 360, 84, 378)(67, 361, 85, 379)(68, 362, 86, 380)(69, 363, 87, 381)(70, 364, 88, 382)(71, 365, 89, 383)(72, 366, 90, 384)(91, 385, 115, 409)(92, 386, 116, 410)(93, 387, 117, 411)(94, 388, 118, 412)(95, 389, 119, 413)(96, 390, 108, 402)(97, 391, 120, 414)(98, 392, 121, 415)(99, 393, 111, 405)(100, 394, 122, 416)(101, 395, 123, 417)(102, 396, 124, 418)(103, 397, 134, 428)(104, 398, 191, 485)(105, 399, 128, 422)(106, 400, 166, 460)(107, 401, 194, 488)(109, 403, 143, 437)(110, 404, 127, 421)(112, 406, 133, 427)(113, 407, 197, 491)(114, 408, 164, 458)(125, 419, 203, 497)(126, 420, 218, 512)(129, 423, 223, 517)(130, 424, 224, 518)(131, 425, 226, 520)(132, 426, 228, 522)(135, 429, 232, 526)(136, 430, 234, 528)(137, 431, 236, 530)(138, 432, 238, 532)(139, 433, 240, 534)(140, 434, 241, 535)(141, 435, 243, 537)(142, 436, 245, 539)(144, 438, 199, 493)(145, 439, 211, 505)(146, 440, 207, 501)(147, 441, 231, 525)(148, 442, 250, 544)(149, 443, 220, 514)(150, 444, 251, 545)(151, 445, 252, 546)(152, 446, 254, 548)(153, 447, 256, 550)(154, 448, 248, 542)(155, 449, 257, 551)(156, 450, 259, 553)(157, 451, 212, 506)(158, 452, 261, 555)(159, 453, 263, 557)(160, 454, 200, 494)(161, 455, 264, 558)(162, 456, 222, 516)(163, 457, 215, 509)(165, 459, 201, 495)(167, 461, 204, 498)(168, 462, 267, 561)(169, 463, 184, 478)(170, 464, 268, 562)(171, 465, 196, 490)(172, 466, 198, 492)(173, 467, 192, 486)(174, 468, 195, 489)(175, 469, 178, 472)(176, 470, 272, 566)(177, 471, 274, 568)(179, 473, 275, 569)(180, 474, 189, 483)(181, 475, 190, 484)(182, 476, 186, 480)(183, 477, 188, 482)(185, 479, 279, 573)(187, 481, 209, 503)(193, 487, 230, 524)(202, 496, 282, 576)(205, 499, 285, 579)(206, 500, 286, 580)(208, 502, 288, 582)(210, 504, 290, 584)(213, 507, 292, 586)(214, 508, 293, 587)(216, 510, 276, 570)(217, 511, 291, 585)(219, 513, 269, 563)(221, 515, 283, 577)(225, 519, 262, 556)(227, 521, 287, 581)(229, 523, 255, 549)(233, 527, 294, 588)(235, 529, 258, 552)(237, 531, 280, 574)(239, 533, 246, 540)(242, 536, 265, 559)(244, 538, 273, 567)(247, 541, 281, 575)(249, 543, 289, 583)(253, 547, 270, 564)(260, 554, 277, 571)(266, 560, 284, 578)(271, 565, 278, 572)(589, 883, 591, 885, 592, 886)(590, 884, 593, 887, 594, 888)(595, 889, 599, 893, 600, 894)(596, 890, 601, 895, 602, 896)(597, 891, 603, 897, 604, 898)(598, 892, 605, 899, 606, 900)(607, 901, 615, 909, 616, 910)(608, 902, 617, 911, 618, 912)(609, 903, 619, 913, 620, 914)(610, 904, 621, 915, 622, 916)(611, 905, 623, 917, 624, 918)(612, 906, 625, 919, 626, 920)(613, 907, 627, 921, 628, 922)(614, 908, 629, 923, 630, 924)(631, 925, 643, 937, 644, 938)(632, 926, 635, 929, 645, 939)(633, 927, 646, 940, 647, 941)(634, 928, 648, 942, 649, 943)(636, 930, 650, 944, 651, 945)(637, 931, 652, 946, 653, 947)(638, 932, 641, 935, 654, 948)(639, 933, 655, 949, 656, 950)(640, 934, 657, 951, 658, 952)(642, 936, 659, 953, 660, 954)(661, 955, 679, 973, 680, 974)(662, 956, 664, 958, 681, 975)(663, 957, 682, 976, 683, 977)(665, 959, 684, 978, 685, 979)(666, 960, 686, 980, 687, 981)(667, 961, 668, 962, 688, 982)(669, 963, 689, 983, 690, 984)(670, 964, 691, 985, 692, 986)(671, 965, 673, 967, 693, 987)(672, 966, 694, 988, 695, 989)(674, 968, 696, 990, 697, 991)(675, 969, 698, 992, 699, 993)(676, 970, 677, 971, 700, 994)(678, 972, 701, 995, 702, 996)(703, 997, 787, 1081, 813, 1107)(704, 998, 706, 1000, 791, 1085)(705, 999, 789, 1083, 796, 1090)(707, 1001, 711, 1005, 799, 1093)(708, 1002, 793, 1087, 770, 1064)(709, 1003, 795, 1089, 807, 1101)(710, 1004, 797, 1091, 765, 1059)(712, 1006, 801, 1095, 768, 1062)(713, 1007, 803, 1097, 805, 1099)(714, 1008, 792, 1086, 790, 1084)(715, 1009, 808, 1102, 804, 1098)(716, 1010, 810, 1104, 809, 1103)(717, 1011, 771, 1065, 798, 1092)(718, 1012, 769, 1063, 767, 1061)(719, 1013, 762, 1056, 815, 1109)(720, 1014, 760, 1054, 758, 1052)(721, 1015, 818, 1112, 756, 1050)(722, 1016, 819, 1113, 817, 1111)(723, 1017, 745, 1039, 821, 1115)(724, 1018, 764, 1058, 747, 1041)(725, 1019, 757, 1051, 825, 1119)(726, 1020, 749, 1043, 746, 1040)(727, 1021, 739, 1033, 794, 1088)(728, 1022, 773, 1067, 741, 1035)(729, 1023, 766, 1060, 832, 1126)(730, 1024, 743, 1037, 740, 1034)(731, 1025, 835, 1129, 761, 1055)(732, 1026, 836, 1130, 823, 1117)(733, 1027, 837, 1131, 744, 1038)(734, 1028, 831, 1125, 827, 1121)(735, 1029, 788, 1082, 830, 1124)(736, 1030, 802, 1096, 738, 1032)(737, 1031, 824, 1118, 834, 1128)(742, 1036, 784, 1078, 841, 1135)(748, 1042, 777, 1071, 848, 1142)(750, 1044, 814, 1108, 843, 1137)(751, 1045, 820, 1114, 846, 1140)(752, 1046, 854, 1148, 759, 1053)(753, 1047, 811, 1105, 850, 1144)(754, 1048, 806, 1100, 779, 1073)(755, 1049, 828, 1122, 853, 1147)(763, 1057, 774, 1068, 859, 1153)(772, 1066, 780, 1074, 866, 1160)(775, 1069, 812, 1106, 857, 1151)(776, 1070, 839, 1133, 858, 1152)(778, 1072, 844, 1138, 861, 1155)(781, 1075, 816, 1110, 864, 1158)(782, 1076, 785, 1079, 838, 1132)(783, 1077, 847, 1141, 865, 1159)(786, 1080, 851, 1145, 868, 1162)(800, 1094, 855, 1149, 872, 1166)(822, 1116, 871, 1165, 869, 1163)(826, 1120, 879, 1173, 877, 1171)(829, 1123, 876, 1170, 873, 1167)(833, 1127, 870, 1164, 881, 1175)(840, 1134, 862, 1156, 880, 1174)(842, 1136, 878, 1172, 867, 1161)(845, 1139, 863, 1157, 874, 1168)(849, 1143, 875, 1169, 860, 1154)(852, 1146, 856, 1150, 882, 1176) L = (1, 590)(2, 589)(3, 595)(4, 596)(5, 597)(6, 598)(7, 591)(8, 592)(9, 593)(10, 594)(11, 607)(12, 608)(13, 609)(14, 610)(15, 611)(16, 612)(17, 613)(18, 614)(19, 599)(20, 600)(21, 601)(22, 602)(23, 603)(24, 604)(25, 605)(26, 606)(27, 631)(28, 632)(29, 625)(30, 633)(31, 634)(32, 628)(33, 635)(34, 636)(35, 637)(36, 638)(37, 617)(38, 639)(39, 640)(40, 620)(41, 641)(42, 642)(43, 615)(44, 616)(45, 618)(46, 619)(47, 621)(48, 622)(49, 623)(50, 624)(51, 626)(52, 627)(53, 629)(54, 630)(55, 661)(56, 662)(57, 663)(58, 664)(59, 665)(60, 666)(61, 667)(62, 668)(63, 669)(64, 670)(65, 671)(66, 672)(67, 673)(68, 674)(69, 675)(70, 676)(71, 677)(72, 678)(73, 643)(74, 644)(75, 645)(76, 646)(77, 647)(78, 648)(79, 649)(80, 650)(81, 651)(82, 652)(83, 653)(84, 654)(85, 655)(86, 656)(87, 657)(88, 658)(89, 659)(90, 660)(91, 703)(92, 704)(93, 705)(94, 706)(95, 707)(96, 696)(97, 708)(98, 709)(99, 699)(100, 710)(101, 711)(102, 712)(103, 722)(104, 779)(105, 716)(106, 754)(107, 782)(108, 684)(109, 731)(110, 715)(111, 687)(112, 721)(113, 785)(114, 752)(115, 679)(116, 680)(117, 681)(118, 682)(119, 683)(120, 685)(121, 686)(122, 688)(123, 689)(124, 690)(125, 791)(126, 806)(127, 698)(128, 693)(129, 811)(130, 812)(131, 814)(132, 816)(133, 700)(134, 691)(135, 820)(136, 822)(137, 824)(138, 826)(139, 828)(140, 829)(141, 831)(142, 833)(143, 697)(144, 787)(145, 799)(146, 795)(147, 819)(148, 838)(149, 808)(150, 839)(151, 840)(152, 842)(153, 844)(154, 836)(155, 845)(156, 847)(157, 800)(158, 849)(159, 851)(160, 788)(161, 852)(162, 810)(163, 803)(164, 702)(165, 789)(166, 694)(167, 792)(168, 855)(169, 772)(170, 856)(171, 784)(172, 786)(173, 780)(174, 783)(175, 766)(176, 860)(177, 862)(178, 763)(179, 863)(180, 777)(181, 778)(182, 774)(183, 776)(184, 757)(185, 867)(186, 770)(187, 797)(188, 771)(189, 768)(190, 769)(191, 692)(192, 761)(193, 818)(194, 695)(195, 762)(196, 759)(197, 701)(198, 760)(199, 732)(200, 748)(201, 753)(202, 870)(203, 713)(204, 755)(205, 873)(206, 874)(207, 734)(208, 876)(209, 775)(210, 878)(211, 733)(212, 745)(213, 880)(214, 881)(215, 751)(216, 864)(217, 879)(218, 714)(219, 857)(220, 737)(221, 871)(222, 750)(223, 717)(224, 718)(225, 850)(226, 719)(227, 875)(228, 720)(229, 843)(230, 781)(231, 735)(232, 723)(233, 882)(234, 724)(235, 846)(236, 725)(237, 868)(238, 726)(239, 834)(240, 727)(241, 728)(242, 853)(243, 729)(244, 861)(245, 730)(246, 827)(247, 869)(248, 742)(249, 877)(250, 736)(251, 738)(252, 739)(253, 858)(254, 740)(255, 817)(256, 741)(257, 743)(258, 823)(259, 744)(260, 865)(261, 746)(262, 813)(263, 747)(264, 749)(265, 830)(266, 872)(267, 756)(268, 758)(269, 807)(270, 841)(271, 866)(272, 764)(273, 832)(274, 765)(275, 767)(276, 804)(277, 848)(278, 859)(279, 773)(280, 825)(281, 835)(282, 790)(283, 809)(284, 854)(285, 793)(286, 794)(287, 815)(288, 796)(289, 837)(290, 798)(291, 805)(292, 801)(293, 802)(294, 821)(295, 883)(296, 884)(297, 885)(298, 886)(299, 887)(300, 888)(301, 889)(302, 890)(303, 891)(304, 892)(305, 893)(306, 894)(307, 895)(308, 896)(309, 897)(310, 898)(311, 899)(312, 900)(313, 901)(314, 902)(315, 903)(316, 904)(317, 905)(318, 906)(319, 907)(320, 908)(321, 909)(322, 910)(323, 911)(324, 912)(325, 913)(326, 914)(327, 915)(328, 916)(329, 917)(330, 918)(331, 919)(332, 920)(333, 921)(334, 922)(335, 923)(336, 924)(337, 925)(338, 926)(339, 927)(340, 928)(341, 929)(342, 930)(343, 931)(344, 932)(345, 933)(346, 934)(347, 935)(348, 936)(349, 937)(350, 938)(351, 939)(352, 940)(353, 941)(354, 942)(355, 943)(356, 944)(357, 945)(358, 946)(359, 947)(360, 948)(361, 949)(362, 950)(363, 951)(364, 952)(365, 953)(366, 954)(367, 955)(368, 956)(369, 957)(370, 958)(371, 959)(372, 960)(373, 961)(374, 962)(375, 963)(376, 964)(377, 965)(378, 966)(379, 967)(380, 968)(381, 969)(382, 970)(383, 971)(384, 972)(385, 973)(386, 974)(387, 975)(388, 976)(389, 977)(390, 978)(391, 979)(392, 980)(393, 981)(394, 982)(395, 983)(396, 984)(397, 985)(398, 986)(399, 987)(400, 988)(401, 989)(402, 990)(403, 991)(404, 992)(405, 993)(406, 994)(407, 995)(408, 996)(409, 997)(410, 998)(411, 999)(412, 1000)(413, 1001)(414, 1002)(415, 1003)(416, 1004)(417, 1005)(418, 1006)(419, 1007)(420, 1008)(421, 1009)(422, 1010)(423, 1011)(424, 1012)(425, 1013)(426, 1014)(427, 1015)(428, 1016)(429, 1017)(430, 1018)(431, 1019)(432, 1020)(433, 1021)(434, 1022)(435, 1023)(436, 1024)(437, 1025)(438, 1026)(439, 1027)(440, 1028)(441, 1029)(442, 1030)(443, 1031)(444, 1032)(445, 1033)(446, 1034)(447, 1035)(448, 1036)(449, 1037)(450, 1038)(451, 1039)(452, 1040)(453, 1041)(454, 1042)(455, 1043)(456, 1044)(457, 1045)(458, 1046)(459, 1047)(460, 1048)(461, 1049)(462, 1050)(463, 1051)(464, 1052)(465, 1053)(466, 1054)(467, 1055)(468, 1056)(469, 1057)(470, 1058)(471, 1059)(472, 1060)(473, 1061)(474, 1062)(475, 1063)(476, 1064)(477, 1065)(478, 1066)(479, 1067)(480, 1068)(481, 1069)(482, 1070)(483, 1071)(484, 1072)(485, 1073)(486, 1074)(487, 1075)(488, 1076)(489, 1077)(490, 1078)(491, 1079)(492, 1080)(493, 1081)(494, 1082)(495, 1083)(496, 1084)(497, 1085)(498, 1086)(499, 1087)(500, 1088)(501, 1089)(502, 1090)(503, 1091)(504, 1092)(505, 1093)(506, 1094)(507, 1095)(508, 1096)(509, 1097)(510, 1098)(511, 1099)(512, 1100)(513, 1101)(514, 1102)(515, 1103)(516, 1104)(517, 1105)(518, 1106)(519, 1107)(520, 1108)(521, 1109)(522, 1110)(523, 1111)(524, 1112)(525, 1113)(526, 1114)(527, 1115)(528, 1116)(529, 1117)(530, 1118)(531, 1119)(532, 1120)(533, 1121)(534, 1122)(535, 1123)(536, 1124)(537, 1125)(538, 1126)(539, 1127)(540, 1128)(541, 1129)(542, 1130)(543, 1131)(544, 1132)(545, 1133)(546, 1134)(547, 1135)(548, 1136)(549, 1137)(550, 1138)(551, 1139)(552, 1140)(553, 1141)(554, 1142)(555, 1143)(556, 1144)(557, 1145)(558, 1146)(559, 1147)(560, 1148)(561, 1149)(562, 1150)(563, 1151)(564, 1152)(565, 1153)(566, 1154)(567, 1155)(568, 1156)(569, 1157)(570, 1158)(571, 1159)(572, 1160)(573, 1161)(574, 1162)(575, 1163)(576, 1164)(577, 1165)(578, 1166)(579, 1167)(580, 1168)(581, 1169)(582, 1170)(583, 1171)(584, 1172)(585, 1173)(586, 1174)(587, 1175)(588, 1176) local type(s) :: { ( 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E15.1370 Graph:: bipartite v = 245 e = 588 f = 315 degree seq :: [ 4^147, 6^98 ] E15.1368 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14}) Quotient :: dipole Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2 * Y2^2 * Y1^-1, (Y2^2 * Y1^-1)^3, Y2^14, Y2^3 * Y1^-1 * Y2^-5 * Y1 * Y2^4 * Y1^-1 * Y2^-6 * Y1^-1 ] Map:: R = (1, 295, 2, 296, 4, 298)(3, 297, 8, 302, 10, 304)(5, 299, 12, 306, 6, 300)(7, 301, 15, 309, 11, 305)(9, 303, 18, 312, 20, 314)(13, 307, 25, 319, 23, 317)(14, 308, 24, 318, 28, 322)(16, 310, 31, 325, 29, 323)(17, 311, 33, 327, 21, 315)(19, 313, 36, 330, 38, 332)(22, 316, 30, 324, 42, 336)(26, 320, 47, 341, 45, 339)(27, 321, 49, 343, 51, 345)(32, 326, 56, 350, 55, 349)(34, 328, 59, 353, 58, 352)(35, 329, 53, 347, 39, 333)(37, 331, 63, 357, 65, 359)(40, 334, 52, 346, 44, 338)(41, 335, 68, 362, 70, 364)(43, 337, 46, 340, 54, 348)(48, 342, 76, 370, 74, 368)(50, 344, 79, 373, 81, 375)(57, 351, 87, 381, 85, 379)(60, 354, 91, 385, 90, 384)(61, 355, 93, 387, 82, 376)(62, 356, 89, 383, 66, 360)(64, 358, 97, 391, 99, 393)(67, 361, 72, 366, 102, 396)(69, 363, 104, 398, 106, 400)(71, 365, 83, 377, 108, 402)(73, 367, 75, 369, 78, 372)(77, 371, 114, 408, 112, 406)(80, 374, 118, 412, 120, 414)(84, 378, 86, 380, 103, 397)(88, 382, 128, 422, 126, 420)(92, 386, 134, 428, 132, 426)(94, 388, 125, 419, 127, 421)(95, 389, 137, 431, 130, 424)(96, 390, 122, 416, 100, 394)(98, 392, 141, 435, 143, 437)(101, 395, 121, 415, 117, 411)(105, 399, 148, 442, 150, 444)(107, 401, 151, 445, 147, 441)(109, 403, 131, 425, 133, 427)(110, 404, 116, 410, 155, 449)(111, 405, 113, 407, 123, 417)(115, 409, 160, 454, 158, 452)(119, 413, 164, 458, 166, 460)(124, 418, 146, 440, 171, 465)(129, 423, 176, 470, 174, 468)(135, 429, 182, 476, 180, 474)(136, 430, 184, 478, 172, 466)(138, 432, 179, 473, 181, 475)(139, 433, 187, 481, 168, 462)(140, 434, 177, 471, 144, 438)(142, 436, 191, 485, 192, 486)(145, 439, 162, 456, 195, 489)(149, 443, 199, 493, 200, 494)(152, 446, 197, 491, 203, 497)(153, 447, 204, 498, 178, 472)(154, 448, 167, 461, 163, 457)(156, 450, 169, 463, 208, 502)(157, 451, 159, 453, 161, 455)(165, 459, 216, 510, 217, 511)(170, 464, 201, 495, 198, 492)(173, 467, 175, 469, 196, 490)(183, 477, 232, 526, 230, 524)(185, 479, 224, 518, 225, 519)(186, 480, 235, 529, 228, 522)(188, 482, 222, 516, 233, 527)(189, 483, 238, 532, 226, 520)(190, 484, 219, 513, 193, 487)(194, 488, 218, 512, 215, 509)(202, 496, 248, 542, 247, 541)(205, 499, 229, 523, 231, 525)(206, 500, 214, 508, 252, 546)(207, 501, 250, 544, 245, 539)(209, 503, 212, 506, 255, 549)(210, 504, 211, 505, 220, 514)(213, 507, 227, 521, 243, 537)(221, 515, 246, 540, 264, 558)(223, 517, 244, 538, 267, 561)(234, 528, 260, 554, 268, 562)(236, 530, 272, 566, 273, 567)(237, 531, 275, 569, 265, 559)(239, 533, 270, 564, 274, 568)(240, 534, 256, 550, 263, 557)(241, 535, 257, 551, 242, 536)(249, 543, 281, 575, 271, 565)(251, 545, 262, 556, 261, 555)(253, 547, 279, 573, 284, 578)(254, 548, 282, 576, 259, 553)(258, 552, 287, 581, 269, 563)(266, 560, 290, 584, 280, 574)(276, 570, 292, 586, 289, 583)(277, 571, 285, 579, 288, 582)(278, 572, 291, 585, 286, 580)(283, 577, 293, 587, 294, 588)(589, 883, 591, 885, 597, 891, 607, 901, 625, 919, 652, 946, 686, 980, 730, 1024, 703, 997, 665, 959, 636, 930, 614, 908, 601, 895, 593, 887)(590, 884, 594, 888, 602, 896, 615, 909, 638, 932, 668, 962, 707, 1001, 753, 1047, 717, 1011, 676, 970, 645, 939, 620, 914, 604, 898, 595, 889)(592, 886, 599, 893, 610, 904, 629, 923, 657, 951, 693, 987, 737, 1031, 771, 1065, 723, 1017, 680, 974, 648, 942, 622, 916, 605, 899, 596, 890)(598, 892, 609, 903, 628, 922, 655, 949, 689, 983, 733, 1027, 782, 1076, 822, 1116, 773, 1067, 724, 1018, 682, 976, 649, 943, 623, 917, 606, 900)(600, 894, 611, 905, 631, 925, 659, 953, 695, 989, 740, 1034, 790, 1084, 837, 1131, 793, 1087, 741, 1035, 697, 991, 660, 954, 632, 926, 612, 906)(603, 897, 617, 911, 641, 935, 670, 964, 710, 1004, 756, 1050, 807, 1101, 851, 1145, 808, 1102, 757, 1051, 711, 1005, 671, 965, 642, 936, 618, 912)(608, 902, 627, 921, 619, 913, 643, 937, 672, 966, 712, 1006, 758, 1052, 809, 1103, 824, 1118, 774, 1068, 726, 1020, 683, 977, 650, 944, 624, 918)(613, 907, 633, 927, 661, 955, 698, 992, 742, 1036, 794, 1088, 839, 1133, 832, 1126, 784, 1078, 734, 1028, 691, 985, 656, 950, 630, 924, 634, 928)(616, 910, 640, 934, 621, 915, 646, 940, 677, 971, 718, 1012, 765, 1059, 814, 1108, 845, 1139, 800, 1094, 749, 1043, 704, 998, 666, 960, 637, 931)(626, 920, 654, 948, 647, 941, 678, 972, 719, 1013, 766, 1060, 815, 1109, 857, 1151, 864, 1158, 825, 1119, 776, 1070, 727, 1021, 684, 978, 651, 945)(635, 929, 662, 956, 699, 993, 744, 1038, 795, 1089, 841, 1135, 871, 1165, 846, 1140, 801, 1095, 750, 1044, 705, 999, 667, 961, 639, 933, 663, 957)(644, 938, 673, 967, 713, 1007, 760, 1054, 810, 1104, 853, 1147, 879, 1173, 867, 1161, 833, 1127, 785, 1079, 735, 1029, 692, 986, 658, 952, 674, 968)(653, 947, 688, 982, 681, 975, 715, 1009, 675, 969, 714, 1008, 761, 1055, 811, 1105, 854, 1148, 865, 1159, 827, 1121, 777, 1071, 728, 1022, 685, 979)(664, 958, 700, 994, 745, 1039, 797, 1091, 842, 1136, 873, 1167, 868, 1162, 834, 1128, 786, 1080, 736, 1030, 694, 988, 739, 1033, 696, 990, 701, 995)(669, 963, 709, 1003, 690, 984, 721, 1015, 679, 973, 720, 1014, 767, 1061, 816, 1110, 858, 1152, 876, 1170, 847, 1141, 802, 1096, 751, 1045, 706, 1000)(687, 981, 732, 1026, 725, 1019, 769, 1063, 722, 1016, 768, 1062, 817, 1111, 859, 1153, 881, 1175, 872, 1166, 866, 1160, 828, 1122, 778, 1072, 729, 1023)(702, 996, 746, 1040, 798, 1092, 844, 1138, 874, 1168, 863, 1157, 877, 1171, 848, 1142, 803, 1097, 752, 1046, 708, 1002, 755, 1049, 743, 1037, 747, 1041)(716, 1010, 762, 1056, 812, 1106, 856, 1150, 880, 1174, 875, 1169, 882, 1176, 869, 1163, 835, 1129, 787, 1081, 738, 1032, 789, 1083, 759, 1053, 763, 1057)(731, 1025, 781, 1075, 775, 1069, 821, 1115, 772, 1066, 813, 1107, 764, 1058, 805, 1099, 850, 1144, 840, 1134, 870, 1164, 843, 1137, 829, 1123, 779, 1073)(748, 1042, 780, 1074, 830, 1124, 826, 1120, 862, 1156, 823, 1117, 861, 1155, 820, 1114, 788, 1082, 836, 1130, 791, 1085, 838, 1132, 796, 1090, 799, 1093)(754, 1048, 806, 1100, 783, 1077, 831, 1125, 792, 1086, 819, 1113, 770, 1064, 818, 1112, 860, 1154, 852, 1146, 878, 1172, 855, 1149, 849, 1143, 804, 1098) L = (1, 591)(2, 594)(3, 597)(4, 599)(5, 589)(6, 602)(7, 590)(8, 592)(9, 607)(10, 609)(11, 610)(12, 611)(13, 593)(14, 615)(15, 617)(16, 595)(17, 596)(18, 598)(19, 625)(20, 627)(21, 628)(22, 629)(23, 631)(24, 600)(25, 633)(26, 601)(27, 638)(28, 640)(29, 641)(30, 603)(31, 643)(32, 604)(33, 646)(34, 605)(35, 606)(36, 608)(37, 652)(38, 654)(39, 619)(40, 655)(41, 657)(42, 634)(43, 659)(44, 612)(45, 661)(46, 613)(47, 662)(48, 614)(49, 616)(50, 668)(51, 663)(52, 621)(53, 670)(54, 618)(55, 672)(56, 673)(57, 620)(58, 677)(59, 678)(60, 622)(61, 623)(62, 624)(63, 626)(64, 686)(65, 688)(66, 647)(67, 689)(68, 630)(69, 693)(70, 674)(71, 695)(72, 632)(73, 698)(74, 699)(75, 635)(76, 700)(77, 636)(78, 637)(79, 639)(80, 707)(81, 709)(82, 710)(83, 642)(84, 712)(85, 713)(86, 644)(87, 714)(88, 645)(89, 718)(90, 719)(91, 720)(92, 648)(93, 715)(94, 649)(95, 650)(96, 651)(97, 653)(98, 730)(99, 732)(100, 681)(101, 733)(102, 721)(103, 656)(104, 658)(105, 737)(106, 739)(107, 740)(108, 701)(109, 660)(110, 742)(111, 744)(112, 745)(113, 664)(114, 746)(115, 665)(116, 666)(117, 667)(118, 669)(119, 753)(120, 755)(121, 690)(122, 756)(123, 671)(124, 758)(125, 760)(126, 761)(127, 675)(128, 762)(129, 676)(130, 765)(131, 766)(132, 767)(133, 679)(134, 768)(135, 680)(136, 682)(137, 769)(138, 683)(139, 684)(140, 685)(141, 687)(142, 703)(143, 781)(144, 725)(145, 782)(146, 691)(147, 692)(148, 694)(149, 771)(150, 789)(151, 696)(152, 790)(153, 697)(154, 794)(155, 747)(156, 795)(157, 797)(158, 798)(159, 702)(160, 780)(161, 704)(162, 705)(163, 706)(164, 708)(165, 717)(166, 806)(167, 743)(168, 807)(169, 711)(170, 809)(171, 763)(172, 810)(173, 811)(174, 812)(175, 716)(176, 805)(177, 814)(178, 815)(179, 816)(180, 817)(181, 722)(182, 818)(183, 723)(184, 813)(185, 724)(186, 726)(187, 821)(188, 727)(189, 728)(190, 729)(191, 731)(192, 830)(193, 775)(194, 822)(195, 831)(196, 734)(197, 735)(198, 736)(199, 738)(200, 836)(201, 759)(202, 837)(203, 838)(204, 819)(205, 741)(206, 839)(207, 841)(208, 799)(209, 842)(210, 844)(211, 748)(212, 749)(213, 750)(214, 751)(215, 752)(216, 754)(217, 850)(218, 783)(219, 851)(220, 757)(221, 824)(222, 853)(223, 854)(224, 856)(225, 764)(226, 845)(227, 857)(228, 858)(229, 859)(230, 860)(231, 770)(232, 788)(233, 772)(234, 773)(235, 861)(236, 774)(237, 776)(238, 862)(239, 777)(240, 778)(241, 779)(242, 826)(243, 792)(244, 784)(245, 785)(246, 786)(247, 787)(248, 791)(249, 793)(250, 796)(251, 832)(252, 870)(253, 871)(254, 873)(255, 829)(256, 874)(257, 800)(258, 801)(259, 802)(260, 803)(261, 804)(262, 840)(263, 808)(264, 878)(265, 879)(266, 865)(267, 849)(268, 880)(269, 864)(270, 876)(271, 881)(272, 852)(273, 820)(274, 823)(275, 877)(276, 825)(277, 827)(278, 828)(279, 833)(280, 834)(281, 835)(282, 843)(283, 846)(284, 866)(285, 868)(286, 863)(287, 882)(288, 847)(289, 848)(290, 855)(291, 867)(292, 875)(293, 872)(294, 869)(295, 883)(296, 884)(297, 885)(298, 886)(299, 887)(300, 888)(301, 889)(302, 890)(303, 891)(304, 892)(305, 893)(306, 894)(307, 895)(308, 896)(309, 897)(310, 898)(311, 899)(312, 900)(313, 901)(314, 902)(315, 903)(316, 904)(317, 905)(318, 906)(319, 907)(320, 908)(321, 909)(322, 910)(323, 911)(324, 912)(325, 913)(326, 914)(327, 915)(328, 916)(329, 917)(330, 918)(331, 919)(332, 920)(333, 921)(334, 922)(335, 923)(336, 924)(337, 925)(338, 926)(339, 927)(340, 928)(341, 929)(342, 930)(343, 931)(344, 932)(345, 933)(346, 934)(347, 935)(348, 936)(349, 937)(350, 938)(351, 939)(352, 940)(353, 941)(354, 942)(355, 943)(356, 944)(357, 945)(358, 946)(359, 947)(360, 948)(361, 949)(362, 950)(363, 951)(364, 952)(365, 953)(366, 954)(367, 955)(368, 956)(369, 957)(370, 958)(371, 959)(372, 960)(373, 961)(374, 962)(375, 963)(376, 964)(377, 965)(378, 966)(379, 967)(380, 968)(381, 969)(382, 970)(383, 971)(384, 972)(385, 973)(386, 974)(387, 975)(388, 976)(389, 977)(390, 978)(391, 979)(392, 980)(393, 981)(394, 982)(395, 983)(396, 984)(397, 985)(398, 986)(399, 987)(400, 988)(401, 989)(402, 990)(403, 991)(404, 992)(405, 993)(406, 994)(407, 995)(408, 996)(409, 997)(410, 998)(411, 999)(412, 1000)(413, 1001)(414, 1002)(415, 1003)(416, 1004)(417, 1005)(418, 1006)(419, 1007)(420, 1008)(421, 1009)(422, 1010)(423, 1011)(424, 1012)(425, 1013)(426, 1014)(427, 1015)(428, 1016)(429, 1017)(430, 1018)(431, 1019)(432, 1020)(433, 1021)(434, 1022)(435, 1023)(436, 1024)(437, 1025)(438, 1026)(439, 1027)(440, 1028)(441, 1029)(442, 1030)(443, 1031)(444, 1032)(445, 1033)(446, 1034)(447, 1035)(448, 1036)(449, 1037)(450, 1038)(451, 1039)(452, 1040)(453, 1041)(454, 1042)(455, 1043)(456, 1044)(457, 1045)(458, 1046)(459, 1047)(460, 1048)(461, 1049)(462, 1050)(463, 1051)(464, 1052)(465, 1053)(466, 1054)(467, 1055)(468, 1056)(469, 1057)(470, 1058)(471, 1059)(472, 1060)(473, 1061)(474, 1062)(475, 1063)(476, 1064)(477, 1065)(478, 1066)(479, 1067)(480, 1068)(481, 1069)(482, 1070)(483, 1071)(484, 1072)(485, 1073)(486, 1074)(487, 1075)(488, 1076)(489, 1077)(490, 1078)(491, 1079)(492, 1080)(493, 1081)(494, 1082)(495, 1083)(496, 1084)(497, 1085)(498, 1086)(499, 1087)(500, 1088)(501, 1089)(502, 1090)(503, 1091)(504, 1092)(505, 1093)(506, 1094)(507, 1095)(508, 1096)(509, 1097)(510, 1098)(511, 1099)(512, 1100)(513, 1101)(514, 1102)(515, 1103)(516, 1104)(517, 1105)(518, 1106)(519, 1107)(520, 1108)(521, 1109)(522, 1110)(523, 1111)(524, 1112)(525, 1113)(526, 1114)(527, 1115)(528, 1116)(529, 1117)(530, 1118)(531, 1119)(532, 1120)(533, 1121)(534, 1122)(535, 1123)(536, 1124)(537, 1125)(538, 1126)(539, 1127)(540, 1128)(541, 1129)(542, 1130)(543, 1131)(544, 1132)(545, 1133)(546, 1134)(547, 1135)(548, 1136)(549, 1137)(550, 1138)(551, 1139)(552, 1140)(553, 1141)(554, 1142)(555, 1143)(556, 1144)(557, 1145)(558, 1146)(559, 1147)(560, 1148)(561, 1149)(562, 1150)(563, 1151)(564, 1152)(565, 1153)(566, 1154)(567, 1155)(568, 1156)(569, 1157)(570, 1158)(571, 1159)(572, 1160)(573, 1161)(574, 1162)(575, 1163)(576, 1164)(577, 1165)(578, 1166)(579, 1167)(580, 1168)(581, 1169)(582, 1170)(583, 1171)(584, 1172)(585, 1173)(586, 1174)(587, 1175)(588, 1176) local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1369 Graph:: bipartite v = 119 e = 588 f = 441 degree seq :: [ 6^98, 28^21 ] E15.1369 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14}) Quotient :: dipole Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-1)^3, Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2, Y3^14, Y3^-3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^4 * Y2 * Y3^-4 * Y2 * Y3^-4 * Y2 * Y3^4 * Y2, (Y3^-1 * Y1^-1)^14 ] Map:: polytopal R = (1, 295)(2, 296)(3, 297)(4, 298)(5, 299)(6, 300)(7, 301)(8, 302)(9, 303)(10, 304)(11, 305)(12, 306)(13, 307)(14, 308)(15, 309)(16, 310)(17, 311)(18, 312)(19, 313)(20, 314)(21, 315)(22, 316)(23, 317)(24, 318)(25, 319)(26, 320)(27, 321)(28, 322)(29, 323)(30, 324)(31, 325)(32, 326)(33, 327)(34, 328)(35, 329)(36, 330)(37, 331)(38, 332)(39, 333)(40, 334)(41, 335)(42, 336)(43, 337)(44, 338)(45, 339)(46, 340)(47, 341)(48, 342)(49, 343)(50, 344)(51, 345)(52, 346)(53, 347)(54, 348)(55, 349)(56, 350)(57, 351)(58, 352)(59, 353)(60, 354)(61, 355)(62, 356)(63, 357)(64, 358)(65, 359)(66, 360)(67, 361)(68, 362)(69, 363)(70, 364)(71, 365)(72, 366)(73, 367)(74, 368)(75, 369)(76, 370)(77, 371)(78, 372)(79, 373)(80, 374)(81, 375)(82, 376)(83, 377)(84, 378)(85, 379)(86, 380)(87, 381)(88, 382)(89, 383)(90, 384)(91, 385)(92, 386)(93, 387)(94, 388)(95, 389)(96, 390)(97, 391)(98, 392)(99, 393)(100, 394)(101, 395)(102, 396)(103, 397)(104, 398)(105, 399)(106, 400)(107, 401)(108, 402)(109, 403)(110, 404)(111, 405)(112, 406)(113, 407)(114, 408)(115, 409)(116, 410)(117, 411)(118, 412)(119, 413)(120, 414)(121, 415)(122, 416)(123, 417)(124, 418)(125, 419)(126, 420)(127, 421)(128, 422)(129, 423)(130, 424)(131, 425)(132, 426)(133, 427)(134, 428)(135, 429)(136, 430)(137, 431)(138, 432)(139, 433)(140, 434)(141, 435)(142, 436)(143, 437)(144, 438)(145, 439)(146, 440)(147, 441)(148, 442)(149, 443)(150, 444)(151, 445)(152, 446)(153, 447)(154, 448)(155, 449)(156, 450)(157, 451)(158, 452)(159, 453)(160, 454)(161, 455)(162, 456)(163, 457)(164, 458)(165, 459)(166, 460)(167, 461)(168, 462)(169, 463)(170, 464)(171, 465)(172, 466)(173, 467)(174, 468)(175, 469)(176, 470)(177, 471)(178, 472)(179, 473)(180, 474)(181, 475)(182, 476)(183, 477)(184, 478)(185, 479)(186, 480)(187, 481)(188, 482)(189, 483)(190, 484)(191, 485)(192, 486)(193, 487)(194, 488)(195, 489)(196, 490)(197, 491)(198, 492)(199, 493)(200, 494)(201, 495)(202, 496)(203, 497)(204, 498)(205, 499)(206, 500)(207, 501)(208, 502)(209, 503)(210, 504)(211, 505)(212, 506)(213, 507)(214, 508)(215, 509)(216, 510)(217, 511)(218, 512)(219, 513)(220, 514)(221, 515)(222, 516)(223, 517)(224, 518)(225, 519)(226, 520)(227, 521)(228, 522)(229, 523)(230, 524)(231, 525)(232, 526)(233, 527)(234, 528)(235, 529)(236, 530)(237, 531)(238, 532)(239, 533)(240, 534)(241, 535)(242, 536)(243, 537)(244, 538)(245, 539)(246, 540)(247, 541)(248, 542)(249, 543)(250, 544)(251, 545)(252, 546)(253, 547)(254, 548)(255, 549)(256, 550)(257, 551)(258, 552)(259, 553)(260, 554)(261, 555)(262, 556)(263, 557)(264, 558)(265, 559)(266, 560)(267, 561)(268, 562)(269, 563)(270, 564)(271, 565)(272, 566)(273, 567)(274, 568)(275, 569)(276, 570)(277, 571)(278, 572)(279, 573)(280, 574)(281, 575)(282, 576)(283, 577)(284, 578)(285, 579)(286, 580)(287, 581)(288, 582)(289, 583)(290, 584)(291, 585)(292, 586)(293, 587)(294, 588)(589, 883, 590, 884)(591, 885, 595, 889)(592, 886, 597, 891)(593, 887, 599, 893)(594, 888, 601, 895)(596, 890, 604, 898)(598, 892, 607, 901)(600, 894, 610, 904)(602, 896, 613, 907)(603, 897, 615, 909)(605, 899, 618, 912)(606, 900, 620, 914)(608, 902, 623, 917)(609, 903, 625, 919)(611, 905, 628, 922)(612, 906, 630, 924)(614, 908, 633, 927)(616, 910, 636, 930)(617, 911, 638, 932)(619, 913, 641, 935)(621, 915, 644, 938)(622, 916, 646, 940)(624, 918, 649, 943)(626, 920, 652, 946)(627, 921, 654, 948)(629, 923, 657, 951)(631, 925, 660, 954)(632, 926, 662, 956)(634, 928, 665, 959)(635, 929, 651, 945)(637, 931, 668, 962)(639, 933, 663, 957)(640, 934, 671, 965)(642, 936, 674, 968)(643, 937, 659, 953)(645, 939, 677, 971)(647, 941, 655, 949)(648, 942, 680, 974)(650, 944, 683, 977)(653, 947, 686, 980)(656, 950, 689, 983)(658, 952, 692, 986)(661, 955, 695, 989)(664, 958, 698, 992)(666, 960, 701, 995)(667, 961, 703, 997)(669, 963, 706, 1000)(670, 964, 708, 1002)(672, 966, 704, 998)(673, 967, 711, 1005)(675, 969, 714, 1008)(676, 970, 716, 1010)(678, 972, 719, 1013)(679, 973, 721, 1015)(681, 975, 717, 1011)(682, 976, 724, 1018)(684, 978, 727, 1021)(685, 979, 728, 1022)(687, 981, 731, 1025)(688, 982, 733, 1027)(690, 984, 729, 1023)(691, 985, 736, 1030)(693, 987, 739, 1033)(694, 988, 741, 1035)(696, 990, 744, 1038)(697, 991, 746, 1040)(699, 993, 742, 1036)(700, 994, 749, 1043)(702, 996, 752, 1046)(705, 999, 730, 1024)(707, 1001, 755, 1049)(709, 1003, 750, 1044)(710, 1004, 758, 1052)(712, 1006, 747, 1041)(713, 1007, 761, 1055)(715, 1009, 764, 1058)(718, 1012, 743, 1037)(720, 1014, 767, 1061)(722, 1016, 737, 1031)(723, 1017, 770, 1064)(725, 1019, 734, 1028)(726, 1020, 773, 1067)(732, 1026, 778, 1072)(735, 1029, 781, 1075)(738, 1032, 784, 1078)(740, 1034, 787, 1081)(745, 1039, 790, 1084)(748, 1042, 793, 1087)(751, 1045, 796, 1090)(753, 1047, 799, 1093)(754, 1048, 801, 1095)(756, 1050, 804, 1098)(757, 1051, 805, 1099)(759, 1053, 802, 1096)(760, 1054, 808, 1102)(762, 1056, 800, 1094)(763, 1057, 811, 1105)(765, 1059, 814, 1108)(766, 1060, 816, 1110)(768, 1062, 819, 1113)(769, 1063, 820, 1114)(771, 1065, 817, 1111)(772, 1066, 823, 1117)(774, 1068, 815, 1109)(775, 1069, 813, 1107)(776, 1070, 827, 1121)(777, 1071, 829, 1123)(779, 1073, 832, 1126)(780, 1074, 833, 1127)(782, 1076, 830, 1124)(783, 1077, 836, 1130)(785, 1079, 828, 1122)(786, 1080, 839, 1133)(788, 1082, 842, 1136)(789, 1083, 844, 1138)(791, 1085, 847, 1141)(792, 1086, 848, 1142)(794, 1088, 845, 1139)(795, 1089, 851, 1145)(797, 1091, 843, 1137)(798, 1092, 841, 1135)(803, 1097, 831, 1125)(806, 1100, 854, 1148)(807, 1101, 857, 1151)(809, 1103, 852, 1146)(810, 1104, 859, 1153)(812, 1106, 849, 1143)(818, 1112, 846, 1140)(821, 1115, 840, 1134)(822, 1116, 864, 1158)(824, 1118, 837, 1131)(825, 1119, 861, 1155)(826, 1120, 834, 1128)(835, 1129, 869, 1163)(838, 1132, 871, 1165)(850, 1144, 876, 1170)(853, 1147, 873, 1167)(855, 1149, 879, 1173)(856, 1150, 875, 1169)(858, 1152, 872, 1166)(860, 1154, 870, 1164)(862, 1156, 880, 1174)(863, 1157, 868, 1162)(865, 1159, 878, 1172)(866, 1160, 877, 1171)(867, 1161, 881, 1175)(874, 1168, 882, 1176) L = (1, 591)(2, 593)(3, 596)(4, 589)(5, 600)(6, 590)(7, 601)(8, 605)(9, 606)(10, 592)(11, 597)(12, 611)(13, 612)(14, 594)(15, 595)(16, 615)(17, 619)(18, 621)(19, 622)(20, 598)(21, 599)(22, 625)(23, 629)(24, 631)(25, 632)(26, 602)(27, 635)(28, 603)(29, 604)(30, 638)(31, 642)(32, 607)(33, 645)(34, 647)(35, 648)(36, 608)(37, 651)(38, 609)(39, 610)(40, 654)(41, 658)(42, 613)(43, 661)(44, 663)(45, 664)(46, 614)(47, 652)(48, 667)(49, 616)(50, 662)(51, 617)(52, 618)(53, 671)(54, 675)(55, 620)(56, 659)(57, 678)(58, 623)(59, 679)(60, 681)(61, 682)(62, 624)(63, 636)(64, 685)(65, 626)(66, 646)(67, 627)(68, 628)(69, 689)(70, 693)(71, 630)(72, 643)(73, 696)(74, 633)(75, 697)(76, 699)(77, 700)(78, 634)(79, 704)(80, 705)(81, 637)(82, 639)(83, 703)(84, 640)(85, 641)(86, 711)(87, 715)(88, 644)(89, 716)(90, 720)(91, 722)(92, 649)(93, 723)(94, 725)(95, 726)(96, 650)(97, 729)(98, 730)(99, 653)(100, 655)(101, 728)(102, 656)(103, 657)(104, 736)(105, 740)(106, 660)(107, 741)(108, 745)(109, 747)(110, 665)(111, 748)(112, 750)(113, 751)(114, 666)(115, 668)(116, 753)(117, 731)(118, 754)(119, 669)(120, 749)(121, 670)(122, 672)(123, 746)(124, 673)(125, 674)(126, 761)(127, 684)(128, 680)(129, 676)(130, 677)(131, 743)(132, 768)(133, 733)(134, 769)(135, 771)(136, 683)(137, 772)(138, 774)(139, 775)(140, 686)(141, 776)(142, 706)(143, 777)(144, 687)(145, 724)(146, 688)(147, 690)(148, 721)(149, 691)(150, 692)(151, 784)(152, 702)(153, 698)(154, 694)(155, 695)(156, 718)(157, 791)(158, 708)(159, 792)(160, 794)(161, 701)(162, 795)(163, 797)(164, 798)(165, 800)(166, 802)(167, 803)(168, 707)(169, 709)(170, 801)(171, 710)(172, 712)(173, 799)(174, 713)(175, 714)(176, 811)(177, 717)(178, 719)(179, 816)(180, 779)(181, 821)(182, 814)(183, 822)(184, 824)(185, 727)(186, 825)(187, 826)(188, 828)(189, 830)(190, 831)(191, 732)(192, 734)(193, 829)(194, 735)(195, 737)(196, 827)(197, 738)(198, 739)(199, 839)(200, 742)(201, 744)(202, 844)(203, 756)(204, 849)(205, 842)(206, 850)(207, 852)(208, 752)(209, 853)(210, 854)(211, 758)(212, 834)(213, 755)(214, 855)(215, 832)(216, 856)(217, 841)(218, 757)(219, 759)(220, 851)(221, 760)(222, 762)(223, 848)(224, 763)(225, 764)(226, 773)(227, 765)(228, 770)(229, 766)(230, 767)(231, 846)(232, 836)(233, 843)(234, 835)(235, 833)(236, 865)(237, 866)(238, 859)(239, 781)(240, 806)(241, 778)(242, 867)(243, 804)(244, 868)(245, 813)(246, 780)(247, 782)(248, 823)(249, 783)(250, 785)(251, 820)(252, 786)(253, 787)(254, 796)(255, 788)(256, 793)(257, 789)(258, 790)(259, 818)(260, 808)(261, 815)(262, 807)(263, 805)(264, 877)(265, 878)(266, 871)(267, 870)(268, 876)(269, 875)(270, 809)(271, 879)(272, 810)(273, 812)(274, 817)(275, 819)(276, 880)(277, 874)(278, 872)(279, 858)(280, 864)(281, 863)(282, 837)(283, 881)(284, 838)(285, 840)(286, 845)(287, 847)(288, 882)(289, 862)(290, 860)(291, 857)(292, 861)(293, 869)(294, 873)(295, 883)(296, 884)(297, 885)(298, 886)(299, 887)(300, 888)(301, 889)(302, 890)(303, 891)(304, 892)(305, 893)(306, 894)(307, 895)(308, 896)(309, 897)(310, 898)(311, 899)(312, 900)(313, 901)(314, 902)(315, 903)(316, 904)(317, 905)(318, 906)(319, 907)(320, 908)(321, 909)(322, 910)(323, 911)(324, 912)(325, 913)(326, 914)(327, 915)(328, 916)(329, 917)(330, 918)(331, 919)(332, 920)(333, 921)(334, 922)(335, 923)(336, 924)(337, 925)(338, 926)(339, 927)(340, 928)(341, 929)(342, 930)(343, 931)(344, 932)(345, 933)(346, 934)(347, 935)(348, 936)(349, 937)(350, 938)(351, 939)(352, 940)(353, 941)(354, 942)(355, 943)(356, 944)(357, 945)(358, 946)(359, 947)(360, 948)(361, 949)(362, 950)(363, 951)(364, 952)(365, 953)(366, 954)(367, 955)(368, 956)(369, 957)(370, 958)(371, 959)(372, 960)(373, 961)(374, 962)(375, 963)(376, 964)(377, 965)(378, 966)(379, 967)(380, 968)(381, 969)(382, 970)(383, 971)(384, 972)(385, 973)(386, 974)(387, 975)(388, 976)(389, 977)(390, 978)(391, 979)(392, 980)(393, 981)(394, 982)(395, 983)(396, 984)(397, 985)(398, 986)(399, 987)(400, 988)(401, 989)(402, 990)(403, 991)(404, 992)(405, 993)(406, 994)(407, 995)(408, 996)(409, 997)(410, 998)(411, 999)(412, 1000)(413, 1001)(414, 1002)(415, 1003)(416, 1004)(417, 1005)(418, 1006)(419, 1007)(420, 1008)(421, 1009)(422, 1010)(423, 1011)(424, 1012)(425, 1013)(426, 1014)(427, 1015)(428, 1016)(429, 1017)(430, 1018)(431, 1019)(432, 1020)(433, 1021)(434, 1022)(435, 1023)(436, 1024)(437, 1025)(438, 1026)(439, 1027)(440, 1028)(441, 1029)(442, 1030)(443, 1031)(444, 1032)(445, 1033)(446, 1034)(447, 1035)(448, 1036)(449, 1037)(450, 1038)(451, 1039)(452, 1040)(453, 1041)(454, 1042)(455, 1043)(456, 1044)(457, 1045)(458, 1046)(459, 1047)(460, 1048)(461, 1049)(462, 1050)(463, 1051)(464, 1052)(465, 1053)(466, 1054)(467, 1055)(468, 1056)(469, 1057)(470, 1058)(471, 1059)(472, 1060)(473, 1061)(474, 1062)(475, 1063)(476, 1064)(477, 1065)(478, 1066)(479, 1067)(480, 1068)(481, 1069)(482, 1070)(483, 1071)(484, 1072)(485, 1073)(486, 1074)(487, 1075)(488, 1076)(489, 1077)(490, 1078)(491, 1079)(492, 1080)(493, 1081)(494, 1082)(495, 1083)(496, 1084)(497, 1085)(498, 1086)(499, 1087)(500, 1088)(501, 1089)(502, 1090)(503, 1091)(504, 1092)(505, 1093)(506, 1094)(507, 1095)(508, 1096)(509, 1097)(510, 1098)(511, 1099)(512, 1100)(513, 1101)(514, 1102)(515, 1103)(516, 1104)(517, 1105)(518, 1106)(519, 1107)(520, 1108)(521, 1109)(522, 1110)(523, 1111)(524, 1112)(525, 1113)(526, 1114)(527, 1115)(528, 1116)(529, 1117)(530, 1118)(531, 1119)(532, 1120)(533, 1121)(534, 1122)(535, 1123)(536, 1124)(537, 1125)(538, 1126)(539, 1127)(540, 1128)(541, 1129)(542, 1130)(543, 1131)(544, 1132)(545, 1133)(546, 1134)(547, 1135)(548, 1136)(549, 1137)(550, 1138)(551, 1139)(552, 1140)(553, 1141)(554, 1142)(555, 1143)(556, 1144)(557, 1145)(558, 1146)(559, 1147)(560, 1148)(561, 1149)(562, 1150)(563, 1151)(564, 1152)(565, 1153)(566, 1154)(567, 1155)(568, 1156)(569, 1157)(570, 1158)(571, 1159)(572, 1160)(573, 1161)(574, 1162)(575, 1163)(576, 1164)(577, 1165)(578, 1166)(579, 1167)(580, 1168)(581, 1169)(582, 1170)(583, 1171)(584, 1172)(585, 1173)(586, 1174)(587, 1175)(588, 1176) local type(s) :: { ( 6, 28 ), ( 6, 28, 6, 28 ) } Outer automorphisms :: reflexible Dual of E15.1368 Graph:: simple bipartite v = 441 e = 588 f = 119 degree seq :: [ 2^294, 4^147 ] E15.1370 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14}) Quotient :: dipole Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |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)^3, (Y3 * Y1^-1 * Y3 * Y1^-2)^2, Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-1, Y1^14 ] Map:: polytopal R = (1, 295, 2, 296, 5, 299, 11, 305, 21, 315, 37, 331, 63, 357, 97, 391, 96, 390, 62, 356, 36, 330, 20, 314, 10, 304, 4, 298)(3, 297, 7, 301, 15, 309, 27, 321, 47, 341, 79, 373, 115, 409, 165, 459, 127, 421, 87, 381, 54, 348, 31, 325, 17, 311, 8, 302)(6, 300, 13, 307, 25, 319, 43, 337, 73, 367, 109, 403, 155, 449, 204, 498, 164, 458, 114, 408, 78, 372, 46, 340, 26, 320, 14, 308)(9, 303, 18, 312, 32, 326, 55, 349, 88, 382, 128, 422, 177, 471, 220, 514, 173, 467, 122, 416, 84, 378, 51, 345, 29, 323, 16, 310)(12, 306, 23, 317, 41, 335, 69, 363, 105, 399, 150, 444, 200, 494, 252, 546, 203, 497, 154, 448, 108, 402, 72, 366, 42, 336, 24, 318)(19, 313, 34, 328, 58, 352, 91, 385, 133, 427, 181, 475, 232, 526, 261, 555, 207, 501, 159, 453, 111, 405, 74, 368, 57, 351, 33, 327)(22, 316, 39, 333, 67, 361, 53, 347, 85, 379, 123, 417, 174, 468, 221, 515, 251, 545, 199, 493, 149, 443, 104, 398, 68, 362, 40, 334)(28, 322, 49, 343, 70, 364, 45, 339, 76, 370, 103, 397, 147, 441, 192, 486, 243, 537, 218, 512, 172, 466, 120, 414, 83, 377, 50, 344)(30, 324, 52, 346, 71, 365, 106, 400, 145, 439, 194, 488, 241, 535, 231, 525, 180, 474, 132, 426, 90, 384, 56, 350, 75, 369, 44, 338)(35, 329, 60, 354, 92, 386, 135, 429, 182, 476, 234, 528, 272, 566, 217, 511, 170, 464, 119, 413, 82, 376, 48, 342, 81, 375, 59, 353)(38, 332, 65, 359, 101, 395, 77, 371, 112, 406, 160, 454, 208, 502, 262, 556, 285, 579, 248, 542, 196, 490, 146, 440, 102, 396, 66, 360)(61, 355, 94, 388, 136, 430, 184, 478, 235, 529, 277, 571, 289, 583, 259, 553, 206, 500, 156, 450, 131, 425, 89, 383, 130, 424, 93, 387)(64, 358, 99, 393, 143, 437, 107, 401, 152, 446, 126, 420, 175, 469, 223, 517, 273, 567, 282, 576, 245, 539, 193, 487, 144, 438, 100, 394)(80, 374, 117, 411, 151, 445, 121, 415, 161, 455, 113, 407, 162, 456, 198, 492, 249, 543, 281, 575, 271, 565, 215, 509, 169, 463, 118, 412)(86, 380, 125, 419, 153, 447, 201, 495, 247, 541, 283, 577, 275, 569, 229, 523, 179, 473, 129, 423, 158, 452, 110, 404, 157, 451, 124, 418)(95, 389, 138, 432, 185, 479, 237, 531, 278, 572, 284, 578, 269, 563, 214, 508, 168, 462, 116, 410, 167, 461, 134, 428, 171, 465, 137, 431)(98, 392, 141, 435, 190, 484, 148, 442, 197, 491, 163, 457, 209, 503, 264, 558, 290, 584, 276, 570, 279, 573, 242, 536, 191, 485, 142, 436)(139, 433, 187, 481, 238, 532, 244, 538, 280, 574, 250, 544, 286, 580, 256, 550, 228, 522, 178, 472, 227, 521, 183, 477, 230, 524, 186, 480)(140, 434, 188, 482, 239, 533, 195, 489, 246, 540, 202, 496, 254, 548, 211, 505, 267, 561, 233, 527, 270, 564, 236, 530, 240, 534, 189, 483)(166, 460, 212, 506, 253, 547, 216, 510, 263, 557, 219, 513, 265, 559, 210, 504, 266, 560, 287, 581, 294, 588, 291, 585, 268, 562, 213, 507)(176, 470, 225, 519, 255, 549, 288, 582, 293, 587, 292, 586, 274, 568, 226, 520, 258, 552, 205, 499, 257, 551, 222, 516, 260, 554, 224, 518)(589, 883)(590, 884)(591, 885)(592, 886)(593, 887)(594, 888)(595, 889)(596, 890)(597, 891)(598, 892)(599, 893)(600, 894)(601, 895)(602, 896)(603, 897)(604, 898)(605, 899)(606, 900)(607, 901)(608, 902)(609, 903)(610, 904)(611, 905)(612, 906)(613, 907)(614, 908)(615, 909)(616, 910)(617, 911)(618, 912)(619, 913)(620, 914)(621, 915)(622, 916)(623, 917)(624, 918)(625, 919)(626, 920)(627, 921)(628, 922)(629, 923)(630, 924)(631, 925)(632, 926)(633, 927)(634, 928)(635, 929)(636, 930)(637, 931)(638, 932)(639, 933)(640, 934)(641, 935)(642, 936)(643, 937)(644, 938)(645, 939)(646, 940)(647, 941)(648, 942)(649, 943)(650, 944)(651, 945)(652, 946)(653, 947)(654, 948)(655, 949)(656, 950)(657, 951)(658, 952)(659, 953)(660, 954)(661, 955)(662, 956)(663, 957)(664, 958)(665, 959)(666, 960)(667, 961)(668, 962)(669, 963)(670, 964)(671, 965)(672, 966)(673, 967)(674, 968)(675, 969)(676, 970)(677, 971)(678, 972)(679, 973)(680, 974)(681, 975)(682, 976)(683, 977)(684, 978)(685, 979)(686, 980)(687, 981)(688, 982)(689, 983)(690, 984)(691, 985)(692, 986)(693, 987)(694, 988)(695, 989)(696, 990)(697, 991)(698, 992)(699, 993)(700, 994)(701, 995)(702, 996)(703, 997)(704, 998)(705, 999)(706, 1000)(707, 1001)(708, 1002)(709, 1003)(710, 1004)(711, 1005)(712, 1006)(713, 1007)(714, 1008)(715, 1009)(716, 1010)(717, 1011)(718, 1012)(719, 1013)(720, 1014)(721, 1015)(722, 1016)(723, 1017)(724, 1018)(725, 1019)(726, 1020)(727, 1021)(728, 1022)(729, 1023)(730, 1024)(731, 1025)(732, 1026)(733, 1027)(734, 1028)(735, 1029)(736, 1030)(737, 1031)(738, 1032)(739, 1033)(740, 1034)(741, 1035)(742, 1036)(743, 1037)(744, 1038)(745, 1039)(746, 1040)(747, 1041)(748, 1042)(749, 1043)(750, 1044)(751, 1045)(752, 1046)(753, 1047)(754, 1048)(755, 1049)(756, 1050)(757, 1051)(758, 1052)(759, 1053)(760, 1054)(761, 1055)(762, 1056)(763, 1057)(764, 1058)(765, 1059)(766, 1060)(767, 1061)(768, 1062)(769, 1063)(770, 1064)(771, 1065)(772, 1066)(773, 1067)(774, 1068)(775, 1069)(776, 1070)(777, 1071)(778, 1072)(779, 1073)(780, 1074)(781, 1075)(782, 1076)(783, 1077)(784, 1078)(785, 1079)(786, 1080)(787, 1081)(788, 1082)(789, 1083)(790, 1084)(791, 1085)(792, 1086)(793, 1087)(794, 1088)(795, 1089)(796, 1090)(797, 1091)(798, 1092)(799, 1093)(800, 1094)(801, 1095)(802, 1096)(803, 1097)(804, 1098)(805, 1099)(806, 1100)(807, 1101)(808, 1102)(809, 1103)(810, 1104)(811, 1105)(812, 1106)(813, 1107)(814, 1108)(815, 1109)(816, 1110)(817, 1111)(818, 1112)(819, 1113)(820, 1114)(821, 1115)(822, 1116)(823, 1117)(824, 1118)(825, 1119)(826, 1120)(827, 1121)(828, 1122)(829, 1123)(830, 1124)(831, 1125)(832, 1126)(833, 1127)(834, 1128)(835, 1129)(836, 1130)(837, 1131)(838, 1132)(839, 1133)(840, 1134)(841, 1135)(842, 1136)(843, 1137)(844, 1138)(845, 1139)(846, 1140)(847, 1141)(848, 1142)(849, 1143)(850, 1144)(851, 1145)(852, 1146)(853, 1147)(854, 1148)(855, 1149)(856, 1150)(857, 1151)(858, 1152)(859, 1153)(860, 1154)(861, 1155)(862, 1156)(863, 1157)(864, 1158)(865, 1159)(866, 1160)(867, 1161)(868, 1162)(869, 1163)(870, 1164)(871, 1165)(872, 1166)(873, 1167)(874, 1168)(875, 1169)(876, 1170)(877, 1171)(878, 1172)(879, 1173)(880, 1174)(881, 1175)(882, 1176) L = (1, 591)(2, 594)(3, 589)(4, 597)(5, 600)(6, 590)(7, 604)(8, 601)(9, 592)(10, 607)(11, 610)(12, 593)(13, 596)(14, 611)(15, 616)(16, 595)(17, 618)(18, 621)(19, 598)(20, 623)(21, 626)(22, 599)(23, 602)(24, 627)(25, 632)(26, 633)(27, 636)(28, 603)(29, 637)(30, 605)(31, 641)(32, 644)(33, 606)(34, 647)(35, 608)(36, 649)(37, 652)(38, 609)(39, 612)(40, 653)(41, 658)(42, 659)(43, 662)(44, 613)(45, 614)(46, 665)(47, 668)(48, 615)(49, 617)(50, 669)(51, 657)(52, 655)(53, 619)(54, 674)(55, 677)(56, 620)(57, 663)(58, 671)(59, 622)(60, 681)(61, 624)(62, 683)(63, 686)(64, 625)(65, 628)(66, 687)(67, 640)(68, 691)(69, 639)(70, 629)(71, 630)(72, 695)(73, 698)(74, 631)(75, 645)(76, 689)(77, 634)(78, 701)(79, 704)(80, 635)(81, 638)(82, 705)(83, 646)(84, 709)(85, 712)(86, 642)(87, 714)(88, 717)(89, 643)(90, 718)(91, 722)(92, 720)(93, 648)(94, 725)(95, 650)(96, 727)(97, 728)(98, 651)(99, 654)(100, 729)(101, 664)(102, 733)(103, 656)(104, 736)(105, 739)(106, 731)(107, 660)(108, 741)(109, 744)(110, 661)(111, 745)(112, 749)(113, 666)(114, 751)(115, 754)(116, 667)(117, 670)(118, 755)(119, 738)(120, 759)(121, 672)(122, 748)(123, 747)(124, 673)(125, 740)(126, 675)(127, 764)(128, 766)(129, 676)(130, 678)(131, 746)(132, 680)(133, 757)(134, 679)(135, 771)(136, 760)(137, 682)(138, 774)(139, 684)(140, 685)(141, 688)(142, 776)(143, 694)(144, 780)(145, 690)(146, 783)(147, 778)(148, 692)(149, 786)(150, 707)(151, 693)(152, 713)(153, 696)(154, 790)(155, 793)(156, 697)(157, 699)(158, 719)(159, 711)(160, 710)(161, 700)(162, 785)(163, 702)(164, 798)(165, 799)(166, 703)(167, 706)(168, 800)(169, 721)(170, 804)(171, 708)(172, 724)(173, 807)(174, 810)(175, 812)(176, 715)(177, 814)(178, 716)(179, 815)(180, 818)(181, 821)(182, 817)(183, 723)(184, 824)(185, 819)(186, 726)(187, 777)(188, 730)(189, 775)(190, 735)(191, 829)(192, 732)(193, 832)(194, 827)(195, 734)(196, 835)(197, 750)(198, 737)(199, 838)(200, 841)(201, 834)(202, 742)(203, 843)(204, 844)(205, 743)(206, 845)(207, 848)(208, 851)(209, 853)(210, 752)(211, 753)(212, 756)(213, 855)(214, 840)(215, 858)(216, 758)(217, 850)(218, 828)(219, 761)(220, 852)(221, 847)(222, 762)(223, 849)(224, 763)(225, 842)(226, 765)(227, 767)(228, 846)(229, 770)(230, 768)(231, 773)(232, 856)(233, 769)(234, 864)(235, 859)(236, 772)(237, 830)(238, 831)(239, 782)(240, 806)(241, 779)(242, 825)(243, 826)(244, 781)(245, 869)(246, 789)(247, 784)(248, 872)(249, 868)(250, 787)(251, 875)(252, 802)(253, 788)(254, 813)(255, 791)(256, 792)(257, 794)(258, 816)(259, 809)(260, 795)(261, 811)(262, 805)(263, 796)(264, 808)(265, 797)(266, 874)(267, 801)(268, 820)(269, 876)(270, 803)(271, 823)(272, 880)(273, 879)(274, 878)(275, 867)(276, 822)(277, 870)(278, 871)(279, 863)(280, 837)(281, 833)(282, 865)(283, 866)(284, 836)(285, 881)(286, 854)(287, 839)(288, 857)(289, 882)(290, 862)(291, 861)(292, 860)(293, 873)(294, 877)(295, 883)(296, 884)(297, 885)(298, 886)(299, 887)(300, 888)(301, 889)(302, 890)(303, 891)(304, 892)(305, 893)(306, 894)(307, 895)(308, 896)(309, 897)(310, 898)(311, 899)(312, 900)(313, 901)(314, 902)(315, 903)(316, 904)(317, 905)(318, 906)(319, 907)(320, 908)(321, 909)(322, 910)(323, 911)(324, 912)(325, 913)(326, 914)(327, 915)(328, 916)(329, 917)(330, 918)(331, 919)(332, 920)(333, 921)(334, 922)(335, 923)(336, 924)(337, 925)(338, 926)(339, 927)(340, 928)(341, 929)(342, 930)(343, 931)(344, 932)(345, 933)(346, 934)(347, 935)(348, 936)(349, 937)(350, 938)(351, 939)(352, 940)(353, 941)(354, 942)(355, 943)(356, 944)(357, 945)(358, 946)(359, 947)(360, 948)(361, 949)(362, 950)(363, 951)(364, 952)(365, 953)(366, 954)(367, 955)(368, 956)(369, 957)(370, 958)(371, 959)(372, 960)(373, 961)(374, 962)(375, 963)(376, 964)(377, 965)(378, 966)(379, 967)(380, 968)(381, 969)(382, 970)(383, 971)(384, 972)(385, 973)(386, 974)(387, 975)(388, 976)(389, 977)(390, 978)(391, 979)(392, 980)(393, 981)(394, 982)(395, 983)(396, 984)(397, 985)(398, 986)(399, 987)(400, 988)(401, 989)(402, 990)(403, 991)(404, 992)(405, 993)(406, 994)(407, 995)(408, 996)(409, 997)(410, 998)(411, 999)(412, 1000)(413, 1001)(414, 1002)(415, 1003)(416, 1004)(417, 1005)(418, 1006)(419, 1007)(420, 1008)(421, 1009)(422, 1010)(423, 1011)(424, 1012)(425, 1013)(426, 1014)(427, 1015)(428, 1016)(429, 1017)(430, 1018)(431, 1019)(432, 1020)(433, 1021)(434, 1022)(435, 1023)(436, 1024)(437, 1025)(438, 1026)(439, 1027)(440, 1028)(441, 1029)(442, 1030)(443, 1031)(444, 1032)(445, 1033)(446, 1034)(447, 1035)(448, 1036)(449, 1037)(450, 1038)(451, 1039)(452, 1040)(453, 1041)(454, 1042)(455, 1043)(456, 1044)(457, 1045)(458, 1046)(459, 1047)(460, 1048)(461, 1049)(462, 1050)(463, 1051)(464, 1052)(465, 1053)(466, 1054)(467, 1055)(468, 1056)(469, 1057)(470, 1058)(471, 1059)(472, 1060)(473, 1061)(474, 1062)(475, 1063)(476, 1064)(477, 1065)(478, 1066)(479, 1067)(480, 1068)(481, 1069)(482, 1070)(483, 1071)(484, 1072)(485, 1073)(486, 1074)(487, 1075)(488, 1076)(489, 1077)(490, 1078)(491, 1079)(492, 1080)(493, 1081)(494, 1082)(495, 1083)(496, 1084)(497, 1085)(498, 1086)(499, 1087)(500, 1088)(501, 1089)(502, 1090)(503, 1091)(504, 1092)(505, 1093)(506, 1094)(507, 1095)(508, 1096)(509, 1097)(510, 1098)(511, 1099)(512, 1100)(513, 1101)(514, 1102)(515, 1103)(516, 1104)(517, 1105)(518, 1106)(519, 1107)(520, 1108)(521, 1109)(522, 1110)(523, 1111)(524, 1112)(525, 1113)(526, 1114)(527, 1115)(528, 1116)(529, 1117)(530, 1118)(531, 1119)(532, 1120)(533, 1121)(534, 1122)(535, 1123)(536, 1124)(537, 1125)(538, 1126)(539, 1127)(540, 1128)(541, 1129)(542, 1130)(543, 1131)(544, 1132)(545, 1133)(546, 1134)(547, 1135)(548, 1136)(549, 1137)(550, 1138)(551, 1139)(552, 1140)(553, 1141)(554, 1142)(555, 1143)(556, 1144)(557, 1145)(558, 1146)(559, 1147)(560, 1148)(561, 1149)(562, 1150)(563, 1151)(564, 1152)(565, 1153)(566, 1154)(567, 1155)(568, 1156)(569, 1157)(570, 1158)(571, 1159)(572, 1160)(573, 1161)(574, 1162)(575, 1163)(576, 1164)(577, 1165)(578, 1166)(579, 1167)(580, 1168)(581, 1169)(582, 1170)(583, 1171)(584, 1172)(585, 1173)(586, 1174)(587, 1175)(588, 1176) 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 ) } Outer automorphisms :: reflexible Dual of E15.1367 Graph:: simple bipartite v = 315 e = 588 f = 245 degree seq :: [ 2^294, 28^21 ] E15.1371 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14}) Quotient :: dipole Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2)^3, (Y3 * Y2^-1)^3, (Y2^-3 * Y1)^3, Y2^14, Y2^-7 * Y1 * Y2^-2 * Y1 * Y2^5 * Y1 * Y2^-2 * Y1 ] Map:: R = (1, 295, 2, 296)(3, 297, 7, 301)(4, 298, 9, 303)(5, 299, 11, 305)(6, 300, 13, 307)(8, 302, 16, 310)(10, 304, 19, 313)(12, 306, 22, 316)(14, 308, 25, 319)(15, 309, 27, 321)(17, 311, 30, 324)(18, 312, 32, 326)(20, 314, 35, 329)(21, 315, 37, 331)(23, 317, 40, 334)(24, 318, 42, 336)(26, 320, 45, 339)(28, 322, 48, 342)(29, 323, 50, 344)(31, 325, 53, 347)(33, 327, 56, 350)(34, 328, 58, 352)(36, 330, 61, 355)(38, 332, 64, 358)(39, 333, 66, 360)(41, 335, 69, 363)(43, 337, 72, 366)(44, 338, 74, 368)(46, 340, 77, 371)(47, 341, 63, 357)(49, 343, 80, 374)(51, 345, 75, 369)(52, 346, 83, 377)(54, 348, 86, 380)(55, 349, 71, 365)(57, 351, 89, 383)(59, 353, 67, 361)(60, 354, 92, 386)(62, 356, 95, 389)(65, 359, 98, 392)(68, 362, 101, 395)(70, 364, 104, 398)(73, 367, 107, 401)(76, 370, 110, 404)(78, 372, 113, 407)(79, 373, 115, 409)(81, 375, 118, 412)(82, 376, 120, 414)(84, 378, 116, 410)(85, 379, 123, 417)(87, 381, 126, 420)(88, 382, 128, 422)(90, 384, 131, 425)(91, 385, 133, 427)(93, 387, 129, 423)(94, 388, 136, 430)(96, 390, 139, 433)(97, 391, 140, 434)(99, 393, 143, 437)(100, 394, 145, 439)(102, 396, 141, 435)(103, 397, 148, 442)(105, 399, 151, 445)(106, 400, 153, 447)(108, 402, 156, 450)(109, 403, 158, 452)(111, 405, 154, 448)(112, 406, 161, 455)(114, 408, 164, 458)(117, 411, 142, 436)(119, 413, 167, 461)(121, 415, 162, 456)(122, 416, 170, 464)(124, 418, 159, 453)(125, 419, 173, 467)(127, 421, 176, 470)(130, 424, 155, 449)(132, 426, 179, 473)(134, 428, 149, 443)(135, 429, 182, 476)(137, 431, 146, 440)(138, 432, 185, 479)(144, 438, 190, 484)(147, 441, 193, 487)(150, 444, 196, 490)(152, 446, 199, 493)(157, 451, 202, 496)(160, 454, 205, 499)(163, 457, 208, 502)(165, 459, 211, 505)(166, 460, 213, 507)(168, 462, 216, 510)(169, 463, 217, 511)(171, 465, 214, 508)(172, 466, 220, 514)(174, 468, 212, 506)(175, 469, 223, 517)(177, 471, 226, 520)(178, 472, 228, 522)(180, 474, 231, 525)(181, 475, 232, 526)(183, 477, 229, 523)(184, 478, 235, 529)(186, 480, 227, 521)(187, 481, 225, 519)(188, 482, 239, 533)(189, 483, 241, 535)(191, 485, 244, 538)(192, 486, 245, 539)(194, 488, 242, 536)(195, 489, 248, 542)(197, 491, 240, 534)(198, 492, 251, 545)(200, 494, 254, 548)(201, 495, 256, 550)(203, 497, 259, 553)(204, 498, 260, 554)(206, 500, 257, 551)(207, 501, 263, 557)(209, 503, 255, 549)(210, 504, 253, 547)(215, 509, 243, 537)(218, 512, 266, 560)(219, 513, 269, 563)(221, 515, 264, 558)(222, 516, 271, 565)(224, 518, 261, 555)(230, 524, 258, 552)(233, 527, 252, 546)(234, 528, 276, 570)(236, 530, 249, 543)(237, 531, 273, 567)(238, 532, 246, 540)(247, 541, 281, 575)(250, 544, 283, 577)(262, 556, 288, 582)(265, 559, 285, 579)(267, 561, 291, 585)(268, 562, 287, 581)(270, 564, 284, 578)(272, 566, 282, 576)(274, 568, 292, 586)(275, 569, 280, 574)(277, 571, 290, 584)(278, 572, 289, 583)(279, 573, 293, 587)(286, 580, 294, 588)(589, 883, 591, 885, 596, 890, 605, 899, 619, 913, 642, 936, 675, 969, 715, 1009, 684, 978, 650, 944, 624, 918, 608, 902, 598, 892, 592, 886)(590, 884, 593, 887, 600, 894, 611, 905, 629, 923, 658, 952, 693, 987, 740, 1034, 702, 996, 666, 960, 634, 928, 614, 908, 602, 896, 594, 888)(595, 889, 601, 895, 612, 906, 631, 925, 661, 955, 696, 990, 745, 1039, 791, 1085, 756, 1050, 707, 1001, 669, 963, 637, 931, 616, 910, 603, 897)(597, 891, 606, 900, 621, 915, 645, 939, 678, 972, 720, 1014, 768, 1062, 779, 1073, 732, 1026, 687, 981, 653, 947, 626, 920, 609, 903, 599, 893)(604, 898, 615, 909, 635, 929, 652, 946, 685, 979, 729, 1023, 776, 1070, 828, 1122, 806, 1100, 757, 1051, 709, 1003, 670, 964, 639, 933, 617, 911)(607, 901, 622, 916, 647, 941, 679, 973, 722, 1016, 769, 1063, 821, 1115, 843, 1137, 788, 1082, 742, 1036, 694, 988, 660, 954, 643, 937, 620, 914)(610, 904, 625, 919, 651, 945, 636, 930, 667, 961, 704, 998, 753, 1047, 800, 1094, 834, 1128, 780, 1074, 734, 1028, 688, 982, 655, 949, 627, 921)(613, 907, 632, 926, 663, 957, 697, 991, 747, 1041, 792, 1086, 849, 1143, 815, 1109, 765, 1059, 717, 1011, 676, 970, 644, 938, 659, 953, 630, 924)(618, 912, 638, 932, 662, 956, 633, 927, 664, 958, 699, 993, 748, 1042, 794, 1088, 850, 1144, 807, 1101, 759, 1053, 710, 1004, 672, 966, 640, 934)(623, 917, 648, 942, 681, 975, 723, 1017, 771, 1065, 822, 1116, 835, 1129, 782, 1076, 735, 1029, 690, 984, 656, 950, 628, 922, 654, 948, 646, 940)(641, 935, 671, 965, 703, 997, 668, 962, 705, 999, 731, 1025, 777, 1071, 830, 1124, 867, 1161, 858, 1152, 809, 1103, 760, 1054, 712, 1006, 673, 967)(649, 943, 682, 976, 725, 1019, 772, 1066, 824, 1118, 865, 1159, 874, 1168, 845, 1139, 789, 1083, 744, 1038, 718, 1012, 677, 971, 716, 1010, 680, 974)(657, 951, 689, 983, 728, 1022, 686, 980, 730, 1024, 706, 1000, 754, 1048, 802, 1096, 855, 1149, 870, 1164, 837, 1131, 783, 1077, 737, 1031, 691, 985)(665, 959, 700, 994, 750, 1044, 795, 1089, 852, 1146, 877, 1171, 862, 1156, 817, 1111, 766, 1060, 719, 1013, 743, 1037, 695, 989, 741, 1035, 698, 992)(674, 968, 711, 1005, 746, 1040, 708, 1002, 749, 1043, 701, 995, 751, 1045, 797, 1091, 853, 1147, 878, 1172, 860, 1154, 810, 1104, 762, 1056, 713, 1007)(683, 977, 726, 1020, 774, 1068, 825, 1119, 866, 1160, 872, 1166, 838, 1132, 785, 1079, 738, 1032, 692, 986, 736, 1030, 721, 1015, 733, 1027, 724, 1018)(714, 1008, 761, 1055, 799, 1093, 758, 1052, 801, 1095, 755, 1049, 803, 1097, 832, 1126, 868, 1162, 864, 1158, 880, 1174, 861, 1155, 812, 1106, 763, 1057)(727, 1021, 775, 1069, 826, 1120, 859, 1153, 879, 1173, 857, 1151, 875, 1169, 847, 1141, 818, 1112, 767, 1061, 816, 1110, 770, 1064, 814, 1108, 773, 1067)(739, 1033, 784, 1078, 827, 1121, 781, 1075, 829, 1123, 778, 1072, 831, 1125, 804, 1098, 856, 1150, 876, 1170, 882, 1176, 873, 1167, 840, 1134, 786, 1080)(752, 1046, 798, 1092, 854, 1148, 871, 1165, 881, 1175, 869, 1163, 863, 1157, 819, 1113, 846, 1140, 790, 1084, 844, 1138, 793, 1087, 842, 1136, 796, 1090)(764, 1058, 811, 1105, 848, 1142, 808, 1102, 851, 1145, 805, 1099, 841, 1135, 787, 1081, 839, 1133, 820, 1114, 836, 1130, 823, 1117, 833, 1127, 813, 1107) L = (1, 590)(2, 589)(3, 595)(4, 597)(5, 599)(6, 601)(7, 591)(8, 604)(9, 592)(10, 607)(11, 593)(12, 610)(13, 594)(14, 613)(15, 615)(16, 596)(17, 618)(18, 620)(19, 598)(20, 623)(21, 625)(22, 600)(23, 628)(24, 630)(25, 602)(26, 633)(27, 603)(28, 636)(29, 638)(30, 605)(31, 641)(32, 606)(33, 644)(34, 646)(35, 608)(36, 649)(37, 609)(38, 652)(39, 654)(40, 611)(41, 657)(42, 612)(43, 660)(44, 662)(45, 614)(46, 665)(47, 651)(48, 616)(49, 668)(50, 617)(51, 663)(52, 671)(53, 619)(54, 674)(55, 659)(56, 621)(57, 677)(58, 622)(59, 655)(60, 680)(61, 624)(62, 683)(63, 635)(64, 626)(65, 686)(66, 627)(67, 647)(68, 689)(69, 629)(70, 692)(71, 643)(72, 631)(73, 695)(74, 632)(75, 639)(76, 698)(77, 634)(78, 701)(79, 703)(80, 637)(81, 706)(82, 708)(83, 640)(84, 704)(85, 711)(86, 642)(87, 714)(88, 716)(89, 645)(90, 719)(91, 721)(92, 648)(93, 717)(94, 724)(95, 650)(96, 727)(97, 728)(98, 653)(99, 731)(100, 733)(101, 656)(102, 729)(103, 736)(104, 658)(105, 739)(106, 741)(107, 661)(108, 744)(109, 746)(110, 664)(111, 742)(112, 749)(113, 666)(114, 752)(115, 667)(116, 672)(117, 730)(118, 669)(119, 755)(120, 670)(121, 750)(122, 758)(123, 673)(124, 747)(125, 761)(126, 675)(127, 764)(128, 676)(129, 681)(130, 743)(131, 678)(132, 767)(133, 679)(134, 737)(135, 770)(136, 682)(137, 734)(138, 773)(139, 684)(140, 685)(141, 690)(142, 705)(143, 687)(144, 778)(145, 688)(146, 725)(147, 781)(148, 691)(149, 722)(150, 784)(151, 693)(152, 787)(153, 694)(154, 699)(155, 718)(156, 696)(157, 790)(158, 697)(159, 712)(160, 793)(161, 700)(162, 709)(163, 796)(164, 702)(165, 799)(166, 801)(167, 707)(168, 804)(169, 805)(170, 710)(171, 802)(172, 808)(173, 713)(174, 800)(175, 811)(176, 715)(177, 814)(178, 816)(179, 720)(180, 819)(181, 820)(182, 723)(183, 817)(184, 823)(185, 726)(186, 815)(187, 813)(188, 827)(189, 829)(190, 732)(191, 832)(192, 833)(193, 735)(194, 830)(195, 836)(196, 738)(197, 828)(198, 839)(199, 740)(200, 842)(201, 844)(202, 745)(203, 847)(204, 848)(205, 748)(206, 845)(207, 851)(208, 751)(209, 843)(210, 841)(211, 753)(212, 762)(213, 754)(214, 759)(215, 831)(216, 756)(217, 757)(218, 854)(219, 857)(220, 760)(221, 852)(222, 859)(223, 763)(224, 849)(225, 775)(226, 765)(227, 774)(228, 766)(229, 771)(230, 846)(231, 768)(232, 769)(233, 840)(234, 864)(235, 772)(236, 837)(237, 861)(238, 834)(239, 776)(240, 785)(241, 777)(242, 782)(243, 803)(244, 779)(245, 780)(246, 826)(247, 869)(248, 783)(249, 824)(250, 871)(251, 786)(252, 821)(253, 798)(254, 788)(255, 797)(256, 789)(257, 794)(258, 818)(259, 791)(260, 792)(261, 812)(262, 876)(263, 795)(264, 809)(265, 873)(266, 806)(267, 879)(268, 875)(269, 807)(270, 872)(271, 810)(272, 870)(273, 825)(274, 880)(275, 868)(276, 822)(277, 878)(278, 877)(279, 881)(280, 863)(281, 835)(282, 860)(283, 838)(284, 858)(285, 853)(286, 882)(287, 856)(288, 850)(289, 866)(290, 865)(291, 855)(292, 862)(293, 867)(294, 874)(295, 883)(296, 884)(297, 885)(298, 886)(299, 887)(300, 888)(301, 889)(302, 890)(303, 891)(304, 892)(305, 893)(306, 894)(307, 895)(308, 896)(309, 897)(310, 898)(311, 899)(312, 900)(313, 901)(314, 902)(315, 903)(316, 904)(317, 905)(318, 906)(319, 907)(320, 908)(321, 909)(322, 910)(323, 911)(324, 912)(325, 913)(326, 914)(327, 915)(328, 916)(329, 917)(330, 918)(331, 919)(332, 920)(333, 921)(334, 922)(335, 923)(336, 924)(337, 925)(338, 926)(339, 927)(340, 928)(341, 929)(342, 930)(343, 931)(344, 932)(345, 933)(346, 934)(347, 935)(348, 936)(349, 937)(350, 938)(351, 939)(352, 940)(353, 941)(354, 942)(355, 943)(356, 944)(357, 945)(358, 946)(359, 947)(360, 948)(361, 949)(362, 950)(363, 951)(364, 952)(365, 953)(366, 954)(367, 955)(368, 956)(369, 957)(370, 958)(371, 959)(372, 960)(373, 961)(374, 962)(375, 963)(376, 964)(377, 965)(378, 966)(379, 967)(380, 968)(381, 969)(382, 970)(383, 971)(384, 972)(385, 973)(386, 974)(387, 975)(388, 976)(389, 977)(390, 978)(391, 979)(392, 980)(393, 981)(394, 982)(395, 983)(396, 984)(397, 985)(398, 986)(399, 987)(400, 988)(401, 989)(402, 990)(403, 991)(404, 992)(405, 993)(406, 994)(407, 995)(408, 996)(409, 997)(410, 998)(411, 999)(412, 1000)(413, 1001)(414, 1002)(415, 1003)(416, 1004)(417, 1005)(418, 1006)(419, 1007)(420, 1008)(421, 1009)(422, 1010)(423, 1011)(424, 1012)(425, 1013)(426, 1014)(427, 1015)(428, 1016)(429, 1017)(430, 1018)(431, 1019)(432, 1020)(433, 1021)(434, 1022)(435, 1023)(436, 1024)(437, 1025)(438, 1026)(439, 1027)(440, 1028)(441, 1029)(442, 1030)(443, 1031)(444, 1032)(445, 1033)(446, 1034)(447, 1035)(448, 1036)(449, 1037)(450, 1038)(451, 1039)(452, 1040)(453, 1041)(454, 1042)(455, 1043)(456, 1044)(457, 1045)(458, 1046)(459, 1047)(460, 1048)(461, 1049)(462, 1050)(463, 1051)(464, 1052)(465, 1053)(466, 1054)(467, 1055)(468, 1056)(469, 1057)(470, 1058)(471, 1059)(472, 1060)(473, 1061)(474, 1062)(475, 1063)(476, 1064)(477, 1065)(478, 1066)(479, 1067)(480, 1068)(481, 1069)(482, 1070)(483, 1071)(484, 1072)(485, 1073)(486, 1074)(487, 1075)(488, 1076)(489, 1077)(490, 1078)(491, 1079)(492, 1080)(493, 1081)(494, 1082)(495, 1083)(496, 1084)(497, 1085)(498, 1086)(499, 1087)(500, 1088)(501, 1089)(502, 1090)(503, 1091)(504, 1092)(505, 1093)(506, 1094)(507, 1095)(508, 1096)(509, 1097)(510, 1098)(511, 1099)(512, 1100)(513, 1101)(514, 1102)(515, 1103)(516, 1104)(517, 1105)(518, 1106)(519, 1107)(520, 1108)(521, 1109)(522, 1110)(523, 1111)(524, 1112)(525, 1113)(526, 1114)(527, 1115)(528, 1116)(529, 1117)(530, 1118)(531, 1119)(532, 1120)(533, 1121)(534, 1122)(535, 1123)(536, 1124)(537, 1125)(538, 1126)(539, 1127)(540, 1128)(541, 1129)(542, 1130)(543, 1131)(544, 1132)(545, 1133)(546, 1134)(547, 1135)(548, 1136)(549, 1137)(550, 1138)(551, 1139)(552, 1140)(553, 1141)(554, 1142)(555, 1143)(556, 1144)(557, 1145)(558, 1146)(559, 1147)(560, 1148)(561, 1149)(562, 1150)(563, 1151)(564, 1152)(565, 1153)(566, 1154)(567, 1155)(568, 1156)(569, 1157)(570, 1158)(571, 1159)(572, 1160)(573, 1161)(574, 1162)(575, 1163)(576, 1164)(577, 1165)(578, 1166)(579, 1167)(580, 1168)(581, 1169)(582, 1170)(583, 1171)(584, 1172)(585, 1173)(586, 1174)(587, 1175)(588, 1176) 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 ) } Outer automorphisms :: reflexible Dual of E15.1372 Graph:: bipartite v = 168 e = 588 f = 392 degree seq :: [ 4^147, 28^21 ] E15.1372 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14}) Quotient :: dipole Aut^+ = ((C7 x C7) : C3) : C2 (small group id <294, 7>) Aut = $<588, 35>$ (small group id <588, 35>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3^2 * Y1^-1, (Y3^2 * Y1^-1)^3, Y3^3 * Y1^-1 * Y3^-5 * Y1 * Y3^4 * Y1^-1 * Y3^-6 * Y1^-1, (Y3 * Y2^-1)^14 ] Map:: polytopal R = (1, 295, 2, 296, 4, 298)(3, 297, 8, 302, 10, 304)(5, 299, 12, 306, 6, 300)(7, 301, 15, 309, 11, 305)(9, 303, 18, 312, 20, 314)(13, 307, 25, 319, 23, 317)(14, 308, 24, 318, 28, 322)(16, 310, 31, 325, 29, 323)(17, 311, 33, 327, 21, 315)(19, 313, 36, 330, 38, 332)(22, 316, 30, 324, 42, 336)(26, 320, 47, 341, 45, 339)(27, 321, 49, 343, 51, 345)(32, 326, 56, 350, 55, 349)(34, 328, 59, 353, 58, 352)(35, 329, 53, 347, 39, 333)(37, 331, 63, 357, 65, 359)(40, 334, 52, 346, 44, 338)(41, 335, 68, 362, 70, 364)(43, 337, 46, 340, 54, 348)(48, 342, 76, 370, 74, 368)(50, 344, 79, 373, 81, 375)(57, 351, 87, 381, 85, 379)(60, 354, 91, 385, 90, 384)(61, 355, 93, 387, 82, 376)(62, 356, 89, 383, 66, 360)(64, 358, 97, 391, 99, 393)(67, 361, 72, 366, 102, 396)(69, 363, 104, 398, 106, 400)(71, 365, 83, 377, 108, 402)(73, 367, 75, 369, 78, 372)(77, 371, 114, 408, 112, 406)(80, 374, 118, 412, 120, 414)(84, 378, 86, 380, 103, 397)(88, 382, 128, 422, 126, 420)(92, 386, 134, 428, 132, 426)(94, 388, 125, 419, 127, 421)(95, 389, 137, 431, 130, 424)(96, 390, 122, 416, 100, 394)(98, 392, 141, 435, 143, 437)(101, 395, 121, 415, 117, 411)(105, 399, 148, 442, 150, 444)(107, 401, 151, 445, 147, 441)(109, 403, 131, 425, 133, 427)(110, 404, 116, 410, 155, 449)(111, 405, 113, 407, 123, 417)(115, 409, 160, 454, 158, 452)(119, 413, 164, 458, 166, 460)(124, 418, 146, 440, 171, 465)(129, 423, 176, 470, 174, 468)(135, 429, 182, 476, 180, 474)(136, 430, 184, 478, 172, 466)(138, 432, 179, 473, 181, 475)(139, 433, 187, 481, 168, 462)(140, 434, 177, 471, 144, 438)(142, 436, 191, 485, 192, 486)(145, 439, 162, 456, 195, 489)(149, 443, 199, 493, 200, 494)(152, 446, 197, 491, 203, 497)(153, 447, 204, 498, 178, 472)(154, 448, 167, 461, 163, 457)(156, 450, 169, 463, 208, 502)(157, 451, 159, 453, 161, 455)(165, 459, 216, 510, 217, 511)(170, 464, 201, 495, 198, 492)(173, 467, 175, 469, 196, 490)(183, 477, 232, 526, 230, 524)(185, 479, 224, 518, 225, 519)(186, 480, 235, 529, 228, 522)(188, 482, 222, 516, 233, 527)(189, 483, 238, 532, 226, 520)(190, 484, 219, 513, 193, 487)(194, 488, 218, 512, 215, 509)(202, 496, 248, 542, 247, 541)(205, 499, 229, 523, 231, 525)(206, 500, 214, 508, 252, 546)(207, 501, 250, 544, 245, 539)(209, 503, 212, 506, 255, 549)(210, 504, 211, 505, 220, 514)(213, 507, 227, 521, 243, 537)(221, 515, 246, 540, 264, 558)(223, 517, 244, 538, 267, 561)(234, 528, 260, 554, 268, 562)(236, 530, 272, 566, 273, 567)(237, 531, 275, 569, 265, 559)(239, 533, 270, 564, 274, 568)(240, 534, 256, 550, 263, 557)(241, 535, 257, 551, 242, 536)(249, 543, 281, 575, 271, 565)(251, 545, 262, 556, 261, 555)(253, 547, 279, 573, 284, 578)(254, 548, 282, 576, 259, 553)(258, 552, 287, 581, 269, 563)(266, 560, 290, 584, 280, 574)(276, 570, 292, 586, 289, 583)(277, 571, 285, 579, 288, 582)(278, 572, 291, 585, 286, 580)(283, 577, 293, 587, 294, 588)(589, 883)(590, 884)(591, 885)(592, 886)(593, 887)(594, 888)(595, 889)(596, 890)(597, 891)(598, 892)(599, 893)(600, 894)(601, 895)(602, 896)(603, 897)(604, 898)(605, 899)(606, 900)(607, 901)(608, 902)(609, 903)(610, 904)(611, 905)(612, 906)(613, 907)(614, 908)(615, 909)(616, 910)(617, 911)(618, 912)(619, 913)(620, 914)(621, 915)(622, 916)(623, 917)(624, 918)(625, 919)(626, 920)(627, 921)(628, 922)(629, 923)(630, 924)(631, 925)(632, 926)(633, 927)(634, 928)(635, 929)(636, 930)(637, 931)(638, 932)(639, 933)(640, 934)(641, 935)(642, 936)(643, 937)(644, 938)(645, 939)(646, 940)(647, 941)(648, 942)(649, 943)(650, 944)(651, 945)(652, 946)(653, 947)(654, 948)(655, 949)(656, 950)(657, 951)(658, 952)(659, 953)(660, 954)(661, 955)(662, 956)(663, 957)(664, 958)(665, 959)(666, 960)(667, 961)(668, 962)(669, 963)(670, 964)(671, 965)(672, 966)(673, 967)(674, 968)(675, 969)(676, 970)(677, 971)(678, 972)(679, 973)(680, 974)(681, 975)(682, 976)(683, 977)(684, 978)(685, 979)(686, 980)(687, 981)(688, 982)(689, 983)(690, 984)(691, 985)(692, 986)(693, 987)(694, 988)(695, 989)(696, 990)(697, 991)(698, 992)(699, 993)(700, 994)(701, 995)(702, 996)(703, 997)(704, 998)(705, 999)(706, 1000)(707, 1001)(708, 1002)(709, 1003)(710, 1004)(711, 1005)(712, 1006)(713, 1007)(714, 1008)(715, 1009)(716, 1010)(717, 1011)(718, 1012)(719, 1013)(720, 1014)(721, 1015)(722, 1016)(723, 1017)(724, 1018)(725, 1019)(726, 1020)(727, 1021)(728, 1022)(729, 1023)(730, 1024)(731, 1025)(732, 1026)(733, 1027)(734, 1028)(735, 1029)(736, 1030)(737, 1031)(738, 1032)(739, 1033)(740, 1034)(741, 1035)(742, 1036)(743, 1037)(744, 1038)(745, 1039)(746, 1040)(747, 1041)(748, 1042)(749, 1043)(750, 1044)(751, 1045)(752, 1046)(753, 1047)(754, 1048)(755, 1049)(756, 1050)(757, 1051)(758, 1052)(759, 1053)(760, 1054)(761, 1055)(762, 1056)(763, 1057)(764, 1058)(765, 1059)(766, 1060)(767, 1061)(768, 1062)(769, 1063)(770, 1064)(771, 1065)(772, 1066)(773, 1067)(774, 1068)(775, 1069)(776, 1070)(777, 1071)(778, 1072)(779, 1073)(780, 1074)(781, 1075)(782, 1076)(783, 1077)(784, 1078)(785, 1079)(786, 1080)(787, 1081)(788, 1082)(789, 1083)(790, 1084)(791, 1085)(792, 1086)(793, 1087)(794, 1088)(795, 1089)(796, 1090)(797, 1091)(798, 1092)(799, 1093)(800, 1094)(801, 1095)(802, 1096)(803, 1097)(804, 1098)(805, 1099)(806, 1100)(807, 1101)(808, 1102)(809, 1103)(810, 1104)(811, 1105)(812, 1106)(813, 1107)(814, 1108)(815, 1109)(816, 1110)(817, 1111)(818, 1112)(819, 1113)(820, 1114)(821, 1115)(822, 1116)(823, 1117)(824, 1118)(825, 1119)(826, 1120)(827, 1121)(828, 1122)(829, 1123)(830, 1124)(831, 1125)(832, 1126)(833, 1127)(834, 1128)(835, 1129)(836, 1130)(837, 1131)(838, 1132)(839, 1133)(840, 1134)(841, 1135)(842, 1136)(843, 1137)(844, 1138)(845, 1139)(846, 1140)(847, 1141)(848, 1142)(849, 1143)(850, 1144)(851, 1145)(852, 1146)(853, 1147)(854, 1148)(855, 1149)(856, 1150)(857, 1151)(858, 1152)(859, 1153)(860, 1154)(861, 1155)(862, 1156)(863, 1157)(864, 1158)(865, 1159)(866, 1160)(867, 1161)(868, 1162)(869, 1163)(870, 1164)(871, 1165)(872, 1166)(873, 1167)(874, 1168)(875, 1169)(876, 1170)(877, 1171)(878, 1172)(879, 1173)(880, 1174)(881, 1175)(882, 1176) L = (1, 591)(2, 594)(3, 597)(4, 599)(5, 589)(6, 602)(7, 590)(8, 592)(9, 607)(10, 609)(11, 610)(12, 611)(13, 593)(14, 615)(15, 617)(16, 595)(17, 596)(18, 598)(19, 625)(20, 627)(21, 628)(22, 629)(23, 631)(24, 600)(25, 633)(26, 601)(27, 638)(28, 640)(29, 641)(30, 603)(31, 643)(32, 604)(33, 646)(34, 605)(35, 606)(36, 608)(37, 652)(38, 654)(39, 619)(40, 655)(41, 657)(42, 634)(43, 659)(44, 612)(45, 661)(46, 613)(47, 662)(48, 614)(49, 616)(50, 668)(51, 663)(52, 621)(53, 670)(54, 618)(55, 672)(56, 673)(57, 620)(58, 677)(59, 678)(60, 622)(61, 623)(62, 624)(63, 626)(64, 686)(65, 688)(66, 647)(67, 689)(68, 630)(69, 693)(70, 674)(71, 695)(72, 632)(73, 698)(74, 699)(75, 635)(76, 700)(77, 636)(78, 637)(79, 639)(80, 707)(81, 709)(82, 710)(83, 642)(84, 712)(85, 713)(86, 644)(87, 714)(88, 645)(89, 718)(90, 719)(91, 720)(92, 648)(93, 715)(94, 649)(95, 650)(96, 651)(97, 653)(98, 730)(99, 732)(100, 681)(101, 733)(102, 721)(103, 656)(104, 658)(105, 737)(106, 739)(107, 740)(108, 701)(109, 660)(110, 742)(111, 744)(112, 745)(113, 664)(114, 746)(115, 665)(116, 666)(117, 667)(118, 669)(119, 753)(120, 755)(121, 690)(122, 756)(123, 671)(124, 758)(125, 760)(126, 761)(127, 675)(128, 762)(129, 676)(130, 765)(131, 766)(132, 767)(133, 679)(134, 768)(135, 680)(136, 682)(137, 769)(138, 683)(139, 684)(140, 685)(141, 687)(142, 703)(143, 781)(144, 725)(145, 782)(146, 691)(147, 692)(148, 694)(149, 771)(150, 789)(151, 696)(152, 790)(153, 697)(154, 794)(155, 747)(156, 795)(157, 797)(158, 798)(159, 702)(160, 780)(161, 704)(162, 705)(163, 706)(164, 708)(165, 717)(166, 806)(167, 743)(168, 807)(169, 711)(170, 809)(171, 763)(172, 810)(173, 811)(174, 812)(175, 716)(176, 805)(177, 814)(178, 815)(179, 816)(180, 817)(181, 722)(182, 818)(183, 723)(184, 813)(185, 724)(186, 726)(187, 821)(188, 727)(189, 728)(190, 729)(191, 731)(192, 830)(193, 775)(194, 822)(195, 831)(196, 734)(197, 735)(198, 736)(199, 738)(200, 836)(201, 759)(202, 837)(203, 838)(204, 819)(205, 741)(206, 839)(207, 841)(208, 799)(209, 842)(210, 844)(211, 748)(212, 749)(213, 750)(214, 751)(215, 752)(216, 754)(217, 850)(218, 783)(219, 851)(220, 757)(221, 824)(222, 853)(223, 854)(224, 856)(225, 764)(226, 845)(227, 857)(228, 858)(229, 859)(230, 860)(231, 770)(232, 788)(233, 772)(234, 773)(235, 861)(236, 774)(237, 776)(238, 862)(239, 777)(240, 778)(241, 779)(242, 826)(243, 792)(244, 784)(245, 785)(246, 786)(247, 787)(248, 791)(249, 793)(250, 796)(251, 832)(252, 870)(253, 871)(254, 873)(255, 829)(256, 874)(257, 800)(258, 801)(259, 802)(260, 803)(261, 804)(262, 840)(263, 808)(264, 878)(265, 879)(266, 865)(267, 849)(268, 880)(269, 864)(270, 876)(271, 881)(272, 852)(273, 820)(274, 823)(275, 877)(276, 825)(277, 827)(278, 828)(279, 833)(280, 834)(281, 835)(282, 843)(283, 846)(284, 866)(285, 868)(286, 863)(287, 882)(288, 847)(289, 848)(290, 855)(291, 867)(292, 875)(293, 872)(294, 869)(295, 883)(296, 884)(297, 885)(298, 886)(299, 887)(300, 888)(301, 889)(302, 890)(303, 891)(304, 892)(305, 893)(306, 894)(307, 895)(308, 896)(309, 897)(310, 898)(311, 899)(312, 900)(313, 901)(314, 902)(315, 903)(316, 904)(317, 905)(318, 906)(319, 907)(320, 908)(321, 909)(322, 910)(323, 911)(324, 912)(325, 913)(326, 914)(327, 915)(328, 916)(329, 917)(330, 918)(331, 919)(332, 920)(333, 921)(334, 922)(335, 923)(336, 924)(337, 925)(338, 926)(339, 927)(340, 928)(341, 929)(342, 930)(343, 931)(344, 932)(345, 933)(346, 934)(347, 935)(348, 936)(349, 937)(350, 938)(351, 939)(352, 940)(353, 941)(354, 942)(355, 943)(356, 944)(357, 945)(358, 946)(359, 947)(360, 948)(361, 949)(362, 950)(363, 951)(364, 952)(365, 953)(366, 954)(367, 955)(368, 956)(369, 957)(370, 958)(371, 959)(372, 960)(373, 961)(374, 962)(375, 963)(376, 964)(377, 965)(378, 966)(379, 967)(380, 968)(381, 969)(382, 970)(383, 971)(384, 972)(385, 973)(386, 974)(387, 975)(388, 976)(389, 977)(390, 978)(391, 979)(392, 980)(393, 981)(394, 982)(395, 983)(396, 984)(397, 985)(398, 986)(399, 987)(400, 988)(401, 989)(402, 990)(403, 991)(404, 992)(405, 993)(406, 994)(407, 995)(408, 996)(409, 997)(410, 998)(411, 999)(412, 1000)(413, 1001)(414, 1002)(415, 1003)(416, 1004)(417, 1005)(418, 1006)(419, 1007)(420, 1008)(421, 1009)(422, 1010)(423, 1011)(424, 1012)(425, 1013)(426, 1014)(427, 1015)(428, 1016)(429, 1017)(430, 1018)(431, 1019)(432, 1020)(433, 1021)(434, 1022)(435, 1023)(436, 1024)(437, 1025)(438, 1026)(439, 1027)(440, 1028)(441, 1029)(442, 1030)(443, 1031)(444, 1032)(445, 1033)(446, 1034)(447, 1035)(448, 1036)(449, 1037)(450, 1038)(451, 1039)(452, 1040)(453, 1041)(454, 1042)(455, 1043)(456, 1044)(457, 1045)(458, 1046)(459, 1047)(460, 1048)(461, 1049)(462, 1050)(463, 1051)(464, 1052)(465, 1053)(466, 1054)(467, 1055)(468, 1056)(469, 1057)(470, 1058)(471, 1059)(472, 1060)(473, 1061)(474, 1062)(475, 1063)(476, 1064)(477, 1065)(478, 1066)(479, 1067)(480, 1068)(481, 1069)(482, 1070)(483, 1071)(484, 1072)(485, 1073)(486, 1074)(487, 1075)(488, 1076)(489, 1077)(490, 1078)(491, 1079)(492, 1080)(493, 1081)(494, 1082)(495, 1083)(496, 1084)(497, 1085)(498, 1086)(499, 1087)(500, 1088)(501, 1089)(502, 1090)(503, 1091)(504, 1092)(505, 1093)(506, 1094)(507, 1095)(508, 1096)(509, 1097)(510, 1098)(511, 1099)(512, 1100)(513, 1101)(514, 1102)(515, 1103)(516, 1104)(517, 1105)(518, 1106)(519, 1107)(520, 1108)(521, 1109)(522, 1110)(523, 1111)(524, 1112)(525, 1113)(526, 1114)(527, 1115)(528, 1116)(529, 1117)(530, 1118)(531, 1119)(532, 1120)(533, 1121)(534, 1122)(535, 1123)(536, 1124)(537, 1125)(538, 1126)(539, 1127)(540, 1128)(541, 1129)(542, 1130)(543, 1131)(544, 1132)(545, 1133)(546, 1134)(547, 1135)(548, 1136)(549, 1137)(550, 1138)(551, 1139)(552, 1140)(553, 1141)(554, 1142)(555, 1143)(556, 1144)(557, 1145)(558, 1146)(559, 1147)(560, 1148)(561, 1149)(562, 1150)(563, 1151)(564, 1152)(565, 1153)(566, 1154)(567, 1155)(568, 1156)(569, 1157)(570, 1158)(571, 1159)(572, 1160)(573, 1161)(574, 1162)(575, 1163)(576, 1164)(577, 1165)(578, 1166)(579, 1167)(580, 1168)(581, 1169)(582, 1170)(583, 1171)(584, 1172)(585, 1173)(586, 1174)(587, 1175)(588, 1176) local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E15.1371 Graph:: simple bipartite v = 392 e = 588 f = 168 degree seq :: [ 2^294, 6^98 ] E15.1373 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 6}) Quotient :: regular Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T1^-1 * T2)^4, (T1^2 * T2 * T1)^3, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1, (T1 * T2 * T1^-1 * T2)^4 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 29, 18, 8)(6, 13, 25, 46, 28, 14)(9, 19, 35, 61, 37, 20)(12, 23, 42, 73, 45, 24)(16, 31, 54, 91, 56, 32)(17, 33, 57, 82, 48, 26)(21, 38, 66, 78, 68, 39)(22, 40, 69, 51, 72, 41)(27, 49, 83, 118, 75, 43)(30, 52, 87, 128, 90, 53)(34, 59, 98, 139, 100, 60)(36, 63, 103, 153, 105, 64)(44, 76, 119, 165, 112, 70)(47, 79, 123, 173, 126, 80)(50, 85, 132, 95, 134, 86)(55, 93, 142, 193, 136, 88)(58, 96, 146, 202, 148, 97)(62, 101, 145, 94, 144, 102)(65, 106, 157, 211, 158, 107)(67, 71, 113, 166, 161, 109)(74, 115, 169, 224, 171, 116)(77, 121, 177, 129, 178, 122)(81, 127, 183, 241, 180, 124)(84, 130, 185, 245, 187, 131)(89, 137, 174, 228, 168, 114)(92, 140, 196, 254, 198, 141)(99, 111, 163, 221, 208, 150)(104, 155, 214, 268, 210, 152)(108, 159, 215, 156, 189, 133)(110, 125, 181, 225, 220, 162)(117, 172, 232, 287, 230, 170)(120, 175, 234, 290, 236, 176)(135, 191, 251, 284, 235, 184)(138, 188, 248, 199, 247, 195)(143, 200, 259, 294, 238, 186)(147, 204, 263, 302, 250, 190)(149, 206, 264, 205, 260, 201)(151, 197, 257, 277, 266, 209)(154, 212, 269, 313, 271, 213)(160, 219, 275, 315, 274, 218)(164, 223, 279, 317, 278, 222)(167, 226, 281, 319, 283, 227)(179, 239, 295, 276, 282, 233)(182, 237, 293, 244, 292, 243)(192, 253, 291, 324, 304, 252)(194, 255, 289, 321, 288, 231)(203, 261, 309, 328, 310, 262)(207, 242, 298, 318, 311, 265)(216, 272, 307, 258, 301, 249)(217, 270, 280, 229, 285, 273)(240, 297, 320, 303, 326, 296)(246, 299, 327, 308, 267, 300)(256, 306, 330, 312, 316, 305)(286, 323, 314, 325, 332, 322)(329, 334, 331, 335, 336, 333) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 34)(19, 36)(20, 31)(23, 43)(24, 44)(25, 47)(28, 50)(29, 51)(32, 55)(33, 58)(35, 62)(37, 65)(38, 67)(39, 63)(40, 70)(41, 71)(42, 74)(45, 77)(46, 78)(48, 81)(49, 84)(52, 88)(53, 89)(54, 92)(56, 94)(57, 95)(59, 99)(60, 96)(61, 73)(64, 104)(66, 108)(68, 110)(69, 111)(72, 114)(75, 117)(76, 120)(79, 124)(80, 125)(82, 128)(83, 129)(85, 133)(86, 130)(87, 135)(90, 138)(91, 139)(93, 143)(97, 147)(98, 149)(100, 151)(101, 152)(102, 121)(103, 154)(105, 156)(106, 116)(107, 140)(109, 160)(112, 164)(113, 167)(115, 170)(118, 173)(119, 174)(122, 175)(123, 179)(126, 182)(127, 184)(131, 186)(132, 188)(134, 190)(136, 192)(137, 194)(141, 197)(142, 199)(144, 201)(145, 200)(146, 203)(148, 205)(150, 207)(153, 211)(155, 204)(157, 216)(158, 217)(159, 218)(161, 208)(162, 212)(163, 222)(165, 224)(166, 225)(168, 226)(169, 229)(171, 231)(172, 233)(176, 235)(177, 237)(178, 238)(180, 240)(181, 242)(183, 244)(185, 246)(187, 247)(189, 249)(191, 252)(193, 254)(195, 255)(196, 256)(198, 258)(202, 241)(206, 265)(209, 261)(210, 267)(213, 270)(214, 264)(215, 263)(219, 257)(220, 276)(221, 277)(223, 280)(227, 282)(228, 284)(230, 286)(232, 289)(234, 291)(236, 292)(239, 296)(243, 298)(245, 287)(248, 301)(250, 299)(251, 303)(253, 305)(259, 308)(260, 293)(262, 297)(266, 312)(268, 313)(269, 314)(271, 311)(272, 288)(273, 306)(274, 310)(275, 307)(278, 316)(279, 318)(281, 320)(283, 321)(285, 322)(290, 317)(294, 324)(295, 325)(300, 323)(302, 328)(304, 329)(309, 331)(315, 319)(326, 333)(327, 334)(330, 335)(332, 336) local type(s) :: { ( 4^6 ) } Outer automorphisms :: reflexible Dual of E15.1374 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 56 e = 168 f = 84 degree seq :: [ 6^56 ] E15.1374 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 6}) Quotient :: regular Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T2)^2, (F * T1)^2, (T1^-1 * T2)^6, (T2 * T1^-2 * T2 * T1^-1)^3, (T2 * T1^-1 * T2 * T1)^4, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 41, 25)(15, 26, 44, 27)(21, 35, 59, 36)(22, 37, 62, 38)(23, 39, 65, 40)(29, 48, 79, 49)(30, 50, 82, 51)(32, 53, 86, 54)(33, 55, 89, 56)(34, 57, 92, 58)(42, 69, 110, 70)(43, 71, 112, 72)(45, 74, 117, 75)(46, 76, 96, 60)(47, 77, 121, 78)(52, 84, 131, 85)(61, 97, 145, 98)(63, 100, 149, 101)(64, 102, 134, 87)(66, 104, 123, 105)(67, 106, 93, 107)(68, 108, 159, 109)(73, 115, 167, 116)(80, 91, 139, 125)(81, 126, 180, 127)(83, 129, 183, 130)(88, 135, 187, 136)(90, 137, 190, 138)(94, 141, 132, 142)(95, 128, 182, 143)(99, 148, 178, 124)(103, 153, 206, 154)(111, 162, 217, 163)(113, 165, 204, 151)(114, 166, 184, 155)(118, 158, 147, 170)(119, 171, 227, 172)(120, 173, 229, 174)(122, 176, 133, 177)(140, 193, 248, 194)(144, 198, 216, 161)(146, 200, 247, 192)(150, 196, 189, 203)(152, 179, 236, 205)(156, 209, 265, 210)(157, 211, 268, 212)(160, 214, 207, 215)(164, 219, 225, 169)(168, 223, 208, 224)(175, 231, 288, 232)(181, 238, 191, 233)(185, 188, 245, 241)(186, 242, 299, 243)(195, 251, 307, 252)(197, 253, 249, 254)(199, 256, 260, 202)(201, 258, 250, 259)(213, 271, 301, 272)(218, 257, 311, 270)(220, 274, 267, 278)(221, 226, 261, 279)(222, 280, 300, 281)(228, 263, 269, 282)(230, 266, 318, 287)(234, 291, 331, 292)(235, 293, 289, 294)(237, 295, 298, 240)(239, 296, 290, 297)(244, 302, 304, 246)(255, 303, 326, 309)(262, 276, 308, 313)(264, 316, 332, 306)(273, 312, 334, 322)(275, 323, 320, 305)(277, 315, 321, 324)(283, 310, 333, 327)(284, 314, 325, 328)(285, 329, 330, 286)(317, 336, 335, 319) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 42)(25, 43)(26, 45)(27, 46)(28, 47)(31, 52)(35, 60)(36, 61)(37, 63)(38, 64)(39, 66)(40, 67)(41, 68)(44, 73)(48, 80)(49, 81)(50, 83)(51, 69)(53, 87)(54, 88)(55, 90)(56, 91)(57, 93)(58, 94)(59, 95)(62, 99)(65, 103)(70, 111)(71, 113)(72, 114)(74, 118)(75, 119)(76, 120)(77, 122)(78, 123)(79, 124)(82, 128)(84, 132)(85, 133)(86, 116)(89, 108)(92, 140)(96, 144)(97, 146)(98, 147)(100, 150)(101, 151)(102, 152)(104, 155)(105, 156)(106, 157)(107, 158)(109, 160)(110, 161)(112, 164)(115, 168)(117, 169)(121, 175)(125, 179)(126, 171)(127, 181)(129, 184)(130, 185)(131, 186)(134, 173)(135, 188)(136, 189)(137, 191)(138, 192)(139, 163)(141, 195)(142, 196)(143, 197)(145, 199)(148, 201)(149, 202)(153, 207)(154, 208)(159, 213)(162, 218)(165, 220)(166, 221)(167, 222)(170, 226)(172, 228)(174, 230)(176, 233)(177, 234)(178, 235)(180, 237)(182, 239)(183, 240)(187, 244)(190, 246)(193, 249)(194, 250)(198, 255)(200, 257)(203, 261)(204, 262)(205, 263)(206, 264)(209, 266)(210, 267)(211, 269)(212, 270)(214, 273)(215, 274)(216, 275)(217, 276)(219, 277)(223, 282)(224, 283)(225, 284)(227, 285)(229, 286)(231, 289)(232, 290)(236, 278)(238, 279)(241, 287)(242, 300)(243, 301)(245, 303)(247, 305)(248, 306)(251, 308)(252, 309)(253, 310)(254, 311)(256, 312)(258, 313)(259, 314)(260, 315)(265, 317)(268, 319)(271, 320)(272, 321)(280, 325)(281, 326)(288, 316)(291, 323)(292, 330)(293, 324)(294, 329)(295, 328)(296, 318)(297, 322)(298, 327)(299, 332)(302, 333)(304, 334)(307, 335)(331, 336) local type(s) :: { ( 6^4 ) } Outer automorphisms :: reflexible Dual of E15.1373 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 84 e = 168 f = 56 degree seq :: [ 4^84 ] E15.1375 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 6}) Quotient :: edge Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^6, (T1 * T2^-2 * T1 * T2^-1)^3, (T1 * T2^-1 * T1 * T2)^4, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] 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, 45, 27)(20, 34, 58, 35)(23, 39, 65, 40)(25, 42, 70, 43)(28, 47, 78, 48)(30, 50, 83, 51)(31, 52, 84, 53)(33, 55, 89, 56)(36, 60, 97, 61)(38, 63, 102, 64)(41, 67, 107, 68)(44, 72, 114, 73)(46, 75, 119, 76)(49, 80, 126, 81)(54, 86, 134, 87)(57, 91, 127, 92)(59, 94, 106, 95)(62, 99, 151, 100)(66, 104, 157, 105)(69, 109, 163, 110)(71, 112, 166, 113)(74, 116, 170, 117)(77, 120, 174, 121)(79, 123, 177, 124)(82, 128, 183, 129)(85, 132, 188, 133)(88, 136, 193, 137)(90, 139, 182, 140)(93, 142, 199, 143)(96, 145, 158, 146)(98, 148, 205, 149)(101, 152, 210, 153)(103, 130, 185, 155)(108, 160, 169, 161)(111, 164, 176, 122)(115, 167, 226, 168)(118, 172, 230, 173)(125, 179, 171, 180)(131, 154, 212, 186)(135, 190, 198, 191)(138, 194, 204, 147)(141, 196, 255, 197)(144, 201, 259, 202)(150, 207, 200, 208)(156, 214, 273, 215)(159, 217, 276, 218)(162, 220, 227, 221)(165, 175, 231, 224)(178, 234, 229, 235)(181, 237, 294, 238)(184, 225, 283, 240)(187, 243, 301, 244)(189, 246, 304, 247)(192, 249, 256, 250)(195, 203, 260, 253)(206, 263, 258, 264)(209, 266, 322, 267)(211, 254, 311, 269)(213, 271, 275, 272)(216, 274, 280, 222)(219, 278, 327, 279)(223, 281, 277, 282)(228, 285, 329, 286)(232, 288, 293, 289)(233, 290, 296, 239)(236, 291, 331, 292)(241, 297, 295, 298)(242, 299, 303, 300)(245, 302, 308, 251)(248, 306, 332, 307)(252, 309, 305, 310)(257, 313, 334, 314)(261, 316, 321, 317)(262, 318, 324, 268)(265, 319, 336, 320)(270, 325, 323, 326)(284, 328, 330, 287)(312, 333, 335, 315)(337, 338)(339, 343)(340, 345)(341, 346)(342, 348)(344, 351)(347, 356)(349, 359)(350, 361)(352, 364)(353, 366)(354, 367)(355, 369)(357, 372)(358, 374)(360, 377)(362, 380)(363, 382)(365, 385)(368, 390)(370, 393)(371, 395)(373, 398)(375, 400)(376, 402)(378, 405)(379, 407)(381, 410)(383, 413)(384, 415)(386, 418)(387, 388)(389, 421)(391, 424)(392, 426)(394, 429)(396, 432)(397, 434)(399, 437)(401, 439)(403, 442)(404, 444)(406, 447)(408, 449)(409, 451)(411, 454)(412, 456)(414, 458)(416, 461)(417, 463)(419, 466)(420, 467)(422, 455)(423, 471)(425, 474)(427, 476)(428, 477)(430, 480)(431, 481)(433, 483)(435, 486)(436, 450)(438, 490)(440, 492)(441, 494)(443, 495)(445, 498)(446, 473)(448, 501)(452, 505)(453, 507)(457, 511)(459, 484)(460, 514)(462, 517)(464, 518)(465, 520)(468, 523)(469, 510)(470, 525)(472, 528)(475, 531)(478, 534)(479, 536)(482, 539)(485, 542)(487, 545)(488, 502)(489, 547)(491, 549)(493, 552)(496, 555)(497, 556)(499, 558)(500, 559)(503, 561)(504, 563)(506, 564)(508, 565)(509, 551)(512, 568)(513, 569)(515, 571)(516, 572)(519, 575)(521, 577)(522, 578)(524, 581)(526, 584)(527, 585)(529, 587)(530, 588)(532, 590)(533, 592)(535, 593)(537, 594)(538, 580)(540, 597)(541, 598)(543, 600)(544, 601)(546, 604)(548, 606)(550, 579)(553, 611)(554, 613)(557, 596)(560, 599)(562, 620)(566, 623)(567, 586)(570, 589)(573, 629)(574, 631)(576, 605)(582, 639)(583, 641)(591, 648)(595, 651)(602, 657)(603, 659)(607, 655)(608, 637)(609, 636)(610, 642)(612, 650)(614, 638)(615, 662)(616, 645)(617, 644)(618, 652)(619, 661)(621, 658)(622, 640)(624, 646)(625, 654)(626, 653)(627, 635)(628, 660)(630, 649)(632, 656)(633, 647)(634, 643)(663, 671)(664, 672)(665, 670)(666, 668)(667, 669) L = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 12, 12 ), ( 12^4 ) } Outer automorphisms :: reflexible Dual of E15.1379 Transitivity :: ET+ Graph:: simple bipartite v = 252 e = 336 f = 56 degree seq :: [ 2^168, 4^84 ] E15.1376 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 6}) Quotient :: edge Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, T2^6, T2^-3 * T1 * T2 * T1 * T2^-2, (T1 * T2^-2)^3, T1^-1 * T2^-3 * T1 * T2^-3 * T1^-1 * T2^2, T2 * T1^-2 * T2^2 * T1^2 * T2 * T1^-1 * T2^-2 * T1^-2 * T2^-2 * T1^-1, T2^3 * T1^-2 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1, T2^2 * T1^-2 * T2 * T1^-1 * T2^2 * T1 * T2^-2 * T1^-1 * T2 * T1^-2 * T2^-2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 10, 24, 14, 5)(2, 7, 17, 37, 20, 8)(4, 12, 27, 46, 22, 9)(6, 15, 32, 63, 35, 16)(11, 26, 52, 90, 48, 23)(13, 29, 57, 102, 60, 30)(18, 39, 74, 121, 70, 36)(19, 40, 76, 128, 79, 41)(21, 43, 80, 133, 83, 44)(25, 51, 42, 72, 92, 49)(28, 56, 99, 157, 98, 54)(31, 50, 93, 86, 55, 61)(33, 65, 112, 172, 109, 62)(34, 66, 114, 177, 117, 67)(38, 73, 68, 111, 123, 71)(45, 84, 138, 110, 64, 85)(47, 87, 141, 211, 144, 88)(53, 96, 153, 226, 152, 95)(58, 104, 164, 239, 161, 101)(59, 105, 166, 244, 168, 106)(69, 118, 181, 261, 184, 119)(75, 126, 190, 270, 189, 125)(77, 94, 151, 224, 193, 127)(78, 130, 196, 278, 198, 131)(81, 135, 202, 281, 200, 132)(82, 136, 204, 284, 206, 137)(89, 145, 216, 201, 134, 146)(91, 147, 218, 275, 221, 148)(97, 155, 229, 247, 169, 107)(100, 159, 234, 308, 233, 158)(103, 163, 120, 185, 240, 162)(108, 170, 248, 291, 209, 140)(113, 175, 252, 317, 251, 174)(115, 124, 188, 268, 255, 176)(116, 179, 257, 320, 259, 180)(122, 186, 265, 212, 222, 149)(129, 195, 171, 250, 276, 194)(139, 150, 223, 238, 289, 207)(142, 213, 292, 306, 254, 210)(143, 214, 294, 334, 295, 215)(154, 228, 167, 246, 304, 227)(156, 231, 296, 256, 178, 232)(160, 236, 249, 277, 311, 237)(165, 243, 313, 328, 312, 242)(173, 208, 290, 262, 267, 187)(182, 241, 297, 217, 199, 260)(183, 263, 323, 293, 324, 264)(191, 272, 197, 280, 327, 271)(192, 273, 230, 305, 329, 274)(203, 283, 332, 310, 331, 282)(205, 286, 333, 309, 235, 287)(219, 299, 321, 335, 307, 298)(220, 300, 279, 330, 316, 301)(225, 302, 266, 325, 285, 303)(245, 315, 269, 326, 288, 314)(253, 319, 258, 322, 336, 318)(337, 338, 342, 340)(339, 345, 357, 347)(341, 349, 354, 343)(344, 355, 369, 351)(346, 359, 383, 361)(348, 352, 370, 364)(350, 367, 394, 365)(353, 372, 405, 374)(356, 378, 413, 376)(358, 381, 417, 379)(360, 385, 427, 386)(362, 380, 418, 389)(363, 390, 433, 391)(366, 395, 411, 375)(368, 398, 444, 400)(371, 404, 451, 402)(373, 407, 458, 408)(377, 414, 449, 401)(382, 422, 475, 420)(384, 425, 478, 423)(387, 424, 479, 430)(388, 431, 441, 396)(392, 403, 452, 436)(393, 437, 496, 439)(397, 443, 501, 440)(399, 446, 509, 447)(406, 456, 518, 454)(409, 455, 519, 460)(410, 461, 466, 415)(412, 463, 528, 465)(416, 468, 535, 470)(419, 435, 494, 472)(421, 476, 539, 471)(426, 438, 498, 481)(428, 485, 555, 483)(429, 484, 556, 486)(432, 473, 541, 490)(434, 492, 566, 491)(442, 503, 527, 462)(445, 507, 585, 506)(448, 510, 515, 453)(450, 512, 590, 514)(457, 464, 530, 521)(459, 523, 602, 522)(467, 533, 589, 511)(469, 537, 567, 493)(474, 543, 624, 544)(477, 546, 591, 548)(480, 489, 563, 550)(482, 553, 629, 549)(487, 551, 616, 534)(488, 561, 581, 502)(495, 516, 594, 571)(497, 574, 584, 572)(499, 573, 646, 577)(500, 578, 582, 504)(505, 570, 645, 579)(508, 513, 592, 586)(517, 596, 536, 598)(520, 526, 607, 599)(524, 600, 658, 595)(525, 605, 615, 532)(529, 611, 565, 609)(531, 610, 664, 613)(538, 618, 622, 542)(540, 569, 643, 621)(545, 588, 654, 619)(547, 601, 638, 562)(552, 576, 612, 632)(554, 634, 644, 583)(557, 560, 614, 636)(558, 604, 656, 635)(559, 637, 653, 627)(564, 623, 655, 608)(568, 642, 670, 641)(575, 580, 650, 625)(587, 652, 657, 593)(597, 626, 662, 606)(603, 617, 620, 661)(628, 659, 663, 631)(630, 640, 648, 665)(633, 668, 672, 660)(639, 671, 666, 651)(647, 649, 669, 667) L = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 4^4 ), ( 4^6 ) } Outer automorphisms :: reflexible Dual of E15.1380 Transitivity :: ET+ Graph:: simple bipartite v = 140 e = 336 f = 168 degree seq :: [ 4^84, 6^56 ] E15.1377 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 6}) Quotient :: edge Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-1)^4, (T1^2 * T2 * T1)^3, (T1 * T2 * T1^-1 * T2)^4, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 34)(19, 36)(20, 31)(23, 43)(24, 44)(25, 47)(28, 50)(29, 51)(32, 55)(33, 58)(35, 62)(37, 65)(38, 67)(39, 63)(40, 70)(41, 71)(42, 74)(45, 77)(46, 78)(48, 81)(49, 84)(52, 88)(53, 89)(54, 92)(56, 94)(57, 95)(59, 99)(60, 96)(61, 73)(64, 104)(66, 108)(68, 110)(69, 111)(72, 114)(75, 117)(76, 120)(79, 124)(80, 125)(82, 128)(83, 129)(85, 133)(86, 130)(87, 135)(90, 138)(91, 139)(93, 143)(97, 147)(98, 149)(100, 151)(101, 152)(102, 121)(103, 154)(105, 156)(106, 116)(107, 140)(109, 160)(112, 164)(113, 167)(115, 170)(118, 173)(119, 174)(122, 175)(123, 179)(126, 182)(127, 184)(131, 186)(132, 188)(134, 190)(136, 192)(137, 194)(141, 197)(142, 199)(144, 201)(145, 200)(146, 203)(148, 205)(150, 207)(153, 211)(155, 204)(157, 216)(158, 217)(159, 218)(161, 208)(162, 212)(163, 222)(165, 224)(166, 225)(168, 226)(169, 229)(171, 231)(172, 233)(176, 235)(177, 237)(178, 238)(180, 240)(181, 242)(183, 244)(185, 246)(187, 247)(189, 249)(191, 252)(193, 254)(195, 255)(196, 256)(198, 258)(202, 241)(206, 265)(209, 261)(210, 267)(213, 270)(214, 264)(215, 263)(219, 257)(220, 276)(221, 277)(223, 280)(227, 282)(228, 284)(230, 286)(232, 289)(234, 291)(236, 292)(239, 296)(243, 298)(245, 287)(248, 301)(250, 299)(251, 303)(253, 305)(259, 308)(260, 293)(262, 297)(266, 312)(268, 313)(269, 314)(271, 311)(272, 288)(273, 306)(274, 310)(275, 307)(278, 316)(279, 318)(281, 320)(283, 321)(285, 322)(290, 317)(294, 324)(295, 325)(300, 323)(302, 328)(304, 329)(309, 331)(315, 319)(326, 333)(327, 334)(330, 335)(332, 336)(337, 338, 341, 347, 346, 340)(339, 343, 351, 365, 354, 344)(342, 349, 361, 382, 364, 350)(345, 355, 371, 397, 373, 356)(348, 359, 378, 409, 381, 360)(352, 367, 390, 427, 392, 368)(353, 369, 393, 418, 384, 362)(357, 374, 402, 414, 404, 375)(358, 376, 405, 387, 408, 377)(363, 385, 419, 454, 411, 379)(366, 388, 423, 464, 426, 389)(370, 395, 434, 475, 436, 396)(372, 399, 439, 489, 441, 400)(380, 412, 455, 501, 448, 406)(383, 415, 459, 509, 462, 416)(386, 421, 468, 431, 470, 422)(391, 429, 478, 529, 472, 424)(394, 432, 482, 538, 484, 433)(398, 437, 481, 430, 480, 438)(401, 442, 493, 547, 494, 443)(403, 407, 449, 502, 497, 445)(410, 451, 505, 560, 507, 452)(413, 457, 513, 465, 514, 458)(417, 463, 519, 577, 516, 460)(420, 466, 521, 581, 523, 467)(425, 473, 510, 564, 504, 450)(428, 476, 532, 590, 534, 477)(435, 447, 499, 557, 544, 486)(440, 491, 550, 604, 546, 488)(444, 495, 551, 492, 525, 469)(446, 461, 517, 561, 556, 498)(453, 508, 568, 623, 566, 506)(456, 511, 570, 626, 572, 512)(471, 527, 587, 620, 571, 520)(474, 524, 584, 535, 583, 531)(479, 536, 595, 630, 574, 522)(483, 540, 599, 638, 586, 526)(485, 542, 600, 541, 596, 537)(487, 533, 593, 613, 602, 545)(490, 548, 605, 649, 607, 549)(496, 555, 611, 651, 610, 554)(500, 559, 615, 653, 614, 558)(503, 562, 617, 655, 619, 563)(515, 575, 631, 612, 618, 569)(518, 573, 629, 580, 628, 579)(528, 589, 627, 660, 640, 588)(530, 591, 625, 657, 624, 567)(539, 597, 645, 664, 646, 598)(543, 578, 634, 654, 647, 601)(552, 608, 643, 594, 637, 585)(553, 606, 616, 565, 621, 609)(576, 633, 656, 639, 662, 632)(582, 635, 663, 644, 603, 636)(592, 642, 666, 648, 652, 641)(622, 659, 650, 661, 668, 658)(665, 670, 667, 671, 672, 669) L = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 8, 8 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E15.1378 Transitivity :: ET+ Graph:: simple bipartite v = 224 e = 336 f = 84 degree seq :: [ 2^168, 6^56 ] E15.1378 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 6}) Quotient :: loop Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^6, (T1 * T2^-2 * T1 * T2^-1)^3, (T1 * T2^-1 * T1 * T2)^4, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 337, 3, 339, 8, 344, 4, 340)(2, 338, 5, 341, 11, 347, 6, 342)(7, 343, 13, 349, 24, 360, 14, 350)(9, 345, 16, 352, 29, 365, 17, 353)(10, 346, 18, 354, 32, 368, 19, 355)(12, 348, 21, 357, 37, 373, 22, 358)(15, 351, 26, 362, 45, 381, 27, 363)(20, 356, 34, 370, 58, 394, 35, 371)(23, 359, 39, 375, 65, 401, 40, 376)(25, 361, 42, 378, 70, 406, 43, 379)(28, 364, 47, 383, 78, 414, 48, 384)(30, 366, 50, 386, 83, 419, 51, 387)(31, 367, 52, 388, 84, 420, 53, 389)(33, 369, 55, 391, 89, 425, 56, 392)(36, 372, 60, 396, 97, 433, 61, 397)(38, 374, 63, 399, 102, 438, 64, 400)(41, 377, 67, 403, 107, 443, 68, 404)(44, 380, 72, 408, 114, 450, 73, 409)(46, 382, 75, 411, 119, 455, 76, 412)(49, 385, 80, 416, 126, 462, 81, 417)(54, 390, 86, 422, 134, 470, 87, 423)(57, 393, 91, 427, 127, 463, 92, 428)(59, 395, 94, 430, 106, 442, 95, 431)(62, 398, 99, 435, 151, 487, 100, 436)(66, 402, 104, 440, 157, 493, 105, 441)(69, 405, 109, 445, 163, 499, 110, 446)(71, 407, 112, 448, 166, 502, 113, 449)(74, 410, 116, 452, 170, 506, 117, 453)(77, 413, 120, 456, 174, 510, 121, 457)(79, 415, 123, 459, 177, 513, 124, 460)(82, 418, 128, 464, 183, 519, 129, 465)(85, 421, 132, 468, 188, 524, 133, 469)(88, 424, 136, 472, 193, 529, 137, 473)(90, 426, 139, 475, 182, 518, 140, 476)(93, 429, 142, 478, 199, 535, 143, 479)(96, 432, 145, 481, 158, 494, 146, 482)(98, 434, 148, 484, 205, 541, 149, 485)(101, 437, 152, 488, 210, 546, 153, 489)(103, 439, 130, 466, 185, 521, 155, 491)(108, 444, 160, 496, 169, 505, 161, 497)(111, 447, 164, 500, 176, 512, 122, 458)(115, 451, 167, 503, 226, 562, 168, 504)(118, 454, 172, 508, 230, 566, 173, 509)(125, 461, 179, 515, 171, 507, 180, 516)(131, 467, 154, 490, 212, 548, 186, 522)(135, 471, 190, 526, 198, 534, 191, 527)(138, 474, 194, 530, 204, 540, 147, 483)(141, 477, 196, 532, 255, 591, 197, 533)(144, 480, 201, 537, 259, 595, 202, 538)(150, 486, 207, 543, 200, 536, 208, 544)(156, 492, 214, 550, 273, 609, 215, 551)(159, 495, 217, 553, 276, 612, 218, 554)(162, 498, 220, 556, 227, 563, 221, 557)(165, 501, 175, 511, 231, 567, 224, 560)(178, 514, 234, 570, 229, 565, 235, 571)(181, 517, 237, 573, 294, 630, 238, 574)(184, 520, 225, 561, 283, 619, 240, 576)(187, 523, 243, 579, 301, 637, 244, 580)(189, 525, 246, 582, 304, 640, 247, 583)(192, 528, 249, 585, 256, 592, 250, 586)(195, 531, 203, 539, 260, 596, 253, 589)(206, 542, 263, 599, 258, 594, 264, 600)(209, 545, 266, 602, 322, 658, 267, 603)(211, 547, 254, 590, 311, 647, 269, 605)(213, 549, 271, 607, 275, 611, 272, 608)(216, 552, 274, 610, 280, 616, 222, 558)(219, 555, 278, 614, 327, 663, 279, 615)(223, 559, 281, 617, 277, 613, 282, 618)(228, 564, 285, 621, 329, 665, 286, 622)(232, 568, 288, 624, 293, 629, 289, 625)(233, 569, 290, 626, 296, 632, 239, 575)(236, 572, 291, 627, 331, 667, 292, 628)(241, 577, 297, 633, 295, 631, 298, 634)(242, 578, 299, 635, 303, 639, 300, 636)(245, 581, 302, 638, 308, 644, 251, 587)(248, 584, 306, 642, 332, 668, 307, 643)(252, 588, 309, 645, 305, 641, 310, 646)(257, 593, 313, 649, 334, 670, 314, 650)(261, 597, 316, 652, 321, 657, 317, 653)(262, 598, 318, 654, 324, 660, 268, 604)(265, 601, 319, 655, 336, 672, 320, 656)(270, 606, 325, 661, 323, 659, 326, 662)(284, 620, 328, 664, 330, 666, 287, 623)(312, 648, 333, 669, 335, 671, 315, 651) L = (1, 338)(2, 337)(3, 343)(4, 345)(5, 346)(6, 348)(7, 339)(8, 351)(9, 340)(10, 341)(11, 356)(12, 342)(13, 359)(14, 361)(15, 344)(16, 364)(17, 366)(18, 367)(19, 369)(20, 347)(21, 372)(22, 374)(23, 349)(24, 377)(25, 350)(26, 380)(27, 382)(28, 352)(29, 385)(30, 353)(31, 354)(32, 390)(33, 355)(34, 393)(35, 395)(36, 357)(37, 398)(38, 358)(39, 400)(40, 402)(41, 360)(42, 405)(43, 407)(44, 362)(45, 410)(46, 363)(47, 413)(48, 415)(49, 365)(50, 418)(51, 388)(52, 387)(53, 421)(54, 368)(55, 424)(56, 426)(57, 370)(58, 429)(59, 371)(60, 432)(61, 434)(62, 373)(63, 437)(64, 375)(65, 439)(66, 376)(67, 442)(68, 444)(69, 378)(70, 447)(71, 379)(72, 449)(73, 451)(74, 381)(75, 454)(76, 456)(77, 383)(78, 458)(79, 384)(80, 461)(81, 463)(82, 386)(83, 466)(84, 467)(85, 389)(86, 455)(87, 471)(88, 391)(89, 474)(90, 392)(91, 476)(92, 477)(93, 394)(94, 480)(95, 481)(96, 396)(97, 483)(98, 397)(99, 486)(100, 450)(101, 399)(102, 490)(103, 401)(104, 492)(105, 494)(106, 403)(107, 495)(108, 404)(109, 498)(110, 473)(111, 406)(112, 501)(113, 408)(114, 436)(115, 409)(116, 505)(117, 507)(118, 411)(119, 422)(120, 412)(121, 511)(122, 414)(123, 484)(124, 514)(125, 416)(126, 517)(127, 417)(128, 518)(129, 520)(130, 419)(131, 420)(132, 523)(133, 510)(134, 525)(135, 423)(136, 528)(137, 446)(138, 425)(139, 531)(140, 427)(141, 428)(142, 534)(143, 536)(144, 430)(145, 431)(146, 539)(147, 433)(148, 459)(149, 542)(150, 435)(151, 545)(152, 502)(153, 547)(154, 438)(155, 549)(156, 440)(157, 552)(158, 441)(159, 443)(160, 555)(161, 556)(162, 445)(163, 558)(164, 559)(165, 448)(166, 488)(167, 561)(168, 563)(169, 452)(170, 564)(171, 453)(172, 565)(173, 551)(174, 469)(175, 457)(176, 568)(177, 569)(178, 460)(179, 571)(180, 572)(181, 462)(182, 464)(183, 575)(184, 465)(185, 577)(186, 578)(187, 468)(188, 581)(189, 470)(190, 584)(191, 585)(192, 472)(193, 587)(194, 588)(195, 475)(196, 590)(197, 592)(198, 478)(199, 593)(200, 479)(201, 594)(202, 580)(203, 482)(204, 597)(205, 598)(206, 485)(207, 600)(208, 601)(209, 487)(210, 604)(211, 489)(212, 606)(213, 491)(214, 579)(215, 509)(216, 493)(217, 611)(218, 613)(219, 496)(220, 497)(221, 596)(222, 499)(223, 500)(224, 599)(225, 503)(226, 620)(227, 504)(228, 506)(229, 508)(230, 623)(231, 586)(232, 512)(233, 513)(234, 589)(235, 515)(236, 516)(237, 629)(238, 631)(239, 519)(240, 605)(241, 521)(242, 522)(243, 550)(244, 538)(245, 524)(246, 639)(247, 641)(248, 526)(249, 527)(250, 567)(251, 529)(252, 530)(253, 570)(254, 532)(255, 648)(256, 533)(257, 535)(258, 537)(259, 651)(260, 557)(261, 540)(262, 541)(263, 560)(264, 543)(265, 544)(266, 657)(267, 659)(268, 546)(269, 576)(270, 548)(271, 655)(272, 637)(273, 636)(274, 642)(275, 553)(276, 650)(277, 554)(278, 638)(279, 662)(280, 645)(281, 644)(282, 652)(283, 661)(284, 562)(285, 658)(286, 640)(287, 566)(288, 646)(289, 654)(290, 653)(291, 635)(292, 660)(293, 573)(294, 649)(295, 574)(296, 656)(297, 647)(298, 643)(299, 627)(300, 609)(301, 608)(302, 614)(303, 582)(304, 622)(305, 583)(306, 610)(307, 634)(308, 617)(309, 616)(310, 624)(311, 633)(312, 591)(313, 630)(314, 612)(315, 595)(316, 618)(317, 626)(318, 625)(319, 607)(320, 632)(321, 602)(322, 621)(323, 603)(324, 628)(325, 619)(326, 615)(327, 671)(328, 672)(329, 670)(330, 668)(331, 669)(332, 666)(333, 667)(334, 665)(335, 663)(336, 664) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E15.1377 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 84 e = 336 f = 224 degree seq :: [ 8^84 ] E15.1379 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 6}) Quotient :: loop Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, T2^6, T2^-3 * T1 * T2 * T1 * T2^-2, (T1 * T2^-2)^3, T1^-1 * T2^-3 * T1 * T2^-3 * T1^-1 * T2^2, T2 * T1^-2 * T2^2 * T1^2 * T2 * T1^-1 * T2^-2 * T1^-2 * T2^-2 * T1^-1, T2^3 * T1^-2 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1, T2^2 * T1^-2 * T2 * T1^-1 * T2^2 * T1 * T2^-2 * T1^-1 * T2 * T1^-2 * T2^-2 * T1^-1 ] Map:: R = (1, 337, 3, 339, 10, 346, 24, 360, 14, 350, 5, 341)(2, 338, 7, 343, 17, 353, 37, 373, 20, 356, 8, 344)(4, 340, 12, 348, 27, 363, 46, 382, 22, 358, 9, 345)(6, 342, 15, 351, 32, 368, 63, 399, 35, 371, 16, 352)(11, 347, 26, 362, 52, 388, 90, 426, 48, 384, 23, 359)(13, 349, 29, 365, 57, 393, 102, 438, 60, 396, 30, 366)(18, 354, 39, 375, 74, 410, 121, 457, 70, 406, 36, 372)(19, 355, 40, 376, 76, 412, 128, 464, 79, 415, 41, 377)(21, 357, 43, 379, 80, 416, 133, 469, 83, 419, 44, 380)(25, 361, 51, 387, 42, 378, 72, 408, 92, 428, 49, 385)(28, 364, 56, 392, 99, 435, 157, 493, 98, 434, 54, 390)(31, 367, 50, 386, 93, 429, 86, 422, 55, 391, 61, 397)(33, 369, 65, 401, 112, 448, 172, 508, 109, 445, 62, 398)(34, 370, 66, 402, 114, 450, 177, 513, 117, 453, 67, 403)(38, 374, 73, 409, 68, 404, 111, 447, 123, 459, 71, 407)(45, 381, 84, 420, 138, 474, 110, 446, 64, 400, 85, 421)(47, 383, 87, 423, 141, 477, 211, 547, 144, 480, 88, 424)(53, 389, 96, 432, 153, 489, 226, 562, 152, 488, 95, 431)(58, 394, 104, 440, 164, 500, 239, 575, 161, 497, 101, 437)(59, 395, 105, 441, 166, 502, 244, 580, 168, 504, 106, 442)(69, 405, 118, 454, 181, 517, 261, 597, 184, 520, 119, 455)(75, 411, 126, 462, 190, 526, 270, 606, 189, 525, 125, 461)(77, 413, 94, 430, 151, 487, 224, 560, 193, 529, 127, 463)(78, 414, 130, 466, 196, 532, 278, 614, 198, 534, 131, 467)(81, 417, 135, 471, 202, 538, 281, 617, 200, 536, 132, 468)(82, 418, 136, 472, 204, 540, 284, 620, 206, 542, 137, 473)(89, 425, 145, 481, 216, 552, 201, 537, 134, 470, 146, 482)(91, 427, 147, 483, 218, 554, 275, 611, 221, 557, 148, 484)(97, 433, 155, 491, 229, 565, 247, 583, 169, 505, 107, 443)(100, 436, 159, 495, 234, 570, 308, 644, 233, 569, 158, 494)(103, 439, 163, 499, 120, 456, 185, 521, 240, 576, 162, 498)(108, 444, 170, 506, 248, 584, 291, 627, 209, 545, 140, 476)(113, 449, 175, 511, 252, 588, 317, 653, 251, 587, 174, 510)(115, 451, 124, 460, 188, 524, 268, 604, 255, 591, 176, 512)(116, 452, 179, 515, 257, 593, 320, 656, 259, 595, 180, 516)(122, 458, 186, 522, 265, 601, 212, 548, 222, 558, 149, 485)(129, 465, 195, 531, 171, 507, 250, 586, 276, 612, 194, 530)(139, 475, 150, 486, 223, 559, 238, 574, 289, 625, 207, 543)(142, 478, 213, 549, 292, 628, 306, 642, 254, 590, 210, 546)(143, 479, 214, 550, 294, 630, 334, 670, 295, 631, 215, 551)(154, 490, 228, 564, 167, 503, 246, 582, 304, 640, 227, 563)(156, 492, 231, 567, 296, 632, 256, 592, 178, 514, 232, 568)(160, 496, 236, 572, 249, 585, 277, 613, 311, 647, 237, 573)(165, 501, 243, 579, 313, 649, 328, 664, 312, 648, 242, 578)(173, 509, 208, 544, 290, 626, 262, 598, 267, 603, 187, 523)(182, 518, 241, 577, 297, 633, 217, 553, 199, 535, 260, 596)(183, 519, 263, 599, 323, 659, 293, 629, 324, 660, 264, 600)(191, 527, 272, 608, 197, 533, 280, 616, 327, 663, 271, 607)(192, 528, 273, 609, 230, 566, 305, 641, 329, 665, 274, 610)(203, 539, 283, 619, 332, 668, 310, 646, 331, 667, 282, 618)(205, 541, 286, 622, 333, 669, 309, 645, 235, 571, 287, 623)(219, 555, 299, 635, 321, 657, 335, 671, 307, 643, 298, 634)(220, 556, 300, 636, 279, 615, 330, 666, 316, 652, 301, 637)(225, 561, 302, 638, 266, 602, 325, 661, 285, 621, 303, 639)(245, 581, 315, 651, 269, 605, 326, 662, 288, 624, 314, 650)(253, 589, 319, 655, 258, 594, 322, 658, 336, 672, 318, 654) L = (1, 338)(2, 342)(3, 345)(4, 337)(5, 349)(6, 340)(7, 341)(8, 355)(9, 357)(10, 359)(11, 339)(12, 352)(13, 354)(14, 367)(15, 344)(16, 370)(17, 372)(18, 343)(19, 369)(20, 378)(21, 347)(22, 381)(23, 383)(24, 385)(25, 346)(26, 380)(27, 390)(28, 348)(29, 350)(30, 395)(31, 394)(32, 398)(33, 351)(34, 364)(35, 404)(36, 405)(37, 407)(38, 353)(39, 366)(40, 356)(41, 414)(42, 413)(43, 358)(44, 418)(45, 417)(46, 422)(47, 361)(48, 425)(49, 427)(50, 360)(51, 424)(52, 431)(53, 362)(54, 433)(55, 363)(56, 403)(57, 437)(58, 365)(59, 411)(60, 388)(61, 443)(62, 444)(63, 446)(64, 368)(65, 377)(66, 371)(67, 452)(68, 451)(69, 374)(70, 456)(71, 458)(72, 373)(73, 455)(74, 461)(75, 375)(76, 463)(77, 376)(78, 449)(79, 410)(80, 468)(81, 379)(82, 389)(83, 435)(84, 382)(85, 476)(86, 475)(87, 384)(88, 479)(89, 478)(90, 438)(91, 386)(92, 485)(93, 484)(94, 387)(95, 441)(96, 473)(97, 391)(98, 492)(99, 494)(100, 392)(101, 496)(102, 498)(103, 393)(104, 397)(105, 396)(106, 503)(107, 501)(108, 400)(109, 507)(110, 509)(111, 399)(112, 510)(113, 401)(114, 512)(115, 402)(116, 436)(117, 448)(118, 406)(119, 519)(120, 518)(121, 464)(122, 408)(123, 523)(124, 409)(125, 466)(126, 442)(127, 528)(128, 530)(129, 412)(130, 415)(131, 533)(132, 535)(133, 537)(134, 416)(135, 421)(136, 419)(137, 541)(138, 543)(139, 420)(140, 539)(141, 546)(142, 423)(143, 430)(144, 489)(145, 426)(146, 553)(147, 428)(148, 556)(149, 555)(150, 429)(151, 551)(152, 561)(153, 563)(154, 432)(155, 434)(156, 566)(157, 469)(158, 472)(159, 516)(160, 439)(161, 574)(162, 481)(163, 573)(164, 578)(165, 440)(166, 488)(167, 527)(168, 500)(169, 570)(170, 445)(171, 585)(172, 513)(173, 447)(174, 515)(175, 467)(176, 590)(177, 592)(178, 450)(179, 453)(180, 594)(181, 596)(182, 454)(183, 460)(184, 526)(185, 457)(186, 459)(187, 602)(188, 600)(189, 605)(190, 607)(191, 462)(192, 465)(193, 611)(194, 521)(195, 610)(196, 525)(197, 589)(198, 487)(199, 470)(200, 598)(201, 567)(202, 618)(203, 471)(204, 569)(205, 490)(206, 538)(207, 624)(208, 474)(209, 588)(210, 591)(211, 601)(212, 477)(213, 482)(214, 480)(215, 616)(216, 576)(217, 629)(218, 634)(219, 483)(220, 486)(221, 560)(222, 604)(223, 637)(224, 614)(225, 581)(226, 547)(227, 550)(228, 623)(229, 609)(230, 491)(231, 493)(232, 642)(233, 643)(234, 645)(235, 495)(236, 497)(237, 646)(238, 584)(239, 580)(240, 612)(241, 499)(242, 582)(243, 505)(244, 650)(245, 502)(246, 504)(247, 554)(248, 572)(249, 506)(250, 508)(251, 652)(252, 654)(253, 511)(254, 514)(255, 548)(256, 586)(257, 587)(258, 571)(259, 524)(260, 536)(261, 626)(262, 517)(263, 520)(264, 658)(265, 638)(266, 522)(267, 617)(268, 656)(269, 615)(270, 597)(271, 599)(272, 564)(273, 529)(274, 664)(275, 565)(276, 632)(277, 531)(278, 636)(279, 532)(280, 534)(281, 620)(282, 622)(283, 545)(284, 661)(285, 540)(286, 542)(287, 655)(288, 544)(289, 575)(290, 662)(291, 559)(292, 659)(293, 549)(294, 640)(295, 628)(296, 552)(297, 668)(298, 644)(299, 558)(300, 557)(301, 653)(302, 562)(303, 671)(304, 648)(305, 568)(306, 670)(307, 621)(308, 583)(309, 579)(310, 577)(311, 649)(312, 665)(313, 669)(314, 625)(315, 639)(316, 657)(317, 627)(318, 619)(319, 608)(320, 635)(321, 593)(322, 595)(323, 663)(324, 633)(325, 603)(326, 606)(327, 631)(328, 613)(329, 630)(330, 651)(331, 647)(332, 672)(333, 667)(334, 641)(335, 666)(336, 660) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E15.1375 Transitivity :: ET+ VT+ AT Graph:: v = 56 e = 336 f = 252 degree seq :: [ 12^56 ] E15.1380 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 6}) Quotient :: loop Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-1)^4, (T1^2 * T2 * T1)^3, (T1 * T2 * T1^-1 * T2)^4, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 337, 3, 339)(2, 338, 6, 342)(4, 340, 9, 345)(5, 341, 12, 348)(7, 343, 16, 352)(8, 344, 17, 353)(10, 346, 21, 357)(11, 347, 22, 358)(13, 349, 26, 362)(14, 350, 27, 363)(15, 351, 30, 366)(18, 354, 34, 370)(19, 355, 36, 372)(20, 356, 31, 367)(23, 359, 43, 379)(24, 360, 44, 380)(25, 361, 47, 383)(28, 364, 50, 386)(29, 365, 51, 387)(32, 368, 55, 391)(33, 369, 58, 394)(35, 371, 62, 398)(37, 373, 65, 401)(38, 374, 67, 403)(39, 375, 63, 399)(40, 376, 70, 406)(41, 377, 71, 407)(42, 378, 74, 410)(45, 381, 77, 413)(46, 382, 78, 414)(48, 384, 81, 417)(49, 385, 84, 420)(52, 388, 88, 424)(53, 389, 89, 425)(54, 390, 92, 428)(56, 392, 94, 430)(57, 393, 95, 431)(59, 395, 99, 435)(60, 396, 96, 432)(61, 397, 73, 409)(64, 400, 104, 440)(66, 402, 108, 444)(68, 404, 110, 446)(69, 405, 111, 447)(72, 408, 114, 450)(75, 411, 117, 453)(76, 412, 120, 456)(79, 415, 124, 460)(80, 416, 125, 461)(82, 418, 128, 464)(83, 419, 129, 465)(85, 421, 133, 469)(86, 422, 130, 466)(87, 423, 135, 471)(90, 426, 138, 474)(91, 427, 139, 475)(93, 429, 143, 479)(97, 433, 147, 483)(98, 434, 149, 485)(100, 436, 151, 487)(101, 437, 152, 488)(102, 438, 121, 457)(103, 439, 154, 490)(105, 441, 156, 492)(106, 442, 116, 452)(107, 443, 140, 476)(109, 445, 160, 496)(112, 448, 164, 500)(113, 449, 167, 503)(115, 451, 170, 506)(118, 454, 173, 509)(119, 455, 174, 510)(122, 458, 175, 511)(123, 459, 179, 515)(126, 462, 182, 518)(127, 463, 184, 520)(131, 467, 186, 522)(132, 468, 188, 524)(134, 470, 190, 526)(136, 472, 192, 528)(137, 473, 194, 530)(141, 477, 197, 533)(142, 478, 199, 535)(144, 480, 201, 537)(145, 481, 200, 536)(146, 482, 203, 539)(148, 484, 205, 541)(150, 486, 207, 543)(153, 489, 211, 547)(155, 491, 204, 540)(157, 493, 216, 552)(158, 494, 217, 553)(159, 495, 218, 554)(161, 497, 208, 544)(162, 498, 212, 548)(163, 499, 222, 558)(165, 501, 224, 560)(166, 502, 225, 561)(168, 504, 226, 562)(169, 505, 229, 565)(171, 507, 231, 567)(172, 508, 233, 569)(176, 512, 235, 571)(177, 513, 237, 573)(178, 514, 238, 574)(180, 516, 240, 576)(181, 517, 242, 578)(183, 519, 244, 580)(185, 521, 246, 582)(187, 523, 247, 583)(189, 525, 249, 585)(191, 527, 252, 588)(193, 529, 254, 590)(195, 531, 255, 591)(196, 532, 256, 592)(198, 534, 258, 594)(202, 538, 241, 577)(206, 542, 265, 601)(209, 545, 261, 597)(210, 546, 267, 603)(213, 549, 270, 606)(214, 550, 264, 600)(215, 551, 263, 599)(219, 555, 257, 593)(220, 556, 276, 612)(221, 557, 277, 613)(223, 559, 280, 616)(227, 563, 282, 618)(228, 564, 284, 620)(230, 566, 286, 622)(232, 568, 289, 625)(234, 570, 291, 627)(236, 572, 292, 628)(239, 575, 296, 632)(243, 579, 298, 634)(245, 581, 287, 623)(248, 584, 301, 637)(250, 586, 299, 635)(251, 587, 303, 639)(253, 589, 305, 641)(259, 595, 308, 644)(260, 596, 293, 629)(262, 598, 297, 633)(266, 602, 312, 648)(268, 604, 313, 649)(269, 605, 314, 650)(271, 607, 311, 647)(272, 608, 288, 624)(273, 609, 306, 642)(274, 610, 310, 646)(275, 611, 307, 643)(278, 614, 316, 652)(279, 615, 318, 654)(281, 617, 320, 656)(283, 619, 321, 657)(285, 621, 322, 658)(290, 626, 317, 653)(294, 630, 324, 660)(295, 631, 325, 661)(300, 636, 323, 659)(302, 638, 328, 664)(304, 640, 329, 665)(309, 645, 331, 667)(315, 651, 319, 655)(326, 662, 333, 669)(327, 663, 334, 670)(330, 666, 335, 671)(332, 668, 336, 672) L = (1, 338)(2, 341)(3, 343)(4, 337)(5, 347)(6, 349)(7, 351)(8, 339)(9, 355)(10, 340)(11, 346)(12, 359)(13, 361)(14, 342)(15, 365)(16, 367)(17, 369)(18, 344)(19, 371)(20, 345)(21, 374)(22, 376)(23, 378)(24, 348)(25, 382)(26, 353)(27, 385)(28, 350)(29, 354)(30, 388)(31, 390)(32, 352)(33, 393)(34, 395)(35, 397)(36, 399)(37, 356)(38, 402)(39, 357)(40, 405)(41, 358)(42, 409)(43, 363)(44, 412)(45, 360)(46, 364)(47, 415)(48, 362)(49, 419)(50, 421)(51, 408)(52, 423)(53, 366)(54, 427)(55, 429)(56, 368)(57, 418)(58, 432)(59, 434)(60, 370)(61, 373)(62, 437)(63, 439)(64, 372)(65, 442)(66, 414)(67, 407)(68, 375)(69, 387)(70, 380)(71, 449)(72, 377)(73, 381)(74, 451)(75, 379)(76, 455)(77, 457)(78, 404)(79, 459)(80, 383)(81, 463)(82, 384)(83, 454)(84, 466)(85, 468)(86, 386)(87, 464)(88, 391)(89, 473)(90, 389)(91, 392)(92, 476)(93, 478)(94, 480)(95, 470)(96, 482)(97, 394)(98, 475)(99, 447)(100, 396)(101, 481)(102, 398)(103, 489)(104, 491)(105, 400)(106, 493)(107, 401)(108, 495)(109, 403)(110, 461)(111, 499)(112, 406)(113, 502)(114, 425)(115, 505)(116, 410)(117, 508)(118, 411)(119, 501)(120, 511)(121, 513)(122, 413)(123, 509)(124, 417)(125, 517)(126, 416)(127, 519)(128, 426)(129, 514)(130, 521)(131, 420)(132, 431)(133, 444)(134, 422)(135, 527)(136, 424)(137, 510)(138, 524)(139, 436)(140, 532)(141, 428)(142, 529)(143, 536)(144, 438)(145, 430)(146, 538)(147, 540)(148, 433)(149, 542)(150, 435)(151, 533)(152, 440)(153, 441)(154, 548)(155, 550)(156, 525)(157, 547)(158, 443)(159, 551)(160, 555)(161, 445)(162, 446)(163, 557)(164, 559)(165, 448)(166, 497)(167, 562)(168, 450)(169, 560)(170, 453)(171, 452)(172, 568)(173, 462)(174, 564)(175, 570)(176, 456)(177, 465)(178, 458)(179, 575)(180, 460)(181, 561)(182, 573)(183, 577)(184, 471)(185, 581)(186, 479)(187, 467)(188, 584)(189, 469)(190, 483)(191, 587)(192, 589)(193, 472)(194, 591)(195, 474)(196, 590)(197, 593)(198, 477)(199, 583)(200, 595)(201, 485)(202, 484)(203, 597)(204, 599)(205, 596)(206, 600)(207, 578)(208, 486)(209, 487)(210, 488)(211, 494)(212, 605)(213, 490)(214, 604)(215, 492)(216, 608)(217, 606)(218, 496)(219, 611)(220, 498)(221, 544)(222, 500)(223, 615)(224, 507)(225, 556)(226, 617)(227, 503)(228, 504)(229, 621)(230, 506)(231, 530)(232, 623)(233, 515)(234, 626)(235, 520)(236, 512)(237, 629)(238, 522)(239, 631)(240, 633)(241, 516)(242, 634)(243, 518)(244, 628)(245, 523)(246, 635)(247, 531)(248, 535)(249, 552)(250, 526)(251, 620)(252, 528)(253, 627)(254, 534)(255, 625)(256, 642)(257, 613)(258, 637)(259, 630)(260, 537)(261, 645)(262, 539)(263, 638)(264, 541)(265, 543)(266, 545)(267, 636)(268, 546)(269, 649)(270, 616)(271, 549)(272, 643)(273, 553)(274, 554)(275, 651)(276, 618)(277, 602)(278, 558)(279, 653)(280, 565)(281, 655)(282, 569)(283, 563)(284, 571)(285, 609)(286, 659)(287, 566)(288, 567)(289, 657)(290, 572)(291, 660)(292, 579)(293, 580)(294, 574)(295, 612)(296, 576)(297, 656)(298, 654)(299, 663)(300, 582)(301, 585)(302, 586)(303, 662)(304, 588)(305, 592)(306, 666)(307, 594)(308, 603)(309, 664)(310, 598)(311, 601)(312, 652)(313, 607)(314, 661)(315, 610)(316, 641)(317, 614)(318, 647)(319, 619)(320, 639)(321, 624)(322, 622)(323, 650)(324, 640)(325, 668)(326, 632)(327, 644)(328, 646)(329, 670)(330, 648)(331, 671)(332, 658)(333, 665)(334, 667)(335, 672)(336, 669) local type(s) :: { ( 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.1376 Transitivity :: ET+ VT+ AT Graph:: simple v = 168 e = 336 f = 140 degree seq :: [ 4^168 ] E15.1381 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^6, (Y3 * Y2^-1)^6, Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1, (Y1 * Y2^-1 * Y1 * Y2)^4, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 ] Map:: R = (1, 337, 2, 338)(3, 339, 7, 343)(4, 340, 9, 345)(5, 341, 10, 346)(6, 342, 12, 348)(8, 344, 15, 351)(11, 347, 20, 356)(13, 349, 23, 359)(14, 350, 25, 361)(16, 352, 28, 364)(17, 353, 30, 366)(18, 354, 31, 367)(19, 355, 33, 369)(21, 357, 36, 372)(22, 358, 38, 374)(24, 360, 41, 377)(26, 362, 44, 380)(27, 363, 46, 382)(29, 365, 49, 385)(32, 368, 54, 390)(34, 370, 57, 393)(35, 371, 59, 395)(37, 373, 62, 398)(39, 375, 64, 400)(40, 376, 66, 402)(42, 378, 69, 405)(43, 379, 71, 407)(45, 381, 74, 410)(47, 383, 77, 413)(48, 384, 79, 415)(50, 386, 82, 418)(51, 387, 52, 388)(53, 389, 85, 421)(55, 391, 88, 424)(56, 392, 90, 426)(58, 394, 93, 429)(60, 396, 96, 432)(61, 397, 98, 434)(63, 399, 101, 437)(65, 401, 103, 439)(67, 403, 106, 442)(68, 404, 108, 444)(70, 406, 111, 447)(72, 408, 113, 449)(73, 409, 115, 451)(75, 411, 118, 454)(76, 412, 120, 456)(78, 414, 122, 458)(80, 416, 125, 461)(81, 417, 127, 463)(83, 419, 130, 466)(84, 420, 131, 467)(86, 422, 119, 455)(87, 423, 135, 471)(89, 425, 138, 474)(91, 427, 140, 476)(92, 428, 141, 477)(94, 430, 144, 480)(95, 431, 145, 481)(97, 433, 147, 483)(99, 435, 150, 486)(100, 436, 114, 450)(102, 438, 154, 490)(104, 440, 156, 492)(105, 441, 158, 494)(107, 443, 159, 495)(109, 445, 162, 498)(110, 446, 137, 473)(112, 448, 165, 501)(116, 452, 169, 505)(117, 453, 171, 507)(121, 457, 175, 511)(123, 459, 148, 484)(124, 460, 178, 514)(126, 462, 181, 517)(128, 464, 182, 518)(129, 465, 184, 520)(132, 468, 187, 523)(133, 469, 174, 510)(134, 470, 189, 525)(136, 472, 192, 528)(139, 475, 195, 531)(142, 478, 198, 534)(143, 479, 200, 536)(146, 482, 203, 539)(149, 485, 206, 542)(151, 487, 209, 545)(152, 488, 166, 502)(153, 489, 211, 547)(155, 491, 213, 549)(157, 493, 216, 552)(160, 496, 219, 555)(161, 497, 220, 556)(163, 499, 222, 558)(164, 500, 223, 559)(167, 503, 225, 561)(168, 504, 227, 563)(170, 506, 228, 564)(172, 508, 229, 565)(173, 509, 215, 551)(176, 512, 232, 568)(177, 513, 233, 569)(179, 515, 235, 571)(180, 516, 236, 572)(183, 519, 239, 575)(185, 521, 241, 577)(186, 522, 242, 578)(188, 524, 245, 581)(190, 526, 248, 584)(191, 527, 249, 585)(193, 529, 251, 587)(194, 530, 252, 588)(196, 532, 254, 590)(197, 533, 256, 592)(199, 535, 257, 593)(201, 537, 258, 594)(202, 538, 244, 580)(204, 540, 261, 597)(205, 541, 262, 598)(207, 543, 264, 600)(208, 544, 265, 601)(210, 546, 268, 604)(212, 548, 270, 606)(214, 550, 243, 579)(217, 553, 275, 611)(218, 554, 277, 613)(221, 557, 260, 596)(224, 560, 263, 599)(226, 562, 284, 620)(230, 566, 287, 623)(231, 567, 250, 586)(234, 570, 253, 589)(237, 573, 293, 629)(238, 574, 295, 631)(240, 576, 269, 605)(246, 582, 303, 639)(247, 583, 305, 641)(255, 591, 312, 648)(259, 595, 315, 651)(266, 602, 321, 657)(267, 603, 323, 659)(271, 607, 319, 655)(272, 608, 301, 637)(273, 609, 300, 636)(274, 610, 306, 642)(276, 612, 314, 650)(278, 614, 302, 638)(279, 615, 326, 662)(280, 616, 309, 645)(281, 617, 308, 644)(282, 618, 316, 652)(283, 619, 325, 661)(285, 621, 322, 658)(286, 622, 304, 640)(288, 624, 310, 646)(289, 625, 318, 654)(290, 626, 317, 653)(291, 627, 299, 635)(292, 628, 324, 660)(294, 630, 313, 649)(296, 632, 320, 656)(297, 633, 311, 647)(298, 634, 307, 643)(327, 663, 335, 671)(328, 664, 336, 672)(329, 665, 334, 670)(330, 666, 332, 668)(331, 667, 333, 669)(673, 1009, 675, 1011, 680, 1016, 676, 1012)(674, 1010, 677, 1013, 683, 1019, 678, 1014)(679, 1015, 685, 1021, 696, 1032, 686, 1022)(681, 1017, 688, 1024, 701, 1037, 689, 1025)(682, 1018, 690, 1026, 704, 1040, 691, 1027)(684, 1020, 693, 1029, 709, 1045, 694, 1030)(687, 1023, 698, 1034, 717, 1053, 699, 1035)(692, 1028, 706, 1042, 730, 1066, 707, 1043)(695, 1031, 711, 1047, 737, 1073, 712, 1048)(697, 1033, 714, 1050, 742, 1078, 715, 1051)(700, 1036, 719, 1055, 750, 1086, 720, 1056)(702, 1038, 722, 1058, 755, 1091, 723, 1059)(703, 1039, 724, 1060, 756, 1092, 725, 1061)(705, 1041, 727, 1063, 761, 1097, 728, 1064)(708, 1044, 732, 1068, 769, 1105, 733, 1069)(710, 1046, 735, 1071, 774, 1110, 736, 1072)(713, 1049, 739, 1075, 779, 1115, 740, 1076)(716, 1052, 744, 1080, 786, 1122, 745, 1081)(718, 1054, 747, 1083, 791, 1127, 748, 1084)(721, 1057, 752, 1088, 798, 1134, 753, 1089)(726, 1062, 758, 1094, 806, 1142, 759, 1095)(729, 1065, 763, 1099, 799, 1135, 764, 1100)(731, 1067, 766, 1102, 778, 1114, 767, 1103)(734, 1070, 771, 1107, 823, 1159, 772, 1108)(738, 1074, 776, 1112, 829, 1165, 777, 1113)(741, 1077, 781, 1117, 835, 1171, 782, 1118)(743, 1079, 784, 1120, 838, 1174, 785, 1121)(746, 1082, 788, 1124, 842, 1178, 789, 1125)(749, 1085, 792, 1128, 846, 1182, 793, 1129)(751, 1087, 795, 1131, 849, 1185, 796, 1132)(754, 1090, 800, 1136, 855, 1191, 801, 1137)(757, 1093, 804, 1140, 860, 1196, 805, 1141)(760, 1096, 808, 1144, 865, 1201, 809, 1145)(762, 1098, 811, 1147, 854, 1190, 812, 1148)(765, 1101, 814, 1150, 871, 1207, 815, 1151)(768, 1104, 817, 1153, 830, 1166, 818, 1154)(770, 1106, 820, 1156, 877, 1213, 821, 1157)(773, 1109, 824, 1160, 882, 1218, 825, 1161)(775, 1111, 802, 1138, 857, 1193, 827, 1163)(780, 1116, 832, 1168, 841, 1177, 833, 1169)(783, 1119, 836, 1172, 848, 1184, 794, 1130)(787, 1123, 839, 1175, 898, 1234, 840, 1176)(790, 1126, 844, 1180, 902, 1238, 845, 1181)(797, 1133, 851, 1187, 843, 1179, 852, 1188)(803, 1139, 826, 1162, 884, 1220, 858, 1194)(807, 1143, 862, 1198, 870, 1206, 863, 1199)(810, 1146, 866, 1202, 876, 1212, 819, 1155)(813, 1149, 868, 1204, 927, 1263, 869, 1205)(816, 1152, 873, 1209, 931, 1267, 874, 1210)(822, 1158, 879, 1215, 872, 1208, 880, 1216)(828, 1164, 886, 1222, 945, 1281, 887, 1223)(831, 1167, 889, 1225, 948, 1284, 890, 1226)(834, 1170, 892, 1228, 899, 1235, 893, 1229)(837, 1173, 847, 1183, 903, 1239, 896, 1232)(850, 1186, 906, 1242, 901, 1237, 907, 1243)(853, 1189, 909, 1245, 966, 1302, 910, 1246)(856, 1192, 897, 1233, 955, 1291, 912, 1248)(859, 1195, 915, 1251, 973, 1309, 916, 1252)(861, 1197, 918, 1254, 976, 1312, 919, 1255)(864, 1200, 921, 1257, 928, 1264, 922, 1258)(867, 1203, 875, 1211, 932, 1268, 925, 1261)(878, 1214, 935, 1271, 930, 1266, 936, 1272)(881, 1217, 938, 1274, 994, 1330, 939, 1275)(883, 1219, 926, 1262, 983, 1319, 941, 1277)(885, 1221, 943, 1279, 947, 1283, 944, 1280)(888, 1224, 946, 1282, 952, 1288, 894, 1230)(891, 1227, 950, 1286, 999, 1335, 951, 1287)(895, 1231, 953, 1289, 949, 1285, 954, 1290)(900, 1236, 957, 1293, 1001, 1337, 958, 1294)(904, 1240, 960, 1296, 965, 1301, 961, 1297)(905, 1241, 962, 1298, 968, 1304, 911, 1247)(908, 1244, 963, 1299, 1003, 1339, 964, 1300)(913, 1249, 969, 1305, 967, 1303, 970, 1306)(914, 1250, 971, 1307, 975, 1311, 972, 1308)(917, 1253, 974, 1310, 980, 1316, 923, 1259)(920, 1256, 978, 1314, 1004, 1340, 979, 1315)(924, 1260, 981, 1317, 977, 1313, 982, 1318)(929, 1265, 985, 1321, 1006, 1342, 986, 1322)(933, 1269, 988, 1324, 993, 1329, 989, 1325)(934, 1270, 990, 1326, 996, 1332, 940, 1276)(937, 1273, 991, 1327, 1008, 1344, 992, 1328)(942, 1278, 997, 1333, 995, 1331, 998, 1334)(956, 1292, 1000, 1336, 1002, 1338, 959, 1295)(984, 1320, 1005, 1341, 1007, 1343, 987, 1323) L = (1, 674)(2, 673)(3, 679)(4, 681)(5, 682)(6, 684)(7, 675)(8, 687)(9, 676)(10, 677)(11, 692)(12, 678)(13, 695)(14, 697)(15, 680)(16, 700)(17, 702)(18, 703)(19, 705)(20, 683)(21, 708)(22, 710)(23, 685)(24, 713)(25, 686)(26, 716)(27, 718)(28, 688)(29, 721)(30, 689)(31, 690)(32, 726)(33, 691)(34, 729)(35, 731)(36, 693)(37, 734)(38, 694)(39, 736)(40, 738)(41, 696)(42, 741)(43, 743)(44, 698)(45, 746)(46, 699)(47, 749)(48, 751)(49, 701)(50, 754)(51, 724)(52, 723)(53, 757)(54, 704)(55, 760)(56, 762)(57, 706)(58, 765)(59, 707)(60, 768)(61, 770)(62, 709)(63, 773)(64, 711)(65, 775)(66, 712)(67, 778)(68, 780)(69, 714)(70, 783)(71, 715)(72, 785)(73, 787)(74, 717)(75, 790)(76, 792)(77, 719)(78, 794)(79, 720)(80, 797)(81, 799)(82, 722)(83, 802)(84, 803)(85, 725)(86, 791)(87, 807)(88, 727)(89, 810)(90, 728)(91, 812)(92, 813)(93, 730)(94, 816)(95, 817)(96, 732)(97, 819)(98, 733)(99, 822)(100, 786)(101, 735)(102, 826)(103, 737)(104, 828)(105, 830)(106, 739)(107, 831)(108, 740)(109, 834)(110, 809)(111, 742)(112, 837)(113, 744)(114, 772)(115, 745)(116, 841)(117, 843)(118, 747)(119, 758)(120, 748)(121, 847)(122, 750)(123, 820)(124, 850)(125, 752)(126, 853)(127, 753)(128, 854)(129, 856)(130, 755)(131, 756)(132, 859)(133, 846)(134, 861)(135, 759)(136, 864)(137, 782)(138, 761)(139, 867)(140, 763)(141, 764)(142, 870)(143, 872)(144, 766)(145, 767)(146, 875)(147, 769)(148, 795)(149, 878)(150, 771)(151, 881)(152, 838)(153, 883)(154, 774)(155, 885)(156, 776)(157, 888)(158, 777)(159, 779)(160, 891)(161, 892)(162, 781)(163, 894)(164, 895)(165, 784)(166, 824)(167, 897)(168, 899)(169, 788)(170, 900)(171, 789)(172, 901)(173, 887)(174, 805)(175, 793)(176, 904)(177, 905)(178, 796)(179, 907)(180, 908)(181, 798)(182, 800)(183, 911)(184, 801)(185, 913)(186, 914)(187, 804)(188, 917)(189, 806)(190, 920)(191, 921)(192, 808)(193, 923)(194, 924)(195, 811)(196, 926)(197, 928)(198, 814)(199, 929)(200, 815)(201, 930)(202, 916)(203, 818)(204, 933)(205, 934)(206, 821)(207, 936)(208, 937)(209, 823)(210, 940)(211, 825)(212, 942)(213, 827)(214, 915)(215, 845)(216, 829)(217, 947)(218, 949)(219, 832)(220, 833)(221, 932)(222, 835)(223, 836)(224, 935)(225, 839)(226, 956)(227, 840)(228, 842)(229, 844)(230, 959)(231, 922)(232, 848)(233, 849)(234, 925)(235, 851)(236, 852)(237, 965)(238, 967)(239, 855)(240, 941)(241, 857)(242, 858)(243, 886)(244, 874)(245, 860)(246, 975)(247, 977)(248, 862)(249, 863)(250, 903)(251, 865)(252, 866)(253, 906)(254, 868)(255, 984)(256, 869)(257, 871)(258, 873)(259, 987)(260, 893)(261, 876)(262, 877)(263, 896)(264, 879)(265, 880)(266, 993)(267, 995)(268, 882)(269, 912)(270, 884)(271, 991)(272, 973)(273, 972)(274, 978)(275, 889)(276, 986)(277, 890)(278, 974)(279, 998)(280, 981)(281, 980)(282, 988)(283, 997)(284, 898)(285, 994)(286, 976)(287, 902)(288, 982)(289, 990)(290, 989)(291, 971)(292, 996)(293, 909)(294, 985)(295, 910)(296, 992)(297, 983)(298, 979)(299, 963)(300, 945)(301, 944)(302, 950)(303, 918)(304, 958)(305, 919)(306, 946)(307, 970)(308, 953)(309, 952)(310, 960)(311, 969)(312, 927)(313, 966)(314, 948)(315, 931)(316, 954)(317, 962)(318, 961)(319, 943)(320, 968)(321, 938)(322, 957)(323, 939)(324, 964)(325, 955)(326, 951)(327, 1007)(328, 1008)(329, 1006)(330, 1004)(331, 1005)(332, 1002)(333, 1003)(334, 1001)(335, 999)(336, 1000)(337, 1009)(338, 1010)(339, 1011)(340, 1012)(341, 1013)(342, 1014)(343, 1015)(344, 1016)(345, 1017)(346, 1018)(347, 1019)(348, 1020)(349, 1021)(350, 1022)(351, 1023)(352, 1024)(353, 1025)(354, 1026)(355, 1027)(356, 1028)(357, 1029)(358, 1030)(359, 1031)(360, 1032)(361, 1033)(362, 1034)(363, 1035)(364, 1036)(365, 1037)(366, 1038)(367, 1039)(368, 1040)(369, 1041)(370, 1042)(371, 1043)(372, 1044)(373, 1045)(374, 1046)(375, 1047)(376, 1048)(377, 1049)(378, 1050)(379, 1051)(380, 1052)(381, 1053)(382, 1054)(383, 1055)(384, 1056)(385, 1057)(386, 1058)(387, 1059)(388, 1060)(389, 1061)(390, 1062)(391, 1063)(392, 1064)(393, 1065)(394, 1066)(395, 1067)(396, 1068)(397, 1069)(398, 1070)(399, 1071)(400, 1072)(401, 1073)(402, 1074)(403, 1075)(404, 1076)(405, 1077)(406, 1078)(407, 1079)(408, 1080)(409, 1081)(410, 1082)(411, 1083)(412, 1084)(413, 1085)(414, 1086)(415, 1087)(416, 1088)(417, 1089)(418, 1090)(419, 1091)(420, 1092)(421, 1093)(422, 1094)(423, 1095)(424, 1096)(425, 1097)(426, 1098)(427, 1099)(428, 1100)(429, 1101)(430, 1102)(431, 1103)(432, 1104)(433, 1105)(434, 1106)(435, 1107)(436, 1108)(437, 1109)(438, 1110)(439, 1111)(440, 1112)(441, 1113)(442, 1114)(443, 1115)(444, 1116)(445, 1117)(446, 1118)(447, 1119)(448, 1120)(449, 1121)(450, 1122)(451, 1123)(452, 1124)(453, 1125)(454, 1126)(455, 1127)(456, 1128)(457, 1129)(458, 1130)(459, 1131)(460, 1132)(461, 1133)(462, 1134)(463, 1135)(464, 1136)(465, 1137)(466, 1138)(467, 1139)(468, 1140)(469, 1141)(470, 1142)(471, 1143)(472, 1144)(473, 1145)(474, 1146)(475, 1147)(476, 1148)(477, 1149)(478, 1150)(479, 1151)(480, 1152)(481, 1153)(482, 1154)(483, 1155)(484, 1156)(485, 1157)(486, 1158)(487, 1159)(488, 1160)(489, 1161)(490, 1162)(491, 1163)(492, 1164)(493, 1165)(494, 1166)(495, 1167)(496, 1168)(497, 1169)(498, 1170)(499, 1171)(500, 1172)(501, 1173)(502, 1174)(503, 1175)(504, 1176)(505, 1177)(506, 1178)(507, 1179)(508, 1180)(509, 1181)(510, 1182)(511, 1183)(512, 1184)(513, 1185)(514, 1186)(515, 1187)(516, 1188)(517, 1189)(518, 1190)(519, 1191)(520, 1192)(521, 1193)(522, 1194)(523, 1195)(524, 1196)(525, 1197)(526, 1198)(527, 1199)(528, 1200)(529, 1201)(530, 1202)(531, 1203)(532, 1204)(533, 1205)(534, 1206)(535, 1207)(536, 1208)(537, 1209)(538, 1210)(539, 1211)(540, 1212)(541, 1213)(542, 1214)(543, 1215)(544, 1216)(545, 1217)(546, 1218)(547, 1219)(548, 1220)(549, 1221)(550, 1222)(551, 1223)(552, 1224)(553, 1225)(554, 1226)(555, 1227)(556, 1228)(557, 1229)(558, 1230)(559, 1231)(560, 1232)(561, 1233)(562, 1234)(563, 1235)(564, 1236)(565, 1237)(566, 1238)(567, 1239)(568, 1240)(569, 1241)(570, 1242)(571, 1243)(572, 1244)(573, 1245)(574, 1246)(575, 1247)(576, 1248)(577, 1249)(578, 1250)(579, 1251)(580, 1252)(581, 1253)(582, 1254)(583, 1255)(584, 1256)(585, 1257)(586, 1258)(587, 1259)(588, 1260)(589, 1261)(590, 1262)(591, 1263)(592, 1264)(593, 1265)(594, 1266)(595, 1267)(596, 1268)(597, 1269)(598, 1270)(599, 1271)(600, 1272)(601, 1273)(602, 1274)(603, 1275)(604, 1276)(605, 1277)(606, 1278)(607, 1279)(608, 1280)(609, 1281)(610, 1282)(611, 1283)(612, 1284)(613, 1285)(614, 1286)(615, 1287)(616, 1288)(617, 1289)(618, 1290)(619, 1291)(620, 1292)(621, 1293)(622, 1294)(623, 1295)(624, 1296)(625, 1297)(626, 1298)(627, 1299)(628, 1300)(629, 1301)(630, 1302)(631, 1303)(632, 1304)(633, 1305)(634, 1306)(635, 1307)(636, 1308)(637, 1309)(638, 1310)(639, 1311)(640, 1312)(641, 1313)(642, 1314)(643, 1315)(644, 1316)(645, 1317)(646, 1318)(647, 1319)(648, 1320)(649, 1321)(650, 1322)(651, 1323)(652, 1324)(653, 1325)(654, 1326)(655, 1327)(656, 1328)(657, 1329)(658, 1330)(659, 1331)(660, 1332)(661, 1333)(662, 1334)(663, 1335)(664, 1336)(665, 1337)(666, 1338)(667, 1339)(668, 1340)(669, 1341)(670, 1342)(671, 1343)(672, 1344) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E15.1384 Graph:: bipartite v = 252 e = 672 f = 392 degree seq :: [ 4^168, 8^84 ] E15.1382 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2 * Y1)^2, Y1^4, Y2^6, Y2^6, (Y2^2 * Y1^-1)^3, Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^2 * Y1^-2 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2 * Y2 ] Map:: R = (1, 337, 2, 338, 6, 342, 4, 340)(3, 339, 9, 345, 21, 357, 11, 347)(5, 341, 13, 349, 18, 354, 7, 343)(8, 344, 19, 355, 33, 369, 15, 351)(10, 346, 23, 359, 47, 383, 25, 361)(12, 348, 16, 352, 34, 370, 28, 364)(14, 350, 31, 367, 58, 394, 29, 365)(17, 353, 36, 372, 69, 405, 38, 374)(20, 356, 42, 378, 77, 413, 40, 376)(22, 358, 45, 381, 81, 417, 43, 379)(24, 360, 49, 385, 91, 427, 50, 386)(26, 362, 44, 380, 82, 418, 53, 389)(27, 363, 54, 390, 97, 433, 55, 391)(30, 366, 59, 395, 75, 411, 39, 375)(32, 368, 62, 398, 108, 444, 64, 400)(35, 371, 68, 404, 115, 451, 66, 402)(37, 373, 71, 407, 122, 458, 72, 408)(41, 377, 78, 414, 113, 449, 65, 401)(46, 382, 86, 422, 139, 475, 84, 420)(48, 384, 89, 425, 142, 478, 87, 423)(51, 387, 88, 424, 143, 479, 94, 430)(52, 388, 95, 431, 105, 441, 60, 396)(56, 392, 67, 403, 116, 452, 100, 436)(57, 393, 101, 437, 160, 496, 103, 439)(61, 397, 107, 443, 165, 501, 104, 440)(63, 399, 110, 446, 173, 509, 111, 447)(70, 406, 120, 456, 182, 518, 118, 454)(73, 409, 119, 455, 183, 519, 124, 460)(74, 410, 125, 461, 130, 466, 79, 415)(76, 412, 127, 463, 192, 528, 129, 465)(80, 416, 132, 468, 199, 535, 134, 470)(83, 419, 99, 435, 158, 494, 136, 472)(85, 421, 140, 476, 203, 539, 135, 471)(90, 426, 102, 438, 162, 498, 145, 481)(92, 428, 149, 485, 219, 555, 147, 483)(93, 429, 148, 484, 220, 556, 150, 486)(96, 432, 137, 473, 205, 541, 154, 490)(98, 434, 156, 492, 230, 566, 155, 491)(106, 442, 167, 503, 191, 527, 126, 462)(109, 445, 171, 507, 249, 585, 170, 506)(112, 448, 174, 510, 179, 515, 117, 453)(114, 450, 176, 512, 254, 590, 178, 514)(121, 457, 128, 464, 194, 530, 185, 521)(123, 459, 187, 523, 266, 602, 186, 522)(131, 467, 197, 533, 253, 589, 175, 511)(133, 469, 201, 537, 231, 567, 157, 493)(138, 474, 207, 543, 288, 624, 208, 544)(141, 477, 210, 546, 255, 591, 212, 548)(144, 480, 153, 489, 227, 563, 214, 550)(146, 482, 217, 553, 293, 629, 213, 549)(151, 487, 215, 551, 280, 616, 198, 534)(152, 488, 225, 561, 245, 581, 166, 502)(159, 495, 180, 516, 258, 594, 235, 571)(161, 497, 238, 574, 248, 584, 236, 572)(163, 499, 237, 573, 310, 646, 241, 577)(164, 500, 242, 578, 246, 582, 168, 504)(169, 505, 234, 570, 309, 645, 243, 579)(172, 508, 177, 513, 256, 592, 250, 586)(181, 517, 260, 596, 200, 536, 262, 598)(184, 520, 190, 526, 271, 607, 263, 599)(188, 524, 264, 600, 322, 658, 259, 595)(189, 525, 269, 605, 279, 615, 196, 532)(193, 529, 275, 611, 229, 565, 273, 609)(195, 531, 274, 610, 328, 664, 277, 613)(202, 538, 282, 618, 286, 622, 206, 542)(204, 540, 233, 569, 307, 643, 285, 621)(209, 545, 252, 588, 318, 654, 283, 619)(211, 547, 265, 601, 302, 638, 226, 562)(216, 552, 240, 576, 276, 612, 296, 632)(218, 554, 298, 634, 308, 644, 247, 583)(221, 557, 224, 560, 278, 614, 300, 636)(222, 558, 268, 604, 320, 656, 299, 635)(223, 559, 301, 637, 317, 653, 291, 627)(228, 564, 287, 623, 319, 655, 272, 608)(232, 568, 306, 642, 334, 670, 305, 641)(239, 575, 244, 580, 314, 650, 289, 625)(251, 587, 316, 652, 321, 657, 257, 593)(261, 597, 290, 626, 326, 662, 270, 606)(267, 603, 281, 617, 284, 620, 325, 661)(292, 628, 323, 659, 327, 663, 295, 631)(294, 630, 304, 640, 312, 648, 329, 665)(297, 633, 332, 668, 336, 672, 324, 660)(303, 639, 335, 671, 330, 666, 315, 651)(311, 647, 313, 649, 333, 669, 331, 667)(673, 1009, 675, 1011, 682, 1018, 696, 1032, 686, 1022, 677, 1013)(674, 1010, 679, 1015, 689, 1025, 709, 1045, 692, 1028, 680, 1016)(676, 1012, 684, 1020, 699, 1035, 718, 1054, 694, 1030, 681, 1017)(678, 1014, 687, 1023, 704, 1040, 735, 1071, 707, 1043, 688, 1024)(683, 1019, 698, 1034, 724, 1060, 762, 1098, 720, 1056, 695, 1031)(685, 1021, 701, 1037, 729, 1065, 774, 1110, 732, 1068, 702, 1038)(690, 1026, 711, 1047, 746, 1082, 793, 1129, 742, 1078, 708, 1044)(691, 1027, 712, 1048, 748, 1084, 800, 1136, 751, 1087, 713, 1049)(693, 1029, 715, 1051, 752, 1088, 805, 1141, 755, 1091, 716, 1052)(697, 1033, 723, 1059, 714, 1050, 744, 1080, 764, 1100, 721, 1057)(700, 1036, 728, 1064, 771, 1107, 829, 1165, 770, 1106, 726, 1062)(703, 1039, 722, 1058, 765, 1101, 758, 1094, 727, 1063, 733, 1069)(705, 1041, 737, 1073, 784, 1120, 844, 1180, 781, 1117, 734, 1070)(706, 1042, 738, 1074, 786, 1122, 849, 1185, 789, 1125, 739, 1075)(710, 1046, 745, 1081, 740, 1076, 783, 1119, 795, 1131, 743, 1079)(717, 1053, 756, 1092, 810, 1146, 782, 1118, 736, 1072, 757, 1093)(719, 1055, 759, 1095, 813, 1149, 883, 1219, 816, 1152, 760, 1096)(725, 1061, 768, 1104, 825, 1161, 898, 1234, 824, 1160, 767, 1103)(730, 1066, 776, 1112, 836, 1172, 911, 1247, 833, 1169, 773, 1109)(731, 1067, 777, 1113, 838, 1174, 916, 1252, 840, 1176, 778, 1114)(741, 1077, 790, 1126, 853, 1189, 933, 1269, 856, 1192, 791, 1127)(747, 1083, 798, 1134, 862, 1198, 942, 1278, 861, 1197, 797, 1133)(749, 1085, 766, 1102, 823, 1159, 896, 1232, 865, 1201, 799, 1135)(750, 1086, 802, 1138, 868, 1204, 950, 1286, 870, 1206, 803, 1139)(753, 1089, 807, 1143, 874, 1210, 953, 1289, 872, 1208, 804, 1140)(754, 1090, 808, 1144, 876, 1212, 956, 1292, 878, 1214, 809, 1145)(761, 1097, 817, 1153, 888, 1224, 873, 1209, 806, 1142, 818, 1154)(763, 1099, 819, 1155, 890, 1226, 947, 1283, 893, 1229, 820, 1156)(769, 1105, 827, 1163, 901, 1237, 919, 1255, 841, 1177, 779, 1115)(772, 1108, 831, 1167, 906, 1242, 980, 1316, 905, 1241, 830, 1166)(775, 1111, 835, 1171, 792, 1128, 857, 1193, 912, 1248, 834, 1170)(780, 1116, 842, 1178, 920, 1256, 963, 1299, 881, 1217, 812, 1148)(785, 1121, 847, 1183, 924, 1260, 989, 1325, 923, 1259, 846, 1182)(787, 1123, 796, 1132, 860, 1196, 940, 1276, 927, 1263, 848, 1184)(788, 1124, 851, 1187, 929, 1265, 992, 1328, 931, 1267, 852, 1188)(794, 1130, 858, 1194, 937, 1273, 884, 1220, 894, 1230, 821, 1157)(801, 1137, 867, 1203, 843, 1179, 922, 1258, 948, 1284, 866, 1202)(811, 1147, 822, 1158, 895, 1231, 910, 1246, 961, 1297, 879, 1215)(814, 1150, 885, 1221, 964, 1300, 978, 1314, 926, 1262, 882, 1218)(815, 1151, 886, 1222, 966, 1302, 1006, 1342, 967, 1303, 887, 1223)(826, 1162, 900, 1236, 839, 1175, 918, 1254, 976, 1312, 899, 1235)(828, 1164, 903, 1239, 968, 1304, 928, 1264, 850, 1186, 904, 1240)(832, 1168, 908, 1244, 921, 1257, 949, 1285, 983, 1319, 909, 1245)(837, 1173, 915, 1251, 985, 1321, 1000, 1336, 984, 1320, 914, 1250)(845, 1181, 880, 1216, 962, 1298, 934, 1270, 939, 1275, 859, 1195)(854, 1190, 913, 1249, 969, 1305, 889, 1225, 871, 1207, 932, 1268)(855, 1191, 935, 1271, 995, 1331, 965, 1301, 996, 1332, 936, 1272)(863, 1199, 944, 1280, 869, 1205, 952, 1288, 999, 1335, 943, 1279)(864, 1200, 945, 1281, 902, 1238, 977, 1313, 1001, 1337, 946, 1282)(875, 1211, 955, 1291, 1004, 1340, 982, 1318, 1003, 1339, 954, 1290)(877, 1213, 958, 1294, 1005, 1341, 981, 1317, 907, 1243, 959, 1295)(891, 1227, 971, 1307, 993, 1329, 1007, 1343, 979, 1315, 970, 1306)(892, 1228, 972, 1308, 951, 1287, 1002, 1338, 988, 1324, 973, 1309)(897, 1233, 974, 1310, 938, 1274, 997, 1333, 957, 1293, 975, 1311)(917, 1253, 987, 1323, 941, 1277, 998, 1334, 960, 1296, 986, 1322)(925, 1261, 991, 1327, 930, 1266, 994, 1330, 1008, 1344, 990, 1326) L = (1, 675)(2, 679)(3, 682)(4, 684)(5, 673)(6, 687)(7, 689)(8, 674)(9, 676)(10, 696)(11, 698)(12, 699)(13, 701)(14, 677)(15, 704)(16, 678)(17, 709)(18, 711)(19, 712)(20, 680)(21, 715)(22, 681)(23, 683)(24, 686)(25, 723)(26, 724)(27, 718)(28, 728)(29, 729)(30, 685)(31, 722)(32, 735)(33, 737)(34, 738)(35, 688)(36, 690)(37, 692)(38, 745)(39, 746)(40, 748)(41, 691)(42, 744)(43, 752)(44, 693)(45, 756)(46, 694)(47, 759)(48, 695)(49, 697)(50, 765)(51, 714)(52, 762)(53, 768)(54, 700)(55, 733)(56, 771)(57, 774)(58, 776)(59, 777)(60, 702)(61, 703)(62, 705)(63, 707)(64, 757)(65, 784)(66, 786)(67, 706)(68, 783)(69, 790)(70, 708)(71, 710)(72, 764)(73, 740)(74, 793)(75, 798)(76, 800)(77, 766)(78, 802)(79, 713)(80, 805)(81, 807)(82, 808)(83, 716)(84, 810)(85, 717)(86, 727)(87, 813)(88, 719)(89, 817)(90, 720)(91, 819)(92, 721)(93, 758)(94, 823)(95, 725)(96, 825)(97, 827)(98, 726)(99, 829)(100, 831)(101, 730)(102, 732)(103, 835)(104, 836)(105, 838)(106, 731)(107, 769)(108, 842)(109, 734)(110, 736)(111, 795)(112, 844)(113, 847)(114, 849)(115, 796)(116, 851)(117, 739)(118, 853)(119, 741)(120, 857)(121, 742)(122, 858)(123, 743)(124, 860)(125, 747)(126, 862)(127, 749)(128, 751)(129, 867)(130, 868)(131, 750)(132, 753)(133, 755)(134, 818)(135, 874)(136, 876)(137, 754)(138, 782)(139, 822)(140, 780)(141, 883)(142, 885)(143, 886)(144, 760)(145, 888)(146, 761)(147, 890)(148, 763)(149, 794)(150, 895)(151, 896)(152, 767)(153, 898)(154, 900)(155, 901)(156, 903)(157, 770)(158, 772)(159, 906)(160, 908)(161, 773)(162, 775)(163, 792)(164, 911)(165, 915)(166, 916)(167, 918)(168, 778)(169, 779)(170, 920)(171, 922)(172, 781)(173, 880)(174, 785)(175, 924)(176, 787)(177, 789)(178, 904)(179, 929)(180, 788)(181, 933)(182, 913)(183, 935)(184, 791)(185, 912)(186, 937)(187, 845)(188, 940)(189, 797)(190, 942)(191, 944)(192, 945)(193, 799)(194, 801)(195, 843)(196, 950)(197, 952)(198, 803)(199, 932)(200, 804)(201, 806)(202, 953)(203, 955)(204, 956)(205, 958)(206, 809)(207, 811)(208, 962)(209, 812)(210, 814)(211, 816)(212, 894)(213, 964)(214, 966)(215, 815)(216, 873)(217, 871)(218, 947)(219, 971)(220, 972)(221, 820)(222, 821)(223, 910)(224, 865)(225, 974)(226, 824)(227, 826)(228, 839)(229, 919)(230, 977)(231, 968)(232, 828)(233, 830)(234, 980)(235, 959)(236, 921)(237, 832)(238, 961)(239, 833)(240, 834)(241, 969)(242, 837)(243, 985)(244, 840)(245, 987)(246, 976)(247, 841)(248, 963)(249, 949)(250, 948)(251, 846)(252, 989)(253, 991)(254, 882)(255, 848)(256, 850)(257, 992)(258, 994)(259, 852)(260, 854)(261, 856)(262, 939)(263, 995)(264, 855)(265, 884)(266, 997)(267, 859)(268, 927)(269, 998)(270, 861)(271, 863)(272, 869)(273, 902)(274, 864)(275, 893)(276, 866)(277, 983)(278, 870)(279, 1002)(280, 999)(281, 872)(282, 875)(283, 1004)(284, 878)(285, 975)(286, 1005)(287, 877)(288, 986)(289, 879)(290, 934)(291, 881)(292, 978)(293, 996)(294, 1006)(295, 887)(296, 928)(297, 889)(298, 891)(299, 993)(300, 951)(301, 892)(302, 938)(303, 897)(304, 899)(305, 1001)(306, 926)(307, 970)(308, 905)(309, 907)(310, 1003)(311, 909)(312, 914)(313, 1000)(314, 917)(315, 941)(316, 973)(317, 923)(318, 925)(319, 930)(320, 931)(321, 1007)(322, 1008)(323, 965)(324, 936)(325, 957)(326, 960)(327, 943)(328, 984)(329, 946)(330, 988)(331, 954)(332, 982)(333, 981)(334, 967)(335, 979)(336, 990)(337, 1009)(338, 1010)(339, 1011)(340, 1012)(341, 1013)(342, 1014)(343, 1015)(344, 1016)(345, 1017)(346, 1018)(347, 1019)(348, 1020)(349, 1021)(350, 1022)(351, 1023)(352, 1024)(353, 1025)(354, 1026)(355, 1027)(356, 1028)(357, 1029)(358, 1030)(359, 1031)(360, 1032)(361, 1033)(362, 1034)(363, 1035)(364, 1036)(365, 1037)(366, 1038)(367, 1039)(368, 1040)(369, 1041)(370, 1042)(371, 1043)(372, 1044)(373, 1045)(374, 1046)(375, 1047)(376, 1048)(377, 1049)(378, 1050)(379, 1051)(380, 1052)(381, 1053)(382, 1054)(383, 1055)(384, 1056)(385, 1057)(386, 1058)(387, 1059)(388, 1060)(389, 1061)(390, 1062)(391, 1063)(392, 1064)(393, 1065)(394, 1066)(395, 1067)(396, 1068)(397, 1069)(398, 1070)(399, 1071)(400, 1072)(401, 1073)(402, 1074)(403, 1075)(404, 1076)(405, 1077)(406, 1078)(407, 1079)(408, 1080)(409, 1081)(410, 1082)(411, 1083)(412, 1084)(413, 1085)(414, 1086)(415, 1087)(416, 1088)(417, 1089)(418, 1090)(419, 1091)(420, 1092)(421, 1093)(422, 1094)(423, 1095)(424, 1096)(425, 1097)(426, 1098)(427, 1099)(428, 1100)(429, 1101)(430, 1102)(431, 1103)(432, 1104)(433, 1105)(434, 1106)(435, 1107)(436, 1108)(437, 1109)(438, 1110)(439, 1111)(440, 1112)(441, 1113)(442, 1114)(443, 1115)(444, 1116)(445, 1117)(446, 1118)(447, 1119)(448, 1120)(449, 1121)(450, 1122)(451, 1123)(452, 1124)(453, 1125)(454, 1126)(455, 1127)(456, 1128)(457, 1129)(458, 1130)(459, 1131)(460, 1132)(461, 1133)(462, 1134)(463, 1135)(464, 1136)(465, 1137)(466, 1138)(467, 1139)(468, 1140)(469, 1141)(470, 1142)(471, 1143)(472, 1144)(473, 1145)(474, 1146)(475, 1147)(476, 1148)(477, 1149)(478, 1150)(479, 1151)(480, 1152)(481, 1153)(482, 1154)(483, 1155)(484, 1156)(485, 1157)(486, 1158)(487, 1159)(488, 1160)(489, 1161)(490, 1162)(491, 1163)(492, 1164)(493, 1165)(494, 1166)(495, 1167)(496, 1168)(497, 1169)(498, 1170)(499, 1171)(500, 1172)(501, 1173)(502, 1174)(503, 1175)(504, 1176)(505, 1177)(506, 1178)(507, 1179)(508, 1180)(509, 1181)(510, 1182)(511, 1183)(512, 1184)(513, 1185)(514, 1186)(515, 1187)(516, 1188)(517, 1189)(518, 1190)(519, 1191)(520, 1192)(521, 1193)(522, 1194)(523, 1195)(524, 1196)(525, 1197)(526, 1198)(527, 1199)(528, 1200)(529, 1201)(530, 1202)(531, 1203)(532, 1204)(533, 1205)(534, 1206)(535, 1207)(536, 1208)(537, 1209)(538, 1210)(539, 1211)(540, 1212)(541, 1213)(542, 1214)(543, 1215)(544, 1216)(545, 1217)(546, 1218)(547, 1219)(548, 1220)(549, 1221)(550, 1222)(551, 1223)(552, 1224)(553, 1225)(554, 1226)(555, 1227)(556, 1228)(557, 1229)(558, 1230)(559, 1231)(560, 1232)(561, 1233)(562, 1234)(563, 1235)(564, 1236)(565, 1237)(566, 1238)(567, 1239)(568, 1240)(569, 1241)(570, 1242)(571, 1243)(572, 1244)(573, 1245)(574, 1246)(575, 1247)(576, 1248)(577, 1249)(578, 1250)(579, 1251)(580, 1252)(581, 1253)(582, 1254)(583, 1255)(584, 1256)(585, 1257)(586, 1258)(587, 1259)(588, 1260)(589, 1261)(590, 1262)(591, 1263)(592, 1264)(593, 1265)(594, 1266)(595, 1267)(596, 1268)(597, 1269)(598, 1270)(599, 1271)(600, 1272)(601, 1273)(602, 1274)(603, 1275)(604, 1276)(605, 1277)(606, 1278)(607, 1279)(608, 1280)(609, 1281)(610, 1282)(611, 1283)(612, 1284)(613, 1285)(614, 1286)(615, 1287)(616, 1288)(617, 1289)(618, 1290)(619, 1291)(620, 1292)(621, 1293)(622, 1294)(623, 1295)(624, 1296)(625, 1297)(626, 1298)(627, 1299)(628, 1300)(629, 1301)(630, 1302)(631, 1303)(632, 1304)(633, 1305)(634, 1306)(635, 1307)(636, 1308)(637, 1309)(638, 1310)(639, 1311)(640, 1312)(641, 1313)(642, 1314)(643, 1315)(644, 1316)(645, 1317)(646, 1318)(647, 1319)(648, 1320)(649, 1321)(650, 1322)(651, 1323)(652, 1324)(653, 1325)(654, 1326)(655, 1327)(656, 1328)(657, 1329)(658, 1330)(659, 1331)(660, 1332)(661, 1333)(662, 1334)(663, 1335)(664, 1336)(665, 1337)(666, 1338)(667, 1339)(668, 1340)(669, 1341)(670, 1342)(671, 1343)(672, 1344) local type(s) :: { ( 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 E15.1383 Graph:: bipartite v = 140 e = 672 f = 504 degree seq :: [ 8^84, 12^56 ] E15.1383 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, (Y3 * Y2)^4, (Y3^-3 * Y2)^3, (Y3^-1 * Y1^-1)^6, (Y3^-1 * Y2 * Y3 * Y2)^4, Y3^-1 * Y2 * Y3 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1 ] Map:: polytopal R = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672)(673, 1009, 674, 1010)(675, 1011, 679, 1015)(676, 1012, 681, 1017)(677, 1013, 683, 1019)(678, 1014, 685, 1021)(680, 1016, 689, 1025)(682, 1018, 693, 1029)(684, 1020, 696, 1032)(686, 1022, 700, 1036)(687, 1023, 699, 1035)(688, 1024, 702, 1038)(690, 1026, 706, 1042)(691, 1027, 707, 1043)(692, 1028, 694, 1030)(695, 1031, 713, 1049)(697, 1033, 717, 1053)(698, 1034, 718, 1054)(701, 1037, 723, 1059)(703, 1039, 727, 1063)(704, 1040, 726, 1062)(705, 1041, 729, 1065)(708, 1044, 735, 1071)(709, 1045, 737, 1073)(710, 1046, 738, 1074)(711, 1047, 733, 1069)(712, 1048, 741, 1077)(714, 1050, 745, 1081)(715, 1051, 744, 1080)(716, 1052, 747, 1083)(719, 1055, 753, 1089)(720, 1056, 755, 1091)(721, 1057, 756, 1092)(722, 1058, 751, 1087)(724, 1060, 761, 1097)(725, 1061, 762, 1098)(728, 1064, 767, 1103)(730, 1066, 771, 1107)(731, 1067, 770, 1106)(732, 1068, 772, 1108)(734, 1070, 774, 1110)(736, 1072, 768, 1104)(739, 1075, 781, 1117)(740, 1076, 782, 1118)(742, 1078, 785, 1121)(743, 1079, 786, 1122)(746, 1082, 791, 1127)(748, 1084, 795, 1131)(749, 1085, 794, 1130)(750, 1086, 796, 1132)(752, 1088, 798, 1134)(754, 1090, 792, 1128)(757, 1093, 805, 1141)(758, 1094, 806, 1142)(759, 1095, 803, 1139)(760, 1096, 808, 1144)(763, 1099, 812, 1148)(764, 1100, 814, 1150)(765, 1101, 815, 1151)(766, 1102, 810, 1146)(769, 1105, 818, 1154)(773, 1109, 824, 1160)(775, 1111, 828, 1164)(776, 1112, 827, 1163)(777, 1113, 821, 1157)(778, 1114, 817, 1153)(779, 1115, 783, 1119)(780, 1116, 831, 1167)(784, 1120, 836, 1172)(787, 1123, 840, 1176)(788, 1124, 842, 1178)(789, 1125, 843, 1179)(790, 1126, 838, 1174)(793, 1129, 846, 1182)(797, 1133, 852, 1188)(799, 1135, 856, 1192)(800, 1136, 855, 1191)(801, 1137, 849, 1185)(802, 1138, 845, 1181)(804, 1140, 859, 1195)(807, 1143, 863, 1199)(809, 1145, 866, 1202)(811, 1147, 839, 1175)(813, 1149, 864, 1200)(816, 1152, 872, 1208)(819, 1155, 847, 1183)(820, 1156, 879, 1215)(822, 1158, 876, 1212)(823, 1159, 880, 1216)(825, 1161, 884, 1220)(826, 1162, 854, 1190)(829, 1165, 888, 1224)(830, 1166, 889, 1225)(832, 1168, 860, 1196)(833, 1169, 891, 1227)(834, 1170, 882, 1218)(835, 1171, 893, 1229)(837, 1173, 896, 1232)(841, 1177, 894, 1230)(844, 1180, 902, 1238)(848, 1184, 909, 1245)(850, 1186, 906, 1242)(851, 1187, 910, 1246)(853, 1189, 914, 1250)(857, 1193, 918, 1254)(858, 1194, 919, 1255)(861, 1197, 921, 1257)(862, 1198, 912, 1248)(865, 1201, 920, 1256)(867, 1203, 928, 1264)(868, 1204, 899, 1235)(869, 1205, 898, 1234)(870, 1206, 926, 1262)(871, 1207, 924, 1260)(873, 1209, 932, 1268)(874, 1210, 933, 1269)(875, 1211, 907, 1243)(877, 1213, 905, 1241)(878, 1214, 934, 1270)(881, 1217, 925, 1261)(883, 1219, 940, 1276)(885, 1221, 917, 1253)(886, 1222, 943, 1279)(887, 1223, 915, 1251)(890, 1226, 895, 1231)(892, 1228, 948, 1284)(897, 1233, 954, 1290)(900, 1236, 952, 1288)(901, 1237, 950, 1286)(903, 1239, 958, 1294)(904, 1240, 959, 1295)(908, 1244, 960, 1296)(911, 1247, 951, 1287)(913, 1249, 966, 1302)(916, 1252, 969, 1305)(922, 1258, 974, 1310)(923, 1259, 971, 1307)(927, 1263, 972, 1308)(929, 1265, 978, 1314)(930, 1266, 961, 1297)(931, 1267, 979, 1315)(935, 1271, 956, 1292)(936, 1272, 970, 1306)(937, 1273, 981, 1317)(938, 1274, 976, 1312)(939, 1275, 985, 1321)(941, 1277, 973, 1309)(942, 1278, 986, 1322)(944, 1280, 962, 1298)(945, 1281, 949, 1285)(946, 1282, 953, 1289)(947, 1283, 967, 1303)(955, 1291, 991, 1327)(957, 1293, 992, 1328)(963, 1299, 994, 1330)(964, 1300, 989, 1325)(965, 1301, 998, 1334)(968, 1304, 999, 1335)(975, 1311, 1001, 1337)(977, 1313, 1002, 1338)(980, 1316, 1003, 1339)(982, 1318, 997, 1333)(983, 1319, 1000, 1336)(984, 1320, 995, 1331)(987, 1323, 996, 1332)(988, 1324, 1004, 1340)(990, 1326, 1005, 1341)(993, 1329, 1006, 1342)(1007, 1343, 1008, 1344) L = (1, 675)(2, 677)(3, 680)(4, 673)(5, 684)(6, 674)(7, 687)(8, 690)(9, 691)(10, 676)(11, 694)(12, 697)(13, 698)(14, 678)(15, 701)(16, 679)(17, 704)(18, 682)(19, 708)(20, 681)(21, 710)(22, 712)(23, 683)(24, 715)(25, 686)(26, 719)(27, 685)(28, 721)(29, 724)(30, 725)(31, 688)(32, 728)(33, 689)(34, 731)(35, 733)(36, 736)(37, 692)(38, 739)(39, 693)(40, 742)(41, 743)(42, 695)(43, 746)(44, 696)(45, 749)(46, 751)(47, 754)(48, 699)(49, 757)(50, 700)(51, 759)(52, 703)(53, 763)(54, 702)(55, 765)(56, 768)(57, 769)(58, 705)(59, 750)(60, 706)(61, 773)(62, 707)(63, 776)(64, 709)(65, 778)(66, 772)(67, 761)(68, 711)(69, 783)(70, 714)(71, 787)(72, 713)(73, 789)(74, 792)(75, 793)(76, 716)(77, 732)(78, 717)(79, 797)(80, 718)(81, 800)(82, 720)(83, 802)(84, 796)(85, 785)(86, 722)(87, 807)(88, 723)(89, 740)(90, 810)(91, 813)(92, 726)(93, 801)(94, 727)(95, 816)(96, 730)(97, 819)(98, 729)(99, 821)(100, 823)(101, 825)(102, 826)(103, 734)(104, 790)(105, 735)(106, 829)(107, 737)(108, 738)(109, 833)(110, 808)(111, 835)(112, 741)(113, 758)(114, 838)(115, 841)(116, 744)(117, 777)(118, 745)(119, 844)(120, 748)(121, 847)(122, 747)(123, 849)(124, 851)(125, 853)(126, 854)(127, 752)(128, 766)(129, 753)(130, 857)(131, 755)(132, 756)(133, 861)(134, 836)(135, 864)(136, 865)(137, 760)(138, 867)(139, 762)(140, 869)(141, 764)(142, 871)(143, 781)(144, 874)(145, 767)(146, 876)(147, 878)(148, 770)(149, 870)(150, 771)(151, 881)(152, 882)(153, 775)(154, 885)(155, 774)(156, 873)(157, 884)(158, 779)(159, 890)(160, 780)(161, 887)(162, 782)(163, 894)(164, 895)(165, 784)(166, 897)(167, 786)(168, 899)(169, 788)(170, 901)(171, 805)(172, 904)(173, 791)(174, 906)(175, 908)(176, 794)(177, 900)(178, 795)(179, 911)(180, 912)(181, 799)(182, 915)(183, 798)(184, 903)(185, 914)(186, 803)(187, 920)(188, 804)(189, 917)(190, 806)(191, 923)(192, 809)(193, 925)(194, 926)(195, 929)(196, 811)(197, 822)(198, 812)(199, 930)(200, 814)(201, 815)(202, 934)(203, 817)(204, 935)(205, 818)(206, 820)(207, 937)(208, 909)(209, 832)(210, 939)(211, 824)(212, 830)(213, 942)(214, 827)(215, 828)(216, 944)(217, 940)(218, 946)(219, 831)(220, 834)(221, 949)(222, 837)(223, 951)(224, 952)(225, 955)(226, 839)(227, 850)(228, 840)(229, 956)(230, 842)(231, 843)(232, 960)(233, 845)(234, 961)(235, 846)(236, 848)(237, 963)(238, 879)(239, 860)(240, 965)(241, 852)(242, 858)(243, 968)(244, 855)(245, 856)(246, 970)(247, 966)(248, 972)(249, 859)(250, 862)(251, 975)(252, 863)(253, 892)(254, 958)(255, 866)(256, 969)(257, 868)(258, 978)(259, 872)(260, 888)(261, 980)(262, 875)(263, 982)(264, 877)(265, 983)(266, 880)(267, 986)(268, 981)(269, 883)(270, 886)(271, 977)(272, 953)(273, 889)(274, 987)(275, 891)(276, 976)(277, 988)(278, 893)(279, 922)(280, 932)(281, 896)(282, 943)(283, 898)(284, 991)(285, 902)(286, 918)(287, 993)(288, 905)(289, 995)(290, 907)(291, 996)(292, 910)(293, 999)(294, 994)(295, 913)(296, 916)(297, 990)(298, 927)(299, 919)(300, 1000)(301, 921)(302, 989)(303, 948)(304, 924)(305, 928)(306, 931)(307, 1002)(308, 945)(309, 933)(310, 936)(311, 997)(312, 938)(313, 1001)(314, 941)(315, 947)(316, 974)(317, 950)(318, 954)(319, 957)(320, 1005)(321, 971)(322, 959)(323, 962)(324, 984)(325, 964)(326, 1004)(327, 967)(328, 973)(329, 1007)(330, 985)(331, 979)(332, 1008)(333, 998)(334, 992)(335, 1003)(336, 1006)(337, 1009)(338, 1010)(339, 1011)(340, 1012)(341, 1013)(342, 1014)(343, 1015)(344, 1016)(345, 1017)(346, 1018)(347, 1019)(348, 1020)(349, 1021)(350, 1022)(351, 1023)(352, 1024)(353, 1025)(354, 1026)(355, 1027)(356, 1028)(357, 1029)(358, 1030)(359, 1031)(360, 1032)(361, 1033)(362, 1034)(363, 1035)(364, 1036)(365, 1037)(366, 1038)(367, 1039)(368, 1040)(369, 1041)(370, 1042)(371, 1043)(372, 1044)(373, 1045)(374, 1046)(375, 1047)(376, 1048)(377, 1049)(378, 1050)(379, 1051)(380, 1052)(381, 1053)(382, 1054)(383, 1055)(384, 1056)(385, 1057)(386, 1058)(387, 1059)(388, 1060)(389, 1061)(390, 1062)(391, 1063)(392, 1064)(393, 1065)(394, 1066)(395, 1067)(396, 1068)(397, 1069)(398, 1070)(399, 1071)(400, 1072)(401, 1073)(402, 1074)(403, 1075)(404, 1076)(405, 1077)(406, 1078)(407, 1079)(408, 1080)(409, 1081)(410, 1082)(411, 1083)(412, 1084)(413, 1085)(414, 1086)(415, 1087)(416, 1088)(417, 1089)(418, 1090)(419, 1091)(420, 1092)(421, 1093)(422, 1094)(423, 1095)(424, 1096)(425, 1097)(426, 1098)(427, 1099)(428, 1100)(429, 1101)(430, 1102)(431, 1103)(432, 1104)(433, 1105)(434, 1106)(435, 1107)(436, 1108)(437, 1109)(438, 1110)(439, 1111)(440, 1112)(441, 1113)(442, 1114)(443, 1115)(444, 1116)(445, 1117)(446, 1118)(447, 1119)(448, 1120)(449, 1121)(450, 1122)(451, 1123)(452, 1124)(453, 1125)(454, 1126)(455, 1127)(456, 1128)(457, 1129)(458, 1130)(459, 1131)(460, 1132)(461, 1133)(462, 1134)(463, 1135)(464, 1136)(465, 1137)(466, 1138)(467, 1139)(468, 1140)(469, 1141)(470, 1142)(471, 1143)(472, 1144)(473, 1145)(474, 1146)(475, 1147)(476, 1148)(477, 1149)(478, 1150)(479, 1151)(480, 1152)(481, 1153)(482, 1154)(483, 1155)(484, 1156)(485, 1157)(486, 1158)(487, 1159)(488, 1160)(489, 1161)(490, 1162)(491, 1163)(492, 1164)(493, 1165)(494, 1166)(495, 1167)(496, 1168)(497, 1169)(498, 1170)(499, 1171)(500, 1172)(501, 1173)(502, 1174)(503, 1175)(504, 1176)(505, 1177)(506, 1178)(507, 1179)(508, 1180)(509, 1181)(510, 1182)(511, 1183)(512, 1184)(513, 1185)(514, 1186)(515, 1187)(516, 1188)(517, 1189)(518, 1190)(519, 1191)(520, 1192)(521, 1193)(522, 1194)(523, 1195)(524, 1196)(525, 1197)(526, 1198)(527, 1199)(528, 1200)(529, 1201)(530, 1202)(531, 1203)(532, 1204)(533, 1205)(534, 1206)(535, 1207)(536, 1208)(537, 1209)(538, 1210)(539, 1211)(540, 1212)(541, 1213)(542, 1214)(543, 1215)(544, 1216)(545, 1217)(546, 1218)(547, 1219)(548, 1220)(549, 1221)(550, 1222)(551, 1223)(552, 1224)(553, 1225)(554, 1226)(555, 1227)(556, 1228)(557, 1229)(558, 1230)(559, 1231)(560, 1232)(561, 1233)(562, 1234)(563, 1235)(564, 1236)(565, 1237)(566, 1238)(567, 1239)(568, 1240)(569, 1241)(570, 1242)(571, 1243)(572, 1244)(573, 1245)(574, 1246)(575, 1247)(576, 1248)(577, 1249)(578, 1250)(579, 1251)(580, 1252)(581, 1253)(582, 1254)(583, 1255)(584, 1256)(585, 1257)(586, 1258)(587, 1259)(588, 1260)(589, 1261)(590, 1262)(591, 1263)(592, 1264)(593, 1265)(594, 1266)(595, 1267)(596, 1268)(597, 1269)(598, 1270)(599, 1271)(600, 1272)(601, 1273)(602, 1274)(603, 1275)(604, 1276)(605, 1277)(606, 1278)(607, 1279)(608, 1280)(609, 1281)(610, 1282)(611, 1283)(612, 1284)(613, 1285)(614, 1286)(615, 1287)(616, 1288)(617, 1289)(618, 1290)(619, 1291)(620, 1292)(621, 1293)(622, 1294)(623, 1295)(624, 1296)(625, 1297)(626, 1298)(627, 1299)(628, 1300)(629, 1301)(630, 1302)(631, 1303)(632, 1304)(633, 1305)(634, 1306)(635, 1307)(636, 1308)(637, 1309)(638, 1310)(639, 1311)(640, 1312)(641, 1313)(642, 1314)(643, 1315)(644, 1316)(645, 1317)(646, 1318)(647, 1319)(648, 1320)(649, 1321)(650, 1322)(651, 1323)(652, 1324)(653, 1325)(654, 1326)(655, 1327)(656, 1328)(657, 1329)(658, 1330)(659, 1331)(660, 1332)(661, 1333)(662, 1334)(663, 1335)(664, 1336)(665, 1337)(666, 1338)(667, 1339)(668, 1340)(669, 1341)(670, 1342)(671, 1343)(672, 1344) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E15.1382 Graph:: simple bipartite v = 504 e = 672 f = 140 degree seq :: [ 2^336, 4^168 ] E15.1384 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^6, (Y3 * Y1^-1)^4, (Y1^2 * Y3 * Y1)^3, Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1 * Y3 * Y1^-2, (Y1 * Y3 * Y1^-1 * Y3)^4 ] Map:: polytopal R = (1, 337, 2, 338, 5, 341, 11, 347, 10, 346, 4, 340)(3, 339, 7, 343, 15, 351, 29, 365, 18, 354, 8, 344)(6, 342, 13, 349, 25, 361, 46, 382, 28, 364, 14, 350)(9, 345, 19, 355, 35, 371, 61, 397, 37, 373, 20, 356)(12, 348, 23, 359, 42, 378, 73, 409, 45, 381, 24, 360)(16, 352, 31, 367, 54, 390, 91, 427, 56, 392, 32, 368)(17, 353, 33, 369, 57, 393, 82, 418, 48, 384, 26, 362)(21, 357, 38, 374, 66, 402, 78, 414, 68, 404, 39, 375)(22, 358, 40, 376, 69, 405, 51, 387, 72, 408, 41, 377)(27, 363, 49, 385, 83, 419, 118, 454, 75, 411, 43, 379)(30, 366, 52, 388, 87, 423, 128, 464, 90, 426, 53, 389)(34, 370, 59, 395, 98, 434, 139, 475, 100, 436, 60, 396)(36, 372, 63, 399, 103, 439, 153, 489, 105, 441, 64, 400)(44, 380, 76, 412, 119, 455, 165, 501, 112, 448, 70, 406)(47, 383, 79, 415, 123, 459, 173, 509, 126, 462, 80, 416)(50, 386, 85, 421, 132, 468, 95, 431, 134, 470, 86, 422)(55, 391, 93, 429, 142, 478, 193, 529, 136, 472, 88, 424)(58, 394, 96, 432, 146, 482, 202, 538, 148, 484, 97, 433)(62, 398, 101, 437, 145, 481, 94, 430, 144, 480, 102, 438)(65, 401, 106, 442, 157, 493, 211, 547, 158, 494, 107, 443)(67, 403, 71, 407, 113, 449, 166, 502, 161, 497, 109, 445)(74, 410, 115, 451, 169, 505, 224, 560, 171, 507, 116, 452)(77, 413, 121, 457, 177, 513, 129, 465, 178, 514, 122, 458)(81, 417, 127, 463, 183, 519, 241, 577, 180, 516, 124, 460)(84, 420, 130, 466, 185, 521, 245, 581, 187, 523, 131, 467)(89, 425, 137, 473, 174, 510, 228, 564, 168, 504, 114, 450)(92, 428, 140, 476, 196, 532, 254, 590, 198, 534, 141, 477)(99, 435, 111, 447, 163, 499, 221, 557, 208, 544, 150, 486)(104, 440, 155, 491, 214, 550, 268, 604, 210, 546, 152, 488)(108, 444, 159, 495, 215, 551, 156, 492, 189, 525, 133, 469)(110, 446, 125, 461, 181, 517, 225, 561, 220, 556, 162, 498)(117, 453, 172, 508, 232, 568, 287, 623, 230, 566, 170, 506)(120, 456, 175, 511, 234, 570, 290, 626, 236, 572, 176, 512)(135, 471, 191, 527, 251, 587, 284, 620, 235, 571, 184, 520)(138, 474, 188, 524, 248, 584, 199, 535, 247, 583, 195, 531)(143, 479, 200, 536, 259, 595, 294, 630, 238, 574, 186, 522)(147, 483, 204, 540, 263, 599, 302, 638, 250, 586, 190, 526)(149, 485, 206, 542, 264, 600, 205, 541, 260, 596, 201, 537)(151, 487, 197, 533, 257, 593, 277, 613, 266, 602, 209, 545)(154, 490, 212, 548, 269, 605, 313, 649, 271, 607, 213, 549)(160, 496, 219, 555, 275, 611, 315, 651, 274, 610, 218, 554)(164, 500, 223, 559, 279, 615, 317, 653, 278, 614, 222, 558)(167, 503, 226, 562, 281, 617, 319, 655, 283, 619, 227, 563)(179, 515, 239, 575, 295, 631, 276, 612, 282, 618, 233, 569)(182, 518, 237, 573, 293, 629, 244, 580, 292, 628, 243, 579)(192, 528, 253, 589, 291, 627, 324, 660, 304, 640, 252, 588)(194, 530, 255, 591, 289, 625, 321, 657, 288, 624, 231, 567)(203, 539, 261, 597, 309, 645, 328, 664, 310, 646, 262, 598)(207, 543, 242, 578, 298, 634, 318, 654, 311, 647, 265, 601)(216, 552, 272, 608, 307, 643, 258, 594, 301, 637, 249, 585)(217, 553, 270, 606, 280, 616, 229, 565, 285, 621, 273, 609)(240, 576, 297, 633, 320, 656, 303, 639, 326, 662, 296, 632)(246, 582, 299, 635, 327, 663, 308, 644, 267, 603, 300, 636)(256, 592, 306, 642, 330, 666, 312, 648, 316, 652, 305, 641)(286, 622, 323, 659, 314, 650, 325, 661, 332, 668, 322, 658)(329, 665, 334, 670, 331, 667, 335, 671, 336, 672, 333, 669)(673, 1009)(674, 1010)(675, 1011)(676, 1012)(677, 1013)(678, 1014)(679, 1015)(680, 1016)(681, 1017)(682, 1018)(683, 1019)(684, 1020)(685, 1021)(686, 1022)(687, 1023)(688, 1024)(689, 1025)(690, 1026)(691, 1027)(692, 1028)(693, 1029)(694, 1030)(695, 1031)(696, 1032)(697, 1033)(698, 1034)(699, 1035)(700, 1036)(701, 1037)(702, 1038)(703, 1039)(704, 1040)(705, 1041)(706, 1042)(707, 1043)(708, 1044)(709, 1045)(710, 1046)(711, 1047)(712, 1048)(713, 1049)(714, 1050)(715, 1051)(716, 1052)(717, 1053)(718, 1054)(719, 1055)(720, 1056)(721, 1057)(722, 1058)(723, 1059)(724, 1060)(725, 1061)(726, 1062)(727, 1063)(728, 1064)(729, 1065)(730, 1066)(731, 1067)(732, 1068)(733, 1069)(734, 1070)(735, 1071)(736, 1072)(737, 1073)(738, 1074)(739, 1075)(740, 1076)(741, 1077)(742, 1078)(743, 1079)(744, 1080)(745, 1081)(746, 1082)(747, 1083)(748, 1084)(749, 1085)(750, 1086)(751, 1087)(752, 1088)(753, 1089)(754, 1090)(755, 1091)(756, 1092)(757, 1093)(758, 1094)(759, 1095)(760, 1096)(761, 1097)(762, 1098)(763, 1099)(764, 1100)(765, 1101)(766, 1102)(767, 1103)(768, 1104)(769, 1105)(770, 1106)(771, 1107)(772, 1108)(773, 1109)(774, 1110)(775, 1111)(776, 1112)(777, 1113)(778, 1114)(779, 1115)(780, 1116)(781, 1117)(782, 1118)(783, 1119)(784, 1120)(785, 1121)(786, 1122)(787, 1123)(788, 1124)(789, 1125)(790, 1126)(791, 1127)(792, 1128)(793, 1129)(794, 1130)(795, 1131)(796, 1132)(797, 1133)(798, 1134)(799, 1135)(800, 1136)(801, 1137)(802, 1138)(803, 1139)(804, 1140)(805, 1141)(806, 1142)(807, 1143)(808, 1144)(809, 1145)(810, 1146)(811, 1147)(812, 1148)(813, 1149)(814, 1150)(815, 1151)(816, 1152)(817, 1153)(818, 1154)(819, 1155)(820, 1156)(821, 1157)(822, 1158)(823, 1159)(824, 1160)(825, 1161)(826, 1162)(827, 1163)(828, 1164)(829, 1165)(830, 1166)(831, 1167)(832, 1168)(833, 1169)(834, 1170)(835, 1171)(836, 1172)(837, 1173)(838, 1174)(839, 1175)(840, 1176)(841, 1177)(842, 1178)(843, 1179)(844, 1180)(845, 1181)(846, 1182)(847, 1183)(848, 1184)(849, 1185)(850, 1186)(851, 1187)(852, 1188)(853, 1189)(854, 1190)(855, 1191)(856, 1192)(857, 1193)(858, 1194)(859, 1195)(860, 1196)(861, 1197)(862, 1198)(863, 1199)(864, 1200)(865, 1201)(866, 1202)(867, 1203)(868, 1204)(869, 1205)(870, 1206)(871, 1207)(872, 1208)(873, 1209)(874, 1210)(875, 1211)(876, 1212)(877, 1213)(878, 1214)(879, 1215)(880, 1216)(881, 1217)(882, 1218)(883, 1219)(884, 1220)(885, 1221)(886, 1222)(887, 1223)(888, 1224)(889, 1225)(890, 1226)(891, 1227)(892, 1228)(893, 1229)(894, 1230)(895, 1231)(896, 1232)(897, 1233)(898, 1234)(899, 1235)(900, 1236)(901, 1237)(902, 1238)(903, 1239)(904, 1240)(905, 1241)(906, 1242)(907, 1243)(908, 1244)(909, 1245)(910, 1246)(911, 1247)(912, 1248)(913, 1249)(914, 1250)(915, 1251)(916, 1252)(917, 1253)(918, 1254)(919, 1255)(920, 1256)(921, 1257)(922, 1258)(923, 1259)(924, 1260)(925, 1261)(926, 1262)(927, 1263)(928, 1264)(929, 1265)(930, 1266)(931, 1267)(932, 1268)(933, 1269)(934, 1270)(935, 1271)(936, 1272)(937, 1273)(938, 1274)(939, 1275)(940, 1276)(941, 1277)(942, 1278)(943, 1279)(944, 1280)(945, 1281)(946, 1282)(947, 1283)(948, 1284)(949, 1285)(950, 1286)(951, 1287)(952, 1288)(953, 1289)(954, 1290)(955, 1291)(956, 1292)(957, 1293)(958, 1294)(959, 1295)(960, 1296)(961, 1297)(962, 1298)(963, 1299)(964, 1300)(965, 1301)(966, 1302)(967, 1303)(968, 1304)(969, 1305)(970, 1306)(971, 1307)(972, 1308)(973, 1309)(974, 1310)(975, 1311)(976, 1312)(977, 1313)(978, 1314)(979, 1315)(980, 1316)(981, 1317)(982, 1318)(983, 1319)(984, 1320)(985, 1321)(986, 1322)(987, 1323)(988, 1324)(989, 1325)(990, 1326)(991, 1327)(992, 1328)(993, 1329)(994, 1330)(995, 1331)(996, 1332)(997, 1333)(998, 1334)(999, 1335)(1000, 1336)(1001, 1337)(1002, 1338)(1003, 1339)(1004, 1340)(1005, 1341)(1006, 1342)(1007, 1343)(1008, 1344) L = (1, 675)(2, 678)(3, 673)(4, 681)(5, 684)(6, 674)(7, 688)(8, 689)(9, 676)(10, 693)(11, 694)(12, 677)(13, 698)(14, 699)(15, 702)(16, 679)(17, 680)(18, 706)(19, 708)(20, 703)(21, 682)(22, 683)(23, 715)(24, 716)(25, 719)(26, 685)(27, 686)(28, 722)(29, 723)(30, 687)(31, 692)(32, 727)(33, 730)(34, 690)(35, 734)(36, 691)(37, 737)(38, 739)(39, 735)(40, 742)(41, 743)(42, 746)(43, 695)(44, 696)(45, 749)(46, 750)(47, 697)(48, 753)(49, 756)(50, 700)(51, 701)(52, 760)(53, 761)(54, 764)(55, 704)(56, 766)(57, 767)(58, 705)(59, 771)(60, 768)(61, 745)(62, 707)(63, 711)(64, 776)(65, 709)(66, 780)(67, 710)(68, 782)(69, 783)(70, 712)(71, 713)(72, 786)(73, 733)(74, 714)(75, 789)(76, 792)(77, 717)(78, 718)(79, 796)(80, 797)(81, 720)(82, 800)(83, 801)(84, 721)(85, 805)(86, 802)(87, 807)(88, 724)(89, 725)(90, 810)(91, 811)(92, 726)(93, 815)(94, 728)(95, 729)(96, 732)(97, 819)(98, 821)(99, 731)(100, 823)(101, 824)(102, 793)(103, 826)(104, 736)(105, 828)(106, 788)(107, 812)(108, 738)(109, 832)(110, 740)(111, 741)(112, 836)(113, 839)(114, 744)(115, 842)(116, 778)(117, 747)(118, 845)(119, 846)(120, 748)(121, 774)(122, 847)(123, 851)(124, 751)(125, 752)(126, 854)(127, 856)(128, 754)(129, 755)(130, 758)(131, 858)(132, 860)(133, 757)(134, 862)(135, 759)(136, 864)(137, 866)(138, 762)(139, 763)(140, 779)(141, 869)(142, 871)(143, 765)(144, 873)(145, 872)(146, 875)(147, 769)(148, 877)(149, 770)(150, 879)(151, 772)(152, 773)(153, 883)(154, 775)(155, 876)(156, 777)(157, 888)(158, 889)(159, 890)(160, 781)(161, 880)(162, 884)(163, 894)(164, 784)(165, 896)(166, 897)(167, 785)(168, 898)(169, 901)(170, 787)(171, 903)(172, 905)(173, 790)(174, 791)(175, 794)(176, 907)(177, 909)(178, 910)(179, 795)(180, 912)(181, 914)(182, 798)(183, 916)(184, 799)(185, 918)(186, 803)(187, 919)(188, 804)(189, 921)(190, 806)(191, 924)(192, 808)(193, 926)(194, 809)(195, 927)(196, 928)(197, 813)(198, 930)(199, 814)(200, 817)(201, 816)(202, 913)(203, 818)(204, 827)(205, 820)(206, 937)(207, 822)(208, 833)(209, 933)(210, 939)(211, 825)(212, 834)(213, 942)(214, 936)(215, 935)(216, 829)(217, 830)(218, 831)(219, 929)(220, 948)(221, 949)(222, 835)(223, 952)(224, 837)(225, 838)(226, 840)(227, 954)(228, 956)(229, 841)(230, 958)(231, 843)(232, 961)(233, 844)(234, 963)(235, 848)(236, 964)(237, 849)(238, 850)(239, 968)(240, 852)(241, 874)(242, 853)(243, 970)(244, 855)(245, 959)(246, 857)(247, 859)(248, 973)(249, 861)(250, 971)(251, 975)(252, 863)(253, 977)(254, 865)(255, 867)(256, 868)(257, 891)(258, 870)(259, 980)(260, 965)(261, 881)(262, 969)(263, 887)(264, 886)(265, 878)(266, 984)(267, 882)(268, 985)(269, 986)(270, 885)(271, 983)(272, 960)(273, 978)(274, 982)(275, 979)(276, 892)(277, 893)(278, 988)(279, 990)(280, 895)(281, 992)(282, 899)(283, 993)(284, 900)(285, 994)(286, 902)(287, 917)(288, 944)(289, 904)(290, 989)(291, 906)(292, 908)(293, 932)(294, 996)(295, 997)(296, 911)(297, 934)(298, 915)(299, 922)(300, 995)(301, 920)(302, 1000)(303, 923)(304, 1001)(305, 925)(306, 945)(307, 947)(308, 931)(309, 1003)(310, 946)(311, 943)(312, 938)(313, 940)(314, 941)(315, 991)(316, 950)(317, 962)(318, 951)(319, 987)(320, 953)(321, 955)(322, 957)(323, 972)(324, 966)(325, 967)(326, 1005)(327, 1006)(328, 974)(329, 976)(330, 1007)(331, 981)(332, 1008)(333, 998)(334, 999)(335, 1002)(336, 1004)(337, 1009)(338, 1010)(339, 1011)(340, 1012)(341, 1013)(342, 1014)(343, 1015)(344, 1016)(345, 1017)(346, 1018)(347, 1019)(348, 1020)(349, 1021)(350, 1022)(351, 1023)(352, 1024)(353, 1025)(354, 1026)(355, 1027)(356, 1028)(357, 1029)(358, 1030)(359, 1031)(360, 1032)(361, 1033)(362, 1034)(363, 1035)(364, 1036)(365, 1037)(366, 1038)(367, 1039)(368, 1040)(369, 1041)(370, 1042)(371, 1043)(372, 1044)(373, 1045)(374, 1046)(375, 1047)(376, 1048)(377, 1049)(378, 1050)(379, 1051)(380, 1052)(381, 1053)(382, 1054)(383, 1055)(384, 1056)(385, 1057)(386, 1058)(387, 1059)(388, 1060)(389, 1061)(390, 1062)(391, 1063)(392, 1064)(393, 1065)(394, 1066)(395, 1067)(396, 1068)(397, 1069)(398, 1070)(399, 1071)(400, 1072)(401, 1073)(402, 1074)(403, 1075)(404, 1076)(405, 1077)(406, 1078)(407, 1079)(408, 1080)(409, 1081)(410, 1082)(411, 1083)(412, 1084)(413, 1085)(414, 1086)(415, 1087)(416, 1088)(417, 1089)(418, 1090)(419, 1091)(420, 1092)(421, 1093)(422, 1094)(423, 1095)(424, 1096)(425, 1097)(426, 1098)(427, 1099)(428, 1100)(429, 1101)(430, 1102)(431, 1103)(432, 1104)(433, 1105)(434, 1106)(435, 1107)(436, 1108)(437, 1109)(438, 1110)(439, 1111)(440, 1112)(441, 1113)(442, 1114)(443, 1115)(444, 1116)(445, 1117)(446, 1118)(447, 1119)(448, 1120)(449, 1121)(450, 1122)(451, 1123)(452, 1124)(453, 1125)(454, 1126)(455, 1127)(456, 1128)(457, 1129)(458, 1130)(459, 1131)(460, 1132)(461, 1133)(462, 1134)(463, 1135)(464, 1136)(465, 1137)(466, 1138)(467, 1139)(468, 1140)(469, 1141)(470, 1142)(471, 1143)(472, 1144)(473, 1145)(474, 1146)(475, 1147)(476, 1148)(477, 1149)(478, 1150)(479, 1151)(480, 1152)(481, 1153)(482, 1154)(483, 1155)(484, 1156)(485, 1157)(486, 1158)(487, 1159)(488, 1160)(489, 1161)(490, 1162)(491, 1163)(492, 1164)(493, 1165)(494, 1166)(495, 1167)(496, 1168)(497, 1169)(498, 1170)(499, 1171)(500, 1172)(501, 1173)(502, 1174)(503, 1175)(504, 1176)(505, 1177)(506, 1178)(507, 1179)(508, 1180)(509, 1181)(510, 1182)(511, 1183)(512, 1184)(513, 1185)(514, 1186)(515, 1187)(516, 1188)(517, 1189)(518, 1190)(519, 1191)(520, 1192)(521, 1193)(522, 1194)(523, 1195)(524, 1196)(525, 1197)(526, 1198)(527, 1199)(528, 1200)(529, 1201)(530, 1202)(531, 1203)(532, 1204)(533, 1205)(534, 1206)(535, 1207)(536, 1208)(537, 1209)(538, 1210)(539, 1211)(540, 1212)(541, 1213)(542, 1214)(543, 1215)(544, 1216)(545, 1217)(546, 1218)(547, 1219)(548, 1220)(549, 1221)(550, 1222)(551, 1223)(552, 1224)(553, 1225)(554, 1226)(555, 1227)(556, 1228)(557, 1229)(558, 1230)(559, 1231)(560, 1232)(561, 1233)(562, 1234)(563, 1235)(564, 1236)(565, 1237)(566, 1238)(567, 1239)(568, 1240)(569, 1241)(570, 1242)(571, 1243)(572, 1244)(573, 1245)(574, 1246)(575, 1247)(576, 1248)(577, 1249)(578, 1250)(579, 1251)(580, 1252)(581, 1253)(582, 1254)(583, 1255)(584, 1256)(585, 1257)(586, 1258)(587, 1259)(588, 1260)(589, 1261)(590, 1262)(591, 1263)(592, 1264)(593, 1265)(594, 1266)(595, 1267)(596, 1268)(597, 1269)(598, 1270)(599, 1271)(600, 1272)(601, 1273)(602, 1274)(603, 1275)(604, 1276)(605, 1277)(606, 1278)(607, 1279)(608, 1280)(609, 1281)(610, 1282)(611, 1283)(612, 1284)(613, 1285)(614, 1286)(615, 1287)(616, 1288)(617, 1289)(618, 1290)(619, 1291)(620, 1292)(621, 1293)(622, 1294)(623, 1295)(624, 1296)(625, 1297)(626, 1298)(627, 1299)(628, 1300)(629, 1301)(630, 1302)(631, 1303)(632, 1304)(633, 1305)(634, 1306)(635, 1307)(636, 1308)(637, 1309)(638, 1310)(639, 1311)(640, 1312)(641, 1313)(642, 1314)(643, 1315)(644, 1316)(645, 1317)(646, 1318)(647, 1319)(648, 1320)(649, 1321)(650, 1322)(651, 1323)(652, 1324)(653, 1325)(654, 1326)(655, 1327)(656, 1328)(657, 1329)(658, 1330)(659, 1331)(660, 1332)(661, 1333)(662, 1334)(663, 1335)(664, 1336)(665, 1337)(666, 1338)(667, 1339)(668, 1340)(669, 1341)(670, 1342)(671, 1343)(672, 1344) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E15.1381 Graph:: simple bipartite v = 392 e = 672 f = 252 degree seq :: [ 2^336, 12^56 ] E15.1385 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y3 * Y2^-1)^4, (Y2 * Y1)^4, (Y2^-2 * Y1 * Y2^-1)^3, Y2^-1 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2 * Y1 * Y2^-1 * Y1)^4 ] Map:: R = (1, 337, 2, 338)(3, 339, 7, 343)(4, 340, 9, 345)(5, 341, 11, 347)(6, 342, 13, 349)(8, 344, 17, 353)(10, 346, 21, 357)(12, 348, 24, 360)(14, 350, 28, 364)(15, 351, 27, 363)(16, 352, 30, 366)(18, 354, 34, 370)(19, 355, 35, 371)(20, 356, 22, 358)(23, 359, 41, 377)(25, 361, 45, 381)(26, 362, 46, 382)(29, 365, 51, 387)(31, 367, 55, 391)(32, 368, 54, 390)(33, 369, 57, 393)(36, 372, 63, 399)(37, 373, 65, 401)(38, 374, 66, 402)(39, 375, 61, 397)(40, 376, 69, 405)(42, 378, 73, 409)(43, 379, 72, 408)(44, 380, 75, 411)(47, 383, 81, 417)(48, 384, 83, 419)(49, 385, 84, 420)(50, 386, 79, 415)(52, 388, 89, 425)(53, 389, 90, 426)(56, 392, 95, 431)(58, 394, 99, 435)(59, 395, 98, 434)(60, 396, 100, 436)(62, 398, 102, 438)(64, 400, 96, 432)(67, 403, 109, 445)(68, 404, 110, 446)(70, 406, 113, 449)(71, 407, 114, 450)(74, 410, 119, 455)(76, 412, 123, 459)(77, 413, 122, 458)(78, 414, 124, 460)(80, 416, 126, 462)(82, 418, 120, 456)(85, 421, 133, 469)(86, 422, 134, 470)(87, 423, 131, 467)(88, 424, 136, 472)(91, 427, 140, 476)(92, 428, 142, 478)(93, 429, 143, 479)(94, 430, 138, 474)(97, 433, 146, 482)(101, 437, 152, 488)(103, 439, 156, 492)(104, 440, 155, 491)(105, 441, 149, 485)(106, 442, 145, 481)(107, 443, 111, 447)(108, 444, 159, 495)(112, 448, 164, 500)(115, 451, 168, 504)(116, 452, 170, 506)(117, 453, 171, 507)(118, 454, 166, 502)(121, 457, 174, 510)(125, 461, 180, 516)(127, 463, 184, 520)(128, 464, 183, 519)(129, 465, 177, 513)(130, 466, 173, 509)(132, 468, 187, 523)(135, 471, 191, 527)(137, 473, 194, 530)(139, 475, 167, 503)(141, 477, 192, 528)(144, 480, 200, 536)(147, 483, 175, 511)(148, 484, 207, 543)(150, 486, 204, 540)(151, 487, 208, 544)(153, 489, 212, 548)(154, 490, 182, 518)(157, 493, 216, 552)(158, 494, 217, 553)(160, 496, 188, 524)(161, 497, 219, 555)(162, 498, 210, 546)(163, 499, 221, 557)(165, 501, 224, 560)(169, 505, 222, 558)(172, 508, 230, 566)(176, 512, 237, 573)(178, 514, 234, 570)(179, 515, 238, 574)(181, 517, 242, 578)(185, 521, 246, 582)(186, 522, 247, 583)(189, 525, 249, 585)(190, 526, 240, 576)(193, 529, 248, 584)(195, 531, 256, 592)(196, 532, 227, 563)(197, 533, 226, 562)(198, 534, 254, 590)(199, 535, 252, 588)(201, 537, 260, 596)(202, 538, 261, 597)(203, 539, 235, 571)(205, 541, 233, 569)(206, 542, 262, 598)(209, 545, 253, 589)(211, 547, 268, 604)(213, 549, 245, 581)(214, 550, 271, 607)(215, 551, 243, 579)(218, 554, 223, 559)(220, 556, 276, 612)(225, 561, 282, 618)(228, 564, 280, 616)(229, 565, 278, 614)(231, 567, 286, 622)(232, 568, 287, 623)(236, 572, 288, 624)(239, 575, 279, 615)(241, 577, 294, 630)(244, 580, 297, 633)(250, 586, 302, 638)(251, 587, 299, 635)(255, 591, 300, 636)(257, 593, 306, 642)(258, 594, 289, 625)(259, 595, 307, 643)(263, 599, 284, 620)(264, 600, 298, 634)(265, 601, 309, 645)(266, 602, 304, 640)(267, 603, 313, 649)(269, 605, 301, 637)(270, 606, 314, 650)(272, 608, 290, 626)(273, 609, 277, 613)(274, 610, 281, 617)(275, 611, 295, 631)(283, 619, 319, 655)(285, 621, 320, 656)(291, 627, 322, 658)(292, 628, 317, 653)(293, 629, 326, 662)(296, 632, 327, 663)(303, 639, 329, 665)(305, 641, 330, 666)(308, 644, 331, 667)(310, 646, 325, 661)(311, 647, 328, 664)(312, 648, 323, 659)(315, 651, 324, 660)(316, 652, 332, 668)(318, 654, 333, 669)(321, 657, 334, 670)(335, 671, 336, 672)(673, 1009, 675, 1011, 680, 1016, 690, 1026, 682, 1018, 676, 1012)(674, 1010, 677, 1013, 684, 1020, 697, 1033, 686, 1022, 678, 1014)(679, 1015, 687, 1023, 701, 1037, 724, 1060, 703, 1039, 688, 1024)(681, 1017, 691, 1027, 708, 1044, 736, 1072, 709, 1045, 692, 1028)(683, 1019, 694, 1030, 712, 1048, 742, 1078, 714, 1050, 695, 1031)(685, 1021, 698, 1034, 719, 1055, 754, 1090, 720, 1056, 699, 1035)(689, 1025, 704, 1040, 728, 1064, 768, 1104, 730, 1066, 705, 1041)(693, 1029, 710, 1046, 739, 1075, 761, 1097, 740, 1076, 711, 1047)(696, 1032, 715, 1051, 746, 1082, 792, 1128, 748, 1084, 716, 1052)(700, 1036, 721, 1057, 757, 1093, 785, 1121, 758, 1094, 722, 1058)(702, 1038, 725, 1061, 763, 1099, 813, 1149, 764, 1100, 726, 1062)(706, 1042, 731, 1067, 750, 1086, 717, 1053, 749, 1085, 732, 1068)(707, 1043, 733, 1069, 773, 1109, 825, 1161, 775, 1111, 734, 1070)(713, 1049, 743, 1079, 787, 1123, 841, 1177, 788, 1124, 744, 1080)(718, 1054, 751, 1087, 797, 1133, 853, 1189, 799, 1135, 752, 1088)(723, 1059, 759, 1095, 807, 1143, 864, 1200, 809, 1145, 760, 1096)(727, 1063, 765, 1101, 801, 1137, 753, 1089, 800, 1136, 766, 1102)(729, 1065, 769, 1105, 819, 1155, 878, 1214, 820, 1156, 770, 1106)(735, 1071, 776, 1112, 790, 1126, 745, 1081, 789, 1125, 777, 1113)(737, 1073, 778, 1114, 829, 1165, 884, 1220, 830, 1166, 779, 1115)(738, 1074, 772, 1108, 823, 1159, 881, 1217, 832, 1168, 780, 1116)(741, 1077, 783, 1119, 835, 1171, 894, 1230, 837, 1173, 784, 1120)(747, 1083, 793, 1129, 847, 1183, 908, 1244, 848, 1184, 794, 1130)(755, 1091, 802, 1138, 857, 1193, 914, 1250, 858, 1194, 803, 1139)(756, 1092, 796, 1132, 851, 1187, 911, 1247, 860, 1196, 804, 1140)(762, 1098, 810, 1146, 867, 1203, 929, 1265, 868, 1204, 811, 1147)(767, 1103, 816, 1152, 874, 1210, 934, 1270, 875, 1211, 817, 1153)(771, 1107, 821, 1157, 870, 1206, 812, 1148, 869, 1205, 822, 1158)(774, 1110, 826, 1162, 885, 1221, 942, 1278, 886, 1222, 827, 1163)(781, 1117, 833, 1169, 887, 1223, 828, 1164, 873, 1209, 815, 1151)(782, 1118, 808, 1144, 865, 1201, 925, 1261, 892, 1228, 834, 1170)(786, 1122, 838, 1174, 897, 1233, 955, 1291, 898, 1234, 839, 1175)(791, 1127, 844, 1180, 904, 1240, 960, 1296, 905, 1241, 845, 1181)(795, 1131, 849, 1185, 900, 1236, 840, 1176, 899, 1235, 850, 1186)(798, 1134, 854, 1190, 915, 1251, 968, 1304, 916, 1252, 855, 1191)(805, 1141, 861, 1197, 917, 1253, 856, 1192, 903, 1239, 843, 1179)(806, 1142, 836, 1172, 895, 1231, 951, 1287, 922, 1258, 862, 1198)(814, 1150, 871, 1207, 930, 1266, 978, 1314, 931, 1267, 872, 1208)(818, 1154, 876, 1212, 935, 1271, 982, 1318, 936, 1272, 877, 1213)(824, 1160, 882, 1218, 939, 1275, 986, 1322, 941, 1277, 883, 1219)(831, 1167, 890, 1226, 946, 1282, 987, 1323, 947, 1283, 891, 1227)(842, 1178, 901, 1237, 956, 1292, 991, 1327, 957, 1293, 902, 1238)(846, 1182, 906, 1242, 961, 1297, 995, 1331, 962, 1298, 907, 1243)(852, 1188, 912, 1248, 965, 1301, 999, 1335, 967, 1303, 913, 1249)(859, 1195, 920, 1256, 972, 1308, 1000, 1336, 973, 1309, 921, 1257)(863, 1199, 923, 1259, 975, 1311, 948, 1284, 976, 1312, 924, 1260)(866, 1202, 926, 1262, 958, 1294, 918, 1254, 970, 1306, 927, 1263)(879, 1215, 937, 1273, 983, 1319, 997, 1333, 964, 1300, 910, 1246)(880, 1216, 909, 1245, 963, 1299, 996, 1332, 984, 1320, 938, 1274)(888, 1224, 944, 1280, 953, 1289, 896, 1232, 952, 1288, 932, 1268)(889, 1225, 940, 1276, 981, 1317, 933, 1269, 980, 1316, 945, 1281)(893, 1229, 949, 1285, 988, 1324, 974, 1310, 989, 1325, 950, 1286)(919, 1255, 966, 1302, 994, 1330, 959, 1295, 993, 1329, 971, 1307)(928, 1264, 969, 1305, 990, 1326, 954, 1290, 943, 1279, 977, 1313)(979, 1315, 1002, 1338, 985, 1321, 1001, 1337, 1007, 1343, 1003, 1339)(992, 1328, 1005, 1341, 998, 1334, 1004, 1340, 1008, 1344, 1006, 1342) L = (1, 674)(2, 673)(3, 679)(4, 681)(5, 683)(6, 685)(7, 675)(8, 689)(9, 676)(10, 693)(11, 677)(12, 696)(13, 678)(14, 700)(15, 699)(16, 702)(17, 680)(18, 706)(19, 707)(20, 694)(21, 682)(22, 692)(23, 713)(24, 684)(25, 717)(26, 718)(27, 687)(28, 686)(29, 723)(30, 688)(31, 727)(32, 726)(33, 729)(34, 690)(35, 691)(36, 735)(37, 737)(38, 738)(39, 733)(40, 741)(41, 695)(42, 745)(43, 744)(44, 747)(45, 697)(46, 698)(47, 753)(48, 755)(49, 756)(50, 751)(51, 701)(52, 761)(53, 762)(54, 704)(55, 703)(56, 767)(57, 705)(58, 771)(59, 770)(60, 772)(61, 711)(62, 774)(63, 708)(64, 768)(65, 709)(66, 710)(67, 781)(68, 782)(69, 712)(70, 785)(71, 786)(72, 715)(73, 714)(74, 791)(75, 716)(76, 795)(77, 794)(78, 796)(79, 722)(80, 798)(81, 719)(82, 792)(83, 720)(84, 721)(85, 805)(86, 806)(87, 803)(88, 808)(89, 724)(90, 725)(91, 812)(92, 814)(93, 815)(94, 810)(95, 728)(96, 736)(97, 818)(98, 731)(99, 730)(100, 732)(101, 824)(102, 734)(103, 828)(104, 827)(105, 821)(106, 817)(107, 783)(108, 831)(109, 739)(110, 740)(111, 779)(112, 836)(113, 742)(114, 743)(115, 840)(116, 842)(117, 843)(118, 838)(119, 746)(120, 754)(121, 846)(122, 749)(123, 748)(124, 750)(125, 852)(126, 752)(127, 856)(128, 855)(129, 849)(130, 845)(131, 759)(132, 859)(133, 757)(134, 758)(135, 863)(136, 760)(137, 866)(138, 766)(139, 839)(140, 763)(141, 864)(142, 764)(143, 765)(144, 872)(145, 778)(146, 769)(147, 847)(148, 879)(149, 777)(150, 876)(151, 880)(152, 773)(153, 884)(154, 854)(155, 776)(156, 775)(157, 888)(158, 889)(159, 780)(160, 860)(161, 891)(162, 882)(163, 893)(164, 784)(165, 896)(166, 790)(167, 811)(168, 787)(169, 894)(170, 788)(171, 789)(172, 902)(173, 802)(174, 793)(175, 819)(176, 909)(177, 801)(178, 906)(179, 910)(180, 797)(181, 914)(182, 826)(183, 800)(184, 799)(185, 918)(186, 919)(187, 804)(188, 832)(189, 921)(190, 912)(191, 807)(192, 813)(193, 920)(194, 809)(195, 928)(196, 899)(197, 898)(198, 926)(199, 924)(200, 816)(201, 932)(202, 933)(203, 907)(204, 822)(205, 905)(206, 934)(207, 820)(208, 823)(209, 925)(210, 834)(211, 940)(212, 825)(213, 917)(214, 943)(215, 915)(216, 829)(217, 830)(218, 895)(219, 833)(220, 948)(221, 835)(222, 841)(223, 890)(224, 837)(225, 954)(226, 869)(227, 868)(228, 952)(229, 950)(230, 844)(231, 958)(232, 959)(233, 877)(234, 850)(235, 875)(236, 960)(237, 848)(238, 851)(239, 951)(240, 862)(241, 966)(242, 853)(243, 887)(244, 969)(245, 885)(246, 857)(247, 858)(248, 865)(249, 861)(250, 974)(251, 971)(252, 871)(253, 881)(254, 870)(255, 972)(256, 867)(257, 978)(258, 961)(259, 979)(260, 873)(261, 874)(262, 878)(263, 956)(264, 970)(265, 981)(266, 976)(267, 985)(268, 883)(269, 973)(270, 986)(271, 886)(272, 962)(273, 949)(274, 953)(275, 967)(276, 892)(277, 945)(278, 901)(279, 911)(280, 900)(281, 946)(282, 897)(283, 991)(284, 935)(285, 992)(286, 903)(287, 904)(288, 908)(289, 930)(290, 944)(291, 994)(292, 989)(293, 998)(294, 913)(295, 947)(296, 999)(297, 916)(298, 936)(299, 923)(300, 927)(301, 941)(302, 922)(303, 1001)(304, 938)(305, 1002)(306, 929)(307, 931)(308, 1003)(309, 937)(310, 997)(311, 1000)(312, 995)(313, 939)(314, 942)(315, 996)(316, 1004)(317, 964)(318, 1005)(319, 955)(320, 957)(321, 1006)(322, 963)(323, 984)(324, 987)(325, 982)(326, 965)(327, 968)(328, 983)(329, 975)(330, 977)(331, 980)(332, 988)(333, 990)(334, 993)(335, 1008)(336, 1007)(337, 1009)(338, 1010)(339, 1011)(340, 1012)(341, 1013)(342, 1014)(343, 1015)(344, 1016)(345, 1017)(346, 1018)(347, 1019)(348, 1020)(349, 1021)(350, 1022)(351, 1023)(352, 1024)(353, 1025)(354, 1026)(355, 1027)(356, 1028)(357, 1029)(358, 1030)(359, 1031)(360, 1032)(361, 1033)(362, 1034)(363, 1035)(364, 1036)(365, 1037)(366, 1038)(367, 1039)(368, 1040)(369, 1041)(370, 1042)(371, 1043)(372, 1044)(373, 1045)(374, 1046)(375, 1047)(376, 1048)(377, 1049)(378, 1050)(379, 1051)(380, 1052)(381, 1053)(382, 1054)(383, 1055)(384, 1056)(385, 1057)(386, 1058)(387, 1059)(388, 1060)(389, 1061)(390, 1062)(391, 1063)(392, 1064)(393, 1065)(394, 1066)(395, 1067)(396, 1068)(397, 1069)(398, 1070)(399, 1071)(400, 1072)(401, 1073)(402, 1074)(403, 1075)(404, 1076)(405, 1077)(406, 1078)(407, 1079)(408, 1080)(409, 1081)(410, 1082)(411, 1083)(412, 1084)(413, 1085)(414, 1086)(415, 1087)(416, 1088)(417, 1089)(418, 1090)(419, 1091)(420, 1092)(421, 1093)(422, 1094)(423, 1095)(424, 1096)(425, 1097)(426, 1098)(427, 1099)(428, 1100)(429, 1101)(430, 1102)(431, 1103)(432, 1104)(433, 1105)(434, 1106)(435, 1107)(436, 1108)(437, 1109)(438, 1110)(439, 1111)(440, 1112)(441, 1113)(442, 1114)(443, 1115)(444, 1116)(445, 1117)(446, 1118)(447, 1119)(448, 1120)(449, 1121)(450, 1122)(451, 1123)(452, 1124)(453, 1125)(454, 1126)(455, 1127)(456, 1128)(457, 1129)(458, 1130)(459, 1131)(460, 1132)(461, 1133)(462, 1134)(463, 1135)(464, 1136)(465, 1137)(466, 1138)(467, 1139)(468, 1140)(469, 1141)(470, 1142)(471, 1143)(472, 1144)(473, 1145)(474, 1146)(475, 1147)(476, 1148)(477, 1149)(478, 1150)(479, 1151)(480, 1152)(481, 1153)(482, 1154)(483, 1155)(484, 1156)(485, 1157)(486, 1158)(487, 1159)(488, 1160)(489, 1161)(490, 1162)(491, 1163)(492, 1164)(493, 1165)(494, 1166)(495, 1167)(496, 1168)(497, 1169)(498, 1170)(499, 1171)(500, 1172)(501, 1173)(502, 1174)(503, 1175)(504, 1176)(505, 1177)(506, 1178)(507, 1179)(508, 1180)(509, 1181)(510, 1182)(511, 1183)(512, 1184)(513, 1185)(514, 1186)(515, 1187)(516, 1188)(517, 1189)(518, 1190)(519, 1191)(520, 1192)(521, 1193)(522, 1194)(523, 1195)(524, 1196)(525, 1197)(526, 1198)(527, 1199)(528, 1200)(529, 1201)(530, 1202)(531, 1203)(532, 1204)(533, 1205)(534, 1206)(535, 1207)(536, 1208)(537, 1209)(538, 1210)(539, 1211)(540, 1212)(541, 1213)(542, 1214)(543, 1215)(544, 1216)(545, 1217)(546, 1218)(547, 1219)(548, 1220)(549, 1221)(550, 1222)(551, 1223)(552, 1224)(553, 1225)(554, 1226)(555, 1227)(556, 1228)(557, 1229)(558, 1230)(559, 1231)(560, 1232)(561, 1233)(562, 1234)(563, 1235)(564, 1236)(565, 1237)(566, 1238)(567, 1239)(568, 1240)(569, 1241)(570, 1242)(571, 1243)(572, 1244)(573, 1245)(574, 1246)(575, 1247)(576, 1248)(577, 1249)(578, 1250)(579, 1251)(580, 1252)(581, 1253)(582, 1254)(583, 1255)(584, 1256)(585, 1257)(586, 1258)(587, 1259)(588, 1260)(589, 1261)(590, 1262)(591, 1263)(592, 1264)(593, 1265)(594, 1266)(595, 1267)(596, 1268)(597, 1269)(598, 1270)(599, 1271)(600, 1272)(601, 1273)(602, 1274)(603, 1275)(604, 1276)(605, 1277)(606, 1278)(607, 1279)(608, 1280)(609, 1281)(610, 1282)(611, 1283)(612, 1284)(613, 1285)(614, 1286)(615, 1287)(616, 1288)(617, 1289)(618, 1290)(619, 1291)(620, 1292)(621, 1293)(622, 1294)(623, 1295)(624, 1296)(625, 1297)(626, 1298)(627, 1299)(628, 1300)(629, 1301)(630, 1302)(631, 1303)(632, 1304)(633, 1305)(634, 1306)(635, 1307)(636, 1308)(637, 1309)(638, 1310)(639, 1311)(640, 1312)(641, 1313)(642, 1314)(643, 1315)(644, 1316)(645, 1317)(646, 1318)(647, 1319)(648, 1320)(649, 1321)(650, 1322)(651, 1323)(652, 1324)(653, 1325)(654, 1326)(655, 1327)(656, 1328)(657, 1329)(658, 1330)(659, 1331)(660, 1332)(661, 1333)(662, 1334)(663, 1335)(664, 1336)(665, 1337)(666, 1338)(667, 1339)(668, 1340)(669, 1341)(670, 1342)(671, 1343)(672, 1344) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E15.1386 Graph:: bipartite v = 224 e = 672 f = 420 degree seq :: [ 4^168, 12^56 ] E15.1386 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = PSL(3,2) : C2 (small group id <336, 208>) Aut = $<672, 1254>$ (small group id <672, 1254>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-3 * Y1 * Y3 * Y1 * Y3^-2, (Y1 * Y3^-2)^3, Y1^-1 * Y3^-3 * Y1 * Y3^-3 * Y1^-1 * Y3^2, (Y3 * Y2^-1)^6, Y3 * Y1^-2 * Y3^2 * Y1^2 * Y3 * Y1^-1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1, Y3^3 * Y1^-2 * Y3^-3 * Y1^-1 * Y3 * Y1^-1 * Y3^-2 * Y1^-1 * Y3 * Y1^-1, Y3^2 * Y1^-2 * Y3 * Y1^-1 * Y3^2 * Y1 * Y3^-2 * Y1^-1 * Y3 * Y1^-2 * Y3^-2 * Y1^-1 ] Map:: polytopal R = (1, 337, 2, 338, 6, 342, 4, 340)(3, 339, 9, 345, 21, 357, 11, 347)(5, 341, 13, 349, 18, 354, 7, 343)(8, 344, 19, 355, 33, 369, 15, 351)(10, 346, 23, 359, 47, 383, 25, 361)(12, 348, 16, 352, 34, 370, 28, 364)(14, 350, 31, 367, 58, 394, 29, 365)(17, 353, 36, 372, 69, 405, 38, 374)(20, 356, 42, 378, 77, 413, 40, 376)(22, 358, 45, 381, 81, 417, 43, 379)(24, 360, 49, 385, 91, 427, 50, 386)(26, 362, 44, 380, 82, 418, 53, 389)(27, 363, 54, 390, 97, 433, 55, 391)(30, 366, 59, 395, 75, 411, 39, 375)(32, 368, 62, 398, 108, 444, 64, 400)(35, 371, 68, 404, 115, 451, 66, 402)(37, 373, 71, 407, 122, 458, 72, 408)(41, 377, 78, 414, 113, 449, 65, 401)(46, 382, 86, 422, 139, 475, 84, 420)(48, 384, 89, 425, 142, 478, 87, 423)(51, 387, 88, 424, 143, 479, 94, 430)(52, 388, 95, 431, 105, 441, 60, 396)(56, 392, 67, 403, 116, 452, 100, 436)(57, 393, 101, 437, 160, 496, 103, 439)(61, 397, 107, 443, 165, 501, 104, 440)(63, 399, 110, 446, 173, 509, 111, 447)(70, 406, 120, 456, 182, 518, 118, 454)(73, 409, 119, 455, 183, 519, 124, 460)(74, 410, 125, 461, 130, 466, 79, 415)(76, 412, 127, 463, 192, 528, 129, 465)(80, 416, 132, 468, 199, 535, 134, 470)(83, 419, 99, 435, 158, 494, 136, 472)(85, 421, 140, 476, 203, 539, 135, 471)(90, 426, 102, 438, 162, 498, 145, 481)(92, 428, 149, 485, 219, 555, 147, 483)(93, 429, 148, 484, 220, 556, 150, 486)(96, 432, 137, 473, 205, 541, 154, 490)(98, 434, 156, 492, 230, 566, 155, 491)(106, 442, 167, 503, 191, 527, 126, 462)(109, 445, 171, 507, 249, 585, 170, 506)(112, 448, 174, 510, 179, 515, 117, 453)(114, 450, 176, 512, 254, 590, 178, 514)(121, 457, 128, 464, 194, 530, 185, 521)(123, 459, 187, 523, 266, 602, 186, 522)(131, 467, 197, 533, 253, 589, 175, 511)(133, 469, 201, 537, 231, 567, 157, 493)(138, 474, 207, 543, 288, 624, 208, 544)(141, 477, 210, 546, 255, 591, 212, 548)(144, 480, 153, 489, 227, 563, 214, 550)(146, 482, 217, 553, 293, 629, 213, 549)(151, 487, 215, 551, 280, 616, 198, 534)(152, 488, 225, 561, 245, 581, 166, 502)(159, 495, 180, 516, 258, 594, 235, 571)(161, 497, 238, 574, 248, 584, 236, 572)(163, 499, 237, 573, 310, 646, 241, 577)(164, 500, 242, 578, 246, 582, 168, 504)(169, 505, 234, 570, 309, 645, 243, 579)(172, 508, 177, 513, 256, 592, 250, 586)(181, 517, 260, 596, 200, 536, 262, 598)(184, 520, 190, 526, 271, 607, 263, 599)(188, 524, 264, 600, 322, 658, 259, 595)(189, 525, 269, 605, 279, 615, 196, 532)(193, 529, 275, 611, 229, 565, 273, 609)(195, 531, 274, 610, 328, 664, 277, 613)(202, 538, 282, 618, 286, 622, 206, 542)(204, 540, 233, 569, 307, 643, 285, 621)(209, 545, 252, 588, 318, 654, 283, 619)(211, 547, 265, 601, 302, 638, 226, 562)(216, 552, 240, 576, 276, 612, 296, 632)(218, 554, 298, 634, 308, 644, 247, 583)(221, 557, 224, 560, 278, 614, 300, 636)(222, 558, 268, 604, 320, 656, 299, 635)(223, 559, 301, 637, 317, 653, 291, 627)(228, 564, 287, 623, 319, 655, 272, 608)(232, 568, 306, 642, 334, 670, 305, 641)(239, 575, 244, 580, 314, 650, 289, 625)(251, 587, 316, 652, 321, 657, 257, 593)(261, 597, 290, 626, 326, 662, 270, 606)(267, 603, 281, 617, 284, 620, 325, 661)(292, 628, 323, 659, 327, 663, 295, 631)(294, 630, 304, 640, 312, 648, 329, 665)(297, 633, 332, 668, 336, 672, 324, 660)(303, 639, 335, 671, 330, 666, 315, 651)(311, 647, 313, 649, 333, 669, 331, 667)(673, 1009)(674, 1010)(675, 1011)(676, 1012)(677, 1013)(678, 1014)(679, 1015)(680, 1016)(681, 1017)(682, 1018)(683, 1019)(684, 1020)(685, 1021)(686, 1022)(687, 1023)(688, 1024)(689, 1025)(690, 1026)(691, 1027)(692, 1028)(693, 1029)(694, 1030)(695, 1031)(696, 1032)(697, 1033)(698, 1034)(699, 1035)(700, 1036)(701, 1037)(702, 1038)(703, 1039)(704, 1040)(705, 1041)(706, 1042)(707, 1043)(708, 1044)(709, 1045)(710, 1046)(711, 1047)(712, 1048)(713, 1049)(714, 1050)(715, 1051)(716, 1052)(717, 1053)(718, 1054)(719, 1055)(720, 1056)(721, 1057)(722, 1058)(723, 1059)(724, 1060)(725, 1061)(726, 1062)(727, 1063)(728, 1064)(729, 1065)(730, 1066)(731, 1067)(732, 1068)(733, 1069)(734, 1070)(735, 1071)(736, 1072)(737, 1073)(738, 1074)(739, 1075)(740, 1076)(741, 1077)(742, 1078)(743, 1079)(744, 1080)(745, 1081)(746, 1082)(747, 1083)(748, 1084)(749, 1085)(750, 1086)(751, 1087)(752, 1088)(753, 1089)(754, 1090)(755, 1091)(756, 1092)(757, 1093)(758, 1094)(759, 1095)(760, 1096)(761, 1097)(762, 1098)(763, 1099)(764, 1100)(765, 1101)(766, 1102)(767, 1103)(768, 1104)(769, 1105)(770, 1106)(771, 1107)(772, 1108)(773, 1109)(774, 1110)(775, 1111)(776, 1112)(777, 1113)(778, 1114)(779, 1115)(780, 1116)(781, 1117)(782, 1118)(783, 1119)(784, 1120)(785, 1121)(786, 1122)(787, 1123)(788, 1124)(789, 1125)(790, 1126)(791, 1127)(792, 1128)(793, 1129)(794, 1130)(795, 1131)(796, 1132)(797, 1133)(798, 1134)(799, 1135)(800, 1136)(801, 1137)(802, 1138)(803, 1139)(804, 1140)(805, 1141)(806, 1142)(807, 1143)(808, 1144)(809, 1145)(810, 1146)(811, 1147)(812, 1148)(813, 1149)(814, 1150)(815, 1151)(816, 1152)(817, 1153)(818, 1154)(819, 1155)(820, 1156)(821, 1157)(822, 1158)(823, 1159)(824, 1160)(825, 1161)(826, 1162)(827, 1163)(828, 1164)(829, 1165)(830, 1166)(831, 1167)(832, 1168)(833, 1169)(834, 1170)(835, 1171)(836, 1172)(837, 1173)(838, 1174)(839, 1175)(840, 1176)(841, 1177)(842, 1178)(843, 1179)(844, 1180)(845, 1181)(846, 1182)(847, 1183)(848, 1184)(849, 1185)(850, 1186)(851, 1187)(852, 1188)(853, 1189)(854, 1190)(855, 1191)(856, 1192)(857, 1193)(858, 1194)(859, 1195)(860, 1196)(861, 1197)(862, 1198)(863, 1199)(864, 1200)(865, 1201)(866, 1202)(867, 1203)(868, 1204)(869, 1205)(870, 1206)(871, 1207)(872, 1208)(873, 1209)(874, 1210)(875, 1211)(876, 1212)(877, 1213)(878, 1214)(879, 1215)(880, 1216)(881, 1217)(882, 1218)(883, 1219)(884, 1220)(885, 1221)(886, 1222)(887, 1223)(888, 1224)(889, 1225)(890, 1226)(891, 1227)(892, 1228)(893, 1229)(894, 1230)(895, 1231)(896, 1232)(897, 1233)(898, 1234)(899, 1235)(900, 1236)(901, 1237)(902, 1238)(903, 1239)(904, 1240)(905, 1241)(906, 1242)(907, 1243)(908, 1244)(909, 1245)(910, 1246)(911, 1247)(912, 1248)(913, 1249)(914, 1250)(915, 1251)(916, 1252)(917, 1253)(918, 1254)(919, 1255)(920, 1256)(921, 1257)(922, 1258)(923, 1259)(924, 1260)(925, 1261)(926, 1262)(927, 1263)(928, 1264)(929, 1265)(930, 1266)(931, 1267)(932, 1268)(933, 1269)(934, 1270)(935, 1271)(936, 1272)(937, 1273)(938, 1274)(939, 1275)(940, 1276)(941, 1277)(942, 1278)(943, 1279)(944, 1280)(945, 1281)(946, 1282)(947, 1283)(948, 1284)(949, 1285)(950, 1286)(951, 1287)(952, 1288)(953, 1289)(954, 1290)(955, 1291)(956, 1292)(957, 1293)(958, 1294)(959, 1295)(960, 1296)(961, 1297)(962, 1298)(963, 1299)(964, 1300)(965, 1301)(966, 1302)(967, 1303)(968, 1304)(969, 1305)(970, 1306)(971, 1307)(972, 1308)(973, 1309)(974, 1310)(975, 1311)(976, 1312)(977, 1313)(978, 1314)(979, 1315)(980, 1316)(981, 1317)(982, 1318)(983, 1319)(984, 1320)(985, 1321)(986, 1322)(987, 1323)(988, 1324)(989, 1325)(990, 1326)(991, 1327)(992, 1328)(993, 1329)(994, 1330)(995, 1331)(996, 1332)(997, 1333)(998, 1334)(999, 1335)(1000, 1336)(1001, 1337)(1002, 1338)(1003, 1339)(1004, 1340)(1005, 1341)(1006, 1342)(1007, 1343)(1008, 1344) L = (1, 675)(2, 679)(3, 682)(4, 684)(5, 673)(6, 687)(7, 689)(8, 674)(9, 676)(10, 696)(11, 698)(12, 699)(13, 701)(14, 677)(15, 704)(16, 678)(17, 709)(18, 711)(19, 712)(20, 680)(21, 715)(22, 681)(23, 683)(24, 686)(25, 723)(26, 724)(27, 718)(28, 728)(29, 729)(30, 685)(31, 722)(32, 735)(33, 737)(34, 738)(35, 688)(36, 690)(37, 692)(38, 745)(39, 746)(40, 748)(41, 691)(42, 744)(43, 752)(44, 693)(45, 756)(46, 694)(47, 759)(48, 695)(49, 697)(50, 765)(51, 714)(52, 762)(53, 768)(54, 700)(55, 733)(56, 771)(57, 774)(58, 776)(59, 777)(60, 702)(61, 703)(62, 705)(63, 707)(64, 757)(65, 784)(66, 786)(67, 706)(68, 783)(69, 790)(70, 708)(71, 710)(72, 764)(73, 740)(74, 793)(75, 798)(76, 800)(77, 766)(78, 802)(79, 713)(80, 805)(81, 807)(82, 808)(83, 716)(84, 810)(85, 717)(86, 727)(87, 813)(88, 719)(89, 817)(90, 720)(91, 819)(92, 721)(93, 758)(94, 823)(95, 725)(96, 825)(97, 827)(98, 726)(99, 829)(100, 831)(101, 730)(102, 732)(103, 835)(104, 836)(105, 838)(106, 731)(107, 769)(108, 842)(109, 734)(110, 736)(111, 795)(112, 844)(113, 847)(114, 849)(115, 796)(116, 851)(117, 739)(118, 853)(119, 741)(120, 857)(121, 742)(122, 858)(123, 743)(124, 860)(125, 747)(126, 862)(127, 749)(128, 751)(129, 867)(130, 868)(131, 750)(132, 753)(133, 755)(134, 818)(135, 874)(136, 876)(137, 754)(138, 782)(139, 822)(140, 780)(141, 883)(142, 885)(143, 886)(144, 760)(145, 888)(146, 761)(147, 890)(148, 763)(149, 794)(150, 895)(151, 896)(152, 767)(153, 898)(154, 900)(155, 901)(156, 903)(157, 770)(158, 772)(159, 906)(160, 908)(161, 773)(162, 775)(163, 792)(164, 911)(165, 915)(166, 916)(167, 918)(168, 778)(169, 779)(170, 920)(171, 922)(172, 781)(173, 880)(174, 785)(175, 924)(176, 787)(177, 789)(178, 904)(179, 929)(180, 788)(181, 933)(182, 913)(183, 935)(184, 791)(185, 912)(186, 937)(187, 845)(188, 940)(189, 797)(190, 942)(191, 944)(192, 945)(193, 799)(194, 801)(195, 843)(196, 950)(197, 952)(198, 803)(199, 932)(200, 804)(201, 806)(202, 953)(203, 955)(204, 956)(205, 958)(206, 809)(207, 811)(208, 962)(209, 812)(210, 814)(211, 816)(212, 894)(213, 964)(214, 966)(215, 815)(216, 873)(217, 871)(218, 947)(219, 971)(220, 972)(221, 820)(222, 821)(223, 910)(224, 865)(225, 974)(226, 824)(227, 826)(228, 839)(229, 919)(230, 977)(231, 968)(232, 828)(233, 830)(234, 980)(235, 959)(236, 921)(237, 832)(238, 961)(239, 833)(240, 834)(241, 969)(242, 837)(243, 985)(244, 840)(245, 987)(246, 976)(247, 841)(248, 963)(249, 949)(250, 948)(251, 846)(252, 989)(253, 991)(254, 882)(255, 848)(256, 850)(257, 992)(258, 994)(259, 852)(260, 854)(261, 856)(262, 939)(263, 995)(264, 855)(265, 884)(266, 997)(267, 859)(268, 927)(269, 998)(270, 861)(271, 863)(272, 869)(273, 902)(274, 864)(275, 893)(276, 866)(277, 983)(278, 870)(279, 1002)(280, 999)(281, 872)(282, 875)(283, 1004)(284, 878)(285, 975)(286, 1005)(287, 877)(288, 986)(289, 879)(290, 934)(291, 881)(292, 978)(293, 996)(294, 1006)(295, 887)(296, 928)(297, 889)(298, 891)(299, 993)(300, 951)(301, 892)(302, 938)(303, 897)(304, 899)(305, 1001)(306, 926)(307, 970)(308, 905)(309, 907)(310, 1003)(311, 909)(312, 914)(313, 1000)(314, 917)(315, 941)(316, 973)(317, 923)(318, 925)(319, 930)(320, 931)(321, 1007)(322, 1008)(323, 965)(324, 936)(325, 957)(326, 960)(327, 943)(328, 984)(329, 946)(330, 988)(331, 954)(332, 982)(333, 981)(334, 967)(335, 979)(336, 990)(337, 1009)(338, 1010)(339, 1011)(340, 1012)(341, 1013)(342, 1014)(343, 1015)(344, 1016)(345, 1017)(346, 1018)(347, 1019)(348, 1020)(349, 1021)(350, 1022)(351, 1023)(352, 1024)(353, 1025)(354, 1026)(355, 1027)(356, 1028)(357, 1029)(358, 1030)(359, 1031)(360, 1032)(361, 1033)(362, 1034)(363, 1035)(364, 1036)(365, 1037)(366, 1038)(367, 1039)(368, 1040)(369, 1041)(370, 1042)(371, 1043)(372, 1044)(373, 1045)(374, 1046)(375, 1047)(376, 1048)(377, 1049)(378, 1050)(379, 1051)(380, 1052)(381, 1053)(382, 1054)(383, 1055)(384, 1056)(385, 1057)(386, 1058)(387, 1059)(388, 1060)(389, 1061)(390, 1062)(391, 1063)(392, 1064)(393, 1065)(394, 1066)(395, 1067)(396, 1068)(397, 1069)(398, 1070)(399, 1071)(400, 1072)(401, 1073)(402, 1074)(403, 1075)(404, 1076)(405, 1077)(406, 1078)(407, 1079)(408, 1080)(409, 1081)(410, 1082)(411, 1083)(412, 1084)(413, 1085)(414, 1086)(415, 1087)(416, 1088)(417, 1089)(418, 1090)(419, 1091)(420, 1092)(421, 1093)(422, 1094)(423, 1095)(424, 1096)(425, 1097)(426, 1098)(427, 1099)(428, 1100)(429, 1101)(430, 1102)(431, 1103)(432, 1104)(433, 1105)(434, 1106)(435, 1107)(436, 1108)(437, 1109)(438, 1110)(439, 1111)(440, 1112)(441, 1113)(442, 1114)(443, 1115)(444, 1116)(445, 1117)(446, 1118)(447, 1119)(448, 1120)(449, 1121)(450, 1122)(451, 1123)(452, 1124)(453, 1125)(454, 1126)(455, 1127)(456, 1128)(457, 1129)(458, 1130)(459, 1131)(460, 1132)(461, 1133)(462, 1134)(463, 1135)(464, 1136)(465, 1137)(466, 1138)(467, 1139)(468, 1140)(469, 1141)(470, 1142)(471, 1143)(472, 1144)(473, 1145)(474, 1146)(475, 1147)(476, 1148)(477, 1149)(478, 1150)(479, 1151)(480, 1152)(481, 1153)(482, 1154)(483, 1155)(484, 1156)(485, 1157)(486, 1158)(487, 1159)(488, 1160)(489, 1161)(490, 1162)(491, 1163)(492, 1164)(493, 1165)(494, 1166)(495, 1167)(496, 1168)(497, 1169)(498, 1170)(499, 1171)(500, 1172)(501, 1173)(502, 1174)(503, 1175)(504, 1176)(505, 1177)(506, 1178)(507, 1179)(508, 1180)(509, 1181)(510, 1182)(511, 1183)(512, 1184)(513, 1185)(514, 1186)(515, 1187)(516, 1188)(517, 1189)(518, 1190)(519, 1191)(520, 1192)(521, 1193)(522, 1194)(523, 1195)(524, 1196)(525, 1197)(526, 1198)(527, 1199)(528, 1200)(529, 1201)(530, 1202)(531, 1203)(532, 1204)(533, 1205)(534, 1206)(535, 1207)(536, 1208)(537, 1209)(538, 1210)(539, 1211)(540, 1212)(541, 1213)(542, 1214)(543, 1215)(544, 1216)(545, 1217)(546, 1218)(547, 1219)(548, 1220)(549, 1221)(550, 1222)(551, 1223)(552, 1224)(553, 1225)(554, 1226)(555, 1227)(556, 1228)(557, 1229)(558, 1230)(559, 1231)(560, 1232)(561, 1233)(562, 1234)(563, 1235)(564, 1236)(565, 1237)(566, 1238)(567, 1239)(568, 1240)(569, 1241)(570, 1242)(571, 1243)(572, 1244)(573, 1245)(574, 1246)(575, 1247)(576, 1248)(577, 1249)(578, 1250)(579, 1251)(580, 1252)(581, 1253)(582, 1254)(583, 1255)(584, 1256)(585, 1257)(586, 1258)(587, 1259)(588, 1260)(589, 1261)(590, 1262)(591, 1263)(592, 1264)(593, 1265)(594, 1266)(595, 1267)(596, 1268)(597, 1269)(598, 1270)(599, 1271)(600, 1272)(601, 1273)(602, 1274)(603, 1275)(604, 1276)(605, 1277)(606, 1278)(607, 1279)(608, 1280)(609, 1281)(610, 1282)(611, 1283)(612, 1284)(613, 1285)(614, 1286)(615, 1287)(616, 1288)(617, 1289)(618, 1290)(619, 1291)(620, 1292)(621, 1293)(622, 1294)(623, 1295)(624, 1296)(625, 1297)(626, 1298)(627, 1299)(628, 1300)(629, 1301)(630, 1302)(631, 1303)(632, 1304)(633, 1305)(634, 1306)(635, 1307)(636, 1308)(637, 1309)(638, 1310)(639, 1311)(640, 1312)(641, 1313)(642, 1314)(643, 1315)(644, 1316)(645, 1317)(646, 1318)(647, 1319)(648, 1320)(649, 1321)(650, 1322)(651, 1323)(652, 1324)(653, 1325)(654, 1326)(655, 1327)(656, 1328)(657, 1329)(658, 1330)(659, 1331)(660, 1332)(661, 1333)(662, 1334)(663, 1335)(664, 1336)(665, 1337)(666, 1338)(667, 1339)(668, 1340)(669, 1341)(670, 1342)(671, 1343)(672, 1344) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E15.1385 Graph:: simple bipartite v = 420 e = 672 f = 224 degree seq :: [ 2^336, 8^84 ] E15.1387 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 3, 12}) Quotient :: halfedge Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X2^2, (X2 * X1)^3, X1^12, (X1^2 * X2 * X1^-1 * X2 * X1^2)^2, (X2 * X1^-6)^2, X1 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^2 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 21, 37, 63, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 79, 104, 91, 54, 31, 17, 8)(6, 13, 25, 43, 73, 119, 103, 128, 78, 46, 26, 14)(9, 18, 32, 55, 92, 106, 64, 105, 86, 51, 29, 16)(12, 23, 41, 69, 113, 101, 61, 102, 118, 72, 42, 24)(19, 34, 58, 97, 108, 66, 38, 65, 107, 96, 57, 33)(22, 39, 67, 109, 99, 59, 35, 60, 100, 112, 68, 40)(28, 49, 83, 132, 181, 142, 90, 143, 186, 135, 84, 50)(30, 52, 87, 138, 176, 127, 80, 129, 171, 123, 75, 44)(45, 76, 124, 172, 222, 166, 120, 167, 217, 162, 115, 70)(48, 81, 130, 177, 140, 88, 53, 89, 141, 180, 131, 82)(56, 94, 146, 195, 246, 188, 137, 154, 206, 198, 147, 95)(71, 116, 163, 218, 204, 152, 159, 213, 265, 209, 156, 110)(74, 121, 168, 223, 174, 125, 77, 126, 175, 226, 169, 122)(85, 136, 187, 244, 194, 145, 93, 144, 193, 240, 183, 133)(98, 150, 202, 259, 261, 205, 153, 111, 157, 210, 203, 151)(114, 160, 214, 269, 220, 164, 117, 165, 221, 272, 215, 161)(134, 184, 241, 297, 250, 192, 237, 295, 318, 291, 234, 178)(139, 190, 248, 266, 315, 284, 228, 179, 235, 292, 249, 191)(148, 199, 256, 306, 258, 201, 149, 200, 257, 304, 253, 196)(155, 207, 262, 310, 267, 211, 158, 212, 268, 312, 263, 208)(170, 227, 283, 327, 288, 232, 189, 247, 302, 324, 280, 224)(173, 230, 286, 255, 305, 320, 274, 225, 281, 252, 287, 231)(182, 238, 277, 219, 276, 242, 185, 243, 298, 314, 271, 239)(197, 254, 279, 323, 301, 245, 300, 325, 282, 326, 303, 251)(216, 273, 319, 336, 322, 278, 229, 285, 328, 335, 317, 270)(233, 289, 329, 307, 309, 293, 236, 294, 330, 308, 260, 290)(264, 313, 299, 332, 334, 316, 275, 321, 296, 331, 333, 311) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 80)(50, 81)(51, 85)(52, 88)(54, 90)(55, 93)(57, 94)(58, 98)(60, 101)(62, 103)(63, 104)(66, 105)(67, 110)(68, 111)(69, 114)(72, 117)(73, 120)(75, 121)(76, 125)(78, 127)(79, 128)(82, 129)(83, 133)(84, 134)(86, 137)(87, 139)(89, 142)(91, 106)(92, 143)(95, 144)(96, 148)(97, 149)(99, 150)(100, 152)(102, 119)(107, 153)(108, 154)(109, 155)(112, 158)(113, 159)(115, 160)(116, 164)(118, 166)(122, 167)(123, 170)(124, 173)(126, 176)(130, 178)(131, 179)(132, 182)(135, 185)(136, 188)(138, 189)(140, 190)(141, 192)(145, 186)(146, 196)(147, 197)(151, 200)(156, 207)(157, 211)(161, 213)(162, 216)(163, 219)(165, 222)(168, 224)(169, 225)(171, 228)(172, 229)(174, 230)(175, 232)(177, 233)(180, 236)(181, 237)(183, 238)(184, 242)(187, 245)(191, 247)(193, 251)(194, 243)(195, 252)(198, 255)(199, 205)(201, 206)(202, 208)(203, 260)(204, 212)(209, 264)(210, 266)(214, 270)(215, 271)(217, 274)(218, 275)(220, 276)(221, 278)(223, 279)(226, 282)(227, 284)(231, 285)(234, 289)(235, 293)(239, 295)(240, 296)(241, 269)(244, 299)(246, 300)(248, 290)(249, 263)(250, 294)(253, 287)(254, 286)(256, 307)(257, 308)(258, 305)(259, 292)(261, 309)(262, 311)(265, 314)(267, 315)(268, 316)(272, 318)(273, 320)(277, 321)(280, 323)(281, 325)(283, 310)(288, 326)(291, 322)(297, 317)(298, 313)(301, 332)(302, 312)(303, 331)(304, 328)(306, 319)(324, 334)(327, 333)(329, 336)(330, 335) local type(s) :: { ( 3^12 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 28 e = 168 f = 112 degree seq :: [ 12^28 ] E15.1388 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 3, 12}) Quotient :: halfedge Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X2^2, X1^3, (X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1 * X2 * X1)^2, X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1, (X1^-1 * X2)^12 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(59, 83, 84)(60, 85, 86)(61, 87, 88)(62, 89, 90)(63, 91, 92)(64, 93, 94)(65, 95, 96)(66, 97, 98)(75, 107, 108)(76, 109, 110)(77, 111, 112)(78, 113, 114)(79, 115, 116)(80, 117, 118)(81, 119, 120)(82, 121, 122)(99, 139, 140)(100, 141, 142)(101, 143, 144)(102, 145, 146)(103, 147, 148)(104, 149, 150)(105, 151, 152)(106, 153, 154)(123, 242, 240)(124, 235, 217)(125, 244, 162)(126, 194, 318)(127, 216, 311)(128, 247, 335)(129, 249, 191)(130, 241, 224)(131, 231, 333)(132, 252, 178)(133, 253, 155)(134, 165, 226)(135, 177, 260)(136, 255, 228)(137, 257, 193)(138, 258, 305)(156, 211, 214)(157, 233, 237)(158, 196, 199)(159, 271, 272)(160, 180, 183)(161, 256, 273)(163, 186, 189)(164, 275, 276)(166, 171, 175)(167, 220, 280)(168, 206, 209)(169, 234, 282)(170, 262, 225)(172, 223, 229)(173, 266, 286)(174, 287, 289)(176, 204, 292)(179, 293, 296)(181, 298, 299)(182, 300, 301)(184, 248, 285)(185, 250, 259)(187, 307, 254)(188, 308, 309)(190, 310, 246)(192, 227, 316)(195, 205, 221)(197, 320, 321)(198, 313, 319)(200, 314, 281)(201, 232, 322)(202, 263, 324)(203, 210, 326)(207, 327, 219)(208, 306, 328)(212, 270, 261)(213, 239, 304)(215, 294, 267)(218, 265, 302)(222, 295, 269)(230, 297, 332)(236, 268, 288)(238, 303, 264)(243, 279, 329)(245, 334, 330)(251, 277, 290)(274, 284, 325)(278, 317, 283)(291, 336, 312)(315, 323, 331) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(107, 222)(108, 224)(109, 226)(110, 176)(111, 228)(112, 230)(113, 232)(114, 212)(115, 193)(116, 234)(117, 211)(118, 225)(119, 209)(120, 238)(121, 210)(122, 240)(139, 258)(140, 261)(141, 262)(142, 167)(143, 264)(144, 208)(145, 265)(146, 235)(147, 203)(148, 266)(149, 233)(150, 244)(151, 229)(152, 216)(153, 231)(154, 269)(155, 188)(156, 198)(157, 182)(158, 213)(159, 173)(160, 236)(161, 178)(162, 274)(163, 267)(164, 169)(165, 277)(166, 278)(168, 281)(170, 283)(171, 284)(172, 285)(174, 288)(175, 290)(177, 246)(179, 294)(180, 297)(181, 292)(183, 302)(184, 217)(185, 304)(186, 306)(187, 280)(189, 249)(190, 241)(191, 312)(192, 314)(194, 279)(195, 319)(196, 247)(197, 318)(199, 322)(200, 270)(201, 243)(202, 248)(204, 245)(205, 301)(206, 308)(207, 273)(214, 329)(215, 320)(218, 330)(219, 310)(220, 291)(221, 309)(223, 313)(227, 276)(237, 334)(239, 298)(242, 331)(250, 286)(251, 324)(252, 287)(253, 336)(254, 326)(255, 271)(256, 303)(257, 299)(259, 328)(260, 300)(263, 272)(268, 307)(275, 311)(282, 293)(289, 335)(295, 315)(296, 332)(305, 323)(316, 325)(317, 327)(321, 333) local type(s) :: { ( 12^3 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 112 e = 168 f = 28 degree seq :: [ 3^112 ] E15.1389 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X1^2, X2^3, (X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1)^2, X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1, (X2^-1 * X1)^12 ] Map:: polytopal R = (1, 2)(3, 7)(4, 8)(5, 9)(6, 10)(11, 19)(12, 20)(13, 21)(14, 22)(15, 23)(16, 24)(17, 25)(18, 26)(27, 43)(28, 44)(29, 45)(30, 46)(31, 47)(32, 48)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(59, 91)(60, 92)(61, 93)(62, 94)(63, 95)(64, 96)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(123, 201)(124, 157)(125, 202)(126, 235)(127, 206)(128, 234)(129, 187)(130, 236)(131, 238)(132, 169)(133, 239)(134, 241)(135, 164)(136, 240)(137, 243)(138, 244)(139, 233)(140, 155)(141, 245)(142, 247)(143, 213)(144, 246)(145, 209)(146, 216)(147, 250)(148, 171)(149, 194)(150, 218)(151, 160)(152, 221)(153, 195)(154, 197)(156, 255)(158, 231)(159, 263)(161, 270)(162, 190)(163, 272)(165, 277)(166, 279)(167, 223)(168, 251)(170, 193)(172, 175)(173, 205)(174, 292)(176, 295)(177, 282)(178, 199)(179, 300)(180, 297)(181, 220)(182, 302)(183, 275)(184, 191)(185, 305)(186, 304)(188, 212)(189, 276)(192, 269)(196, 283)(198, 256)(200, 262)(203, 293)(204, 268)(207, 318)(208, 317)(210, 308)(211, 230)(214, 226)(215, 321)(217, 288)(219, 261)(222, 298)(224, 323)(225, 327)(227, 259)(228, 314)(229, 330)(232, 248)(237, 260)(242, 266)(249, 264)(252, 258)(253, 285)(254, 331)(257, 290)(265, 310)(267, 315)(271, 326)(273, 336)(274, 333)(278, 328)(280, 332)(281, 334)(284, 319)(286, 324)(287, 291)(289, 307)(294, 313)(296, 316)(299, 325)(301, 306)(303, 312)(309, 320)(311, 329)(322, 335)(337, 339, 340)(338, 341, 342)(343, 347, 348)(344, 349, 350)(345, 351, 352)(346, 353, 354)(355, 363, 364)(356, 365, 366)(357, 367, 368)(358, 369, 370)(359, 371, 372)(360, 373, 374)(361, 375, 376)(362, 377, 378)(379, 395, 396)(380, 397, 398)(381, 399, 400)(382, 401, 402)(383, 403, 404)(384, 405, 406)(385, 407, 408)(386, 409, 410)(387, 411, 412)(388, 413, 414)(389, 415, 416)(390, 417, 418)(391, 419, 420)(392, 421, 422)(393, 423, 424)(394, 425, 426)(427, 459, 460)(428, 461, 462)(429, 463, 464)(430, 465, 466)(431, 467, 468)(432, 469, 470)(433, 471, 472)(434, 473, 474)(435, 475, 476)(436, 477, 478)(437, 479, 480)(438, 481, 482)(439, 483, 484)(440, 485, 486)(441, 487, 488)(442, 489, 490)(443, 506, 580)(444, 552, 658)(445, 554, 543)(446, 556, 534)(447, 557, 541)(448, 558, 660)(449, 559, 661)(450, 561, 493)(451, 531, 591)(452, 563, 665)(453, 547, 656)(454, 550, 538)(455, 565, 628)(456, 548, 542)(457, 567, 574)(458, 569, 498)(491, 572, 590)(492, 592, 594)(494, 596, 598)(495, 600, 602)(496, 603, 605)(497, 601, 607)(499, 593, 609)(500, 610, 612)(501, 597, 614)(502, 589, 616)(503, 617, 619)(504, 604, 620)(505, 621, 623)(507, 624, 625)(508, 533, 537)(509, 626, 627)(510, 629, 630)(511, 526, 529)(512, 553, 564)(513, 632, 634)(514, 566, 635)(515, 595, 622)(516, 560, 568)(517, 611, 637)(518, 539, 546)(519, 639, 575)(520, 549, 576)(521, 581, 577)(522, 544, 551)(523, 618, 642)(524, 555, 643)(525, 644, 645)(527, 646, 647)(528, 638, 648)(530, 540, 649)(532, 650, 582)(535, 585, 583)(536, 631, 652)(545, 633, 655)(562, 640, 664)(570, 584, 668)(571, 587, 573)(578, 636, 659)(579, 599, 586)(588, 615, 670)(606, 666, 663)(608, 669, 667)(613, 651, 671)(641, 653, 662)(654, 657, 672) L = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 24, 24 ), ( 24^3 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 280 e = 336 f = 28 degree seq :: [ 2^168, 3^112 ] E15.1390 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X1^3, (X2^-1 * X1^-1)^2, (X2^2 * X1^-1 * X2^3)^2, X2^12, X2 * X1^-1 * X2^-2 * X1 * X2^-2 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1 * X2^2 * X1^-1, X2^-2 * X1^-1 * X2^5 * X1 * X2^-1 * X1 * X2^6 * X1 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 12, 6)(7, 15, 11)(9, 18, 20)(13, 25, 23)(14, 24, 28)(16, 31, 29)(17, 33, 21)(19, 36, 38)(22, 30, 42)(26, 47, 45)(27, 49, 51)(32, 57, 55)(34, 61, 59)(35, 63, 39)(37, 66, 68)(40, 60, 72)(41, 73, 75)(43, 46, 78)(44, 79, 52)(48, 85, 83)(50, 88, 90)(53, 56, 94)(54, 95, 76)(58, 101, 99)(62, 107, 105)(64, 111, 109)(65, 113, 69)(67, 116, 102)(70, 110, 121)(71, 122, 124)(74, 127, 129)(77, 132, 134)(80, 138, 136)(81, 84, 140)(82, 141, 135)(86, 128, 143)(87, 144, 91)(89, 147, 108)(92, 137, 152)(93, 153, 155)(96, 159, 157)(97, 100, 161)(98, 162, 156)(103, 106, 165)(104, 166, 125)(112, 175, 173)(114, 178, 176)(115, 180, 118)(117, 148, 170)(119, 177, 182)(120, 183, 184)(123, 187, 142)(126, 190, 130)(131, 158, 192)(133, 194, 163)(139, 200, 201)(145, 205, 203)(146, 207, 149)(150, 204, 209)(151, 210, 211)(154, 214, 168)(160, 220, 221)(164, 223, 225)(167, 229, 227)(169, 231, 226)(171, 174, 233)(172, 234, 185)(179, 242, 240)(181, 244, 243)(186, 249, 188)(189, 228, 251)(191, 253, 252)(193, 255, 195)(196, 202, 260)(197, 199, 262)(198, 263, 212)(206, 257, 269)(208, 272, 271)(213, 277, 215)(216, 222, 282)(217, 219, 284)(218, 285, 254)(224, 290, 236)(230, 279, 296)(232, 273, 268)(235, 287, 286)(237, 301, 299)(238, 241, 302)(239, 283, 245)(246, 308, 247)(248, 267, 270)(250, 310, 288)(256, 311, 294)(258, 291, 289)(259, 315, 316)(261, 293, 295)(264, 280, 265)(266, 278, 317)(274, 323, 275)(276, 312, 313)(281, 326, 327)(292, 297, 330)(298, 318, 304)(300, 328, 333)(303, 331, 325)(305, 320, 335)(306, 307, 336)(309, 324, 332)(314, 329, 319)(321, 322, 334)(337, 339, 345, 355, 373, 403, 453, 422, 384, 362, 349, 341)(338, 342, 350, 363, 386, 425, 484, 438, 394, 368, 352, 343)(340, 347, 358, 377, 410, 464, 506, 444, 398, 370, 353, 344)(346, 357, 376, 407, 459, 421, 479, 465, 448, 400, 371, 354)(348, 359, 379, 413, 469, 437, 452, 404, 454, 416, 380, 360)(351, 365, 389, 429, 490, 443, 483, 426, 485, 432, 390, 366)(356, 375, 406, 456, 420, 383, 419, 478, 515, 450, 401, 372)(361, 381, 417, 475, 517, 451, 402, 374, 405, 455, 418, 382)(364, 388, 428, 487, 436, 393, 435, 499, 542, 481, 423, 385)(367, 391, 433, 496, 544, 482, 424, 387, 427, 486, 434, 392)(369, 395, 439, 500, 560, 511, 463, 411, 466, 503, 440, 396)(378, 412, 467, 505, 442, 397, 441, 504, 566, 527, 462, 409)(399, 445, 507, 568, 634, 578, 523, 460, 524, 571, 508, 446)(408, 461, 525, 573, 510, 447, 509, 572, 636, 586, 522, 458)(414, 471, 532, 595, 535, 474, 516, 579, 642, 592, 529, 468)(415, 472, 533, 597, 650, 593, 530, 470, 531, 594, 534, 473)(430, 492, 552, 617, 555, 495, 543, 607, 657, 614, 549, 489)(431, 493, 553, 619, 661, 615, 550, 491, 551, 616, 554, 494)(449, 512, 574, 621, 600, 536, 476, 520, 583, 639, 575, 513)(457, 521, 584, 641, 577, 514, 576, 640, 659, 645, 582, 519)(477, 518, 581, 620, 663, 643, 580, 537, 601, 613, 602, 538)(480, 539, 603, 570, 622, 556, 497, 547, 611, 654, 604, 540)(488, 548, 612, 656, 606, 541, 605, 655, 666, 660, 610, 546)(498, 545, 609, 569, 635, 658, 608, 557, 623, 585, 624, 558)(501, 562, 628, 665, 631, 565, 526, 588, 648, 599, 625, 559)(502, 563, 629, 598, 652, 664, 626, 561, 627, 591, 630, 564)(528, 590, 638, 671, 649, 589, 632, 667, 644, 668, 633, 567)(587, 647, 672, 662, 618, 646, 669, 651, 596, 653, 670, 637) L = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 4^3 ), ( 4^12 ) } Outer automorphisms :: chiral Dual of E15.1392 Transitivity :: ET+ Graph:: simple bipartite v = 140 e = 336 f = 168 degree seq :: [ 3^112, 12^28 ] E15.1391 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X2^2, (X2 * X1)^3, X1^12, X1^-3 * X2 * X1^6 * X2 * X1^-3, X1 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 * X2 * X1^-2 * X2 * X1^-2 * X2 * X1 ] Map:: polytopal R = (1, 2, 5, 11, 21, 37, 63, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 79, 104, 91, 54, 31, 17, 8)(6, 13, 25, 43, 73, 119, 103, 128, 78, 46, 26, 14)(9, 18, 32, 55, 92, 106, 64, 105, 86, 51, 29, 16)(12, 23, 41, 69, 113, 101, 61, 102, 118, 72, 42, 24)(19, 34, 58, 97, 108, 66, 38, 65, 107, 96, 57, 33)(22, 39, 67, 109, 99, 59, 35, 60, 100, 112, 68, 40)(28, 49, 83, 132, 181, 142, 90, 143, 186, 135, 84, 50)(30, 52, 87, 138, 176, 127, 80, 129, 171, 123, 75, 44)(45, 76, 124, 172, 222, 166, 120, 167, 217, 162, 115, 70)(48, 81, 130, 177, 140, 88, 53, 89, 141, 180, 131, 82)(56, 94, 146, 195, 246, 188, 137, 154, 206, 198, 147, 95)(71, 116, 163, 218, 204, 152, 159, 213, 265, 209, 156, 110)(74, 121, 168, 223, 174, 125, 77, 126, 175, 226, 169, 122)(85, 136, 187, 244, 194, 145, 93, 144, 193, 240, 183, 133)(98, 150, 202, 259, 261, 205, 153, 111, 157, 210, 203, 151)(114, 160, 214, 269, 220, 164, 117, 165, 221, 272, 215, 161)(134, 184, 241, 297, 250, 192, 237, 295, 318, 291, 234, 178)(139, 190, 248, 266, 315, 284, 228, 179, 235, 292, 249, 191)(148, 199, 256, 306, 258, 201, 149, 200, 257, 304, 253, 196)(155, 207, 262, 310, 267, 211, 158, 212, 268, 312, 263, 208)(170, 227, 283, 327, 288, 232, 189, 247, 302, 324, 280, 224)(173, 230, 286, 255, 305, 320, 274, 225, 281, 252, 287, 231)(182, 238, 277, 219, 276, 242, 185, 243, 298, 314, 271, 239)(197, 254, 279, 323, 301, 245, 300, 325, 282, 326, 303, 251)(216, 273, 319, 336, 322, 278, 229, 285, 328, 335, 317, 270)(233, 289, 329, 307, 309, 293, 236, 294, 330, 308, 260, 290)(264, 313, 299, 332, 334, 316, 275, 321, 296, 331, 333, 311)(337, 339)(338, 342)(340, 345)(341, 348)(343, 352)(344, 349)(346, 355)(347, 358)(350, 359)(351, 364)(353, 366)(354, 369)(356, 371)(357, 374)(360, 375)(361, 380)(362, 381)(363, 384)(365, 385)(367, 389)(368, 392)(370, 395)(372, 397)(373, 400)(376, 401)(377, 406)(378, 407)(379, 410)(382, 413)(383, 416)(386, 417)(387, 421)(388, 424)(390, 426)(391, 429)(393, 430)(394, 434)(396, 437)(398, 439)(399, 440)(402, 441)(403, 446)(404, 447)(405, 450)(408, 453)(409, 456)(411, 457)(412, 461)(414, 463)(415, 464)(418, 465)(419, 469)(420, 470)(422, 473)(423, 475)(425, 478)(427, 442)(428, 479)(431, 480)(432, 484)(433, 485)(435, 486)(436, 488)(438, 455)(443, 489)(444, 490)(445, 491)(448, 494)(449, 495)(451, 496)(452, 500)(454, 502)(458, 503)(459, 506)(460, 509)(462, 512)(466, 514)(467, 515)(468, 518)(471, 521)(472, 524)(474, 525)(476, 526)(477, 528)(481, 522)(482, 532)(483, 533)(487, 536)(492, 543)(493, 547)(497, 549)(498, 552)(499, 555)(501, 558)(504, 560)(505, 561)(507, 564)(508, 565)(510, 566)(511, 568)(513, 569)(516, 572)(517, 573)(519, 574)(520, 578)(523, 581)(527, 583)(529, 587)(530, 579)(531, 588)(534, 591)(535, 541)(537, 542)(538, 544)(539, 596)(540, 548)(545, 600)(546, 602)(550, 606)(551, 607)(553, 610)(554, 611)(556, 612)(557, 614)(559, 615)(562, 618)(563, 620)(567, 621)(570, 625)(571, 629)(575, 631)(576, 632)(577, 605)(580, 635)(582, 636)(584, 626)(585, 599)(586, 630)(589, 623)(590, 622)(592, 643)(593, 644)(594, 641)(595, 628)(597, 645)(598, 647)(601, 650)(603, 651)(604, 652)(608, 654)(609, 656)(613, 657)(616, 659)(617, 661)(619, 646)(624, 662)(627, 658)(633, 653)(634, 649)(637, 668)(638, 648)(639, 667)(640, 664)(642, 655)(660, 670)(663, 669)(665, 672)(666, 671) L = (1, 337)(2, 338)(3, 339)(4, 340)(5, 341)(6, 342)(7, 343)(8, 344)(9, 345)(10, 346)(11, 347)(12, 348)(13, 349)(14, 350)(15, 351)(16, 352)(17, 353)(18, 354)(19, 355)(20, 356)(21, 357)(22, 358)(23, 359)(24, 360)(25, 361)(26, 362)(27, 363)(28, 364)(29, 365)(30, 366)(31, 367)(32, 368)(33, 369)(34, 370)(35, 371)(36, 372)(37, 373)(38, 374)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 380)(45, 381)(46, 382)(47, 383)(48, 384)(49, 385)(50, 386)(51, 387)(52, 388)(53, 389)(54, 390)(55, 391)(56, 392)(57, 393)(58, 394)(59, 395)(60, 396)(61, 397)(62, 398)(63, 399)(64, 400)(65, 401)(66, 402)(67, 403)(68, 404)(69, 405)(70, 406)(71, 407)(72, 408)(73, 409)(74, 410)(75, 411)(76, 412)(77, 413)(78, 414)(79, 415)(80, 416)(81, 417)(82, 418)(83, 419)(84, 420)(85, 421)(86, 422)(87, 423)(88, 424)(89, 425)(90, 426)(91, 427)(92, 428)(93, 429)(94, 430)(95, 431)(96, 432)(97, 433)(98, 434)(99, 435)(100, 436)(101, 437)(102, 438)(103, 439)(104, 440)(105, 441)(106, 442)(107, 443)(108, 444)(109, 445)(110, 446)(111, 447)(112, 448)(113, 449)(114, 450)(115, 451)(116, 452)(117, 453)(118, 454)(119, 455)(120, 456)(121, 457)(122, 458)(123, 459)(124, 460)(125, 461)(126, 462)(127, 463)(128, 464)(129, 465)(130, 466)(131, 467)(132, 468)(133, 469)(134, 470)(135, 471)(136, 472)(137, 473)(138, 474)(139, 475)(140, 476)(141, 477)(142, 478)(143, 479)(144, 480)(145, 481)(146, 482)(147, 483)(148, 484)(149, 485)(150, 486)(151, 487)(152, 488)(153, 489)(154, 490)(155, 491)(156, 492)(157, 493)(158, 494)(159, 495)(160, 496)(161, 497)(162, 498)(163, 499)(164, 500)(165, 501)(166, 502)(167, 503)(168, 504)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 6, 6 ), ( 6^12 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 196 e = 336 f = 112 degree seq :: [ 2^168, 12^28 ] E15.1392 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X1^2, X2^3, (X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1)^2, X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1, (X2^-1 * X1)^12 ] Map:: polytopal non-degenerate R = (1, 337, 2, 338)(3, 339, 7, 343)(4, 340, 8, 344)(5, 341, 9, 345)(6, 342, 10, 346)(11, 347, 19, 355)(12, 348, 20, 356)(13, 349, 21, 357)(14, 350, 22, 358)(15, 351, 23, 359)(16, 352, 24, 360)(17, 353, 25, 361)(18, 354, 26, 362)(27, 363, 43, 379)(28, 364, 44, 380)(29, 365, 45, 381)(30, 366, 46, 382)(31, 367, 47, 383)(32, 368, 48, 384)(33, 369, 49, 385)(34, 370, 50, 386)(35, 371, 51, 387)(36, 372, 52, 388)(37, 373, 53, 389)(38, 374, 54, 390)(39, 375, 55, 391)(40, 376, 56, 392)(41, 377, 57, 393)(42, 378, 58, 394)(59, 395, 91, 427)(60, 396, 92, 428)(61, 397, 93, 429)(62, 398, 94, 430)(63, 399, 95, 431)(64, 400, 96, 432)(65, 401, 97, 433)(66, 402, 98, 434)(67, 403, 99, 435)(68, 404, 100, 436)(69, 405, 101, 437)(70, 406, 102, 438)(71, 407, 103, 439)(72, 408, 104, 440)(73, 409, 105, 441)(74, 410, 106, 442)(75, 411, 107, 443)(76, 412, 108, 444)(77, 413, 109, 445)(78, 414, 110, 446)(79, 415, 111, 447)(80, 416, 112, 448)(81, 417, 113, 449)(82, 418, 114, 450)(83, 419, 115, 451)(84, 420, 116, 452)(85, 421, 117, 453)(86, 422, 118, 454)(87, 423, 119, 455)(88, 424, 120, 456)(89, 425, 121, 457)(90, 426, 122, 458)(123, 459, 242, 578)(124, 460, 183, 519)(125, 461, 155, 491)(126, 462, 244, 580)(127, 463, 246, 582)(128, 464, 247, 583)(129, 465, 245, 581)(130, 466, 204, 540)(131, 467, 218, 554)(132, 468, 211, 547)(133, 469, 168, 504)(134, 470, 203, 539)(135, 471, 253, 589)(136, 472, 254, 590)(137, 473, 252, 588)(138, 474, 257, 593)(139, 475, 240, 576)(140, 476, 213, 549)(141, 477, 156, 492)(142, 478, 259, 595)(143, 479, 201, 537)(144, 480, 261, 597)(145, 481, 260, 596)(146, 482, 224, 560)(147, 483, 184, 520)(148, 484, 255, 591)(149, 485, 171, 507)(150, 486, 225, 561)(151, 487, 265, 601)(152, 488, 228, 564)(153, 489, 233, 569)(154, 490, 268, 604)(157, 493, 219, 555)(158, 494, 192, 528)(159, 495, 185, 521)(160, 496, 214, 550)(161, 497, 180, 516)(162, 498, 227, 563)(163, 499, 198, 534)(164, 500, 176, 512)(165, 501, 210, 546)(166, 502, 170, 506)(167, 503, 182, 518)(169, 505, 273, 609)(172, 508, 275, 611)(173, 509, 188, 524)(174, 510, 229, 565)(175, 511, 279, 615)(177, 513, 237, 573)(178, 514, 283, 619)(179, 515, 235, 571)(181, 517, 266, 602)(186, 522, 291, 627)(187, 523, 292, 628)(189, 525, 217, 553)(190, 526, 297, 633)(191, 527, 300, 636)(193, 529, 302, 638)(194, 530, 303, 639)(195, 531, 222, 558)(196, 532, 306, 642)(197, 533, 308, 644)(199, 535, 311, 647)(200, 536, 294, 630)(202, 538, 312, 648)(205, 541, 296, 632)(206, 542, 314, 650)(207, 543, 241, 577)(208, 544, 316, 652)(209, 545, 317, 653)(212, 548, 288, 624)(215, 551, 319, 655)(216, 552, 278, 614)(220, 556, 236, 572)(221, 557, 299, 635)(223, 559, 324, 660)(226, 562, 305, 641)(230, 566, 272, 608)(231, 567, 307, 643)(232, 568, 284, 620)(234, 570, 331, 667)(238, 574, 258, 594)(239, 575, 310, 646)(243, 579, 328, 664)(248, 584, 333, 669)(249, 585, 298, 634)(250, 586, 329, 665)(251, 587, 335, 671)(256, 592, 270, 606)(262, 598, 277, 613)(263, 599, 327, 663)(264, 600, 332, 668)(267, 603, 285, 621)(269, 605, 325, 661)(271, 607, 322, 658)(274, 610, 326, 662)(276, 612, 334, 670)(280, 616, 323, 659)(281, 617, 289, 625)(282, 618, 318, 654)(286, 622, 290, 626)(287, 623, 313, 649)(293, 629, 301, 637)(295, 631, 330, 666)(304, 640, 315, 651)(309, 645, 320, 656)(321, 657, 336, 672) L = (1, 339)(2, 341)(3, 340)(4, 337)(5, 342)(6, 338)(7, 347)(8, 349)(9, 351)(10, 353)(11, 348)(12, 343)(13, 350)(14, 344)(15, 352)(16, 345)(17, 354)(18, 346)(19, 363)(20, 365)(21, 367)(22, 369)(23, 371)(24, 373)(25, 375)(26, 377)(27, 364)(28, 355)(29, 366)(30, 356)(31, 368)(32, 357)(33, 370)(34, 358)(35, 372)(36, 359)(37, 374)(38, 360)(39, 376)(40, 361)(41, 378)(42, 362)(43, 395)(44, 397)(45, 399)(46, 401)(47, 403)(48, 405)(49, 407)(50, 409)(51, 411)(52, 413)(53, 415)(54, 417)(55, 419)(56, 421)(57, 423)(58, 425)(59, 396)(60, 379)(61, 398)(62, 380)(63, 400)(64, 381)(65, 402)(66, 382)(67, 404)(68, 383)(69, 406)(70, 384)(71, 408)(72, 385)(73, 410)(74, 386)(75, 412)(76, 387)(77, 414)(78, 388)(79, 416)(80, 389)(81, 418)(82, 390)(83, 420)(84, 391)(85, 422)(86, 392)(87, 424)(88, 393)(89, 426)(90, 394)(91, 459)(92, 461)(93, 463)(94, 465)(95, 467)(96, 469)(97, 471)(98, 473)(99, 475)(100, 477)(101, 479)(102, 481)(103, 483)(104, 485)(105, 487)(106, 489)(107, 551)(108, 560)(109, 561)(110, 562)(111, 564)(112, 565)(113, 567)(114, 568)(115, 569)(116, 555)(117, 553)(118, 570)(119, 571)(120, 573)(121, 575)(122, 576)(123, 460)(124, 427)(125, 462)(126, 428)(127, 464)(128, 429)(129, 466)(130, 430)(131, 468)(132, 431)(133, 470)(134, 432)(135, 472)(136, 433)(137, 474)(138, 434)(139, 476)(140, 435)(141, 478)(142, 436)(143, 480)(144, 437)(145, 482)(146, 438)(147, 484)(148, 439)(149, 486)(150, 440)(151, 488)(152, 441)(153, 490)(154, 442)(155, 454)(156, 539)(157, 527)(158, 446)(159, 533)(160, 511)(161, 545)(162, 505)(163, 580)(164, 595)(165, 605)(166, 607)(167, 587)(168, 558)(169, 508)(170, 600)(171, 524)(172, 498)(173, 612)(174, 577)(175, 514)(176, 616)(177, 518)(178, 496)(179, 620)(180, 622)(181, 623)(182, 618)(183, 450)(184, 588)(185, 626)(186, 458)(187, 629)(188, 610)(189, 631)(190, 634)(191, 530)(192, 637)(193, 502)(194, 493)(195, 640)(196, 643)(197, 536)(198, 645)(199, 516)(200, 495)(201, 590)(202, 579)(203, 542)(204, 649)(205, 500)(206, 492)(207, 651)(208, 589)(209, 548)(210, 586)(211, 521)(212, 497)(213, 540)(214, 654)(215, 593)(216, 656)(217, 657)(218, 457)(219, 658)(220, 604)(221, 659)(222, 608)(223, 528)(224, 661)(225, 584)(226, 494)(227, 662)(228, 647)(229, 636)(230, 665)(231, 666)(232, 519)(233, 660)(234, 491)(235, 599)(236, 627)(237, 582)(238, 668)(239, 554)(240, 522)(241, 614)(242, 556)(243, 594)(244, 598)(245, 543)(246, 456)(247, 633)(248, 445)(249, 670)(250, 601)(251, 592)(252, 625)(253, 602)(254, 638)(255, 550)(256, 503)(257, 443)(258, 538)(259, 541)(260, 585)(261, 642)(262, 499)(263, 455)(264, 603)(265, 546)(266, 544)(267, 506)(268, 578)(269, 606)(270, 501)(271, 529)(272, 504)(273, 672)(274, 507)(275, 566)(276, 613)(277, 509)(278, 510)(279, 597)(280, 617)(281, 512)(282, 513)(283, 552)(284, 621)(285, 515)(286, 535)(287, 624)(288, 517)(289, 520)(290, 547)(291, 655)(292, 532)(293, 630)(294, 523)(295, 632)(296, 525)(297, 644)(298, 635)(299, 526)(300, 448)(301, 559)(302, 537)(303, 557)(304, 641)(305, 531)(306, 615)(307, 628)(308, 583)(309, 646)(310, 534)(311, 447)(312, 653)(313, 549)(314, 574)(315, 581)(316, 609)(317, 669)(318, 591)(319, 572)(320, 619)(321, 453)(322, 452)(323, 639)(324, 451)(325, 444)(326, 663)(327, 563)(328, 671)(329, 611)(330, 449)(331, 664)(332, 650)(333, 648)(334, 596)(335, 667)(336, 652) local type(s) :: { ( 3, 12, 3, 12 ) } Outer automorphisms :: chiral Dual of E15.1390 Transitivity :: ET+ VT+ Graph:: simple v = 168 e = 336 f = 140 degree seq :: [ 4^168 ] E15.1393 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X1^3, (X2^-1 * X1^-1)^2, (X2^2 * X1^-1 * X2^3)^2, X2^12, X2 * X1^-1 * X2^-2 * X1 * X2^-2 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1 * X2^2 * X1^-1, X2^-2 * X1^-1 * X2^5 * X1 * X2^-1 * X1 * X2^6 * X1 ] Map:: R = (1, 337, 2, 338, 4, 340)(3, 339, 8, 344, 10, 346)(5, 341, 12, 348, 6, 342)(7, 343, 15, 351, 11, 347)(9, 345, 18, 354, 20, 356)(13, 349, 25, 361, 23, 359)(14, 350, 24, 360, 28, 364)(16, 352, 31, 367, 29, 365)(17, 353, 33, 369, 21, 357)(19, 355, 36, 372, 38, 374)(22, 358, 30, 366, 42, 378)(26, 362, 47, 383, 45, 381)(27, 363, 49, 385, 51, 387)(32, 368, 57, 393, 55, 391)(34, 370, 61, 397, 59, 395)(35, 371, 63, 399, 39, 375)(37, 373, 66, 402, 68, 404)(40, 376, 60, 396, 72, 408)(41, 377, 73, 409, 75, 411)(43, 379, 46, 382, 78, 414)(44, 380, 79, 415, 52, 388)(48, 384, 85, 421, 83, 419)(50, 386, 88, 424, 90, 426)(53, 389, 56, 392, 94, 430)(54, 390, 95, 431, 76, 412)(58, 394, 101, 437, 99, 435)(62, 398, 107, 443, 105, 441)(64, 400, 111, 447, 109, 445)(65, 401, 113, 449, 69, 405)(67, 403, 116, 452, 102, 438)(70, 406, 110, 446, 121, 457)(71, 407, 122, 458, 124, 460)(74, 410, 127, 463, 129, 465)(77, 413, 132, 468, 134, 470)(80, 416, 138, 474, 136, 472)(81, 417, 84, 420, 140, 476)(82, 418, 141, 477, 135, 471)(86, 422, 128, 464, 143, 479)(87, 423, 144, 480, 91, 427)(89, 425, 147, 483, 108, 444)(92, 428, 137, 473, 152, 488)(93, 429, 153, 489, 155, 491)(96, 432, 159, 495, 157, 493)(97, 433, 100, 436, 161, 497)(98, 434, 162, 498, 156, 492)(103, 439, 106, 442, 165, 501)(104, 440, 166, 502, 125, 461)(112, 448, 175, 511, 173, 509)(114, 450, 178, 514, 176, 512)(115, 451, 180, 516, 118, 454)(117, 453, 148, 484, 170, 506)(119, 455, 177, 513, 182, 518)(120, 456, 183, 519, 184, 520)(123, 459, 187, 523, 142, 478)(126, 462, 190, 526, 130, 466)(131, 467, 158, 494, 192, 528)(133, 469, 194, 530, 163, 499)(139, 475, 200, 536, 201, 537)(145, 481, 205, 541, 203, 539)(146, 482, 207, 543, 149, 485)(150, 486, 204, 540, 209, 545)(151, 487, 210, 546, 211, 547)(154, 490, 214, 550, 168, 504)(160, 496, 220, 556, 221, 557)(164, 500, 223, 559, 225, 561)(167, 503, 229, 565, 227, 563)(169, 505, 231, 567, 226, 562)(171, 507, 174, 510, 233, 569)(172, 508, 234, 570, 185, 521)(179, 515, 242, 578, 240, 576)(181, 517, 244, 580, 243, 579)(186, 522, 249, 585, 188, 524)(189, 525, 228, 564, 251, 587)(191, 527, 253, 589, 252, 588)(193, 529, 255, 591, 195, 531)(196, 532, 202, 538, 260, 596)(197, 533, 199, 535, 262, 598)(198, 534, 263, 599, 212, 548)(206, 542, 257, 593, 269, 605)(208, 544, 272, 608, 271, 607)(213, 549, 277, 613, 215, 551)(216, 552, 222, 558, 282, 618)(217, 553, 219, 555, 284, 620)(218, 554, 285, 621, 254, 590)(224, 560, 290, 626, 236, 572)(230, 566, 279, 615, 296, 632)(232, 568, 273, 609, 268, 604)(235, 571, 287, 623, 286, 622)(237, 573, 301, 637, 299, 635)(238, 574, 241, 577, 302, 638)(239, 575, 283, 619, 245, 581)(246, 582, 308, 644, 247, 583)(248, 584, 267, 603, 270, 606)(250, 586, 310, 646, 288, 624)(256, 592, 311, 647, 294, 630)(258, 594, 291, 627, 289, 625)(259, 595, 315, 651, 316, 652)(261, 597, 293, 629, 295, 631)(264, 600, 280, 616, 265, 601)(266, 602, 278, 614, 317, 653)(274, 610, 323, 659, 275, 611)(276, 612, 312, 648, 313, 649)(281, 617, 326, 662, 327, 663)(292, 628, 297, 633, 330, 666)(298, 634, 318, 654, 304, 640)(300, 636, 328, 664, 333, 669)(303, 639, 331, 667, 325, 661)(305, 641, 320, 656, 335, 671)(306, 642, 307, 643, 336, 672)(309, 645, 324, 660, 332, 668)(314, 650, 329, 665, 319, 655)(321, 657, 322, 658, 334, 670) L = (1, 339)(2, 342)(3, 345)(4, 347)(5, 337)(6, 350)(7, 338)(8, 340)(9, 355)(10, 357)(11, 358)(12, 359)(13, 341)(14, 363)(15, 365)(16, 343)(17, 344)(18, 346)(19, 373)(20, 375)(21, 376)(22, 377)(23, 379)(24, 348)(25, 381)(26, 349)(27, 386)(28, 388)(29, 389)(30, 351)(31, 391)(32, 352)(33, 395)(34, 353)(35, 354)(36, 356)(37, 403)(38, 405)(39, 406)(40, 407)(41, 410)(42, 412)(43, 413)(44, 360)(45, 417)(46, 361)(47, 419)(48, 362)(49, 364)(50, 425)(51, 427)(52, 428)(53, 429)(54, 366)(55, 433)(56, 367)(57, 435)(58, 368)(59, 439)(60, 369)(61, 441)(62, 370)(63, 445)(64, 371)(65, 372)(66, 374)(67, 453)(68, 454)(69, 455)(70, 456)(71, 459)(72, 461)(73, 378)(74, 464)(75, 466)(76, 467)(77, 469)(78, 471)(79, 472)(80, 380)(81, 475)(82, 382)(83, 478)(84, 383)(85, 479)(86, 384)(87, 385)(88, 387)(89, 484)(90, 485)(91, 486)(92, 487)(93, 490)(94, 492)(95, 493)(96, 390)(97, 496)(98, 392)(99, 499)(100, 393)(101, 452)(102, 394)(103, 500)(104, 396)(105, 504)(106, 397)(107, 483)(108, 398)(109, 507)(110, 399)(111, 509)(112, 400)(113, 512)(114, 401)(115, 402)(116, 404)(117, 422)(118, 416)(119, 418)(120, 420)(121, 521)(122, 408)(123, 421)(124, 524)(125, 525)(126, 409)(127, 411)(128, 506)(129, 448)(130, 503)(131, 505)(132, 414)(133, 437)(134, 531)(135, 532)(136, 533)(137, 415)(138, 516)(139, 517)(140, 520)(141, 518)(142, 515)(143, 465)(144, 539)(145, 423)(146, 424)(147, 426)(148, 438)(149, 432)(150, 434)(151, 436)(152, 548)(153, 430)(154, 443)(155, 551)(156, 552)(157, 553)(158, 431)(159, 543)(160, 544)(161, 547)(162, 545)(163, 542)(164, 560)(165, 562)(166, 563)(167, 440)(168, 566)(169, 442)(170, 444)(171, 568)(172, 446)(173, 572)(174, 447)(175, 463)(176, 574)(177, 449)(178, 576)(179, 450)(180, 579)(181, 451)(182, 581)(183, 457)(184, 583)(185, 584)(186, 458)(187, 460)(188, 571)(189, 573)(190, 588)(191, 462)(192, 590)(193, 468)(194, 470)(195, 594)(196, 595)(197, 597)(198, 473)(199, 474)(200, 476)(201, 601)(202, 477)(203, 603)(204, 480)(205, 605)(206, 481)(207, 607)(208, 482)(209, 609)(210, 488)(211, 611)(212, 612)(213, 489)(214, 491)(215, 616)(216, 617)(217, 619)(218, 494)(219, 495)(220, 497)(221, 623)(222, 498)(223, 501)(224, 511)(225, 627)(226, 628)(227, 629)(228, 502)(229, 526)(230, 527)(231, 528)(232, 634)(233, 635)(234, 622)(235, 508)(236, 636)(237, 510)(238, 621)(239, 513)(240, 640)(241, 514)(242, 523)(243, 642)(244, 537)(245, 620)(246, 519)(247, 639)(248, 641)(249, 624)(250, 522)(251, 647)(252, 648)(253, 632)(254, 638)(255, 630)(256, 529)(257, 530)(258, 534)(259, 535)(260, 653)(261, 650)(262, 652)(263, 625)(264, 536)(265, 613)(266, 538)(267, 570)(268, 540)(269, 655)(270, 541)(271, 657)(272, 557)(273, 569)(274, 546)(275, 654)(276, 656)(277, 602)(278, 549)(279, 550)(280, 554)(281, 555)(282, 646)(283, 661)(284, 663)(285, 600)(286, 556)(287, 585)(288, 558)(289, 559)(290, 561)(291, 591)(292, 665)(293, 598)(294, 564)(295, 565)(296, 667)(297, 567)(298, 578)(299, 658)(300, 586)(301, 587)(302, 671)(303, 575)(304, 659)(305, 577)(306, 592)(307, 580)(308, 668)(309, 582)(310, 669)(311, 672)(312, 599)(313, 589)(314, 593)(315, 596)(316, 664)(317, 670)(318, 604)(319, 666)(320, 606)(321, 614)(322, 608)(323, 645)(324, 610)(325, 615)(326, 618)(327, 643)(328, 626)(329, 631)(330, 660)(331, 644)(332, 633)(333, 651)(334, 637)(335, 649)(336, 662) local type(s) :: { ( 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 112 e = 336 f = 196 degree seq :: [ 6^112 ] E15.1394 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) Aut = ((C7 x Q8) : C3) : C2 (small group id <336, 134>) |r| :: 1 Presentation :: [ X2^2, (X2 * X1)^3, X1^12, X1^-3 * X2 * X1^6 * X2 * X1^-3, X1 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 * X2 * X1^-2 * X2 * X1^-2 * X2 * X1 ] Map:: R = (1, 337, 2, 338, 5, 341, 11, 347, 21, 357, 37, 373, 63, 399, 62, 398, 36, 372, 20, 356, 10, 346, 4, 340)(3, 339, 7, 343, 15, 351, 27, 363, 47, 383, 79, 415, 104, 440, 91, 427, 54, 390, 31, 367, 17, 353, 8, 344)(6, 342, 13, 349, 25, 361, 43, 379, 73, 409, 119, 455, 103, 439, 128, 464, 78, 414, 46, 382, 26, 362, 14, 350)(9, 345, 18, 354, 32, 368, 55, 391, 92, 428, 106, 442, 64, 400, 105, 441, 86, 422, 51, 387, 29, 365, 16, 352)(12, 348, 23, 359, 41, 377, 69, 405, 113, 449, 101, 437, 61, 397, 102, 438, 118, 454, 72, 408, 42, 378, 24, 360)(19, 355, 34, 370, 58, 394, 97, 433, 108, 444, 66, 402, 38, 374, 65, 401, 107, 443, 96, 432, 57, 393, 33, 369)(22, 358, 39, 375, 67, 403, 109, 445, 99, 435, 59, 395, 35, 371, 60, 396, 100, 436, 112, 448, 68, 404, 40, 376)(28, 364, 49, 385, 83, 419, 132, 468, 181, 517, 142, 478, 90, 426, 143, 479, 186, 522, 135, 471, 84, 420, 50, 386)(30, 366, 52, 388, 87, 423, 138, 474, 176, 512, 127, 463, 80, 416, 129, 465, 171, 507, 123, 459, 75, 411, 44, 380)(45, 381, 76, 412, 124, 460, 172, 508, 222, 558, 166, 502, 120, 456, 167, 503, 217, 553, 162, 498, 115, 451, 70, 406)(48, 384, 81, 417, 130, 466, 177, 513, 140, 476, 88, 424, 53, 389, 89, 425, 141, 477, 180, 516, 131, 467, 82, 418)(56, 392, 94, 430, 146, 482, 195, 531, 246, 582, 188, 524, 137, 473, 154, 490, 206, 542, 198, 534, 147, 483, 95, 431)(71, 407, 116, 452, 163, 499, 218, 554, 204, 540, 152, 488, 159, 495, 213, 549, 265, 601, 209, 545, 156, 492, 110, 446)(74, 410, 121, 457, 168, 504, 223, 559, 174, 510, 125, 461, 77, 413, 126, 462, 175, 511, 226, 562, 169, 505, 122, 458)(85, 421, 136, 472, 187, 523, 244, 580, 194, 530, 145, 481, 93, 429, 144, 480, 193, 529, 240, 576, 183, 519, 133, 469)(98, 434, 150, 486, 202, 538, 259, 595, 261, 597, 205, 541, 153, 489, 111, 447, 157, 493, 210, 546, 203, 539, 151, 487)(114, 450, 160, 496, 214, 550, 269, 605, 220, 556, 164, 500, 117, 453, 165, 501, 221, 557, 272, 608, 215, 551, 161, 497)(134, 470, 184, 520, 241, 577, 297, 633, 250, 586, 192, 528, 237, 573, 295, 631, 318, 654, 291, 627, 234, 570, 178, 514)(139, 475, 190, 526, 248, 584, 266, 602, 315, 651, 284, 620, 228, 564, 179, 515, 235, 571, 292, 628, 249, 585, 191, 527)(148, 484, 199, 535, 256, 592, 306, 642, 258, 594, 201, 537, 149, 485, 200, 536, 257, 593, 304, 640, 253, 589, 196, 532)(155, 491, 207, 543, 262, 598, 310, 646, 267, 603, 211, 547, 158, 494, 212, 548, 268, 604, 312, 648, 263, 599, 208, 544)(170, 506, 227, 563, 283, 619, 327, 663, 288, 624, 232, 568, 189, 525, 247, 583, 302, 638, 324, 660, 280, 616, 224, 560)(173, 509, 230, 566, 286, 622, 255, 591, 305, 641, 320, 656, 274, 610, 225, 561, 281, 617, 252, 588, 287, 623, 231, 567)(182, 518, 238, 574, 277, 613, 219, 555, 276, 612, 242, 578, 185, 521, 243, 579, 298, 634, 314, 650, 271, 607, 239, 575)(197, 533, 254, 590, 279, 615, 323, 659, 301, 637, 245, 581, 300, 636, 325, 661, 282, 618, 326, 662, 303, 639, 251, 587)(216, 552, 273, 609, 319, 655, 336, 672, 322, 658, 278, 614, 229, 565, 285, 621, 328, 664, 335, 671, 317, 653, 270, 606)(233, 569, 289, 625, 329, 665, 307, 643, 309, 645, 293, 629, 236, 572, 294, 630, 330, 666, 308, 644, 260, 596, 290, 626)(264, 600, 313, 649, 299, 635, 332, 668, 334, 670, 316, 652, 275, 611, 321, 657, 296, 632, 331, 667, 333, 669, 311, 647) L = (1, 339)(2, 342)(3, 337)(4, 345)(5, 348)(6, 338)(7, 352)(8, 349)(9, 340)(10, 355)(11, 358)(12, 341)(13, 344)(14, 359)(15, 364)(16, 343)(17, 366)(18, 369)(19, 346)(20, 371)(21, 374)(22, 347)(23, 350)(24, 375)(25, 380)(26, 381)(27, 384)(28, 351)(29, 385)(30, 353)(31, 389)(32, 392)(33, 354)(34, 395)(35, 356)(36, 397)(37, 400)(38, 357)(39, 360)(40, 401)(41, 406)(42, 407)(43, 410)(44, 361)(45, 362)(46, 413)(47, 416)(48, 363)(49, 365)(50, 417)(51, 421)(52, 424)(53, 367)(54, 426)(55, 429)(56, 368)(57, 430)(58, 434)(59, 370)(60, 437)(61, 372)(62, 439)(63, 440)(64, 373)(65, 376)(66, 441)(67, 446)(68, 447)(69, 450)(70, 377)(71, 378)(72, 453)(73, 456)(74, 379)(75, 457)(76, 461)(77, 382)(78, 463)(79, 464)(80, 383)(81, 386)(82, 465)(83, 469)(84, 470)(85, 387)(86, 473)(87, 475)(88, 388)(89, 478)(90, 390)(91, 442)(92, 479)(93, 391)(94, 393)(95, 480)(96, 484)(97, 485)(98, 394)(99, 486)(100, 488)(101, 396)(102, 455)(103, 398)(104, 399)(105, 402)(106, 427)(107, 489)(108, 490)(109, 491)(110, 403)(111, 404)(112, 494)(113, 495)(114, 405)(115, 496)(116, 500)(117, 408)(118, 502)(119, 438)(120, 409)(121, 411)(122, 503)(123, 506)(124, 509)(125, 412)(126, 512)(127, 414)(128, 415)(129, 418)(130, 514)(131, 515)(132, 518)(133, 419)(134, 420)(135, 521)(136, 524)(137, 422)(138, 525)(139, 423)(140, 526)(141, 528)(142, 425)(143, 428)(144, 431)(145, 522)(146, 532)(147, 533)(148, 432)(149, 433)(150, 435)(151, 536)(152, 436)(153, 443)(154, 444)(155, 445)(156, 543)(157, 547)(158, 448)(159, 449)(160, 451)(161, 549)(162, 552)(163, 555)(164, 452)(165, 558)(166, 454)(167, 458)(168, 560)(169, 561)(170, 459)(171, 564)(172, 565)(173, 460)(174, 566)(175, 568)(176, 462)(177, 569)(178, 466)(179, 467)(180, 572)(181, 573)(182, 468)(183, 574)(184, 578)(185, 471)(186, 481)(187, 581)(188, 472)(189, 474)(190, 476)(191, 583)(192, 477)(193, 587)(194, 579)(195, 588)(196, 482)(197, 483)(198, 591)(199, 541)(200, 487)(201, 542)(202, 544)(203, 596)(204, 548)(205, 535)(206, 537)(207, 492)(208, 538)(209, 600)(210, 602)(211, 493)(212, 540)(213, 497)(214, 606)(215, 607)(216, 498)(217, 610)(218, 611)(219, 499)(220, 612)(221, 614)(222, 501)(223, 615)(224, 504)(225, 505)(226, 618)(227, 620)(228, 507)(229, 508)(230, 510)(231, 621)(232, 511)(233, 513)(234, 625)(235, 629)(236, 516)(237, 517)(238, 519)(239, 631)(240, 632)(241, 605)(242, 520)(243, 530)(244, 635)(245, 523)(246, 636)(247, 527)(248, 626)(249, 599)(250, 630)(251, 529)(252, 531)(253, 623)(254, 622)(255, 534)(256, 643)(257, 644)(258, 641)(259, 628)(260, 539)(261, 645)(262, 647)(263, 585)(264, 545)(265, 650)(266, 546)(267, 651)(268, 652)(269, 577)(270, 550)(271, 551)(272, 654)(273, 656)(274, 553)(275, 554)(276, 556)(277, 657)(278, 557)(279, 559)(280, 659)(281, 661)(282, 562)(283, 646)(284, 563)(285, 567)(286, 590)(287, 589)(288, 662)(289, 570)(290, 584)(291, 658)(292, 595)(293, 571)(294, 586)(295, 575)(296, 576)(297, 653)(298, 649)(299, 580)(300, 582)(301, 668)(302, 648)(303, 667)(304, 664)(305, 594)(306, 655)(307, 592)(308, 593)(309, 597)(310, 619)(311, 598)(312, 638)(313, 634)(314, 601)(315, 603)(316, 604)(317, 633)(318, 608)(319, 642)(320, 609)(321, 613)(322, 627)(323, 616)(324, 670)(325, 617)(326, 624)(327, 669)(328, 640)(329, 672)(330, 671)(331, 639)(332, 637)(333, 663)(334, 660)(335, 666)(336, 665) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 28 e = 336 f = 280 degree seq :: [ 24^28 ] E15.1395 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 9}) Quotient :: regular Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^9, (T1^-3 * T2 * T1^3 * T2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3 * T2 * T1 * T2 * T1^-2 * T2 * T1^-4, (T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1)^2 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 21, 36, 20, 10, 4)(3, 7, 15, 27, 46, 53, 31, 17, 8)(6, 13, 25, 42, 69, 74, 45, 26, 14)(9, 18, 32, 54, 86, 81, 50, 29, 16)(12, 23, 40, 65, 103, 108, 68, 41, 24)(19, 34, 57, 91, 140, 139, 90, 56, 33)(22, 38, 63, 99, 153, 158, 102, 64, 39)(28, 48, 78, 121, 185, 190, 124, 79, 49)(30, 51, 82, 127, 194, 172, 112, 71, 43)(35, 59, 94, 145, 220, 219, 144, 93, 58)(37, 61, 97, 149, 227, 232, 152, 98, 62)(44, 72, 113, 173, 261, 246, 162, 105, 66)(47, 76, 119, 181, 273, 231, 184, 120, 77)(52, 84, 130, 199, 297, 296, 198, 129, 83)(55, 88, 136, 207, 308, 313, 210, 137, 89)(60, 96, 148, 225, 330, 329, 224, 147, 95)(67, 106, 163, 247, 351, 340, 236, 155, 100)(70, 110, 169, 255, 360, 328, 258, 170, 111)(73, 115, 176, 266, 221, 325, 265, 175, 114)(75, 117, 179, 270, 376, 343, 240, 180, 118)(80, 125, 191, 286, 228, 333, 281, 187, 122)(85, 132, 202, 302, 373, 402, 301, 201, 131)(87, 134, 205, 305, 238, 157, 239, 206, 135)(92, 142, 216, 319, 411, 413, 322, 217, 143)(101, 156, 237, 341, 426, 420, 334, 229, 150)(104, 160, 243, 346, 320, 218, 323, 244, 161)(107, 165, 250, 215, 141, 214, 318, 249, 164)(109, 167, 253, 357, 380, 277, 336, 254, 168)(116, 178, 269, 213, 317, 387, 285, 268, 177)(123, 188, 282, 342, 403, 448, 379, 275, 182)(126, 193, 289, 392, 298, 399, 391, 288, 192)(128, 196, 293, 394, 445, 372, 397, 294, 197)(133, 203, 304, 290, 356, 251, 166, 252, 204)(138, 211, 314, 235, 154, 234, 338, 310, 208)(146, 222, 326, 415, 470, 471, 416, 327, 223)(151, 230, 335, 421, 474, 472, 418, 331, 226)(159, 241, 344, 428, 440, 364, 417, 345, 242)(171, 259, 365, 378, 274, 377, 439, 362, 256)(174, 263, 370, 444, 467, 410, 321, 371, 264)(183, 276, 352, 435, 483, 482, 434, 350, 271)(186, 279, 382, 450, 395, 295, 398, 383, 280)(189, 284, 355, 292, 195, 291, 393, 386, 283)(200, 299, 400, 459, 496, 486, 446, 401, 300)(209, 311, 354, 248, 353, 436, 460, 404, 306)(212, 316, 359, 332, 388, 454, 466, 409, 315)(233, 337, 422, 476, 469, 414, 324, 303, 272)(245, 349, 433, 438, 361, 437, 480, 431, 347)(257, 363, 427, 385, 453, 493, 478, 425, 358)(260, 367, 307, 369, 262, 368, 443, 442, 366)(267, 374, 278, 381, 449, 463, 407, 312, 375)(287, 389, 455, 494, 495, 457, 396, 456, 390)(309, 405, 461, 491, 451, 384, 419, 462, 406)(339, 424, 468, 412, 430, 479, 499, 477, 423)(348, 432, 475, 441, 485, 502, 497, 473, 429)(408, 464, 498, 481, 501, 489, 452, 492, 465)(447, 488, 487, 458, 490, 503, 504, 500, 484) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 37)(24, 38)(25, 43)(26, 44)(27, 47)(29, 48)(31, 52)(32, 55)(34, 58)(36, 60)(39, 61)(40, 66)(41, 67)(42, 70)(45, 73)(46, 75)(49, 76)(50, 80)(51, 83)(53, 85)(54, 87)(56, 88)(57, 92)(59, 95)(62, 96)(63, 100)(64, 101)(65, 104)(68, 107)(69, 109)(71, 110)(72, 114)(74, 116)(77, 117)(78, 122)(79, 123)(81, 126)(82, 128)(84, 131)(86, 133)(89, 134)(90, 138)(91, 141)(93, 142)(94, 146)(97, 150)(98, 151)(99, 154)(102, 157)(103, 159)(105, 160)(106, 164)(108, 166)(111, 167)(112, 171)(113, 174)(115, 177)(118, 132)(119, 182)(120, 183)(121, 186)(124, 189)(125, 192)(127, 195)(129, 196)(130, 200)(135, 203)(136, 208)(137, 209)(139, 212)(140, 213)(143, 214)(144, 218)(145, 221)(147, 222)(148, 226)(149, 228)(152, 231)(153, 233)(155, 234)(156, 238)(158, 240)(161, 241)(162, 245)(163, 248)(165, 251)(168, 178)(169, 256)(170, 257)(172, 260)(173, 262)(175, 263)(176, 267)(179, 271)(180, 272)(181, 274)(184, 277)(185, 278)(187, 279)(188, 283)(190, 285)(191, 287)(193, 204)(194, 290)(197, 291)(198, 295)(199, 298)(201, 299)(202, 303)(205, 306)(206, 307)(207, 309)(210, 312)(211, 315)(215, 317)(216, 320)(217, 321)(219, 324)(220, 302)(223, 325)(224, 328)(225, 297)(227, 332)(229, 333)(230, 273)(232, 336)(235, 337)(236, 339)(237, 342)(239, 343)(242, 252)(243, 347)(244, 348)(246, 350)(247, 352)(249, 353)(250, 355)(253, 358)(254, 359)(255, 361)(258, 364)(259, 366)(261, 270)(264, 368)(265, 372)(266, 373)(268, 374)(269, 316)(275, 377)(276, 380)(280, 381)(281, 384)(282, 385)(284, 387)(286, 388)(288, 389)(289, 345)(292, 356)(293, 395)(294, 396)(296, 331)(300, 399)(301, 313)(304, 367)(305, 403)(308, 400)(310, 405)(311, 407)(314, 408)(318, 410)(319, 412)(322, 401)(323, 414)(326, 360)(327, 397)(329, 417)(330, 392)(334, 419)(335, 378)(338, 423)(340, 425)(341, 427)(344, 429)(346, 430)(349, 434)(351, 357)(354, 435)(362, 437)(363, 440)(365, 441)(369, 376)(370, 445)(371, 446)(375, 402)(379, 447)(382, 451)(383, 452)(386, 453)(390, 454)(391, 413)(393, 457)(394, 458)(398, 418)(404, 448)(406, 459)(409, 464)(411, 455)(415, 438)(416, 456)(420, 473)(421, 475)(422, 465)(424, 478)(426, 428)(431, 479)(432, 469)(433, 481)(436, 467)(439, 484)(442, 485)(443, 486)(444, 487)(449, 489)(450, 490)(460, 488)(461, 477)(462, 497)(463, 483)(466, 471)(468, 494)(470, 498)(472, 492)(474, 476)(480, 500)(482, 501)(491, 503)(493, 495)(496, 502)(499, 504) local type(s) :: { ( 3^9 ) } Outer automorphisms :: reflexible Dual of E15.1396 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 56 e = 252 f = 168 degree seq :: [ 9^56 ] E15.1396 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 9}) Quotient :: regular Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^9, (T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1)^2, (T2 * T1 * T2 * T1^-1)^7 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(59, 83, 84)(60, 85, 86)(61, 87, 88)(62, 89, 90)(63, 91, 92)(64, 93, 94)(65, 95, 96)(66, 97, 98)(75, 107, 108)(76, 109, 110)(77, 111, 112)(78, 113, 114)(79, 115, 116)(80, 117, 118)(81, 119, 120)(82, 121, 122)(99, 138, 139)(100, 140, 141)(101, 142, 143)(102, 144, 145)(103, 146, 147)(104, 148, 149)(105, 150, 151)(106, 152, 123)(124, 167, 168)(125, 169, 170)(126, 171, 172)(127, 173, 174)(128, 175, 176)(129, 177, 178)(130, 179, 180)(131, 181, 182)(132, 183, 184)(133, 185, 186)(134, 187, 188)(135, 189, 190)(136, 191, 192)(137, 193, 194)(153, 312, 299)(154, 314, 420)(155, 316, 357)(156, 318, 360)(157, 320, 489)(158, 322, 218)(159, 323, 419)(160, 233, 305)(161, 282, 433)(162, 326, 255)(163, 327, 492)(164, 329, 493)(165, 330, 291)(166, 331, 263)(195, 365, 328)(196, 300, 404)(197, 301, 481)(198, 368, 461)(199, 341, 499)(200, 370, 221)(201, 371, 403)(202, 224, 268)(203, 254, 413)(204, 374, 237)(205, 375, 503)(206, 376, 498)(207, 377, 275)(208, 378, 279)(209, 290, 287)(210, 311, 308)(211, 347, 342)(212, 274, 271)(213, 384, 386)(214, 258, 256)(215, 337, 390)(216, 240, 238)(217, 389, 394)(219, 247, 245)(220, 382, 398)(222, 399, 400)(223, 232, 227)(225, 385, 406)(226, 361, 407)(228, 380, 411)(229, 355, 412)(230, 393, 414)(231, 415, 416)(234, 381, 422)(235, 423, 352)(236, 397, 424)(239, 366, 426)(241, 354, 340)(242, 383, 430)(243, 431, 432)(244, 405, 359)(246, 292, 434)(248, 436, 438)(249, 319, 409)(250, 440, 304)(251, 410, 441)(252, 388, 372)(253, 442, 443)(257, 313, 446)(259, 364, 448)(260, 346, 418)(261, 449, 267)(262, 421, 450)(264, 392, 297)(265, 451, 452)(266, 453, 454)(269, 455, 458)(270, 343, 425)(272, 408, 460)(273, 379, 462)(276, 295, 402)(277, 465, 284)(278, 429, 466)(280, 396, 324)(281, 467, 351)(283, 468, 469)(285, 470, 463)(286, 472, 353)(288, 417, 474)(289, 302, 444)(293, 439, 476)(294, 348, 477)(296, 321, 369)(298, 479, 336)(303, 363, 482)(306, 335, 475)(307, 483, 445)(309, 401, 457)(310, 332, 350)(315, 338, 486)(317, 487, 488)(325, 491, 485)(333, 387, 428)(334, 484, 495)(339, 496, 447)(344, 427, 500)(345, 480, 373)(349, 502, 501)(356, 494, 395)(358, 473, 459)(362, 391, 437)(367, 464, 497)(435, 504, 490)(456, 478, 471) L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 107)(108, 153)(109, 154)(110, 155)(111, 156)(112, 157)(113, 158)(114, 159)(115, 160)(116, 161)(117, 162)(118, 163)(119, 164)(120, 165)(121, 166)(122, 138)(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)(167, 333)(168, 335)(169, 210)(170, 325)(171, 337)(172, 338)(173, 340)(174, 289)(175, 343)(176, 345)(177, 266)(178, 346)(179, 348)(180, 181)(182, 349)(183, 324)(184, 351)(185, 222)(186, 353)(187, 355)(188, 356)(189, 245)(190, 359)(191, 361)(192, 278)(193, 272)(194, 364)(209, 300)(211, 280)(212, 314)(213, 252)(214, 387)(215, 264)(216, 391)(217, 242)(218, 295)(219, 395)(220, 228)(221, 319)(223, 401)(224, 403)(225, 234)(226, 326)(227, 408)(229, 381)(230, 249)(231, 374)(232, 417)(233, 419)(235, 383)(236, 260)(237, 425)(238, 376)(239, 407)(240, 427)(241, 315)(243, 380)(244, 276)(246, 416)(247, 435)(248, 367)(250, 388)(251, 291)(253, 382)(254, 297)(255, 445)(256, 329)(257, 400)(258, 447)(259, 293)(261, 392)(262, 275)(263, 354)(265, 385)(267, 426)(268, 317)(269, 456)(270, 459)(271, 453)(273, 461)(274, 463)(277, 396)(279, 436)(281, 389)(282, 372)(283, 322)(284, 434)(285, 471)(286, 473)(287, 468)(288, 331)(290, 475)(292, 402)(294, 305)(296, 393)(298, 404)(299, 455)(301, 384)(302, 430)(303, 370)(304, 446)(306, 478)(307, 358)(308, 363)(309, 378)(310, 360)(311, 458)(312, 362)(313, 409)(316, 347)(318, 438)(320, 472)(321, 397)(323, 487)(327, 423)(328, 470)(330, 415)(332, 411)(334, 390)(336, 449)(339, 497)(341, 483)(342, 484)(344, 477)(350, 412)(352, 462)(357, 464)(365, 494)(366, 418)(368, 448)(369, 405)(371, 502)(373, 420)(375, 431)(377, 399)(379, 422)(386, 495)(394, 469)(398, 482)(406, 454)(410, 451)(413, 452)(414, 493)(421, 467)(424, 498)(428, 492)(429, 442)(432, 444)(433, 443)(437, 503)(439, 481)(440, 480)(441, 460)(450, 474)(457, 466)(465, 485)(476, 500)(479, 489)(486, 504)(488, 490)(491, 499)(496, 501) local type(s) :: { ( 9^3 ) } Outer automorphisms :: reflexible Dual of E15.1395 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 168 e = 252 f = 56 degree seq :: [ 3^168 ] E15.1397 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 9}) Quotient :: edge Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^9, (T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1)^2, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2 * T1 * T2^-1 * T1)^7 ] Map:: polytopal R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 59, 60)(44, 61, 62)(45, 63, 64)(46, 65, 66)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(51, 75, 76)(52, 77, 78)(53, 79, 80)(54, 81, 82)(55, 83, 84)(56, 85, 86)(57, 87, 88)(58, 89, 90)(91, 122, 123)(92, 124, 125)(93, 126, 127)(94, 128, 129)(95, 130, 131)(96, 132, 133)(97, 134, 135)(98, 136, 137)(99, 138, 139)(100, 140, 141)(101, 142, 143)(102, 144, 145)(103, 146, 147)(104, 148, 149)(105, 150, 151)(106, 152, 107)(108, 153, 154)(109, 155, 156)(110, 157, 158)(111, 159, 160)(112, 161, 162)(113, 163, 164)(114, 165, 166)(115, 167, 168)(116, 169, 170)(117, 171, 172)(118, 173, 174)(119, 175, 176)(120, 177, 178)(121, 179, 180)(181, 339, 493)(182, 340, 390)(183, 342, 250)(184, 343, 316)(185, 344, 494)(186, 259, 443)(187, 217, 247)(188, 347, 341)(189, 348, 437)(190, 330, 464)(191, 350, 220)(192, 308, 388)(193, 311, 458)(194, 353, 496)(195, 354, 497)(196, 355, 391)(197, 357, 255)(198, 358, 436)(199, 359, 499)(200, 284, 324)(201, 224, 272)(202, 362, 356)(203, 363, 414)(204, 365, 473)(205, 277, 213)(206, 367, 380)(207, 369, 424)(208, 370, 502)(209, 245, 244)(210, 240, 239)(211, 270, 269)(212, 274, 273)(214, 281, 280)(215, 243, 242)(216, 229, 228)(218, 226, 225)(219, 351, 349)(221, 366, 364)(222, 315, 392)(223, 394, 386)(227, 279, 278)(230, 400, 401)(231, 403, 389)(232, 404, 405)(233, 407, 381)(234, 409, 410)(235, 412, 395)(236, 413, 415)(237, 417, 378)(238, 346, 345)(241, 361, 360)(246, 425, 375)(248, 428, 429)(249, 431, 309)(251, 416, 432)(252, 423, 372)(253, 434, 338)(254, 435, 408)(256, 314, 438)(257, 399, 376)(258, 440, 441)(260, 304, 445)(261, 406, 446)(262, 447, 448)(263, 427, 374)(264, 449, 302)(265, 450, 418)(266, 325, 451)(267, 289, 453)(268, 398, 379)(271, 455, 377)(275, 459, 371)(276, 397, 387)(282, 463, 373)(283, 318, 465)(285, 426, 466)(286, 393, 317)(287, 467, 468)(288, 457, 319)(290, 306, 433)(291, 469, 303)(292, 299, 471)(293, 385, 331)(294, 329, 305)(295, 456, 475)(296, 402, 442)(297, 476, 313)(298, 322, 383)(300, 477, 439)(301, 478, 479)(307, 421, 474)(310, 481, 482)(312, 422, 419)(320, 334, 480)(321, 462, 485)(323, 396, 487)(326, 483, 452)(327, 368, 489)(328, 411, 430)(332, 461, 460)(333, 470, 488)(335, 490, 454)(336, 491, 492)(337, 444, 420)(352, 495, 382)(384, 484, 498)(472, 501, 500)(486, 504, 503)(505, 506)(507, 511)(508, 512)(509, 513)(510, 514)(515, 523)(516, 524)(517, 525)(518, 526)(519, 527)(520, 528)(521, 529)(522, 530)(531, 547)(532, 548)(533, 549)(534, 550)(535, 551)(536, 552)(537, 553)(538, 554)(539, 555)(540, 556)(541, 557)(542, 558)(543, 559)(544, 560)(545, 561)(546, 562)(563, 595)(564, 596)(565, 597)(566, 598)(567, 599)(568, 600)(569, 601)(570, 602)(571, 603)(572, 604)(573, 605)(574, 606)(575, 607)(576, 608)(577, 609)(578, 610)(579, 611)(580, 612)(581, 613)(582, 614)(583, 615)(584, 616)(585, 617)(586, 618)(587, 619)(588, 620)(589, 621)(590, 622)(591, 623)(592, 624)(593, 625)(594, 626)(627, 685)(628, 686)(629, 687)(630, 688)(631, 689)(632, 690)(633, 691)(634, 692)(635, 693)(636, 694)(637, 695)(638, 696)(639, 697)(640, 698)(641, 642)(643, 699)(644, 700)(645, 701)(646, 702)(647, 703)(648, 704)(649, 705)(650, 706)(651, 707)(652, 708)(653, 709)(654, 710)(655, 711)(656, 712)(657, 742)(658, 808)(659, 810)(660, 736)(661, 813)(662, 746)(663, 816)(664, 740)(665, 817)(666, 819)(667, 821)(668, 823)(669, 825)(670, 671)(672, 827)(673, 780)(674, 829)(675, 830)(676, 766)(677, 833)(678, 782)(679, 836)(680, 723)(681, 837)(682, 774)(683, 775)(684, 841)(713, 875)(714, 877)(715, 879)(716, 881)(717, 864)(718, 884)(719, 886)(720, 831)(721, 888)(722, 799)(724, 849)(725, 892)(726, 894)(727, 897)(728, 900)(729, 764)(730, 789)(731, 858)(732, 754)(733, 811)(734, 895)(735, 906)(737, 910)(738, 891)(739, 915)(741, 920)(743, 759)(744, 924)(745, 843)(747, 926)(748, 770)(749, 928)(750, 874)(751, 851)(752, 883)(753, 934)(755, 820)(756, 818)(757, 835)(758, 832)(760, 940)(761, 917)(762, 880)(763, 946)(765, 794)(767, 793)(768, 802)(769, 800)(771, 956)(772, 852)(773, 795)(776, 866)(777, 805)(778, 962)(779, 857)(781, 822)(783, 965)(784, 840)(785, 961)(786, 966)(787, 882)(788, 950)(790, 804)(791, 968)(792, 803)(796, 974)(797, 867)(798, 876)(801, 977)(806, 984)(807, 885)(809, 936)(812, 839)(814, 980)(815, 838)(824, 869)(826, 855)(828, 878)(834, 992)(842, 975)(844, 981)(845, 989)(846, 912)(847, 978)(848, 952)(850, 994)(853, 995)(854, 944)(856, 988)(859, 954)(860, 1002)(861, 899)(862, 948)(863, 972)(865, 1004)(868, 996)(870, 931)(871, 1005)(872, 991)(873, 987)(887, 947)(889, 935)(890, 983)(893, 955)(896, 932)(898, 927)(901, 939)(902, 916)(903, 907)(904, 998)(905, 938)(908, 1003)(909, 913)(911, 921)(914, 953)(918, 982)(919, 969)(922, 949)(923, 1000)(925, 1006)(929, 1007)(930, 997)(933, 957)(937, 970)(941, 973)(942, 945)(943, 979)(951, 986)(958, 993)(959, 1008)(960, 1001)(963, 990)(964, 999)(967, 976)(971, 985) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 673)(170, 674)(171, 675)(172, 676)(173, 677)(174, 678)(175, 679)(176, 680)(177, 681)(178, 682)(179, 683)(180, 684)(181, 685)(182, 686)(183, 687)(184, 688)(185, 689)(186, 690)(187, 691)(188, 692)(189, 693)(190, 694)(191, 695)(192, 696)(193, 697)(194, 698)(195, 699)(196, 700)(197, 701)(198, 702)(199, 703)(200, 704)(201, 705)(202, 706)(203, 707)(204, 708)(205, 709)(206, 710)(207, 711)(208, 712)(209, 713)(210, 714)(211, 715)(212, 716)(213, 717)(214, 718)(215, 719)(216, 720)(217, 721)(218, 722)(219, 723)(220, 724)(221, 725)(222, 726)(223, 727)(224, 728)(225, 729)(226, 730)(227, 731)(228, 732)(229, 733)(230, 734)(231, 735)(232, 736)(233, 737)(234, 738)(235, 739)(236, 740)(237, 741)(238, 742)(239, 743)(240, 744)(241, 745)(242, 746)(243, 747)(244, 748)(245, 749)(246, 750)(247, 751)(248, 752)(249, 753)(250, 754)(251, 755)(252, 756)(253, 757)(254, 758)(255, 759)(256, 760)(257, 761)(258, 762)(259, 763)(260, 764)(261, 765)(262, 766)(263, 767)(264, 768)(265, 769)(266, 770)(267, 771)(268, 772)(269, 773)(270, 774)(271, 775)(272, 776)(273, 777)(274, 778)(275, 779)(276, 780)(277, 781)(278, 782)(279, 783)(280, 784)(281, 785)(282, 786)(283, 787)(284, 788)(285, 789)(286, 790)(287, 791)(288, 792)(289, 793)(290, 794)(291, 795)(292, 796)(293, 797)(294, 798)(295, 799)(296, 800)(297, 801)(298, 802)(299, 803)(300, 804)(301, 805)(302, 806)(303, 807)(304, 808)(305, 809)(306, 810)(307, 811)(308, 812)(309, 813)(310, 814)(311, 815)(312, 816)(313, 817)(314, 818)(315, 819)(316, 820)(317, 821)(318, 822)(319, 823)(320, 824)(321, 825)(322, 826)(323, 827)(324, 828)(325, 829)(326, 830)(327, 831)(328, 832)(329, 833)(330, 834)(331, 835)(332, 836)(333, 837)(334, 838)(335, 839)(336, 840)(337, 841)(338, 842)(339, 843)(340, 844)(341, 845)(342, 846)(343, 847)(344, 848)(345, 849)(346, 850)(347, 851)(348, 852)(349, 853)(350, 854)(351, 855)(352, 856)(353, 857)(354, 858)(355, 859)(356, 860)(357, 861)(358, 862)(359, 863)(360, 864)(361, 865)(362, 866)(363, 867)(364, 868)(365, 869)(366, 870)(367, 871)(368, 872)(369, 873)(370, 874)(371, 875)(372, 876)(373, 877)(374, 878)(375, 879)(376, 880)(377, 881)(378, 882)(379, 883)(380, 884)(381, 885)(382, 886)(383, 887)(384, 888)(385, 889)(386, 890)(387, 891)(388, 892)(389, 893)(390, 894)(391, 895)(392, 896)(393, 897)(394, 898)(395, 899)(396, 900)(397, 901)(398, 902)(399, 903)(400, 904)(401, 905)(402, 906)(403, 907)(404, 908)(405, 909)(406, 910)(407, 911)(408, 912)(409, 913)(410, 914)(411, 915)(412, 916)(413, 917)(414, 918)(415, 919)(416, 920)(417, 921)(418, 922)(419, 923)(420, 924)(421, 925)(422, 926)(423, 927)(424, 928)(425, 929)(426, 930)(427, 931)(428, 932)(429, 933)(430, 934)(431, 935)(432, 936)(433, 937)(434, 938)(435, 939)(436, 940)(437, 941)(438, 942)(439, 943)(440, 944)(441, 945)(442, 946)(443, 947)(444, 948)(445, 949)(446, 950)(447, 951)(448, 952)(449, 953)(450, 954)(451, 955)(452, 956)(453, 957)(454, 958)(455, 959)(456, 960)(457, 961)(458, 962)(459, 963)(460, 964)(461, 965)(462, 966)(463, 967)(464, 968)(465, 969)(466, 970)(467, 971)(468, 972)(469, 973)(470, 974)(471, 975)(472, 976)(473, 977)(474, 978)(475, 979)(476, 980)(477, 981)(478, 982)(479, 983)(480, 984)(481, 985)(482, 986)(483, 987)(484, 988)(485, 989)(486, 990)(487, 991)(488, 992)(489, 993)(490, 994)(491, 995)(492, 996)(493, 997)(494, 998)(495, 999)(496, 1000)(497, 1001)(498, 1002)(499, 1003)(500, 1004)(501, 1005)(502, 1006)(503, 1007)(504, 1008) local type(s) :: { ( 18, 18 ), ( 18^3 ) } Outer automorphisms :: reflexible Dual of E15.1401 Transitivity :: ET+ Graph:: simple bipartite v = 420 e = 504 f = 56 degree seq :: [ 2^252, 3^168 ] E15.1398 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 9}) Quotient :: edge Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^9, (T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2)^2, T2^2 * T1^-1 * T2^-2 * T1 * T2^3 * T1 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^-3 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 37, 48, 26, 13, 5)(2, 6, 14, 27, 50, 58, 32, 16, 7)(4, 11, 22, 41, 73, 62, 34, 17, 8)(10, 21, 40, 70, 116, 107, 64, 35, 18)(12, 23, 43, 76, 125, 131, 79, 44, 24)(15, 29, 53, 90, 147, 153, 93, 54, 30)(20, 39, 69, 113, 183, 176, 109, 65, 36)(25, 45, 80, 132, 209, 215, 135, 81, 46)(28, 52, 89, 144, 231, 224, 140, 85, 49)(31, 55, 94, 154, 245, 251, 157, 95, 56)(33, 59, 99, 161, 258, 264, 164, 100, 60)(38, 68, 112, 180, 288, 285, 178, 110, 66)(42, 75, 123, 196, 312, 305, 192, 119, 72)(47, 82, 136, 216, 336, 341, 219, 137, 83)(51, 88, 143, 228, 284, 351, 226, 141, 86)(57, 96, 158, 252, 378, 381, 255, 159, 97)(61, 101, 165, 265, 390, 337, 268, 166, 102)(63, 104, 168, 270, 394, 310, 273, 169, 105)(67, 111, 179, 286, 409, 342, 220, 138, 84)(71, 118, 190, 300, 218, 339, 296, 186, 115)(74, 122, 195, 309, 350, 408, 307, 193, 120)(77, 127, 202, 320, 254, 379, 316, 198, 124)(78, 128, 203, 322, 287, 181, 290, 204, 129)(87, 142, 227, 352, 407, 281, 256, 160, 98)(91, 149, 238, 364, 267, 391, 361, 234, 146)(92, 150, 239, 366, 353, 229, 355, 240, 151)(103, 121, 194, 308, 329, 440, 347, 269, 167)(106, 170, 274, 400, 328, 210, 330, 275, 171)(108, 173, 277, 402, 479, 420, 405, 278, 174)(114, 185, 294, 213, 134, 212, 332, 291, 182)(117, 189, 299, 419, 304, 424, 418, 297, 187)(126, 201, 319, 280, 175, 279, 406, 317, 199)(130, 205, 325, 436, 372, 246, 373, 326, 206)(133, 211, 331, 441, 437, 463, 439, 327, 208)(139, 221, 343, 444, 403, 431, 447, 344, 222)(145, 233, 359, 249, 156, 248, 375, 356, 230)(148, 237, 363, 346, 223, 345, 448, 362, 235)(152, 241, 369, 461, 383, 259, 384, 370, 242)(155, 247, 374, 465, 462, 468, 464, 371, 244)(162, 260, 385, 470, 401, 438, 469, 382, 257)(163, 261, 386, 426, 311, 197, 314, 387, 262)(172, 188, 298, 207, 200, 318, 243, 236, 276)(177, 282, 354, 449, 498, 467, 376, 250, 283)(184, 293, 413, 485, 417, 340, 377, 253, 292)(191, 302, 423, 480, 445, 456, 478, 399, 303)(214, 333, 306, 410, 289, 411, 483, 443, 334)(217, 338, 313, 427, 490, 502, 455, 392, 335)(225, 348, 425, 395, 474, 472, 388, 263, 349)(232, 358, 451, 492, 430, 380, 389, 266, 357)(271, 396, 475, 491, 429, 315, 428, 473, 393)(272, 397, 476, 488, 421, 301, 422, 477, 398)(295, 415, 487, 458, 367, 459, 504, 482, 416)(321, 414, 486, 435, 324, 404, 481, 493, 432)(323, 434, 495, 501, 454, 360, 453, 494, 433)(365, 452, 500, 460, 368, 446, 497, 503, 457)(412, 442, 496, 489, 471, 499, 450, 466, 484)(505, 506, 508)(507, 512, 514)(509, 516, 510)(511, 519, 515)(513, 522, 524)(517, 529, 527)(518, 528, 532)(520, 535, 533)(521, 537, 525)(523, 540, 542)(526, 534, 546)(530, 551, 549)(531, 553, 555)(536, 561, 559)(538, 565, 563)(539, 567, 543)(541, 570, 571)(544, 564, 575)(545, 576, 578)(547, 550, 581)(548, 582, 556)(552, 588, 586)(554, 590, 591)(557, 560, 595)(558, 596, 579)(562, 602, 600)(566, 607, 605)(568, 610, 608)(569, 612, 572)(573, 609, 618)(574, 619, 621)(577, 624, 625)(580, 628, 630)(583, 634, 632)(584, 587, 637)(585, 638, 631)(589, 643, 592)(593, 633, 649)(594, 650, 652)(597, 656, 654)(598, 601, 659)(599, 660, 653)(603, 606, 666)(604, 667, 622)(611, 676, 674)(613, 679, 677)(614, 681, 615)(616, 678, 685)(617, 686, 688)(620, 691, 692)(623, 695, 626)(627, 655, 701)(629, 703, 704)(635, 711, 709)(636, 712, 714)(639, 718, 716)(640, 642, 721)(641, 722, 715)(644, 727, 725)(645, 729, 646)(647, 726, 733)(648, 734, 736)(651, 739, 740)(657, 747, 745)(658, 748, 750)(661, 754, 752)(662, 664, 757)(663, 758, 751)(665, 761, 763)(668, 767, 765)(669, 671, 770)(670, 771, 764)(672, 675, 775)(673, 776, 689)(680, 785, 783)(682, 788, 786)(683, 787, 755)(684, 791, 793)(687, 796, 760)(690, 799, 693)(694, 766, 805)(696, 808, 806)(697, 810, 698)(699, 807, 814)(700, 815, 817)(702, 819, 705)(706, 717, 825)(707, 710, 827)(708, 828, 737)(713, 832, 833)(719, 812, 837)(720, 839, 841)(723, 844, 843)(724, 816, 842)(728, 851, 849)(730, 854, 852)(731, 853, 768)(732, 857, 858)(735, 861, 773)(738, 864, 741)(742, 753, 869)(743, 746, 871)(744, 872, 818)(749, 876, 790)(756, 881, 845)(759, 884, 883)(762, 887, 856)(769, 893, 885)(772, 896, 895)(774, 897, 899)(777, 903, 901)(778, 780, 866)(779, 905, 900)(781, 784, 907)(782, 908, 794)(789, 912, 855)(792, 914, 811)(795, 916, 797)(798, 902, 918)(800, 921, 919)(801, 829, 802)(803, 920, 924)(804, 925, 835)(809, 846, 928)(813, 898, 929)(820, 934, 932)(821, 873, 822)(823, 933, 935)(824, 936, 878)(826, 937, 915)(830, 941, 938)(831, 942, 834)(836, 838, 946)(840, 894, 882)(847, 850, 949)(848, 950, 859)(860, 954, 862)(863, 939, 956)(865, 959, 957)(867, 958, 960)(868, 961, 889)(870, 962, 953)(874, 966, 963)(875, 967, 877)(879, 880, 970)(886, 972, 888)(890, 892, 975)(891, 964, 926)(904, 952, 944)(906, 948, 984)(909, 986, 985)(910, 911, 965)(913, 940, 922)(917, 988, 971)(923, 983, 927)(930, 993, 931)(943, 968, 973)(945, 992, 999)(947, 994, 1000)(951, 995, 1001)(955, 1003, 976)(969, 997, 1008)(974, 1007, 979)(977, 996, 978)(980, 982, 1005)(981, 1004, 990)(987, 998, 1006)(989, 1002, 991) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 673)(170, 674)(171, 675)(172, 676)(173, 677)(174, 678)(175, 679)(176, 680)(177, 681)(178, 682)(179, 683)(180, 684)(181, 685)(182, 686)(183, 687)(184, 688)(185, 689)(186, 690)(187, 691)(188, 692)(189, 693)(190, 694)(191, 695)(192, 696)(193, 697)(194, 698)(195, 699)(196, 700)(197, 701)(198, 702)(199, 703)(200, 704)(201, 705)(202, 706)(203, 707)(204, 708)(205, 709)(206, 710)(207, 711)(208, 712)(209, 713)(210, 714)(211, 715)(212, 716)(213, 717)(214, 718)(215, 719)(216, 720)(217, 721)(218, 722)(219, 723)(220, 724)(221, 725)(222, 726)(223, 727)(224, 728)(225, 729)(226, 730)(227, 731)(228, 732)(229, 733)(230, 734)(231, 735)(232, 736)(233, 737)(234, 738)(235, 739)(236, 740)(237, 741)(238, 742)(239, 743)(240, 744)(241, 745)(242, 746)(243, 747)(244, 748)(245, 749)(246, 750)(247, 751)(248, 752)(249, 753)(250, 754)(251, 755)(252, 756)(253, 757)(254, 758)(255, 759)(256, 760)(257, 761)(258, 762)(259, 763)(260, 764)(261, 765)(262, 766)(263, 767)(264, 768)(265, 769)(266, 770)(267, 771)(268, 772)(269, 773)(270, 774)(271, 775)(272, 776)(273, 777)(274, 778)(275, 779)(276, 780)(277, 781)(278, 782)(279, 783)(280, 784)(281, 785)(282, 786)(283, 787)(284, 788)(285, 789)(286, 790)(287, 791)(288, 792)(289, 793)(290, 794)(291, 795)(292, 796)(293, 797)(294, 798)(295, 799)(296, 800)(297, 801)(298, 802)(299, 803)(300, 804)(301, 805)(302, 806)(303, 807)(304, 808)(305, 809)(306, 810)(307, 811)(308, 812)(309, 813)(310, 814)(311, 815)(312, 816)(313, 817)(314, 818)(315, 819)(316, 820)(317, 821)(318, 822)(319, 823)(320, 824)(321, 825)(322, 826)(323, 827)(324, 828)(325, 829)(326, 830)(327, 831)(328, 832)(329, 833)(330, 834)(331, 835)(332, 836)(333, 837)(334, 838)(335, 839)(336, 840)(337, 841)(338, 842)(339, 843)(340, 844)(341, 845)(342, 846)(343, 847)(344, 848)(345, 849)(346, 850)(347, 851)(348, 852)(349, 853)(350, 854)(351, 855)(352, 856)(353, 857)(354, 858)(355, 859)(356, 860)(357, 861)(358, 862)(359, 863)(360, 864)(361, 865)(362, 866)(363, 867)(364, 868)(365, 869)(366, 870)(367, 871)(368, 872)(369, 873)(370, 874)(371, 875)(372, 876)(373, 877)(374, 878)(375, 879)(376, 880)(377, 881)(378, 882)(379, 883)(380, 884)(381, 885)(382, 886)(383, 887)(384, 888)(385, 889)(386, 890)(387, 891)(388, 892)(389, 893)(390, 894)(391, 895)(392, 896)(393, 897)(394, 898)(395, 899)(396, 900)(397, 901)(398, 902)(399, 903)(400, 904)(401, 905)(402, 906)(403, 907)(404, 908)(405, 909)(406, 910)(407, 911)(408, 912)(409, 913)(410, 914)(411, 915)(412, 916)(413, 917)(414, 918)(415, 919)(416, 920)(417, 921)(418, 922)(419, 923)(420, 924)(421, 925)(422, 926)(423, 927)(424, 928)(425, 929)(426, 930)(427, 931)(428, 932)(429, 933)(430, 934)(431, 935)(432, 936)(433, 937)(434, 938)(435, 939)(436, 940)(437, 941)(438, 942)(439, 943)(440, 944)(441, 945)(442, 946)(443, 947)(444, 948)(445, 949)(446, 950)(447, 951)(448, 952)(449, 953)(450, 954)(451, 955)(452, 956)(453, 957)(454, 958)(455, 959)(456, 960)(457, 961)(458, 962)(459, 963)(460, 964)(461, 965)(462, 966)(463, 967)(464, 968)(465, 969)(466, 970)(467, 971)(468, 972)(469, 973)(470, 974)(471, 975)(472, 976)(473, 977)(474, 978)(475, 979)(476, 980)(477, 981)(478, 982)(479, 983)(480, 984)(481, 985)(482, 986)(483, 987)(484, 988)(485, 989)(486, 990)(487, 991)(488, 992)(489, 993)(490, 994)(491, 995)(492, 996)(493, 997)(494, 998)(495, 999)(496, 1000)(497, 1001)(498, 1002)(499, 1003)(500, 1004)(501, 1005)(502, 1006)(503, 1007)(504, 1008) local type(s) :: { ( 4^3 ), ( 4^9 ) } Outer automorphisms :: reflexible Dual of E15.1402 Transitivity :: ET+ Graph:: simple bipartite v = 224 e = 504 f = 252 degree seq :: [ 3^168, 9^56 ] E15.1399 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 9}) Quotient :: edge Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^9, (T1^-3 * T2 * T1^3 * T2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3 * T2 * T1 * T2 * T1^-2 * T2 * T1^-4, (T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1)^2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 37)(24, 38)(25, 43)(26, 44)(27, 47)(29, 48)(31, 52)(32, 55)(34, 58)(36, 60)(39, 61)(40, 66)(41, 67)(42, 70)(45, 73)(46, 75)(49, 76)(50, 80)(51, 83)(53, 85)(54, 87)(56, 88)(57, 92)(59, 95)(62, 96)(63, 100)(64, 101)(65, 104)(68, 107)(69, 109)(71, 110)(72, 114)(74, 116)(77, 117)(78, 122)(79, 123)(81, 126)(82, 128)(84, 131)(86, 133)(89, 134)(90, 138)(91, 141)(93, 142)(94, 146)(97, 150)(98, 151)(99, 154)(102, 157)(103, 159)(105, 160)(106, 164)(108, 166)(111, 167)(112, 171)(113, 174)(115, 177)(118, 132)(119, 182)(120, 183)(121, 186)(124, 189)(125, 192)(127, 195)(129, 196)(130, 200)(135, 203)(136, 208)(137, 209)(139, 212)(140, 213)(143, 214)(144, 218)(145, 221)(147, 222)(148, 226)(149, 228)(152, 231)(153, 233)(155, 234)(156, 238)(158, 240)(161, 241)(162, 245)(163, 248)(165, 251)(168, 178)(169, 256)(170, 257)(172, 260)(173, 262)(175, 263)(176, 267)(179, 271)(180, 272)(181, 274)(184, 277)(185, 278)(187, 279)(188, 283)(190, 285)(191, 287)(193, 204)(194, 290)(197, 291)(198, 295)(199, 298)(201, 299)(202, 303)(205, 306)(206, 307)(207, 309)(210, 312)(211, 315)(215, 317)(216, 320)(217, 321)(219, 324)(220, 302)(223, 325)(224, 328)(225, 297)(227, 332)(229, 333)(230, 273)(232, 336)(235, 337)(236, 339)(237, 342)(239, 343)(242, 252)(243, 347)(244, 348)(246, 350)(247, 352)(249, 353)(250, 355)(253, 358)(254, 359)(255, 361)(258, 364)(259, 366)(261, 270)(264, 368)(265, 372)(266, 373)(268, 374)(269, 316)(275, 377)(276, 380)(280, 381)(281, 384)(282, 385)(284, 387)(286, 388)(288, 389)(289, 345)(292, 356)(293, 395)(294, 396)(296, 331)(300, 399)(301, 313)(304, 367)(305, 403)(308, 400)(310, 405)(311, 407)(314, 408)(318, 410)(319, 412)(322, 401)(323, 414)(326, 360)(327, 397)(329, 417)(330, 392)(334, 419)(335, 378)(338, 423)(340, 425)(341, 427)(344, 429)(346, 430)(349, 434)(351, 357)(354, 435)(362, 437)(363, 440)(365, 441)(369, 376)(370, 445)(371, 446)(375, 402)(379, 447)(382, 451)(383, 452)(386, 453)(390, 454)(391, 413)(393, 457)(394, 458)(398, 418)(404, 448)(406, 459)(409, 464)(411, 455)(415, 438)(416, 456)(420, 473)(421, 475)(422, 465)(424, 478)(426, 428)(431, 479)(432, 469)(433, 481)(436, 467)(439, 484)(442, 485)(443, 486)(444, 487)(449, 489)(450, 490)(460, 488)(461, 477)(462, 497)(463, 483)(466, 471)(468, 494)(470, 498)(472, 492)(474, 476)(480, 500)(482, 501)(491, 503)(493, 495)(496, 502)(499, 504)(505, 506, 509, 515, 525, 540, 524, 514, 508)(507, 511, 519, 531, 550, 557, 535, 521, 512)(510, 517, 529, 546, 573, 578, 549, 530, 518)(513, 522, 536, 558, 590, 585, 554, 533, 520)(516, 527, 544, 569, 607, 612, 572, 545, 528)(523, 538, 561, 595, 644, 643, 594, 560, 537)(526, 542, 567, 603, 657, 662, 606, 568, 543)(532, 552, 582, 625, 689, 694, 628, 583, 553)(534, 555, 586, 631, 698, 676, 616, 575, 547)(539, 563, 598, 649, 724, 723, 648, 597, 562)(541, 565, 601, 653, 731, 736, 656, 602, 566)(548, 576, 617, 677, 765, 750, 666, 609, 570)(551, 580, 623, 685, 777, 735, 688, 624, 581)(556, 588, 634, 703, 801, 800, 702, 633, 587)(559, 592, 640, 711, 812, 817, 714, 641, 593)(564, 600, 652, 729, 834, 833, 728, 651, 599)(571, 610, 667, 751, 855, 844, 740, 659, 604)(574, 614, 673, 759, 864, 832, 762, 674, 615)(577, 619, 680, 770, 725, 829, 769, 679, 618)(579, 621, 683, 774, 880, 847, 744, 684, 622)(584, 629, 695, 790, 732, 837, 785, 691, 626)(589, 636, 706, 806, 877, 906, 805, 705, 635)(591, 638, 709, 809, 742, 661, 743, 710, 639)(596, 646, 720, 823, 915, 917, 826, 721, 647)(605, 660, 741, 845, 930, 924, 838, 733, 654)(608, 664, 747, 850, 824, 722, 827, 748, 665)(611, 669, 754, 719, 645, 718, 822, 753, 668)(613, 671, 757, 861, 884, 781, 840, 758, 672)(620, 682, 773, 717, 821, 891, 789, 772, 681)(627, 692, 786, 846, 907, 952, 883, 779, 686)(630, 697, 793, 896, 802, 903, 895, 792, 696)(632, 700, 797, 898, 949, 876, 901, 798, 701)(637, 707, 808, 794, 860, 755, 670, 756, 708)(642, 715, 818, 739, 658, 738, 842, 814, 712)(650, 726, 830, 919, 974, 975, 920, 831, 727)(655, 734, 839, 925, 978, 976, 922, 835, 730)(663, 745, 848, 932, 944, 868, 921, 849, 746)(675, 763, 869, 882, 778, 881, 943, 866, 760)(678, 767, 874, 948, 971, 914, 825, 875, 768)(687, 780, 856, 939, 987, 986, 938, 854, 775)(690, 783, 886, 954, 899, 799, 902, 887, 784)(693, 788, 859, 796, 699, 795, 897, 890, 787)(704, 803, 904, 963, 1000, 990, 950, 905, 804)(713, 815, 858, 752, 857, 940, 964, 908, 810)(716, 820, 863, 836, 892, 958, 970, 913, 819)(737, 841, 926, 980, 973, 918, 828, 807, 776)(749, 853, 937, 942, 865, 941, 984, 935, 851)(761, 867, 931, 889, 957, 997, 982, 929, 862)(764, 871, 811, 873, 766, 872, 947, 946, 870)(771, 878, 782, 885, 953, 967, 911, 816, 879)(791, 893, 959, 998, 999, 961, 900, 960, 894)(813, 909, 965, 995, 955, 888, 923, 966, 910)(843, 928, 972, 916, 934, 983, 1003, 981, 927)(852, 936, 979, 945, 989, 1006, 1001, 977, 933)(912, 968, 1002, 985, 1005, 993, 956, 996, 969)(951, 992, 991, 962, 994, 1007, 1008, 1004, 988) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 673)(170, 674)(171, 675)(172, 676)(173, 677)(174, 678)(175, 679)(176, 680)(177, 681)(178, 682)(179, 683)(180, 684)(181, 685)(182, 686)(183, 687)(184, 688)(185, 689)(186, 690)(187, 691)(188, 692)(189, 693)(190, 694)(191, 695)(192, 696)(193, 697)(194, 698)(195, 699)(196, 700)(197, 701)(198, 702)(199, 703)(200, 704)(201, 705)(202, 706)(203, 707)(204, 708)(205, 709)(206, 710)(207, 711)(208, 712)(209, 713)(210, 714)(211, 715)(212, 716)(213, 717)(214, 718)(215, 719)(216, 720)(217, 721)(218, 722)(219, 723)(220, 724)(221, 725)(222, 726)(223, 727)(224, 728)(225, 729)(226, 730)(227, 731)(228, 732)(229, 733)(230, 734)(231, 735)(232, 736)(233, 737)(234, 738)(235, 739)(236, 740)(237, 741)(238, 742)(239, 743)(240, 744)(241, 745)(242, 746)(243, 747)(244, 748)(245, 749)(246, 750)(247, 751)(248, 752)(249, 753)(250, 754)(251, 755)(252, 756)(253, 757)(254, 758)(255, 759)(256, 760)(257, 761)(258, 762)(259, 763)(260, 764)(261, 765)(262, 766)(263, 767)(264, 768)(265, 769)(266, 770)(267, 771)(268, 772)(269, 773)(270, 774)(271, 775)(272, 776)(273, 777)(274, 778)(275, 779)(276, 780)(277, 781)(278, 782)(279, 783)(280, 784)(281, 785)(282, 786)(283, 787)(284, 788)(285, 789)(286, 790)(287, 791)(288, 792)(289, 793)(290, 794)(291, 795)(292, 796)(293, 797)(294, 798)(295, 799)(296, 800)(297, 801)(298, 802)(299, 803)(300, 804)(301, 805)(302, 806)(303, 807)(304, 808)(305, 809)(306, 810)(307, 811)(308, 812)(309, 813)(310, 814)(311, 815)(312, 816)(313, 817)(314, 818)(315, 819)(316, 820)(317, 821)(318, 822)(319, 823)(320, 824)(321, 825)(322, 826)(323, 827)(324, 828)(325, 829)(326, 830)(327, 831)(328, 832)(329, 833)(330, 834)(331, 835)(332, 836)(333, 837)(334, 838)(335, 839)(336, 840)(337, 841)(338, 842)(339, 843)(340, 844)(341, 845)(342, 846)(343, 847)(344, 848)(345, 849)(346, 850)(347, 851)(348, 852)(349, 853)(350, 854)(351, 855)(352, 856)(353, 857)(354, 858)(355, 859)(356, 860)(357, 861)(358, 862)(359, 863)(360, 864)(361, 865)(362, 866)(363, 867)(364, 868)(365, 869)(366, 870)(367, 871)(368, 872)(369, 873)(370, 874)(371, 875)(372, 876)(373, 877)(374, 878)(375, 879)(376, 880)(377, 881)(378, 882)(379, 883)(380, 884)(381, 885)(382, 886)(383, 887)(384, 888)(385, 889)(386, 890)(387, 891)(388, 892)(389, 893)(390, 894)(391, 895)(392, 896)(393, 897)(394, 898)(395, 899)(396, 900)(397, 901)(398, 902)(399, 903)(400, 904)(401, 905)(402, 906)(403, 907)(404, 908)(405, 909)(406, 910)(407, 911)(408, 912)(409, 913)(410, 914)(411, 915)(412, 916)(413, 917)(414, 918)(415, 919)(416, 920)(417, 921)(418, 922)(419, 923)(420, 924)(421, 925)(422, 926)(423, 927)(424, 928)(425, 929)(426, 930)(427, 931)(428, 932)(429, 933)(430, 934)(431, 935)(432, 936)(433, 937)(434, 938)(435, 939)(436, 940)(437, 941)(438, 942)(439, 943)(440, 944)(441, 945)(442, 946)(443, 947)(444, 948)(445, 949)(446, 950)(447, 951)(448, 952)(449, 953)(450, 954)(451, 955)(452, 956)(453, 957)(454, 958)(455, 959)(456, 960)(457, 961)(458, 962)(459, 963)(460, 964)(461, 965)(462, 966)(463, 967)(464, 968)(465, 969)(466, 970)(467, 971)(468, 972)(469, 973)(470, 974)(471, 975)(472, 976)(473, 977)(474, 978)(475, 979)(476, 980)(477, 981)(478, 982)(479, 983)(480, 984)(481, 985)(482, 986)(483, 987)(484, 988)(485, 989)(486, 990)(487, 991)(488, 992)(489, 993)(490, 994)(491, 995)(492, 996)(493, 997)(494, 998)(495, 999)(496, 1000)(497, 1001)(498, 1002)(499, 1003)(500, 1004)(501, 1005)(502, 1006)(503, 1007)(504, 1008) local type(s) :: { ( 6, 6 ), ( 6^9 ) } Outer automorphisms :: reflexible Dual of E15.1400 Transitivity :: ET+ Graph:: simple bipartite v = 308 e = 504 f = 168 degree seq :: [ 2^252, 9^56 ] E15.1400 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 9}) Quotient :: loop Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1)^9, (T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1)^2, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2 * T1 * T2^-1 * T1)^7 ] Map:: R = (1, 505, 3, 507, 4, 508)(2, 506, 5, 509, 6, 510)(7, 511, 11, 515, 12, 516)(8, 512, 13, 517, 14, 518)(9, 513, 15, 519, 16, 520)(10, 514, 17, 521, 18, 522)(19, 523, 27, 531, 28, 532)(20, 524, 29, 533, 30, 534)(21, 525, 31, 535, 32, 536)(22, 526, 33, 537, 34, 538)(23, 527, 35, 539, 36, 540)(24, 528, 37, 541, 38, 542)(25, 529, 39, 543, 40, 544)(26, 530, 41, 545, 42, 546)(43, 547, 59, 563, 60, 564)(44, 548, 61, 565, 62, 566)(45, 549, 63, 567, 64, 568)(46, 550, 65, 569, 66, 570)(47, 551, 67, 571, 68, 572)(48, 552, 69, 573, 70, 574)(49, 553, 71, 575, 72, 576)(50, 554, 73, 577, 74, 578)(51, 555, 75, 579, 76, 580)(52, 556, 77, 581, 78, 582)(53, 557, 79, 583, 80, 584)(54, 558, 81, 585, 82, 586)(55, 559, 83, 587, 84, 588)(56, 560, 85, 589, 86, 590)(57, 561, 87, 591, 88, 592)(58, 562, 89, 593, 90, 594)(91, 595, 122, 626, 123, 627)(92, 596, 124, 628, 125, 629)(93, 597, 126, 630, 127, 631)(94, 598, 128, 632, 129, 633)(95, 599, 130, 634, 131, 635)(96, 600, 132, 636, 133, 637)(97, 601, 134, 638, 135, 639)(98, 602, 136, 640, 137, 641)(99, 603, 138, 642, 139, 643)(100, 604, 140, 644, 141, 645)(101, 605, 142, 646, 143, 647)(102, 606, 144, 648, 145, 649)(103, 607, 146, 650, 147, 651)(104, 608, 148, 652, 149, 653)(105, 609, 150, 654, 151, 655)(106, 610, 152, 656, 107, 611)(108, 612, 153, 657, 154, 658)(109, 613, 155, 659, 156, 660)(110, 614, 157, 661, 158, 662)(111, 615, 159, 663, 160, 664)(112, 616, 161, 665, 162, 666)(113, 617, 163, 667, 164, 668)(114, 618, 165, 669, 166, 670)(115, 619, 167, 671, 168, 672)(116, 620, 169, 673, 170, 674)(117, 621, 171, 675, 172, 676)(118, 622, 173, 677, 174, 678)(119, 623, 175, 679, 176, 680)(120, 624, 177, 681, 178, 682)(121, 625, 179, 683, 180, 684)(181, 685, 327, 831, 237, 741)(182, 686, 230, 734, 391, 895)(183, 687, 223, 727, 381, 885)(184, 688, 260, 764, 407, 911)(185, 689, 331, 835, 478, 982)(186, 690, 333, 837, 283, 787)(187, 691, 335, 839, 241, 745)(188, 692, 337, 841, 377, 881)(189, 693, 338, 842, 479, 983)(190, 694, 334, 838, 480, 984)(191, 695, 278, 782, 449, 953)(192, 696, 228, 732, 389, 893)(193, 697, 250, 754, 414, 918)(194, 698, 293, 797, 224, 728)(195, 699, 325, 829, 248, 752)(196, 700, 239, 743, 400, 904)(197, 701, 232, 736, 393, 897)(198, 702, 265, 769, 427, 931)(199, 703, 344, 848, 486, 990)(200, 704, 346, 850, 291, 795)(201, 705, 348, 852, 229, 733)(202, 706, 350, 854, 365, 869)(203, 707, 351, 855, 473, 977)(204, 708, 347, 851, 487, 991)(205, 709, 286, 790, 453, 957)(206, 710, 218, 722, 375, 879)(207, 711, 238, 742, 398, 902)(208, 712, 354, 858, 233, 737)(209, 713, 356, 860, 357, 861)(210, 714, 359, 863, 360, 864)(211, 715, 306, 810, 312, 816)(212, 716, 363, 867, 364, 868)(213, 717, 282, 786, 285, 789)(214, 718, 366, 870, 367, 871)(215, 719, 369, 873, 370, 874)(216, 720, 371, 875, 324, 828)(217, 721, 373, 877, 374, 878)(219, 723, 290, 794, 252, 756)(220, 724, 376, 880, 294, 798)(221, 725, 256, 760, 277, 781)(222, 726, 378, 882, 379, 883)(225, 729, 383, 887, 384, 888)(226, 730, 318, 822, 386, 890)(227, 731, 388, 892, 292, 796)(231, 735, 342, 846, 305, 809)(234, 738, 394, 898, 326, 830)(235, 739, 395, 899, 382, 886)(236, 740, 397, 901, 313, 817)(240, 744, 268, 772, 273, 777)(242, 746, 329, 833, 340, 844)(243, 747, 404, 908, 311, 815)(244, 748, 258, 762, 263, 767)(245, 749, 299, 803, 406, 910)(246, 750, 408, 912, 409, 913)(247, 751, 411, 915, 412, 916)(249, 753, 301, 805, 320, 824)(251, 755, 416, 920, 417, 921)(253, 757, 385, 889, 361, 865)(254, 758, 280, 784, 288, 792)(255, 759, 420, 924, 307, 811)(257, 761, 422, 926, 423, 927)(259, 763, 425, 929, 426, 930)(261, 765, 428, 932, 429, 933)(262, 766, 304, 808, 430, 934)(264, 768, 432, 936, 433, 937)(266, 770, 434, 938, 435, 939)(267, 771, 437, 941, 438, 942)(269, 773, 343, 847, 330, 834)(270, 774, 402, 906, 295, 799)(271, 775, 441, 945, 442, 946)(272, 776, 281, 785, 443, 947)(274, 778, 444, 948, 445, 949)(275, 779, 440, 944, 314, 818)(276, 780, 317, 821, 447, 951)(279, 783, 387, 891, 362, 866)(284, 788, 448, 952, 452, 956)(287, 791, 372, 876, 355, 859)(289, 793, 455, 959, 339, 843)(296, 800, 457, 961, 458, 962)(297, 801, 460, 964, 303, 807)(298, 802, 431, 935, 308, 812)(300, 804, 390, 894, 332, 836)(302, 806, 461, 965, 464, 968)(309, 813, 466, 970, 454, 958)(310, 814, 459, 963, 467, 971)(315, 819, 468, 972, 469, 973)(316, 820, 470, 974, 322, 826)(319, 823, 368, 872, 358, 862)(321, 825, 471, 975, 474, 978)(323, 827, 341, 845, 446, 950)(328, 832, 415, 919, 476, 980)(336, 840, 419, 923, 481, 985)(345, 849, 401, 905, 399, 903)(349, 853, 451, 955, 489, 993)(352, 856, 463, 967, 491, 995)(353, 857, 488, 992, 462, 966)(380, 884, 405, 909, 403, 907)(392, 896, 424, 928, 421, 925)(396, 900, 439, 943, 436, 940)(410, 914, 477, 981, 456, 960)(413, 917, 484, 988, 483, 987)(418, 922, 482, 986, 494, 998)(450, 954, 490, 994, 475, 979)(465, 969, 504, 1008, 472, 976)(485, 989, 497, 1001, 501, 1005)(492, 996, 502, 1006, 496, 1000)(493, 997, 503, 1007, 495, 999)(498, 1002, 500, 1004, 499, 1003) L = (1, 506)(2, 505)(3, 511)(4, 512)(5, 513)(6, 514)(7, 507)(8, 508)(9, 509)(10, 510)(11, 523)(12, 524)(13, 525)(14, 526)(15, 527)(16, 528)(17, 529)(18, 530)(19, 515)(20, 516)(21, 517)(22, 518)(23, 519)(24, 520)(25, 521)(26, 522)(27, 547)(28, 548)(29, 549)(30, 550)(31, 551)(32, 552)(33, 553)(34, 554)(35, 555)(36, 556)(37, 557)(38, 558)(39, 559)(40, 560)(41, 561)(42, 562)(43, 531)(44, 532)(45, 533)(46, 534)(47, 535)(48, 536)(49, 537)(50, 538)(51, 539)(52, 540)(53, 541)(54, 542)(55, 543)(56, 544)(57, 545)(58, 546)(59, 595)(60, 596)(61, 597)(62, 598)(63, 599)(64, 600)(65, 601)(66, 602)(67, 603)(68, 604)(69, 605)(70, 606)(71, 607)(72, 608)(73, 609)(74, 610)(75, 611)(76, 612)(77, 613)(78, 614)(79, 615)(80, 616)(81, 617)(82, 618)(83, 619)(84, 620)(85, 621)(86, 622)(87, 623)(88, 624)(89, 625)(90, 626)(91, 563)(92, 564)(93, 565)(94, 566)(95, 567)(96, 568)(97, 569)(98, 570)(99, 571)(100, 572)(101, 573)(102, 574)(103, 575)(104, 576)(105, 577)(106, 578)(107, 579)(108, 580)(109, 581)(110, 582)(111, 583)(112, 584)(113, 585)(114, 586)(115, 587)(116, 588)(117, 589)(118, 590)(119, 591)(120, 592)(121, 593)(122, 594)(123, 685)(124, 686)(125, 687)(126, 688)(127, 689)(128, 690)(129, 691)(130, 692)(131, 693)(132, 694)(133, 695)(134, 696)(135, 697)(136, 698)(137, 642)(138, 641)(139, 699)(140, 700)(141, 701)(142, 702)(143, 703)(144, 704)(145, 705)(146, 706)(147, 707)(148, 708)(149, 709)(150, 710)(151, 711)(152, 712)(153, 796)(154, 798)(155, 799)(156, 800)(157, 802)(158, 803)(159, 739)(160, 770)(161, 806)(162, 807)(163, 809)(164, 811)(165, 760)(166, 671)(167, 670)(168, 723)(169, 815)(170, 817)(171, 818)(172, 819)(173, 821)(174, 822)(175, 757)(176, 813)(177, 825)(178, 826)(179, 828)(180, 830)(181, 627)(182, 628)(183, 629)(184, 630)(185, 631)(186, 632)(187, 633)(188, 634)(189, 635)(190, 636)(191, 637)(192, 638)(193, 639)(194, 640)(195, 643)(196, 644)(197, 645)(198, 646)(199, 647)(200, 648)(201, 649)(202, 650)(203, 651)(204, 652)(205, 653)(206, 654)(207, 655)(208, 656)(209, 859)(210, 862)(211, 865)(212, 866)(213, 869)(214, 836)(215, 872)(216, 823)(217, 876)(218, 791)(219, 672)(220, 849)(221, 881)(222, 774)(223, 884)(224, 886)(225, 764)(226, 889)(227, 891)(228, 783)(229, 854)(230, 894)(231, 804)(232, 896)(233, 888)(234, 769)(235, 663)(236, 900)(237, 883)(238, 779)(239, 903)(240, 905)(241, 841)(242, 906)(243, 907)(244, 909)(245, 899)(246, 911)(247, 914)(248, 871)(249, 917)(250, 857)(251, 919)(252, 868)(253, 679)(254, 922)(255, 923)(256, 669)(257, 925)(258, 928)(259, 887)(260, 729)(261, 931)(262, 812)(263, 935)(264, 898)(265, 738)(266, 664)(267, 940)(268, 943)(269, 882)(270, 726)(271, 944)(272, 787)(273, 837)(274, 902)(275, 742)(276, 950)(277, 861)(278, 952)(279, 732)(280, 954)(281, 955)(282, 839)(283, 776)(284, 941)(285, 816)(286, 920)(287, 722)(288, 958)(289, 945)(290, 852)(291, 843)(292, 657)(293, 864)(294, 658)(295, 659)(296, 660)(297, 963)(298, 661)(299, 662)(300, 735)(301, 967)(302, 665)(303, 666)(304, 969)(305, 667)(306, 910)(307, 668)(308, 766)(309, 680)(310, 926)(311, 673)(312, 789)(313, 674)(314, 675)(315, 676)(316, 915)(317, 677)(318, 678)(319, 720)(320, 977)(321, 681)(322, 682)(323, 932)(324, 683)(325, 890)(326, 684)(327, 878)(328, 960)(329, 981)(330, 870)(331, 973)(332, 718)(333, 777)(334, 978)(335, 786)(336, 975)(337, 745)(338, 927)(339, 795)(340, 850)(341, 987)(342, 988)(343, 880)(344, 989)(345, 724)(346, 844)(347, 966)(348, 794)(349, 992)(350, 733)(351, 934)(352, 918)(353, 754)(354, 874)(355, 713)(356, 937)(357, 781)(358, 714)(359, 949)(360, 797)(361, 715)(362, 716)(363, 930)(364, 756)(365, 717)(366, 834)(367, 752)(368, 719)(369, 974)(370, 858)(371, 995)(372, 721)(373, 957)(374, 831)(375, 994)(376, 847)(377, 725)(378, 773)(379, 741)(380, 727)(381, 929)(382, 728)(383, 763)(384, 737)(385, 730)(386, 829)(387, 731)(388, 953)(389, 986)(390, 734)(391, 964)(392, 736)(393, 936)(394, 768)(395, 749)(396, 740)(397, 948)(398, 778)(399, 743)(400, 996)(401, 744)(402, 746)(403, 747)(404, 997)(405, 748)(406, 810)(407, 750)(408, 980)(409, 951)(410, 751)(411, 820)(412, 983)(413, 753)(414, 856)(415, 755)(416, 790)(417, 939)(418, 758)(419, 759)(420, 979)(421, 761)(422, 814)(423, 842)(424, 762)(425, 885)(426, 867)(427, 765)(428, 827)(429, 956)(430, 855)(431, 767)(432, 897)(433, 860)(434, 942)(435, 921)(436, 771)(437, 788)(438, 938)(439, 772)(440, 775)(441, 793)(442, 971)(443, 970)(444, 901)(445, 863)(446, 780)(447, 913)(448, 782)(449, 892)(450, 784)(451, 785)(452, 933)(453, 877)(454, 792)(455, 998)(456, 832)(457, 990)(458, 1007)(459, 801)(460, 895)(461, 991)(462, 851)(463, 805)(464, 1002)(465, 808)(466, 947)(467, 946)(468, 1003)(469, 835)(470, 873)(471, 840)(472, 985)(473, 824)(474, 838)(475, 924)(476, 912)(477, 833)(478, 1006)(479, 916)(480, 1001)(481, 976)(482, 893)(483, 845)(484, 846)(485, 848)(486, 961)(487, 965)(488, 853)(489, 999)(490, 879)(491, 875)(492, 904)(493, 908)(494, 959)(495, 993)(496, 1008)(497, 984)(498, 968)(499, 972)(500, 1005)(501, 1004)(502, 982)(503, 962)(504, 1000) local type(s) :: { ( 2, 9, 2, 9, 2, 9 ) } Outer automorphisms :: reflexible Dual of E15.1399 Transitivity :: ET+ VT+ AT Graph:: v = 168 e = 504 f = 308 degree seq :: [ 6^168 ] E15.1401 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 9}) Quotient :: loop Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^9, (T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2)^2, T2^2 * T1^-1 * T2^-2 * T1 * T2^3 * T1 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^-3 * T1^-1 ] Map:: R = (1, 505, 3, 507, 9, 513, 19, 523, 37, 541, 48, 552, 26, 530, 13, 517, 5, 509)(2, 506, 6, 510, 14, 518, 27, 531, 50, 554, 58, 562, 32, 536, 16, 520, 7, 511)(4, 508, 11, 515, 22, 526, 41, 545, 73, 577, 62, 566, 34, 538, 17, 521, 8, 512)(10, 514, 21, 525, 40, 544, 70, 574, 116, 620, 107, 611, 64, 568, 35, 539, 18, 522)(12, 516, 23, 527, 43, 547, 76, 580, 125, 629, 131, 635, 79, 583, 44, 548, 24, 528)(15, 519, 29, 533, 53, 557, 90, 594, 147, 651, 153, 657, 93, 597, 54, 558, 30, 534)(20, 524, 39, 543, 69, 573, 113, 617, 183, 687, 176, 680, 109, 613, 65, 569, 36, 540)(25, 529, 45, 549, 80, 584, 132, 636, 209, 713, 215, 719, 135, 639, 81, 585, 46, 550)(28, 532, 52, 556, 89, 593, 144, 648, 231, 735, 224, 728, 140, 644, 85, 589, 49, 553)(31, 535, 55, 559, 94, 598, 154, 658, 245, 749, 251, 755, 157, 661, 95, 599, 56, 560)(33, 537, 59, 563, 99, 603, 161, 665, 258, 762, 264, 768, 164, 668, 100, 604, 60, 564)(38, 542, 68, 572, 112, 616, 180, 684, 288, 792, 285, 789, 178, 682, 110, 614, 66, 570)(42, 546, 75, 579, 123, 627, 196, 700, 312, 816, 305, 809, 192, 696, 119, 623, 72, 576)(47, 551, 82, 586, 136, 640, 216, 720, 336, 840, 341, 845, 219, 723, 137, 641, 83, 587)(51, 555, 88, 592, 143, 647, 228, 732, 284, 788, 351, 855, 226, 730, 141, 645, 86, 590)(57, 561, 96, 600, 158, 662, 252, 756, 378, 882, 381, 885, 255, 759, 159, 663, 97, 601)(61, 565, 101, 605, 165, 669, 265, 769, 390, 894, 337, 841, 268, 772, 166, 670, 102, 606)(63, 567, 104, 608, 168, 672, 270, 774, 394, 898, 310, 814, 273, 777, 169, 673, 105, 609)(67, 571, 111, 615, 179, 683, 286, 790, 409, 913, 342, 846, 220, 724, 138, 642, 84, 588)(71, 575, 118, 622, 190, 694, 300, 804, 218, 722, 339, 843, 296, 800, 186, 690, 115, 619)(74, 578, 122, 626, 195, 699, 309, 813, 350, 854, 408, 912, 307, 811, 193, 697, 120, 624)(77, 581, 127, 631, 202, 706, 320, 824, 254, 758, 379, 883, 316, 820, 198, 702, 124, 628)(78, 582, 128, 632, 203, 707, 322, 826, 287, 791, 181, 685, 290, 794, 204, 708, 129, 633)(87, 591, 142, 646, 227, 731, 352, 856, 407, 911, 281, 785, 256, 760, 160, 664, 98, 602)(91, 595, 149, 653, 238, 742, 364, 868, 267, 771, 391, 895, 361, 865, 234, 738, 146, 650)(92, 596, 150, 654, 239, 743, 366, 870, 353, 857, 229, 733, 355, 859, 240, 744, 151, 655)(103, 607, 121, 625, 194, 698, 308, 812, 329, 833, 440, 944, 347, 851, 269, 773, 167, 671)(106, 610, 170, 674, 274, 778, 400, 904, 328, 832, 210, 714, 330, 834, 275, 779, 171, 675)(108, 612, 173, 677, 277, 781, 402, 906, 479, 983, 420, 924, 405, 909, 278, 782, 174, 678)(114, 618, 185, 689, 294, 798, 213, 717, 134, 638, 212, 716, 332, 836, 291, 795, 182, 686)(117, 621, 189, 693, 299, 803, 419, 923, 304, 808, 424, 928, 418, 922, 297, 801, 187, 691)(126, 630, 201, 705, 319, 823, 280, 784, 175, 679, 279, 783, 406, 910, 317, 821, 199, 703)(130, 634, 205, 709, 325, 829, 436, 940, 372, 876, 246, 750, 373, 877, 326, 830, 206, 710)(133, 637, 211, 715, 331, 835, 441, 945, 437, 941, 463, 967, 439, 943, 327, 831, 208, 712)(139, 643, 221, 725, 343, 847, 444, 948, 403, 907, 431, 935, 447, 951, 344, 848, 222, 726)(145, 649, 233, 737, 359, 863, 249, 753, 156, 660, 248, 752, 375, 879, 356, 860, 230, 734)(148, 652, 237, 741, 363, 867, 346, 850, 223, 727, 345, 849, 448, 952, 362, 866, 235, 739)(152, 656, 241, 745, 369, 873, 461, 965, 383, 887, 259, 763, 384, 888, 370, 874, 242, 746)(155, 659, 247, 751, 374, 878, 465, 969, 462, 966, 468, 972, 464, 968, 371, 875, 244, 748)(162, 666, 260, 764, 385, 889, 470, 974, 401, 905, 438, 942, 469, 973, 382, 886, 257, 761)(163, 667, 261, 765, 386, 890, 426, 930, 311, 815, 197, 701, 314, 818, 387, 891, 262, 766)(172, 676, 188, 692, 298, 802, 207, 711, 200, 704, 318, 822, 243, 747, 236, 740, 276, 780)(177, 681, 282, 786, 354, 858, 449, 953, 498, 1002, 467, 971, 376, 880, 250, 754, 283, 787)(184, 688, 293, 797, 413, 917, 485, 989, 417, 921, 340, 844, 377, 881, 253, 757, 292, 796)(191, 695, 302, 806, 423, 927, 480, 984, 445, 949, 456, 960, 478, 982, 399, 903, 303, 807)(214, 718, 333, 837, 306, 810, 410, 914, 289, 793, 411, 915, 483, 987, 443, 947, 334, 838)(217, 721, 338, 842, 313, 817, 427, 931, 490, 994, 502, 1006, 455, 959, 392, 896, 335, 839)(225, 729, 348, 852, 425, 929, 395, 899, 474, 978, 472, 976, 388, 892, 263, 767, 349, 853)(232, 736, 358, 862, 451, 955, 492, 996, 430, 934, 380, 884, 389, 893, 266, 770, 357, 861)(271, 775, 396, 900, 475, 979, 491, 995, 429, 933, 315, 819, 428, 932, 473, 977, 393, 897)(272, 776, 397, 901, 476, 980, 488, 992, 421, 925, 301, 805, 422, 926, 477, 981, 398, 902)(295, 799, 415, 919, 487, 991, 458, 962, 367, 871, 459, 963, 504, 1008, 482, 986, 416, 920)(321, 825, 414, 918, 486, 990, 435, 939, 324, 828, 404, 908, 481, 985, 493, 997, 432, 936)(323, 827, 434, 938, 495, 999, 501, 1005, 454, 958, 360, 864, 453, 957, 494, 998, 433, 937)(365, 869, 452, 956, 500, 1004, 460, 964, 368, 872, 446, 950, 497, 1001, 503, 1007, 457, 961)(412, 916, 442, 946, 496, 1000, 489, 993, 471, 975, 499, 1003, 450, 954, 466, 970, 484, 988) L = (1, 506)(2, 508)(3, 512)(4, 505)(5, 516)(6, 509)(7, 519)(8, 514)(9, 522)(10, 507)(11, 511)(12, 510)(13, 529)(14, 528)(15, 515)(16, 535)(17, 537)(18, 524)(19, 540)(20, 513)(21, 521)(22, 534)(23, 517)(24, 532)(25, 527)(26, 551)(27, 553)(28, 518)(29, 520)(30, 546)(31, 533)(32, 561)(33, 525)(34, 565)(35, 567)(36, 542)(37, 570)(38, 523)(39, 539)(40, 564)(41, 576)(42, 526)(43, 550)(44, 582)(45, 530)(46, 581)(47, 549)(48, 588)(49, 555)(50, 590)(51, 531)(52, 548)(53, 560)(54, 596)(55, 536)(56, 595)(57, 559)(58, 602)(59, 538)(60, 575)(61, 563)(62, 607)(63, 543)(64, 610)(65, 612)(66, 571)(67, 541)(68, 569)(69, 609)(70, 619)(71, 544)(72, 578)(73, 624)(74, 545)(75, 558)(76, 628)(77, 547)(78, 556)(79, 634)(80, 587)(81, 638)(82, 552)(83, 637)(84, 586)(85, 643)(86, 591)(87, 554)(88, 589)(89, 633)(90, 650)(91, 557)(92, 579)(93, 656)(94, 601)(95, 660)(96, 562)(97, 659)(98, 600)(99, 606)(100, 667)(101, 566)(102, 666)(103, 605)(104, 568)(105, 618)(106, 608)(107, 676)(108, 572)(109, 679)(110, 681)(111, 614)(112, 678)(113, 686)(114, 573)(115, 621)(116, 691)(117, 574)(118, 604)(119, 695)(120, 625)(121, 577)(122, 623)(123, 655)(124, 630)(125, 703)(126, 580)(127, 585)(128, 583)(129, 649)(130, 632)(131, 711)(132, 712)(133, 584)(134, 631)(135, 718)(136, 642)(137, 722)(138, 721)(139, 592)(140, 727)(141, 729)(142, 645)(143, 726)(144, 734)(145, 593)(146, 652)(147, 739)(148, 594)(149, 599)(150, 597)(151, 701)(152, 654)(153, 747)(154, 748)(155, 598)(156, 653)(157, 754)(158, 664)(159, 758)(160, 757)(161, 761)(162, 603)(163, 622)(164, 767)(165, 671)(166, 771)(167, 770)(168, 675)(169, 776)(170, 611)(171, 775)(172, 674)(173, 613)(174, 685)(175, 677)(176, 785)(177, 615)(178, 788)(179, 787)(180, 791)(181, 616)(182, 688)(183, 796)(184, 617)(185, 673)(186, 799)(187, 692)(188, 620)(189, 690)(190, 766)(191, 626)(192, 808)(193, 810)(194, 697)(195, 807)(196, 815)(197, 627)(198, 819)(199, 704)(200, 629)(201, 702)(202, 717)(203, 710)(204, 828)(205, 635)(206, 827)(207, 709)(208, 714)(209, 832)(210, 636)(211, 641)(212, 639)(213, 825)(214, 716)(215, 812)(216, 839)(217, 640)(218, 715)(219, 844)(220, 816)(221, 644)(222, 733)(223, 725)(224, 851)(225, 646)(226, 854)(227, 853)(228, 857)(229, 647)(230, 736)(231, 861)(232, 648)(233, 708)(234, 864)(235, 740)(236, 651)(237, 738)(238, 753)(239, 746)(240, 872)(241, 657)(242, 871)(243, 745)(244, 750)(245, 876)(246, 658)(247, 663)(248, 661)(249, 869)(250, 752)(251, 683)(252, 881)(253, 662)(254, 751)(255, 884)(256, 687)(257, 763)(258, 887)(259, 665)(260, 670)(261, 668)(262, 805)(263, 765)(264, 731)(265, 893)(266, 669)(267, 764)(268, 896)(269, 735)(270, 897)(271, 672)(272, 689)(273, 903)(274, 780)(275, 905)(276, 866)(277, 784)(278, 908)(279, 680)(280, 907)(281, 783)(282, 682)(283, 755)(284, 786)(285, 912)(286, 749)(287, 793)(288, 914)(289, 684)(290, 782)(291, 916)(292, 760)(293, 795)(294, 902)(295, 693)(296, 921)(297, 829)(298, 801)(299, 920)(300, 925)(301, 694)(302, 696)(303, 814)(304, 806)(305, 846)(306, 698)(307, 792)(308, 837)(309, 898)(310, 699)(311, 817)(312, 842)(313, 700)(314, 744)(315, 705)(316, 934)(317, 873)(318, 821)(319, 933)(320, 936)(321, 706)(322, 937)(323, 707)(324, 737)(325, 802)(326, 941)(327, 942)(328, 833)(329, 713)(330, 831)(331, 804)(332, 838)(333, 719)(334, 946)(335, 841)(336, 894)(337, 720)(338, 724)(339, 723)(340, 843)(341, 756)(342, 928)(343, 850)(344, 950)(345, 728)(346, 949)(347, 849)(348, 730)(349, 768)(350, 852)(351, 789)(352, 762)(353, 858)(354, 732)(355, 848)(356, 954)(357, 773)(358, 860)(359, 939)(360, 741)(361, 959)(362, 778)(363, 958)(364, 961)(365, 742)(366, 962)(367, 743)(368, 818)(369, 822)(370, 966)(371, 967)(372, 790)(373, 875)(374, 824)(375, 880)(376, 970)(377, 845)(378, 840)(379, 759)(380, 883)(381, 769)(382, 972)(383, 856)(384, 886)(385, 868)(386, 892)(387, 964)(388, 975)(389, 885)(390, 882)(391, 772)(392, 895)(393, 899)(394, 929)(395, 774)(396, 779)(397, 777)(398, 918)(399, 901)(400, 952)(401, 900)(402, 948)(403, 781)(404, 794)(405, 986)(406, 911)(407, 965)(408, 855)(409, 940)(410, 811)(411, 826)(412, 797)(413, 988)(414, 798)(415, 800)(416, 924)(417, 919)(418, 913)(419, 983)(420, 803)(421, 835)(422, 891)(423, 923)(424, 809)(425, 813)(426, 993)(427, 930)(428, 820)(429, 935)(430, 932)(431, 823)(432, 878)(433, 915)(434, 830)(435, 956)(436, 922)(437, 938)(438, 834)(439, 968)(440, 904)(441, 992)(442, 836)(443, 994)(444, 984)(445, 847)(446, 859)(447, 995)(448, 944)(449, 870)(450, 862)(451, 1003)(452, 863)(453, 865)(454, 960)(455, 957)(456, 867)(457, 889)(458, 953)(459, 874)(460, 926)(461, 910)(462, 963)(463, 877)(464, 973)(465, 997)(466, 879)(467, 917)(468, 888)(469, 943)(470, 1007)(471, 890)(472, 955)(473, 996)(474, 977)(475, 974)(476, 982)(477, 1004)(478, 1005)(479, 927)(480, 906)(481, 909)(482, 985)(483, 998)(484, 971)(485, 1002)(486, 981)(487, 989)(488, 999)(489, 931)(490, 1000)(491, 1001)(492, 978)(493, 1008)(494, 1006)(495, 945)(496, 947)(497, 951)(498, 991)(499, 976)(500, 990)(501, 980)(502, 987)(503, 979)(504, 969) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E15.1397 Transitivity :: ET+ VT+ AT Graph:: v = 56 e = 504 f = 420 degree seq :: [ 18^56 ] E15.1402 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 9}) Quotient :: loop Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^9, (T1^-3 * T2 * T1^3 * T2 * T1^-1)^2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3 * T2 * T1 * T2 * T1^-2 * T2 * T1^-4, (T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1)^2 ] Map:: polyhedral non-degenerate R = (1, 505, 3, 507)(2, 506, 6, 510)(4, 508, 9, 513)(5, 509, 12, 516)(7, 511, 16, 520)(8, 512, 13, 517)(10, 514, 19, 523)(11, 515, 22, 526)(14, 518, 23, 527)(15, 519, 28, 532)(17, 521, 30, 534)(18, 522, 33, 537)(20, 524, 35, 539)(21, 525, 37, 541)(24, 528, 38, 542)(25, 529, 43, 547)(26, 530, 44, 548)(27, 531, 47, 551)(29, 533, 48, 552)(31, 535, 52, 556)(32, 536, 55, 559)(34, 538, 58, 562)(36, 540, 60, 564)(39, 543, 61, 565)(40, 544, 66, 570)(41, 545, 67, 571)(42, 546, 70, 574)(45, 549, 73, 577)(46, 550, 75, 579)(49, 553, 76, 580)(50, 554, 80, 584)(51, 555, 83, 587)(53, 557, 85, 589)(54, 558, 87, 591)(56, 560, 88, 592)(57, 561, 92, 596)(59, 563, 95, 599)(62, 566, 96, 600)(63, 567, 100, 604)(64, 568, 101, 605)(65, 569, 104, 608)(68, 572, 107, 611)(69, 573, 109, 613)(71, 575, 110, 614)(72, 576, 114, 618)(74, 578, 116, 620)(77, 581, 117, 621)(78, 582, 122, 626)(79, 583, 123, 627)(81, 585, 126, 630)(82, 586, 128, 632)(84, 588, 131, 635)(86, 590, 133, 637)(89, 593, 134, 638)(90, 594, 138, 642)(91, 595, 141, 645)(93, 597, 142, 646)(94, 598, 146, 650)(97, 601, 150, 654)(98, 602, 151, 655)(99, 603, 154, 658)(102, 606, 157, 661)(103, 607, 159, 663)(105, 609, 160, 664)(106, 610, 164, 668)(108, 612, 166, 670)(111, 615, 167, 671)(112, 616, 171, 675)(113, 617, 174, 678)(115, 619, 177, 681)(118, 622, 132, 636)(119, 623, 182, 686)(120, 624, 183, 687)(121, 625, 186, 690)(124, 628, 189, 693)(125, 629, 192, 696)(127, 631, 195, 699)(129, 633, 196, 700)(130, 634, 200, 704)(135, 639, 203, 707)(136, 640, 208, 712)(137, 641, 209, 713)(139, 643, 212, 716)(140, 644, 213, 717)(143, 647, 214, 718)(144, 648, 218, 722)(145, 649, 221, 725)(147, 651, 222, 726)(148, 652, 226, 730)(149, 653, 228, 732)(152, 656, 231, 735)(153, 657, 233, 737)(155, 659, 234, 738)(156, 660, 238, 742)(158, 662, 240, 744)(161, 665, 241, 745)(162, 666, 245, 749)(163, 667, 248, 752)(165, 669, 251, 755)(168, 672, 178, 682)(169, 673, 256, 760)(170, 674, 257, 761)(172, 676, 260, 764)(173, 677, 262, 766)(175, 679, 263, 767)(176, 680, 267, 771)(179, 683, 271, 775)(180, 684, 272, 776)(181, 685, 274, 778)(184, 688, 277, 781)(185, 689, 278, 782)(187, 691, 279, 783)(188, 692, 283, 787)(190, 694, 285, 789)(191, 695, 287, 791)(193, 697, 204, 708)(194, 698, 290, 794)(197, 701, 291, 795)(198, 702, 295, 799)(199, 703, 298, 802)(201, 705, 299, 803)(202, 706, 303, 807)(205, 709, 306, 810)(206, 710, 307, 811)(207, 711, 309, 813)(210, 714, 312, 816)(211, 715, 315, 819)(215, 719, 317, 821)(216, 720, 320, 824)(217, 721, 321, 825)(219, 723, 324, 828)(220, 724, 302, 806)(223, 727, 325, 829)(224, 728, 328, 832)(225, 729, 297, 801)(227, 731, 332, 836)(229, 733, 333, 837)(230, 734, 273, 777)(232, 736, 336, 840)(235, 739, 337, 841)(236, 740, 339, 843)(237, 741, 342, 846)(239, 743, 343, 847)(242, 746, 252, 756)(243, 747, 347, 851)(244, 748, 348, 852)(246, 750, 350, 854)(247, 751, 352, 856)(249, 753, 353, 857)(250, 754, 355, 859)(253, 757, 358, 862)(254, 758, 359, 863)(255, 759, 361, 865)(258, 762, 364, 868)(259, 763, 366, 870)(261, 765, 270, 774)(264, 768, 368, 872)(265, 769, 372, 876)(266, 770, 373, 877)(268, 772, 374, 878)(269, 773, 316, 820)(275, 779, 377, 881)(276, 780, 380, 884)(280, 784, 381, 885)(281, 785, 384, 888)(282, 786, 385, 889)(284, 788, 387, 891)(286, 790, 388, 892)(288, 792, 389, 893)(289, 793, 345, 849)(292, 796, 356, 860)(293, 797, 395, 899)(294, 798, 396, 900)(296, 800, 331, 835)(300, 804, 399, 903)(301, 805, 313, 817)(304, 808, 367, 871)(305, 809, 403, 907)(308, 812, 400, 904)(310, 814, 405, 909)(311, 815, 407, 911)(314, 818, 408, 912)(318, 822, 410, 914)(319, 823, 412, 916)(322, 826, 401, 905)(323, 827, 414, 918)(326, 830, 360, 864)(327, 831, 397, 901)(329, 833, 417, 921)(330, 834, 392, 896)(334, 838, 419, 923)(335, 839, 378, 882)(338, 842, 423, 927)(340, 844, 425, 929)(341, 845, 427, 931)(344, 848, 429, 933)(346, 850, 430, 934)(349, 853, 434, 938)(351, 855, 357, 861)(354, 858, 435, 939)(362, 866, 437, 941)(363, 867, 440, 944)(365, 869, 441, 945)(369, 873, 376, 880)(370, 874, 445, 949)(371, 875, 446, 950)(375, 879, 402, 906)(379, 883, 447, 951)(382, 886, 451, 955)(383, 887, 452, 956)(386, 890, 453, 957)(390, 894, 454, 958)(391, 895, 413, 917)(393, 897, 457, 961)(394, 898, 458, 962)(398, 902, 418, 922)(404, 908, 448, 952)(406, 910, 459, 963)(409, 913, 464, 968)(411, 915, 455, 959)(415, 919, 438, 942)(416, 920, 456, 960)(420, 924, 473, 977)(421, 925, 475, 979)(422, 926, 465, 969)(424, 928, 478, 982)(426, 930, 428, 932)(431, 935, 479, 983)(432, 936, 469, 973)(433, 937, 481, 985)(436, 940, 467, 971)(439, 943, 484, 988)(442, 946, 485, 989)(443, 947, 486, 990)(444, 948, 487, 991)(449, 953, 489, 993)(450, 954, 490, 994)(460, 964, 488, 992)(461, 965, 477, 981)(462, 966, 497, 1001)(463, 967, 483, 987)(466, 970, 471, 975)(468, 972, 494, 998)(470, 974, 498, 1002)(472, 976, 492, 996)(474, 978, 476, 980)(480, 984, 500, 1004)(482, 986, 501, 1005)(491, 995, 503, 1007)(493, 997, 495, 999)(496, 1000, 502, 1006)(499, 1003, 504, 1008) L = (1, 506)(2, 509)(3, 511)(4, 505)(5, 515)(6, 517)(7, 519)(8, 507)(9, 522)(10, 508)(11, 525)(12, 527)(13, 529)(14, 510)(15, 531)(16, 513)(17, 512)(18, 536)(19, 538)(20, 514)(21, 540)(22, 542)(23, 544)(24, 516)(25, 546)(26, 518)(27, 550)(28, 552)(29, 520)(30, 555)(31, 521)(32, 558)(33, 523)(34, 561)(35, 563)(36, 524)(37, 565)(38, 567)(39, 526)(40, 569)(41, 528)(42, 573)(43, 534)(44, 576)(45, 530)(46, 557)(47, 580)(48, 582)(49, 532)(50, 533)(51, 586)(52, 588)(53, 535)(54, 590)(55, 592)(56, 537)(57, 595)(58, 539)(59, 598)(60, 600)(61, 601)(62, 541)(63, 603)(64, 543)(65, 607)(66, 548)(67, 610)(68, 545)(69, 578)(70, 614)(71, 547)(72, 617)(73, 619)(74, 549)(75, 621)(76, 623)(77, 551)(78, 625)(79, 553)(80, 629)(81, 554)(82, 631)(83, 556)(84, 634)(85, 636)(86, 585)(87, 638)(88, 640)(89, 559)(90, 560)(91, 644)(92, 646)(93, 562)(94, 649)(95, 564)(96, 652)(97, 653)(98, 566)(99, 657)(100, 571)(101, 660)(102, 568)(103, 612)(104, 664)(105, 570)(106, 667)(107, 669)(108, 572)(109, 671)(110, 673)(111, 574)(112, 575)(113, 677)(114, 577)(115, 680)(116, 682)(117, 683)(118, 579)(119, 685)(120, 581)(121, 689)(122, 584)(123, 692)(124, 583)(125, 695)(126, 697)(127, 698)(128, 700)(129, 587)(130, 703)(131, 589)(132, 706)(133, 707)(134, 709)(135, 591)(136, 711)(137, 593)(138, 715)(139, 594)(140, 643)(141, 718)(142, 720)(143, 596)(144, 597)(145, 724)(146, 726)(147, 599)(148, 729)(149, 731)(150, 605)(151, 734)(152, 602)(153, 662)(154, 738)(155, 604)(156, 741)(157, 743)(158, 606)(159, 745)(160, 747)(161, 608)(162, 609)(163, 751)(164, 611)(165, 754)(166, 756)(167, 757)(168, 613)(169, 759)(170, 615)(171, 763)(172, 616)(173, 765)(174, 767)(175, 618)(176, 770)(177, 620)(178, 773)(179, 774)(180, 622)(181, 777)(182, 627)(183, 780)(184, 624)(185, 694)(186, 783)(187, 626)(188, 786)(189, 788)(190, 628)(191, 790)(192, 630)(193, 793)(194, 676)(195, 795)(196, 797)(197, 632)(198, 633)(199, 801)(200, 803)(201, 635)(202, 806)(203, 808)(204, 637)(205, 809)(206, 639)(207, 812)(208, 642)(209, 815)(210, 641)(211, 818)(212, 820)(213, 821)(214, 822)(215, 645)(216, 823)(217, 647)(218, 827)(219, 648)(220, 723)(221, 829)(222, 830)(223, 650)(224, 651)(225, 834)(226, 655)(227, 736)(228, 837)(229, 654)(230, 839)(231, 688)(232, 656)(233, 841)(234, 842)(235, 658)(236, 659)(237, 845)(238, 661)(239, 710)(240, 684)(241, 848)(242, 663)(243, 850)(244, 665)(245, 853)(246, 666)(247, 855)(248, 857)(249, 668)(250, 719)(251, 670)(252, 708)(253, 861)(254, 672)(255, 864)(256, 675)(257, 867)(258, 674)(259, 869)(260, 871)(261, 750)(262, 872)(263, 874)(264, 678)(265, 679)(266, 725)(267, 878)(268, 681)(269, 717)(270, 880)(271, 687)(272, 737)(273, 735)(274, 881)(275, 686)(276, 856)(277, 840)(278, 885)(279, 886)(280, 690)(281, 691)(282, 846)(283, 693)(284, 859)(285, 772)(286, 732)(287, 893)(288, 696)(289, 896)(290, 860)(291, 897)(292, 699)(293, 898)(294, 701)(295, 902)(296, 702)(297, 800)(298, 903)(299, 904)(300, 704)(301, 705)(302, 877)(303, 776)(304, 794)(305, 742)(306, 713)(307, 873)(308, 817)(309, 909)(310, 712)(311, 858)(312, 879)(313, 714)(314, 739)(315, 716)(316, 863)(317, 891)(318, 753)(319, 915)(320, 722)(321, 875)(322, 721)(323, 748)(324, 807)(325, 769)(326, 919)(327, 727)(328, 762)(329, 728)(330, 833)(331, 730)(332, 892)(333, 785)(334, 733)(335, 925)(336, 758)(337, 926)(338, 814)(339, 928)(340, 740)(341, 930)(342, 907)(343, 744)(344, 932)(345, 746)(346, 824)(347, 749)(348, 936)(349, 937)(350, 775)(351, 844)(352, 939)(353, 940)(354, 752)(355, 796)(356, 755)(357, 884)(358, 761)(359, 836)(360, 832)(361, 941)(362, 760)(363, 931)(364, 921)(365, 882)(366, 764)(367, 811)(368, 947)(369, 766)(370, 948)(371, 768)(372, 901)(373, 906)(374, 782)(375, 771)(376, 847)(377, 943)(378, 778)(379, 779)(380, 781)(381, 953)(382, 954)(383, 784)(384, 923)(385, 957)(386, 787)(387, 789)(388, 958)(389, 959)(390, 791)(391, 792)(392, 802)(393, 890)(394, 949)(395, 799)(396, 960)(397, 798)(398, 887)(399, 895)(400, 963)(401, 804)(402, 805)(403, 952)(404, 810)(405, 965)(406, 813)(407, 816)(408, 968)(409, 819)(410, 825)(411, 917)(412, 934)(413, 826)(414, 828)(415, 974)(416, 831)(417, 849)(418, 835)(419, 966)(420, 838)(421, 978)(422, 980)(423, 843)(424, 972)(425, 862)(426, 924)(427, 889)(428, 944)(429, 852)(430, 983)(431, 851)(432, 979)(433, 942)(434, 854)(435, 987)(436, 964)(437, 984)(438, 865)(439, 866)(440, 868)(441, 989)(442, 870)(443, 946)(444, 971)(445, 876)(446, 905)(447, 992)(448, 883)(449, 967)(450, 899)(451, 888)(452, 996)(453, 997)(454, 970)(455, 998)(456, 894)(457, 900)(458, 994)(459, 1000)(460, 908)(461, 995)(462, 910)(463, 911)(464, 1002)(465, 912)(466, 913)(467, 914)(468, 916)(469, 918)(470, 975)(471, 920)(472, 922)(473, 933)(474, 976)(475, 945)(476, 973)(477, 927)(478, 929)(479, 1003)(480, 935)(481, 1005)(482, 938)(483, 986)(484, 951)(485, 1006)(486, 950)(487, 962)(488, 991)(489, 956)(490, 1007)(491, 955)(492, 969)(493, 982)(494, 999)(495, 961)(496, 990)(497, 977)(498, 985)(499, 981)(500, 988)(501, 993)(502, 1001)(503, 1008)(504, 1004) local type(s) :: { ( 3, 9, 3, 9 ) } Outer automorphisms :: reflexible Dual of E15.1398 Transitivity :: ET+ VT+ AT Graph:: simple v = 252 e = 504 f = 224 degree seq :: [ 4^252 ] E15.1403 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 9}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^9, (Y3 * Y2^-1)^9, (Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2 * Y1 * Y2^-1 * Y1)^7 ] Map:: R = (1, 505, 2, 506)(3, 507, 7, 511)(4, 508, 8, 512)(5, 509, 9, 513)(6, 510, 10, 514)(11, 515, 19, 523)(12, 516, 20, 524)(13, 517, 21, 525)(14, 518, 22, 526)(15, 519, 23, 527)(16, 520, 24, 528)(17, 521, 25, 529)(18, 522, 26, 530)(27, 531, 43, 547)(28, 532, 44, 548)(29, 533, 45, 549)(30, 534, 46, 550)(31, 535, 47, 551)(32, 536, 48, 552)(33, 537, 49, 553)(34, 538, 50, 554)(35, 539, 51, 555)(36, 540, 52, 556)(37, 541, 53, 557)(38, 542, 54, 558)(39, 543, 55, 559)(40, 544, 56, 560)(41, 545, 57, 561)(42, 546, 58, 562)(59, 563, 91, 595)(60, 564, 92, 596)(61, 565, 93, 597)(62, 566, 94, 598)(63, 567, 95, 599)(64, 568, 96, 600)(65, 569, 97, 601)(66, 570, 98, 602)(67, 571, 99, 603)(68, 572, 100, 604)(69, 573, 101, 605)(70, 574, 102, 606)(71, 575, 103, 607)(72, 576, 104, 608)(73, 577, 105, 609)(74, 578, 106, 610)(75, 579, 107, 611)(76, 580, 108, 612)(77, 581, 109, 613)(78, 582, 110, 614)(79, 583, 111, 615)(80, 584, 112, 616)(81, 585, 113, 617)(82, 586, 114, 618)(83, 587, 115, 619)(84, 588, 116, 620)(85, 589, 117, 621)(86, 590, 118, 622)(87, 591, 119, 623)(88, 592, 120, 624)(89, 593, 121, 625)(90, 594, 122, 626)(123, 627, 181, 685)(124, 628, 182, 686)(125, 629, 183, 687)(126, 630, 184, 688)(127, 631, 185, 689)(128, 632, 186, 690)(129, 633, 187, 691)(130, 634, 188, 692)(131, 635, 189, 693)(132, 636, 190, 694)(133, 637, 191, 695)(134, 638, 192, 696)(135, 639, 193, 697)(136, 640, 194, 698)(137, 641, 138, 642)(139, 643, 195, 699)(140, 644, 196, 700)(141, 645, 197, 701)(142, 646, 198, 702)(143, 647, 199, 703)(144, 648, 200, 704)(145, 649, 201, 705)(146, 650, 202, 706)(147, 651, 203, 707)(148, 652, 204, 708)(149, 653, 205, 709)(150, 654, 206, 710)(151, 655, 207, 711)(152, 656, 208, 712)(153, 657, 292, 796)(154, 658, 293, 797)(155, 659, 295, 799)(156, 660, 297, 801)(157, 661, 298, 802)(158, 662, 300, 804)(159, 663, 228, 732)(160, 664, 291, 795)(161, 665, 302, 806)(162, 666, 304, 808)(163, 667, 305, 809)(164, 668, 306, 810)(165, 669, 255, 759)(166, 670, 167, 671)(168, 672, 220, 724)(169, 673, 311, 815)(170, 674, 312, 816)(171, 675, 314, 818)(172, 676, 316, 820)(173, 677, 317, 821)(174, 678, 319, 823)(175, 679, 243, 747)(176, 680, 310, 814)(177, 681, 321, 825)(178, 682, 323, 827)(179, 683, 324, 828)(180, 684, 325, 829)(209, 713, 358, 862)(210, 714, 361, 865)(211, 715, 365, 869)(212, 716, 368, 872)(213, 717, 340, 844)(214, 718, 372, 876)(215, 719, 373, 877)(216, 720, 303, 807)(217, 721, 379, 883)(218, 722, 281, 785)(219, 723, 354, 858)(221, 725, 274, 778)(222, 726, 390, 894)(223, 727, 391, 895)(224, 728, 264, 768)(225, 729, 397, 901)(226, 730, 398, 902)(227, 731, 289, 793)(229, 733, 405, 909)(230, 734, 322, 826)(231, 735, 409, 913)(232, 736, 384, 888)(233, 737, 412, 916)(234, 738, 259, 763)(235, 739, 349, 853)(236, 740, 378, 882)(237, 741, 416, 920)(238, 742, 269, 773)(239, 743, 419, 923)(240, 744, 420, 924)(241, 745, 408, 912)(242, 746, 422, 926)(244, 748, 426, 930)(245, 749, 402, 906)(246, 750, 364, 868)(247, 751, 428, 932)(248, 752, 329, 833)(249, 753, 335, 839)(250, 754, 343, 847)(251, 755, 360, 864)(252, 756, 431, 935)(253, 757, 434, 938)(254, 758, 403, 907)(256, 760, 436, 940)(257, 761, 438, 942)(258, 762, 440, 944)(260, 764, 442, 946)(261, 765, 404, 908)(262, 766, 444, 948)(263, 767, 423, 927)(265, 769, 448, 952)(266, 770, 383, 887)(267, 771, 449, 953)(268, 772, 450, 954)(270, 774, 339, 843)(271, 775, 336, 840)(272, 776, 346, 850)(273, 777, 344, 848)(275, 779, 454, 958)(276, 780, 377, 881)(277, 781, 367, 871)(278, 782, 415, 919)(279, 783, 456, 960)(280, 784, 382, 886)(282, 786, 334, 838)(283, 787, 460, 964)(284, 788, 315, 819)(285, 789, 313, 817)(286, 790, 309, 813)(287, 791, 463, 967)(288, 792, 401, 905)(290, 794, 348, 852)(294, 798, 371, 875)(296, 800, 410, 914)(299, 803, 471, 975)(301, 805, 376, 880)(307, 811, 435, 939)(308, 812, 473, 977)(318, 822, 333, 837)(320, 824, 407, 911)(326, 830, 411, 915)(327, 831, 394, 898)(328, 832, 484, 988)(330, 834, 353, 857)(331, 835, 478, 982)(332, 836, 350, 854)(337, 841, 455, 959)(338, 842, 479, 983)(341, 845, 363, 867)(342, 846, 474, 978)(345, 849, 490, 994)(347, 851, 432, 936)(351, 855, 451, 955)(352, 856, 493, 997)(355, 859, 487, 991)(356, 860, 375, 879)(357, 861, 387, 891)(359, 863, 458, 962)(362, 866, 459, 963)(366, 870, 465, 969)(369, 873, 480, 984)(370, 874, 443, 947)(374, 878, 466, 970)(380, 884, 457, 961)(381, 885, 482, 986)(385, 889, 453, 957)(386, 890, 433, 937)(388, 892, 489, 993)(389, 893, 427, 931)(392, 896, 446, 950)(393, 897, 430, 934)(395, 899, 495, 999)(396, 900, 421, 925)(399, 903, 464, 968)(400, 904, 497, 1001)(406, 910, 496, 1000)(413, 917, 441, 945)(414, 918, 418, 922)(417, 921, 447, 951)(424, 928, 468, 972)(425, 929, 429, 933)(437, 941, 439, 943)(445, 949, 462, 966)(452, 956, 475, 979)(461, 965, 477, 981)(467, 971, 491, 995)(469, 973, 498, 1002)(470, 974, 502, 1006)(472, 976, 494, 998)(476, 980, 503, 1007)(481, 985, 485, 989)(483, 987, 486, 990)(488, 992, 504, 1008)(492, 996, 501, 1005)(499, 1003, 500, 1004)(1009, 1513, 1011, 1515, 1012, 1516)(1010, 1514, 1013, 1517, 1014, 1518)(1015, 1519, 1019, 1523, 1020, 1524)(1016, 1520, 1021, 1525, 1022, 1526)(1017, 1521, 1023, 1527, 1024, 1528)(1018, 1522, 1025, 1529, 1026, 1530)(1027, 1531, 1035, 1539, 1036, 1540)(1028, 1532, 1037, 1541, 1038, 1542)(1029, 1533, 1039, 1543, 1040, 1544)(1030, 1534, 1041, 1545, 1042, 1546)(1031, 1535, 1043, 1547, 1044, 1548)(1032, 1536, 1045, 1549, 1046, 1550)(1033, 1537, 1047, 1551, 1048, 1552)(1034, 1538, 1049, 1553, 1050, 1554)(1051, 1555, 1067, 1571, 1068, 1572)(1052, 1556, 1069, 1573, 1070, 1574)(1053, 1557, 1071, 1575, 1072, 1576)(1054, 1558, 1073, 1577, 1074, 1578)(1055, 1559, 1075, 1579, 1076, 1580)(1056, 1560, 1077, 1581, 1078, 1582)(1057, 1561, 1079, 1583, 1080, 1584)(1058, 1562, 1081, 1585, 1082, 1586)(1059, 1563, 1083, 1587, 1084, 1588)(1060, 1564, 1085, 1589, 1086, 1590)(1061, 1565, 1087, 1591, 1088, 1592)(1062, 1566, 1089, 1593, 1090, 1594)(1063, 1567, 1091, 1595, 1092, 1596)(1064, 1568, 1093, 1597, 1094, 1598)(1065, 1569, 1095, 1599, 1096, 1600)(1066, 1570, 1097, 1601, 1098, 1602)(1099, 1603, 1130, 1634, 1131, 1635)(1100, 1604, 1132, 1636, 1133, 1637)(1101, 1605, 1134, 1638, 1135, 1639)(1102, 1606, 1136, 1640, 1137, 1641)(1103, 1607, 1138, 1642, 1139, 1643)(1104, 1608, 1140, 1644, 1141, 1645)(1105, 1609, 1142, 1646, 1143, 1647)(1106, 1610, 1144, 1648, 1145, 1649)(1107, 1611, 1146, 1650, 1147, 1651)(1108, 1612, 1148, 1652, 1149, 1653)(1109, 1613, 1150, 1654, 1151, 1655)(1110, 1614, 1152, 1656, 1153, 1657)(1111, 1615, 1154, 1658, 1155, 1659)(1112, 1616, 1156, 1660, 1157, 1661)(1113, 1617, 1158, 1662, 1159, 1663)(1114, 1618, 1160, 1664, 1115, 1619)(1116, 1620, 1161, 1665, 1162, 1666)(1117, 1621, 1163, 1667, 1164, 1668)(1118, 1622, 1165, 1669, 1166, 1670)(1119, 1623, 1167, 1671, 1168, 1672)(1120, 1624, 1169, 1673, 1170, 1674)(1121, 1625, 1171, 1675, 1172, 1676)(1122, 1626, 1173, 1677, 1174, 1678)(1123, 1627, 1175, 1679, 1176, 1680)(1124, 1628, 1177, 1681, 1178, 1682)(1125, 1629, 1179, 1683, 1180, 1684)(1126, 1630, 1181, 1685, 1182, 1686)(1127, 1631, 1183, 1687, 1184, 1688)(1128, 1632, 1185, 1689, 1186, 1690)(1129, 1633, 1187, 1691, 1188, 1692)(1189, 1693, 1335, 1839, 1244, 1748)(1190, 1694, 1245, 1749, 1425, 1929)(1191, 1695, 1225, 1729, 1388, 1892)(1192, 1696, 1289, 1793, 1444, 1948)(1193, 1697, 1339, 1843, 1485, 1989)(1194, 1698, 1341, 1845, 1292, 1796)(1195, 1699, 1342, 1846, 1257, 1761)(1196, 1700, 1343, 1847, 1398, 1902)(1197, 1701, 1345, 1849, 1495, 1999)(1198, 1702, 1346, 1850, 1496, 2000)(1199, 1703, 1266, 1770, 1449, 1953)(1200, 1704, 1242, 1746, 1414, 1918)(1201, 1705, 1249, 1753, 1429, 1933)(1202, 1706, 1302, 1806, 1233, 1737)(1203, 1707, 1334, 1838, 1254, 1758)(1204, 1708, 1255, 1759, 1437, 1941)(1205, 1709, 1234, 1738, 1407, 1911)(1206, 1710, 1297, 1801, 1468, 1972)(1207, 1711, 1353, 1857, 1499, 2003)(1208, 1712, 1355, 1859, 1275, 1779)(1209, 1713, 1356, 1860, 1243, 1747)(1210, 1714, 1357, 1861, 1380, 1884)(1211, 1715, 1359, 1863, 1462, 1966)(1212, 1716, 1360, 1864, 1502, 2006)(1213, 1717, 1271, 1775, 1454, 1958)(1214, 1718, 1232, 1736, 1403, 1907)(1215, 1719, 1238, 1742, 1415, 1919)(1216, 1720, 1365, 1869, 1240, 1744)(1217, 1721, 1367, 1871, 1368, 1872)(1218, 1722, 1370, 1874, 1372, 1876)(1219, 1723, 1374, 1878, 1375, 1879)(1220, 1724, 1315, 1819, 1321, 1825)(1221, 1725, 1377, 1881, 1379, 1883)(1222, 1726, 1290, 1794, 1293, 1797)(1223, 1727, 1382, 1886, 1301, 1805)(1224, 1728, 1384, 1888, 1386, 1890)(1226, 1730, 1390, 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1776, 1399, 1903, 1373, 1877)(1274, 1778, 1441, 1945, 1457, 1961)(1276, 1780, 1455, 1959, 1312, 1816)(1277, 1781, 1424, 1928, 1369, 1873)(1279, 1783, 1459, 1963, 1294, 1798)(1280, 1784, 1458, 1962, 1460, 1964)(1281, 1785, 1461, 1965, 1331, 1835)(1282, 1786, 1362, 1866, 1348, 1852)(1284, 1788, 1438, 1942, 1446, 1950)(1286, 1790, 1354, 1858, 1463, 1967)(1288, 1792, 1465, 1969, 1466, 1970)(1291, 1795, 1385, 1889, 1470, 1974)(1296, 1800, 1472, 1976, 1473, 1977)(1299, 1803, 1371, 1875, 1476, 1980)(1303, 1807, 1311, 1815, 1351, 1855)(1304, 1808, 1452, 1956, 1349, 1853)(1305, 1809, 1475, 1979, 1350, 1854)(1306, 1810, 1471, 1975, 1317, 1821)(1309, 1813, 1474, 1978, 1467, 1971)(1310, 1814, 1480, 1984, 1478, 1982)(1316, 1820, 1391, 1895, 1483, 1987)(1318, 1822, 1378, 1882, 1456, 1960)(1322, 1826, 1330, 1834, 1481, 1985)(1324, 1828, 1484, 1988, 1486, 1990)(1328, 1832, 1361, 1865, 1488, 1992)(1329, 1833, 1489, 1993, 1487, 1991)(1336, 1840, 1433, 1937, 1469, 1973)(1337, 1841, 1436, 1940, 1381, 1885)(1344, 1848, 1492, 1996, 1494, 1998)(1347, 1851, 1497, 2001, 1404, 1908)(1358, 1862, 1482, 1986, 1477, 1981)(1364, 1868, 1426, 1930, 1430, 1934)(1387, 1891, 1442, 1946, 1439, 1943)(1394, 1898, 1434, 1938, 1504, 2008)(1397, 1901, 1450, 1954, 1503, 2007)(1401, 1905, 1428, 1932, 1505, 2009)(1406, 1910, 1464, 1968, 1423, 1927)(1410, 1914, 1491, 1995, 1493, 1997)(1412, 1916, 1506, 2010, 1500, 2004)(1413, 1917, 1479, 1983, 1418, 1922)(1416, 1920, 1509, 2013, 1501, 2005)(1422, 1926, 1427, 1931, 1490, 1994)(1498, 2002, 1512, 2016, 1507, 2011)(1508, 2012, 1511, 2015, 1510, 2014) L = (1, 1010)(2, 1009)(3, 1015)(4, 1016)(5, 1017)(6, 1018)(7, 1011)(8, 1012)(9, 1013)(10, 1014)(11, 1027)(12, 1028)(13, 1029)(14, 1030)(15, 1031)(16, 1032)(17, 1033)(18, 1034)(19, 1019)(20, 1020)(21, 1021)(22, 1022)(23, 1023)(24, 1024)(25, 1025)(26, 1026)(27, 1051)(28, 1052)(29, 1053)(30, 1054)(31, 1055)(32, 1056)(33, 1057)(34, 1058)(35, 1059)(36, 1060)(37, 1061)(38, 1062)(39, 1063)(40, 1064)(41, 1065)(42, 1066)(43, 1035)(44, 1036)(45, 1037)(46, 1038)(47, 1039)(48, 1040)(49, 1041)(50, 1042)(51, 1043)(52, 1044)(53, 1045)(54, 1046)(55, 1047)(56, 1048)(57, 1049)(58, 1050)(59, 1099)(60, 1100)(61, 1101)(62, 1102)(63, 1103)(64, 1104)(65, 1105)(66, 1106)(67, 1107)(68, 1108)(69, 1109)(70, 1110)(71, 1111)(72, 1112)(73, 1113)(74, 1114)(75, 1115)(76, 1116)(77, 1117)(78, 1118)(79, 1119)(80, 1120)(81, 1121)(82, 1122)(83, 1123)(84, 1124)(85, 1125)(86, 1126)(87, 1127)(88, 1128)(89, 1129)(90, 1130)(91, 1067)(92, 1068)(93, 1069)(94, 1070)(95, 1071)(96, 1072)(97, 1073)(98, 1074)(99, 1075)(100, 1076)(101, 1077)(102, 1078)(103, 1079)(104, 1080)(105, 1081)(106, 1082)(107, 1083)(108, 1084)(109, 1085)(110, 1086)(111, 1087)(112, 1088)(113, 1089)(114, 1090)(115, 1091)(116, 1092)(117, 1093)(118, 1094)(119, 1095)(120, 1096)(121, 1097)(122, 1098)(123, 1189)(124, 1190)(125, 1191)(126, 1192)(127, 1193)(128, 1194)(129, 1195)(130, 1196)(131, 1197)(132, 1198)(133, 1199)(134, 1200)(135, 1201)(136, 1202)(137, 1146)(138, 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1413)(230, 1330)(231, 1417)(232, 1392)(233, 1420)(234, 1267)(235, 1357)(236, 1386)(237, 1424)(238, 1277)(239, 1427)(240, 1428)(241, 1416)(242, 1430)(243, 1183)(244, 1434)(245, 1410)(246, 1372)(247, 1436)(248, 1337)(249, 1343)(250, 1351)(251, 1368)(252, 1439)(253, 1442)(254, 1411)(255, 1173)(256, 1444)(257, 1446)(258, 1448)(259, 1242)(260, 1450)(261, 1412)(262, 1452)(263, 1431)(264, 1232)(265, 1456)(266, 1391)(267, 1457)(268, 1458)(269, 1246)(270, 1347)(271, 1344)(272, 1354)(273, 1352)(274, 1229)(275, 1462)(276, 1385)(277, 1375)(278, 1423)(279, 1464)(280, 1390)(281, 1226)(282, 1342)(283, 1468)(284, 1323)(285, 1321)(286, 1317)(287, 1471)(288, 1409)(289, 1235)(290, 1356)(291, 1168)(292, 1161)(293, 1162)(294, 1379)(295, 1163)(296, 1418)(297, 1164)(298, 1165)(299, 1479)(300, 1166)(301, 1384)(302, 1169)(303, 1224)(304, 1170)(305, 1171)(306, 1172)(307, 1443)(308, 1481)(309, 1294)(310, 1184)(311, 1177)(312, 1178)(313, 1293)(314, 1179)(315, 1292)(316, 1180)(317, 1181)(318, 1341)(319, 1182)(320, 1415)(321, 1185)(322, 1238)(323, 1186)(324, 1187)(325, 1188)(326, 1419)(327, 1402)(328, 1492)(329, 1256)(330, 1361)(331, 1486)(332, 1358)(333, 1326)(334, 1290)(335, 1257)(336, 1279)(337, 1463)(338, 1487)(339, 1278)(340, 1221)(341, 1371)(342, 1482)(343, 1258)(344, 1281)(345, 1498)(346, 1280)(347, 1440)(348, 1298)(349, 1243)(350, 1340)(351, 1459)(352, 1501)(353, 1338)(354, 1227)(355, 1495)(356, 1383)(357, 1395)(358, 1217)(359, 1466)(360, 1259)(361, 1218)(362, 1467)(363, 1349)(364, 1254)(365, 1219)(366, 1473)(367, 1285)(368, 1220)(369, 1488)(370, 1451)(371, 1302)(372, 1222)(373, 1223)(374, 1474)(375, 1364)(376, 1309)(377, 1284)(378, 1244)(379, 1225)(380, 1465)(381, 1490)(382, 1288)(383, 1274)(384, 1240)(385, 1461)(386, 1441)(387, 1365)(388, 1497)(389, 1435)(390, 1230)(391, 1231)(392, 1454)(393, 1438)(394, 1335)(395, 1503)(396, 1429)(397, 1233)(398, 1234)(399, 1472)(400, 1505)(401, 1296)(402, 1253)(403, 1262)(404, 1269)(405, 1237)(406, 1504)(407, 1328)(408, 1249)(409, 1239)(410, 1304)(411, 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1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E15.1406 Graph:: bipartite v = 420 e = 1008 f = 560 degree seq :: [ 4^252, 6^168 ] E15.1404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 9}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^9, (Y2^4 * Y1^-1 * Y2^2 * Y1^-1)^2, Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1 * Y2^-3 * Y1^-1 ] Map:: R = (1, 505, 2, 506, 4, 508)(3, 507, 8, 512, 10, 514)(5, 509, 12, 516, 6, 510)(7, 511, 15, 519, 11, 515)(9, 513, 18, 522, 20, 524)(13, 517, 25, 529, 23, 527)(14, 518, 24, 528, 28, 532)(16, 520, 31, 535, 29, 533)(17, 521, 33, 537, 21, 525)(19, 523, 36, 540, 38, 542)(22, 526, 30, 534, 42, 546)(26, 530, 47, 551, 45, 549)(27, 531, 49, 553, 51, 555)(32, 536, 57, 561, 55, 559)(34, 538, 61, 565, 59, 563)(35, 539, 63, 567, 39, 543)(37, 541, 66, 570, 67, 571)(40, 544, 60, 564, 71, 575)(41, 545, 72, 576, 74, 578)(43, 547, 46, 550, 77, 581)(44, 548, 78, 582, 52, 556)(48, 552, 84, 588, 82, 586)(50, 554, 86, 590, 87, 591)(53, 557, 56, 560, 91, 595)(54, 558, 92, 596, 75, 579)(58, 562, 98, 602, 96, 600)(62, 566, 103, 607, 101, 605)(64, 568, 106, 610, 104, 608)(65, 569, 108, 612, 68, 572)(69, 573, 105, 609, 114, 618)(70, 574, 115, 619, 117, 621)(73, 577, 120, 624, 121, 625)(76, 580, 124, 628, 126, 630)(79, 583, 130, 634, 128, 632)(80, 584, 83, 587, 133, 637)(81, 585, 134, 638, 127, 631)(85, 589, 139, 643, 88, 592)(89, 593, 129, 633, 145, 649)(90, 594, 146, 650, 148, 652)(93, 597, 152, 656, 150, 654)(94, 598, 97, 601, 155, 659)(95, 599, 156, 660, 149, 653)(99, 603, 102, 606, 162, 666)(100, 604, 163, 667, 118, 622)(107, 611, 172, 676, 170, 674)(109, 613, 175, 679, 173, 677)(110, 614, 177, 681, 111, 615)(112, 616, 174, 678, 181, 685)(113, 617, 182, 686, 184, 688)(116, 620, 187, 691, 188, 692)(119, 623, 191, 695, 122, 626)(123, 627, 151, 655, 197, 701)(125, 629, 199, 703, 200, 704)(131, 635, 207, 711, 205, 709)(132, 636, 208, 712, 210, 714)(135, 639, 214, 718, 212, 716)(136, 640, 138, 642, 217, 721)(137, 641, 218, 722, 211, 715)(140, 644, 223, 727, 221, 725)(141, 645, 225, 729, 142, 646)(143, 647, 222, 726, 229, 733)(144, 648, 230, 734, 232, 736)(147, 651, 235, 739, 236, 740)(153, 657, 243, 747, 241, 745)(154, 658, 244, 748, 246, 750)(157, 661, 250, 754, 248, 752)(158, 662, 160, 664, 253, 757)(159, 663, 254, 758, 247, 751)(161, 665, 257, 761, 259, 763)(164, 668, 263, 767, 261, 765)(165, 669, 167, 671, 266, 770)(166, 670, 267, 771, 260, 764)(168, 672, 171, 675, 271, 775)(169, 673, 272, 776, 185, 689)(176, 680, 281, 785, 279, 783)(178, 682, 284, 788, 282, 786)(179, 683, 283, 787, 251, 755)(180, 684, 287, 791, 289, 793)(183, 687, 292, 796, 256, 760)(186, 690, 295, 799, 189, 693)(190, 694, 262, 766, 301, 805)(192, 696, 304, 808, 302, 806)(193, 697, 306, 810, 194, 698)(195, 699, 303, 807, 310, 814)(196, 700, 311, 815, 313, 817)(198, 702, 315, 819, 201, 705)(202, 706, 213, 717, 321, 825)(203, 707, 206, 710, 323, 827)(204, 708, 324, 828, 233, 737)(209, 713, 328, 832, 329, 833)(215, 719, 308, 812, 333, 837)(216, 720, 335, 839, 337, 841)(219, 723, 340, 844, 339, 843)(220, 724, 312, 816, 338, 842)(224, 728, 347, 851, 345, 849)(226, 730, 350, 854, 348, 852)(227, 731, 349, 853, 264, 768)(228, 732, 353, 857, 354, 858)(231, 735, 357, 861, 269, 773)(234, 738, 360, 864, 237, 741)(238, 742, 249, 753, 365, 869)(239, 743, 242, 746, 367, 871)(240, 744, 368, 872, 314, 818)(245, 749, 372, 876, 286, 790)(252, 756, 377, 881, 341, 845)(255, 759, 380, 884, 379, 883)(258, 762, 383, 887, 352, 856)(265, 769, 389, 893, 381, 885)(268, 772, 392, 896, 391, 895)(270, 774, 393, 897, 395, 899)(273, 777, 399, 903, 397, 901)(274, 778, 276, 780, 362, 866)(275, 779, 401, 905, 396, 900)(277, 781, 280, 784, 403, 907)(278, 782, 404, 908, 290, 794)(285, 789, 408, 912, 351, 855)(288, 792, 410, 914, 307, 811)(291, 795, 412, 916, 293, 797)(294, 798, 398, 902, 414, 918)(296, 800, 417, 921, 415, 919)(297, 801, 325, 829, 298, 802)(299, 803, 416, 920, 420, 924)(300, 804, 421, 925, 331, 835)(305, 809, 342, 846, 424, 928)(309, 813, 394, 898, 425, 929)(316, 820, 430, 934, 428, 932)(317, 821, 369, 873, 318, 822)(319, 823, 429, 933, 431, 935)(320, 824, 432, 936, 374, 878)(322, 826, 433, 937, 411, 915)(326, 830, 437, 941, 434, 938)(327, 831, 438, 942, 330, 834)(332, 836, 334, 838, 442, 946)(336, 840, 390, 894, 378, 882)(343, 847, 346, 850, 445, 949)(344, 848, 446, 950, 355, 859)(356, 860, 450, 954, 358, 862)(359, 863, 435, 939, 452, 956)(361, 865, 455, 959, 453, 957)(363, 867, 454, 958, 456, 960)(364, 868, 457, 961, 385, 889)(366, 870, 458, 962, 449, 953)(370, 874, 462, 966, 459, 963)(371, 875, 463, 967, 373, 877)(375, 879, 376, 880, 466, 970)(382, 886, 468, 972, 384, 888)(386, 890, 388, 892, 471, 975)(387, 891, 460, 964, 422, 926)(400, 904, 448, 952, 440, 944)(402, 906, 444, 948, 480, 984)(405, 909, 482, 986, 481, 985)(406, 910, 407, 911, 461, 965)(409, 913, 436, 940, 418, 922)(413, 917, 484, 988, 467, 971)(419, 923, 479, 983, 423, 927)(426, 930, 489, 993, 427, 931)(439, 943, 464, 968, 469, 973)(441, 945, 488, 992, 495, 999)(443, 947, 490, 994, 496, 1000)(447, 951, 491, 995, 497, 1001)(451, 955, 499, 1003, 472, 976)(465, 969, 493, 997, 504, 1008)(470, 974, 503, 1007, 475, 979)(473, 977, 492, 996, 474, 978)(476, 980, 478, 982, 501, 1005)(477, 981, 500, 1004, 486, 990)(483, 987, 494, 998, 502, 1006)(485, 989, 498, 1002, 487, 991)(1009, 1513, 1011, 1515, 1017, 1521, 1027, 1531, 1045, 1549, 1056, 1560, 1034, 1538, 1021, 1525, 1013, 1517)(1010, 1514, 1014, 1518, 1022, 1526, 1035, 1539, 1058, 1562, 1066, 1570, 1040, 1544, 1024, 1528, 1015, 1519)(1012, 1516, 1019, 1523, 1030, 1534, 1049, 1553, 1081, 1585, 1070, 1574, 1042, 1546, 1025, 1529, 1016, 1520)(1018, 1522, 1029, 1533, 1048, 1552, 1078, 1582, 1124, 1628, 1115, 1619, 1072, 1576, 1043, 1547, 1026, 1530)(1020, 1524, 1031, 1535, 1051, 1555, 1084, 1588, 1133, 1637, 1139, 1643, 1087, 1591, 1052, 1556, 1032, 1536)(1023, 1527, 1037, 1541, 1061, 1565, 1098, 1602, 1155, 1659, 1161, 1665, 1101, 1605, 1062, 1566, 1038, 1542)(1028, 1532, 1047, 1551, 1077, 1581, 1121, 1625, 1191, 1695, 1184, 1688, 1117, 1621, 1073, 1577, 1044, 1548)(1033, 1537, 1053, 1557, 1088, 1592, 1140, 1644, 1217, 1721, 1223, 1727, 1143, 1647, 1089, 1593, 1054, 1558)(1036, 1540, 1060, 1564, 1097, 1601, 1152, 1656, 1239, 1743, 1232, 1736, 1148, 1652, 1093, 1597, 1057, 1561)(1039, 1543, 1063, 1567, 1102, 1606, 1162, 1666, 1253, 1757, 1259, 1763, 1165, 1669, 1103, 1607, 1064, 1568)(1041, 1545, 1067, 1571, 1107, 1611, 1169, 1673, 1266, 1770, 1272, 1776, 1172, 1676, 1108, 1612, 1068, 1572)(1046, 1550, 1076, 1580, 1120, 1624, 1188, 1692, 1296, 1800, 1293, 1797, 1186, 1690, 1118, 1622, 1074, 1578)(1050, 1554, 1083, 1587, 1131, 1635, 1204, 1708, 1320, 1824, 1313, 1817, 1200, 1704, 1127, 1631, 1080, 1584)(1055, 1559, 1090, 1594, 1144, 1648, 1224, 1728, 1344, 1848, 1349, 1853, 1227, 1731, 1145, 1649, 1091, 1595)(1059, 1563, 1096, 1600, 1151, 1655, 1236, 1740, 1292, 1796, 1359, 1863, 1234, 1738, 1149, 1653, 1094, 1598)(1065, 1569, 1104, 1608, 1166, 1670, 1260, 1764, 1386, 1890, 1389, 1893, 1263, 1767, 1167, 1671, 1105, 1609)(1069, 1573, 1109, 1613, 1173, 1677, 1273, 1777, 1398, 1902, 1345, 1849, 1276, 1780, 1174, 1678, 1110, 1614)(1071, 1575, 1112, 1616, 1176, 1680, 1278, 1782, 1402, 1906, 1318, 1822, 1281, 1785, 1177, 1681, 1113, 1617)(1075, 1579, 1119, 1623, 1187, 1691, 1294, 1798, 1417, 1921, 1350, 1854, 1228, 1732, 1146, 1650, 1092, 1596)(1079, 1583, 1126, 1630, 1198, 1702, 1308, 1812, 1226, 1730, 1347, 1851, 1304, 1808, 1194, 1698, 1123, 1627)(1082, 1586, 1130, 1634, 1203, 1707, 1317, 1821, 1358, 1862, 1416, 1920, 1315, 1819, 1201, 1705, 1128, 1632)(1085, 1589, 1135, 1639, 1210, 1714, 1328, 1832, 1262, 1766, 1387, 1891, 1324, 1828, 1206, 1710, 1132, 1636)(1086, 1590, 1136, 1640, 1211, 1715, 1330, 1834, 1295, 1799, 1189, 1693, 1298, 1802, 1212, 1716, 1137, 1641)(1095, 1599, 1150, 1654, 1235, 1739, 1360, 1864, 1415, 1919, 1289, 1793, 1264, 1768, 1168, 1672, 1106, 1610)(1099, 1603, 1157, 1661, 1246, 1750, 1372, 1876, 1275, 1779, 1399, 1903, 1369, 1873, 1242, 1746, 1154, 1658)(1100, 1604, 1158, 1662, 1247, 1751, 1374, 1878, 1361, 1865, 1237, 1741, 1363, 1867, 1248, 1752, 1159, 1663)(1111, 1615, 1129, 1633, 1202, 1706, 1316, 1820, 1337, 1841, 1448, 1952, 1355, 1859, 1277, 1781, 1175, 1679)(1114, 1618, 1178, 1682, 1282, 1786, 1408, 1912, 1336, 1840, 1218, 1722, 1338, 1842, 1283, 1787, 1179, 1683)(1116, 1620, 1181, 1685, 1285, 1789, 1410, 1914, 1487, 1991, 1428, 1932, 1413, 1917, 1286, 1790, 1182, 1686)(1122, 1626, 1193, 1697, 1302, 1806, 1221, 1725, 1142, 1646, 1220, 1724, 1340, 1844, 1299, 1803, 1190, 1694)(1125, 1629, 1197, 1701, 1307, 1811, 1427, 1931, 1312, 1816, 1432, 1936, 1426, 1930, 1305, 1809, 1195, 1699)(1134, 1638, 1209, 1713, 1327, 1831, 1288, 1792, 1183, 1687, 1287, 1791, 1414, 1918, 1325, 1829, 1207, 1711)(1138, 1642, 1213, 1717, 1333, 1837, 1444, 1948, 1380, 1884, 1254, 1758, 1381, 1885, 1334, 1838, 1214, 1718)(1141, 1645, 1219, 1723, 1339, 1843, 1449, 1953, 1445, 1949, 1471, 1975, 1447, 1951, 1335, 1839, 1216, 1720)(1147, 1651, 1229, 1733, 1351, 1855, 1452, 1956, 1411, 1915, 1439, 1943, 1455, 1959, 1352, 1856, 1230, 1734)(1153, 1657, 1241, 1745, 1367, 1871, 1257, 1761, 1164, 1668, 1256, 1760, 1383, 1887, 1364, 1868, 1238, 1742)(1156, 1660, 1245, 1749, 1371, 1875, 1354, 1858, 1231, 1735, 1353, 1857, 1456, 1960, 1370, 1874, 1243, 1747)(1160, 1664, 1249, 1753, 1377, 1881, 1469, 1973, 1391, 1895, 1267, 1771, 1392, 1896, 1378, 1882, 1250, 1754)(1163, 1667, 1255, 1759, 1382, 1886, 1473, 1977, 1470, 1974, 1476, 1980, 1472, 1976, 1379, 1883, 1252, 1756)(1170, 1674, 1268, 1772, 1393, 1897, 1478, 1982, 1409, 1913, 1446, 1950, 1477, 1981, 1390, 1894, 1265, 1769)(1171, 1675, 1269, 1773, 1394, 1898, 1434, 1938, 1319, 1823, 1205, 1709, 1322, 1826, 1395, 1899, 1270, 1774)(1180, 1684, 1196, 1700, 1306, 1810, 1215, 1719, 1208, 1712, 1326, 1830, 1251, 1755, 1244, 1748, 1284, 1788)(1185, 1689, 1290, 1794, 1362, 1866, 1457, 1961, 1506, 2010, 1475, 1979, 1384, 1888, 1258, 1762, 1291, 1795)(1192, 1696, 1301, 1805, 1421, 1925, 1493, 1997, 1425, 1929, 1348, 1852, 1385, 1889, 1261, 1765, 1300, 1804)(1199, 1703, 1310, 1814, 1431, 1935, 1488, 1992, 1453, 1957, 1464, 1968, 1486, 1990, 1407, 1911, 1311, 1815)(1222, 1726, 1341, 1845, 1314, 1818, 1418, 1922, 1297, 1801, 1419, 1923, 1491, 1995, 1451, 1955, 1342, 1846)(1225, 1729, 1346, 1850, 1321, 1825, 1435, 1939, 1498, 2002, 1510, 2014, 1463, 1967, 1400, 1904, 1343, 1847)(1233, 1737, 1356, 1860, 1433, 1937, 1403, 1907, 1482, 1986, 1480, 1984, 1396, 1900, 1271, 1775, 1357, 1861)(1240, 1744, 1366, 1870, 1459, 1963, 1500, 2004, 1438, 1942, 1388, 1892, 1397, 1901, 1274, 1778, 1365, 1869)(1279, 1783, 1404, 1908, 1483, 1987, 1499, 2003, 1437, 1941, 1323, 1827, 1436, 1940, 1481, 1985, 1401, 1905)(1280, 1784, 1405, 1909, 1484, 1988, 1496, 2000, 1429, 1933, 1309, 1813, 1430, 1934, 1485, 1989, 1406, 1910)(1303, 1807, 1423, 1927, 1495, 1999, 1466, 1970, 1375, 1879, 1467, 1971, 1512, 2016, 1490, 1994, 1424, 1928)(1329, 1833, 1422, 1926, 1494, 1998, 1443, 1947, 1332, 1836, 1412, 1916, 1489, 1993, 1501, 2005, 1440, 1944)(1331, 1835, 1442, 1946, 1503, 2007, 1509, 2013, 1462, 1966, 1368, 1872, 1461, 1965, 1502, 2006, 1441, 1945)(1373, 1877, 1460, 1964, 1508, 2012, 1468, 1972, 1376, 1880, 1454, 1958, 1505, 2009, 1511, 2015, 1465, 1969)(1420, 1924, 1450, 1954, 1504, 2008, 1497, 2001, 1479, 1983, 1507, 2011, 1458, 1962, 1474, 1978, 1492, 1996) L = (1, 1011)(2, 1014)(3, 1017)(4, 1019)(5, 1009)(6, 1022)(7, 1010)(8, 1012)(9, 1027)(10, 1029)(11, 1030)(12, 1031)(13, 1013)(14, 1035)(15, 1037)(16, 1015)(17, 1016)(18, 1018)(19, 1045)(20, 1047)(21, 1048)(22, 1049)(23, 1051)(24, 1020)(25, 1053)(26, 1021)(27, 1058)(28, 1060)(29, 1061)(30, 1023)(31, 1063)(32, 1024)(33, 1067)(34, 1025)(35, 1026)(36, 1028)(37, 1056)(38, 1076)(39, 1077)(40, 1078)(41, 1081)(42, 1083)(43, 1084)(44, 1032)(45, 1088)(46, 1033)(47, 1090)(48, 1034)(49, 1036)(50, 1066)(51, 1096)(52, 1097)(53, 1098)(54, 1038)(55, 1102)(56, 1039)(57, 1104)(58, 1040)(59, 1107)(60, 1041)(61, 1109)(62, 1042)(63, 1112)(64, 1043)(65, 1044)(66, 1046)(67, 1119)(68, 1120)(69, 1121)(70, 1124)(71, 1126)(72, 1050)(73, 1070)(74, 1130)(75, 1131)(76, 1133)(77, 1135)(78, 1136)(79, 1052)(80, 1140)(81, 1054)(82, 1144)(83, 1055)(84, 1075)(85, 1057)(86, 1059)(87, 1150)(88, 1151)(89, 1152)(90, 1155)(91, 1157)(92, 1158)(93, 1062)(94, 1162)(95, 1064)(96, 1166)(97, 1065)(98, 1095)(99, 1169)(100, 1068)(101, 1173)(102, 1069)(103, 1129)(104, 1176)(105, 1071)(106, 1178)(107, 1072)(108, 1181)(109, 1073)(110, 1074)(111, 1187)(112, 1188)(113, 1191)(114, 1193)(115, 1079)(116, 1115)(117, 1197)(118, 1198)(119, 1080)(120, 1082)(121, 1202)(122, 1203)(123, 1204)(124, 1085)(125, 1139)(126, 1209)(127, 1210)(128, 1211)(129, 1086)(130, 1213)(131, 1087)(132, 1217)(133, 1219)(134, 1220)(135, 1089)(136, 1224)(137, 1091)(138, 1092)(139, 1229)(140, 1093)(141, 1094)(142, 1235)(143, 1236)(144, 1239)(145, 1241)(146, 1099)(147, 1161)(148, 1245)(149, 1246)(150, 1247)(151, 1100)(152, 1249)(153, 1101)(154, 1253)(155, 1255)(156, 1256)(157, 1103)(158, 1260)(159, 1105)(160, 1106)(161, 1266)(162, 1268)(163, 1269)(164, 1108)(165, 1273)(166, 1110)(167, 1111)(168, 1278)(169, 1113)(170, 1282)(171, 1114)(172, 1196)(173, 1285)(174, 1116)(175, 1287)(176, 1117)(177, 1290)(178, 1118)(179, 1294)(180, 1296)(181, 1298)(182, 1122)(183, 1184)(184, 1301)(185, 1302)(186, 1123)(187, 1125)(188, 1306)(189, 1307)(190, 1308)(191, 1310)(192, 1127)(193, 1128)(194, 1316)(195, 1317)(196, 1320)(197, 1322)(198, 1132)(199, 1134)(200, 1326)(201, 1327)(202, 1328)(203, 1330)(204, 1137)(205, 1333)(206, 1138)(207, 1208)(208, 1141)(209, 1223)(210, 1338)(211, 1339)(212, 1340)(213, 1142)(214, 1341)(215, 1143)(216, 1344)(217, 1346)(218, 1347)(219, 1145)(220, 1146)(221, 1351)(222, 1147)(223, 1353)(224, 1148)(225, 1356)(226, 1149)(227, 1360)(228, 1292)(229, 1363)(230, 1153)(231, 1232)(232, 1366)(233, 1367)(234, 1154)(235, 1156)(236, 1284)(237, 1371)(238, 1372)(239, 1374)(240, 1159)(241, 1377)(242, 1160)(243, 1244)(244, 1163)(245, 1259)(246, 1381)(247, 1382)(248, 1383)(249, 1164)(250, 1291)(251, 1165)(252, 1386)(253, 1300)(254, 1387)(255, 1167)(256, 1168)(257, 1170)(258, 1272)(259, 1392)(260, 1393)(261, 1394)(262, 1171)(263, 1357)(264, 1172)(265, 1398)(266, 1365)(267, 1399)(268, 1174)(269, 1175)(270, 1402)(271, 1404)(272, 1405)(273, 1177)(274, 1408)(275, 1179)(276, 1180)(277, 1410)(278, 1182)(279, 1414)(280, 1183)(281, 1264)(282, 1362)(283, 1185)(284, 1359)(285, 1186)(286, 1417)(287, 1189)(288, 1293)(289, 1419)(290, 1212)(291, 1190)(292, 1192)(293, 1421)(294, 1221)(295, 1423)(296, 1194)(297, 1195)(298, 1215)(299, 1427)(300, 1226)(301, 1430)(302, 1431)(303, 1199)(304, 1432)(305, 1200)(306, 1418)(307, 1201)(308, 1337)(309, 1358)(310, 1281)(311, 1205)(312, 1313)(313, 1435)(314, 1395)(315, 1436)(316, 1206)(317, 1207)(318, 1251)(319, 1288)(320, 1262)(321, 1422)(322, 1295)(323, 1442)(324, 1412)(325, 1444)(326, 1214)(327, 1216)(328, 1218)(329, 1448)(330, 1283)(331, 1449)(332, 1299)(333, 1314)(334, 1222)(335, 1225)(336, 1349)(337, 1276)(338, 1321)(339, 1304)(340, 1385)(341, 1227)(342, 1228)(343, 1452)(344, 1230)(345, 1456)(346, 1231)(347, 1277)(348, 1433)(349, 1233)(350, 1416)(351, 1234)(352, 1415)(353, 1237)(354, 1457)(355, 1248)(356, 1238)(357, 1240)(358, 1459)(359, 1257)(360, 1461)(361, 1242)(362, 1243)(363, 1354)(364, 1275)(365, 1460)(366, 1361)(367, 1467)(368, 1454)(369, 1469)(370, 1250)(371, 1252)(372, 1254)(373, 1334)(374, 1473)(375, 1364)(376, 1258)(377, 1261)(378, 1389)(379, 1324)(380, 1397)(381, 1263)(382, 1265)(383, 1267)(384, 1378)(385, 1478)(386, 1434)(387, 1270)(388, 1271)(389, 1274)(390, 1345)(391, 1369)(392, 1343)(393, 1279)(394, 1318)(395, 1482)(396, 1483)(397, 1484)(398, 1280)(399, 1311)(400, 1336)(401, 1446)(402, 1487)(403, 1439)(404, 1489)(405, 1286)(406, 1325)(407, 1289)(408, 1315)(409, 1350)(410, 1297)(411, 1491)(412, 1450)(413, 1493)(414, 1494)(415, 1495)(416, 1303)(417, 1348)(418, 1305)(419, 1312)(420, 1413)(421, 1309)(422, 1485)(423, 1488)(424, 1426)(425, 1403)(426, 1319)(427, 1498)(428, 1481)(429, 1323)(430, 1388)(431, 1455)(432, 1329)(433, 1331)(434, 1503)(435, 1332)(436, 1380)(437, 1471)(438, 1477)(439, 1335)(440, 1355)(441, 1445)(442, 1504)(443, 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1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) 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 E15.1405 Graph:: bipartite v = 224 e = 1008 f = 756 degree seq :: [ 6^168, 18^56 ] E15.1405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 9}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^9, (Y3^-3 * Y2 * Y3^3 * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^9, (Y3^-1 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2)^2 ] Map:: polytopal R = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 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1838)(1230, 1734, 1336, 1840)(1232, 1736, 1278, 1782)(1234, 1738, 1276, 1780)(1236, 1740, 1341, 1845)(1237, 1741, 1343, 1847)(1239, 1743, 1346, 1850)(1241, 1745, 1349, 1853)(1242, 1746, 1350, 1854)(1243, 1747, 1352, 1856)(1245, 1749, 1310, 1814)(1247, 1751, 1356, 1860)(1248, 1752, 1358, 1862)(1251, 1755, 1289, 1793)(1252, 1756, 1362, 1866)(1258, 1762, 1367, 1871)(1259, 1763, 1369, 1873)(1261, 1765, 1372, 1876)(1263, 1767, 1375, 1879)(1264, 1768, 1376, 1880)(1265, 1769, 1377, 1881)(1267, 1771, 1338, 1842)(1269, 1773, 1381, 1885)(1270, 1774, 1383, 1887)(1273, 1777, 1322, 1826)(1274, 1778, 1386, 1890)(1279, 1783, 1389, 1893)(1281, 1785, 1360, 1864)(1283, 1787, 1393, 1897)(1284, 1788, 1303, 1807)(1286, 1790, 1395, 1899)(1287, 1791, 1396, 1900)(1290, 1794, 1345, 1849)(1292, 1796, 1388, 1892)(1293, 1797, 1317, 1821)(1295, 1799, 1401, 1905)(1296, 1800, 1403, 1907)(1298, 1802, 1404, 1908)(1300, 1804, 1363, 1867)(1302, 1806, 1359, 1863)(1304, 1808, 1342, 1846)(1306, 1810, 1408, 1912)(1308, 1812, 1357, 1861)(1309, 1813, 1365, 1869)(1311, 1815, 1364, 1868)(1312, 1816, 1411, 1915)(1314, 1818, 1384, 1888)(1316, 1820, 1414, 1918)(1319, 1823, 1416, 1920)(1320, 1824, 1417, 1921)(1323, 1827, 1371, 1875)(1326, 1830, 1418, 1922)(1327, 1831, 1420, 1924)(1329, 1833, 1421, 1925)(1331, 1835, 1387, 1891)(1333, 1837, 1368, 1872)(1335, 1839, 1424, 1928)(1337, 1841, 1382, 1886)(1339, 1843, 1351, 1855)(1340, 1844, 1427, 1931)(1344, 1848, 1431, 1935)(1347, 1851, 1422, 1926)(1348, 1852, 1433, 1937)(1353, 1857, 1436, 1940)(1354, 1858, 1410, 1914)(1355, 1859, 1438, 1942)(1361, 1865, 1398, 1902)(1366, 1870, 1442, 1946)(1370, 1874, 1445, 1949)(1373, 1877, 1406, 1910)(1374, 1878, 1447, 1951)(1378, 1882, 1448, 1952)(1379, 1883, 1426, 1930)(1380, 1884, 1450, 1954)(1385, 1889, 1399, 1903)(1390, 1894, 1454, 1958)(1391, 1895, 1440, 1944)(1392, 1896, 1456, 1960)(1394, 1898, 1449, 1953)(1397, 1901, 1452, 1956)(1400, 1904, 1461, 1965)(1402, 1906, 1446, 1950)(1405, 1909, 1441, 1945)(1407, 1911, 1429, 1933)(1409, 1913, 1439, 1943)(1412, 1916, 1451, 1955)(1413, 1917, 1470, 1974)(1415, 1919, 1437, 1941)(1419, 1923, 1432, 1936)(1423, 1927, 1443, 1947)(1425, 1929, 1434, 1938)(1428, 1932, 1482, 1986)(1430, 1934, 1483, 1987)(1435, 1939, 1486, 1990)(1444, 1948, 1492, 1996)(1453, 1957, 1499, 2003)(1455, 1959, 1500, 2004)(1457, 1961, 1466, 1970)(1458, 1962, 1476, 1980)(1459, 1963, 1495, 1999)(1460, 1964, 1498, 2002)(1462, 1966, 1494, 1998)(1463, 1967, 1472, 1976)(1464, 1968, 1477, 1981)(1465, 1969, 1501, 2005)(1467, 1971, 1493, 1997)(1468, 1972, 1502, 2006)(1469, 1973, 1505, 2009)(1471, 1975, 1479, 1983)(1473, 1977, 1487, 1991)(1474, 1978, 1490, 1994)(1475, 1979, 1485, 1989)(1478, 1982, 1506, 2010)(1480, 1984, 1484, 1988)(1481, 1985, 1507, 2011)(1488, 1992, 1496, 2000)(1489, 1993, 1508, 2012)(1491, 1995, 1509, 2013)(1497, 2001, 1510, 2014)(1503, 2007, 1504, 2008)(1511, 2015, 1512, 2016) L = (1, 1011)(2, 1013)(3, 1016)(4, 1009)(5, 1020)(6, 1010)(7, 1021)(8, 1025)(9, 1026)(10, 1012)(11, 1017)(12, 1031)(13, 1032)(14, 1014)(15, 1015)(16, 1035)(17, 1039)(18, 1041)(19, 1042)(20, 1018)(21, 1019)(22, 1045)(23, 1049)(24, 1051)(25, 1052)(26, 1022)(27, 1055)(28, 1023)(29, 1024)(30, 1058)(31, 1044)(32, 1027)(33, 1064)(34, 1066)(35, 1067)(36, 1028)(37, 1069)(38, 1029)(39, 1030)(40, 1072)(41, 1054)(42, 1033)(43, 1078)(44, 1080)(45, 1081)(46, 1034)(47, 1084)(48, 1085)(49, 1036)(50, 1088)(51, 1037)(52, 1038)(53, 1091)(54, 1040)(55, 1094)(56, 1098)(57, 1043)(58, 1101)(59, 1103)(60, 1104)(61, 1106)(62, 1107)(63, 1046)(64, 1109)(65, 1047)(66, 1048)(67, 1112)(68, 1050)(69, 1115)(70, 1087)(71, 1053)(72, 1121)(73, 1123)(74, 1124)(75, 1056)(76, 1127)(77, 1129)(78, 1130)(79, 1057)(80, 1133)(81, 1134)(82, 1059)(83, 1137)(84, 1060)(85, 1061)(86, 1141)(87, 1062)(88, 1063)(89, 1144)(90, 1071)(91, 1065)(92, 1148)(93, 1152)(94, 1068)(95, 1155)(96, 1156)(97, 1070)(98, 1159)(99, 1161)(100, 1162)(101, 1164)(102, 1165)(103, 1073)(104, 1168)(105, 1074)(106, 1075)(107, 1172)(108, 1076)(109, 1077)(110, 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1755)(748, 1756)(749, 1757)(750, 1758)(751, 1759)(752, 1760)(753, 1761)(754, 1762)(755, 1763)(756, 1764)(757, 1765)(758, 1766)(759, 1767)(760, 1768)(761, 1769)(762, 1770)(763, 1771)(764, 1772)(765, 1773)(766, 1774)(767, 1775)(768, 1776)(769, 1777)(770, 1778)(771, 1779)(772, 1780)(773, 1781)(774, 1782)(775, 1783)(776, 1784)(777, 1785)(778, 1786)(779, 1787)(780, 1788)(781, 1789)(782, 1790)(783, 1791)(784, 1792)(785, 1793)(786, 1794)(787, 1795)(788, 1796)(789, 1797)(790, 1798)(791, 1799)(792, 1800)(793, 1801)(794, 1802)(795, 1803)(796, 1804)(797, 1805)(798, 1806)(799, 1807)(800, 1808)(801, 1809)(802, 1810)(803, 1811)(804, 1812)(805, 1813)(806, 1814)(807, 1815)(808, 1816)(809, 1817)(810, 1818)(811, 1819)(812, 1820)(813, 1821)(814, 1822)(815, 1823)(816, 1824)(817, 1825)(818, 1826)(819, 1827)(820, 1828)(821, 1829)(822, 1830)(823, 1831)(824, 1832)(825, 1833)(826, 1834)(827, 1835)(828, 1836)(829, 1837)(830, 1838)(831, 1839)(832, 1840)(833, 1841)(834, 1842)(835, 1843)(836, 1844)(837, 1845)(838, 1846)(839, 1847)(840, 1848)(841, 1849)(842, 1850)(843, 1851)(844, 1852)(845, 1853)(846, 1854)(847, 1855)(848, 1856)(849, 1857)(850, 1858)(851, 1859)(852, 1860)(853, 1861)(854, 1862)(855, 1863)(856, 1864)(857, 1865)(858, 1866)(859, 1867)(860, 1868)(861, 1869)(862, 1870)(863, 1871)(864, 1872)(865, 1873)(866, 1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 6, 18 ), ( 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E15.1404 Graph:: simple bipartite v = 756 e = 1008 f = 224 degree seq :: [ 2^504, 4^252 ] E15.1406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 9}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y1 * Y3)^3, (R * Y2 * Y3)^2, Y1^9, (Y3 * Y1^3 * Y3 * Y1^-4)^2, Y3 * Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 505, 2, 506, 5, 509, 11, 515, 21, 525, 36, 540, 20, 524, 10, 514, 4, 508)(3, 507, 7, 511, 15, 519, 27, 531, 46, 550, 53, 557, 31, 535, 17, 521, 8, 512)(6, 510, 13, 517, 25, 529, 42, 546, 69, 573, 74, 578, 45, 549, 26, 530, 14, 518)(9, 513, 18, 522, 32, 536, 54, 558, 86, 590, 81, 585, 50, 554, 29, 533, 16, 520)(12, 516, 23, 527, 40, 544, 65, 569, 103, 607, 108, 612, 68, 572, 41, 545, 24, 528)(19, 523, 34, 538, 57, 561, 91, 595, 140, 644, 139, 643, 90, 594, 56, 560, 33, 537)(22, 526, 38, 542, 63, 567, 99, 603, 153, 657, 158, 662, 102, 606, 64, 568, 39, 543)(28, 532, 48, 552, 78, 582, 121, 625, 185, 689, 190, 694, 124, 628, 79, 583, 49, 553)(30, 534, 51, 555, 82, 586, 127, 631, 194, 698, 172, 676, 112, 616, 71, 575, 43, 547)(35, 539, 59, 563, 94, 598, 145, 649, 220, 724, 219, 723, 144, 648, 93, 597, 58, 562)(37, 541, 61, 565, 97, 601, 149, 653, 227, 731, 232, 736, 152, 656, 98, 602, 62, 566)(44, 548, 72, 576, 113, 617, 173, 677, 261, 765, 246, 750, 162, 666, 105, 609, 66, 570)(47, 551, 76, 580, 119, 623, 181, 685, 273, 777, 231, 735, 184, 688, 120, 624, 77, 581)(52, 556, 84, 588, 130, 634, 199, 703, 297, 801, 296, 800, 198, 702, 129, 633, 83, 587)(55, 559, 88, 592, 136, 640, 207, 711, 308, 812, 313, 817, 210, 714, 137, 641, 89, 593)(60, 564, 96, 600, 148, 652, 225, 729, 330, 834, 329, 833, 224, 728, 147, 651, 95, 599)(67, 571, 106, 610, 163, 667, 247, 751, 351, 855, 340, 844, 236, 740, 155, 659, 100, 604)(70, 574, 110, 614, 169, 673, 255, 759, 360, 864, 328, 832, 258, 762, 170, 674, 111, 615)(73, 577, 115, 619, 176, 680, 266, 770, 221, 725, 325, 829, 265, 769, 175, 679, 114, 618)(75, 579, 117, 621, 179, 683, 270, 774, 376, 880, 343, 847, 240, 744, 180, 684, 118, 622)(80, 584, 125, 629, 191, 695, 286, 790, 228, 732, 333, 837, 281, 785, 187, 691, 122, 626)(85, 589, 132, 636, 202, 706, 302, 806, 373, 877, 402, 906, 301, 805, 201, 705, 131, 635)(87, 591, 134, 638, 205, 709, 305, 809, 238, 742, 157, 661, 239, 743, 206, 710, 135, 639)(92, 596, 142, 646, 216, 720, 319, 823, 411, 915, 413, 917, 322, 826, 217, 721, 143, 647)(101, 605, 156, 660, 237, 741, 341, 845, 426, 930, 420, 924, 334, 838, 229, 733, 150, 654)(104, 608, 160, 664, 243, 747, 346, 850, 320, 824, 218, 722, 323, 827, 244, 748, 161, 665)(107, 611, 165, 669, 250, 754, 215, 719, 141, 645, 214, 718, 318, 822, 249, 753, 164, 668)(109, 613, 167, 671, 253, 757, 357, 861, 380, 884, 277, 781, 336, 840, 254, 758, 168, 672)(116, 620, 178, 682, 269, 773, 213, 717, 317, 821, 387, 891, 285, 789, 268, 772, 177, 681)(123, 627, 188, 692, 282, 786, 342, 846, 403, 907, 448, 952, 379, 883, 275, 779, 182, 686)(126, 630, 193, 697, 289, 793, 392, 896, 298, 802, 399, 903, 391, 895, 288, 792, 192, 696)(128, 632, 196, 700, 293, 797, 394, 898, 445, 949, 372, 876, 397, 901, 294, 798, 197, 701)(133, 637, 203, 707, 304, 808, 290, 794, 356, 860, 251, 755, 166, 670, 252, 756, 204, 708)(138, 642, 211, 715, 314, 818, 235, 739, 154, 658, 234, 738, 338, 842, 310, 814, 208, 712)(146, 650, 222, 726, 326, 830, 415, 919, 470, 974, 471, 975, 416, 920, 327, 831, 223, 727)(151, 655, 230, 734, 335, 839, 421, 925, 474, 978, 472, 976, 418, 922, 331, 835, 226, 730)(159, 663, 241, 745, 344, 848, 428, 932, 440, 944, 364, 868, 417, 921, 345, 849, 242, 746)(171, 675, 259, 763, 365, 869, 378, 882, 274, 778, 377, 881, 439, 943, 362, 866, 256, 760)(174, 678, 263, 767, 370, 874, 444, 948, 467, 971, 410, 914, 321, 825, 371, 875, 264, 768)(183, 687, 276, 780, 352, 856, 435, 939, 483, 987, 482, 986, 434, 938, 350, 854, 271, 775)(186, 690, 279, 783, 382, 886, 450, 954, 395, 899, 295, 799, 398, 902, 383, 887, 280, 784)(189, 693, 284, 788, 355, 859, 292, 796, 195, 699, 291, 795, 393, 897, 386, 890, 283, 787)(200, 704, 299, 803, 400, 904, 459, 963, 496, 1000, 486, 990, 446, 950, 401, 905, 300, 804)(209, 713, 311, 815, 354, 858, 248, 752, 353, 857, 436, 940, 460, 964, 404, 908, 306, 810)(212, 716, 316, 820, 359, 863, 332, 836, 388, 892, 454, 958, 466, 970, 409, 913, 315, 819)(233, 737, 337, 841, 422, 926, 476, 980, 469, 973, 414, 918, 324, 828, 303, 807, 272, 776)(245, 749, 349, 853, 433, 937, 438, 942, 361, 865, 437, 941, 480, 984, 431, 935, 347, 851)(257, 761, 363, 867, 427, 931, 385, 889, 453, 957, 493, 997, 478, 982, 425, 929, 358, 862)(260, 764, 367, 871, 307, 811, 369, 873, 262, 766, 368, 872, 443, 947, 442, 946, 366, 870)(267, 771, 374, 878, 278, 782, 381, 885, 449, 953, 463, 967, 407, 911, 312, 816, 375, 879)(287, 791, 389, 893, 455, 959, 494, 998, 495, 999, 457, 961, 396, 900, 456, 960, 390, 894)(309, 813, 405, 909, 461, 965, 491, 995, 451, 955, 384, 888, 419, 923, 462, 966, 406, 910)(339, 843, 424, 928, 468, 972, 412, 916, 430, 934, 479, 983, 499, 1003, 477, 981, 423, 927)(348, 852, 432, 936, 475, 979, 441, 945, 485, 989, 502, 1006, 497, 1001, 473, 977, 429, 933)(408, 912, 464, 968, 498, 1002, 481, 985, 501, 1005, 489, 993, 452, 956, 492, 996, 465, 969)(447, 951, 488, 992, 487, 991, 458, 962, 490, 994, 503, 1007, 504, 1008, 500, 1004, 484, 988)(1009, 1513)(1010, 1514)(1011, 1515)(1012, 1516)(1013, 1517)(1014, 1518)(1015, 1519)(1016, 1520)(1017, 1521)(1018, 1522)(1019, 1523)(1020, 1524)(1021, 1525)(1022, 1526)(1023, 1527)(1024, 1528)(1025, 1529)(1026, 1530)(1027, 1531)(1028, 1532)(1029, 1533)(1030, 1534)(1031, 1535)(1032, 1536)(1033, 1537)(1034, 1538)(1035, 1539)(1036, 1540)(1037, 1541)(1038, 1542)(1039, 1543)(1040, 1544)(1041, 1545)(1042, 1546)(1043, 1547)(1044, 1548)(1045, 1549)(1046, 1550)(1047, 1551)(1048, 1552)(1049, 1553)(1050, 1554)(1051, 1555)(1052, 1556)(1053, 1557)(1054, 1558)(1055, 1559)(1056, 1560)(1057, 1561)(1058, 1562)(1059, 1563)(1060, 1564)(1061, 1565)(1062, 1566)(1063, 1567)(1064, 1568)(1065, 1569)(1066, 1570)(1067, 1571)(1068, 1572)(1069, 1573)(1070, 1574)(1071, 1575)(1072, 1576)(1073, 1577)(1074, 1578)(1075, 1579)(1076, 1580)(1077, 1581)(1078, 1582)(1079, 1583)(1080, 1584)(1081, 1585)(1082, 1586)(1083, 1587)(1084, 1588)(1085, 1589)(1086, 1590)(1087, 1591)(1088, 1592)(1089, 1593)(1090, 1594)(1091, 1595)(1092, 1596)(1093, 1597)(1094, 1598)(1095, 1599)(1096, 1600)(1097, 1601)(1098, 1602)(1099, 1603)(1100, 1604)(1101, 1605)(1102, 1606)(1103, 1607)(1104, 1608)(1105, 1609)(1106, 1610)(1107, 1611)(1108, 1612)(1109, 1613)(1110, 1614)(1111, 1615)(1112, 1616)(1113, 1617)(1114, 1618)(1115, 1619)(1116, 1620)(1117, 1621)(1118, 1622)(1119, 1623)(1120, 1624)(1121, 1625)(1122, 1626)(1123, 1627)(1124, 1628)(1125, 1629)(1126, 1630)(1127, 1631)(1128, 1632)(1129, 1633)(1130, 1634)(1131, 1635)(1132, 1636)(1133, 1637)(1134, 1638)(1135, 1639)(1136, 1640)(1137, 1641)(1138, 1642)(1139, 1643)(1140, 1644)(1141, 1645)(1142, 1646)(1143, 1647)(1144, 1648)(1145, 1649)(1146, 1650)(1147, 1651)(1148, 1652)(1149, 1653)(1150, 1654)(1151, 1655)(1152, 1656)(1153, 1657)(1154, 1658)(1155, 1659)(1156, 1660)(1157, 1661)(1158, 1662)(1159, 1663)(1160, 1664)(1161, 1665)(1162, 1666)(1163, 1667)(1164, 1668)(1165, 1669)(1166, 1670)(1167, 1671)(1168, 1672)(1169, 1673)(1170, 1674)(1171, 1675)(1172, 1676)(1173, 1677)(1174, 1678)(1175, 1679)(1176, 1680)(1177, 1681)(1178, 1682)(1179, 1683)(1180, 1684)(1181, 1685)(1182, 1686)(1183, 1687)(1184, 1688)(1185, 1689)(1186, 1690)(1187, 1691)(1188, 1692)(1189, 1693)(1190, 1694)(1191, 1695)(1192, 1696)(1193, 1697)(1194, 1698)(1195, 1699)(1196, 1700)(1197, 1701)(1198, 1702)(1199, 1703)(1200, 1704)(1201, 1705)(1202, 1706)(1203, 1707)(1204, 1708)(1205, 1709)(1206, 1710)(1207, 1711)(1208, 1712)(1209, 1713)(1210, 1714)(1211, 1715)(1212, 1716)(1213, 1717)(1214, 1718)(1215, 1719)(1216, 1720)(1217, 1721)(1218, 1722)(1219, 1723)(1220, 1724)(1221, 1725)(1222, 1726)(1223, 1727)(1224, 1728)(1225, 1729)(1226, 1730)(1227, 1731)(1228, 1732)(1229, 1733)(1230, 1734)(1231, 1735)(1232, 1736)(1233, 1737)(1234, 1738)(1235, 1739)(1236, 1740)(1237, 1741)(1238, 1742)(1239, 1743)(1240, 1744)(1241, 1745)(1242, 1746)(1243, 1747)(1244, 1748)(1245, 1749)(1246, 1750)(1247, 1751)(1248, 1752)(1249, 1753)(1250, 1754)(1251, 1755)(1252, 1756)(1253, 1757)(1254, 1758)(1255, 1759)(1256, 1760)(1257, 1761)(1258, 1762)(1259, 1763)(1260, 1764)(1261, 1765)(1262, 1766)(1263, 1767)(1264, 1768)(1265, 1769)(1266, 1770)(1267, 1771)(1268, 1772)(1269, 1773)(1270, 1774)(1271, 1775)(1272, 1776)(1273, 1777)(1274, 1778)(1275, 1779)(1276, 1780)(1277, 1781)(1278, 1782)(1279, 1783)(1280, 1784)(1281, 1785)(1282, 1786)(1283, 1787)(1284, 1788)(1285, 1789)(1286, 1790)(1287, 1791)(1288, 1792)(1289, 1793)(1290, 1794)(1291, 1795)(1292, 1796)(1293, 1797)(1294, 1798)(1295, 1799)(1296, 1800)(1297, 1801)(1298, 1802)(1299, 1803)(1300, 1804)(1301, 1805)(1302, 1806)(1303, 1807)(1304, 1808)(1305, 1809)(1306, 1810)(1307, 1811)(1308, 1812)(1309, 1813)(1310, 1814)(1311, 1815)(1312, 1816)(1313, 1817)(1314, 1818)(1315, 1819)(1316, 1820)(1317, 1821)(1318, 1822)(1319, 1823)(1320, 1824)(1321, 1825)(1322, 1826)(1323, 1827)(1324, 1828)(1325, 1829)(1326, 1830)(1327, 1831)(1328, 1832)(1329, 1833)(1330, 1834)(1331, 1835)(1332, 1836)(1333, 1837)(1334, 1838)(1335, 1839)(1336, 1840)(1337, 1841)(1338, 1842)(1339, 1843)(1340, 1844)(1341, 1845)(1342, 1846)(1343, 1847)(1344, 1848)(1345, 1849)(1346, 1850)(1347, 1851)(1348, 1852)(1349, 1853)(1350, 1854)(1351, 1855)(1352, 1856)(1353, 1857)(1354, 1858)(1355, 1859)(1356, 1860)(1357, 1861)(1358, 1862)(1359, 1863)(1360, 1864)(1361, 1865)(1362, 1866)(1363, 1867)(1364, 1868)(1365, 1869)(1366, 1870)(1367, 1871)(1368, 1872)(1369, 1873)(1370, 1874)(1371, 1875)(1372, 1876)(1373, 1877)(1374, 1878)(1375, 1879)(1376, 1880)(1377, 1881)(1378, 1882)(1379, 1883)(1380, 1884)(1381, 1885)(1382, 1886)(1383, 1887)(1384, 1888)(1385, 1889)(1386, 1890)(1387, 1891)(1388, 1892)(1389, 1893)(1390, 1894)(1391, 1895)(1392, 1896)(1393, 1897)(1394, 1898)(1395, 1899)(1396, 1900)(1397, 1901)(1398, 1902)(1399, 1903)(1400, 1904)(1401, 1905)(1402, 1906)(1403, 1907)(1404, 1908)(1405, 1909)(1406, 1910)(1407, 1911)(1408, 1912)(1409, 1913)(1410, 1914)(1411, 1915)(1412, 1916)(1413, 1917)(1414, 1918)(1415, 1919)(1416, 1920)(1417, 1921)(1418, 1922)(1419, 1923)(1420, 1924)(1421, 1925)(1422, 1926)(1423, 1927)(1424, 1928)(1425, 1929)(1426, 1930)(1427, 1931)(1428, 1932)(1429, 1933)(1430, 1934)(1431, 1935)(1432, 1936)(1433, 1937)(1434, 1938)(1435, 1939)(1436, 1940)(1437, 1941)(1438, 1942)(1439, 1943)(1440, 1944)(1441, 1945)(1442, 1946)(1443, 1947)(1444, 1948)(1445, 1949)(1446, 1950)(1447, 1951)(1448, 1952)(1449, 1953)(1450, 1954)(1451, 1955)(1452, 1956)(1453, 1957)(1454, 1958)(1455, 1959)(1456, 1960)(1457, 1961)(1458, 1962)(1459, 1963)(1460, 1964)(1461, 1965)(1462, 1966)(1463, 1967)(1464, 1968)(1465, 1969)(1466, 1970)(1467, 1971)(1468, 1972)(1469, 1973)(1470, 1974)(1471, 1975)(1472, 1976)(1473, 1977)(1474, 1978)(1475, 1979)(1476, 1980)(1477, 1981)(1478, 1982)(1479, 1983)(1480, 1984)(1481, 1985)(1482, 1986)(1483, 1987)(1484, 1988)(1485, 1989)(1486, 1990)(1487, 1991)(1488, 1992)(1489, 1993)(1490, 1994)(1491, 1995)(1492, 1996)(1493, 1997)(1494, 1998)(1495, 1999)(1496, 2000)(1497, 2001)(1498, 2002)(1499, 2003)(1500, 2004)(1501, 2005)(1502, 2006)(1503, 2007)(1504, 2008)(1505, 2009)(1506, 2010)(1507, 2011)(1508, 2012)(1509, 2013)(1510, 2014)(1511, 2015)(1512, 2016) L = (1, 1011)(2, 1014)(3, 1009)(4, 1017)(5, 1020)(6, 1010)(7, 1024)(8, 1021)(9, 1012)(10, 1027)(11, 1030)(12, 1013)(13, 1016)(14, 1031)(15, 1036)(16, 1015)(17, 1038)(18, 1041)(19, 1018)(20, 1043)(21, 1045)(22, 1019)(23, 1022)(24, 1046)(25, 1051)(26, 1052)(27, 1055)(28, 1023)(29, 1056)(30, 1025)(31, 1060)(32, 1063)(33, 1026)(34, 1066)(35, 1028)(36, 1068)(37, 1029)(38, 1032)(39, 1069)(40, 1074)(41, 1075)(42, 1078)(43, 1033)(44, 1034)(45, 1081)(46, 1083)(47, 1035)(48, 1037)(49, 1084)(50, 1088)(51, 1091)(52, 1039)(53, 1093)(54, 1095)(55, 1040)(56, 1096)(57, 1100)(58, 1042)(59, 1103)(60, 1044)(61, 1047)(62, 1104)(63, 1108)(64, 1109)(65, 1112)(66, 1048)(67, 1049)(68, 1115)(69, 1117)(70, 1050)(71, 1118)(72, 1122)(73, 1053)(74, 1124)(75, 1054)(76, 1057)(77, 1125)(78, 1130)(79, 1131)(80, 1058)(81, 1134)(82, 1136)(83, 1059)(84, 1139)(85, 1061)(86, 1141)(87, 1062)(88, 1064)(89, 1142)(90, 1146)(91, 1149)(92, 1065)(93, 1150)(94, 1154)(95, 1067)(96, 1070)(97, 1158)(98, 1159)(99, 1162)(100, 1071)(101, 1072)(102, 1165)(103, 1167)(104, 1073)(105, 1168)(106, 1172)(107, 1076)(108, 1174)(109, 1077)(110, 1079)(111, 1175)(112, 1179)(113, 1182)(114, 1080)(115, 1185)(116, 1082)(117, 1085)(118, 1140)(119, 1190)(120, 1191)(121, 1194)(122, 1086)(123, 1087)(124, 1197)(125, 1200)(126, 1089)(127, 1203)(128, 1090)(129, 1204)(130, 1208)(131, 1092)(132, 1126)(133, 1094)(134, 1097)(135, 1211)(136, 1216)(137, 1217)(138, 1098)(139, 1220)(140, 1221)(141, 1099)(142, 1101)(143, 1222)(144, 1226)(145, 1229)(146, 1102)(147, 1230)(148, 1234)(149, 1236)(150, 1105)(151, 1106)(152, 1239)(153, 1241)(154, 1107)(155, 1242)(156, 1246)(157, 1110)(158, 1248)(159, 1111)(160, 1113)(161, 1249)(162, 1253)(163, 1256)(164, 1114)(165, 1259)(166, 1116)(167, 1119)(168, 1186)(169, 1264)(170, 1265)(171, 1120)(172, 1268)(173, 1270)(174, 1121)(175, 1271)(176, 1275)(177, 1123)(178, 1176)(179, 1279)(180, 1280)(181, 1282)(182, 1127)(183, 1128)(184, 1285)(185, 1286)(186, 1129)(187, 1287)(188, 1291)(189, 1132)(190, 1293)(191, 1295)(192, 1133)(193, 1212)(194, 1298)(195, 1135)(196, 1137)(197, 1299)(198, 1303)(199, 1306)(200, 1138)(201, 1307)(202, 1311)(203, 1143)(204, 1201)(205, 1314)(206, 1315)(207, 1317)(208, 1144)(209, 1145)(210, 1320)(211, 1323)(212, 1147)(213, 1148)(214, 1151)(215, 1325)(216, 1328)(217, 1329)(218, 1152)(219, 1332)(220, 1310)(221, 1153)(222, 1155)(223, 1333)(224, 1336)(225, 1305)(226, 1156)(227, 1340)(228, 1157)(229, 1341)(230, 1281)(231, 1160)(232, 1344)(233, 1161)(234, 1163)(235, 1345)(236, 1347)(237, 1350)(238, 1164)(239, 1351)(240, 1166)(241, 1169)(242, 1260)(243, 1355)(244, 1356)(245, 1170)(246, 1358)(247, 1360)(248, 1171)(249, 1361)(250, 1363)(251, 1173)(252, 1250)(253, 1366)(254, 1367)(255, 1369)(256, 1177)(257, 1178)(258, 1372)(259, 1374)(260, 1180)(261, 1278)(262, 1181)(263, 1183)(264, 1376)(265, 1380)(266, 1381)(267, 1184)(268, 1382)(269, 1324)(270, 1269)(271, 1187)(272, 1188)(273, 1238)(274, 1189)(275, 1385)(276, 1388)(277, 1192)(278, 1193)(279, 1195)(280, 1389)(281, 1392)(282, 1393)(283, 1196)(284, 1395)(285, 1198)(286, 1396)(287, 1199)(288, 1397)(289, 1353)(290, 1202)(291, 1205)(292, 1364)(293, 1403)(294, 1404)(295, 1206)(296, 1339)(297, 1233)(298, 1207)(299, 1209)(300, 1407)(301, 1321)(302, 1228)(303, 1210)(304, 1375)(305, 1411)(306, 1213)(307, 1214)(308, 1408)(309, 1215)(310, 1413)(311, 1415)(312, 1218)(313, 1309)(314, 1416)(315, 1219)(316, 1277)(317, 1223)(318, 1418)(319, 1420)(320, 1224)(321, 1225)(322, 1409)(323, 1422)(324, 1227)(325, 1231)(326, 1368)(327, 1405)(328, 1232)(329, 1425)(330, 1400)(331, 1304)(332, 1235)(333, 1237)(334, 1427)(335, 1386)(336, 1240)(337, 1243)(338, 1431)(339, 1244)(340, 1433)(341, 1435)(342, 1245)(343, 1247)(344, 1437)(345, 1297)(346, 1438)(347, 1251)(348, 1252)(349, 1442)(350, 1254)(351, 1365)(352, 1255)(353, 1257)(354, 1443)(355, 1258)(356, 1300)(357, 1359)(358, 1261)(359, 1262)(360, 1334)(361, 1263)(362, 1445)(363, 1448)(364, 1266)(365, 1449)(366, 1267)(367, 1312)(368, 1272)(369, 1384)(370, 1453)(371, 1454)(372, 1273)(373, 1274)(374, 1276)(375, 1410)(376, 1377)(377, 1283)(378, 1343)(379, 1455)(380, 1284)(381, 1288)(382, 1459)(383, 1460)(384, 1289)(385, 1290)(386, 1461)(387, 1292)(388, 1294)(389, 1296)(390, 1462)(391, 1421)(392, 1338)(393, 1465)(394, 1466)(395, 1301)(396, 1302)(397, 1335)(398, 1426)(399, 1308)(400, 1316)(401, 1330)(402, 1383)(403, 1313)(404, 1456)(405, 1318)(406, 1467)(407, 1319)(408, 1322)(409, 1472)(410, 1326)(411, 1463)(412, 1327)(413, 1399)(414, 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1604)(597, 1605)(598, 1606)(599, 1607)(600, 1608)(601, 1609)(602, 1610)(603, 1611)(604, 1612)(605, 1613)(606, 1614)(607, 1615)(608, 1616)(609, 1617)(610, 1618)(611, 1619)(612, 1620)(613, 1621)(614, 1622)(615, 1623)(616, 1624)(617, 1625)(618, 1626)(619, 1627)(620, 1628)(621, 1629)(622, 1630)(623, 1631)(624, 1632)(625, 1633)(626, 1634)(627, 1635)(628, 1636)(629, 1637)(630, 1638)(631, 1639)(632, 1640)(633, 1641)(634, 1642)(635, 1643)(636, 1644)(637, 1645)(638, 1646)(639, 1647)(640, 1648)(641, 1649)(642, 1650)(643, 1651)(644, 1652)(645, 1653)(646, 1654)(647, 1655)(648, 1656)(649, 1657)(650, 1658)(651, 1659)(652, 1660)(653, 1661)(654, 1662)(655, 1663)(656, 1664)(657, 1665)(658, 1666)(659, 1667)(660, 1668)(661, 1669)(662, 1670)(663, 1671)(664, 1672)(665, 1673)(666, 1674)(667, 1675)(668, 1676)(669, 1677)(670, 1678)(671, 1679)(672, 1680)(673, 1681)(674, 1682)(675, 1683)(676, 1684)(677, 1685)(678, 1686)(679, 1687)(680, 1688)(681, 1689)(682, 1690)(683, 1691)(684, 1692)(685, 1693)(686, 1694)(687, 1695)(688, 1696)(689, 1697)(690, 1698)(691, 1699)(692, 1700)(693, 1701)(694, 1702)(695, 1703)(696, 1704)(697, 1705)(698, 1706)(699, 1707)(700, 1708)(701, 1709)(702, 1710)(703, 1711)(704, 1712)(705, 1713)(706, 1714)(707, 1715)(708, 1716)(709, 1717)(710, 1718)(711, 1719)(712, 1720)(713, 1721)(714, 1722)(715, 1723)(716, 1724)(717, 1725)(718, 1726)(719, 1727)(720, 1728)(721, 1729)(722, 1730)(723, 1731)(724, 1732)(725, 1733)(726, 1734)(727, 1735)(728, 1736)(729, 1737)(730, 1738)(731, 1739)(732, 1740)(733, 1741)(734, 1742)(735, 1743)(736, 1744)(737, 1745)(738, 1746)(739, 1747)(740, 1748)(741, 1749)(742, 1750)(743, 1751)(744, 1752)(745, 1753)(746, 1754)(747, 1755)(748, 1756)(749, 1757)(750, 1758)(751, 1759)(752, 1760)(753, 1761)(754, 1762)(755, 1763)(756, 1764)(757, 1765)(758, 1766)(759, 1767)(760, 1768)(761, 1769)(762, 1770)(763, 1771)(764, 1772)(765, 1773)(766, 1774)(767, 1775)(768, 1776)(769, 1777)(770, 1778)(771, 1779)(772, 1780)(773, 1781)(774, 1782)(775, 1783)(776, 1784)(777, 1785)(778, 1786)(779, 1787)(780, 1788)(781, 1789)(782, 1790)(783, 1791)(784, 1792)(785, 1793)(786, 1794)(787, 1795)(788, 1796)(789, 1797)(790, 1798)(791, 1799)(792, 1800)(793, 1801)(794, 1802)(795, 1803)(796, 1804)(797, 1805)(798, 1806)(799, 1807)(800, 1808)(801, 1809)(802, 1810)(803, 1811)(804, 1812)(805, 1813)(806, 1814)(807, 1815)(808, 1816)(809, 1817)(810, 1818)(811, 1819)(812, 1820)(813, 1821)(814, 1822)(815, 1823)(816, 1824)(817, 1825)(818, 1826)(819, 1827)(820, 1828)(821, 1829)(822, 1830)(823, 1831)(824, 1832)(825, 1833)(826, 1834)(827, 1835)(828, 1836)(829, 1837)(830, 1838)(831, 1839)(832, 1840)(833, 1841)(834, 1842)(835, 1843)(836, 1844)(837, 1845)(838, 1846)(839, 1847)(840, 1848)(841, 1849)(842, 1850)(843, 1851)(844, 1852)(845, 1853)(846, 1854)(847, 1855)(848, 1856)(849, 1857)(850, 1858)(851, 1859)(852, 1860)(853, 1861)(854, 1862)(855, 1863)(856, 1864)(857, 1865)(858, 1866)(859, 1867)(860, 1868)(861, 1869)(862, 1870)(863, 1871)(864, 1872)(865, 1873)(866, 1874)(867, 1875)(868, 1876)(869, 1877)(870, 1878)(871, 1879)(872, 1880)(873, 1881)(874, 1882)(875, 1883)(876, 1884)(877, 1885)(878, 1886)(879, 1887)(880, 1888)(881, 1889)(882, 1890)(883, 1891)(884, 1892)(885, 1893)(886, 1894)(887, 1895)(888, 1896)(889, 1897)(890, 1898)(891, 1899)(892, 1900)(893, 1901)(894, 1902)(895, 1903)(896, 1904)(897, 1905)(898, 1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E15.1403 Graph:: simple bipartite v = 560 e = 1008 f = 420 degree seq :: [ 2^504, 18^56 ] E15.1407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 9}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2)^3, (Y3 * Y2^-1)^3, Y2^9, (R * Y2^-3 * Y1)^2, (Y2^2 * Y1 * Y2^-4 * Y1 * Y2)^2, (Y2^-1 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2)^2 ] Map:: R = (1, 505, 2, 506)(3, 507, 7, 511)(4, 508, 9, 513)(5, 509, 11, 515)(6, 510, 13, 517)(8, 512, 16, 520)(10, 514, 19, 523)(12, 516, 22, 526)(14, 518, 25, 529)(15, 519, 27, 531)(17, 521, 30, 534)(18, 522, 32, 536)(20, 524, 35, 539)(21, 525, 37, 541)(23, 527, 40, 544)(24, 528, 42, 546)(26, 530, 45, 549)(28, 532, 48, 552)(29, 533, 50, 554)(31, 535, 53, 557)(33, 537, 55, 559)(34, 538, 57, 561)(36, 540, 60, 564)(38, 542, 62, 566)(39, 543, 64, 568)(41, 545, 67, 571)(43, 547, 69, 573)(44, 548, 71, 575)(46, 550, 74, 578)(47, 551, 75, 579)(49, 553, 78, 582)(51, 555, 81, 585)(52, 556, 83, 587)(54, 558, 86, 590)(56, 560, 89, 593)(58, 562, 92, 596)(59, 563, 94, 598)(61, 565, 97, 601)(63, 567, 100, 604)(65, 569, 102, 606)(66, 570, 104, 608)(68, 572, 107, 611)(70, 574, 110, 614)(72, 576, 112, 616)(73, 577, 114, 618)(76, 580, 118, 622)(77, 581, 120, 624)(79, 583, 123, 627)(80, 584, 124, 628)(82, 586, 127, 631)(84, 588, 130, 634)(85, 589, 96, 600)(87, 591, 134, 638)(88, 592, 136, 640)(90, 594, 139, 643)(91, 595, 140, 644)(93, 597, 143, 647)(95, 599, 146, 650)(98, 602, 150, 654)(99, 603, 152, 656)(101, 605, 155, 659)(103, 607, 158, 662)(105, 609, 161, 665)(106, 610, 116, 620)(108, 612, 165, 669)(109, 613, 167, 671)(111, 615, 170, 674)(113, 617, 173, 677)(115, 619, 176, 680)(117, 621, 179, 683)(119, 623, 182, 686)(121, 625, 184, 688)(122, 626, 186, 690)(125, 629, 190, 694)(126, 630, 192, 696)(128, 632, 195, 699)(129, 633, 196, 700)(131, 635, 199, 703)(132, 636, 201, 705)(133, 637, 203, 707)(135, 639, 206, 710)(137, 641, 208, 712)(138, 642, 210, 714)(141, 645, 214, 718)(142, 646, 216, 720)(144, 648, 219, 723)(145, 649, 220, 724)(147, 651, 223, 727)(148, 652, 225, 729)(149, 653, 227, 731)(151, 655, 230, 734)(153, 657, 232, 736)(154, 658, 212, 716)(156, 660, 236, 740)(157, 661, 238, 742)(159, 663, 241, 745)(160, 664, 242, 746)(162, 666, 245, 749)(163, 667, 247, 751)(164, 668, 249, 753)(166, 670, 252, 756)(168, 672, 254, 758)(169, 673, 188, 692)(171, 675, 258, 762)(172, 676, 260, 764)(174, 678, 263, 767)(175, 679, 264, 768)(177, 681, 267, 771)(178, 682, 269, 773)(180, 684, 272, 776)(181, 685, 274, 778)(183, 687, 277, 781)(185, 689, 280, 784)(187, 691, 283, 787)(189, 693, 286, 790)(191, 695, 289, 793)(193, 697, 291, 795)(194, 698, 293, 797)(197, 701, 297, 801)(198, 702, 299, 803)(200, 704, 248, 752)(202, 706, 246, 750)(204, 708, 305, 809)(205, 709, 307, 811)(207, 711, 310, 814)(209, 713, 313, 817)(211, 715, 316, 820)(213, 717, 317, 821)(215, 719, 320, 824)(217, 721, 322, 826)(218, 722, 324, 828)(221, 725, 326, 830)(222, 726, 328, 832)(224, 728, 270, 774)(226, 730, 268, 772)(228, 732, 333, 837)(229, 733, 335, 839)(231, 735, 338, 842)(233, 737, 341, 845)(234, 738, 342, 846)(235, 739, 344, 848)(237, 741, 302, 806)(239, 743, 348, 852)(240, 744, 350, 854)(243, 747, 281, 785)(244, 748, 354, 858)(250, 754, 359, 863)(251, 755, 361, 865)(253, 757, 364, 868)(255, 759, 367, 871)(256, 760, 368, 872)(257, 761, 369, 873)(259, 763, 330, 834)(261, 765, 373, 877)(262, 766, 375, 879)(265, 769, 314, 818)(266, 770, 378, 882)(271, 775, 381, 885)(273, 777, 352, 856)(275, 779, 385, 889)(276, 780, 295, 799)(278, 782, 387, 891)(279, 783, 388, 892)(282, 786, 337, 841)(284, 788, 380, 884)(285, 789, 309, 813)(287, 791, 393, 897)(288, 792, 395, 899)(290, 794, 396, 900)(292, 796, 355, 859)(294, 798, 351, 855)(296, 800, 334, 838)(298, 802, 400, 904)(300, 804, 349, 853)(301, 805, 357, 861)(303, 807, 356, 860)(304, 808, 403, 907)(306, 810, 376, 880)(308, 812, 406, 910)(311, 815, 408, 912)(312, 816, 409, 913)(315, 819, 363, 867)(318, 822, 410, 914)(319, 823, 412, 916)(321, 825, 413, 917)(323, 827, 379, 883)(325, 829, 360, 864)(327, 831, 416, 920)(329, 833, 374, 878)(331, 835, 343, 847)(332, 836, 419, 923)(336, 840, 423, 927)(339, 843, 414, 918)(340, 844, 425, 929)(345, 849, 428, 932)(346, 850, 402, 906)(347, 851, 430, 934)(353, 857, 390, 894)(358, 862, 434, 938)(362, 866, 437, 941)(365, 869, 398, 902)(366, 870, 439, 943)(370, 874, 440, 944)(371, 875, 418, 922)(372, 876, 442, 946)(377, 881, 391, 895)(382, 886, 446, 950)(383, 887, 432, 936)(384, 888, 448, 952)(386, 890, 441, 945)(389, 893, 444, 948)(392, 896, 453, 957)(394, 898, 438, 942)(397, 901, 433, 937)(399, 903, 421, 925)(401, 905, 431, 935)(404, 908, 443, 947)(405, 909, 462, 966)(407, 911, 429, 933)(411, 915, 424, 928)(415, 919, 435, 939)(417, 921, 426, 930)(420, 924, 474, 978)(422, 926, 475, 979)(427, 931, 478, 982)(436, 940, 484, 988)(445, 949, 491, 995)(447, 951, 492, 996)(449, 953, 458, 962)(450, 954, 468, 972)(451, 955, 487, 991)(452, 956, 490, 994)(454, 958, 486, 990)(455, 959, 464, 968)(456, 960, 469, 973)(457, 961, 493, 997)(459, 963, 485, 989)(460, 964, 494, 998)(461, 965, 497, 1001)(463, 967, 471, 975)(465, 969, 479, 983)(466, 970, 482, 986)(467, 971, 477, 981)(470, 974, 498, 1002)(472, 976, 476, 980)(473, 977, 499, 1003)(480, 984, 488, 992)(481, 985, 500, 1004)(483, 987, 501, 1005)(489, 993, 502, 1006)(495, 999, 496, 1000)(503, 1007, 504, 1008)(1009, 1513, 1011, 1515, 1016, 1520, 1025, 1529, 1039, 1543, 1044, 1548, 1028, 1532, 1018, 1522, 1012, 1516)(1010, 1514, 1013, 1517, 1020, 1524, 1031, 1535, 1049, 1553, 1054, 1558, 1034, 1538, 1022, 1526, 1014, 1518)(1015, 1519, 1021, 1525, 1032, 1536, 1051, 1555, 1078, 1582, 1087, 1591, 1057, 1561, 1036, 1540, 1023, 1527)(1017, 1521, 1026, 1530, 1041, 1545, 1064, 1568, 1098, 1602, 1071, 1575, 1046, 1550, 1029, 1533, 1019, 1523)(1024, 1528, 1035, 1539, 1055, 1559, 1084, 1588, 1127, 1631, 1136, 1640, 1090, 1594, 1059, 1563, 1037, 1541)(1027, 1531, 1042, 1546, 1066, 1570, 1101, 1605, 1152, 1656, 1143, 1647, 1095, 1599, 1062, 1566, 1040, 1544)(1030, 1534, 1045, 1549, 1069, 1573, 1106, 1610, 1159, 1663, 1167, 1671, 1111, 1615, 1073, 1577, 1047, 1551)(1033, 1537, 1052, 1556, 1080, 1584, 1121, 1625, 1182, 1686, 1174, 1678, 1116, 1620, 1076, 1580, 1050, 1554)(1038, 1542, 1058, 1562, 1088, 1592, 1133, 1637, 1199, 1703, 1208, 1712, 1139, 1643, 1092, 1596, 1060, 1564)(1043, 1547, 1067, 1571, 1103, 1607, 1155, 1659, 1232, 1736, 1223, 1727, 1149, 1653, 1099, 1603, 1065, 1569)(1048, 1552, 1072, 1576, 1109, 1613, 1164, 1668, 1245, 1749, 1254, 1758, 1170, 1674, 1113, 1617, 1074, 1578)(1053, 1557, 1081, 1585, 1123, 1627, 1185, 1689, 1276, 1780, 1267, 1771, 1179, 1683, 1119, 1623, 1079, 1583)(1056, 1560, 1085, 1589, 1129, 1633, 1193, 1697, 1289, 1793, 1281, 1785, 1188, 1692, 1125, 1629, 1083, 1587)(1061, 1565, 1091, 1595, 1137, 1641, 1205, 1709, 1306, 1810, 1311, 1815, 1210, 1714, 1140, 1644, 1093, 1597)(1063, 1567, 1094, 1598, 1141, 1645, 1212, 1716, 1314, 1818, 1322, 1826, 1217, 1721, 1145, 1649, 1096, 1600)(1068, 1572, 1104, 1608, 1156, 1660, 1234, 1738, 1339, 1843, 1335, 1839, 1229, 1733, 1153, 1657, 1102, 1606)(1070, 1574, 1107, 1611, 1161, 1665, 1241, 1745, 1305, 1809, 1342, 1846, 1236, 1740, 1157, 1661, 1105, 1609)(1075, 1579, 1112, 1616, 1168, 1672, 1251, 1755, 1361, 1865, 1365, 1869, 1256, 1760, 1171, 1675, 1114, 1618)(1077, 1581, 1115, 1619, 1172, 1676, 1258, 1762, 1368, 1872, 1334, 1838, 1263, 1767, 1176, 1680, 1117, 1621)(1082, 1586, 1124, 1628, 1186, 1690, 1278, 1782, 1388, 1892, 1385, 1889, 1273, 1777, 1183, 1687, 1122, 1626)(1086, 1590, 1130, 1634, 1195, 1699, 1292, 1796, 1231, 1735, 1336, 1840, 1286, 1790, 1191, 1695, 1128, 1632)(1089, 1593, 1134, 1638, 1201, 1705, 1300, 1804, 1406, 1910, 1402, 1906, 1295, 1799, 1197, 1701, 1132, 1636)(1097, 1601, 1144, 1648, 1215, 1719, 1319, 1823, 1307, 1811, 1207, 1711, 1309, 1813, 1219, 1723, 1146, 1650)(1100, 1604, 1148, 1652, 1221, 1725, 1326, 1830, 1419, 1923, 1422, 1926, 1331, 1835, 1225, 1729, 1150, 1654)(1108, 1612, 1162, 1666, 1242, 1746, 1351, 1855, 1275, 1779, 1386, 1890, 1347, 1851, 1239, 1743, 1160, 1664)(1110, 1614, 1165, 1669, 1247, 1751, 1357, 1861, 1416, 1920, 1437, 1941, 1353, 1857, 1243, 1747, 1163, 1667)(1118, 1622, 1175, 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1968, 1473, 1977, 1415, 1919, 1318, 1822)(1238, 1742, 1343, 1847, 1430, 1934, 1474, 1978, 1417, 1921, 1321, 1825, 1399, 1903, 1291, 1795, 1345, 1849)(1240, 1744, 1346, 1850, 1432, 1936, 1485, 1989, 1496, 2000, 1450, 1954, 1381, 1885, 1434, 1938, 1348, 1852)(1255, 1759, 1297, 1801, 1403, 1907, 1463, 1967, 1503, 2007, 1476, 1980, 1420, 1924, 1328, 1832, 1277, 1781)(1260, 1764, 1371, 1875, 1324, 1828, 1398, 1902, 1288, 1792, 1396, 1900, 1460, 1964, 1444, 1948, 1369, 1873)(1262, 1766, 1374, 1878, 1439, 1943, 1356, 1860, 1438, 1942, 1488, 1992, 1494, 1998, 1446, 1950, 1372, 1876)(1280, 1784, 1391, 1895, 1455, 1959, 1443, 1947, 1367, 1871, 1442, 1946, 1491, 1995, 1453, 1957, 1389, 1893)(1313, 1817, 1411, 1915, 1468, 1972, 1481, 1985, 1427, 1931, 1341, 1845, 1429, 1933, 1469, 1973, 1412, 1916)(1393, 1897, 1458, 1962, 1493, 1997, 1445, 1949, 1492, 1996, 1510, 2014, 1505, 2009, 1501, 2005, 1456, 1960)(1401, 1905, 1462, 1966, 1475, 1979, 1418, 1922, 1454, 1958, 1499, 2003, 1511, 2015, 1502, 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1906)(899, 1907)(900, 1908)(901, 1909)(902, 1910)(903, 1911)(904, 1912)(905, 1913)(906, 1914)(907, 1915)(908, 1916)(909, 1917)(910, 1918)(911, 1919)(912, 1920)(913, 1921)(914, 1922)(915, 1923)(916, 1924)(917, 1925)(918, 1926)(919, 1927)(920, 1928)(921, 1929)(922, 1930)(923, 1931)(924, 1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) 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 ) } Outer automorphisms :: reflexible Dual of E15.1408 Graph:: bipartite v = 308 e = 1008 f = 672 degree seq :: [ 4^252, 18^56 ] E15.1408 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 9}) Quotient :: dipole Aut^+ = PSL(2,8) (small group id <504, 156>) Aut = $<1008, 880>$ (small group id <1008, 880>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^9, (Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2)^2, (Y3 * Y2^-1)^9, Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^3 * Y1 * Y3^-3 * Y1^-1 * Y3 * Y1^-1 * Y3^-3 * Y1^-1 ] Map:: polytopal R = (1, 505, 2, 506, 4, 508)(3, 507, 8, 512, 10, 514)(5, 509, 12, 516, 6, 510)(7, 511, 15, 519, 11, 515)(9, 513, 18, 522, 20, 524)(13, 517, 25, 529, 23, 527)(14, 518, 24, 528, 28, 532)(16, 520, 31, 535, 29, 533)(17, 521, 33, 537, 21, 525)(19, 523, 36, 540, 38, 542)(22, 526, 30, 534, 42, 546)(26, 530, 47, 551, 45, 549)(27, 531, 49, 553, 51, 555)(32, 536, 57, 561, 55, 559)(34, 538, 61, 565, 59, 563)(35, 539, 63, 567, 39, 543)(37, 541, 66, 570, 67, 571)(40, 544, 60, 564, 71, 575)(41, 545, 72, 576, 74, 578)(43, 547, 46, 550, 77, 581)(44, 548, 78, 582, 52, 556)(48, 552, 84, 588, 82, 586)(50, 554, 86, 590, 87, 591)(53, 557, 56, 560, 91, 595)(54, 558, 92, 596, 75, 579)(58, 562, 98, 602, 96, 600)(62, 566, 103, 607, 101, 605)(64, 568, 106, 610, 104, 608)(65, 569, 108, 612, 68, 572)(69, 573, 105, 609, 114, 618)(70, 574, 115, 619, 117, 621)(73, 577, 120, 624, 121, 625)(76, 580, 124, 628, 126, 630)(79, 583, 130, 634, 128, 632)(80, 584, 83, 587, 133, 637)(81, 585, 134, 638, 127, 631)(85, 589, 139, 643, 88, 592)(89, 593, 129, 633, 145, 649)(90, 594, 146, 650, 148, 652)(93, 597, 152, 656, 150, 654)(94, 598, 97, 601, 155, 659)(95, 599, 156, 660, 149, 653)(99, 603, 102, 606, 162, 666)(100, 604, 163, 667, 118, 622)(107, 611, 172, 676, 170, 674)(109, 613, 175, 679, 173, 677)(110, 614, 177, 681, 111, 615)(112, 616, 174, 678, 181, 685)(113, 617, 182, 686, 184, 688)(116, 620, 187, 691, 188, 692)(119, 623, 191, 695, 122, 626)(123, 627, 151, 655, 197, 701)(125, 629, 199, 703, 200, 704)(131, 635, 207, 711, 205, 709)(132, 636, 208, 712, 210, 714)(135, 639, 214, 718, 212, 716)(136, 640, 138, 642, 217, 721)(137, 641, 218, 722, 211, 715)(140, 644, 223, 727, 221, 725)(141, 645, 225, 729, 142, 646)(143, 647, 222, 726, 229, 733)(144, 648, 230, 734, 232, 736)(147, 651, 235, 739, 236, 740)(153, 657, 243, 747, 241, 745)(154, 658, 244, 748, 246, 750)(157, 661, 250, 754, 248, 752)(158, 662, 160, 664, 253, 757)(159, 663, 254, 758, 247, 751)(161, 665, 257, 761, 259, 763)(164, 668, 263, 767, 261, 765)(165, 669, 167, 671, 266, 770)(166, 670, 267, 771, 260, 764)(168, 672, 171, 675, 271, 775)(169, 673, 272, 776, 185, 689)(176, 680, 281, 785, 279, 783)(178, 682, 284, 788, 282, 786)(179, 683, 283, 787, 251, 755)(180, 684, 287, 791, 289, 793)(183, 687, 292, 796, 256, 760)(186, 690, 295, 799, 189, 693)(190, 694, 262, 766, 301, 805)(192, 696, 304, 808, 302, 806)(193, 697, 306, 810, 194, 698)(195, 699, 303, 807, 310, 814)(196, 700, 311, 815, 313, 817)(198, 702, 315, 819, 201, 705)(202, 706, 213, 717, 321, 825)(203, 707, 206, 710, 323, 827)(204, 708, 324, 828, 233, 737)(209, 713, 328, 832, 329, 833)(215, 719, 308, 812, 333, 837)(216, 720, 335, 839, 337, 841)(219, 723, 340, 844, 339, 843)(220, 724, 312, 816, 338, 842)(224, 728, 347, 851, 345, 849)(226, 730, 350, 854, 348, 852)(227, 731, 349, 853, 264, 768)(228, 732, 353, 857, 354, 858)(231, 735, 357, 861, 269, 773)(234, 738, 360, 864, 237, 741)(238, 742, 249, 753, 365, 869)(239, 743, 242, 746, 367, 871)(240, 744, 368, 872, 314, 818)(245, 749, 372, 876, 286, 790)(252, 756, 377, 881, 341, 845)(255, 759, 380, 884, 379, 883)(258, 762, 383, 887, 352, 856)(265, 769, 389, 893, 381, 885)(268, 772, 392, 896, 391, 895)(270, 774, 393, 897, 395, 899)(273, 777, 399, 903, 397, 901)(274, 778, 276, 780, 362, 866)(275, 779, 401, 905, 396, 900)(277, 781, 280, 784, 403, 907)(278, 782, 404, 908, 290, 794)(285, 789, 408, 912, 351, 855)(288, 792, 410, 914, 307, 811)(291, 795, 412, 916, 293, 797)(294, 798, 398, 902, 414, 918)(296, 800, 417, 921, 415, 919)(297, 801, 325, 829, 298, 802)(299, 803, 416, 920, 420, 924)(300, 804, 421, 925, 331, 835)(305, 809, 342, 846, 424, 928)(309, 813, 394, 898, 425, 929)(316, 820, 430, 934, 428, 932)(317, 821, 369, 873, 318, 822)(319, 823, 429, 933, 431, 935)(320, 824, 432, 936, 374, 878)(322, 826, 433, 937, 411, 915)(326, 830, 437, 941, 434, 938)(327, 831, 438, 942, 330, 834)(332, 836, 334, 838, 442, 946)(336, 840, 390, 894, 378, 882)(343, 847, 346, 850, 445, 949)(344, 848, 446, 950, 355, 859)(356, 860, 450, 954, 358, 862)(359, 863, 435, 939, 452, 956)(361, 865, 455, 959, 453, 957)(363, 867, 454, 958, 456, 960)(364, 868, 457, 961, 385, 889)(366, 870, 458, 962, 449, 953)(370, 874, 462, 966, 459, 963)(371, 875, 463, 967, 373, 877)(375, 879, 376, 880, 466, 970)(382, 886, 468, 972, 384, 888)(386, 890, 388, 892, 471, 975)(387, 891, 460, 964, 422, 926)(400, 904, 448, 952, 440, 944)(402, 906, 444, 948, 480, 984)(405, 909, 482, 986, 481, 985)(406, 910, 407, 911, 461, 965)(409, 913, 436, 940, 418, 922)(413, 917, 484, 988, 467, 971)(419, 923, 479, 983, 423, 927)(426, 930, 489, 993, 427, 931)(439, 943, 464, 968, 469, 973)(441, 945, 488, 992, 495, 999)(443, 947, 490, 994, 496, 1000)(447, 951, 491, 995, 497, 1001)(451, 955, 499, 1003, 472, 976)(465, 969, 493, 997, 504, 1008)(470, 974, 503, 1007, 475, 979)(473, 977, 492, 996, 474, 978)(476, 980, 478, 982, 501, 1005)(477, 981, 500, 1004, 486, 990)(483, 987, 494, 998, 502, 1006)(485, 989, 498, 1002, 487, 991)(1009, 1513)(1010, 1514)(1011, 1515)(1012, 1516)(1013, 1517)(1014, 1518)(1015, 1519)(1016, 1520)(1017, 1521)(1018, 1522)(1019, 1523)(1020, 1524)(1021, 1525)(1022, 1526)(1023, 1527)(1024, 1528)(1025, 1529)(1026, 1530)(1027, 1531)(1028, 1532)(1029, 1533)(1030, 1534)(1031, 1535)(1032, 1536)(1033, 1537)(1034, 1538)(1035, 1539)(1036, 1540)(1037, 1541)(1038, 1542)(1039, 1543)(1040, 1544)(1041, 1545)(1042, 1546)(1043, 1547)(1044, 1548)(1045, 1549)(1046, 1550)(1047, 1551)(1048, 1552)(1049, 1553)(1050, 1554)(1051, 1555)(1052, 1556)(1053, 1557)(1054, 1558)(1055, 1559)(1056, 1560)(1057, 1561)(1058, 1562)(1059, 1563)(1060, 1564)(1061, 1565)(1062, 1566)(1063, 1567)(1064, 1568)(1065, 1569)(1066, 1570)(1067, 1571)(1068, 1572)(1069, 1573)(1070, 1574)(1071, 1575)(1072, 1576)(1073, 1577)(1074, 1578)(1075, 1579)(1076, 1580)(1077, 1581)(1078, 1582)(1079, 1583)(1080, 1584)(1081, 1585)(1082, 1586)(1083, 1587)(1084, 1588)(1085, 1589)(1086, 1590)(1087, 1591)(1088, 1592)(1089, 1593)(1090, 1594)(1091, 1595)(1092, 1596)(1093, 1597)(1094, 1598)(1095, 1599)(1096, 1600)(1097, 1601)(1098, 1602)(1099, 1603)(1100, 1604)(1101, 1605)(1102, 1606)(1103, 1607)(1104, 1608)(1105, 1609)(1106, 1610)(1107, 1611)(1108, 1612)(1109, 1613)(1110, 1614)(1111, 1615)(1112, 1616)(1113, 1617)(1114, 1618)(1115, 1619)(1116, 1620)(1117, 1621)(1118, 1622)(1119, 1623)(1120, 1624)(1121, 1625)(1122, 1626)(1123, 1627)(1124, 1628)(1125, 1629)(1126, 1630)(1127, 1631)(1128, 1632)(1129, 1633)(1130, 1634)(1131, 1635)(1132, 1636)(1133, 1637)(1134, 1638)(1135, 1639)(1136, 1640)(1137, 1641)(1138, 1642)(1139, 1643)(1140, 1644)(1141, 1645)(1142, 1646)(1143, 1647)(1144, 1648)(1145, 1649)(1146, 1650)(1147, 1651)(1148, 1652)(1149, 1653)(1150, 1654)(1151, 1655)(1152, 1656)(1153, 1657)(1154, 1658)(1155, 1659)(1156, 1660)(1157, 1661)(1158, 1662)(1159, 1663)(1160, 1664)(1161, 1665)(1162, 1666)(1163, 1667)(1164, 1668)(1165, 1669)(1166, 1670)(1167, 1671)(1168, 1672)(1169, 1673)(1170, 1674)(1171, 1675)(1172, 1676)(1173, 1677)(1174, 1678)(1175, 1679)(1176, 1680)(1177, 1681)(1178, 1682)(1179, 1683)(1180, 1684)(1181, 1685)(1182, 1686)(1183, 1687)(1184, 1688)(1185, 1689)(1186, 1690)(1187, 1691)(1188, 1692)(1189, 1693)(1190, 1694)(1191, 1695)(1192, 1696)(1193, 1697)(1194, 1698)(1195, 1699)(1196, 1700)(1197, 1701)(1198, 1702)(1199, 1703)(1200, 1704)(1201, 1705)(1202, 1706)(1203, 1707)(1204, 1708)(1205, 1709)(1206, 1710)(1207, 1711)(1208, 1712)(1209, 1713)(1210, 1714)(1211, 1715)(1212, 1716)(1213, 1717)(1214, 1718)(1215, 1719)(1216, 1720)(1217, 1721)(1218, 1722)(1219, 1723)(1220, 1724)(1221, 1725)(1222, 1726)(1223, 1727)(1224, 1728)(1225, 1729)(1226, 1730)(1227, 1731)(1228, 1732)(1229, 1733)(1230, 1734)(1231, 1735)(1232, 1736)(1233, 1737)(1234, 1738)(1235, 1739)(1236, 1740)(1237, 1741)(1238, 1742)(1239, 1743)(1240, 1744)(1241, 1745)(1242, 1746)(1243, 1747)(1244, 1748)(1245, 1749)(1246, 1750)(1247, 1751)(1248, 1752)(1249, 1753)(1250, 1754)(1251, 1755)(1252, 1756)(1253, 1757)(1254, 1758)(1255, 1759)(1256, 1760)(1257, 1761)(1258, 1762)(1259, 1763)(1260, 1764)(1261, 1765)(1262, 1766)(1263, 1767)(1264, 1768)(1265, 1769)(1266, 1770)(1267, 1771)(1268, 1772)(1269, 1773)(1270, 1774)(1271, 1775)(1272, 1776)(1273, 1777)(1274, 1778)(1275, 1779)(1276, 1780)(1277, 1781)(1278, 1782)(1279, 1783)(1280, 1784)(1281, 1785)(1282, 1786)(1283, 1787)(1284, 1788)(1285, 1789)(1286, 1790)(1287, 1791)(1288, 1792)(1289, 1793)(1290, 1794)(1291, 1795)(1292, 1796)(1293, 1797)(1294, 1798)(1295, 1799)(1296, 1800)(1297, 1801)(1298, 1802)(1299, 1803)(1300, 1804)(1301, 1805)(1302, 1806)(1303, 1807)(1304, 1808)(1305, 1809)(1306, 1810)(1307, 1811)(1308, 1812)(1309, 1813)(1310, 1814)(1311, 1815)(1312, 1816)(1313, 1817)(1314, 1818)(1315, 1819)(1316, 1820)(1317, 1821)(1318, 1822)(1319, 1823)(1320, 1824)(1321, 1825)(1322, 1826)(1323, 1827)(1324, 1828)(1325, 1829)(1326, 1830)(1327, 1831)(1328, 1832)(1329, 1833)(1330, 1834)(1331, 1835)(1332, 1836)(1333, 1837)(1334, 1838)(1335, 1839)(1336, 1840)(1337, 1841)(1338, 1842)(1339, 1843)(1340, 1844)(1341, 1845)(1342, 1846)(1343, 1847)(1344, 1848)(1345, 1849)(1346, 1850)(1347, 1851)(1348, 1852)(1349, 1853)(1350, 1854)(1351, 1855)(1352, 1856)(1353, 1857)(1354, 1858)(1355, 1859)(1356, 1860)(1357, 1861)(1358, 1862)(1359, 1863)(1360, 1864)(1361, 1865)(1362, 1866)(1363, 1867)(1364, 1868)(1365, 1869)(1366, 1870)(1367, 1871)(1368, 1872)(1369, 1873)(1370, 1874)(1371, 1875)(1372, 1876)(1373, 1877)(1374, 1878)(1375, 1879)(1376, 1880)(1377, 1881)(1378, 1882)(1379, 1883)(1380, 1884)(1381, 1885)(1382, 1886)(1383, 1887)(1384, 1888)(1385, 1889)(1386, 1890)(1387, 1891)(1388, 1892)(1389, 1893)(1390, 1894)(1391, 1895)(1392, 1896)(1393, 1897)(1394, 1898)(1395, 1899)(1396, 1900)(1397, 1901)(1398, 1902)(1399, 1903)(1400, 1904)(1401, 1905)(1402, 1906)(1403, 1907)(1404, 1908)(1405, 1909)(1406, 1910)(1407, 1911)(1408, 1912)(1409, 1913)(1410, 1914)(1411, 1915)(1412, 1916)(1413, 1917)(1414, 1918)(1415, 1919)(1416, 1920)(1417, 1921)(1418, 1922)(1419, 1923)(1420, 1924)(1421, 1925)(1422, 1926)(1423, 1927)(1424, 1928)(1425, 1929)(1426, 1930)(1427, 1931)(1428, 1932)(1429, 1933)(1430, 1934)(1431, 1935)(1432, 1936)(1433, 1937)(1434, 1938)(1435, 1939)(1436, 1940)(1437, 1941)(1438, 1942)(1439, 1943)(1440, 1944)(1441, 1945)(1442, 1946)(1443, 1947)(1444, 1948)(1445, 1949)(1446, 1950)(1447, 1951)(1448, 1952)(1449, 1953)(1450, 1954)(1451, 1955)(1452, 1956)(1453, 1957)(1454, 1958)(1455, 1959)(1456, 1960)(1457, 1961)(1458, 1962)(1459, 1963)(1460, 1964)(1461, 1965)(1462, 1966)(1463, 1967)(1464, 1968)(1465, 1969)(1466, 1970)(1467, 1971)(1468, 1972)(1469, 1973)(1470, 1974)(1471, 1975)(1472, 1976)(1473, 1977)(1474, 1978)(1475, 1979)(1476, 1980)(1477, 1981)(1478, 1982)(1479, 1983)(1480, 1984)(1481, 1985)(1482, 1986)(1483, 1987)(1484, 1988)(1485, 1989)(1486, 1990)(1487, 1991)(1488, 1992)(1489, 1993)(1490, 1994)(1491, 1995)(1492, 1996)(1493, 1997)(1494, 1998)(1495, 1999)(1496, 2000)(1497, 2001)(1498, 2002)(1499, 2003)(1500, 2004)(1501, 2005)(1502, 2006)(1503, 2007)(1504, 2008)(1505, 2009)(1506, 2010)(1507, 2011)(1508, 2012)(1509, 2013)(1510, 2014)(1511, 2015)(1512, 2016) L = (1, 1011)(2, 1014)(3, 1017)(4, 1019)(5, 1009)(6, 1022)(7, 1010)(8, 1012)(9, 1027)(10, 1029)(11, 1030)(12, 1031)(13, 1013)(14, 1035)(15, 1037)(16, 1015)(17, 1016)(18, 1018)(19, 1045)(20, 1047)(21, 1048)(22, 1049)(23, 1051)(24, 1020)(25, 1053)(26, 1021)(27, 1058)(28, 1060)(29, 1061)(30, 1023)(31, 1063)(32, 1024)(33, 1067)(34, 1025)(35, 1026)(36, 1028)(37, 1056)(38, 1076)(39, 1077)(40, 1078)(41, 1081)(42, 1083)(43, 1084)(44, 1032)(45, 1088)(46, 1033)(47, 1090)(48, 1034)(49, 1036)(50, 1066)(51, 1096)(52, 1097)(53, 1098)(54, 1038)(55, 1102)(56, 1039)(57, 1104)(58, 1040)(59, 1107)(60, 1041)(61, 1109)(62, 1042)(63, 1112)(64, 1043)(65, 1044)(66, 1046)(67, 1119)(68, 1120)(69, 1121)(70, 1124)(71, 1126)(72, 1050)(73, 1070)(74, 1130)(75, 1131)(76, 1133)(77, 1135)(78, 1136)(79, 1052)(80, 1140)(81, 1054)(82, 1144)(83, 1055)(84, 1075)(85, 1057)(86, 1059)(87, 1150)(88, 1151)(89, 1152)(90, 1155)(91, 1157)(92, 1158)(93, 1062)(94, 1162)(95, 1064)(96, 1166)(97, 1065)(98, 1095)(99, 1169)(100, 1068)(101, 1173)(102, 1069)(103, 1129)(104, 1176)(105, 1071)(106, 1178)(107, 1072)(108, 1181)(109, 1073)(110, 1074)(111, 1187)(112, 1188)(113, 1191)(114, 1193)(115, 1079)(116, 1115)(117, 1197)(118, 1198)(119, 1080)(120, 1082)(121, 1202)(122, 1203)(123, 1204)(124, 1085)(125, 1139)(126, 1209)(127, 1210)(128, 1211)(129, 1086)(130, 1213)(131, 1087)(132, 1217)(133, 1219)(134, 1220)(135, 1089)(136, 1224)(137, 1091)(138, 1092)(139, 1229)(140, 1093)(141, 1094)(142, 1235)(143, 1236)(144, 1239)(145, 1241)(146, 1099)(147, 1161)(148, 1245)(149, 1246)(150, 1247)(151, 1100)(152, 1249)(153, 1101)(154, 1253)(155, 1255)(156, 1256)(157, 1103)(158, 1260)(159, 1105)(160, 1106)(161, 1266)(162, 1268)(163, 1269)(164, 1108)(165, 1273)(166, 1110)(167, 1111)(168, 1278)(169, 1113)(170, 1282)(171, 1114)(172, 1196)(173, 1285)(174, 1116)(175, 1287)(176, 1117)(177, 1290)(178, 1118)(179, 1294)(180, 1296)(181, 1298)(182, 1122)(183, 1184)(184, 1301)(185, 1302)(186, 1123)(187, 1125)(188, 1306)(189, 1307)(190, 1308)(191, 1310)(192, 1127)(193, 1128)(194, 1316)(195, 1317)(196, 1320)(197, 1322)(198, 1132)(199, 1134)(200, 1326)(201, 1327)(202, 1328)(203, 1330)(204, 1137)(205, 1333)(206, 1138)(207, 1208)(208, 1141)(209, 1223)(210, 1338)(211, 1339)(212, 1340)(213, 1142)(214, 1341)(215, 1143)(216, 1344)(217, 1346)(218, 1347)(219, 1145)(220, 1146)(221, 1351)(222, 1147)(223, 1353)(224, 1148)(225, 1356)(226, 1149)(227, 1360)(228, 1292)(229, 1363)(230, 1153)(231, 1232)(232, 1366)(233, 1367)(234, 1154)(235, 1156)(236, 1284)(237, 1371)(238, 1372)(239, 1374)(240, 1159)(241, 1377)(242, 1160)(243, 1244)(244, 1163)(245, 1259)(246, 1381)(247, 1382)(248, 1383)(249, 1164)(250, 1291)(251, 1165)(252, 1386)(253, 1300)(254, 1387)(255, 1167)(256, 1168)(257, 1170)(258, 1272)(259, 1392)(260, 1393)(261, 1394)(262, 1171)(263, 1357)(264, 1172)(265, 1398)(266, 1365)(267, 1399)(268, 1174)(269, 1175)(270, 1402)(271, 1404)(272, 1405)(273, 1177)(274, 1408)(275, 1179)(276, 1180)(277, 1410)(278, 1182)(279, 1414)(280, 1183)(281, 1264)(282, 1362)(283, 1185)(284, 1359)(285, 1186)(286, 1417)(287, 1189)(288, 1293)(289, 1419)(290, 1212)(291, 1190)(292, 1192)(293, 1421)(294, 1221)(295, 1423)(296, 1194)(297, 1195)(298, 1215)(299, 1427)(300, 1226)(301, 1430)(302, 1431)(303, 1199)(304, 1432)(305, 1200)(306, 1418)(307, 1201)(308, 1337)(309, 1358)(310, 1281)(311, 1205)(312, 1313)(313, 1435)(314, 1395)(315, 1436)(316, 1206)(317, 1207)(318, 1251)(319, 1288)(320, 1262)(321, 1422)(322, 1295)(323, 1442)(324, 1412)(325, 1444)(326, 1214)(327, 1216)(328, 1218)(329, 1448)(330, 1283)(331, 1449)(332, 1299)(333, 1314)(334, 1222)(335, 1225)(336, 1349)(337, 1276)(338, 1321)(339, 1304)(340, 1385)(341, 1227)(342, 1228)(343, 1452)(344, 1230)(345, 1456)(346, 1231)(347, 1277)(348, 1433)(349, 1233)(350, 1416)(351, 1234)(352, 1415)(353, 1237)(354, 1457)(355, 1248)(356, 1238)(357, 1240)(358, 1459)(359, 1257)(360, 1461)(361, 1242)(362, 1243)(363, 1354)(364, 1275)(365, 1460)(366, 1361)(367, 1467)(368, 1454)(369, 1469)(370, 1250)(371, 1252)(372, 1254)(373, 1334)(374, 1473)(375, 1364)(376, 1258)(377, 1261)(378, 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1932)(925, 1933)(926, 1934)(927, 1935)(928, 1936)(929, 1937)(930, 1938)(931, 1939)(932, 1940)(933, 1941)(934, 1942)(935, 1943)(936, 1944)(937, 1945)(938, 1946)(939, 1947)(940, 1948)(941, 1949)(942, 1950)(943, 1951)(944, 1952)(945, 1953)(946, 1954)(947, 1955)(948, 1956)(949, 1957)(950, 1958)(951, 1959)(952, 1960)(953, 1961)(954, 1962)(955, 1963)(956, 1964)(957, 1965)(958, 1966)(959, 1967)(960, 1968)(961, 1969)(962, 1970)(963, 1971)(964, 1972)(965, 1973)(966, 1974)(967, 1975)(968, 1976)(969, 1977)(970, 1978)(971, 1979)(972, 1980)(973, 1981)(974, 1982)(975, 1983)(976, 1984)(977, 1985)(978, 1986)(979, 1987)(980, 1988)(981, 1989)(982, 1990)(983, 1991)(984, 1992)(985, 1993)(986, 1994)(987, 1995)(988, 1996)(989, 1997)(990, 1998)(991, 1999)(992, 2000)(993, 2001)(994, 2002)(995, 2003)(996, 2004)(997, 2005)(998, 2006)(999, 2007)(1000, 2008)(1001, 2009)(1002, 2010)(1003, 2011)(1004, 2012)(1005, 2013)(1006, 2014)(1007, 2015)(1008, 2016) local type(s) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E15.1407 Graph:: simple bipartite v = 672 e = 1008 f = 308 degree seq :: [ 2^504, 6^168 ] ## Checksum: 1408 records. ## Written on: Sat Oct 19 20:14:15 CEST 2019