## Begin on: Sat Oct 19 20:39:02 CEST 2019 ENUMERATION No. of records: 1142 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 24 (20 non-degenerate) 2 [ E3b] : 116 (92 non-degenerate) 2* [E3*b] : 116 (92 non-degenerate) 2ex [E3*c] : 1 (1 non-degenerate) 2*ex [ E3c] : 1 (1 non-degenerate) 2P [ E2] : 30 (27 non-degenerate) 2Pex [ E1a] : 2 (2 non-degenerate) 3 [ E5a] : 714 (446 non-degenerate) 4 [ E4] : 55 (24 non-degenerate) 4* [ E4*] : 55 (24 non-degenerate) 4P [ E6] : 14 (2 non-degenerate) 5 [ E3a] : 6 (4 non-degenerate) 5* [E3*a] : 6 (4 non-degenerate) 5P [ E5b] : 2 (1 non-degenerate) E20.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ B, A, B, A, B, A, A, B, A, B, A, B, A, A, B, A, B, A, B, B, A, B, A, B, A, B, B, A, B, A, B, A, A, B, A, B, A, B, A, B, S^2, S^-1 * A * S * B, S^-1 * B * S * A, S^-1 * Z * S * Z, Z^20, (Z^-1 * A * B^-1 * A^-1 * B)^20 ] Map:: R = (1, 22, 42, 62, 2, 24, 44, 64, 4, 26, 46, 66, 6, 28, 48, 68, 8, 30, 50, 70, 10, 32, 52, 72, 12, 34, 54, 74, 14, 36, 56, 76, 16, 38, 58, 78, 18, 40, 60, 80, 20, 39, 59, 79, 19, 37, 57, 77, 17, 35, 55, 75, 15, 33, 53, 73, 13, 31, 51, 71, 11, 29, 49, 69, 9, 27, 47, 67, 7, 25, 45, 65, 5, 23, 43, 63, 3, 21, 41, 61) 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) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ A^2, S^2, B^2, B * A, S * B * S * A, Z^-1 * A * Z * A, (S * Z)^2, Z^5 * B * Z^5 ] Map:: R = (1, 22, 42, 62, 2, 25, 45, 65, 5, 29, 49, 69, 9, 33, 53, 73, 13, 37, 57, 77, 17, 39, 59, 79, 19, 35, 55, 75, 15, 31, 51, 71, 11, 27, 47, 67, 7, 23, 43, 63, 3, 26, 46, 66, 6, 30, 50, 70, 10, 34, 54, 74, 14, 38, 58, 78, 18, 40, 60, 80, 20, 36, 56, 76, 16, 32, 52, 72, 12, 28, 48, 68, 8, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 46)(3, 41)(4, 47)(5, 50)(6, 42)(7, 44)(8, 51)(9, 54)(10, 45)(11, 48)(12, 55)(13, 58)(14, 49)(15, 52)(16, 59)(17, 60)(18, 53)(19, 56)(20, 57)(21, 63)(22, 66)(23, 61)(24, 67)(25, 70)(26, 62)(27, 64)(28, 71)(29, 74)(30, 65)(31, 68)(32, 75)(33, 78)(34, 69)(35, 72)(36, 79)(37, 80)(38, 73)(39, 76)(40, 77) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, B * A^-1, A^4, B^4, (A^-1 * B^-1)^2, (S * Z)^2, S * B * S * A, (A^-1, Z^-1), A * Z^-5 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63, 3, 27, 47, 67, 7, 34, 54, 74, 14, 39, 59, 79, 19, 37, 57, 77, 17, 29, 49, 69, 9, 36, 56, 76, 16, 40, 60, 80, 20, 38, 58, 78, 18, 32, 52, 72, 12, 25, 45, 65, 5, 28, 48, 68, 8, 35, 55, 75, 15, 31, 51, 71, 11, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 56)(8, 42)(9, 45)(10, 57)(11, 53)(12, 44)(13, 59)(14, 60)(15, 46)(16, 48)(17, 52)(18, 51)(19, 58)(20, 55)(21, 65)(22, 68)(23, 61)(24, 72)(25, 69)(26, 75)(27, 62)(28, 76)(29, 63)(30, 64)(31, 78)(32, 77)(33, 71)(34, 66)(35, 80)(36, 67)(37, 70)(38, 79)(39, 73)(40, 74) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, B * A^-1, A^4, S * A * S * B, (S * Z)^2, (A^-1, Z^-1), A^-1 * Z^-5, A * Z^-1 * A * Z^-1 * A * Z^-3 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 33, 53, 73, 13, 32, 52, 72, 12, 25, 45, 65, 5, 28, 48, 68, 8, 35, 55, 75, 15, 39, 59, 79, 19, 37, 57, 77, 17, 29, 49, 69, 9, 36, 56, 76, 16, 40, 60, 80, 20, 38, 58, 78, 18, 30, 50, 70, 10, 23, 43, 63, 3, 27, 47, 67, 7, 34, 54, 74, 14, 31, 51, 71, 11, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 56)(8, 42)(9, 45)(10, 57)(11, 58)(12, 44)(13, 51)(14, 60)(15, 46)(16, 48)(17, 52)(18, 59)(19, 53)(20, 55)(21, 65)(22, 68)(23, 61)(24, 72)(25, 69)(26, 75)(27, 62)(28, 76)(29, 63)(30, 64)(31, 73)(32, 77)(33, 79)(34, 66)(35, 80)(36, 67)(37, 70)(38, 71)(39, 78)(40, 74) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, B * A^-1, B^-1 * A, (Z, A^-1), S * A * S * B, (S * Z)^2, A^5, Z^2 * B^-1 * Z^2, B^5, A^-1 * B^-1 * A^-2 * B^-1 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 30, 50, 70, 10, 23, 43, 63, 3, 27, 47, 67, 7, 34, 54, 74, 14, 37, 57, 77, 17, 29, 49, 69, 9, 35, 55, 75, 15, 40, 60, 80, 20, 39, 59, 79, 19, 33, 53, 73, 13, 36, 56, 76, 16, 38, 58, 78, 18, 32, 52, 72, 12, 25, 45, 65, 5, 28, 48, 68, 8, 31, 51, 71, 11, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 55)(8, 42)(9, 53)(10, 57)(11, 46)(12, 44)(13, 45)(14, 60)(15, 56)(16, 48)(17, 59)(18, 51)(19, 52)(20, 58)(21, 65)(22, 68)(23, 61)(24, 72)(25, 73)(26, 71)(27, 62)(28, 76)(29, 63)(30, 64)(31, 78)(32, 79)(33, 69)(34, 66)(35, 67)(36, 75)(37, 70)(38, 80)(39, 77)(40, 74) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, B * Z^-1 * A^-1 * Z, (A^-1, Z^-1), S * B * S * A, Z^-1 * B * Z * A^-1, (S * Z)^2, A^2 * B * A^2, Z^-1 * B * Z^-1 * A * Z^-2, Z * B * Z^2 * A^2 * Z ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 34, 54, 74, 14, 29, 49, 69, 9, 37, 57, 77, 17, 39, 59, 79, 19, 32, 52, 72, 12, 25, 45, 65, 5, 28, 48, 68, 8, 36, 56, 76, 16, 30, 50, 70, 10, 23, 43, 63, 3, 27, 47, 67, 7, 35, 55, 75, 15, 40, 60, 80, 20, 33, 53, 73, 13, 38, 58, 78, 18, 31, 51, 71, 11, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 55)(7, 57)(8, 42)(9, 53)(10, 54)(11, 56)(12, 44)(13, 45)(14, 60)(15, 59)(16, 46)(17, 58)(18, 48)(19, 51)(20, 52)(21, 65)(22, 68)(23, 61)(24, 72)(25, 73)(26, 76)(27, 62)(28, 78)(29, 63)(30, 64)(31, 79)(32, 80)(33, 69)(34, 70)(35, 66)(36, 71)(37, 67)(38, 77)(39, 75)(40, 74) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A^-2 * B^2, S * B * S * A, (S * Z)^2, (A, Z), A^2 * B * A^2, A^2 * Z^4, A^-1 * Z^2 * B^-1 * Z * A^-1 * Z ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 34, 54, 74, 14, 33, 53, 73, 13, 38, 58, 78, 18, 40, 60, 80, 20, 30, 50, 70, 10, 23, 43, 63, 3, 27, 47, 67, 7, 35, 55, 75, 15, 32, 52, 72, 12, 25, 45, 65, 5, 28, 48, 68, 8, 36, 56, 76, 16, 39, 59, 79, 19, 29, 49, 69, 9, 37, 57, 77, 17, 31, 51, 71, 11, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 55)(7, 57)(8, 42)(9, 53)(10, 59)(11, 60)(12, 44)(13, 45)(14, 52)(15, 51)(16, 46)(17, 58)(18, 48)(19, 54)(20, 56)(21, 65)(22, 68)(23, 61)(24, 72)(25, 73)(26, 76)(27, 62)(28, 78)(29, 63)(30, 64)(31, 75)(32, 74)(33, 69)(34, 79)(35, 66)(36, 80)(37, 67)(38, 77)(39, 70)(40, 71) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, A * B^-1, Z^2 * A^-1, (S * Z)^2, S * B * S * A, A^4 * B * A^5, (B^-1 * Z)^20 ] Map:: R = (1, 22, 42, 62, 2, 23, 43, 63, 3, 26, 46, 66, 6, 27, 47, 67, 7, 30, 50, 70, 10, 31, 51, 71, 11, 34, 54, 74, 14, 35, 55, 75, 15, 38, 58, 78, 18, 39, 59, 79, 19, 40, 60, 80, 20, 37, 57, 77, 17, 36, 56, 76, 16, 33, 53, 73, 13, 32, 52, 72, 12, 29, 49, 69, 9, 28, 48, 68, 8, 25, 45, 65, 5, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 46)(3, 47)(4, 42)(5, 41)(6, 50)(7, 51)(8, 44)(9, 45)(10, 54)(11, 55)(12, 48)(13, 49)(14, 58)(15, 59)(16, 52)(17, 53)(18, 60)(19, 57)(20, 56)(21, 65)(22, 64)(23, 61)(24, 68)(25, 69)(26, 62)(27, 63)(28, 72)(29, 73)(30, 66)(31, 67)(32, 76)(33, 77)(34, 70)(35, 71)(36, 80)(37, 79)(38, 74)(39, 75)(40, 78) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^2 * A, S * A * S * B, (S * Z)^2, A^10, (B * Z)^20 ] Map:: R = (1, 22, 42, 62, 2, 25, 45, 65, 5, 26, 46, 66, 6, 29, 49, 69, 9, 30, 50, 70, 10, 33, 53, 73, 13, 34, 54, 74, 14, 37, 57, 77, 17, 38, 58, 78, 18, 39, 59, 79, 19, 40, 60, 80, 20, 35, 55, 75, 15, 36, 56, 76, 16, 31, 51, 71, 11, 32, 52, 72, 12, 27, 47, 67, 7, 28, 48, 68, 8, 23, 43, 63, 3, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 44)(3, 47)(4, 48)(5, 41)(6, 42)(7, 51)(8, 52)(9, 45)(10, 46)(11, 55)(12, 56)(13, 49)(14, 50)(15, 59)(16, 60)(17, 53)(18, 54)(19, 57)(20, 58)(21, 65)(22, 66)(23, 61)(24, 62)(25, 69)(26, 70)(27, 63)(28, 64)(29, 73)(30, 74)(31, 67)(32, 68)(33, 77)(34, 78)(35, 71)(36, 72)(37, 79)(38, 80)(39, 75)(40, 76) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {20, 20}) Quotient :: toric Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, A^-1 * B, Z * B * Z^-1 * A^-1, Z^-1 * B * Z * A^-1, (S * Z)^2, S * B * S * A, Z * A^-1 * Z * B^-2, Z^-1 * B^-1 * Z^-5 ] Map:: R = (1, 22, 42, 62, 2, 26, 46, 66, 6, 34, 54, 74, 14, 38, 58, 78, 18, 32, 52, 72, 12, 25, 45, 65, 5, 28, 48, 68, 8, 29, 49, 69, 9, 36, 56, 76, 16, 40, 60, 80, 20, 39, 59, 79, 19, 33, 53, 73, 13, 30, 50, 70, 10, 23, 43, 63, 3, 27, 47, 67, 7, 35, 55, 75, 15, 37, 57, 77, 17, 31, 51, 71, 11, 24, 44, 64, 4, 21, 41, 61) L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 55)(7, 56)(8, 42)(9, 46)(10, 48)(11, 53)(12, 44)(13, 45)(14, 57)(15, 60)(16, 54)(17, 59)(18, 51)(19, 52)(20, 58)(21, 65)(22, 68)(23, 61)(24, 72)(25, 73)(26, 69)(27, 62)(28, 70)(29, 63)(30, 64)(31, 78)(32, 79)(33, 71)(34, 76)(35, 66)(36, 67)(37, 74)(38, 80)(39, 77)(40, 75) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.11 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C38 (small group id <38, 2>) Aut = D76 (small group id <76, 3>) |r| :: 2 Presentation :: [ Z^2, S^2, B * A^-1, (S * Z)^2, S * A * S * B, A * Z * A^-1 * Z, A^19 ] Map:: R = (1, 40, 78, 116, 2, 39, 77, 115)(3, 43, 81, 119, 5, 41, 79, 117)(4, 44, 82, 120, 6, 42, 80, 118)(7, 47, 85, 123, 9, 45, 83, 121)(8, 48, 86, 124, 10, 46, 84, 122)(11, 51, 89, 127, 13, 49, 87, 125)(12, 52, 90, 128, 14, 50, 88, 126)(15, 55, 93, 131, 17, 53, 91, 129)(16, 56, 94, 132, 18, 54, 92, 130)(19, 59, 97, 135, 21, 57, 95, 133)(20, 60, 98, 136, 22, 58, 96, 134)(23, 63, 101, 139, 25, 61, 99, 137)(24, 64, 102, 140, 26, 62, 100, 138)(27, 67, 105, 143, 29, 65, 103, 141)(28, 68, 106, 144, 30, 66, 104, 142)(31, 71, 109, 147, 33, 69, 107, 145)(32, 72, 110, 148, 34, 70, 108, 146)(35, 75, 113, 151, 37, 73, 111, 149)(36, 76, 114, 152, 38, 74, 112, 150) L = (1, 79)(2, 81)(3, 83)(4, 77)(5, 85)(6, 78)(7, 87)(8, 80)(9, 89)(10, 82)(11, 91)(12, 84)(13, 93)(14, 86)(15, 95)(16, 88)(17, 97)(18, 90)(19, 99)(20, 92)(21, 101)(22, 94)(23, 103)(24, 96)(25, 105)(26, 98)(27, 107)(28, 100)(29, 109)(30, 102)(31, 111)(32, 104)(33, 113)(34, 106)(35, 112)(36, 108)(37, 114)(38, 110)(39, 118)(40, 120)(41, 115)(42, 122)(43, 116)(44, 124)(45, 117)(46, 126)(47, 119)(48, 128)(49, 121)(50, 130)(51, 123)(52, 132)(53, 125)(54, 134)(55, 127)(56, 136)(57, 129)(58, 138)(59, 131)(60, 140)(61, 133)(62, 142)(63, 135)(64, 144)(65, 137)(66, 146)(67, 139)(68, 148)(69, 141)(70, 150)(71, 143)(72, 152)(73, 145)(74, 149)(75, 147)(76, 151) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 19 e = 76 f = 19 degree seq :: [ 8^19 ] E20.12 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D38 (small group id <38, 1>) Aut = D76 (small group id <76, 3>) |r| :: 2 Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^19 ] Map:: R = (1, 40, 78, 116, 2, 39, 77, 115)(3, 43, 81, 119, 5, 41, 79, 117)(4, 44, 82, 120, 6, 42, 80, 118)(7, 47, 85, 123, 9, 45, 83, 121)(8, 48, 86, 124, 10, 46, 84, 122)(11, 51, 89, 127, 13, 49, 87, 125)(12, 52, 90, 128, 14, 50, 88, 126)(15, 63, 101, 139, 25, 53, 91, 129)(16, 65, 103, 141, 27, 54, 92, 130)(17, 68, 106, 144, 30, 55, 93, 131)(18, 70, 108, 146, 32, 56, 94, 132)(19, 72, 110, 148, 34, 57, 95, 133)(20, 66, 104, 142, 28, 58, 96, 134)(21, 75, 113, 151, 37, 59, 97, 135)(22, 76, 114, 152, 38, 60, 98, 136)(23, 73, 111, 149, 35, 61, 99, 137)(24, 71, 109, 147, 33, 62, 100, 138)(26, 67, 105, 143, 29, 64, 102, 140)(31, 74, 112, 150, 36, 69, 107, 145) L = (1, 79)(2, 80)(3, 77)(4, 78)(5, 83)(6, 84)(7, 81)(8, 82)(9, 87)(10, 88)(11, 85)(12, 86)(13, 91)(14, 96)(15, 89)(16, 104)(17, 101)(18, 106)(19, 103)(20, 90)(21, 108)(22, 110)(23, 113)(24, 114)(25, 93)(26, 111)(27, 95)(28, 92)(29, 107)(30, 94)(31, 105)(32, 97)(33, 112)(34, 98)(35, 102)(36, 109)(37, 99)(38, 100)(39, 117)(40, 118)(41, 115)(42, 116)(43, 121)(44, 122)(45, 119)(46, 120)(47, 125)(48, 126)(49, 123)(50, 124)(51, 129)(52, 134)(53, 127)(54, 142)(55, 139)(56, 144)(57, 141)(58, 128)(59, 146)(60, 148)(61, 151)(62, 152)(63, 131)(64, 149)(65, 133)(66, 130)(67, 145)(68, 132)(69, 143)(70, 135)(71, 150)(72, 136)(73, 140)(74, 147)(75, 137)(76, 138) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 19 e = 76 f = 19 degree seq :: [ 8^19 ] E20.13 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D38 (small group id <38, 1>) Aut = D76 (small group id <76, 3>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * A * S * B, (S * Z)^2, A * Z * B^-1 * Z, A^10 * B^-9 ] Map:: non-degenerate R = (1, 40, 78, 116, 2, 39, 77, 115)(3, 44, 82, 120, 6, 41, 79, 117)(4, 43, 81, 119, 5, 42, 80, 118)(7, 48, 86, 124, 10, 45, 83, 121)(8, 47, 85, 123, 9, 46, 84, 122)(11, 52, 90, 128, 14, 49, 87, 125)(12, 51, 89, 127, 13, 50, 88, 126)(15, 56, 94, 132, 18, 53, 91, 129)(16, 55, 93, 131, 17, 54, 92, 130)(19, 60, 98, 136, 22, 57, 95, 133)(20, 59, 97, 135, 21, 58, 96, 134)(23, 64, 102, 140, 26, 61, 99, 137)(24, 63, 101, 139, 25, 62, 100, 138)(27, 68, 106, 144, 30, 65, 103, 141)(28, 67, 105, 143, 29, 66, 104, 142)(31, 72, 110, 148, 34, 69, 107, 145)(32, 71, 109, 147, 33, 70, 108, 146)(35, 76, 114, 152, 38, 73, 111, 149)(36, 75, 113, 151, 37, 74, 112, 150) L = (1, 79)(2, 81)(3, 83)(4, 77)(5, 85)(6, 78)(7, 87)(8, 80)(9, 89)(10, 82)(11, 91)(12, 84)(13, 93)(14, 86)(15, 95)(16, 88)(17, 97)(18, 90)(19, 99)(20, 92)(21, 101)(22, 94)(23, 103)(24, 96)(25, 105)(26, 98)(27, 107)(28, 100)(29, 109)(30, 102)(31, 111)(32, 104)(33, 113)(34, 106)(35, 112)(36, 108)(37, 114)(38, 110)(39, 117)(40, 119)(41, 121)(42, 115)(43, 123)(44, 116)(45, 125)(46, 118)(47, 127)(48, 120)(49, 129)(50, 122)(51, 131)(52, 124)(53, 133)(54, 126)(55, 135)(56, 128)(57, 137)(58, 130)(59, 139)(60, 132)(61, 141)(62, 134)(63, 143)(64, 136)(65, 145)(66, 138)(67, 147)(68, 140)(69, 149)(70, 142)(71, 151)(72, 144)(73, 150)(74, 146)(75, 152)(76, 148) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 19 e = 76 f = 19 degree seq :: [ 8^19 ] E20.14 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C38 (small group id <38, 2>) Aut = C38 x C2 (small group id <76, 4>) |r| :: 2 Presentation :: [ Z^2, S^2, B^-1 * A^-1, (S * Z)^2, S * B * S * A, A * Z * A^-1 * Z, B * Z * B^-1 * Z, A^10 * B^-9 ] Map:: non-degenerate R = (1, 40, 78, 116, 2, 39, 77, 115)(3, 43, 81, 119, 5, 41, 79, 117)(4, 44, 82, 120, 6, 42, 80, 118)(7, 47, 85, 123, 9, 45, 83, 121)(8, 48, 86, 124, 10, 46, 84, 122)(11, 51, 89, 127, 13, 49, 87, 125)(12, 52, 90, 128, 14, 50, 88, 126)(15, 55, 93, 131, 17, 53, 91, 129)(16, 56, 94, 132, 18, 54, 92, 130)(19, 59, 97, 135, 21, 57, 95, 133)(20, 60, 98, 136, 22, 58, 96, 134)(23, 63, 101, 139, 25, 61, 99, 137)(24, 64, 102, 140, 26, 62, 100, 138)(27, 67, 105, 143, 29, 65, 103, 141)(28, 68, 106, 144, 30, 66, 104, 142)(31, 71, 109, 147, 33, 69, 107, 145)(32, 72, 110, 148, 34, 70, 108, 146)(35, 75, 113, 151, 37, 73, 111, 149)(36, 76, 114, 152, 38, 74, 112, 150) L = (1, 79)(2, 81)(3, 83)(4, 77)(5, 85)(6, 78)(7, 87)(8, 80)(9, 89)(10, 82)(11, 91)(12, 84)(13, 93)(14, 86)(15, 95)(16, 88)(17, 97)(18, 90)(19, 99)(20, 92)(21, 101)(22, 94)(23, 103)(24, 96)(25, 105)(26, 98)(27, 107)(28, 100)(29, 109)(30, 102)(31, 111)(32, 104)(33, 113)(34, 106)(35, 112)(36, 108)(37, 114)(38, 110)(39, 117)(40, 119)(41, 121)(42, 115)(43, 123)(44, 116)(45, 125)(46, 118)(47, 127)(48, 120)(49, 129)(50, 122)(51, 131)(52, 124)(53, 133)(54, 126)(55, 135)(56, 128)(57, 137)(58, 130)(59, 139)(60, 132)(61, 141)(62, 134)(63, 143)(64, 136)(65, 145)(66, 138)(67, 147)(68, 140)(69, 149)(70, 142)(71, 151)(72, 144)(73, 150)(74, 146)(75, 152)(76, 148) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 19 e = 76 f = 19 degree seq :: [ 8^19 ] E20.15 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^10, (Y3^-1 * Y1^-1)^21, (Y3 * Y2^-1)^21 ] Map:: R = (1, 22, 2, 23, 6, 27, 10, 31, 14, 35, 18, 39, 21, 42, 17, 38, 13, 34, 9, 30, 5, 26, 3, 24, 7, 28, 11, 32, 15, 36, 19, 40, 20, 41, 16, 37, 12, 33, 8, 29, 4, 25)(43, 64, 45, 66, 44, 65, 49, 70, 48, 69, 53, 74, 52, 73, 57, 78, 56, 77, 61, 82, 60, 81, 62, 83, 63, 84, 58, 79, 59, 80, 54, 75, 55, 76, 50, 71, 51, 72, 46, 67, 47, 68) 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) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.16 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-10, (Y3^-1 * Y1^-1)^21, (Y3 * Y2^-1)^21 ] Map:: R = (1, 22, 2, 23, 6, 27, 10, 31, 14, 35, 18, 39, 20, 41, 16, 37, 12, 33, 8, 29, 3, 24, 5, 26, 7, 28, 11, 32, 15, 36, 19, 40, 21, 42, 17, 38, 13, 34, 9, 30, 4, 25)(43, 64, 45, 66, 46, 67, 50, 71, 51, 72, 54, 75, 55, 76, 58, 79, 59, 80, 62, 83, 63, 84, 60, 81, 61, 82, 56, 77, 57, 78, 52, 73, 53, 74, 48, 69, 49, 70, 44, 65, 47, 68) 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) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.17 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y2^-4 * Y1, Y1^5 * Y2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^21, (Y3 * Y2^-1)^21 ] Map:: R = (1, 22, 2, 23, 6, 27, 14, 35, 12, 33, 5, 26, 8, 29, 16, 37, 20, 41, 19, 40, 13, 34, 9, 30, 17, 38, 21, 42, 18, 39, 10, 31, 3, 24, 7, 28, 15, 36, 11, 32, 4, 25)(43, 64, 45, 66, 51, 72, 50, 71, 44, 65, 49, 70, 59, 80, 58, 79, 48, 69, 57, 78, 63, 84, 62, 83, 56, 77, 53, 74, 60, 81, 61, 82, 54, 75, 46, 67, 52, 73, 55, 76, 47, 68) 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) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.18 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2 * Y1 * Y2^3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-4, (Y3 * Y2^-1)^21, (Y3^-1 * Y1^-1)^21 ] Map:: R = (1, 22, 2, 23, 6, 27, 14, 35, 10, 31, 3, 24, 7, 28, 15, 36, 20, 41, 18, 39, 9, 30, 13, 34, 17, 38, 21, 42, 19, 40, 12, 33, 5, 26, 8, 29, 16, 37, 11, 32, 4, 25)(43, 64, 45, 66, 51, 72, 54, 75, 46, 67, 52, 73, 60, 81, 61, 82, 53, 74, 56, 77, 62, 83, 63, 84, 58, 79, 48, 69, 57, 78, 59, 80, 50, 71, 44, 65, 49, 70, 55, 76, 47, 68) 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) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.19 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 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, Y3^3, (Y2^-1, Y3), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y2)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-2, Y1^-1 * Y3^2 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 19, 40, 13, 34, 21, 42, 14, 35, 4, 25, 10, 31, 17, 38, 6, 27, 3, 24, 9, 30, 18, 39, 7, 28, 11, 32, 20, 41, 15, 36, 12, 33, 16, 37, 5, 26)(43, 64, 45, 66, 44, 65, 51, 72, 50, 71, 60, 81, 61, 82, 49, 70, 55, 76, 53, 74, 63, 84, 62, 83, 56, 77, 57, 78, 46, 67, 54, 75, 52, 73, 58, 79, 59, 80, 47, 68, 48, 69) L = (1, 46)(2, 52)(3, 54)(4, 49)(5, 56)(6, 57)(7, 43)(8, 59)(9, 58)(10, 53)(11, 44)(12, 55)(13, 45)(14, 60)(15, 61)(16, 63)(17, 62)(18, 47)(19, 48)(20, 50)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.20 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y3^-1 * Y1^2 * Y2, Y1 * Y3^-1 * Y1 * Y2, Y2 * Y1^2 * Y3^-1, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y3 * Y1^-1 * Y2^3, Y3 * Y1 * Y2 * Y3 * Y1, Y2 * Y3^-1 * Y2 * Y1^-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 * Y3 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 20, 41, 15, 36, 3, 24, 9, 30, 4, 25, 10, 31, 19, 40, 13, 34, 18, 39, 14, 35, 17, 38, 7, 28, 12, 33, 6, 27, 11, 32, 21, 42, 16, 37, 5, 26)(43, 64, 45, 66, 55, 76, 54, 75, 47, 68, 57, 78, 61, 82, 49, 70, 58, 79, 62, 83, 52, 73, 59, 80, 63, 84, 50, 71, 46, 67, 56, 77, 53, 74, 44, 65, 51, 72, 60, 81, 48, 69) L = (1, 46)(2, 52)(3, 56)(4, 49)(5, 51)(6, 50)(7, 43)(8, 61)(9, 59)(10, 54)(11, 62)(12, 44)(13, 53)(14, 58)(15, 60)(16, 45)(17, 47)(18, 63)(19, 48)(20, 55)(21, 57)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.21 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 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 * Y1^-3, (R * Y2)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y3)^2, Y1 * Y3^-3 * Y2^-1, Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, (Y2^-1 * Y3)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 7, 28, 11, 32, 20, 41, 19, 40, 12, 33, 17, 38, 13, 34, 3, 24, 6, 27, 10, 31, 14, 35, 18, 39, 15, 36, 21, 42, 16, 37, 4, 25, 9, 30, 5, 26)(43, 64, 45, 66, 47, 68, 55, 76, 51, 72, 59, 80, 46, 67, 54, 75, 58, 79, 61, 82, 63, 84, 62, 83, 57, 78, 53, 74, 60, 81, 49, 70, 56, 77, 50, 71, 52, 73, 44, 65, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 57)(5, 58)(6, 59)(7, 43)(8, 47)(9, 63)(10, 55)(11, 44)(12, 53)(13, 61)(14, 45)(15, 52)(16, 60)(17, 62)(18, 48)(19, 49)(20, 50)(21, 56)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.22 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.22 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 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 * Y2^-2, Y2^2 * Y3^-1 * Y1, (R * Y3)^2, (Y3, Y1^-1), Y1^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-4, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3 * Y1 * Y2 * Y3 * Y1, Y2 * Y1^5 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 17, 38, 16, 37, 6, 27, 11, 32, 14, 35, 19, 40, 7, 28, 12, 33, 13, 34, 4, 25, 10, 31, 20, 41, 15, 36, 3, 24, 9, 30, 21, 42, 18, 39, 5, 26)(43, 64, 45, 66, 55, 76, 53, 74, 44, 65, 51, 72, 46, 67, 56, 77, 50, 71, 63, 84, 52, 73, 61, 82, 59, 80, 60, 81, 62, 83, 49, 70, 58, 79, 47, 68, 57, 78, 54, 75, 48, 69) L = (1, 46)(2, 52)(3, 56)(4, 59)(5, 55)(6, 51)(7, 43)(8, 62)(9, 61)(10, 58)(11, 63)(12, 44)(13, 50)(14, 60)(15, 53)(16, 45)(17, 57)(18, 54)(19, 47)(20, 48)(21, 49)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.21 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.23 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2^-2, (R * Y3)^2, (Y2, Y1^-1), Y2 * Y3^-1 * Y2 * Y1^-1, (R * Y2)^2, Y3 * Y1 * Y2^-2, (R * Y1)^2, (Y3^-1, Y1^-1), Y2 * Y1^2 * Y3 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y1 * Y2 * Y3^-3, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y1 * Y2^19, (Y1^-1 * Y3^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 21, 42, 14, 35, 3, 24, 9, 30, 20, 41, 16, 37, 4, 25, 10, 31, 19, 40, 7, 28, 12, 33, 13, 34, 18, 39, 6, 27, 11, 32, 15, 36, 17, 38, 5, 26)(43, 64, 45, 66, 52, 73, 60, 81, 47, 68, 56, 77, 46, 67, 55, 76, 59, 80, 63, 84, 58, 79, 54, 75, 57, 78, 50, 71, 62, 83, 49, 70, 53, 74, 44, 65, 51, 72, 61, 82, 48, 69) L = (1, 46)(2, 52)(3, 55)(4, 57)(5, 58)(6, 56)(7, 43)(8, 61)(9, 60)(10, 59)(11, 45)(12, 44)(13, 50)(14, 54)(15, 51)(16, 53)(17, 62)(18, 63)(19, 47)(20, 48)(21, 49)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.30 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.24 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3 * Y1^-1, Y2 * Y3^-1 * Y1, Y1^3 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^2 * Y1 * Y2^-1, Y2^5 * Y1^-1, Y2^-2 * Y3^-3 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 7, 28, 6, 27, 10, 31, 17, 38, 16, 37, 15, 36, 18, 39, 19, 40, 21, 42, 20, 41, 11, 32, 12, 33, 14, 35, 13, 34, 3, 24, 4, 25, 9, 30, 5, 26)(43, 64, 45, 66, 53, 74, 60, 81, 52, 73, 44, 65, 46, 67, 54, 75, 61, 82, 59, 80, 50, 71, 51, 72, 56, 77, 63, 84, 58, 79, 49, 70, 47, 68, 55, 76, 62, 83, 57, 78, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 56)(5, 45)(6, 44)(7, 43)(8, 47)(9, 55)(10, 50)(11, 61)(12, 63)(13, 53)(14, 62)(15, 52)(16, 48)(17, 49)(18, 59)(19, 58)(20, 60)(21, 57)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.29 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.25 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 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 * Y1^-1, (Y2^-1, Y3^-1), (Y3, Y1), Y3^-1 * Y1 * Y3^-1 * Y2, Y3^-2 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-3 * Y2^-3 ] Map:: non-degenerate R = (1, 22, 2, 23, 3, 24, 8, 29, 11, 32, 18, 39, 20, 41, 17, 38, 15, 36, 7, 28, 10, 31, 13, 34, 4, 25, 9, 30, 12, 33, 19, 40, 21, 42, 16, 37, 14, 35, 6, 27, 5, 26)(43, 64, 45, 66, 53, 74, 62, 83, 57, 78, 52, 73, 46, 67, 54, 75, 63, 84, 56, 77, 47, 68, 44, 65, 50, 71, 60, 81, 59, 80, 49, 70, 55, 76, 51, 72, 61, 82, 58, 79, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 50)(5, 55)(6, 52)(7, 43)(8, 61)(9, 53)(10, 44)(11, 63)(12, 60)(13, 45)(14, 49)(15, 47)(16, 57)(17, 48)(18, 58)(19, 62)(20, 56)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.26 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.26 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, (Y2, Y1^-1), Y2^-1 * Y3^2 * Y1^-1, Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y1^-2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^3, Y3 * Y2^2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 4, 25, 10, 31, 3, 24, 9, 30, 18, 39, 14, 35, 19, 40, 13, 34, 16, 37, 20, 41, 17, 38, 21, 42, 15, 36, 6, 27, 11, 32, 7, 28, 12, 33, 5, 26)(43, 64, 45, 66, 55, 76, 57, 78, 47, 68, 52, 73, 61, 82, 63, 84, 54, 75, 46, 67, 56, 77, 59, 80, 49, 70, 50, 71, 60, 81, 62, 83, 53, 74, 44, 65, 51, 72, 58, 79, 48, 69) L = (1, 46)(2, 52)(3, 56)(4, 51)(5, 50)(6, 54)(7, 43)(8, 45)(9, 61)(10, 60)(11, 47)(12, 44)(13, 59)(14, 58)(15, 49)(16, 63)(17, 48)(18, 55)(19, 62)(20, 57)(21, 53)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.25 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.27 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 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^-1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^2 * Y2^3, Y3^-2 * Y1^-3, Y2 * Y1^-1 * Y2^2 * Y1^-2, Y3^14, (Y3^-1 * Y1^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 19, 40, 18, 39, 17, 38, 21, 42, 13, 34, 3, 24, 4, 25, 9, 30, 16, 37, 7, 28, 6, 27, 10, 31, 20, 41, 11, 32, 12, 33, 14, 35, 15, 36, 5, 26)(43, 64, 45, 66, 53, 74, 61, 82, 58, 79, 57, 78, 63, 84, 52, 73, 44, 65, 46, 67, 54, 75, 60, 81, 49, 70, 47, 68, 55, 76, 62, 83, 50, 71, 51, 72, 56, 77, 59, 80, 48, 69) L = (1, 46)(2, 51)(3, 54)(4, 56)(5, 45)(6, 44)(7, 43)(8, 58)(9, 57)(10, 50)(11, 60)(12, 59)(13, 53)(14, 63)(15, 55)(16, 47)(17, 52)(18, 48)(19, 49)(20, 61)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.28 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.28 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 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, Y3 * Y2 * Y1, Y1^-2 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^7, Y3^3 * Y2^-1 * Y3^3 * Y1^-1, Y2^9 * Y3^-1, (Y3 * Y2^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 3, 24, 7, 28, 8, 29, 9, 30, 13, 34, 14, 35, 15, 36, 19, 40, 20, 41, 21, 42, 16, 37, 18, 39, 17, 38, 10, 31, 12, 33, 11, 32, 4, 25, 6, 27, 5, 26)(43, 64, 45, 66, 50, 71, 55, 76, 57, 78, 62, 83, 58, 79, 59, 80, 54, 75, 46, 67, 47, 68, 44, 65, 49, 70, 51, 72, 56, 77, 61, 82, 63, 84, 60, 81, 52, 73, 53, 74, 48, 69) L = (1, 46)(2, 48)(3, 47)(4, 52)(5, 53)(6, 54)(7, 43)(8, 44)(9, 45)(10, 58)(11, 59)(12, 60)(13, 49)(14, 50)(15, 51)(16, 61)(17, 63)(18, 62)(19, 55)(20, 56)(21, 57)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.27 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.29 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y1 * Y3^-1 * Y2, Y1^2 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^7, Y2^-1 * Y3^-2 * Y2^-1 * Y3^-3 * Y2^-1, Y2^9 * Y3, (Y3^-1 * Y1^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 3, 24, 4, 25, 8, 29, 9, 30, 10, 31, 14, 35, 15, 36, 16, 37, 20, 41, 21, 42, 19, 40, 18, 39, 17, 38, 13, 34, 12, 33, 11, 32, 7, 28, 6, 27, 5, 26)(43, 64, 45, 66, 50, 71, 52, 73, 57, 78, 62, 83, 61, 82, 59, 80, 54, 75, 49, 70, 47, 68, 44, 65, 46, 67, 51, 72, 56, 77, 58, 79, 63, 84, 60, 81, 55, 76, 53, 74, 48, 69) L = (1, 46)(2, 50)(3, 51)(4, 52)(5, 45)(6, 44)(7, 43)(8, 56)(9, 57)(10, 58)(11, 47)(12, 48)(13, 49)(14, 62)(15, 63)(16, 61)(17, 53)(18, 54)(19, 55)(20, 60)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.24 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.30 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 21, 21, 21}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-3, Y3 * Y2^-3, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y3)^2, Y3 * Y1^-1 * Y3^2 * Y2^-1, Y1^-2 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-2 * Y1 * Y3^-2, Y3^7, (Y3^-1 * Y1^-1)^21 ] Map:: non-degenerate R = (1, 22, 2, 23, 8, 29, 4, 25, 10, 31, 16, 37, 17, 38, 15, 36, 3, 24, 9, 30, 20, 41, 14, 35, 18, 39, 6, 27, 11, 32, 21, 42, 13, 34, 19, 40, 7, 28, 12, 33, 5, 26)(43, 64, 45, 66, 55, 76, 46, 67, 56, 77, 54, 75, 59, 80, 53, 74, 44, 65, 51, 72, 61, 82, 52, 73, 60, 81, 47, 68, 57, 78, 63, 84, 50, 71, 62, 83, 49, 70, 58, 79, 48, 69) L = (1, 46)(2, 52)(3, 56)(4, 59)(5, 50)(6, 55)(7, 43)(8, 58)(9, 60)(10, 57)(11, 61)(12, 44)(13, 54)(14, 53)(15, 62)(16, 45)(17, 51)(18, 63)(19, 47)(20, 48)(21, 49)(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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.23 Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.31 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^-1 * Y2^2, Y3 * Y1^-1 * Y3 * Y1, Y3 * Y2^-1 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^5 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 15, 37, 14, 36, 6, 28, 3, 25, 8, 30, 16, 38, 13, 35, 5, 27)(4, 26, 9, 31, 17, 39, 21, 43, 20, 42, 12, 34, 10, 32, 18, 40, 22, 44, 19, 41, 11, 33)(45, 67, 47, 69, 46, 68, 52, 74, 51, 73, 60, 82, 59, 81, 57, 79, 58, 80, 49, 71, 50, 72)(48, 70, 54, 76, 53, 75, 62, 84, 61, 83, 66, 88, 65, 87, 63, 85, 64, 86, 55, 77, 56, 78) L = (1, 48)(2, 53)(3, 54)(4, 45)(5, 55)(6, 56)(7, 61)(8, 62)(9, 46)(10, 47)(11, 49)(12, 50)(13, 63)(14, 64)(15, 65)(16, 66)(17, 51)(18, 52)(19, 57)(20, 58)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.141 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.32 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1 * Y2^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^-5 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 15, 37, 11, 33, 3, 25, 6, 28, 9, 31, 17, 39, 14, 36, 5, 27)(4, 26, 8, 30, 16, 38, 21, 43, 19, 41, 10, 32, 13, 35, 18, 40, 22, 44, 20, 42, 12, 34)(45, 67, 47, 69, 49, 71, 55, 77, 58, 80, 59, 81, 61, 83, 51, 73, 53, 75, 46, 68, 50, 72)(48, 70, 54, 76, 56, 78, 63, 85, 64, 86, 65, 87, 66, 88, 60, 82, 62, 84, 52, 74, 57, 79) L = (1, 48)(2, 52)(3, 54)(4, 45)(5, 56)(6, 57)(7, 60)(8, 46)(9, 62)(10, 47)(11, 63)(12, 49)(13, 50)(14, 64)(15, 65)(16, 51)(17, 66)(18, 53)(19, 55)(20, 58)(21, 59)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.140 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.33 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2^3 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^2, Y1 * Y2^-1 * Y1^3, Y3 * Y2^2 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 12, 34, 3, 25, 8, 30, 16, 38, 6, 28, 10, 32, 15, 37, 5, 27)(4, 26, 9, 31, 17, 39, 20, 42, 11, 33, 18, 40, 22, 44, 14, 36, 19, 41, 21, 43, 13, 35)(45, 67, 47, 69, 54, 76, 46, 68, 52, 74, 59, 81, 51, 73, 60, 82, 49, 71, 56, 78, 50, 72)(48, 70, 55, 77, 63, 85, 53, 75, 62, 84, 65, 87, 61, 83, 66, 88, 57, 79, 64, 86, 58, 80) L = (1, 48)(2, 53)(3, 55)(4, 45)(5, 57)(6, 58)(7, 61)(8, 62)(9, 46)(10, 63)(11, 47)(12, 64)(13, 49)(14, 50)(15, 65)(16, 66)(17, 51)(18, 52)(19, 54)(20, 56)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.138 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.34 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2^-1 * Y1^-1 * Y2^-2, (Y2, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y3 * Y1 * Y3 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 11, 33, 6, 28, 10, 32, 13, 35, 3, 25, 8, 30, 16, 38, 5, 27)(4, 26, 9, 31, 17, 39, 20, 42, 15, 37, 19, 41, 21, 43, 12, 34, 18, 40, 22, 44, 14, 36)(45, 67, 47, 69, 55, 77, 49, 71, 57, 79, 51, 73, 60, 82, 54, 76, 46, 68, 52, 74, 50, 72)(48, 70, 56, 78, 64, 86, 58, 80, 65, 87, 61, 83, 66, 88, 63, 85, 53, 75, 62, 84, 59, 81) L = (1, 48)(2, 53)(3, 56)(4, 45)(5, 58)(6, 59)(7, 61)(8, 62)(9, 46)(10, 63)(11, 64)(12, 47)(13, 65)(14, 49)(15, 50)(16, 66)(17, 51)(18, 52)(19, 54)(20, 55)(21, 57)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.139 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.35 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y3 * Y1^-1 * Y3, (Y2^-1 * Y3^-1)^2, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y2^-1 * Y1^3, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1, (Y3^-1 * Y1^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 12, 34, 3, 25, 6, 28, 10, 32, 19, 41, 15, 37, 5, 27)(4, 26, 9, 31, 18, 40, 21, 43, 13, 35, 11, 33, 14, 36, 20, 42, 22, 44, 16, 38, 7, 29)(45, 67, 47, 69, 49, 71, 56, 78, 59, 81, 61, 83, 63, 85, 52, 74, 54, 76, 46, 68, 50, 72)(48, 70, 55, 77, 51, 73, 57, 79, 60, 82, 65, 87, 66, 88, 62, 84, 64, 86, 53, 75, 58, 80) L = (1, 48)(2, 53)(3, 55)(4, 46)(5, 51)(6, 58)(7, 45)(8, 62)(9, 52)(10, 64)(11, 50)(12, 57)(13, 47)(14, 54)(15, 60)(16, 49)(17, 65)(18, 61)(19, 66)(20, 63)(21, 56)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.153 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.36 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y1^-1, (Y3, Y1^-1), (Y3, Y2^-1), Y2^-1 * Y1^-1 * Y2^-2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1^2, Y1^-1 * Y2^-1 * Y1^-3, (Y2^-1 * Y1)^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, 18, 40, 7, 29, 12, 34, 19, 41, 21, 43, 14, 36, 20, 42, 22, 44, 16, 38)(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, 51, 73, 60, 82, 65, 87, 62, 84, 66, 88, 63, 85, 54, 76, 64, 86, 56, 78) L = (1, 48)(2, 54)(3, 58)(4, 53)(5, 60)(6, 56)(7, 45)(8, 62)(9, 64)(10, 61)(11, 63)(12, 46)(13, 51)(14, 50)(15, 65)(16, 47)(17, 66)(18, 49)(19, 52)(20, 55)(21, 57)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.148 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.37 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y2, Y3^-1), Y2 * Y1^-3, (R * Y2)^2, Y2^-2 * Y3^-2, (Y3 * Y2)^2, (R * Y3)^2, (Y1^-1, Y3), (R * Y1)^2, (Y2^-1, Y1^-1), Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y1 * Y2^-3, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y1^2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 3, 25, 9, 31, 16, 38, 13, 35, 19, 41, 6, 28, 11, 33, 5, 27)(4, 26, 10, 32, 21, 43, 14, 36, 22, 44, 20, 42, 7, 29, 12, 34, 18, 40, 15, 37, 17, 39)(45, 67, 47, 69, 57, 79, 55, 77, 46, 68, 53, 75, 63, 85, 49, 71, 52, 74, 60, 82, 50, 72)(48, 70, 58, 80, 51, 73, 59, 81, 54, 76, 66, 88, 56, 78, 61, 83, 65, 87, 64, 86, 62, 84) L = (1, 48)(2, 54)(3, 58)(4, 60)(5, 61)(6, 62)(7, 45)(8, 65)(9, 66)(10, 57)(11, 59)(12, 46)(13, 51)(14, 50)(15, 47)(16, 64)(17, 53)(18, 52)(19, 56)(20, 49)(21, 63)(22, 55)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.145 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y2)^2, Y3^-2 * Y2^-2, Y1^3 * Y2, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y2^-4, Y3 * Y1^2 * Y3 * Y2^-1, Y3^-4 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 6, 28, 11, 33, 13, 35, 17, 39, 15, 37, 3, 25, 9, 31, 5, 27)(4, 26, 10, 32, 16, 38, 19, 41, 20, 42, 7, 29, 12, 34, 21, 43, 14, 36, 22, 44, 18, 40)(45, 67, 47, 69, 57, 79, 52, 74, 49, 71, 59, 81, 55, 77, 46, 68, 53, 75, 61, 83, 50, 72)(48, 70, 58, 80, 51, 73, 60, 82, 62, 84, 65, 87, 64, 86, 54, 76, 66, 88, 56, 78, 63, 85) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 62)(6, 63)(7, 45)(8, 60)(9, 66)(10, 59)(11, 64)(12, 46)(13, 51)(14, 50)(15, 65)(16, 47)(17, 56)(18, 57)(19, 53)(20, 49)(21, 52)(22, 55)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.146 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2^-1 * Y3^-1)^2, Y3^-2 * Y2^-2, (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1, Y2^-2 * Y3^2 * Y1 * Y2^-1, Y1 * Y3^4 * Y2^-1, Y2^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 9, 31, 15, 37, 19, 41, 21, 43, 11, 33, 13, 35, 3, 25, 5, 27)(4, 26, 8, 30, 17, 39, 20, 42, 22, 44, 14, 36, 18, 40, 7, 29, 10, 32, 12, 34, 16, 38)(45, 67, 47, 69, 55, 77, 63, 85, 53, 75, 46, 68, 49, 71, 57, 79, 65, 87, 59, 81, 50, 72)(48, 70, 56, 78, 51, 73, 58, 80, 64, 86, 52, 74, 60, 82, 54, 76, 62, 84, 66, 88, 61, 83) L = (1, 48)(2, 52)(3, 56)(4, 59)(5, 60)(6, 61)(7, 45)(8, 63)(9, 64)(10, 46)(11, 51)(12, 50)(13, 54)(14, 47)(15, 66)(16, 53)(17, 65)(18, 49)(19, 58)(20, 55)(21, 62)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.152 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2^-1, Y3^-1), (Y3^-1 * Y2^-1)^2, Y3^2 * Y2^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y2)^2, Y1 * Y2^5, Y1 * Y3^-4 * Y2, Y2^-5 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24, 3, 25, 8, 30, 11, 33, 19, 41, 21, 43, 14, 36, 17, 39, 6, 28, 5, 27)(4, 26, 9, 31, 12, 34, 18, 40, 7, 29, 10, 32, 13, 35, 20, 42, 22, 44, 16, 38, 15, 37)(45, 67, 47, 69, 55, 77, 65, 87, 61, 83, 49, 71, 46, 68, 52, 74, 63, 85, 58, 80, 50, 72)(48, 70, 56, 78, 51, 73, 57, 79, 66, 88, 59, 81, 53, 75, 62, 84, 54, 76, 64, 86, 60, 82) L = (1, 48)(2, 53)(3, 56)(4, 58)(5, 59)(6, 60)(7, 45)(8, 62)(9, 61)(10, 46)(11, 51)(12, 50)(13, 47)(14, 64)(15, 65)(16, 63)(17, 66)(18, 49)(19, 54)(20, 52)(21, 57)(22, 55)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.149 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, (Y3, Y1^-1), (R * Y2)^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y2 * Y3 * Y1, Y3^-4 * Y2, Y1^2 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 14, 36, 18, 40, 6, 28, 3, 25, 9, 31, 21, 43, 17, 39, 5, 27)(4, 26, 10, 32, 20, 42, 13, 35, 22, 44, 16, 38, 12, 34, 19, 41, 7, 29, 11, 33, 15, 37)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 65, 87, 58, 80, 61, 83, 62, 84, 49, 71, 50, 72)(48, 70, 56, 78, 54, 76, 63, 85, 64, 86, 51, 73, 57, 79, 55, 77, 66, 88, 59, 81, 60, 82) L = (1, 48)(2, 54)(3, 56)(4, 58)(5, 59)(6, 60)(7, 45)(8, 64)(9, 63)(10, 62)(11, 46)(12, 61)(13, 47)(14, 57)(15, 52)(16, 65)(17, 55)(18, 66)(19, 49)(20, 50)(21, 51)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.150 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2 * Y3, (Y1^-1, Y2^-1), Y1 * Y3^2 * Y2, (R * Y3)^2, (Y3^-1, Y2^-1), Y1^-1 * Y2 * Y1^-2, (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y2^-1 * Y1^-1, Y1^-1 * Y2^4, Y3^-3 * Y2 * Y3^-1, Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 3, 25, 9, 31, 19, 41, 13, 35, 16, 38, 6, 28, 11, 33, 5, 27)(4, 26, 10, 32, 20, 42, 14, 36, 7, 29, 12, 34, 21, 43, 15, 37, 18, 40, 22, 44, 17, 39)(45, 67, 47, 69, 57, 79, 55, 77, 46, 68, 53, 75, 60, 82, 49, 71, 52, 74, 63, 85, 50, 72)(48, 70, 58, 80, 65, 87, 66, 88, 54, 76, 51, 73, 59, 81, 61, 83, 64, 86, 56, 78, 62, 84) L = (1, 48)(2, 54)(3, 58)(4, 60)(5, 61)(6, 62)(7, 45)(8, 64)(9, 51)(10, 50)(11, 66)(12, 46)(13, 65)(14, 49)(15, 47)(16, 59)(17, 57)(18, 53)(19, 56)(20, 55)(21, 52)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.151 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y3^2 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y3^-1, Y1^3 * Y2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3^-2 * Y1, (R * Y3)^2, (Y2, Y3^-1), Y1 * Y2^-1 * Y3^2 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-3, (Y3^-1 * Y2^-1 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 6, 28, 11, 33, 13, 35, 19, 41, 14, 36, 3, 25, 9, 31, 5, 27)(4, 26, 10, 32, 20, 42, 17, 39, 15, 37, 22, 44, 18, 40, 7, 29, 12, 34, 21, 43, 16, 38)(45, 67, 47, 69, 57, 79, 52, 74, 49, 71, 58, 80, 55, 77, 46, 68, 53, 75, 63, 85, 50, 72)(48, 70, 56, 78, 66, 88, 64, 86, 60, 82, 51, 73, 59, 81, 54, 76, 65, 87, 62, 84, 61, 83) L = (1, 48)(2, 54)(3, 56)(4, 55)(5, 60)(6, 61)(7, 45)(8, 64)(9, 65)(10, 57)(11, 59)(12, 46)(13, 66)(14, 51)(15, 47)(16, 50)(17, 58)(18, 49)(19, 62)(20, 63)(21, 52)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.144 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.44 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y1^-1, Y3^2 * Y1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2^-5 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 8, 30, 14, 36, 16, 38, 19, 41, 10, 32, 12, 34, 3, 25, 5, 27)(4, 26, 7, 29, 9, 31, 15, 37, 17, 39, 21, 43, 22, 44, 18, 40, 20, 42, 11, 33, 13, 35)(45, 67, 47, 69, 54, 76, 60, 82, 52, 74, 46, 68, 49, 71, 56, 78, 63, 85, 58, 80, 50, 72)(48, 70, 55, 77, 62, 84, 65, 87, 59, 81, 51, 73, 57, 79, 64, 86, 66, 88, 61, 83, 53, 75) L = (1, 48)(2, 51)(3, 55)(4, 49)(5, 57)(6, 53)(7, 45)(8, 59)(9, 46)(10, 62)(11, 56)(12, 64)(13, 47)(14, 61)(15, 50)(16, 65)(17, 52)(18, 63)(19, 66)(20, 54)(21, 58)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.142 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.45 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y1 * Y3^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y1 * Y2^5, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 23, 2, 24, 3, 25, 8, 30, 10, 32, 16, 38, 18, 40, 15, 37, 14, 36, 6, 28, 5, 27)(4, 26, 7, 29, 9, 31, 11, 33, 17, 39, 19, 41, 22, 44, 21, 43, 20, 42, 13, 35, 12, 34)(45, 67, 47, 69, 54, 76, 62, 84, 58, 80, 49, 71, 46, 68, 52, 74, 60, 82, 59, 81, 50, 72)(48, 70, 53, 75, 61, 83, 66, 88, 64, 86, 56, 78, 51, 73, 55, 77, 63, 85, 65, 87, 57, 79) L = (1, 48)(2, 51)(3, 53)(4, 49)(5, 56)(6, 57)(7, 45)(8, 55)(9, 46)(10, 61)(11, 47)(12, 50)(13, 58)(14, 64)(15, 65)(16, 63)(17, 52)(18, 66)(19, 54)(20, 59)(21, 62)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.143 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.46 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, Y2 * Y3^2, Y2^-3 * Y1, (Y2^-1, Y1^-1), (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 13, 35, 3, 25, 9, 31, 18, 40, 6, 28, 11, 33, 17, 39, 5, 27)(4, 26, 10, 32, 20, 42, 19, 41, 7, 29, 12, 34, 21, 43, 16, 38, 14, 36, 22, 44, 15, 37)(45, 67, 47, 69, 55, 77, 46, 68, 53, 75, 61, 83, 52, 74, 62, 84, 49, 71, 57, 79, 50, 72)(48, 70, 51, 73, 58, 80, 54, 76, 56, 78, 66, 88, 64, 86, 65, 87, 59, 81, 63, 85, 60, 82) L = (1, 48)(2, 54)(3, 51)(4, 50)(5, 59)(6, 60)(7, 45)(8, 64)(9, 56)(10, 55)(11, 58)(12, 46)(13, 63)(14, 47)(15, 62)(16, 57)(17, 66)(18, 65)(19, 49)(20, 61)(21, 52)(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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.147 Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.47 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1^3 * Y2^2 * Y1^4, Y1^22, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: 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, 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.48 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-2 * Y1^-2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y2^4 * Y1, Y1^-1 * Y2^10, Y1^11, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 11, 33, 15, 37, 19, 41, 22, 44, 17, 39, 14, 36, 9, 31, 4, 26)(3, 25, 7, 29, 5, 27, 8, 30, 12, 34, 16, 38, 20, 42, 21, 43, 18, 40, 13, 35, 10, 32)(45, 67, 47, 69, 53, 75, 57, 79, 61, 83, 65, 87, 63, 85, 60, 82, 55, 77, 52, 74, 46, 68, 51, 73, 48, 70, 54, 76, 58, 80, 62, 84, 66, 88, 64, 86, 59, 81, 56, 78, 50, 72, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^11, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 10, 32, 14, 36, 18, 40, 20, 42, 16, 38, 12, 34, 8, 30, 4, 26)(3, 25, 7, 29, 11, 33, 15, 37, 19, 41, 22, 44, 21, 43, 17, 39, 13, 35, 9, 31, 5, 27)(45, 67, 47, 69, 46, 68, 51, 73, 50, 72, 55, 77, 54, 76, 59, 81, 58, 80, 63, 85, 62, 84, 66, 88, 64, 86, 65, 87, 60, 82, 61, 83, 56, 78, 57, 79, 52, 74, 53, 75, 48, 70, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^11, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 10, 32, 14, 36, 18, 40, 21, 43, 17, 39, 13, 35, 9, 31, 4, 26)(3, 25, 5, 27, 7, 29, 11, 33, 15, 37, 19, 41, 22, 44, 20, 42, 16, 38, 12, 34, 8, 30)(45, 67, 47, 69, 48, 70, 52, 74, 53, 75, 56, 78, 57, 79, 60, 82, 61, 83, 64, 86, 65, 87, 66, 88, 62, 84, 63, 85, 58, 80, 59, 81, 54, 76, 55, 77, 50, 72, 51, 73, 46, 68, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^2 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-5 * Y1, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 13, 35, 15, 37, 20, 42, 22, 44, 17, 39, 9, 31, 11, 33, 4, 26)(3, 25, 7, 29, 12, 34, 5, 27, 8, 30, 14, 36, 19, 41, 21, 43, 16, 38, 18, 40, 10, 32)(45, 67, 47, 69, 53, 75, 60, 82, 64, 86, 58, 80, 50, 72, 56, 78, 48, 70, 54, 76, 61, 83, 65, 87, 59, 81, 52, 74, 46, 68, 51, 73, 55, 77, 62, 84, 66, 88, 63, 85, 57, 79, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.52 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y1, Y2), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1^3, (R * Y2 * Y3^-1)^2, Y2^-6 * Y1^-2, Y1^2 * Y2^6, Y2^6 * Y1^2, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 9, 31, 15, 37, 20, 42, 22, 44, 18, 40, 13, 35, 11, 33, 4, 26)(3, 25, 7, 29, 14, 36, 16, 38, 21, 43, 19, 41, 17, 39, 12, 34, 5, 27, 8, 30, 10, 32)(45, 67, 47, 69, 53, 75, 60, 82, 66, 88, 61, 83, 55, 77, 52, 74, 46, 68, 51, 73, 59, 81, 65, 87, 62, 84, 56, 78, 48, 70, 54, 76, 50, 72, 58, 80, 64, 86, 63, 85, 57, 79, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y1^-1 * Y2^3, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^4 * Y2, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 14, 36, 21, 43, 13, 35, 9, 31, 17, 39, 19, 41, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 20, 42, 12, 34, 5, 27, 8, 30, 16, 38, 22, 44, 18, 40, 10, 32)(45, 67, 47, 69, 53, 75, 52, 74, 46, 68, 51, 73, 61, 83, 60, 82, 50, 72, 59, 81, 63, 85, 66, 88, 58, 80, 64, 86, 55, 77, 62, 84, 65, 87, 56, 78, 48, 70, 54, 76, 57, 79, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, 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, Y2 * Y1 * Y2^3, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-4, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 14, 36, 18, 40, 9, 31, 13, 35, 17, 39, 20, 42, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 22, 44, 21, 43, 12, 34, 5, 27, 8, 30, 16, 38, 19, 41, 10, 32)(45, 67, 47, 69, 53, 75, 56, 78, 48, 70, 54, 76, 62, 84, 65, 87, 55, 77, 63, 85, 58, 80, 66, 88, 64, 86, 60, 82, 50, 72, 59, 81, 61, 83, 52, 74, 46, 68, 51, 73, 57, 79, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2, Y1), (R * Y1)^2, Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-3 * Y2^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y1, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 14, 36, 13, 35, 18, 40, 20, 42, 9, 31, 17, 39, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 12, 34, 5, 27, 8, 30, 16, 38, 19, 41, 22, 44, 21, 43, 10, 32)(45, 67, 47, 69, 53, 75, 63, 85, 58, 80, 56, 78, 48, 70, 54, 76, 64, 86, 60, 82, 50, 72, 59, 81, 55, 77, 65, 87, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 66, 88, 57, 79, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1^-3, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^2 * Y1^2 * Y2, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: R = (1, 23, 2, 24, 6, 28, 14, 36, 9, 31, 17, 39, 21, 43, 13, 35, 18, 40, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 22, 44, 19, 41, 20, 42, 12, 34, 5, 27, 8, 30, 16, 38, 10, 32)(45, 67, 47, 69, 53, 75, 63, 85, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 64, 86, 55, 77, 60, 82, 50, 72, 59, 81, 65, 87, 56, 78, 48, 70, 54, 76, 58, 80, 66, 88, 57, 79, 49, 71) 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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.57 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y1^-1 * Y3, (Y2 * Y1)^2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1^9, Y2^-2 * Y1^3 * Y2^-6, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 11, 33, 15, 37, 19, 41, 22, 44, 17, 39, 14, 36, 9, 31, 4, 26)(3, 25, 7, 29, 5, 27, 8, 30, 12, 34, 16, 38, 20, 42, 21, 43, 18, 40, 13, 35, 10, 32)(45, 67, 47, 69, 53, 75, 57, 79, 61, 83, 65, 87, 63, 85, 60, 82, 55, 77, 52, 74, 46, 68, 51, 73, 48, 70, 54, 76, 58, 80, 62, 84, 66, 88, 64, 86, 59, 81, 56, 78, 50, 72, 49, 71) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 55)(7, 49)(8, 56)(9, 48)(10, 47)(11, 59)(12, 60)(13, 54)(14, 53)(15, 63)(16, 64)(17, 58)(18, 57)(19, 66)(20, 65)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.130 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.58 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1^-1 * Y2^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^2 * Y3^-1 * Y1^3, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 13, 35, 4, 26, 7, 29, 10, 32, 19, 41, 15, 37, 5, 27)(3, 25, 9, 31, 18, 40, 21, 43, 14, 36, 11, 33, 12, 34, 20, 42, 22, 44, 16, 38, 6, 28)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 62, 84, 61, 83, 65, 87, 57, 79, 58, 80, 48, 70, 55, 77, 51, 73, 56, 78, 54, 76, 64, 86, 63, 85, 66, 88, 59, 81, 60, 82, 49, 71, 50, 72) L = (1, 48)(2, 51)(3, 55)(4, 49)(5, 57)(6, 58)(7, 45)(8, 54)(9, 56)(10, 46)(11, 50)(12, 47)(13, 59)(14, 60)(15, 61)(16, 65)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.137 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.59 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y3^2, Y2 * Y1 * Y2, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y1^-3 * Y3^-1 * Y1^-2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 16, 38, 7, 29, 4, 26, 9, 31, 18, 40, 15, 37, 5, 27)(3, 25, 6, 28, 10, 32, 19, 41, 22, 44, 13, 35, 11, 33, 14, 36, 20, 42, 21, 43, 12, 34)(45, 67, 47, 69, 49, 71, 56, 78, 59, 81, 65, 87, 62, 84, 64, 86, 53, 75, 58, 80, 48, 70, 55, 77, 51, 73, 57, 79, 60, 82, 66, 88, 61, 83, 63, 85, 52, 74, 54, 76, 46, 68, 50, 72) L = (1, 48)(2, 53)(3, 55)(4, 46)(5, 51)(6, 58)(7, 45)(8, 62)(9, 52)(10, 64)(11, 50)(12, 57)(13, 47)(14, 54)(15, 60)(16, 49)(17, 59)(18, 61)(19, 65)(20, 63)(21, 66)(22, 56)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.135 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.60 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y2^-2, Y1^-1 * Y2^2 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y1, (Y1, Y2^-1), Y2^-2 * Y3^-2, Y3^-2 * Y1^-1 * Y3^-1, (Y3 * Y2)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^2, Y1^2 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 7, 29, 12, 34, 16, 38, 4, 26, 10, 32, 17, 39, 5, 27)(3, 25, 9, 31, 18, 40, 6, 28, 11, 33, 19, 41, 21, 43, 13, 35, 20, 42, 22, 44, 14, 36)(45, 67, 47, 69, 54, 76, 64, 86, 56, 78, 63, 85, 52, 74, 62, 84, 49, 71, 58, 80, 48, 70, 57, 79, 51, 73, 55, 77, 46, 68, 53, 75, 61, 83, 66, 88, 60, 82, 65, 87, 59, 81, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 58)(7, 45)(8, 61)(9, 64)(10, 51)(11, 47)(12, 46)(13, 50)(14, 65)(15, 49)(16, 52)(17, 56)(18, 66)(19, 53)(20, 55)(21, 62)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.129 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.61 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y2^-2, Y3^2 * Y1^-1 * Y3, Y1 * Y2 * Y3^-1 * Y2, Y2^-2 * Y1^-1 * Y3, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y1^3 * Y3^-1 * Y1, Y3 * Y1^2 * Y3 * Y1, Y1^-2 * Y2^16 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 13, 35, 4, 26, 10, 32, 18, 40, 7, 29, 12, 34, 17, 39, 5, 27)(3, 25, 9, 31, 19, 41, 21, 43, 14, 36, 20, 42, 22, 44, 16, 38, 6, 28, 11, 33, 15, 37)(45, 67, 47, 69, 57, 79, 65, 87, 62, 84, 66, 88, 61, 83, 55, 77, 46, 68, 53, 75, 48, 70, 58, 80, 51, 73, 60, 82, 49, 71, 59, 81, 52, 74, 63, 85, 54, 76, 64, 86, 56, 78, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 56)(5, 57)(6, 53)(7, 45)(8, 62)(9, 64)(10, 61)(11, 63)(12, 46)(13, 51)(14, 50)(15, 65)(16, 47)(17, 52)(18, 49)(19, 66)(20, 55)(21, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.132 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.62 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y2), (Y3 * Y2)^2, Y1^-3 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y2^-2, (Y1^-1, Y2^-1), (R * Y2)^2, Y3 * Y1 * Y3^3, Y2^2 * Y1^2 * Y3^-1, Y2^-1 * Y1 * Y2^-3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 17, 39, 13, 35, 18, 40, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 19, 41, 16, 38, 20, 42, 6, 28, 11, 33, 21, 43, 14, 36, 22, 44, 15, 37)(45, 67, 47, 69, 57, 79, 55, 77, 46, 68, 53, 75, 62, 84, 65, 87, 52, 74, 63, 85, 48, 70, 58, 80, 51, 73, 60, 82, 54, 76, 66, 88, 56, 78, 64, 86, 49, 71, 59, 81, 61, 83, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 62)(6, 63)(7, 45)(8, 49)(9, 66)(10, 57)(11, 60)(12, 46)(13, 51)(14, 50)(15, 65)(16, 47)(17, 52)(18, 56)(19, 59)(20, 53)(21, 64)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.136 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3^-1), (Y3 * Y2)^2, (R * Y3)^2, Y2^-2 * Y3^-2, (R * Y1)^2, Y3 * Y1^-3, (Y1^-1, Y2^-1), (R * Y2)^2, Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y3^-2 * Y1 * Y3^-2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y3 * Y1^2, Y2^14 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 13, 35, 17, 39, 20, 42, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 21, 43, 14, 36, 22, 44, 19, 41, 6, 28, 11, 33, 16, 38, 18, 40, 15, 37)(45, 67, 47, 69, 57, 79, 63, 85, 49, 71, 59, 81, 54, 76, 66, 88, 56, 78, 62, 84, 48, 70, 58, 80, 51, 73, 60, 82, 52, 74, 65, 87, 64, 86, 55, 77, 46, 68, 53, 75, 61, 83, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 52)(6, 62)(7, 45)(8, 57)(9, 66)(10, 64)(11, 59)(12, 46)(13, 51)(14, 50)(15, 65)(16, 47)(17, 56)(18, 53)(19, 60)(20, 49)(21, 63)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.133 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3, (Y2, Y1), (Y2 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3), Y2^-2 * Y3^-2, (R * Y1)^2, Y1 * Y2^-2 * Y3^3, (Y3^-1 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 15, 37, 19, 41, 21, 43, 11, 33, 18, 40, 7, 29, 5, 27)(3, 25, 8, 30, 12, 34, 17, 39, 6, 28, 10, 32, 16, 38, 20, 42, 22, 44, 14, 36, 13, 35)(45, 67, 47, 69, 55, 77, 64, 86, 53, 75, 61, 83, 49, 71, 57, 79, 65, 87, 60, 82, 48, 70, 56, 78, 51, 73, 58, 80, 63, 85, 54, 76, 46, 68, 52, 74, 62, 84, 66, 88, 59, 81, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 46)(6, 60)(7, 45)(8, 61)(9, 63)(10, 64)(11, 51)(12, 50)(13, 52)(14, 47)(15, 65)(16, 66)(17, 54)(18, 49)(19, 55)(20, 58)(21, 62)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.131 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2^-1 * Y3^-1)^2, Y2^-2 * Y3^-2, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y3 * Y2^-4 * Y1^-1, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 11, 33, 19, 41, 22, 44, 15, 37, 16, 38, 4, 26, 5, 27)(3, 25, 8, 30, 14, 36, 20, 42, 21, 43, 17, 39, 18, 40, 6, 28, 9, 31, 12, 34, 13, 35)(45, 67, 47, 69, 55, 77, 65, 87, 60, 82, 53, 75, 46, 68, 52, 74, 63, 85, 61, 83, 48, 70, 56, 78, 51, 73, 58, 80, 66, 88, 62, 84, 49, 71, 57, 79, 54, 76, 64, 86, 59, 81, 50, 72) L = (1, 48)(2, 49)(3, 56)(4, 59)(5, 60)(6, 61)(7, 45)(8, 57)(9, 62)(10, 46)(11, 51)(12, 50)(13, 53)(14, 47)(15, 63)(16, 66)(17, 64)(18, 65)(19, 54)(20, 52)(21, 58)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.134 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y2^-2 * Y3, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y1 * Y3^5, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 12, 34, 18, 40, 20, 42, 16, 38, 14, 36, 7, 29, 5, 27)(3, 25, 8, 30, 11, 33, 17, 39, 19, 41, 22, 44, 21, 43, 15, 37, 13, 35, 6, 28, 10, 32)(45, 67, 47, 69, 48, 70, 55, 77, 56, 78, 63, 85, 64, 86, 65, 87, 58, 80, 57, 79, 49, 71, 54, 76, 46, 68, 52, 74, 53, 75, 61, 83, 62, 84, 66, 88, 60, 82, 59, 81, 51, 73, 50, 72) L = (1, 48)(2, 53)(3, 55)(4, 56)(5, 46)(6, 47)(7, 45)(8, 61)(9, 62)(10, 52)(11, 63)(12, 64)(13, 54)(14, 49)(15, 50)(16, 51)(17, 66)(18, 60)(19, 65)(20, 58)(21, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.70 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y2^-2 * Y3, (Y1^-1 * Y2^-1)^2, (Y1^-1, Y2), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-5 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 16, 38, 18, 40, 21, 43, 13, 35, 14, 36, 4, 26, 5, 27)(3, 25, 8, 30, 6, 28, 9, 31, 15, 37, 17, 39, 22, 44, 19, 41, 20, 42, 11, 33, 12, 34)(45, 67, 47, 69, 48, 70, 55, 77, 57, 79, 63, 85, 62, 84, 61, 83, 54, 76, 53, 75, 46, 68, 52, 74, 49, 71, 56, 78, 58, 80, 64, 86, 65, 87, 66, 88, 60, 82, 59, 81, 51, 73, 50, 72) L = (1, 48)(2, 49)(3, 55)(4, 57)(5, 58)(6, 47)(7, 45)(8, 56)(9, 52)(10, 46)(11, 63)(12, 64)(13, 62)(14, 65)(15, 50)(16, 51)(17, 53)(18, 54)(19, 61)(20, 66)(21, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.68 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^11, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 10, 32, 14, 36, 18, 40, 20, 42, 16, 38, 12, 34, 8, 30, 4, 26)(3, 25, 7, 29, 11, 33, 15, 37, 19, 41, 22, 44, 21, 43, 17, 39, 13, 35, 9, 31, 5, 27)(45, 67, 47, 69, 46, 68, 51, 73, 50, 72, 55, 77, 54, 76, 59, 81, 58, 80, 63, 85, 62, 84, 66, 88, 64, 86, 65, 87, 60, 82, 61, 83, 56, 78, 57, 79, 52, 74, 53, 75, 48, 70, 49, 71) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 47)(6, 54)(7, 55)(8, 48)(9, 49)(10, 58)(11, 59)(12, 52)(13, 53)(14, 62)(15, 63)(16, 56)(17, 57)(18, 64)(19, 66)(20, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.72 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.69 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y1^-2 * Y3^-1 * Y1^-1, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1^-2 * Y3, Y3^4 * Y1, Y2 * Y1 * Y2 * Y1^2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 15, 37, 19, 41, 16, 38, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 17, 39, 6, 28, 11, 33, 20, 42, 18, 40, 22, 44, 13, 35, 21, 43, 14, 36)(45, 67, 47, 69, 48, 70, 57, 79, 59, 81, 64, 86, 52, 74, 61, 83, 49, 71, 58, 80, 60, 82, 66, 88, 56, 78, 55, 77, 46, 68, 53, 75, 54, 76, 65, 87, 63, 85, 62, 84, 51, 73, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 47)(7, 45)(8, 49)(9, 65)(10, 63)(11, 53)(12, 46)(13, 64)(14, 66)(15, 52)(16, 56)(17, 58)(18, 50)(19, 51)(20, 61)(21, 62)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.74 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-2, (Y1^-1, Y3^-1), Y3 * Y1^-3, (Y2^-1, Y1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y3^-3, Y1^-1 * Y2 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 19, 41, 15, 37, 17, 39, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 20, 42, 13, 35, 21, 43, 18, 40, 22, 44, 16, 38, 6, 28, 11, 33, 14, 36)(45, 67, 47, 69, 48, 70, 57, 79, 59, 81, 66, 88, 56, 78, 55, 77, 46, 68, 53, 75, 54, 76, 65, 87, 61, 83, 60, 82, 49, 71, 58, 80, 52, 74, 64, 86, 63, 85, 62, 84, 51, 73, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 52)(6, 47)(7, 45)(8, 63)(9, 65)(10, 61)(11, 53)(12, 46)(13, 66)(14, 64)(15, 56)(16, 58)(17, 49)(18, 50)(19, 51)(20, 62)(21, 60)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.66 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2^-2 * Y3, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1^5, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 16, 38, 15, 37, 7, 29, 4, 26, 10, 32, 18, 40, 13, 35, 5, 27)(3, 25, 9, 31, 17, 39, 21, 43, 14, 36, 6, 28, 11, 33, 19, 41, 22, 44, 20, 42, 12, 34)(45, 67, 47, 69, 48, 70, 55, 77, 46, 68, 53, 75, 54, 76, 63, 85, 52, 74, 61, 83, 62, 84, 66, 88, 60, 82, 65, 87, 57, 79, 64, 86, 59, 81, 58, 80, 49, 71, 56, 78, 51, 73, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 46)(5, 51)(6, 47)(7, 45)(8, 62)(9, 63)(10, 52)(11, 53)(12, 50)(13, 59)(14, 56)(15, 49)(16, 57)(17, 66)(18, 60)(19, 61)(20, 58)(21, 64)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.73 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y2^-2 * Y3, Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y2^-1 * Y1^2 * Y2, Y1^-5 * Y3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 16, 38, 14, 36, 4, 26, 7, 29, 11, 33, 19, 41, 15, 37, 5, 27)(3, 25, 9, 31, 17, 39, 22, 44, 20, 42, 12, 34, 6, 28, 10, 32, 18, 40, 21, 43, 13, 35)(45, 67, 47, 69, 48, 70, 56, 78, 49, 71, 57, 79, 58, 80, 64, 86, 59, 81, 65, 87, 60, 82, 66, 88, 63, 85, 62, 84, 52, 74, 61, 83, 55, 77, 54, 76, 46, 68, 53, 75, 51, 73, 50, 72) L = (1, 48)(2, 51)(3, 56)(4, 49)(5, 58)(6, 47)(7, 45)(8, 55)(9, 50)(10, 53)(11, 46)(12, 57)(13, 64)(14, 59)(15, 60)(16, 63)(17, 54)(18, 61)(19, 52)(20, 65)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.68 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^2, Y1 * Y3^3, Y1^-1 * Y3^-3, (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-1 * Y3 * Y1^-2, Y2 * Y3 * Y2 * Y1^-3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 7, 29, 12, 34, 16, 38, 4, 26, 10, 32, 17, 39, 5, 27)(3, 25, 9, 31, 20, 42, 18, 40, 6, 28, 11, 33, 21, 43, 13, 35, 19, 41, 22, 44, 14, 36)(45, 67, 47, 69, 48, 70, 57, 79, 59, 81, 62, 84, 49, 71, 58, 80, 60, 82, 65, 87, 52, 74, 64, 86, 61, 83, 66, 88, 56, 78, 55, 77, 46, 68, 53, 75, 54, 76, 63, 85, 51, 73, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 47)(7, 45)(8, 61)(9, 63)(10, 51)(11, 53)(12, 46)(13, 62)(14, 65)(15, 49)(16, 52)(17, 56)(18, 58)(19, 50)(20, 66)(21, 64)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.71 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-2, Y1 * Y3^-3, (Y3^-1, Y1^-1), (R * Y2)^2, (Y1, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2 * Y3^2, Y1^-1 * Y3^-2 * Y1^-2 ] 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, 20, 42, 19, 41, 13, 35, 22, 44, 17, 39, 6, 28, 11, 33, 21, 43, 14, 36)(45, 67, 47, 69, 48, 70, 57, 79, 56, 78, 55, 77, 46, 68, 53, 75, 54, 76, 66, 88, 60, 82, 65, 87, 52, 74, 64, 86, 62, 84, 61, 83, 49, 71, 58, 80, 59, 81, 63, 85, 51, 73, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 56)(5, 59)(6, 47)(7, 45)(8, 62)(9, 66)(10, 60)(11, 53)(12, 46)(13, 55)(14, 63)(15, 51)(16, 52)(17, 58)(18, 49)(19, 50)(20, 61)(21, 64)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.69 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-2, Y3 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y1 * Y3^-5, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 16, 38, 18, 40, 20, 42, 12, 34, 13, 35, 4, 26, 5, 27)(3, 25, 8, 30, 11, 33, 17, 39, 19, 41, 21, 43, 22, 44, 14, 36, 15, 37, 6, 28, 9, 31)(45, 67, 47, 69, 51, 73, 55, 77, 60, 82, 63, 85, 64, 86, 66, 88, 57, 79, 59, 81, 49, 71, 53, 75, 46, 68, 52, 74, 54, 76, 61, 83, 62, 84, 65, 87, 56, 78, 58, 80, 48, 70, 50, 72) L = (1, 48)(2, 49)(3, 50)(4, 56)(5, 57)(6, 58)(7, 45)(8, 53)(9, 59)(10, 46)(11, 47)(12, 62)(13, 64)(14, 65)(15, 66)(16, 51)(17, 52)(18, 54)(19, 55)(20, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.99 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, Y3 * Y2^2, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3^5, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 13, 35, 17, 39, 21, 43, 16, 38, 15, 37, 7, 29, 5, 27)(3, 25, 8, 30, 6, 28, 10, 32, 14, 36, 18, 40, 22, 44, 20, 42, 19, 41, 12, 34, 11, 33)(45, 67, 47, 69, 51, 73, 56, 78, 60, 82, 64, 86, 61, 83, 62, 84, 53, 75, 54, 76, 46, 68, 52, 74, 49, 71, 55, 77, 59, 81, 63, 85, 65, 87, 66, 88, 57, 79, 58, 80, 48, 70, 50, 72) L = (1, 48)(2, 53)(3, 50)(4, 57)(5, 46)(6, 58)(7, 45)(8, 54)(9, 61)(10, 62)(11, 52)(12, 47)(13, 65)(14, 66)(15, 49)(16, 51)(17, 60)(18, 64)(19, 55)(20, 56)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.94 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^11, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 10, 32, 14, 36, 18, 40, 21, 43, 17, 39, 13, 35, 9, 31, 4, 26)(3, 25, 5, 27, 7, 29, 11, 33, 15, 37, 19, 41, 22, 44, 20, 42, 16, 38, 12, 34, 8, 30)(45, 67, 47, 69, 48, 70, 52, 74, 53, 75, 56, 78, 57, 79, 60, 82, 61, 83, 64, 86, 65, 87, 66, 88, 62, 84, 63, 85, 58, 80, 59, 81, 54, 76, 55, 77, 50, 72, 51, 73, 46, 68, 49, 71) L = (1, 46)(2, 50)(3, 49)(4, 45)(5, 51)(6, 54)(7, 55)(8, 47)(9, 48)(10, 58)(11, 59)(12, 52)(13, 53)(14, 62)(15, 63)(16, 56)(17, 57)(18, 65)(19, 66)(20, 60)(21, 61)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.101 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.78 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y2, Y1^-3 * Y3, (Y2^-1, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-2 * Y1^-2 * Y3^-1, Y1 * Y3^-4, Y2 * Y1 * Y2 * Y1^2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-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 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 19, 41, 15, 37, 18, 40, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 17, 39, 6, 28, 11, 33, 20, 42, 16, 38, 22, 44, 14, 36, 21, 43, 13, 35)(45, 67, 47, 69, 51, 73, 58, 80, 63, 85, 64, 86, 52, 74, 61, 83, 49, 71, 57, 79, 62, 84, 66, 88, 54, 76, 55, 77, 46, 68, 53, 75, 56, 78, 65, 87, 59, 81, 60, 82, 48, 70, 50, 72) L = (1, 48)(2, 54)(3, 50)(4, 59)(5, 52)(6, 60)(7, 45)(8, 63)(9, 55)(10, 62)(11, 66)(12, 46)(13, 61)(14, 47)(15, 56)(16, 65)(17, 64)(18, 49)(19, 51)(20, 58)(21, 53)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.98 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.79 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1, Y3^-1 * Y1^-3, (R * Y3)^2, (Y3^-1, Y1), (Y2^-1, Y1), (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^-1 * Y2 * Y1^-2 * Y2, Y2 * Y3^-2 * Y2 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 15, 37, 19, 41, 16, 38, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 20, 42, 14, 36, 21, 43, 17, 39, 22, 44, 18, 40, 6, 28, 11, 33, 13, 35)(45, 67, 47, 69, 51, 73, 58, 80, 63, 85, 66, 88, 54, 76, 55, 77, 46, 68, 53, 75, 56, 78, 65, 87, 60, 82, 62, 84, 49, 71, 57, 79, 52, 74, 64, 86, 59, 81, 61, 83, 48, 70, 50, 72) L = (1, 48)(2, 54)(3, 50)(4, 59)(5, 60)(6, 61)(7, 45)(8, 49)(9, 55)(10, 63)(11, 66)(12, 46)(13, 62)(14, 47)(15, 52)(16, 56)(17, 64)(18, 65)(19, 51)(20, 57)(21, 53)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.95 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.80 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y3 * Y2^2, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-5 * Y3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 16, 38, 13, 35, 4, 26, 7, 29, 11, 33, 19, 41, 14, 36, 5, 27)(3, 25, 9, 31, 17, 39, 21, 43, 15, 37, 6, 28, 10, 32, 18, 40, 22, 44, 20, 42, 12, 34)(45, 67, 47, 69, 51, 73, 54, 76, 46, 68, 53, 75, 55, 77, 62, 84, 52, 74, 61, 83, 63, 85, 66, 88, 60, 82, 65, 87, 58, 80, 64, 86, 57, 79, 59, 81, 49, 71, 56, 78, 48, 70, 50, 72) L = (1, 48)(2, 51)(3, 50)(4, 49)(5, 57)(6, 56)(7, 45)(8, 55)(9, 54)(10, 47)(11, 46)(12, 59)(13, 58)(14, 60)(15, 64)(16, 63)(17, 62)(18, 53)(19, 52)(20, 65)(21, 66)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.97 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y3 * Y2^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2), (R * Y2)^2, Y3^-1 * Y1^-5, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 16, 38, 15, 37, 7, 29, 4, 26, 10, 32, 18, 40, 14, 36, 5, 27)(3, 25, 9, 31, 17, 39, 22, 44, 21, 43, 13, 35, 6, 28, 11, 33, 19, 41, 20, 42, 12, 34)(45, 67, 47, 69, 51, 73, 57, 79, 49, 71, 56, 78, 59, 81, 65, 87, 58, 80, 64, 86, 60, 82, 66, 88, 62, 84, 63, 85, 52, 74, 61, 83, 54, 76, 55, 77, 46, 68, 53, 75, 48, 70, 50, 72) L = (1, 48)(2, 54)(3, 50)(4, 46)(5, 51)(6, 53)(7, 45)(8, 62)(9, 55)(10, 52)(11, 61)(12, 57)(13, 47)(14, 59)(15, 49)(16, 58)(17, 63)(18, 60)(19, 66)(20, 65)(21, 56)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.96 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y3^-1 * Y1 * Y3^-2, (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, (Y1, Y3), (R * Y2)^2, Y3^-1 * Y1^4, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2, Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 4, 26, 10, 32, 19, 41, 7, 29, 12, 34, 17, 39, 5, 27)(3, 25, 9, 31, 20, 42, 18, 40, 6, 28, 11, 33, 21, 43, 14, 36, 16, 38, 22, 44, 13, 35)(45, 67, 47, 69, 51, 73, 58, 80, 59, 81, 62, 84, 49, 71, 57, 79, 63, 85, 65, 87, 52, 74, 64, 86, 61, 83, 66, 88, 54, 76, 55, 77, 46, 68, 53, 75, 56, 78, 60, 82, 48, 70, 50, 72) L = (1, 48)(2, 54)(3, 50)(4, 56)(5, 59)(6, 60)(7, 45)(8, 63)(9, 55)(10, 61)(11, 66)(12, 46)(13, 62)(14, 47)(15, 51)(16, 53)(17, 52)(18, 58)(19, 49)(20, 65)(21, 57)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.93 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y2, Y2^-1 * Y3^-1 * Y2^-1, Y3^-3 * Y1^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3 * Y1^-2 * Y3, Y3^-1 * Y1^-4, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 7, 29, 12, 34, 16, 38, 4, 26, 10, 32, 18, 40, 5, 27)(3, 25, 9, 31, 20, 42, 17, 39, 14, 36, 22, 44, 19, 41, 6, 28, 11, 33, 21, 43, 13, 35)(45, 67, 47, 69, 51, 73, 58, 80, 54, 76, 55, 77, 46, 68, 53, 75, 56, 78, 66, 88, 62, 84, 65, 87, 52, 74, 64, 86, 60, 82, 63, 85, 49, 71, 57, 79, 59, 81, 61, 83, 48, 70, 50, 72) L = (1, 48)(2, 54)(3, 50)(4, 59)(5, 60)(6, 61)(7, 45)(8, 62)(9, 55)(10, 51)(11, 58)(12, 46)(13, 63)(14, 47)(15, 49)(16, 52)(17, 57)(18, 56)(19, 64)(20, 65)(21, 66)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.100 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y1^-1 * Y2)^2, Y3 * Y2^-2 * Y1^-1, (R * Y1)^2, Y3 * Y1^-3, Y2^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y2)^2, (Y3^-1, Y2^-1), (Y3^-1, Y1^-1), (R * Y3)^2, (Y2, Y1^-1), Y2 * Y3^2 * Y2 * Y3, Y3 * Y1^-1 * Y3^3, (Y1 * Y3)^11, Y1^-1 * Y3 * Y2^20 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 18, 40, 15, 37, 16, 38, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 19, 41, 13, 35, 20, 42, 22, 44, 17, 39, 21, 43, 14, 36, 6, 28, 11, 33)(45, 67, 47, 69, 52, 74, 63, 85, 54, 76, 64, 86, 59, 81, 61, 83, 51, 73, 58, 80, 49, 71, 55, 77, 46, 68, 53, 75, 48, 70, 57, 79, 62, 84, 66, 88, 60, 82, 65, 87, 56, 78, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 52)(6, 53)(7, 45)(8, 62)(9, 64)(10, 60)(11, 63)(12, 46)(13, 61)(14, 47)(15, 56)(16, 49)(17, 50)(18, 51)(19, 66)(20, 65)(21, 55)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.114 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2^-1, (R * Y1)^2, Y1^-2 * Y2^-2, Y2^-1 * Y3 * Y1 * Y2^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (Y3^-1, Y1), (Y3^-1, Y2^-1), (R * Y2)^2, (Y2^-1 * Y1^-1)^2, Y3^-1 * Y1^-1 * Y3^-3, Y2 * Y3^2 * Y2 * Y3, Y1^-1 * Y2^18 * Y3, (Y1^-1 * Y3)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 15, 37, 18, 40, 16, 38, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 6, 28, 11, 33, 19, 41, 17, 39, 21, 43, 22, 44, 13, 35, 20, 42, 14, 36)(45, 67, 47, 69, 54, 76, 64, 86, 60, 82, 66, 88, 59, 81, 61, 83, 51, 73, 55, 77, 46, 68, 53, 75, 49, 71, 58, 80, 48, 70, 57, 79, 62, 84, 65, 87, 56, 78, 63, 85, 52, 74, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 58)(7, 45)(8, 49)(9, 64)(10, 62)(11, 47)(12, 46)(13, 61)(14, 66)(15, 52)(16, 56)(17, 50)(18, 51)(19, 53)(20, 65)(21, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.112 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y3, Y2^-1), Y3^3 * Y1, (R * Y3)^2, (Y3^-1, Y2), (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1^-3, (Y2^-1 * Y3 * Y1^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 14, 36, 7, 29, 11, 33, 15, 37, 4, 26, 10, 32, 17, 39, 5, 27)(3, 25, 9, 31, 20, 42, 19, 41, 13, 35, 22, 44, 16, 38, 12, 34, 21, 43, 18, 40, 6, 28)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 64, 86, 58, 80, 63, 85, 51, 73, 57, 79, 55, 77, 66, 88, 59, 81, 60, 82, 48, 70, 56, 78, 54, 76, 65, 87, 61, 83, 62, 84, 49, 71, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 58)(5, 59)(6, 60)(7, 45)(8, 61)(9, 65)(10, 51)(11, 46)(12, 63)(13, 47)(14, 49)(15, 52)(16, 64)(17, 55)(18, 66)(19, 50)(20, 62)(21, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.115 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y3 * Y1^-1 * Y3^2, (Y3, Y1^-1), (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1^2, Y3 * Y1 * Y3 * Y1^2, Y1^-4 * Y3, (Y2 * Y3^-1 * Y1^-1)^2, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 4, 26, 9, 31, 18, 40, 7, 29, 11, 33, 17, 39, 5, 27)(3, 25, 6, 28, 10, 32, 20, 42, 12, 34, 16, 38, 21, 43, 14, 36, 19, 41, 22, 44, 13, 35)(45, 67, 47, 69, 49, 71, 57, 79, 61, 83, 66, 88, 55, 77, 63, 85, 51, 73, 58, 80, 62, 84, 65, 87, 53, 75, 60, 82, 48, 70, 56, 78, 59, 81, 64, 86, 52, 74, 54, 76, 46, 68, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 55)(5, 59)(6, 60)(7, 45)(8, 62)(9, 61)(10, 65)(11, 46)(12, 63)(13, 64)(14, 47)(15, 51)(16, 66)(17, 52)(18, 49)(19, 50)(20, 58)(21, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.118 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2 * Y3^-1, Y2 * Y1^-1 * Y2^-1 * Y3, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2^4 * Y1^-1 * Y2^2 * Y1^-1, Y1^11, (Y3^-1 * Y1^-1)^11, Y3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^2 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 13, 35, 15, 37, 20, 42, 22, 44, 17, 39, 9, 31, 11, 33, 4, 26)(3, 25, 7, 29, 12, 34, 5, 27, 8, 30, 14, 36, 19, 41, 21, 43, 16, 38, 18, 40, 10, 32)(45, 67, 47, 69, 53, 75, 60, 82, 64, 86, 58, 80, 50, 72, 56, 78, 48, 70, 54, 76, 61, 83, 65, 87, 59, 81, 52, 74, 46, 68, 51, 73, 55, 77, 62, 84, 66, 88, 63, 85, 57, 79, 49, 71) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 57)(7, 56)(8, 58)(9, 55)(10, 47)(11, 48)(12, 49)(13, 59)(14, 63)(15, 64)(16, 62)(17, 53)(18, 54)(19, 65)(20, 66)(21, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.116 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.89 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2, Y3^-1), (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2^-3, Y3^-1 * Y2 * Y3^-1 * Y2 * Y1, Y2 * Y3 * Y2 * Y3^2, Y1 * Y3^-5, (Y3 * Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 21, 43, 19, 41, 11, 33, 15, 37, 16, 38, 4, 26, 5, 27)(3, 25, 8, 30, 14, 36, 17, 39, 18, 40, 6, 28, 9, 31, 20, 42, 22, 44, 12, 34, 13, 35)(45, 67, 47, 69, 55, 77, 53, 75, 46, 68, 52, 74, 59, 81, 64, 86, 51, 73, 58, 80, 60, 82, 66, 88, 54, 76, 61, 83, 48, 70, 56, 78, 65, 87, 62, 84, 49, 71, 57, 79, 63, 85, 50, 72) L = (1, 48)(2, 49)(3, 56)(4, 59)(5, 60)(6, 61)(7, 45)(8, 57)(9, 62)(10, 46)(11, 65)(12, 64)(13, 66)(14, 47)(15, 63)(16, 55)(17, 52)(18, 58)(19, 54)(20, 50)(21, 51)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.113 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.90 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3 * Y2 * Y3^2 * Y2, Y2 * Y1 * Y2^3, Y1^-1 * Y3^-5 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 15, 37, 11, 33, 19, 41, 21, 43, 18, 40, 7, 29, 5, 27)(3, 25, 8, 30, 12, 34, 22, 44, 20, 42, 17, 39, 6, 28, 10, 32, 16, 38, 14, 36, 13, 35)(45, 67, 47, 69, 55, 77, 61, 83, 49, 71, 57, 79, 59, 81, 64, 86, 51, 73, 58, 80, 53, 75, 66, 88, 62, 84, 60, 82, 48, 70, 56, 78, 65, 87, 54, 76, 46, 68, 52, 74, 63, 85, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 46)(6, 60)(7, 45)(8, 66)(9, 55)(10, 58)(11, 65)(12, 64)(13, 52)(14, 47)(15, 63)(16, 57)(17, 54)(18, 49)(19, 62)(20, 50)(21, 51)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.119 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.91 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, (Y1^-1, Y2^-1), Y1^-1 * Y2 * Y3 * Y2, Y2^-2 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1^-4 * Y2^-1, Y2^18 * Y1^-2 * Y3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 14, 36, 4, 26, 7, 29, 11, 33, 20, 42, 16, 38, 5, 27)(3, 25, 9, 31, 19, 41, 17, 39, 6, 28, 10, 32, 13, 35, 21, 43, 22, 44, 15, 37, 12, 34)(45, 67, 47, 69, 55, 77, 65, 87, 62, 84, 61, 83, 49, 71, 56, 78, 51, 73, 57, 79, 52, 74, 63, 85, 60, 82, 59, 81, 48, 70, 54, 76, 46, 68, 53, 75, 64, 86, 66, 88, 58, 80, 50, 72) L = (1, 48)(2, 51)(3, 54)(4, 49)(5, 58)(6, 59)(7, 45)(8, 55)(9, 57)(10, 56)(11, 46)(12, 50)(13, 47)(14, 60)(15, 61)(16, 62)(17, 66)(18, 64)(19, 65)(20, 52)(21, 53)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.117 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.92 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2 * Y3 * Y2 * Y1, Y1 * Y2^2 * Y3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1), Y1^3 * Y2^-1 * Y1 * Y2^-1, (Y1^-1 * Y3^-1)^11, Y1^-27 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 12, 34, 7, 29, 4, 26, 10, 32, 19, 41, 17, 39, 5, 27)(3, 25, 9, 31, 16, 38, 21, 43, 22, 44, 15, 37, 13, 35, 6, 28, 11, 33, 20, 42, 14, 36)(45, 67, 47, 69, 56, 78, 66, 88, 63, 85, 55, 77, 46, 68, 53, 75, 51, 73, 59, 81, 61, 83, 64, 86, 52, 74, 60, 82, 48, 70, 57, 79, 49, 71, 58, 80, 62, 84, 65, 87, 54, 76, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 46)(5, 51)(6, 60)(7, 45)(8, 63)(9, 50)(10, 52)(11, 65)(12, 49)(13, 53)(14, 59)(15, 47)(16, 55)(17, 56)(18, 61)(19, 62)(20, 66)(21, 64)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.111 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.93 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^2 * Y2^-2, Y1^-3 * Y3^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2), Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y1^-1 * Y3^-3, Y3 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y1 * Y3^-1 * Y2^18 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 15, 37, 18, 40, 16, 38, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 19, 41, 14, 36, 20, 42, 22, 44, 17, 39, 21, 43, 13, 35, 6, 28, 11, 33)(45, 67, 47, 69, 52, 74, 63, 85, 56, 78, 64, 86, 62, 84, 61, 83, 48, 70, 57, 79, 49, 71, 55, 77, 46, 68, 53, 75, 51, 73, 58, 80, 59, 81, 66, 88, 60, 82, 65, 87, 54, 76, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 61)(7, 45)(8, 49)(9, 50)(10, 62)(11, 65)(12, 46)(13, 66)(14, 47)(15, 52)(16, 56)(17, 58)(18, 51)(19, 55)(20, 53)(21, 64)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.82 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.94 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y1^-2, Y3 * Y2^2 * Y1^-1, (Y3^-1, Y2), (Y2^-1, Y1^-1), Y2 * Y3 * Y2 * Y1^-1, (R * Y2)^2, (Y2^-1 * Y1^-1)^2, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^4, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 18, 40, 15, 37, 17, 39, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 6, 28, 11, 33, 19, 41, 16, 38, 21, 43, 22, 44, 14, 36, 20, 42, 13, 35)(45, 67, 47, 69, 56, 78, 64, 86, 61, 83, 66, 88, 62, 84, 60, 82, 48, 70, 55, 77, 46, 68, 53, 75, 49, 71, 57, 79, 51, 73, 58, 80, 59, 81, 65, 87, 54, 76, 63, 85, 52, 74, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 59)(5, 52)(6, 60)(7, 45)(8, 62)(9, 63)(10, 61)(11, 65)(12, 46)(13, 50)(14, 47)(15, 56)(16, 58)(17, 49)(18, 51)(19, 66)(20, 53)(21, 64)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.76 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.95 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, Y3^-2 * Y1 * Y3^-1, (Y3, Y1), (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y1^-1 * Y3 * Y1^-3, Y3 * Y1^2 * Y3 * Y1, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 14, 36, 4, 26, 10, 32, 18, 40, 7, 29, 11, 33, 16, 38, 5, 27)(3, 25, 9, 31, 20, 42, 15, 37, 12, 34, 21, 43, 19, 41, 13, 35, 22, 44, 17, 39, 6, 28)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 64, 86, 58, 80, 59, 81, 48, 70, 56, 78, 54, 76, 65, 87, 62, 84, 63, 85, 51, 73, 57, 79, 55, 77, 66, 88, 60, 82, 61, 83, 49, 71, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 55)(5, 58)(6, 59)(7, 45)(8, 62)(9, 65)(10, 60)(11, 46)(12, 66)(13, 47)(14, 51)(15, 57)(16, 52)(17, 64)(18, 49)(19, 50)(20, 63)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.79 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y3^-1 * Y1^-1 * Y3^-2, Y3^-3 * Y1^-1, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1^-3, Y2 * Y3^2 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 7, 29, 11, 33, 16, 38, 4, 26, 9, 31, 18, 40, 5, 27)(3, 25, 6, 28, 10, 32, 20, 42, 14, 36, 19, 41, 22, 44, 12, 34, 17, 39, 21, 43, 13, 35)(45, 67, 47, 69, 49, 71, 57, 79, 62, 84, 65, 87, 53, 75, 61, 83, 48, 70, 56, 78, 60, 82, 66, 88, 55, 77, 63, 85, 51, 73, 58, 80, 59, 81, 64, 86, 52, 74, 54, 76, 46, 68, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 60)(6, 61)(7, 45)(8, 62)(9, 51)(10, 65)(11, 46)(12, 64)(13, 66)(14, 47)(15, 49)(16, 52)(17, 58)(18, 55)(19, 50)(20, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.81 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^-1 * Y1 * Y2^-1 * Y1^2, Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^5 * Y1, Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 9, 31, 15, 37, 20, 42, 22, 44, 18, 40, 13, 35, 11, 33, 4, 26)(3, 25, 7, 29, 14, 36, 16, 38, 21, 43, 19, 41, 17, 39, 12, 34, 5, 27, 8, 30, 10, 32)(45, 67, 47, 69, 53, 75, 60, 82, 66, 88, 61, 83, 55, 77, 52, 74, 46, 68, 51, 73, 59, 81, 65, 87, 62, 84, 56, 78, 48, 70, 54, 76, 50, 72, 58, 80, 64, 86, 63, 85, 57, 79, 49, 71) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 53)(7, 58)(8, 54)(9, 59)(10, 47)(11, 48)(12, 49)(13, 55)(14, 60)(15, 64)(16, 65)(17, 56)(18, 57)(19, 61)(20, 66)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.80 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.98 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (Y2, Y3), Y2^2 * Y1 * Y3^2, Y3^-1 * Y2^2 * Y3^-2, Y1^-1 * Y2^4 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 15, 37, 19, 41, 11, 33, 21, 43, 18, 40, 7, 29, 5, 27)(3, 25, 8, 30, 12, 34, 20, 42, 17, 39, 6, 28, 10, 32, 16, 38, 22, 44, 14, 36, 13, 35)(45, 67, 47, 69, 55, 77, 54, 76, 46, 68, 52, 74, 65, 87, 60, 82, 48, 70, 56, 78, 62, 84, 66, 88, 53, 75, 64, 86, 51, 73, 58, 80, 59, 81, 61, 83, 49, 71, 57, 79, 63, 85, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 46)(6, 60)(7, 45)(8, 64)(9, 63)(10, 66)(11, 62)(12, 61)(13, 52)(14, 47)(15, 55)(16, 58)(17, 54)(18, 49)(19, 65)(20, 50)(21, 51)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.78 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.99 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y2, Y3^-1), Y2^2 * Y3^-3, Y1 * Y2^4, Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-2 * Y1 * Y3^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 21, 43, 11, 33, 19, 41, 15, 37, 16, 38, 4, 26, 5, 27)(3, 25, 8, 30, 14, 36, 22, 44, 17, 39, 18, 40, 6, 28, 9, 31, 20, 42, 12, 34, 13, 35)(45, 67, 47, 69, 55, 77, 62, 84, 49, 71, 57, 79, 65, 87, 61, 83, 48, 70, 56, 78, 54, 76, 66, 88, 60, 82, 64, 86, 51, 73, 58, 80, 59, 81, 53, 75, 46, 68, 52, 74, 63, 85, 50, 72) L = (1, 48)(2, 49)(3, 56)(4, 59)(5, 60)(6, 61)(7, 45)(8, 57)(9, 62)(10, 46)(11, 54)(12, 53)(13, 64)(14, 47)(15, 55)(16, 63)(17, 58)(18, 66)(19, 65)(20, 50)(21, 51)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.75 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y2^-1 * Y1^-4 * 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^-2, Y2^18 * Y1^-2 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 16, 38, 7, 29, 4, 26, 10, 32, 20, 42, 14, 36, 5, 27)(3, 25, 9, 31, 19, 41, 15, 37, 6, 28, 11, 33, 12, 34, 21, 43, 22, 44, 17, 39, 13, 35)(45, 67, 47, 69, 54, 76, 65, 87, 62, 84, 59, 81, 49, 71, 57, 79, 48, 70, 56, 78, 52, 74, 63, 85, 58, 80, 61, 83, 51, 73, 55, 77, 46, 68, 53, 75, 64, 86, 66, 88, 60, 82, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 46)(5, 51)(6, 57)(7, 45)(8, 64)(9, 65)(10, 52)(11, 47)(12, 53)(13, 55)(14, 60)(15, 61)(16, 49)(17, 50)(18, 58)(19, 66)(20, 62)(21, 63)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.83 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y2 * Y3^-1 * Y2 * Y1, Y2 * Y1 * Y3^-1 * Y2, Y1 * Y2 * Y3^-1 * Y2, (Y1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^4 * Y2^-2, (Y3 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 12, 34, 4, 26, 7, 29, 11, 33, 20, 42, 16, 38, 5, 27)(3, 25, 9, 31, 17, 39, 21, 43, 22, 44, 13, 35, 15, 37, 6, 28, 10, 32, 19, 41, 14, 36)(45, 67, 47, 69, 56, 78, 66, 88, 64, 86, 54, 76, 46, 68, 53, 75, 48, 70, 57, 79, 60, 82, 63, 85, 52, 74, 61, 83, 51, 73, 59, 81, 49, 71, 58, 80, 62, 84, 65, 87, 55, 77, 50, 72) L = (1, 48)(2, 51)(3, 57)(4, 49)(5, 56)(6, 53)(7, 45)(8, 55)(9, 59)(10, 61)(11, 46)(12, 60)(13, 58)(14, 66)(15, 47)(16, 62)(17, 50)(18, 64)(19, 65)(20, 52)(21, 54)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.77 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-2, Y1 * Y3^-3, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y1^2 * Y2 * Y3^-1, Y3 * Y1^-1 * Y2^-2 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^11, Y1^22, Y2^-1 * Y3^2 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 4, 26, 10, 32, 19, 41, 7, 29, 12, 34, 17, 39, 5, 27)(3, 25, 9, 31, 16, 38, 21, 43, 13, 35, 20, 42, 22, 44, 14, 36, 18, 40, 6, 28, 11, 33)(45, 67, 47, 69, 52, 74, 60, 82, 48, 70, 57, 79, 63, 85, 66, 88, 56, 78, 62, 84, 49, 71, 55, 77, 46, 68, 53, 75, 59, 81, 65, 87, 54, 76, 64, 86, 51, 73, 58, 80, 61, 83, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 56)(5, 59)(6, 60)(7, 45)(8, 63)(9, 64)(10, 61)(11, 65)(12, 46)(13, 62)(14, 47)(15, 51)(16, 66)(17, 52)(18, 53)(19, 49)(20, 50)(21, 58)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.122 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.103 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y1^-1 * Y3^-2, (R * Y2)^2, (Y2^-1, Y3^-1), Y1^-2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^3 * Y3^-2, Y2^-2 * Y3^-1 * Y1 * Y3^-1, Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y2^-2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 7, 29, 12, 34, 18, 40, 4, 26, 10, 32, 13, 35, 5, 27)(3, 25, 9, 31, 6, 28, 11, 33, 16, 38, 22, 44, 20, 42, 14, 36, 21, 43, 19, 41, 15, 37)(45, 67, 47, 69, 57, 79, 63, 85, 48, 70, 58, 80, 56, 78, 66, 88, 61, 83, 55, 77, 46, 68, 53, 75, 49, 71, 59, 81, 54, 76, 65, 87, 62, 84, 64, 86, 51, 73, 60, 82, 52, 74, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 62)(6, 63)(7, 45)(8, 57)(9, 65)(10, 51)(11, 59)(12, 46)(13, 56)(14, 55)(15, 64)(16, 47)(17, 49)(18, 52)(19, 66)(20, 50)(21, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.121 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.104 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y1^-1, Y1 * Y2^-2, (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^5 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 12, 34, 17, 39, 20, 42, 15, 37, 13, 35, 7, 29, 5, 27)(3, 25, 8, 30, 10, 32, 16, 38, 18, 40, 22, 44, 21, 43, 19, 41, 14, 36, 11, 33, 6, 28)(45, 67, 47, 69, 46, 68, 52, 74, 48, 70, 54, 76, 53, 75, 60, 82, 56, 78, 62, 84, 61, 83, 66, 88, 64, 86, 65, 87, 59, 81, 63, 85, 57, 79, 58, 80, 51, 73, 55, 77, 49, 71, 50, 72) L = (1, 48)(2, 53)(3, 54)(4, 56)(5, 46)(6, 52)(7, 45)(8, 60)(9, 61)(10, 62)(11, 47)(12, 64)(13, 49)(14, 50)(15, 51)(16, 66)(17, 59)(18, 65)(19, 55)(20, 57)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.123 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y2 * Y1 * Y2, (Y2^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-5 * Y1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 9, 31, 15, 37, 17, 39, 20, 42, 12, 34, 13, 35, 4, 26, 5, 27)(3, 25, 6, 28, 8, 30, 14, 36, 16, 38, 21, 43, 22, 44, 18, 40, 19, 41, 10, 32, 11, 33)(45, 67, 47, 69, 49, 71, 55, 77, 48, 70, 54, 76, 57, 79, 63, 85, 56, 78, 62, 84, 64, 86, 66, 88, 61, 83, 65, 87, 59, 81, 60, 82, 53, 75, 58, 80, 51, 73, 52, 74, 46, 68, 50, 72) L = (1, 48)(2, 49)(3, 54)(4, 56)(5, 57)(6, 55)(7, 45)(8, 47)(9, 46)(10, 62)(11, 63)(12, 61)(13, 64)(14, 50)(15, 51)(16, 52)(17, 53)(18, 65)(19, 66)(20, 59)(21, 58)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.124 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-1, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y2, Y3^-1), (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3, Y2^-2 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 20, 42, 16, 38, 4, 26, 7, 29, 11, 33, 12, 34, 18, 40, 5, 27)(3, 25, 9, 31, 19, 41, 6, 28, 10, 32, 13, 35, 15, 37, 22, 44, 17, 39, 21, 43, 14, 36)(45, 67, 47, 69, 56, 78, 61, 83, 48, 70, 57, 79, 52, 74, 63, 85, 49, 71, 58, 80, 55, 77, 66, 88, 60, 82, 54, 76, 46, 68, 53, 75, 62, 84, 65, 87, 51, 73, 59, 81, 64, 86, 50, 72) L = (1, 48)(2, 51)(3, 57)(4, 49)(5, 60)(6, 61)(7, 45)(8, 55)(9, 59)(10, 65)(11, 46)(12, 52)(13, 58)(14, 54)(15, 47)(16, 62)(17, 63)(18, 64)(19, 66)(20, 56)(21, 50)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.128 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.107 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y3^-1, (Y2, Y3), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y2^-1 * Y1^3 * Y2^-1, Y1^2 * Y3 * Y2^2, Y2 * Y3^-1 * Y2^3, Y3^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 12, 34, 19, 41, 7, 29, 4, 26, 10, 32, 20, 42, 17, 39, 5, 27)(3, 25, 9, 31, 21, 43, 16, 38, 22, 44, 15, 37, 13, 35, 18, 40, 6, 28, 11, 33, 14, 36)(45, 67, 47, 69, 56, 78, 60, 82, 48, 70, 57, 79, 61, 83, 55, 77, 46, 68, 53, 75, 63, 85, 66, 88, 54, 76, 62, 84, 49, 71, 58, 80, 52, 74, 65, 87, 51, 73, 59, 81, 64, 86, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 46)(5, 51)(6, 60)(7, 45)(8, 64)(9, 62)(10, 52)(11, 66)(12, 61)(13, 53)(14, 59)(15, 47)(16, 55)(17, 63)(18, 65)(19, 49)(20, 56)(21, 50)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.127 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.108 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y3^-1, Y2^-1 * Y3 * Y2^-3, (R * Y2 * Y3^-1)^2, Y2 * Y3^5 * Y2, (Y3^-1 * Y1^-1)^11, Y3 * Y1 * Y2 * 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 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 21, 43, 13, 35, 9, 31, 17, 39, 19, 41, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 20, 42, 12, 34, 5, 27, 8, 30, 16, 38, 22, 44, 18, 40, 10, 32)(45, 67, 47, 69, 53, 75, 52, 74, 46, 68, 51, 73, 61, 83, 60, 82, 50, 72, 59, 81, 63, 85, 66, 88, 58, 80, 64, 86, 55, 77, 62, 84, 65, 87, 56, 78, 48, 70, 54, 76, 57, 79, 49, 71) 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, 53)(14, 65)(15, 64)(16, 66)(17, 63)(18, 54)(19, 55)(20, 56)(21, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.120 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1, Y1 * Y2 * Y3 * Y2, (Y3^-1, Y2^-1), (Y1^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3^-2 * Y2, Y3^-1 * Y1 * Y3^-3, Y3^-1 * Y1^-1 * Y2^2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 19, 41, 17, 39, 13, 35, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 20, 42, 14, 36, 6, 28, 11, 33, 21, 43, 18, 40, 16, 38, 22, 44, 15, 37)(45, 67, 47, 69, 57, 79, 62, 84, 48, 70, 58, 80, 49, 71, 59, 81, 61, 83, 65, 87, 52, 74, 64, 86, 56, 78, 66, 88, 63, 85, 55, 77, 46, 68, 53, 75, 51, 73, 60, 82, 54, 76, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 52)(6, 62)(7, 45)(8, 63)(9, 50)(10, 57)(11, 60)(12, 46)(13, 49)(14, 65)(15, 64)(16, 47)(17, 56)(18, 59)(19, 51)(20, 55)(21, 66)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.125 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, (Y2, Y1^-1), (Y3, Y1^-1), Y1^-3 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^2 * Y3 * Y1^-1, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1, Y3^-1 * Y1^-1 * Y3^-3, (Y1 * Y3^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 15, 37, 19, 41, 16, 38, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 20, 42, 14, 36, 17, 39, 22, 44, 18, 40, 6, 28, 11, 33, 21, 43, 13, 35)(45, 67, 47, 69, 56, 78, 61, 83, 48, 70, 55, 77, 46, 68, 53, 75, 59, 81, 66, 88, 54, 76, 65, 87, 52, 74, 64, 86, 63, 85, 62, 84, 49, 71, 57, 79, 51, 73, 58, 80, 60, 82, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 59)(5, 60)(6, 61)(7, 45)(8, 49)(9, 65)(10, 63)(11, 66)(12, 46)(13, 50)(14, 47)(15, 52)(16, 56)(17, 53)(18, 58)(19, 51)(20, 57)(21, 62)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.126 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-2, Y1 * Y3^3, (Y2^-1, Y1^-1), (R * Y1)^2, (Y2^-1, Y3), (R * Y2)^2, (R * Y3)^2, Y2 * Y1^2 * Y3 * Y2, Y2^2 * Y3 * Y1^2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y1^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 7, 29, 12, 34, 16, 38, 4, 26, 10, 32, 18, 40, 5, 27)(3, 25, 9, 31, 20, 42, 22, 44, 14, 36, 17, 39, 21, 43, 13, 35, 19, 41, 6, 28, 11, 33)(45, 67, 47, 69, 52, 74, 64, 86, 51, 73, 58, 80, 60, 82, 65, 87, 54, 76, 63, 85, 49, 71, 55, 77, 46, 68, 53, 75, 59, 81, 66, 88, 56, 78, 61, 83, 48, 70, 57, 79, 62, 84, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 60)(6, 61)(7, 45)(8, 62)(9, 63)(10, 51)(11, 65)(12, 46)(13, 66)(14, 47)(15, 49)(16, 52)(17, 53)(18, 56)(19, 58)(20, 50)(21, 64)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.92 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y1, Y1^-1 * Y2^-2 * Y1^-1, (Y1 * Y2)^2, (Y2^-1, Y1), (R * Y2)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, Y1 * Y3^-1 * Y2^-2 * Y1, Y1^-1 * Y3 * Y2^2 * Y1^-1, Y2^18 * Y3^-1, (Y1^-1 * Y3^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 4, 26, 10, 32, 19, 41, 7, 29, 12, 34, 13, 35, 5, 27)(3, 25, 9, 31, 6, 28, 11, 33, 14, 36, 21, 43, 18, 40, 16, 38, 22, 44, 20, 42, 15, 37)(45, 67, 47, 69, 57, 79, 64, 86, 51, 73, 60, 82, 54, 76, 65, 87, 61, 83, 55, 77, 46, 68, 53, 75, 49, 71, 59, 81, 56, 78, 66, 88, 63, 85, 62, 84, 48, 70, 58, 80, 52, 74, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 56)(5, 61)(6, 62)(7, 45)(8, 63)(9, 65)(10, 57)(11, 60)(12, 46)(13, 52)(14, 66)(15, 55)(16, 47)(17, 51)(18, 59)(19, 49)(20, 50)(21, 64)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.85 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y1^-1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (R * Y2)^2, Y1 * Y3^-5, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 9, 31, 15, 37, 17, 39, 20, 42, 12, 34, 13, 35, 4, 26, 5, 27)(3, 25, 8, 30, 11, 33, 16, 38, 19, 41, 22, 44, 21, 43, 18, 40, 14, 36, 10, 32, 6, 28)(45, 67, 47, 69, 46, 68, 52, 74, 51, 73, 55, 77, 53, 75, 60, 82, 59, 81, 63, 85, 61, 83, 66, 88, 64, 86, 65, 87, 56, 78, 62, 84, 57, 79, 58, 80, 48, 70, 54, 76, 49, 71, 50, 72) L = (1, 48)(2, 49)(3, 54)(4, 56)(5, 57)(6, 58)(7, 45)(8, 50)(9, 46)(10, 62)(11, 47)(12, 61)(13, 64)(14, 65)(15, 51)(16, 52)(17, 53)(18, 66)(19, 55)(20, 59)(21, 63)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.89 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y1 * Y2^2, (Y2^-1, Y3), Y1^-1 * Y2 * Y3 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y3^-5, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 8, 30, 12, 34, 16, 38, 20, 42, 15, 37, 14, 36, 7, 29, 5, 27)(3, 25, 6, 28, 9, 31, 13, 35, 17, 39, 21, 43, 22, 44, 19, 41, 18, 40, 11, 33, 10, 32)(45, 67, 47, 69, 49, 71, 54, 76, 51, 73, 55, 77, 58, 80, 62, 84, 59, 81, 63, 85, 64, 86, 66, 88, 60, 82, 65, 87, 56, 78, 61, 83, 52, 74, 57, 79, 48, 70, 53, 75, 46, 68, 50, 72) L = (1, 48)(2, 52)(3, 53)(4, 56)(5, 46)(6, 57)(7, 45)(8, 60)(9, 61)(10, 50)(11, 47)(12, 64)(13, 65)(14, 49)(15, 51)(16, 59)(17, 66)(18, 54)(19, 55)(20, 58)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.84 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2, Y3), (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1, Y3 * Y2^4, Y2^2 * Y1^3, (Y3^-1 * Y1^-1)^11, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 20, 42, 19, 41, 7, 29, 4, 26, 10, 32, 12, 34, 17, 39, 5, 27)(3, 25, 9, 31, 18, 40, 6, 28, 11, 33, 15, 37, 13, 35, 22, 44, 21, 43, 16, 38, 14, 36)(45, 67, 47, 69, 56, 78, 65, 87, 51, 73, 59, 81, 52, 74, 62, 84, 49, 71, 58, 80, 54, 76, 66, 88, 63, 85, 55, 77, 46, 68, 53, 75, 61, 83, 60, 82, 48, 70, 57, 79, 64, 86, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 46)(5, 51)(6, 60)(7, 45)(8, 56)(9, 66)(10, 52)(11, 58)(12, 64)(13, 53)(14, 59)(15, 47)(16, 55)(17, 63)(18, 65)(19, 49)(20, 61)(21, 50)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.86 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y3, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (Y3^-1, Y2), (R * Y3)^2, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y2^4, Y1^-2 * Y2 * Y1^-1 * Y2, Y1^2 * Y2^2 * Y3^-1, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 12, 34, 16, 38, 4, 26, 7, 29, 11, 33, 20, 42, 18, 40, 5, 27)(3, 25, 9, 31, 17, 39, 21, 43, 22, 44, 13, 35, 15, 37, 19, 41, 6, 28, 10, 32, 14, 36)(45, 67, 47, 69, 56, 78, 65, 87, 51, 73, 59, 81, 62, 84, 54, 76, 46, 68, 53, 75, 60, 82, 66, 88, 55, 77, 63, 85, 49, 71, 58, 80, 52, 74, 61, 83, 48, 70, 57, 79, 64, 86, 50, 72) L = (1, 48)(2, 51)(3, 57)(4, 49)(5, 60)(6, 61)(7, 45)(8, 55)(9, 59)(10, 65)(11, 46)(12, 64)(13, 58)(14, 66)(15, 47)(16, 62)(17, 63)(18, 56)(19, 53)(20, 52)(21, 50)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.88 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y2^2 * Y3 * Y2^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^2 * Y3 * Y1 * Y2^-1 * Y1, Y1^3 * Y3 * Y2^-2 * Y1, Y2^2 * Y3^-5, Y1^3 * Y2^2 * Y3^3, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 18, 40, 9, 31, 13, 35, 17, 39, 20, 42, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 22, 44, 21, 43, 12, 34, 5, 27, 8, 30, 16, 38, 19, 41, 10, 32)(45, 67, 47, 69, 53, 75, 56, 78, 48, 70, 54, 76, 62, 84, 65, 87, 55, 77, 63, 85, 58, 80, 66, 88, 64, 86, 60, 82, 50, 72, 59, 81, 61, 83, 52, 74, 46, 68, 51, 73, 57, 79, 49, 71) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 58)(7, 59)(8, 60)(9, 57)(10, 47)(11, 48)(12, 49)(13, 61)(14, 62)(15, 66)(16, 63)(17, 64)(18, 53)(19, 54)(20, 55)(21, 56)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.91 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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 * Y3^-1, Y1^2 * Y3 * Y1, Y2^-1 * Y1^-1 * Y3 * Y2^-1, (R * Y2)^2, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (Y3, Y2), Y1^-1 * Y2^2 * Y3^2, Y3^-1 * Y1^-1 * Y3^-3, Y3 * Y2 * Y1^-1 * Y3 * Y2, (Y3 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 12, 34, 17, 39, 19, 41, 13, 35, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 20, 42, 16, 38, 6, 28, 11, 33, 21, 43, 18, 40, 14, 36, 22, 44, 15, 37)(45, 67, 47, 69, 57, 79, 62, 84, 51, 73, 60, 82, 49, 71, 59, 81, 63, 85, 65, 87, 52, 74, 64, 86, 54, 76, 66, 88, 61, 83, 55, 77, 46, 68, 53, 75, 48, 70, 58, 80, 56, 78, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 57)(6, 53)(7, 45)(8, 49)(9, 66)(10, 63)(11, 64)(12, 46)(13, 56)(14, 55)(15, 62)(16, 47)(17, 52)(18, 50)(19, 51)(20, 59)(21, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.87 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1^-1 * Y3^-1 * Y2, Y3 * Y1^-3, (Y3^-1, Y2^-1), (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^3, Y2^3 * Y3 * Y2, (Y1 * Y3)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 19, 41, 15, 37, 17, 39, 7, 29, 12, 34, 5, 27)(3, 25, 9, 31, 20, 42, 13, 35, 18, 40, 22, 44, 16, 38, 6, 28, 11, 33, 21, 43, 14, 36)(45, 67, 47, 69, 54, 76, 62, 84, 51, 73, 55, 77, 46, 68, 53, 75, 63, 85, 66, 88, 56, 78, 65, 87, 52, 74, 64, 86, 59, 81, 60, 82, 49, 71, 58, 80, 48, 70, 57, 79, 61, 83, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 59)(5, 52)(6, 58)(7, 45)(8, 63)(9, 62)(10, 61)(11, 47)(12, 46)(13, 60)(14, 64)(15, 56)(16, 65)(17, 49)(18, 50)(19, 51)(20, 66)(21, 53)(22, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.90 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.120 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, (Y1^-1 * Y2)^2, Y2^-2 * Y1^2, (R * Y1)^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-2 * Y1^-3 * Y3, Y2^-3 * Y3 * Y2^-1 * Y1^-1, Y2^6 * Y3, Y1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 14, 36, 4, 26, 7, 29, 11, 33, 21, 43, 16, 38, 5, 27)(3, 25, 9, 31, 20, 42, 15, 37, 18, 40, 12, 34, 13, 35, 22, 44, 17, 39, 6, 28, 10, 32)(45, 67, 47, 69, 52, 74, 64, 86, 58, 80, 62, 84, 51, 73, 57, 79, 65, 87, 61, 83, 49, 71, 54, 76, 46, 68, 53, 75, 63, 85, 59, 81, 48, 70, 56, 78, 55, 77, 66, 88, 60, 82, 50, 72) L = (1, 48)(2, 51)(3, 56)(4, 49)(5, 58)(6, 59)(7, 45)(8, 55)(9, 57)(10, 62)(11, 46)(12, 54)(13, 47)(14, 60)(15, 61)(16, 63)(17, 64)(18, 50)(19, 65)(20, 66)(21, 52)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.108 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.121 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-1, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (R * Y2)^2, Y2^2 * Y1^2, (R * Y3)^2, (Y2, Y3), Y2^2 * Y3 * Y1 * Y3, Y1^4 * Y3 * Y1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-2, Y2^-10 * Y1, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 17, 39, 7, 29, 4, 26, 10, 32, 20, 42, 12, 34, 5, 27)(3, 25, 9, 31, 6, 28, 11, 33, 21, 43, 15, 37, 13, 35, 18, 40, 16, 38, 22, 44, 14, 36)(45, 67, 47, 69, 56, 78, 66, 88, 54, 76, 62, 84, 51, 73, 59, 81, 63, 85, 55, 77, 46, 68, 53, 75, 49, 71, 58, 80, 64, 86, 60, 82, 48, 70, 57, 79, 61, 83, 65, 87, 52, 74, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 46)(5, 51)(6, 60)(7, 45)(8, 64)(9, 62)(10, 52)(11, 66)(12, 61)(13, 53)(14, 59)(15, 47)(16, 55)(17, 49)(18, 50)(19, 56)(20, 63)(21, 58)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.103 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.122 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y1), Y1^2 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y2)^2, Y3^-3 * Y1^2, Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 11, 33, 14, 36, 19, 41, 15, 37, 4, 26, 10, 32, 5, 27)(3, 25, 9, 31, 18, 40, 13, 35, 20, 42, 21, 43, 22, 44, 16, 38, 12, 34, 17, 39, 6, 28)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 62, 84, 51, 73, 57, 79, 55, 77, 64, 86, 58, 80, 65, 87, 63, 85, 66, 88, 59, 81, 60, 82, 48, 70, 56, 78, 54, 76, 61, 83, 49, 71, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 58)(5, 59)(6, 60)(7, 45)(8, 49)(9, 61)(10, 63)(11, 46)(12, 65)(13, 47)(14, 52)(15, 55)(16, 64)(17, 66)(18, 50)(19, 51)(20, 53)(21, 62)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.102 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.123 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-2, (Y3, Y1), Y1^-2 * Y3 * Y1^-1, (Y3, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-3 * Y1^-2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 9, 31, 19, 41, 15, 37, 17, 39, 7, 29, 11, 33, 5, 27)(3, 25, 6, 28, 10, 32, 12, 34, 16, 38, 20, 42, 21, 43, 22, 44, 14, 36, 18, 40, 13, 35)(45, 67, 47, 69, 49, 71, 57, 79, 55, 77, 62, 84, 51, 73, 58, 80, 61, 83, 66, 88, 59, 81, 65, 87, 63, 85, 64, 86, 53, 75, 60, 82, 48, 70, 56, 78, 52, 74, 54, 76, 46, 68, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 52)(6, 60)(7, 45)(8, 63)(9, 61)(10, 64)(11, 46)(12, 65)(13, 54)(14, 47)(15, 55)(16, 66)(17, 49)(18, 50)(19, 51)(20, 58)(21, 62)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.104 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.124 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y1^-1 * Y2^-1 * Y3 * Y2^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-3, Y1^-1 * Y3 * Y2^20 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 17, 39, 19, 41, 21, 43, 15, 37, 11, 33, 4, 26, 5, 27)(3, 25, 8, 30, 14, 36, 6, 28, 9, 31, 16, 38, 18, 40, 22, 44, 20, 42, 12, 34, 13, 35)(45, 67, 47, 69, 55, 77, 64, 86, 63, 85, 60, 82, 51, 73, 58, 80, 49, 71, 57, 79, 59, 81, 66, 88, 61, 83, 53, 75, 46, 68, 52, 74, 48, 70, 56, 78, 65, 87, 62, 84, 54, 76, 50, 72) L = (1, 48)(2, 49)(3, 56)(4, 59)(5, 55)(6, 52)(7, 45)(8, 57)(9, 58)(10, 46)(11, 65)(12, 66)(13, 64)(14, 47)(15, 63)(16, 50)(17, 51)(18, 53)(19, 54)(20, 62)(21, 61)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.105 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.125 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, Y2^-1), Y1 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y3 * Y1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^4 * Y2^2, Y2^18 * Y3^-2 * Y1^-1, (Y1^-1 * Y3^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 13, 35, 19, 41, 21, 43, 17, 39, 15, 37, 7, 29, 5, 27)(3, 25, 8, 30, 11, 33, 18, 40, 20, 42, 22, 44, 16, 38, 14, 36, 6, 28, 10, 32, 12, 34)(45, 67, 47, 69, 53, 75, 62, 84, 65, 87, 60, 82, 51, 73, 54, 76, 46, 68, 52, 74, 57, 79, 64, 86, 61, 83, 58, 80, 49, 71, 56, 78, 48, 70, 55, 77, 63, 85, 66, 88, 59, 81, 50, 72) L = (1, 48)(2, 53)(3, 55)(4, 57)(5, 46)(6, 56)(7, 45)(8, 62)(9, 63)(10, 47)(11, 64)(12, 52)(13, 65)(14, 54)(15, 49)(16, 50)(17, 51)(18, 66)(19, 61)(20, 60)(21, 59)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.109 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y1^-1, Y2^-1), Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y2)^2, Y3^-3 * Y1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3 * Y2^-1, Y1 * Y3^2 * Y1^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2^20 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 4, 26, 10, 32, 13, 35, 7, 29, 12, 34, 19, 41, 5, 27)(3, 25, 9, 31, 20, 42, 22, 44, 14, 36, 6, 28, 11, 33, 16, 38, 21, 43, 18, 40, 15, 37)(45, 67, 47, 69, 57, 79, 55, 77, 46, 68, 53, 75, 51, 73, 60, 82, 52, 74, 64, 86, 56, 78, 65, 87, 61, 83, 66, 88, 63, 85, 62, 84, 48, 70, 58, 80, 49, 71, 59, 81, 54, 76, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 56)(5, 61)(6, 62)(7, 45)(8, 57)(9, 50)(10, 63)(11, 59)(12, 46)(13, 49)(14, 65)(15, 66)(16, 47)(17, 51)(18, 64)(19, 52)(20, 55)(21, 53)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.110 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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), Y2^-1 * Y1 * Y2^-1 * Y3^-1, (Y2, Y3^-1), Y3 * Y2^2 * Y1^-1, Y1 * Y3^3, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y3 * Y1^-1, (R * Y2)^2, Y1 * Y3^-2 * Y1^2, Y2^4 * Y1, (Y3^-1 * Y2 * Y1^-1)^2, (Y3^-1 * Y1)^11, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 15, 37, 7, 29, 12, 34, 16, 38, 4, 26, 10, 32, 18, 40, 5, 27)(3, 25, 9, 31, 17, 39, 21, 43, 14, 36, 19, 41, 6, 28, 11, 33, 20, 42, 22, 44, 13, 35)(45, 67, 47, 69, 56, 78, 63, 85, 49, 71, 57, 79, 51, 73, 58, 80, 62, 84, 66, 88, 59, 81, 65, 87, 54, 76, 64, 86, 52, 74, 61, 83, 48, 70, 55, 77, 46, 68, 53, 75, 60, 82, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 59)(5, 60)(6, 61)(7, 45)(8, 62)(9, 64)(10, 51)(11, 65)(12, 46)(13, 50)(14, 47)(15, 49)(16, 52)(17, 66)(18, 56)(19, 53)(20, 58)(21, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.107 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2, Y1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y1^-3 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-3 * Y1, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 13, 35, 18, 40, 20, 42, 9, 31, 17, 39, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 12, 34, 5, 27, 8, 30, 16, 38, 19, 41, 22, 44, 21, 43, 10, 32)(45, 67, 47, 69, 53, 75, 63, 85, 58, 80, 56, 78, 48, 70, 54, 76, 64, 86, 60, 82, 50, 72, 59, 81, 55, 77, 65, 87, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 66, 88, 57, 79, 49, 71) 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, 57)(15, 56)(16, 63)(17, 55)(18, 64)(19, 66)(20, 53)(21, 54)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.106 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1), (Y2 * Y1^-1)^2, (R * Y2)^2, (Y3^-1, Y2), (R * Y1)^2, Y2^-2 * Y1^2, (R * Y3)^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3, Y2^-2 * Y1^-1 * Y3^-1 * Y1^-2, Y2^2 * Y3 * Y2^2 * Y3 * Y2^2 * Y3 * Y2^2 * Y3 * Y1, Y2^16 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 17, 39, 7, 29, 4, 26, 10, 32, 21, 43, 15, 37, 5, 27)(3, 25, 9, 31, 20, 42, 18, 40, 14, 36, 13, 35, 12, 34, 22, 44, 16, 38, 6, 28, 11, 33)(45, 67, 47, 69, 52, 74, 64, 86, 61, 83, 58, 80, 48, 70, 56, 78, 65, 87, 60, 82, 49, 71, 55, 77, 46, 68, 53, 75, 63, 85, 62, 84, 51, 73, 57, 79, 54, 76, 66, 88, 59, 81, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 46)(5, 51)(6, 58)(7, 45)(8, 65)(9, 66)(10, 52)(11, 57)(12, 53)(13, 47)(14, 55)(15, 61)(16, 62)(17, 49)(18, 50)(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, 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.60 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, (Y2^-1, Y1^-1), Y2^2 * Y1^2, (Y3^-1, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y1^-1 * Y2 * Y1^-2, Y1^22, (Y2^-1 * Y3)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 19, 41, 16, 38, 4, 26, 7, 29, 11, 33, 21, 43, 12, 34, 5, 27)(3, 25, 9, 31, 6, 28, 10, 32, 20, 42, 13, 35, 15, 37, 17, 39, 18, 40, 22, 44, 14, 36)(45, 67, 47, 69, 56, 78, 66, 88, 55, 77, 61, 83, 48, 70, 57, 79, 63, 85, 54, 76, 46, 68, 53, 75, 49, 71, 58, 80, 65, 87, 62, 84, 51, 73, 59, 81, 60, 82, 64, 86, 52, 74, 50, 72) L = (1, 48)(2, 51)(3, 57)(4, 49)(5, 60)(6, 61)(7, 45)(8, 55)(9, 59)(10, 62)(11, 46)(12, 63)(13, 58)(14, 64)(15, 47)(16, 56)(17, 53)(18, 50)(19, 65)(20, 66)(21, 52)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.57 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, (Y3, Y1^-1), Y1^-2 * Y3 * Y1^-1, (R * Y1)^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^-2 * Y2^-1 * Y3, Y1^2 * Y3^3 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 4, 26, 10, 32, 19, 41, 14, 36, 17, 39, 7, 29, 11, 33, 5, 27)(3, 25, 9, 31, 15, 37, 12, 34, 20, 42, 22, 44, 21, 43, 18, 40, 13, 35, 16, 38, 6, 28)(45, 67, 47, 69, 46, 68, 53, 75, 52, 74, 59, 81, 48, 70, 56, 78, 54, 76, 64, 86, 63, 85, 66, 88, 58, 80, 65, 87, 61, 83, 62, 84, 51, 73, 57, 79, 55, 77, 60, 82, 49, 71, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 58)(5, 52)(6, 59)(7, 45)(8, 63)(9, 64)(10, 61)(11, 46)(12, 65)(13, 47)(14, 55)(15, 66)(16, 53)(17, 49)(18, 50)(19, 51)(20, 62)(21, 60)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.64 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.132 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y1^-3, (Y3^-1, Y2^-1), (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y2^-1 * Y1 * Y2^-1, Y3^4 * Y1, Y1 * Y3^-2 * Y1 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 7, 29, 11, 33, 15, 37, 19, 41, 16, 38, 4, 26, 9, 31, 5, 27)(3, 25, 6, 28, 10, 32, 14, 36, 18, 40, 20, 42, 22, 44, 21, 43, 12, 34, 17, 39, 13, 35)(45, 67, 47, 69, 49, 71, 57, 79, 53, 75, 61, 83, 48, 70, 56, 78, 60, 82, 65, 87, 63, 85, 66, 88, 59, 81, 64, 86, 55, 77, 62, 84, 51, 73, 58, 80, 52, 74, 54, 76, 46, 68, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 60)(6, 61)(7, 45)(8, 49)(9, 63)(10, 57)(11, 46)(12, 64)(13, 65)(14, 47)(15, 52)(16, 55)(17, 66)(18, 50)(19, 51)(20, 54)(21, 62)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.61 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.133 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3, (Y2^-1, Y1^-1), (Y2^-1, Y3), Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y2)^2, Y3 * Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^2, Y3^5 * Y1, (Y3^2 * Y2^-1)^2, Y1^-1 * Y3^-1 * Y2^20 ] Map:: non-degenerate R = (1, 23, 2, 24, 4, 26, 9, 31, 15, 37, 18, 40, 21, 43, 17, 39, 11, 33, 7, 29, 5, 27)(3, 25, 8, 30, 12, 34, 6, 28, 10, 32, 16, 38, 19, 41, 22, 44, 20, 42, 14, 36, 13, 35)(45, 67, 47, 69, 55, 77, 64, 86, 62, 84, 60, 82, 48, 70, 56, 78, 49, 71, 57, 79, 61, 83, 66, 88, 59, 81, 54, 76, 46, 68, 52, 74, 51, 73, 58, 80, 65, 87, 63, 85, 53, 75, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 59)(5, 46)(6, 60)(7, 45)(8, 50)(9, 62)(10, 63)(11, 49)(12, 54)(13, 52)(14, 47)(15, 65)(16, 66)(17, 51)(18, 61)(19, 64)(20, 57)(21, 55)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.63 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.134 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y2, Y1^-1), Y2^-2 * Y1 * Y3^-1, Y3 * Y2^2 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, Y1 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y3, Y3^-4 * Y2^2, Y3^2 * Y2^18 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 10, 32, 17, 39, 19, 41, 21, 43, 13, 35, 14, 36, 4, 26, 5, 27)(3, 25, 8, 30, 12, 34, 18, 40, 20, 42, 22, 44, 15, 37, 16, 38, 6, 28, 9, 31, 11, 33)(45, 67, 47, 69, 54, 76, 62, 84, 65, 87, 59, 81, 48, 70, 53, 75, 46, 68, 52, 74, 61, 83, 64, 86, 57, 79, 60, 82, 49, 71, 55, 77, 51, 73, 56, 78, 63, 85, 66, 88, 58, 80, 50, 72) L = (1, 48)(2, 49)(3, 53)(4, 57)(5, 58)(6, 59)(7, 45)(8, 55)(9, 60)(10, 46)(11, 50)(12, 47)(13, 63)(14, 65)(15, 64)(16, 66)(17, 51)(18, 52)(19, 54)(20, 56)(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) :: { ( 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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.65 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.135 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y1^-1, (Y1^-1, Y2), Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-2 * Y1^2, Y1 * Y2^-4 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 17, 39, 7, 29, 12, 34, 13, 35, 4, 26, 10, 32, 18, 40, 5, 27)(3, 25, 9, 31, 20, 42, 22, 44, 16, 38, 6, 28, 11, 33, 14, 36, 21, 43, 19, 41, 15, 37)(45, 67, 47, 69, 57, 79, 55, 77, 46, 68, 53, 75, 48, 70, 58, 80, 52, 74, 64, 86, 54, 76, 65, 87, 61, 83, 66, 88, 62, 84, 63, 85, 51, 73, 60, 82, 49, 71, 59, 81, 56, 78, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 61)(5, 57)(6, 53)(7, 45)(8, 62)(9, 65)(10, 51)(11, 64)(12, 46)(13, 52)(14, 66)(15, 55)(16, 47)(17, 49)(18, 56)(19, 50)(20, 63)(21, 60)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.59 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2^-2, Y3^2 * Y1^-1 * Y3, Y2^2 * Y1^-1 * Y3^-1, Y1 * Y2^-1 * Y3 * Y2^-1, (Y3^-1, Y2), (Y3, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1^-4, Y1 * Y3 * Y2^2 * Y1, (Y1^-1 * 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, 19, 41, 21, 43, 13, 35, 17, 39, 6, 28, 11, 33, 20, 42, 22, 44, 14, 36)(45, 67, 47, 69, 54, 76, 61, 83, 49, 71, 58, 80, 48, 70, 57, 79, 60, 82, 66, 88, 59, 81, 65, 87, 56, 78, 64, 86, 52, 74, 63, 85, 51, 73, 55, 77, 46, 68, 53, 75, 62, 84, 50, 72) L = (1, 48)(2, 54)(3, 57)(4, 56)(5, 59)(6, 58)(7, 45)(8, 62)(9, 61)(10, 60)(11, 47)(12, 46)(13, 64)(14, 65)(15, 51)(16, 52)(17, 66)(18, 49)(19, 50)(20, 53)(21, 55)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.62 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y1^-2 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1 * Y2^3 * Y1, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 9, 31, 17, 39, 21, 43, 13, 35, 18, 40, 11, 33, 4, 26)(3, 25, 7, 29, 15, 37, 22, 44, 19, 41, 20, 42, 12, 34, 5, 27, 8, 30, 16, 38, 10, 32)(45, 67, 47, 69, 53, 75, 63, 85, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 64, 86, 55, 77, 60, 82, 50, 72, 59, 81, 65, 87, 56, 78, 48, 70, 54, 76, 58, 80, 66, 88, 57, 79, 49, 71) 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, 53)(15, 66)(16, 54)(17, 65)(18, 55)(19, 64)(20, 56)(21, 57)(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, 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, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.58 Graph:: bipartite v = 3 e = 44 f = 3 degree seq :: [ 22^2, 44 ] E20.138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2 * Y1^-1 * Y2^2, Y2^-1 * Y3 * Y2 * Y3, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y1, Y2), (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1^-2 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2^2 * Y3 * Y2 * Y1^-1, Y2^-2 * Y3 * Y1^-3 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 17, 39, 11, 33, 21, 43, 16, 38, 6, 28, 10, 32, 20, 42, 13, 35, 4, 26, 9, 31, 19, 41, 12, 34, 3, 25, 8, 30, 18, 40, 14, 36, 22, 44, 15, 37, 5, 27)(45, 67, 47, 69, 54, 76, 46, 68, 52, 74, 64, 86, 51, 73, 62, 84, 57, 79, 61, 83, 58, 80, 48, 70, 55, 77, 66, 88, 53, 75, 65, 87, 59, 81, 63, 85, 60, 82, 49, 71, 56, 78, 50, 72) L = (1, 48)(2, 53)(3, 55)(4, 45)(5, 57)(6, 58)(7, 63)(8, 65)(9, 46)(10, 66)(11, 47)(12, 61)(13, 49)(14, 50)(15, 64)(16, 62)(17, 56)(18, 60)(19, 51)(20, 59)(21, 52)(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 ) } Outer automorphisms :: reflexible Dual of E20.33 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-3 * Y1^-1, (Y2^-1, Y1), Y2 * Y3 * Y2^-1 * Y3, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y3 * Y2^2 * Y1^-2, Y2^-1 * Y3 * Y1^-4, Y1^-1 * Y3 * Y2 * Y1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 17, 39, 15, 37, 22, 44, 13, 35, 3, 25, 8, 30, 18, 40, 14, 36, 4, 26, 9, 31, 19, 41, 11, 33, 6, 28, 10, 32, 20, 42, 12, 34, 21, 43, 16, 38, 5, 27)(45, 67, 47, 69, 55, 77, 49, 71, 57, 79, 63, 85, 60, 82, 66, 88, 53, 75, 65, 87, 59, 81, 48, 70, 56, 78, 61, 83, 58, 80, 64, 86, 51, 73, 62, 84, 54, 76, 46, 68, 52, 74, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 45)(5, 58)(6, 59)(7, 63)(8, 65)(9, 46)(10, 66)(11, 61)(12, 47)(13, 64)(14, 49)(15, 50)(16, 62)(17, 55)(18, 60)(19, 51)(20, 57)(21, 52)(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 ) } Outer automorphisms :: reflexible Dual of E20.34 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y1^-1 * Y3 * Y1^-1, Y1^-2 * Y3 * Y2^-1, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y2^-1 * Y3 * Y1^-1, (R * Y2)^2, (R * Y3)^2, Y2^-2 * Y1 * Y2^-3, Y1^-1 * Y2^2 * Y3 * Y2^2 * Y1^-2, Y1^9 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 15, 37, 14, 36, 18, 40, 22, 44, 19, 41, 13, 35, 3, 25, 8, 30, 4, 26, 9, 31, 6, 28, 10, 32, 16, 38, 21, 43, 20, 42, 11, 33, 17, 39, 12, 34, 5, 27)(45, 67, 47, 69, 55, 77, 62, 84, 54, 76, 46, 68, 52, 74, 61, 83, 66, 88, 60, 82, 51, 73, 48, 70, 56, 78, 63, 85, 65, 87, 59, 81, 53, 75, 49, 71, 57, 79, 64, 86, 58, 80, 50, 72) L = (1, 48)(2, 53)(3, 56)(4, 45)(5, 52)(6, 51)(7, 50)(8, 49)(9, 46)(10, 59)(11, 63)(12, 47)(13, 61)(14, 60)(15, 54)(16, 58)(17, 57)(18, 65)(19, 55)(20, 66)(21, 62)(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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.32 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y3 * Y1^2, Y2 * Y3 * Y1^-2, Y3 * Y1^-1 * Y2 * Y1^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^-1 * Y2^-4, Y2^2 * Y1^18 ] Map:: non-degenerate R = (1, 23, 2, 24, 7, 29, 15, 37, 11, 33, 17, 39, 22, 44, 20, 42, 13, 35, 6, 28, 10, 32, 4, 26, 9, 31, 3, 25, 8, 30, 16, 38, 21, 43, 19, 41, 14, 36, 18, 40, 12, 34, 5, 27)(45, 67, 47, 69, 55, 77, 63, 85, 57, 79, 49, 71, 53, 75, 59, 81, 65, 87, 64, 86, 56, 78, 48, 70, 51, 73, 60, 82, 66, 88, 62, 84, 54, 76, 46, 68, 52, 74, 61, 83, 58, 80, 50, 72) L = (1, 48)(2, 53)(3, 51)(4, 45)(5, 54)(6, 56)(7, 47)(8, 59)(9, 46)(10, 49)(11, 60)(12, 50)(13, 62)(14, 64)(15, 52)(16, 55)(17, 65)(18, 57)(19, 66)(20, 58)(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 ) } Outer automorphisms :: reflexible Dual of E20.31 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.142 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2^-3 * Y1^-1, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y2 * Y1^-7, (Y1^-1 * Y3^-1)^11, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 12, 34, 18, 40, 16, 38, 10, 32, 3, 25, 7, 29, 13, 35, 19, 41, 22, 44, 21, 43, 15, 37, 9, 31, 4, 26, 8, 30, 14, 36, 20, 42, 17, 39, 11, 33, 5, 27)(45, 67, 47, 69, 53, 75, 49, 71, 54, 76, 59, 81, 55, 77, 60, 82, 65, 87, 61, 83, 62, 84, 66, 88, 64, 86, 56, 78, 63, 85, 58, 80, 50, 72, 57, 79, 52, 74, 46, 68, 51, 73, 48, 70) L = (1, 48)(2, 52)(3, 45)(4, 51)(5, 53)(6, 58)(7, 46)(8, 57)(9, 47)(10, 49)(11, 59)(12, 64)(13, 50)(14, 63)(15, 54)(16, 55)(17, 65)(18, 61)(19, 56)(20, 66)(21, 60)(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 ) } Outer automorphisms :: reflexible Dual of E20.44 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.143 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, Y1^-1 * Y3 * Y1 * Y2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y2^-1 * Y1, Y3 * Y1 * Y2 * Y1^-1, Y3^-2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1, Y3 * Y1 * Y2^-4, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, (Y1^-1 * Y2)^11, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 11, 33, 18, 40, 22, 44, 20, 42, 10, 32, 3, 25, 7, 29, 15, 37, 12, 34, 4, 26, 8, 30, 16, 38, 21, 43, 19, 41, 9, 31, 17, 39, 13, 35, 5, 27)(45, 67, 47, 69, 53, 75, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 66, 88, 60, 82, 50, 72, 59, 81, 57, 79, 64, 86, 65, 87, 58, 80, 56, 78, 49, 71, 54, 76, 63, 85, 55, 77, 48, 70) L = (1, 48)(2, 52)(3, 45)(4, 55)(5, 56)(6, 60)(7, 46)(8, 62)(9, 47)(10, 49)(11, 63)(12, 58)(13, 59)(14, 65)(15, 50)(16, 66)(17, 51)(18, 53)(19, 54)(20, 57)(21, 64)(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 ) } Outer automorphisms :: reflexible Dual of E20.45 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.144 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, (Y1, Y3^-1), (Y2^-1, Y1), R * Y2 * R * Y3^-1, (R * Y1)^2, Y1^-1 * Y2 * Y1^-3 * Y2, Y3^-5 * Y1, Y3^-3 * Y2^19, (Y1^-1 * Y3^-1)^11, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 9, 31, 17, 39, 22, 44, 20, 42, 12, 34, 4, 26, 8, 30, 16, 38, 10, 32, 3, 25, 7, 29, 15, 37, 21, 43, 19, 41, 11, 33, 18, 40, 13, 35, 5, 27)(45, 67, 47, 69, 53, 75, 63, 85, 56, 78, 49, 71, 54, 76, 58, 80, 65, 87, 64, 86, 57, 79, 60, 82, 50, 72, 59, 81, 66, 88, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 55, 77, 48, 70) L = (1, 48)(2, 52)(3, 45)(4, 55)(5, 56)(6, 60)(7, 46)(8, 62)(9, 47)(10, 49)(11, 61)(12, 63)(13, 64)(14, 54)(15, 50)(16, 57)(17, 51)(18, 66)(19, 53)(20, 65)(21, 58)(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 ) } Outer automorphisms :: reflexible Dual of E20.43 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.145 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y2 * Y1^3, Y1^-2 * Y2^-1 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3^-1, Y1 * Y3^7, (Y3^-1 * Y1^-1)^11, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 4, 26, 8, 30, 12, 34, 11, 33, 14, 36, 18, 40, 17, 39, 20, 42, 22, 44, 21, 43, 15, 37, 19, 41, 16, 38, 9, 31, 13, 35, 10, 32, 3, 25, 7, 29, 5, 27)(45, 67, 47, 69, 53, 75, 59, 81, 64, 86, 58, 80, 52, 74, 46, 68, 51, 73, 57, 79, 63, 85, 66, 88, 62, 84, 56, 78, 50, 72, 49, 71, 54, 76, 60, 82, 65, 87, 61, 83, 55, 77, 48, 70) L = (1, 48)(2, 52)(3, 45)(4, 55)(5, 50)(6, 56)(7, 46)(8, 58)(9, 47)(10, 49)(11, 61)(12, 62)(13, 51)(14, 64)(15, 53)(16, 54)(17, 65)(18, 66)(19, 57)(20, 59)(21, 60)(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 ) } Outer automorphisms :: reflexible Dual of E20.37 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.146 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, Y2 * Y1^-3, (Y1, Y3^-1), R * Y2 * R * Y3^-1, (R * Y1)^2, Y3^3 * Y1^-1 * Y2^-3 * Y3, (Y1^-1 * Y3^-1)^11, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 3, 25, 7, 29, 12, 34, 9, 31, 13, 35, 18, 40, 15, 37, 19, 41, 22, 44, 21, 43, 16, 38, 20, 42, 17, 39, 10, 32, 14, 36, 11, 33, 4, 26, 8, 30, 5, 27)(45, 67, 47, 69, 53, 75, 59, 81, 65, 87, 61, 83, 55, 77, 49, 71, 50, 72, 56, 78, 62, 84, 66, 88, 64, 86, 58, 80, 52, 74, 46, 68, 51, 73, 57, 79, 63, 85, 60, 82, 54, 76, 48, 70) L = (1, 48)(2, 52)(3, 45)(4, 54)(5, 55)(6, 49)(7, 46)(8, 58)(9, 47)(10, 60)(11, 61)(12, 50)(13, 51)(14, 64)(15, 53)(16, 63)(17, 65)(18, 56)(19, 57)(20, 66)(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 ) } Outer automorphisms :: reflexible Dual of E20.38 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.147 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, Y3^-1 * Y2^-1, (Y1, Y3^-1), (R * Y1)^2, (R * Y3)^2, Y3^2 * Y1^-2 * Y3^2, Y1^-1 * Y3^-1 * Y1^-4, Y3^-1 * Y1^-1 * Y2^-2 * Y1 * Y3^-1, Y2^2 * Y1^-3 * Y3 * Y1^-2, Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^2, (Y3 * Y2^-1)^11 ] Map:: non-degenerate R = (1, 23, 2, 24, 6, 28, 14, 36, 10, 32, 3, 25, 7, 29, 15, 37, 21, 43, 20, 42, 9, 31, 17, 39, 11, 33, 18, 40, 22, 44, 19, 41, 12, 34, 4, 26, 8, 30, 16, 38, 13, 35, 5, 27)(45, 67, 47, 69, 53, 75, 63, 85, 57, 79, 58, 80, 65, 87, 62, 84, 52, 74, 46, 68, 51, 73, 61, 83, 56, 78, 49, 71, 54, 76, 64, 86, 66, 88, 60, 82, 50, 72, 59, 81, 55, 77, 48, 70) L = (1, 48)(2, 52)(3, 45)(4, 55)(5, 56)(6, 60)(7, 46)(8, 62)(9, 47)(10, 49)(11, 59)(12, 61)(13, 63)(14, 57)(15, 50)(16, 66)(17, 51)(18, 65)(19, 53)(20, 54)(21, 58)(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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.46 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.148 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y2^2, Y2^2 * Y3 * Y1^-1, Y3 * Y2^-1 * Y3 * Y1^-1, (Y2^-1, Y1), Y3^2 * Y2^-1 * Y1^-1, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y2, (R * Y2)^2, (R * Y3)^2, Y1 * Y3^4 * Y1, Y1 * Y3 * Y1 * Y3 * Y2 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 14, 36, 4, 26, 10, 32, 20, 42, 13, 35, 3, 25, 9, 31, 19, 41, 16, 38, 6, 28, 11, 33, 21, 43, 17, 39, 7, 29, 12, 34, 22, 44, 15, 37, 5, 27)(45, 67, 47, 69, 56, 78, 48, 70, 55, 77, 46, 68, 53, 75, 66, 88, 54, 76, 65, 87, 52, 74, 63, 85, 59, 81, 64, 86, 61, 83, 62, 84, 60, 82, 49, 71, 57, 79, 51, 73, 58, 80, 50, 72) L = (1, 48)(2, 54)(3, 55)(4, 53)(5, 58)(6, 56)(7, 45)(8, 64)(9, 65)(10, 63)(11, 66)(12, 46)(13, 50)(14, 47)(15, 62)(16, 51)(17, 49)(18, 57)(19, 61)(20, 60)(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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.36 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.149 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-2 * Y1 * Y2^-1, Y2^-1 * Y1^-3, Y3 * Y2 * Y3 * Y1^-1, Y3 * Y2^-3, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, (Y2^-1 * Y3^-1 * Y1^-1)^2, Y1 * Y2^-1 * Y3^3 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 6, 28, 11, 33, 19, 41, 15, 37, 22, 44, 17, 39, 7, 29, 12, 34, 20, 42, 16, 38, 4, 26, 10, 32, 18, 40, 13, 35, 21, 43, 14, 36, 3, 25, 9, 31, 5, 27)(45, 67, 47, 69, 57, 79, 48, 70, 56, 78, 66, 88, 55, 77, 46, 68, 53, 75, 65, 87, 54, 76, 64, 86, 61, 83, 63, 85, 52, 74, 49, 71, 58, 80, 62, 84, 60, 82, 51, 73, 59, 81, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 55)(5, 60)(6, 57)(7, 45)(8, 62)(9, 64)(10, 63)(11, 65)(12, 46)(13, 66)(14, 51)(15, 47)(16, 50)(17, 49)(18, 59)(19, 58)(20, 52)(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 ) } Outer automorphisms :: reflexible Dual of E20.40 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y3^-2, Y1 * Y3 * Y2 * Y3, Y2 * Y1 * Y3^2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y2 * Y1^-1, (R * Y3)^2, Y2^-1 * Y3 * Y2^-2, Y2^-1 * Y1^-1 * Y3^3 * Y1^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 3, 25, 9, 31, 18, 40, 13, 35, 21, 43, 17, 39, 4, 26, 10, 32, 19, 41, 14, 36, 7, 29, 12, 34, 20, 42, 15, 37, 22, 44, 16, 38, 6, 28, 11, 33, 5, 27)(45, 67, 47, 69, 57, 79, 48, 70, 58, 80, 64, 86, 60, 82, 49, 71, 52, 74, 62, 84, 61, 83, 63, 85, 56, 78, 66, 88, 55, 77, 46, 68, 53, 75, 65, 87, 54, 76, 51, 73, 59, 81, 50, 72) L = (1, 48)(2, 54)(3, 58)(4, 60)(5, 61)(6, 57)(7, 45)(8, 63)(9, 51)(10, 50)(11, 65)(12, 46)(13, 64)(14, 49)(15, 47)(16, 62)(17, 66)(18, 56)(19, 55)(20, 52)(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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.41 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y2^-3 * Y3, Y2^-1 * Y3^-1 * Y1^2, Y2 * Y1^-1 * Y3 * Y1^-1, (Y3^-1, Y1), Y3^-2 * Y1^-1 * Y3^-1, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 17, 39, 6, 28, 11, 33, 4, 26, 10, 32, 20, 42, 14, 36, 22, 44, 13, 35, 21, 43, 15, 37, 7, 29, 12, 34, 3, 25, 9, 31, 19, 41, 16, 38, 5, 27)(45, 67, 47, 69, 57, 79, 48, 70, 52, 74, 63, 85, 59, 81, 64, 86, 61, 83, 49, 71, 56, 78, 66, 88, 55, 77, 46, 68, 53, 75, 65, 87, 54, 76, 62, 84, 60, 82, 51, 73, 58, 80, 50, 72) L = (1, 48)(2, 54)(3, 52)(4, 59)(5, 55)(6, 57)(7, 45)(8, 64)(9, 62)(10, 51)(11, 65)(12, 46)(13, 63)(14, 47)(15, 49)(16, 50)(17, 66)(18, 58)(19, 61)(20, 56)(21, 60)(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 ) } Outer automorphisms :: reflexible Dual of E20.42 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 22}) Quotient :: dipole Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y3^-2, Y2^-2 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y1^-1 * Y2 * Y3^2, (R * Y1)^2, (Y1, Y2^-1), Y2^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3^-1 * Y2^-2, Y1^-1 * Y2 * Y3^-2 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 13, 35, 4, 26, 10, 32, 20, 42, 15, 37, 6, 28, 11, 33, 21, 43, 14, 36, 3, 25, 9, 31, 19, 41, 17, 39, 7, 29, 12, 34, 22, 44, 16, 38, 5, 27)(45, 67, 47, 69, 57, 79, 51, 73, 59, 81, 49, 71, 58, 80, 62, 84, 61, 83, 64, 86, 60, 82, 65, 87, 52, 74, 63, 85, 54, 76, 66, 88, 55, 77, 46, 68, 53, 75, 48, 70, 56, 78, 50, 72) L = (1, 48)(2, 54)(3, 56)(4, 55)(5, 57)(6, 53)(7, 45)(8, 64)(9, 66)(10, 65)(11, 63)(12, 46)(13, 50)(14, 51)(15, 47)(16, 62)(17, 49)(18, 59)(19, 60)(20, 58)(21, 61)(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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.39 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.153 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 11, 22, 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^-1 * Y3 * Y2^-1, Y1^-1 * Y3 * Y2 * Y1^-1, (Y3, Y1), (R * Y3)^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^2 * Y2^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 23, 2, 24, 8, 30, 18, 40, 17, 39, 22, 44, 13, 35, 6, 28, 11, 33, 4, 26, 10, 32, 20, 42, 16, 38, 7, 29, 12, 34, 3, 25, 9, 31, 19, 41, 14, 36, 21, 43, 15, 37, 5, 27)(45, 67, 47, 69, 55, 77, 46, 68, 53, 75, 48, 70, 52, 74, 63, 85, 54, 76, 62, 84, 58, 80, 64, 86, 61, 83, 65, 87, 60, 82, 66, 88, 59, 81, 51, 73, 57, 79, 49, 71, 56, 78, 50, 72) L = (1, 48)(2, 54)(3, 52)(4, 58)(5, 55)(6, 53)(7, 45)(8, 64)(9, 62)(10, 65)(11, 63)(12, 46)(13, 47)(14, 66)(15, 50)(16, 49)(17, 51)(18, 60)(19, 61)(20, 59)(21, 57)(22, 56)(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 ) } Outer automorphisms :: reflexible Dual of E20.35 Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.154 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {8, 8, 12, 12}) Quotient :: edge^2 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^-1), (Y1^-1 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, Y2 * Y3 * Y1^-1 * Y3^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y2 * R * Y1, Y2^-2 * Y1^-2, Y2^-3 * Y3^2, Y1^-3 * Y3^2, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y2 * Y1 * Y3^4, (Y1 * Y2 * Y3^2)^4 ] Map:: non-degenerate R = (1, 25, 4, 28, 17, 41, 24, 48, 9, 33, 23, 47, 22, 46, 7, 31)(2, 26, 10, 34, 15, 39, 21, 45, 6, 30, 18, 42, 13, 37, 12, 36)(3, 27, 14, 38, 11, 35, 20, 44, 5, 29, 19, 43, 8, 32, 16, 40)(49, 50, 56, 65, 63, 51, 57, 54, 59, 70, 61, 53)(52, 62, 60, 72, 68, 58, 71, 67, 69, 55, 64, 66)(73, 75, 85, 89, 83, 74, 81, 77, 87, 94, 80, 78)(76, 82, 88, 96, 93, 86, 95, 90, 92, 79, 84, 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) :: { ( 32^12 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E20.157 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 12^4, 16^3 ] E20.155 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {8, 8, 12, 12}) Quotient :: edge^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, (Y1 * Y2)^2, (Y2^-1, Y1^-1), (Y1 * Y2)^2, R * Y1 * R * Y2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y3)^2, (Y2^-1, Y1), Y3 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y3 * Y1^-1, Y2^-2 * Y3^-2 * Y2^-1, Y3 * Y2 * Y3 * Y2^-2, Y1^-3 * Y3^-2, Y1 * Y2 * Y3^-4, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 25, 4, 28, 17, 41, 24, 48, 9, 33, 23, 47, 22, 46, 7, 31)(2, 26, 10, 34, 13, 37, 21, 45, 6, 30, 18, 42, 15, 39, 12, 36)(3, 27, 14, 38, 8, 32, 20, 44, 5, 29, 19, 43, 11, 35, 16, 40)(49, 50, 56, 70, 63, 51, 57, 54, 59, 65, 61, 53)(52, 62, 69, 55, 64, 58, 71, 67, 60, 72, 68, 66)(73, 75, 85, 94, 83, 74, 81, 77, 87, 89, 80, 78)(76, 82, 92, 79, 84, 86, 95, 90, 88, 96, 93, 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) :: { ( 32^12 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E20.156 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 12^4, 16^3 ] E20.156 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {8, 8, 12, 12}) Quotient :: loop^2 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^-1), (Y1^-1 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, Y2 * Y3 * Y1^-1 * Y3^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y2 * R * Y1, Y2^-2 * Y1^-2, Y2^-3 * Y3^2, Y1^-3 * Y3^2, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y2 * Y1 * Y3^4, (Y1 * Y2 * Y3^2)^4 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 17, 41, 65, 89, 24, 48, 72, 96, 9, 33, 57, 81, 23, 47, 71, 95, 22, 46, 70, 94, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 15, 39, 63, 87, 21, 45, 69, 93, 6, 30, 54, 78, 18, 42, 66, 90, 13, 37, 61, 85, 12, 36, 60, 84)(3, 27, 51, 75, 14, 38, 62, 86, 11, 35, 59, 83, 20, 44, 68, 92, 5, 29, 53, 77, 19, 43, 67, 91, 8, 32, 56, 80, 16, 40, 64, 88) L = (1, 26)(2, 32)(3, 33)(4, 38)(5, 25)(6, 35)(7, 40)(8, 41)(9, 30)(10, 47)(11, 46)(12, 48)(13, 29)(14, 36)(15, 27)(16, 42)(17, 39)(18, 28)(19, 45)(20, 34)(21, 31)(22, 37)(23, 43)(24, 44)(49, 75)(50, 81)(51, 85)(52, 82)(53, 87)(54, 73)(55, 84)(56, 78)(57, 77)(58, 88)(59, 74)(60, 91)(61, 89)(62, 95)(63, 94)(64, 96)(65, 83)(66, 92)(67, 76)(68, 79)(69, 86)(70, 80)(71, 90)(72, 93) 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 ) } Outer automorphisms :: reflexible Dual of E20.155 Transitivity :: VT+ Graph:: v = 3 e = 48 f = 7 degree seq :: [ 32^3 ] E20.157 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {8, 8, 12, 12}) Quotient :: loop^2 Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, (Y1 * Y2)^2, (Y2^-1, Y1^-1), (Y1 * Y2)^2, R * Y1 * R * Y2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y3)^2, (Y2^-1, Y1), Y3 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y3 * Y1^-1, Y2^-2 * Y3^-2 * Y2^-1, Y3 * Y2 * Y3 * Y2^-2, Y1^-3 * Y3^-2, Y1 * Y2 * Y3^-4, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 25, 49, 73, 4, 28, 52, 76, 17, 41, 65, 89, 24, 48, 72, 96, 9, 33, 57, 81, 23, 47, 71, 95, 22, 46, 70, 94, 7, 31, 55, 79)(2, 26, 50, 74, 10, 34, 58, 82, 13, 37, 61, 85, 21, 45, 69, 93, 6, 30, 54, 78, 18, 42, 66, 90, 15, 39, 63, 87, 12, 36, 60, 84)(3, 27, 51, 75, 14, 38, 62, 86, 8, 32, 56, 80, 20, 44, 68, 92, 5, 29, 53, 77, 19, 43, 67, 91, 11, 35, 59, 83, 16, 40, 64, 88) L = (1, 26)(2, 32)(3, 33)(4, 38)(5, 25)(6, 35)(7, 40)(8, 46)(9, 30)(10, 47)(11, 41)(12, 48)(13, 29)(14, 45)(15, 27)(16, 34)(17, 37)(18, 28)(19, 36)(20, 42)(21, 31)(22, 39)(23, 43)(24, 44)(49, 75)(50, 81)(51, 85)(52, 82)(53, 87)(54, 73)(55, 84)(56, 78)(57, 77)(58, 92)(59, 74)(60, 86)(61, 94)(62, 95)(63, 89)(64, 96)(65, 80)(66, 88)(67, 76)(68, 79)(69, 91)(70, 83)(71, 90)(72, 93) 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 ) } Outer automorphisms :: reflexible Dual of E20.154 Transitivity :: VT+ Graph:: v = 3 e = 48 f = 7 degree seq :: [ 32^3 ] E20.158 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 12}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2, Y2 * Y1^-2 * Y2^2, Y2 * Y1^3 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 18, 42, 24, 48, 23, 47, 13, 37, 4, 28)(3, 27, 9, 33, 19, 43, 14, 38, 22, 46, 8, 32, 17, 41, 11, 35)(5, 29, 15, 39, 10, 34, 12, 36, 21, 45, 7, 31, 20, 44, 16, 40)(49, 73, 51, 75, 58, 82, 54, 78, 67, 91, 69, 93, 72, 96, 70, 94, 68, 92, 61, 85, 65, 89, 53, 77)(50, 74, 55, 79, 59, 83, 66, 90, 64, 88, 57, 81, 71, 95, 63, 87, 62, 86, 52, 76, 60, 84, 56, 80) 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, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.159 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 12}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y2^3, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-3 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 18, 42, 24, 48, 23, 47, 13, 37, 4, 28)(3, 27, 9, 33, 17, 41, 14, 38, 22, 46, 8, 32, 21, 45, 11, 35)(5, 29, 15, 39, 19, 43, 12, 36, 20, 44, 7, 31, 10, 34, 16, 40)(49, 73, 51, 75, 58, 82, 61, 85, 69, 93, 68, 92, 72, 96, 70, 94, 67, 91, 54, 78, 65, 89, 53, 77)(50, 74, 55, 79, 62, 86, 52, 76, 60, 84, 57, 81, 71, 95, 63, 87, 59, 83, 66, 90, 64, 88, 56, 80) 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, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.160 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 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, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y1^4 * Y3, Y1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y1^2 * Y2^-3, Y1 * Y2^-1 * Y1 * Y2^2, (Y2^-1 * Y1^-2)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 4, 28, 9, 33, 18, 42, 5, 29)(3, 27, 11, 35, 23, 47, 19, 43, 13, 37, 10, 34, 22, 46, 14, 38)(6, 30, 20, 44, 12, 36, 17, 41, 16, 40, 8, 32, 24, 48, 21, 45)(49, 73, 51, 75, 60, 84, 55, 79, 71, 95, 64, 88, 52, 76, 61, 85, 72, 96, 66, 90, 70, 94, 54, 78)(50, 74, 56, 80, 62, 86, 63, 87, 69, 93, 59, 83, 57, 81, 68, 92, 67, 91, 53, 77, 65, 89, 58, 82) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 63)(6, 64)(7, 66)(8, 68)(9, 50)(10, 59)(11, 58)(12, 72)(13, 51)(14, 67)(15, 53)(16, 54)(17, 69)(18, 55)(19, 62)(20, 56)(21, 65)(22, 71)(23, 70)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 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 E20.161 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.161 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 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, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y1^4, Y3 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^2 * Y2^3, Y1 * Y2^-2 * Y1 * Y2, (Y2^-1 * Y1^2)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 4, 28, 9, 33, 18, 42, 5, 29)(3, 27, 11, 35, 22, 46, 19, 43, 13, 37, 10, 34, 24, 48, 14, 38)(6, 30, 20, 44, 23, 47, 17, 41, 16, 40, 8, 32, 12, 36, 21, 45)(49, 73, 51, 75, 60, 84, 66, 90, 72, 96, 64, 88, 52, 76, 61, 85, 71, 95, 55, 79, 70, 94, 54, 78)(50, 74, 56, 80, 67, 91, 53, 77, 65, 89, 59, 83, 57, 81, 68, 92, 62, 86, 63, 87, 69, 93, 58, 82) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 63)(6, 64)(7, 66)(8, 68)(9, 50)(10, 59)(11, 58)(12, 71)(13, 51)(14, 67)(15, 53)(16, 54)(17, 69)(18, 55)(19, 62)(20, 56)(21, 65)(22, 72)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 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 E20.160 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.162 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 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, Y3^3, Y1^2 * Y2 * Y3, (Y3, Y2), Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1^-1 * Y2^-1 * Y3, Y3^-1 * Y2^-4, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 24, 48, 23, 47, 15, 39, 5, 29)(3, 27, 13, 37, 7, 31, 10, 34, 18, 42, 11, 35, 21, 45, 16, 40)(4, 28, 12, 36, 6, 30, 20, 44, 14, 38, 19, 43, 17, 41, 9, 33)(49, 73, 51, 75, 62, 86, 56, 80, 55, 79, 65, 89, 72, 96, 66, 90, 52, 76, 63, 87, 69, 93, 54, 78)(50, 74, 57, 81, 64, 88, 70, 94, 60, 84, 61, 85, 71, 95, 68, 92, 58, 82, 53, 77, 67, 91, 59, 83) L = (1, 52)(2, 58)(3, 63)(4, 55)(5, 61)(6, 66)(7, 49)(8, 54)(9, 53)(10, 60)(11, 68)(12, 50)(13, 57)(14, 69)(15, 65)(16, 67)(17, 51)(18, 56)(19, 71)(20, 70)(21, 72)(22, 59)(23, 64)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.163 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 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, Y3^3, Y1^2 * Y3^-1 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y2^4, Y3 * Y2^-1 * Y1 * Y3^-1 * Y1, Y1^-1 * Y2^2 * Y1^-1 * Y2^-1, (Y3^-1 * Y2^2)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 24, 48, 23, 47, 18, 42, 5, 29)(3, 27, 13, 37, 21, 45, 19, 43, 17, 41, 11, 35, 7, 31, 10, 34)(4, 28, 12, 36, 15, 39, 9, 33, 14, 38, 20, 44, 6, 30, 16, 40)(49, 73, 51, 75, 62, 86, 66, 90, 55, 79, 63, 87, 72, 96, 65, 89, 52, 76, 56, 80, 69, 93, 54, 78)(50, 74, 57, 81, 67, 91, 53, 77, 60, 84, 61, 85, 71, 95, 64, 88, 58, 82, 70, 94, 68, 92, 59, 83) L = (1, 52)(2, 58)(3, 56)(4, 55)(5, 59)(6, 65)(7, 49)(8, 63)(9, 70)(10, 60)(11, 64)(12, 50)(13, 57)(14, 69)(15, 51)(16, 53)(17, 66)(18, 54)(19, 68)(20, 71)(21, 72)(22, 61)(23, 67)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.164 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 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 * Y2^-2, Y1 * Y3 * Y1^-1 * Y3, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y1 * Y3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^6, Y1^8 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 20, 44, 24, 48, 23, 47, 16, 40, 5, 29)(3, 27, 13, 37, 14, 38, 17, 41, 22, 46, 11, 35, 7, 31, 10, 34)(4, 28, 12, 36, 21, 45, 9, 33, 19, 43, 18, 42, 6, 30, 15, 39)(49, 73, 51, 75, 52, 76, 56, 80, 62, 86, 69, 93, 72, 96, 70, 94, 67, 91, 64, 88, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 68, 92, 66, 90, 61, 85, 71, 95, 63, 87, 65, 89, 53, 77, 60, 84, 59, 83) L = (1, 52)(2, 58)(3, 56)(4, 62)(5, 59)(6, 51)(7, 49)(8, 69)(9, 68)(10, 66)(11, 57)(12, 50)(13, 63)(14, 72)(15, 53)(16, 54)(17, 60)(18, 71)(19, 55)(20, 61)(21, 70)(22, 64)(23, 65)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 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 E20.165 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.165 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 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 * Y3^-1 * Y2, Y1 * Y2 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y3^-1 * Y2^-1 * Y1^-2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^3 * Y2^-1, Y3^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 20, 44, 24, 48, 23, 47, 14, 38, 5, 29)(3, 27, 13, 37, 7, 31, 10, 34, 21, 45, 11, 35, 16, 40, 15, 39)(4, 28, 12, 36, 6, 30, 18, 42, 19, 43, 17, 41, 22, 46, 9, 33)(49, 73, 51, 75, 52, 76, 62, 86, 64, 88, 70, 94, 72, 96, 69, 93, 67, 91, 56, 80, 55, 79, 54, 78)(50, 74, 57, 81, 58, 82, 53, 77, 65, 89, 61, 85, 71, 95, 66, 90, 63, 87, 68, 92, 60, 84, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 64)(5, 61)(6, 51)(7, 49)(8, 54)(9, 53)(10, 65)(11, 57)(12, 50)(13, 66)(14, 70)(15, 60)(16, 72)(17, 71)(18, 68)(19, 55)(20, 59)(21, 56)(22, 69)(23, 63)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 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 E20.164 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.166 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 12}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 20, 44, 19, 43, 11, 35, 4, 28)(3, 27, 7, 31, 13, 37, 16, 40, 22, 46, 24, 48, 18, 42, 10, 34)(5, 29, 8, 32, 15, 39, 21, 45, 23, 47, 17, 41, 9, 33, 12, 36)(49, 73, 51, 75, 57, 81, 59, 83, 66, 90, 71, 95, 68, 92, 70, 94, 63, 87, 54, 78, 61, 85, 53, 77)(50, 74, 55, 79, 60, 84, 52, 76, 58, 82, 65, 89, 67, 91, 72, 96, 69, 93, 62, 86, 64, 88, 56, 80) 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, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 12}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 20, 44, 17, 41, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 21, 45, 24, 48, 19, 43, 13, 37, 10, 34)(5, 29, 8, 32, 9, 33, 16, 40, 22, 46, 23, 47, 18, 42, 12, 36)(49, 73, 51, 75, 57, 81, 54, 78, 63, 87, 70, 94, 68, 92, 72, 96, 66, 90, 59, 83, 61, 85, 53, 77)(50, 74, 55, 79, 64, 88, 62, 86, 69, 93, 71, 95, 65, 89, 67, 91, 60, 84, 52, 76, 58, 82, 56, 80) 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, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 12}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3^2, R^2, (Y2^-1, Y1), Y1^-1 * Y3 * Y1 * Y3, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4 * Y3, Y2^2 * Y1 * Y2 * Y1, Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 14, 38, 4, 28, 9, 33, 16, 40, 5, 29)(3, 27, 8, 32, 18, 42, 22, 46, 12, 36, 20, 44, 23, 47, 13, 37)(6, 30, 10, 34, 19, 43, 24, 48, 15, 39, 21, 45, 11, 35, 17, 41)(49, 73, 51, 75, 59, 83, 64, 88, 71, 95, 63, 87, 52, 76, 60, 84, 67, 91, 55, 79, 66, 90, 54, 78)(50, 74, 56, 80, 65, 89, 53, 77, 61, 85, 69, 93, 57, 81, 68, 92, 72, 96, 62, 86, 70, 94, 58, 82) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 64)(8, 68)(9, 50)(10, 69)(11, 67)(12, 51)(13, 70)(14, 53)(15, 54)(16, 55)(17, 72)(18, 71)(19, 59)(20, 56)(21, 58)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 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 E20.169 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 12, 12}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1, Y2), (R * Y2)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^4 * Y3, Y1 * Y2^-1 * Y1 * Y2^-2, Y2^-2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 14, 38, 4, 28, 9, 33, 16, 40, 5, 29)(3, 27, 8, 32, 19, 43, 24, 48, 12, 36, 21, 45, 18, 42, 13, 37)(6, 30, 10, 34, 11, 35, 20, 44, 15, 39, 22, 46, 23, 47, 17, 41)(49, 73, 51, 75, 59, 83, 55, 79, 67, 91, 63, 87, 52, 76, 60, 84, 71, 95, 64, 88, 66, 90, 54, 78)(50, 74, 56, 80, 68, 92, 62, 86, 72, 96, 70, 94, 57, 81, 69, 93, 65, 89, 53, 77, 61, 85, 58, 82) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 64)(8, 69)(9, 50)(10, 70)(11, 71)(12, 51)(13, 72)(14, 53)(15, 54)(16, 55)(17, 68)(18, 67)(19, 66)(20, 65)(21, 56)(22, 58)(23, 59)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 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 E20.168 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 12, 12, 12}) Quotient :: dipole Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2, (R * Y1^-1)^2, (R * Y3)^2, (Y3, Y1^-1), Y3^4, Y3^-2 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 17, 41, 5, 29)(3, 27, 9, 33, 21, 45, 24, 48, 18, 42, 6, 30)(4, 28, 10, 34, 19, 43, 7, 31, 11, 35, 15, 39)(12, 36, 22, 46, 16, 40, 13, 37, 23, 47, 20, 44)(49, 73, 51, 75, 50, 74, 57, 81, 56, 80, 69, 93, 62, 86, 72, 96, 65, 89, 66, 90, 53, 77, 54, 78)(52, 76, 61, 85, 58, 82, 71, 95, 67, 91, 68, 92, 55, 79, 60, 84, 59, 83, 70, 94, 63, 87, 64, 88) L = (1, 52)(2, 58)(3, 60)(4, 62)(5, 63)(6, 68)(7, 49)(8, 67)(9, 70)(10, 65)(11, 50)(12, 72)(13, 51)(14, 55)(15, 56)(16, 54)(17, 59)(18, 71)(19, 53)(20, 69)(21, 64)(22, 66)(23, 57)(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) :: { ( 24^12 ), ( 24^24 ) } Outer automorphisms :: reflexible Dual of E20.171 Graph:: bipartite v = 6 e = 48 f = 4 degree seq :: [ 12^4, 24^2 ] E20.171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 12, 12, 12}) Quotient :: dipole Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^3, Y3^-1 * Y2^2 * Y1^-1, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y1)^2, Y1 * Y2^2 * Y1, (Y3^-1, Y1), Y3^4, Y3 * Y2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1, Y3^-1 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 7, 31, 12, 36, 20, 44, 16, 40, 24, 48, 17, 41, 4, 28, 10, 34, 5, 29)(3, 27, 13, 37, 6, 30, 15, 39, 19, 43, 18, 42, 22, 46, 9, 33, 21, 45, 11, 35, 23, 47, 14, 38)(49, 73, 51, 75, 58, 82, 71, 95, 65, 89, 69, 93, 64, 88, 70, 94, 60, 84, 67, 91, 56, 80, 54, 78)(50, 74, 57, 81, 53, 77, 66, 90, 52, 76, 63, 87, 72, 96, 61, 85, 68, 92, 62, 86, 55, 79, 59, 83) L = (1, 52)(2, 58)(3, 59)(4, 64)(5, 65)(6, 62)(7, 49)(8, 53)(9, 67)(10, 72)(11, 70)(12, 50)(13, 71)(14, 69)(15, 51)(16, 55)(17, 68)(18, 54)(19, 61)(20, 56)(21, 66)(22, 63)(23, 57)(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) :: { ( 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 E20.170 Graph:: bipartite v = 4 e = 48 f = 6 degree seq :: [ 24^4 ] E20.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, (Y1, Y3), Y1^2 * Y3 * Y2, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y2^-1, Y1^-1), (R * Y2)^2, (Y2, Y3), Y2 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y2^2 * Y3^-1, Y1 * Y3^-4, Y1^-1 * Y2 * Y3 * Y1^-3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 14, 38, 5, 29)(3, 27, 9, 33, 7, 31, 12, 36, 24, 48, 15, 39)(4, 28, 10, 34, 6, 30, 11, 35, 23, 47, 18, 42)(13, 37, 19, 43, 16, 40, 20, 44, 21, 45, 17, 41)(49, 73, 51, 75, 61, 85, 66, 90, 70, 94, 60, 84, 68, 92, 54, 78)(50, 74, 57, 81, 67, 91, 52, 76, 62, 86, 72, 96, 69, 93, 59, 83)(53, 77, 63, 87, 65, 89, 71, 95, 56, 80, 55, 79, 64, 88, 58, 82) L = (1, 52)(2, 58)(3, 62)(4, 65)(5, 66)(6, 67)(7, 49)(8, 54)(9, 53)(10, 61)(11, 64)(12, 50)(13, 72)(14, 71)(15, 70)(16, 51)(17, 60)(18, 69)(19, 63)(20, 57)(21, 55)(22, 59)(23, 68)(24, 56)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.178 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 12^4, 16^3 ] E20.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 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 * Y2, Y1^-1 * Y3 * Y2, (R * Y3)^2, Y3^2 * Y2^-1 * Y3, (R * Y1)^2, (R * Y2)^2, Y1^6, Y2^8, (Y1^-1 * Y2^-2)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 18, 42, 14, 38, 5, 29)(3, 27, 9, 33, 19, 43, 23, 47, 16, 40, 7, 31)(4, 28, 10, 34, 20, 44, 22, 46, 15, 39, 6, 30)(11, 35, 21, 45, 24, 48, 17, 41, 13, 37, 12, 36)(49, 73, 51, 75, 59, 83, 68, 92, 66, 90, 71, 95, 65, 89, 54, 78)(50, 74, 57, 81, 69, 93, 70, 94, 62, 86, 64, 88, 61, 85, 52, 76)(53, 77, 55, 79, 60, 84, 58, 82, 56, 80, 67, 91, 72, 96, 63, 87) L = (1, 52)(2, 58)(3, 50)(4, 60)(5, 54)(6, 61)(7, 49)(8, 68)(9, 56)(10, 59)(11, 57)(12, 51)(13, 55)(14, 63)(15, 65)(16, 53)(17, 64)(18, 70)(19, 66)(20, 69)(21, 67)(22, 72)(23, 62)(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) :: { ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.179 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 12^4, 16^3 ] E20.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y3 * Y1^-1 * Y2, Y1^-1 * Y3 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^8, Y1^-1 * Y2^-9 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 14, 38, 20, 44, 17, 41, 11, 35, 5, 29)(3, 27, 9, 33, 15, 39, 21, 45, 24, 48, 19, 43, 13, 37, 7, 31)(4, 28, 10, 34, 16, 40, 22, 46, 23, 47, 18, 42, 12, 36, 6, 30)(49, 73, 51, 75, 58, 82, 56, 80, 63, 87, 70, 94, 68, 92, 72, 96, 66, 90, 59, 83, 61, 85, 54, 78)(50, 74, 57, 81, 64, 88, 62, 86, 69, 93, 71, 95, 65, 89, 67, 91, 60, 84, 53, 77, 55, 79, 52, 76) L = (1, 52)(2, 58)(3, 50)(4, 51)(5, 54)(6, 55)(7, 49)(8, 64)(9, 56)(10, 57)(11, 60)(12, 61)(13, 53)(14, 70)(15, 62)(16, 63)(17, 66)(18, 67)(19, 59)(20, 71)(21, 68)(22, 69)(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) :: { ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ), ( 12, 48, 12, 48, 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 E20.176 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2 * Y1^-1, Y3^-1 * Y2^2 * Y1^-1, Y3^2 * Y1^-1 * Y3, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^2 * Y3 * Y2 * Y1, Y3 * Y1^2 * Y2 * Y1, (Y3 * Y2^-1 * Y3)^2, Y3^-1 * Y1^2 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 22, 46, 13, 37, 16, 40, 5, 29)(3, 27, 9, 33, 18, 42, 7, 31, 12, 36, 21, 45, 23, 47, 14, 38)(4, 28, 10, 34, 17, 41, 6, 30, 11, 35, 20, 44, 24, 48, 15, 39)(49, 73, 51, 75, 58, 82, 64, 88, 71, 95, 63, 87, 70, 94, 60, 84, 68, 92, 56, 80, 66, 90, 54, 78)(50, 74, 57, 81, 65, 89, 53, 77, 62, 86, 52, 76, 61, 85, 69, 93, 72, 96, 67, 91, 55, 79, 59, 83) L = (1, 52)(2, 58)(3, 61)(4, 60)(5, 63)(6, 62)(7, 49)(8, 65)(9, 64)(10, 69)(11, 51)(12, 50)(13, 68)(14, 70)(15, 55)(16, 72)(17, 71)(18, 53)(19, 54)(20, 57)(21, 56)(22, 59)(23, 67)(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, 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 E20.177 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 16^3, 24^2 ] E20.176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 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 * Y2)^2, (Y2, Y3^-1), (Y1, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y3 * Y1^2, Y1^2 * Y3 * Y2^-1 * Y1, Y2^6, Y2^2 * Y3^-8 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 10, 34, 3, 27, 7, 31, 14, 38, 18, 42, 9, 33, 15, 39, 21, 45, 23, 47, 17, 41, 22, 46, 24, 48, 20, 44, 13, 37, 16, 40, 19, 43, 12, 36, 5, 29, 8, 32, 11, 35, 4, 28)(49, 73, 51, 75, 57, 81, 65, 89, 61, 85, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 58, 82, 66, 90, 71, 95, 68, 92, 60, 84)(54, 78, 62, 86, 69, 93, 72, 96, 67, 91, 59, 83) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 58)(7, 62)(8, 59)(9, 63)(10, 51)(11, 52)(12, 53)(13, 64)(14, 66)(15, 69)(16, 67)(17, 70)(18, 57)(19, 60)(20, 61)(21, 71)(22, 72)(23, 65)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 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 E20.174 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 12^4, 48 ] E20.177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, (Y1^-1, Y3^-1), (Y1 * Y3^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1^-2 * Y3, (Y2, Y3^-1), (Y2^-1, Y1), Y1 * Y2^-1 * Y3^2 * Y1, Y2^3 * Y1 * Y3^-1, Y1^-1 * Y2^2 * Y3 * Y2, (Y3^-1 * Y1^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 15, 39, 3, 27, 9, 33, 23, 47, 22, 46, 13, 37, 17, 41, 20, 44, 7, 31, 12, 36, 4, 28, 10, 34, 16, 40, 21, 45, 14, 38, 24, 48, 19, 43, 6, 30, 11, 35, 18, 42, 5, 29)(49, 73, 51, 75, 61, 85, 60, 84, 69, 93, 54, 78)(50, 74, 57, 81, 65, 89, 52, 76, 62, 86, 59, 83)(53, 77, 63, 87, 70, 94, 55, 79, 64, 88, 67, 91)(56, 80, 71, 95, 68, 92, 58, 82, 72, 96, 66, 90) L = (1, 52)(2, 58)(3, 62)(4, 56)(5, 60)(6, 65)(7, 49)(8, 64)(9, 72)(10, 63)(11, 68)(12, 50)(13, 59)(14, 71)(15, 69)(16, 51)(17, 66)(18, 55)(19, 61)(20, 53)(21, 57)(22, 54)(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) :: { ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 16, 24, 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 E20.175 Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 12^4, 48 ] E20.178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^-2 * Y2 * Y3^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1^2 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), (R * Y1)^2, (Y3, Y1^-1), Y3^3 * Y2^-1 * Y3^2, Y3^-2 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1, Y3 * Y1^-9 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 16, 40, 20, 44, 17, 41, 21, 45, 13, 37, 19, 43, 12, 36, 15, 39, 5, 29)(3, 27, 6, 30, 10, 34, 7, 31, 11, 35, 18, 42, 24, 48, 22, 46, 23, 47, 14, 38, 4, 28, 9, 33)(49, 73, 51, 75, 53, 77, 57, 81, 63, 87, 52, 76, 60, 84, 62, 86, 67, 91, 71, 95, 61, 85, 70, 94, 69, 93, 72, 96, 65, 89, 66, 90, 68, 92, 59, 83, 64, 88, 55, 79, 56, 80, 58, 82, 50, 74, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 61)(5, 62)(6, 63)(7, 49)(8, 51)(9, 67)(10, 53)(11, 50)(12, 70)(13, 66)(14, 69)(15, 71)(16, 54)(17, 55)(18, 56)(19, 72)(20, 58)(21, 59)(22, 68)(23, 65)(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, 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, 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 E20.172 Graph:: bipartite v = 3 e = 48 f = 7 degree seq :: [ 24^2, 48 ] E20.179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 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 * Y3, (Y3^-1, Y2), Y1 * Y3 * Y1 * Y2^-1, Y1^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y2)^2, Y3 * Y2^-1 * Y1^2, (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y2^-4, Y1^-1 * Y2^-2 * Y1 * Y2^2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y2 * Y3^-1)^6, Y1^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 13, 37, 20, 44, 12, 36, 19, 43, 16, 40, 21, 45, 17, 41, 14, 38, 5, 29)(3, 27, 9, 33, 18, 42, 23, 47, 24, 48, 22, 46, 15, 39, 6, 30, 11, 35, 7, 31, 4, 28, 10, 34)(49, 73, 51, 75, 60, 84, 70, 94, 62, 86, 52, 76, 61, 85, 71, 95, 69, 93, 59, 83, 50, 74, 57, 81, 67, 91, 63, 87, 53, 77, 58, 82, 68, 92, 72, 96, 65, 89, 55, 79, 56, 80, 66, 90, 64, 88, 54, 78) L = (1, 52)(2, 58)(3, 61)(4, 50)(5, 55)(6, 62)(7, 49)(8, 51)(9, 68)(10, 56)(11, 53)(12, 71)(13, 57)(14, 59)(15, 65)(16, 70)(17, 54)(18, 60)(19, 72)(20, 66)(21, 63)(22, 69)(23, 67)(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, 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, 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 E20.173 Graph:: bipartite v = 3 e = 48 f = 7 degree seq :: [ 24^2, 48 ] E20.180 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2, Y2^2 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-1 * Y3 * Y2^-1, Y1^6, (Y2^-1 * Y1)^4, (Y3^-1 * Y1^-1)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 16, 40, 14, 38, 5, 29)(3, 27, 6, 30, 10, 34, 18, 42, 20, 44, 12, 36)(4, 28, 9, 33, 17, 41, 23, 47, 21, 45, 13, 37)(7, 31, 11, 35, 19, 43, 24, 48, 22, 46, 15, 39)(49, 73, 51, 75, 53, 77, 60, 84, 62, 86, 68, 92, 64, 88, 66, 90, 56, 80, 58, 82, 50, 74, 54, 78)(52, 76, 55, 79, 61, 85, 63, 87, 69, 93, 70, 94, 71, 95, 72, 96, 65, 89, 67, 91, 57, 81, 59, 83) L = (1, 52)(2, 57)(3, 55)(4, 54)(5, 61)(6, 59)(7, 49)(8, 65)(9, 58)(10, 67)(11, 50)(12, 63)(13, 51)(14, 69)(15, 53)(16, 71)(17, 66)(18, 72)(19, 56)(20, 70)(21, 60)(22, 62)(23, 68)(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) :: { ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E20.183 Graph:: bipartite v = 6 e = 48 f = 4 degree seq :: [ 12^4, 24^2 ] E20.181 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, (R * Y3)^2, (Y3, Y1^-1), (R * Y2)^2, (R * Y1)^2, (Y3, Y2^-1), Y3^-1 * Y2 * Y3^-1 * Y1^-2, Y1^-1 * Y3^4, Y1^6, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 18, 42, 5, 29)(3, 27, 6, 30, 10, 34, 21, 45, 15, 39, 13, 37)(4, 28, 9, 33, 14, 38, 20, 44, 24, 48, 16, 40)(7, 31, 11, 35, 23, 47, 12, 36, 17, 41, 19, 43)(49, 73, 51, 75, 53, 77, 61, 85, 66, 90, 63, 87, 70, 94, 69, 93, 56, 80, 58, 82, 50, 74, 54, 78)(52, 76, 60, 84, 64, 88, 71, 95, 72, 96, 59, 83, 68, 92, 55, 79, 62, 86, 67, 91, 57, 81, 65, 89) L = (1, 52)(2, 57)(3, 60)(4, 63)(5, 64)(6, 65)(7, 49)(8, 62)(9, 61)(10, 67)(11, 50)(12, 70)(13, 71)(14, 51)(15, 59)(16, 69)(17, 66)(18, 72)(19, 53)(20, 54)(21, 55)(22, 68)(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) :: { ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48, 16, 48 ) } Outer automorphisms :: reflexible Dual of E20.182 Graph:: bipartite v = 6 e = 48 f = 4 degree seq :: [ 12^4, 24^2 ] E20.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y2, Y2 * Y1 * Y3^-2, Y3^2 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^8, (Y1 * Y2^-1)^6, (Y3^-1 * Y1^-1)^6, Y2^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 12, 36, 18, 42, 17, 41, 11, 35, 5, 29)(3, 27, 7, 31, 13, 37, 19, 43, 23, 47, 22, 46, 16, 40, 10, 34)(4, 28, 8, 32, 14, 38, 20, 44, 24, 48, 21, 45, 15, 39, 9, 33)(49, 73, 51, 75, 57, 81, 53, 77, 58, 82, 63, 87, 59, 83, 64, 88, 69, 93, 65, 89, 70, 94, 72, 96, 66, 90, 71, 95, 68, 92, 60, 84, 67, 91, 62, 86, 54, 78, 61, 85, 56, 80, 50, 74, 55, 79, 52, 76) L = (1, 52)(2, 56)(3, 49)(4, 55)(5, 57)(6, 62)(7, 50)(8, 61)(9, 51)(10, 53)(11, 63)(12, 68)(13, 54)(14, 67)(15, 58)(16, 59)(17, 69)(18, 72)(19, 60)(20, 71)(21, 64)(22, 65)(23, 66)(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, 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, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E20.181 Graph:: bipartite v = 4 e = 48 f = 6 degree seq :: [ 16^3, 48 ] E20.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 8, 12, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, (Y1, Y2^-1), (Y3, Y2^-1), Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y3^2 * Y2^2, Y3 * Y2^-2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-1 * Y2^-2, (Y2 * Y3)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^-4, Y3 * Y1^-2 * Y2 * Y1^-2, (Y3 * Y1)^6, Y1^-1 * Y2^18 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 14, 38, 24, 48, 17, 41, 5, 29)(3, 27, 9, 33, 20, 44, 18, 42, 7, 31, 12, 36, 23, 47, 15, 39)(4, 28, 10, 34, 21, 45, 16, 40, 6, 30, 11, 35, 22, 46, 13, 37)(49, 73, 51, 75, 61, 85, 67, 91, 66, 90, 69, 93, 65, 89, 71, 95, 59, 83, 50, 74, 57, 81, 52, 76, 62, 86, 55, 79, 64, 88, 53, 77, 63, 87, 70, 94, 56, 80, 68, 92, 58, 82, 72, 96, 60, 84, 54, 78) L = (1, 52)(2, 58)(3, 62)(4, 60)(5, 61)(6, 57)(7, 49)(8, 69)(9, 72)(10, 71)(11, 68)(12, 50)(13, 55)(14, 54)(15, 67)(16, 51)(17, 70)(18, 53)(19, 64)(20, 65)(21, 63)(22, 66)(23, 56)(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) :: { ( 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, 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, 12, 24, 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E20.180 Graph:: bipartite v = 4 e = 48 f = 6 degree seq :: [ 16^3, 48 ] E20.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y2^4, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^24 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 21, 45, 18, 42, 10, 34)(5, 29, 8, 32, 16, 40, 22, 46, 19, 43, 12, 36)(9, 33, 17, 41, 23, 47, 24, 48, 20, 44, 13, 37)(49, 73, 51, 75, 57, 81, 56, 80, 50, 74, 55, 79, 65, 89, 64, 88, 54, 78, 63, 87, 71, 95, 70, 94, 62, 86, 69, 93, 72, 96, 67, 91, 59, 83, 66, 90, 68, 92, 60, 84, 52, 76, 58, 82, 61, 85, 53, 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) :: { ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 12^4, 48 ] E20.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2^4 * Y1, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^24 ] Map:: R = (1, 25, 2, 26, 6, 30, 14, 38, 11, 35, 4, 28)(3, 27, 7, 31, 15, 39, 21, 45, 19, 43, 10, 34)(5, 29, 8, 32, 16, 40, 22, 46, 20, 44, 12, 36)(9, 33, 13, 37, 17, 41, 23, 47, 24, 48, 18, 42)(49, 73, 51, 75, 57, 81, 60, 84, 52, 76, 58, 82, 66, 90, 68, 92, 59, 83, 67, 91, 72, 96, 70, 94, 62, 86, 69, 93, 71, 95, 64, 88, 54, 78, 63, 87, 65, 89, 56, 80, 50, 74, 55, 79, 61, 85, 53, 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) :: { ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 12^4, 48 ] E20.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y3^-1 * Y1^-2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), (Y1^-1, Y2^-1), (Y3 * Y1^-1)^2, Y2^-1 * Y1^-1 * Y2^-3, Y2^-1 * Y1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^2 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 10, 34, 4, 28, 5, 29)(3, 27, 8, 32, 14, 38, 19, 43, 12, 36, 13, 37)(6, 30, 9, 33, 18, 42, 21, 45, 15, 39, 16, 40)(11, 35, 17, 41, 20, 44, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 59, 83, 64, 88, 53, 77, 61, 85, 71, 95, 63, 87, 52, 76, 60, 84, 70, 94, 69, 93, 58, 82, 67, 91, 72, 96, 66, 90, 55, 79, 62, 86, 68, 92, 57, 81, 50, 74, 56, 80, 65, 89, 54, 78) L = (1, 52)(2, 53)(3, 60)(4, 55)(5, 58)(6, 63)(7, 49)(8, 61)(9, 64)(10, 50)(11, 70)(12, 62)(13, 67)(14, 51)(15, 66)(16, 69)(17, 71)(18, 54)(19, 56)(20, 59)(21, 57)(22, 68)(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) :: { ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48, 12, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 48 f = 5 degree seq :: [ 12^4, 48 ] E20.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1^-1 * Y2^-3, (R * Y3)^2, (R * Y2)^2, (Y1, Y3), (R * Y1)^2, Y1^4, Y2 * Y3 * Y2 * Y1 * Y3, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 9, 33, 19, 43, 15, 39)(4, 28, 10, 34, 20, 44, 16, 40)(6, 30, 11, 35, 21, 45, 13, 37)(7, 31, 12, 36, 22, 46, 17, 41)(14, 38, 18, 42, 23, 47, 24, 48)(49, 73, 51, 75, 61, 85, 53, 77, 63, 87, 69, 93, 56, 80, 67, 91, 59, 83, 50, 74, 57, 81, 54, 78)(52, 76, 62, 86, 65, 89, 64, 88, 72, 96, 70, 94, 68, 92, 71, 95, 60, 84, 58, 82, 66, 90, 55, 79) L = (1, 52)(2, 58)(3, 62)(4, 51)(5, 64)(6, 55)(7, 49)(8, 68)(9, 66)(10, 57)(11, 60)(12, 50)(13, 65)(14, 61)(15, 72)(16, 63)(17, 53)(18, 54)(19, 71)(20, 67)(21, 70)(22, 56)(23, 59)(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) :: { ( 48^8 ), ( 48^24 ) } Outer automorphisms :: reflexible Dual of E20.197 Graph:: bipartite v = 8 e = 48 f = 2 degree seq :: [ 8^6, 24^2 ] E20.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y2 * Y1^-1 * Y2^2, Y2^3 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (Y1, Y3), (R * Y1)^2, Y1^4, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] 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, 24, 48, 18, 42)(49, 73, 51, 75, 59, 83, 50, 74, 57, 81, 69, 93, 56, 80, 67, 91, 64, 88, 53, 77, 62, 86, 54, 78)(52, 76, 61, 85, 60, 84, 58, 82, 71, 95, 70, 94, 68, 92, 72, 96, 65, 89, 63, 87, 66, 90, 55, 79) L = (1, 52)(2, 58)(3, 61)(4, 51)(5, 63)(6, 55)(7, 49)(8, 68)(9, 71)(10, 57)(11, 60)(12, 50)(13, 59)(14, 66)(15, 62)(16, 65)(17, 53)(18, 54)(19, 72)(20, 67)(21, 70)(22, 56)(23, 69)(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) :: { ( 48^8 ), ( 48^24 ) } Outer automorphisms :: reflexible Dual of E20.198 Graph:: bipartite v = 8 e = 48 f = 2 degree seq :: [ 8^6, 24^2 ] E20.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y1 * Y2, (Y3, Y1^-1), (R * Y3)^2, (Y3, Y2^-1), (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1^-4, (Y2^-1 * Y3)^24 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 18, 42, 7, 31, 11, 35, 21, 45, 15, 39, 4, 28, 9, 33, 17, 41, 5, 29)(3, 27, 6, 30, 10, 34, 20, 44, 14, 38, 19, 43, 23, 47, 24, 48, 12, 36, 16, 40, 22, 46, 13, 37)(49, 73, 51, 75, 53, 77, 61, 85, 65, 89, 70, 94, 57, 81, 64, 88, 52, 76, 60, 84, 63, 87, 72, 96, 69, 93, 71, 95, 59, 83, 67, 91, 55, 79, 62, 86, 66, 90, 68, 92, 56, 80, 58, 82, 50, 74, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 63)(6, 64)(7, 49)(8, 65)(9, 59)(10, 70)(11, 50)(12, 62)(13, 72)(14, 51)(15, 66)(16, 67)(17, 69)(18, 53)(19, 54)(20, 61)(21, 56)(22, 71)(23, 58)(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, 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, 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 E20.194 Graph:: bipartite v = 3 e = 48 f = 7 degree seq :: [ 24^2, 48 ] E20.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 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, Y2), Y2 * Y3 * Y2 * Y1^-1, Y1 * Y2^-2 * Y3^-1, Y2^-1 * Y1 * Y3^-1 * Y2^-1, (Y2, Y3), (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3 * Y1^4, Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-2, Y3^-1 * Y1 * Y2^22 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 7, 31, 12, 36, 22, 46, 15, 39, 4, 28, 10, 34, 17, 41, 5, 29)(3, 27, 9, 33, 20, 44, 16, 40, 14, 38, 23, 47, 18, 42, 6, 30, 11, 35, 21, 45, 24, 48, 13, 37)(49, 73, 51, 75, 60, 84, 71, 95, 65, 89, 72, 96, 67, 91, 64, 88, 52, 76, 59, 83, 50, 74, 57, 81, 70, 94, 66, 90, 53, 77, 61, 85, 55, 79, 62, 86, 58, 82, 69, 93, 56, 80, 68, 92, 63, 87, 54, 78) L = (1, 52)(2, 58)(3, 59)(4, 55)(5, 63)(6, 64)(7, 49)(8, 65)(9, 69)(10, 60)(11, 62)(12, 50)(13, 54)(14, 51)(15, 67)(16, 61)(17, 70)(18, 68)(19, 53)(20, 72)(21, 71)(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) :: { ( 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, 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 E20.193 Graph:: bipartite v = 3 e = 48 f = 7 degree seq :: [ 24^2, 48 ] E20.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1^-2 * Y3, (Y3^-1, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^6, (Y3^-1 * Y1^-1)^4, Y3 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 8, 32, 12, 36, 16, 40, 20, 44, 22, 46, 15, 39, 14, 38, 7, 31, 5, 29)(3, 27, 6, 30, 9, 33, 13, 37, 17, 41, 21, 45, 23, 47, 24, 48, 19, 43, 18, 42, 11, 35, 10, 34)(49, 73, 51, 75, 53, 77, 58, 82, 55, 79, 59, 83, 62, 86, 66, 90, 63, 87, 67, 91, 70, 94, 72, 96, 68, 92, 71, 95, 64, 88, 69, 93, 60, 84, 65, 89, 56, 80, 61, 85, 52, 76, 57, 81, 50, 74, 54, 78) L = (1, 52)(2, 56)(3, 57)(4, 60)(5, 50)(6, 61)(7, 49)(8, 64)(9, 65)(10, 54)(11, 51)(12, 68)(13, 69)(14, 53)(15, 55)(16, 70)(17, 71)(18, 58)(19, 59)(20, 63)(21, 72)(22, 62)(23, 67)(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, 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, 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 E20.195 Graph:: bipartite v = 3 e = 48 f = 7 degree seq :: [ 24^2, 48 ] E20.192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 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 * Y1^2, (R * Y1)^2, (Y2, Y1^-1), (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y2^-4 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y1, Y3^6, Y1^-1 * Y2^-1 * Y3^-3 * Y2^-1, Y2^-1 * Y3^3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28, 9, 33, 15, 39, 11, 35, 22, 46, 19, 43, 21, 45, 18, 42, 7, 31, 5, 29)(3, 27, 8, 32, 12, 36, 23, 47, 24, 48, 20, 44, 17, 41, 6, 30, 10, 34, 16, 40, 14, 38, 13, 37)(49, 73, 51, 75, 59, 83, 68, 92, 55, 79, 62, 86, 57, 81, 71, 95, 69, 93, 58, 82, 50, 74, 56, 80, 70, 94, 65, 89, 53, 77, 61, 85, 63, 87, 72, 96, 66, 90, 64, 88, 52, 76, 60, 84, 67, 91, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 63)(5, 50)(6, 64)(7, 49)(8, 71)(9, 59)(10, 62)(11, 67)(12, 72)(13, 56)(14, 51)(15, 70)(16, 61)(17, 58)(18, 53)(19, 66)(20, 54)(21, 55)(22, 69)(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) :: { ( 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, 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 E20.196 Graph:: bipartite v = 3 e = 48 f = 7 degree seq :: [ 24^2, 48 ] E20.193 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^3, (Y2^-1, Y3^-1), Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3^-1 * Y1^-2, (Y3, Y1), (R * Y2)^2, (R * Y3)^2, Y2^4, (R * Y1)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-2, Y2 * Y3^-1 * Y1^22 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 23, 47, 17, 41, 6, 30, 11, 35, 7, 31, 12, 36, 14, 38, 22, 46, 13, 37, 21, 45, 18, 42, 15, 39, 4, 28, 10, 34, 3, 27, 9, 33, 20, 44, 24, 48, 16, 40, 5, 29)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 57, 81, 69, 93, 59, 83)(52, 76, 62, 86, 71, 95, 64, 88)(53, 77, 58, 82, 70, 94, 65, 89)(55, 79, 56, 80, 68, 92, 66, 90)(60, 84, 67, 91, 72, 96, 63, 87) L = (1, 52)(2, 58)(3, 62)(4, 55)(5, 63)(6, 64)(7, 49)(8, 51)(9, 70)(10, 60)(11, 53)(12, 50)(13, 71)(14, 56)(15, 59)(16, 66)(17, 72)(18, 54)(19, 57)(20, 61)(21, 65)(22, 67)(23, 68)(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) :: { ( 24, 48, 24, 48, 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.190 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 8^6, 48 ] E20.194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y3^3, (Y2, Y1), Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3^-1, Y1^-1), (R * Y2)^2, Y1^2 * Y3 * Y2, (R * Y1)^2, Y2^4, (R * Y3)^2, Y3^-1 * Y1 * Y2 * Y3^-1 * Y1, (Y2^-1 * Y3^-1)^12, (Y3^-1 * Y2)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 23, 47, 15, 39, 3, 27, 9, 33, 7, 31, 12, 36, 18, 42, 22, 46, 13, 37, 21, 45, 16, 40, 17, 41, 4, 28, 10, 34, 6, 30, 11, 35, 20, 44, 24, 48, 14, 38, 5, 29)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 57, 81, 69, 93, 59, 83)(52, 76, 62, 86, 71, 95, 66, 90)(53, 77, 63, 87, 70, 94, 58, 82)(55, 79, 64, 88, 68, 92, 56, 80)(60, 84, 65, 89, 72, 96, 67, 91) L = (1, 52)(2, 58)(3, 62)(4, 55)(5, 65)(6, 66)(7, 49)(8, 54)(9, 53)(10, 60)(11, 70)(12, 50)(13, 71)(14, 64)(15, 72)(16, 51)(17, 57)(18, 56)(19, 59)(20, 61)(21, 63)(22, 67)(23, 68)(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) :: { ( 24, 48, 24, 48, 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.189 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 8^6, 48 ] E20.195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y1^2 * Y2 * Y3, (Y1^-1, Y2), (Y3, Y2), (Y1^-1, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-3 * Y2^2, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 18, 42, 4, 28, 10, 34, 6, 30, 11, 35, 17, 41, 23, 47, 19, 43, 24, 48, 13, 37, 21, 45, 16, 40, 22, 46, 20, 44, 15, 39, 3, 27, 9, 33, 7, 31, 12, 36, 14, 38, 5, 29)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 57, 81, 69, 93, 59, 83)(52, 76, 62, 86, 68, 92, 67, 91)(53, 77, 63, 87, 72, 96, 58, 82)(55, 79, 64, 88, 65, 89, 56, 80)(60, 84, 70, 94, 71, 95, 66, 90) L = (1, 52)(2, 58)(3, 62)(4, 65)(5, 66)(6, 67)(7, 49)(8, 54)(9, 53)(10, 71)(11, 72)(12, 50)(13, 68)(14, 56)(15, 60)(16, 51)(17, 61)(18, 59)(19, 64)(20, 55)(21, 63)(22, 57)(23, 69)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24, 48, 24, 48, 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.191 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 8^6, 48 ] E20.196 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3^-1), Y3 * Y1^2 * Y2^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2^4, (Y2^-1, Y1^-1), Y2 * Y3^-1 * Y1^-2, (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1^2 * Y3^-2, Y2^-2 * Y3^-3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 16, 40, 4, 28, 10, 34, 3, 27, 9, 33, 15, 39, 23, 47, 14, 38, 22, 46, 13, 37, 21, 45, 19, 43, 24, 48, 20, 44, 18, 42, 6, 30, 11, 35, 7, 31, 12, 36, 17, 41, 5, 29)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 57, 81, 69, 93, 59, 83)(52, 76, 62, 86, 68, 92, 65, 89)(53, 77, 58, 82, 70, 94, 66, 90)(55, 79, 56, 80, 63, 87, 67, 91)(60, 84, 64, 88, 71, 95, 72, 96) L = (1, 52)(2, 58)(3, 62)(4, 63)(5, 64)(6, 65)(7, 49)(8, 51)(9, 70)(10, 71)(11, 53)(12, 50)(13, 68)(14, 67)(15, 61)(16, 57)(17, 56)(18, 60)(19, 54)(20, 55)(21, 66)(22, 72)(23, 69)(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) :: { ( 24, 48, 24, 48, 24, 48, 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.192 Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 8^6, 48 ] E20.197 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y2 * Y3 * Y2^-1 * Y1^-1, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-4 * Y3^-1 * Y2^-1, Y1^-2 * Y2^-1 * Y3^-1 * Y1^-2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 14, 38, 12, 36, 5, 29, 8, 32, 16, 40, 22, 46, 19, 43, 13, 37, 18, 42, 24, 48, 20, 44, 9, 33, 17, 41, 23, 47, 21, 45, 10, 34, 3, 27, 7, 31, 15, 39, 11, 35, 4, 28)(49, 73, 51, 75, 57, 81, 67, 91, 60, 84, 52, 76, 58, 82, 68, 92, 70, 94, 62, 86, 59, 83, 69, 93, 72, 96, 64, 88, 54, 78, 63, 87, 71, 95, 66, 90, 56, 80, 50, 74, 55, 79, 65, 89, 61, 85, 53, 77) 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, 60)(15, 59)(16, 70)(17, 71)(18, 72)(19, 61)(20, 57)(21, 58)(22, 67)(23, 69)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E20.187 Graph:: bipartite v = 2 e = 48 f = 8 degree seq :: [ 48^2 ] E20.198 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2 * Y1^-1, Y1^-1 * Y3^2 * Y1^-1, Y2^-2 * Y1 * Y3, (Y3^-1 * Y1)^2, (Y1, Y2^-1), (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (R * Y2)^2, Y3^-3 * Y2^-1 * Y3^-2, Y2^-1 * Y1^-2 * Y3^-1 * Y1^-2, (Y2 * Y3)^6, (Y3^3 * Y2^-1)^3, Y1 * Y3 * Y2^22 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 18, 42, 24, 48, 14, 38, 3, 27, 9, 33, 20, 44, 17, 41, 7, 31, 12, 36, 4, 28, 10, 34, 21, 45, 16, 40, 6, 30, 11, 35, 22, 46, 13, 37, 23, 47, 15, 39, 5, 29)(49, 73, 51, 75, 58, 82, 71, 95, 66, 90, 55, 79, 59, 83, 50, 74, 57, 81, 69, 93, 63, 87, 72, 96, 60, 84, 70, 94, 56, 80, 68, 92, 64, 88, 53, 77, 62, 86, 52, 76, 61, 85, 67, 91, 65, 89, 54, 78) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 62)(7, 49)(8, 69)(9, 71)(10, 67)(11, 51)(12, 50)(13, 68)(14, 70)(15, 55)(16, 72)(17, 53)(18, 54)(19, 64)(20, 63)(21, 66)(22, 57)(23, 65)(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, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E20.188 Graph:: bipartite v = 2 e = 48 f = 8 degree seq :: [ 48^2 ] E20.199 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1, Y1 * Y2^-2, (Y3, Y2^-1), (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^3 * Y2^-1 * Y3^2, 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^-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 * Y2 ] Map:: non-degenerate R = (1, 26, 2, 27, 6, 31, 3, 28, 5, 30)(4, 29, 8, 33, 14, 39, 10, 35, 13, 38)(7, 32, 9, 34, 16, 41, 11, 36, 15, 40)(12, 37, 18, 43, 23, 48, 20, 45, 22, 47)(17, 42, 19, 44, 25, 50, 21, 46, 24, 49)(51, 76, 53, 78, 52, 77, 55, 80, 56, 81)(54, 79, 60, 85, 58, 83, 63, 88, 64, 89)(57, 82, 61, 86, 59, 84, 65, 90, 66, 91)(62, 87, 70, 95, 68, 93, 72, 97, 73, 98)(67, 92, 71, 96, 69, 94, 74, 99, 75, 100) L = (1, 54)(2, 58)(3, 60)(4, 62)(5, 63)(6, 64)(7, 51)(8, 68)(9, 52)(10, 70)(11, 53)(12, 71)(13, 72)(14, 73)(15, 55)(16, 56)(17, 57)(18, 74)(19, 59)(20, 69)(21, 61)(22, 75)(23, 67)(24, 65)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50^10 ) } Outer automorphisms :: reflexible Dual of E20.218 Graph:: bipartite v = 10 e = 50 f = 2 degree seq :: [ 10^10 ] E20.200 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1 * Y2^-1 * Y1, (Y3, Y2^-1), (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3^3 * Y2^-1 * Y3^2, 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, (Y1^-1 * Y3^-1)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 3, 28, 6, 31, 5, 30)(4, 29, 8, 33, 10, 35, 14, 39, 13, 38)(7, 32, 9, 34, 11, 36, 16, 41, 15, 40)(12, 37, 18, 43, 20, 45, 23, 48, 22, 47)(17, 42, 19, 44, 21, 46, 25, 50, 24, 49)(51, 76, 53, 78, 55, 80, 52, 77, 56, 81)(54, 79, 60, 85, 63, 88, 58, 83, 64, 89)(57, 82, 61, 86, 65, 90, 59, 84, 66, 91)(62, 87, 70, 95, 72, 97, 68, 93, 73, 98)(67, 92, 71, 96, 74, 99, 69, 94, 75, 100) L = (1, 54)(2, 58)(3, 60)(4, 62)(5, 63)(6, 64)(7, 51)(8, 68)(9, 52)(10, 70)(11, 53)(12, 71)(13, 72)(14, 73)(15, 55)(16, 56)(17, 57)(18, 75)(19, 59)(20, 74)(21, 61)(22, 69)(23, 67)(24, 65)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50^10 ) } Outer automorphisms :: reflexible Dual of E20.217 Graph:: bipartite v = 10 e = 50 f = 2 degree seq :: [ 10^10 ] E20.201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^5, Y2^5 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^25 ] Map:: R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 19, 44, 10, 35)(5, 30, 8, 33, 15, 40, 20, 45, 12, 37)(9, 34, 16, 41, 22, 47, 24, 49, 18, 43)(13, 38, 17, 42, 23, 48, 25, 50, 21, 46)(51, 76, 53, 78, 59, 84, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 73, 98, 65, 90, 56, 81, 64, 89, 72, 97, 75, 100, 70, 95, 61, 86, 69, 94, 74, 99, 71, 96, 62, 87, 54, 79, 60, 85, 68, 93, 63, 88, 55, 80) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.202 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^5, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-5, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^25 ] Map:: R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 20, 45, 10, 35)(5, 30, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 22, 47, 25, 50, 19, 44)(13, 38, 17, 42, 23, 48, 24, 49, 18, 43)(51, 76, 53, 78, 59, 84, 68, 93, 62, 87, 54, 79, 60, 85, 69, 94, 74, 99, 71, 96, 61, 86, 70, 95, 75, 100, 73, 98, 65, 90, 56, 81, 64, 89, 72, 97, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 63, 88, 55, 80) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.203 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^5, Y1^5, (R * Y2 * Y3^-1)^2, Y2^5 * Y1^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^3 * Y1^-1, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^25 ] Map:: R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 20, 45, 10, 35)(5, 30, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 23, 48, 25, 50, 19, 44)(13, 38, 17, 42, 24, 49, 18, 43, 22, 47)(51, 76, 53, 78, 59, 84, 68, 93, 71, 96, 61, 86, 70, 95, 75, 100, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 72, 97, 62, 87, 54, 79, 60, 85, 69, 94, 74, 99, 65, 90, 56, 81, 64, 89, 73, 98, 63, 88, 55, 80) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.204 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^5, Y1^5, (R * Y2 * Y3^-1)^2, Y2^-5 * Y1^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^25 ] Map:: R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 20, 45, 10, 35)(5, 30, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 24, 49, 23, 48, 19, 44)(13, 38, 17, 42, 18, 43, 25, 50, 22, 47)(51, 76, 53, 78, 59, 84, 68, 93, 65, 90, 56, 81, 64, 89, 74, 99, 72, 97, 62, 87, 54, 79, 60, 85, 69, 94, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 75, 100, 71, 96, 61, 86, 70, 95, 73, 98, 63, 88, 55, 80) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.205 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3^-5, Y1^5, (R * Y2 * Y3^-1)^2, Y2^4 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 19, 44, 10, 35)(5, 30, 8, 33, 15, 40, 20, 45, 12, 37)(9, 34, 16, 41, 22, 47, 24, 49, 18, 43)(13, 38, 17, 42, 23, 48, 25, 50, 21, 46)(51, 76, 53, 78, 59, 84, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 73, 98, 65, 90, 56, 81, 64, 89, 72, 97, 75, 100, 70, 95, 61, 86, 69, 94, 74, 99, 71, 96, 62, 87, 54, 79, 60, 85, 68, 93, 63, 88, 55, 80) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 69)(15, 70)(16, 72)(17, 73)(18, 59)(19, 60)(20, 62)(21, 63)(22, 74)(23, 75)(24, 68)(25, 71)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.209 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.206 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y3 * Y1^2, Y1 * Y3^-2, (R * Y2)^2, (Y1^-1, Y2), (R * Y3)^2, (Y2, Y3), (R * Y1)^2, Y3^-1 * Y2^2 * Y3 * Y2^-2, Y2^4 * Y3^-1 * Y2, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: non-degenerate R = (1, 26, 2, 27, 7, 32, 4, 29, 5, 30)(3, 28, 8, 33, 13, 38, 11, 36, 12, 37)(6, 31, 9, 34, 17, 42, 14, 39, 15, 40)(10, 35, 18, 43, 23, 48, 21, 46, 22, 47)(16, 41, 19, 44, 25, 50, 20, 45, 24, 49)(51, 76, 53, 78, 60, 85, 70, 95, 64, 89, 54, 79, 61, 86, 71, 96, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 74, 99, 65, 90, 55, 80, 62, 87, 72, 97, 75, 100, 67, 92, 57, 82, 63, 88, 73, 98, 66, 91, 56, 81) L = (1, 54)(2, 55)(3, 61)(4, 52)(5, 57)(6, 64)(7, 51)(8, 62)(9, 65)(10, 71)(11, 58)(12, 63)(13, 53)(14, 59)(15, 67)(16, 70)(17, 56)(18, 72)(19, 74)(20, 69)(21, 68)(22, 73)(23, 60)(24, 75)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.210 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.207 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-1, Y3 * Y1 * Y3, Y1 * Y3^-1 * Y1, (R * Y2)^2, (Y2, Y1^-1), (R * Y3)^2, (Y3^-1, Y2), (R * Y1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^2, Y2^2 * Y3^-1 * Y2^3, 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 * Y3^2 ] Map:: non-degenerate R = (1, 26, 2, 27, 4, 29, 7, 32, 5, 30)(3, 28, 8, 33, 11, 36, 13, 38, 12, 37)(6, 31, 9, 34, 14, 39, 17, 42, 15, 40)(10, 35, 18, 43, 21, 46, 23, 48, 22, 47)(16, 41, 19, 44, 20, 45, 25, 50, 24, 49)(51, 76, 53, 78, 60, 85, 70, 95, 64, 89, 54, 79, 61, 86, 71, 96, 74, 99, 65, 90, 55, 80, 62, 87, 72, 97, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 75, 100, 67, 92, 57, 82, 63, 88, 73, 98, 66, 91, 56, 81) L = (1, 54)(2, 57)(3, 61)(4, 55)(5, 52)(6, 64)(7, 51)(8, 63)(9, 67)(10, 71)(11, 62)(12, 58)(13, 53)(14, 65)(15, 59)(16, 70)(17, 56)(18, 73)(19, 75)(20, 74)(21, 72)(22, 68)(23, 60)(24, 69)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.208 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.208 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, Y1^5, Y2^-5 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 20, 45, 10, 35)(5, 30, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 22, 47, 25, 50, 19, 44)(13, 38, 17, 42, 23, 48, 24, 49, 18, 43)(51, 76, 53, 78, 59, 84, 68, 93, 62, 87, 54, 79, 60, 85, 69, 94, 74, 99, 71, 96, 61, 86, 70, 95, 75, 100, 73, 98, 65, 90, 56, 81, 64, 89, 72, 97, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 63, 88, 55, 80) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 72)(17, 73)(18, 63)(19, 59)(20, 60)(21, 62)(22, 75)(23, 74)(24, 68)(25, 69)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.207 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.209 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y3, Y1 * Y3^-1 * Y1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^-2 * Y1^-1 * Y2, Y2^3 * Y3 * Y2^2, (Y2^-1 * Y3)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 4, 29, 7, 32, 5, 30)(3, 28, 8, 33, 11, 36, 13, 38, 12, 37)(6, 31, 9, 34, 14, 39, 17, 42, 15, 40)(10, 35, 18, 43, 21, 46, 23, 48, 22, 47)(16, 41, 19, 44, 24, 49, 20, 45, 25, 50)(51, 76, 53, 78, 60, 85, 70, 95, 67, 92, 57, 82, 63, 88, 73, 98, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 75, 100, 65, 90, 55, 80, 62, 87, 72, 97, 74, 99, 64, 89, 54, 79, 61, 86, 71, 96, 66, 91, 56, 81) L = (1, 54)(2, 57)(3, 61)(4, 55)(5, 52)(6, 64)(7, 51)(8, 63)(9, 67)(10, 71)(11, 62)(12, 58)(13, 53)(14, 65)(15, 59)(16, 74)(17, 56)(18, 73)(19, 70)(20, 66)(21, 72)(22, 68)(23, 60)(24, 75)(25, 69)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.205 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y1 * Y3^-2, (Y2^-1, Y1^-1), (Y1^-1, Y2), (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y2^-2 * Y1^-1 * Y2^2 * Y1, Y2^4 * Y3 * Y2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 26, 2, 27, 7, 32, 4, 29, 5, 30)(3, 28, 8, 33, 13, 38, 11, 36, 12, 37)(6, 31, 9, 34, 17, 42, 14, 39, 15, 40)(10, 35, 18, 43, 23, 48, 21, 46, 22, 47)(16, 41, 19, 44, 20, 45, 24, 49, 25, 50)(51, 76, 53, 78, 60, 85, 70, 95, 67, 92, 57, 82, 63, 88, 73, 98, 75, 100, 65, 90, 55, 80, 62, 87, 72, 97, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 74, 99, 64, 89, 54, 79, 61, 86, 71, 96, 66, 91, 56, 81) L = (1, 54)(2, 55)(3, 61)(4, 52)(5, 57)(6, 64)(7, 51)(8, 62)(9, 65)(10, 71)(11, 58)(12, 63)(13, 53)(14, 59)(15, 67)(16, 74)(17, 56)(18, 72)(19, 75)(20, 66)(21, 68)(22, 73)(23, 60)(24, 69)(25, 70)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.206 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1^2 * Y3^-1, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2), (R * Y2)^2, Y2^4 * Y1^-1 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 26, 2, 27, 4, 29, 7, 32, 5, 30)(3, 28, 8, 33, 11, 36, 13, 38, 12, 37)(6, 31, 9, 34, 14, 39, 17, 42, 15, 40)(10, 35, 18, 43, 20, 45, 22, 47, 21, 46)(16, 41, 19, 44, 23, 48, 25, 50, 24, 49)(51, 76, 53, 78, 60, 85, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 73, 98, 64, 89, 54, 79, 61, 86, 70, 95, 75, 100, 67, 92, 57, 82, 63, 88, 72, 97, 74, 99, 65, 90, 55, 80, 62, 87, 71, 96, 66, 91, 56, 81) L = (1, 54)(2, 57)(3, 61)(4, 55)(5, 52)(6, 64)(7, 51)(8, 63)(9, 67)(10, 70)(11, 62)(12, 58)(13, 53)(14, 65)(15, 59)(16, 73)(17, 56)(18, 72)(19, 75)(20, 71)(21, 68)(22, 60)(23, 74)(24, 69)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.216 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y1 * Y3^-2, (Y2, Y1), (Y3^-1, Y2^-1), (R * Y2)^2, (Y1^-1, Y2), (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^4, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 26, 2, 27, 7, 32, 4, 29, 5, 30)(3, 28, 8, 33, 13, 38, 11, 36, 12, 37)(6, 31, 9, 34, 17, 42, 14, 39, 15, 40)(10, 35, 18, 43, 23, 48, 21, 46, 22, 47)(16, 41, 19, 44, 25, 50, 24, 49, 20, 45)(51, 76, 53, 78, 60, 85, 70, 95, 65, 90, 55, 80, 62, 87, 72, 97, 74, 99, 64, 89, 54, 79, 61, 86, 71, 96, 75, 100, 67, 92, 57, 82, 63, 88, 73, 98, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 66, 91, 56, 81) L = (1, 54)(2, 55)(3, 61)(4, 52)(5, 57)(6, 64)(7, 51)(8, 62)(9, 65)(10, 71)(11, 58)(12, 63)(13, 53)(14, 59)(15, 67)(16, 74)(17, 56)(18, 72)(19, 70)(20, 75)(21, 68)(22, 73)(23, 60)(24, 69)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.214 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y2 * Y3 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y1^5, (R * Y2 * Y3^-1)^2, Y2^2 * Y3 * Y2^2 * Y3 * Y2, Y2 * Y3^-1 * Y2^4 * Y1^-2, (Y3^-1 * Y1^-1)^5, Y3 * Y2^-1 * Y1^2 * Y3 * Y2^-1 * Y1^2 * Y3 * Y2^-1 * Y1^2 * Y3 * Y2^-1 * Y1^2 * Y3 * Y2^-1, (Y2^-1 * Y1)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 20, 45, 10, 35)(5, 30, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 23, 48, 25, 50, 19, 44)(13, 38, 17, 42, 24, 49, 18, 43, 22, 47)(51, 76, 53, 78, 59, 84, 68, 93, 71, 96, 61, 86, 70, 95, 75, 100, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 72, 97, 62, 87, 54, 79, 60, 85, 69, 94, 74, 99, 65, 90, 56, 81, 64, 89, 73, 98, 63, 88, 55, 80) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 73)(17, 74)(18, 72)(19, 59)(20, 60)(21, 62)(22, 63)(23, 75)(24, 68)(25, 69)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.215 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y3 * Y1, Y1 * Y3^-2, (Y2^-1, Y1^-1), (Y2, Y3), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^4 * Y1^-1 * Y2, (Y2^-1 * Y3)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 7, 32, 4, 29, 5, 30)(3, 28, 8, 33, 13, 38, 11, 36, 12, 37)(6, 31, 9, 34, 17, 42, 14, 39, 15, 40)(10, 35, 18, 43, 22, 47, 20, 45, 21, 46)(16, 41, 19, 44, 25, 50, 23, 48, 24, 49)(51, 76, 53, 78, 60, 85, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 75, 100, 67, 92, 57, 82, 63, 88, 72, 97, 73, 98, 64, 89, 54, 79, 61, 86, 70, 95, 74, 99, 65, 90, 55, 80, 62, 87, 71, 96, 66, 91, 56, 81) L = (1, 54)(2, 55)(3, 61)(4, 52)(5, 57)(6, 64)(7, 51)(8, 62)(9, 65)(10, 70)(11, 58)(12, 63)(13, 53)(14, 59)(15, 67)(16, 73)(17, 56)(18, 71)(19, 74)(20, 68)(21, 72)(22, 60)(23, 69)(24, 75)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.212 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y3, Y1 * Y3^-1 * Y1, (Y2, Y1), (R * Y2)^2, (Y1^-1, Y2), (R * Y3)^2, (Y3^-1, Y2), (R * Y1)^2, Y2 * Y1 * Y2^4, (Y2^-1 * Y3)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 4, 29, 7, 32, 5, 30)(3, 28, 8, 33, 11, 36, 13, 38, 12, 37)(6, 31, 9, 34, 14, 39, 17, 42, 15, 40)(10, 35, 18, 43, 21, 46, 23, 48, 22, 47)(16, 41, 19, 44, 24, 49, 25, 50, 20, 45)(51, 76, 53, 78, 60, 85, 70, 95, 65, 90, 55, 80, 62, 87, 72, 97, 75, 100, 67, 92, 57, 82, 63, 88, 73, 98, 74, 99, 64, 89, 54, 79, 61, 86, 71, 96, 69, 94, 59, 84, 52, 77, 58, 83, 68, 93, 66, 91, 56, 81) L = (1, 54)(2, 57)(3, 61)(4, 55)(5, 52)(6, 64)(7, 51)(8, 63)(9, 67)(10, 71)(11, 62)(12, 58)(13, 53)(14, 65)(15, 59)(16, 74)(17, 56)(18, 73)(19, 75)(20, 69)(21, 72)(22, 68)(23, 60)(24, 70)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.213 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y1^5, Y1^5, (R * Y2 * Y3^-1)^2, Y2^-5 * Y1^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 6, 31, 11, 36, 4, 29)(3, 28, 7, 32, 14, 39, 20, 45, 10, 35)(5, 30, 8, 33, 15, 40, 21, 46, 12, 37)(9, 34, 16, 41, 24, 49, 23, 48, 19, 44)(13, 38, 17, 42, 18, 43, 25, 50, 22, 47)(51, 76, 53, 78, 59, 84, 68, 93, 65, 90, 56, 81, 64, 89, 74, 99, 72, 97, 62, 87, 54, 79, 60, 85, 69, 94, 67, 92, 58, 83, 52, 77, 57, 82, 66, 91, 75, 100, 71, 96, 61, 86, 70, 95, 73, 98, 63, 88, 55, 80) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 74)(17, 68)(18, 75)(19, 59)(20, 60)(21, 62)(22, 63)(23, 69)(24, 73)(25, 72)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ), ( 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50 ) } Outer automorphisms :: reflexible Dual of E20.211 Graph:: bipartite v = 6 e = 50 f = 6 degree seq :: [ 10^5, 50 ] E20.217 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, (Y1, Y2^-1), Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-2 * Y1^-1 * Y3, (R * Y1)^2, (Y3, Y1), (R * Y3)^2, (R * Y2)^2, Y2 * Y1^-1 * Y3^2 * Y2, Y1^4 * Y2^-1, Y1 * Y3 * Y1 * Y3^2 * Y2^-1, Y2 * Y3^-6 ] Map:: non-degenerate R = (1, 26, 2, 27, 8, 33, 15, 40, 3, 28, 9, 34, 22, 47, 21, 46, 13, 38, 4, 29, 10, 35, 23, 48, 20, 45, 14, 39, 24, 49, 19, 44, 7, 32, 12, 37, 17, 42, 25, 50, 16, 41, 6, 31, 11, 36, 18, 43, 5, 30)(51, 76, 53, 78, 63, 88, 70, 95, 57, 82, 66, 91, 55, 80, 65, 90, 71, 96, 73, 98, 69, 94, 75, 100, 68, 93, 58, 83, 72, 97, 60, 85, 74, 99, 67, 92, 61, 86, 52, 77, 59, 84, 54, 79, 64, 89, 62, 87, 56, 81) L = (1, 54)(2, 60)(3, 64)(4, 67)(5, 63)(6, 59)(7, 51)(8, 73)(9, 74)(10, 75)(11, 72)(12, 52)(13, 62)(14, 61)(15, 70)(16, 53)(17, 58)(18, 71)(19, 55)(20, 56)(21, 57)(22, 69)(23, 66)(24, 68)(25, 65)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^50 ) } Outer automorphisms :: reflexible Dual of E20.200 Graph:: bipartite v = 2 e = 50 f = 10 degree seq :: [ 50^2 ] E20.218 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, (Y1, Y3), Y3^-1 * Y1^-2 * Y2^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3, Y2^-1), (R * Y2)^2, Y2^-1 * Y3^-2 * Y1 * Y3^-1, Y2 * Y3^3 * Y1^-1, Y3 * Y2^4, Y1 * Y2^-2 * Y1 * Y2^-1, Y2 * Y3^-1 * Y2 * Y3^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y1^23 ] Map:: non-degenerate R = (1, 26, 2, 27, 8, 33, 17, 42, 24, 49, 19, 44, 25, 50, 20, 45, 15, 40, 3, 28, 9, 34, 7, 32, 12, 37, 18, 43, 4, 29, 10, 35, 6, 31, 11, 36, 13, 38, 22, 47, 16, 41, 23, 48, 21, 46, 14, 39, 5, 30)(51, 76, 53, 78, 63, 88, 58, 83, 57, 82, 66, 91, 74, 99, 68, 93, 71, 96, 75, 100, 60, 85, 55, 80, 65, 90, 61, 86, 52, 77, 59, 84, 72, 97, 67, 92, 62, 87, 73, 98, 69, 94, 54, 79, 64, 89, 70, 95, 56, 81) L = (1, 54)(2, 60)(3, 64)(4, 67)(5, 68)(6, 69)(7, 51)(8, 56)(9, 55)(10, 74)(11, 75)(12, 52)(13, 70)(14, 62)(15, 71)(16, 53)(17, 61)(18, 58)(19, 72)(20, 73)(21, 57)(22, 65)(23, 59)(24, 63)(25, 66)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^50 ) } Outer automorphisms :: reflexible Dual of E20.199 Graph:: bipartite v = 2 e = 50 f = 10 degree seq :: [ 50^2 ] E20.219 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 14, 14}) Quotient :: edge^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = C4 x D14 (small group id <56, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, (Y2^-1 * Y1)^2, Y1 * Y3 * Y2 * Y3, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y2^-1 * Y3^2 * Y2^-2 * Y3^-1 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y3^6 * Y2^-1 ] Map:: non-degenerate R = (1, 29, 4, 32, 11, 39, 19, 47, 27, 55, 22, 50, 14, 42, 6, 34, 13, 41, 21, 49, 28, 56, 20, 48, 12, 40, 5, 33)(2, 30, 7, 35, 15, 43, 23, 51, 26, 54, 18, 46, 10, 38, 3, 31, 9, 37, 17, 45, 25, 53, 24, 52, 16, 44, 8, 36)(57, 58, 62, 59)(60, 64, 69, 66)(61, 63, 70, 65)(67, 72, 77, 74)(68, 71, 78, 73)(75, 80, 84, 82)(76, 79, 83, 81)(85, 87, 90, 86)(88, 94, 97, 92)(89, 93, 98, 91)(95, 102, 105, 100)(96, 101, 106, 99)(103, 110, 112, 108)(104, 109, 111, 107) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56^4 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E20.223 Graph:: bipartite v = 16 e = 56 f = 2 degree seq :: [ 4^14, 28^2 ] E20.220 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 14, 14}) Quotient :: edge^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = C4 x D14 (small group id <56, 4>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y1 * Y2^-2 * Y1, Y1^2 * Y2^2, Y2^-1 * Y3^-2 * Y1^-1, Y3^2 * Y2^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2^2 * Y3 * Y1^-1, Y3^5 * Y1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y3^-1, Y1^-1 * Y2^-1 * Y3^2 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 29, 4, 32, 9, 37, 22, 50, 28, 56, 15, 43, 20, 48, 8, 36, 19, 47, 11, 39, 24, 52, 27, 55, 13, 41, 7, 35)(2, 30, 10, 38, 6, 34, 18, 46, 26, 54, 23, 51, 17, 45, 5, 33, 16, 44, 3, 31, 14, 42, 25, 53, 21, 49, 12, 40)(57, 58, 64, 61)(59, 69, 62, 71)(60, 68, 75, 73)(63, 66, 76, 72)(65, 77, 67, 79)(70, 83, 74, 84)(78, 81, 80, 82)(85, 87, 92, 90)(86, 93, 89, 95)(88, 100, 103, 94)(91, 98, 104, 102)(96, 106, 101, 108)(97, 109, 99, 110)(105, 112, 107, 111) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56^4 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E20.225 Graph:: bipartite v = 16 e = 56 f = 2 degree seq :: [ 4^14, 28^2 ] E20.221 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 14, 14}) Quotient :: edge^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = C4 x D14 (small group id <56, 4>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y2^4, Y1^2 * Y2^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1 * Y2^-2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^-1 * Y2^-1 * Y1 * Y3 * Y2^-1, Y3^2 * Y1^-1 * Y3^-1 * Y2, Y3^-1 * Y1 * Y2 * Y1 * Y2^-1, Y3 * Y2^-1 * Y3^-3 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 29, 4, 32, 17, 45, 15, 43, 9, 37, 25, 53, 24, 52, 8, 36, 23, 51, 27, 55, 13, 41, 11, 39, 22, 50, 7, 35)(2, 30, 10, 38, 26, 54, 19, 47, 6, 34, 21, 49, 18, 46, 5, 33, 20, 48, 28, 56, 16, 44, 3, 31, 14, 42, 12, 40)(57, 58, 64, 61)(59, 69, 62, 71)(60, 68, 79, 74)(63, 66, 80, 76)(65, 72, 67, 75)(70, 83, 77, 73)(78, 82, 81, 84)(85, 87, 92, 90)(86, 93, 89, 95)(88, 100, 107, 103)(91, 98, 108, 105)(94, 99, 104, 97)(96, 109, 102, 106)(101, 112, 111, 110) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56^4 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E20.224 Graph:: bipartite v = 16 e = 56 f = 2 degree seq :: [ 4^14, 28^2 ] E20.222 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 14, 14}) 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, Y1^-1 * Y2^-1, Y2^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^4, Y1 * Y3 * Y2 * Y3 * Y2^2 * Y3^2, Y1^5 * Y3^2 * Y2^-2, Y2^14 ] Map:: non-degenerate R = (1, 29, 4, 32, 12, 40, 5, 33)(2, 30, 7, 35, 16, 44, 8, 36)(3, 31, 10, 38, 20, 48, 11, 39)(6, 34, 14, 42, 24, 52, 15, 43)(9, 37, 18, 46, 28, 56, 19, 47)(13, 41, 22, 50, 25, 53, 23, 51)(17, 45, 26, 54, 21, 49, 27, 55)(57, 58, 62, 69, 77, 84, 76, 68, 72, 80, 81, 73, 65, 59)(60, 66, 74, 82, 79, 71, 64, 61, 67, 75, 83, 78, 70, 63)(85, 87, 93, 101, 109, 108, 100, 96, 104, 112, 105, 97, 90, 86)(88, 91, 98, 106, 111, 103, 95, 89, 92, 99, 107, 110, 102, 94) 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) :: { ( 16^8 ), ( 16^14 ) } Outer automorphisms :: reflexible Dual of E20.226 Graph:: bipartite v = 11 e = 56 f = 7 degree seq :: [ 8^7, 14^4 ] E20.223 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 14, 14}) Quotient :: loop^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = C4 x D14 (small group id <56, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, (Y2^-1 * Y1)^2, Y1 * Y3 * Y2 * Y3, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y2^-1 * Y3^2 * Y2^-2 * Y3^-1 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y3^6 * Y2^-1 ] Map:: non-degenerate R = (1, 29, 57, 85, 4, 32, 60, 88, 11, 39, 67, 95, 19, 47, 75, 103, 27, 55, 83, 111, 22, 50, 78, 106, 14, 42, 70, 98, 6, 34, 62, 90, 13, 41, 69, 97, 21, 49, 77, 105, 28, 56, 84, 112, 20, 48, 76, 104, 12, 40, 68, 96, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 15, 43, 71, 99, 23, 51, 79, 107, 26, 54, 82, 110, 18, 46, 74, 102, 10, 38, 66, 94, 3, 31, 59, 87, 9, 37, 65, 93, 17, 45, 73, 101, 25, 53, 81, 109, 24, 52, 80, 108, 16, 44, 72, 100, 8, 36, 64, 92) L = (1, 30)(2, 34)(3, 29)(4, 36)(5, 35)(6, 31)(7, 42)(8, 41)(9, 33)(10, 32)(11, 44)(12, 43)(13, 38)(14, 37)(15, 50)(16, 49)(17, 40)(18, 39)(19, 52)(20, 51)(21, 46)(22, 45)(23, 55)(24, 56)(25, 48)(26, 47)(27, 53)(28, 54)(57, 87)(58, 85)(59, 90)(60, 94)(61, 93)(62, 86)(63, 89)(64, 88)(65, 98)(66, 97)(67, 102)(68, 101)(69, 92)(70, 91)(71, 96)(72, 95)(73, 106)(74, 105)(75, 110)(76, 109)(77, 100)(78, 99)(79, 104)(80, 103)(81, 111)(82, 112)(83, 107)(84, 108) local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.219 Transitivity :: VT+ Graph:: bipartite v = 2 e = 56 f = 16 degree seq :: [ 56^2 ] E20.224 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 14, 14}) Quotient :: loop^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = C4 x D14 (small group id <56, 4>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y1 * Y2^-2 * Y1, Y1^2 * Y2^2, Y2^-1 * Y3^-2 * Y1^-1, Y3^2 * Y2^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2^2 * Y3 * Y1^-1, Y3^5 * Y1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y3^-1, Y1^-1 * Y2^-1 * Y3^2 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 29, 57, 85, 4, 32, 60, 88, 9, 37, 65, 93, 22, 50, 78, 106, 28, 56, 84, 112, 15, 43, 71, 99, 20, 48, 76, 104, 8, 36, 64, 92, 19, 47, 75, 103, 11, 39, 67, 95, 24, 52, 80, 108, 27, 55, 83, 111, 13, 41, 69, 97, 7, 35, 63, 91)(2, 30, 58, 86, 10, 38, 66, 94, 6, 34, 62, 90, 18, 46, 74, 102, 26, 54, 82, 110, 23, 51, 79, 107, 17, 45, 73, 101, 5, 33, 61, 89, 16, 44, 72, 100, 3, 31, 59, 87, 14, 42, 70, 98, 25, 53, 81, 109, 21, 49, 77, 105, 12, 40, 68, 96) L = (1, 30)(2, 36)(3, 41)(4, 40)(5, 29)(6, 43)(7, 38)(8, 33)(9, 49)(10, 48)(11, 51)(12, 47)(13, 34)(14, 55)(15, 31)(16, 35)(17, 32)(18, 56)(19, 45)(20, 44)(21, 39)(22, 53)(23, 37)(24, 54)(25, 52)(26, 50)(27, 46)(28, 42)(57, 87)(58, 93)(59, 92)(60, 100)(61, 95)(62, 85)(63, 98)(64, 90)(65, 89)(66, 88)(67, 86)(68, 106)(69, 109)(70, 104)(71, 110)(72, 103)(73, 108)(74, 91)(75, 94)(76, 102)(77, 112)(78, 101)(79, 111)(80, 96)(81, 99)(82, 97)(83, 105)(84, 107) local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.221 Transitivity :: VT+ Graph:: bipartite v = 2 e = 56 f = 16 degree seq :: [ 56^2 ] E20.225 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 14, 14}) Quotient :: loop^2 Aut^+ = C7 : C4 (small group id <28, 1>) Aut = C4 x D14 (small group id <56, 4>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y2^4, Y1^2 * Y2^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1 * Y2^-2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^-1 * Y2^-1 * Y1 * Y3 * Y2^-1, Y3^2 * Y1^-1 * Y3^-1 * Y2, Y3^-1 * Y1 * Y2 * Y1 * Y2^-1, Y3 * Y2^-1 * Y3^-3 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 29, 57, 85, 4, 32, 60, 88, 17, 45, 73, 101, 15, 43, 71, 99, 9, 37, 65, 93, 25, 53, 81, 109, 24, 52, 80, 108, 8, 36, 64, 92, 23, 51, 79, 107, 27, 55, 83, 111, 13, 41, 69, 97, 11, 39, 67, 95, 22, 50, 78, 106, 7, 35, 63, 91)(2, 30, 58, 86, 10, 38, 66, 94, 26, 54, 82, 110, 19, 47, 75, 103, 6, 34, 62, 90, 21, 49, 77, 105, 18, 46, 74, 102, 5, 33, 61, 89, 20, 48, 76, 104, 28, 56, 84, 112, 16, 44, 72, 100, 3, 31, 59, 87, 14, 42, 70, 98, 12, 40, 68, 96) L = (1, 30)(2, 36)(3, 41)(4, 40)(5, 29)(6, 43)(7, 38)(8, 33)(9, 44)(10, 52)(11, 47)(12, 51)(13, 34)(14, 55)(15, 31)(16, 39)(17, 42)(18, 32)(19, 37)(20, 35)(21, 45)(22, 54)(23, 46)(24, 48)(25, 56)(26, 53)(27, 49)(28, 50)(57, 87)(58, 93)(59, 92)(60, 100)(61, 95)(62, 85)(63, 98)(64, 90)(65, 89)(66, 99)(67, 86)(68, 109)(69, 94)(70, 108)(71, 104)(72, 107)(73, 112)(74, 106)(75, 88)(76, 97)(77, 91)(78, 96)(79, 103)(80, 105)(81, 102)(82, 101)(83, 110)(84, 111) local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.220 Transitivity :: VT+ Graph:: bipartite v = 2 e = 56 f = 16 degree seq :: [ 56^2 ] E20.226 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 14, 14}) 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, Y1^-1 * Y2^-1, Y2^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^4, Y1 * Y3 * Y2 * Y3 * Y2^2 * Y3^2, Y1^5 * Y3^2 * Y2^-2, Y2^14 ] Map:: non-degenerate R = (1, 29, 57, 85, 4, 32, 60, 88, 12, 40, 68, 96, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 16, 44, 72, 100, 8, 36, 64, 92)(3, 31, 59, 87, 10, 38, 66, 94, 20, 48, 76, 104, 11, 39, 67, 95)(6, 34, 62, 90, 14, 42, 70, 98, 24, 52, 80, 108, 15, 43, 71, 99)(9, 37, 65, 93, 18, 46, 74, 102, 28, 56, 84, 112, 19, 47, 75, 103)(13, 41, 69, 97, 22, 50, 78, 106, 25, 53, 81, 109, 23, 51, 79, 107)(17, 45, 73, 101, 26, 54, 82, 110, 21, 49, 77, 105, 27, 55, 83, 111) L = (1, 30)(2, 34)(3, 29)(4, 38)(5, 39)(6, 41)(7, 32)(8, 33)(9, 31)(10, 46)(11, 47)(12, 44)(13, 49)(14, 35)(15, 36)(16, 52)(17, 37)(18, 54)(19, 55)(20, 40)(21, 56)(22, 42)(23, 43)(24, 53)(25, 45)(26, 51)(27, 50)(28, 48)(57, 87)(58, 85)(59, 93)(60, 91)(61, 92)(62, 86)(63, 98)(64, 99)(65, 101)(66, 88)(67, 89)(68, 104)(69, 90)(70, 106)(71, 107)(72, 96)(73, 109)(74, 94)(75, 95)(76, 112)(77, 97)(78, 111)(79, 110)(80, 100)(81, 108)(82, 102)(83, 103)(84, 105) local type(s) :: { ( 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14 ) } Outer automorphisms :: reflexible Dual of E20.222 Transitivity :: VT+ Graph:: v = 7 e = 56 f = 11 degree seq :: [ 16^7 ] E20.227 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^-3 * Y1^2 * Y2^-4, (Y3 * Y2^-1)^14 ] Map:: R = (1, 29, 2, 30, 6, 34, 4, 32)(3, 31, 8, 36, 13, 41, 10, 38)(5, 33, 7, 35, 14, 42, 11, 39)(9, 37, 16, 44, 21, 49, 18, 46)(12, 40, 15, 43, 22, 50, 19, 47)(17, 45, 24, 52, 28, 56, 26, 54)(20, 48, 23, 51, 25, 53, 27, 55)(57, 85, 59, 87, 65, 93, 73, 101, 81, 109, 78, 106, 70, 98, 62, 90, 69, 97, 77, 105, 84, 112, 76, 104, 68, 96, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 82, 110, 74, 102, 66, 94, 60, 88, 67, 95, 75, 103, 83, 111, 80, 108, 72, 100, 64, 92) 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) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3 * Y1, Y1 * Y3 * Y2 * Y1, Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, Y3^-1 * Y1^2 * Y2^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y3^7, Y2^4 * Y3^-3, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 11, 39, 7, 35, 10, 38)(4, 32, 12, 40, 6, 34, 9, 37)(13, 41, 19, 47, 14, 42, 20, 48)(15, 43, 17, 45, 16, 44, 18, 46)(21, 49, 28, 56, 22, 50, 27, 55)(23, 51, 26, 54, 24, 52, 25, 53)(57, 85, 59, 87, 69, 97, 77, 105, 79, 107, 72, 100, 60, 88, 64, 92, 63, 91, 70, 98, 78, 106, 80, 108, 71, 99, 62, 90)(58, 86, 65, 93, 73, 101, 81, 109, 83, 111, 76, 104, 66, 94, 61, 89, 68, 96, 74, 102, 82, 110, 84, 112, 75, 103, 67, 95) L = (1, 60)(2, 66)(3, 64)(4, 71)(5, 67)(6, 72)(7, 57)(8, 62)(9, 61)(10, 75)(11, 76)(12, 58)(13, 63)(14, 59)(15, 79)(16, 80)(17, 68)(18, 65)(19, 83)(20, 84)(21, 70)(22, 69)(23, 78)(24, 77)(25, 74)(26, 73)(27, 82)(28, 81)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.232 Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y1^4, (R * Y2)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-2 * Y3^3 * Y2, Y1^-1 * Y3^-3 * Y2^-1 * Y1^-1, Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 11, 39, 21, 49, 14, 42)(4, 32, 12, 40, 22, 50, 16, 44)(6, 34, 9, 37, 23, 51, 17, 45)(7, 35, 10, 38, 24, 52, 18, 46)(13, 41, 27, 55, 20, 48, 26, 54)(15, 43, 28, 56, 19, 47, 25, 53)(57, 85, 59, 87, 60, 88, 69, 97, 71, 99, 80, 108, 79, 107, 64, 92, 77, 105, 78, 106, 76, 104, 75, 103, 63, 91, 62, 90)(58, 86, 65, 93, 66, 94, 81, 109, 82, 110, 72, 100, 70, 98, 61, 89, 73, 101, 74, 102, 84, 112, 83, 111, 68, 96, 67, 95) L = (1, 60)(2, 66)(3, 69)(4, 71)(5, 74)(6, 59)(7, 57)(8, 78)(9, 81)(10, 82)(11, 65)(12, 58)(13, 80)(14, 73)(15, 79)(16, 61)(17, 84)(18, 83)(19, 62)(20, 63)(21, 76)(22, 75)(23, 77)(24, 64)(25, 72)(26, 70)(27, 67)(28, 68)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2^-1)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, Y1^4, Y1^-2 * Y2 * Y3^-3, Y1^-1 * Y2^-1 * Y3^3 * Y1^-1, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 11, 39, 21, 49, 13, 41)(4, 32, 12, 40, 22, 50, 16, 44)(6, 34, 9, 37, 23, 51, 18, 46)(7, 35, 10, 38, 24, 52, 19, 47)(14, 42, 27, 55, 15, 43, 28, 56)(17, 45, 25, 53, 20, 48, 26, 54)(57, 85, 59, 87, 63, 91, 70, 98, 76, 104, 78, 106, 79, 107, 64, 92, 77, 105, 80, 108, 71, 99, 73, 101, 60, 88, 62, 90)(58, 86, 65, 93, 68, 96, 81, 109, 84, 112, 75, 103, 69, 97, 61, 89, 74, 102, 72, 100, 82, 110, 83, 111, 66, 94, 67, 95) L = (1, 60)(2, 66)(3, 62)(4, 71)(5, 75)(6, 73)(7, 57)(8, 78)(9, 67)(10, 82)(11, 83)(12, 58)(13, 84)(14, 59)(15, 77)(16, 61)(17, 80)(18, 69)(19, 81)(20, 63)(21, 79)(22, 70)(23, 76)(24, 64)(25, 65)(26, 74)(27, 72)(28, 68)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.231 Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, (Y2, Y3), (R * Y3)^2, (R * Y2^-1)^2, Y1^4, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y3 * Y2^-2 * Y3^2, Y1^-2 * Y2^-1 * Y3^-2, Y1^-1 * Y3^-2 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^3, Y3^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 11, 39, 24, 52, 15, 43)(4, 32, 12, 40, 23, 51, 18, 46)(6, 34, 9, 37, 17, 45, 20, 48)(7, 35, 10, 38, 14, 42, 21, 49)(13, 41, 28, 56, 19, 47, 26, 54)(16, 44, 27, 55, 22, 50, 25, 53)(57, 85, 59, 87, 69, 97, 79, 107, 63, 91, 72, 100, 73, 101, 64, 92, 80, 108, 75, 103, 60, 88, 70, 98, 78, 106, 62, 90)(58, 86, 65, 93, 81, 109, 77, 105, 68, 96, 82, 110, 71, 99, 61, 89, 76, 104, 83, 111, 66, 94, 74, 102, 84, 112, 67, 95) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 77)(6, 75)(7, 57)(8, 79)(9, 74)(10, 71)(11, 83)(12, 58)(13, 78)(14, 64)(15, 81)(16, 59)(17, 69)(18, 61)(19, 72)(20, 68)(21, 67)(22, 80)(23, 62)(24, 63)(25, 84)(26, 65)(27, 82)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.230 Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C7 : C4 (small group id <28, 1>) Aut = (C14 x C2) : C2 (small group id <56, 7>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^4, Y2^-1 * Y1^2 * Y3^2, Y2^-3 * Y3 * Y2^-1, Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3^3 * Y2^2, Y3 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 11, 39, 17, 45, 15, 43)(4, 32, 12, 40, 16, 44, 18, 46)(6, 34, 9, 37, 24, 52, 20, 48)(7, 35, 10, 38, 19, 47, 21, 49)(13, 41, 27, 55, 23, 51, 26, 54)(14, 42, 28, 56, 22, 50, 25, 53)(57, 85, 59, 87, 69, 97, 75, 103, 60, 88, 70, 98, 80, 108, 64, 92, 73, 101, 79, 107, 63, 91, 72, 100, 78, 106, 62, 90)(58, 86, 65, 93, 81, 109, 74, 102, 66, 94, 82, 110, 71, 99, 61, 89, 76, 104, 84, 112, 68, 96, 77, 105, 83, 111, 67, 95) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 77)(6, 75)(7, 57)(8, 72)(9, 82)(10, 76)(11, 74)(12, 58)(13, 80)(14, 79)(15, 68)(16, 59)(17, 78)(18, 61)(19, 64)(20, 83)(21, 65)(22, 69)(23, 62)(24, 63)(25, 71)(26, 84)(27, 81)(28, 67)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.228 Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 14, 14}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^-7 * Y1^2, (Y3 * Y2^-1)^14 ] Map:: R = (1, 29, 2, 30, 6, 34, 4, 32)(3, 31, 7, 35, 13, 41, 10, 38)(5, 33, 8, 36, 14, 42, 11, 39)(9, 37, 15, 43, 21, 49, 18, 46)(12, 40, 16, 44, 22, 50, 19, 47)(17, 45, 23, 51, 28, 56, 26, 54)(20, 48, 24, 52, 25, 53, 27, 55)(57, 85, 59, 87, 65, 93, 73, 101, 81, 109, 78, 106, 70, 98, 62, 90, 69, 97, 77, 105, 84, 112, 76, 104, 68, 96, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 83, 111, 75, 103, 67, 95, 60, 88, 66, 94, 74, 102, 82, 110, 80, 108, 72, 100, 64, 92) 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) :: { ( 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 56 f = 9 degree seq :: [ 8^7, 28^2 ] E20.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, Y1 * Y2^-1 * Y1 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y1 * Y2^7, (Y3 * Y2^-1)^28 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 7, 35)(4, 32, 8, 36)(5, 33, 9, 37)(6, 34, 10, 38)(11, 39, 15, 43)(12, 40, 16, 44)(13, 41, 17, 45)(14, 42, 18, 46)(19, 47, 23, 51)(20, 48, 24, 52)(21, 49, 25, 53)(22, 50, 26, 54)(27, 55, 28, 56)(57, 85, 59, 87, 67, 95, 75, 103, 82, 110, 74, 102, 65, 93, 58, 86, 63, 91, 71, 99, 79, 107, 78, 106, 70, 98, 61, 89)(60, 88, 62, 90, 68, 96, 76, 104, 83, 111, 81, 109, 73, 101, 64, 92, 66, 94, 72, 100, 80, 108, 84, 112, 77, 105, 69, 97) L = (1, 60)(2, 64)(3, 62)(4, 61)(5, 69)(6, 57)(7, 66)(8, 65)(9, 73)(10, 58)(11, 68)(12, 59)(13, 70)(14, 77)(15, 72)(16, 63)(17, 74)(18, 81)(19, 76)(20, 67)(21, 78)(22, 84)(23, 80)(24, 71)(25, 82)(26, 83)(27, 75)(28, 79)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56^4 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E20.247 Graph:: bipartite v = 16 e = 56 f = 2 degree seq :: [ 4^14, 28^2 ] E20.235 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1, Y3^-1), Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2 * Y3 * Y2^2, Y2 * Y1 * Y3^-4, Y2^-7 * Y1, (Y2^-1 * Y3)^28 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 7, 35)(4, 32, 8, 36)(5, 33, 9, 37)(6, 34, 10, 38)(11, 39, 19, 47)(12, 40, 20, 48)(13, 41, 21, 49)(14, 42, 22, 50)(15, 43, 23, 51)(16, 44, 24, 52)(17, 45, 25, 53)(18, 46, 26, 54)(27, 55, 28, 56)(57, 85, 59, 87, 67, 95, 74, 102, 78, 106, 80, 108, 65, 93, 58, 86, 63, 91, 75, 103, 82, 110, 70, 98, 72, 100, 61, 89)(60, 88, 68, 96, 73, 101, 62, 90, 69, 97, 83, 111, 79, 107, 64, 92, 76, 104, 81, 109, 66, 94, 77, 105, 84, 112, 71, 99) L = (1, 60)(2, 64)(3, 68)(4, 70)(5, 71)(6, 57)(7, 76)(8, 78)(9, 79)(10, 58)(11, 73)(12, 72)(13, 59)(14, 77)(15, 82)(16, 84)(17, 61)(18, 62)(19, 81)(20, 80)(21, 63)(22, 69)(23, 74)(24, 83)(25, 65)(26, 66)(27, 67)(28, 75)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56^4 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E20.246 Graph:: bipartite v = 16 e = 56 f = 2 degree seq :: [ 4^14, 28^2 ] E20.236 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-1 * Y3, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y2)^2, (Y1, Y2^-1), Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y2^2 * Y3 * Y1^-1, (R * Y3)^2, Y1^-2 * Y3^-2, Y2 * Y3^-2 * Y2^-1 * Y1^-2, Y1^-2 * Y3^5, (Y1 * Y3^-1)^14, (Y3 * Y2^-1)^28 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 25, 53, 16, 44, 4, 32, 10, 38, 7, 35, 12, 40, 22, 50, 26, 54, 15, 43, 5, 33)(3, 31, 9, 37, 20, 48, 27, 55, 18, 46, 6, 34, 11, 39, 21, 49, 14, 42, 23, 51, 28, 56, 17, 45, 24, 52, 13, 41)(57, 85, 59, 87, 68, 96, 79, 107, 81, 109, 74, 102, 61, 89, 69, 97, 63, 91, 70, 98, 75, 103, 83, 111, 71, 99, 80, 108, 66, 94, 77, 105, 64, 92, 76, 104, 82, 110, 73, 101, 60, 88, 67, 95, 58, 86, 65, 93, 78, 106, 84, 112, 72, 100, 62, 90) L = (1, 60)(2, 66)(3, 67)(4, 71)(5, 72)(6, 73)(7, 57)(8, 63)(9, 77)(10, 61)(11, 80)(12, 58)(13, 62)(14, 59)(15, 81)(16, 82)(17, 83)(18, 84)(19, 68)(20, 70)(21, 69)(22, 64)(23, 65)(24, 74)(25, 78)(26, 75)(27, 79)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E20.244 Graph:: bipartite v = 3 e = 56 f = 15 degree seq :: [ 28^2, 56 ] E20.237 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^2 * Y3^2, Y1^-2 * Y3^-2, (Y1, Y3^-1), (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y3^2 * Y1^-1 * Y3^-2 * Y1, Y3^3 * Y1^-4, Y3^7 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 25, 53, 16, 44, 4, 32, 9, 37, 7, 35, 11, 39, 21, 49, 26, 54, 15, 43, 5, 33)(3, 31, 6, 34, 10, 38, 20, 48, 27, 55, 24, 52, 12, 40, 17, 45, 14, 42, 18, 46, 22, 50, 28, 56, 23, 51, 13, 41)(57, 85, 59, 87, 61, 89, 69, 97, 71, 99, 79, 107, 82, 110, 84, 112, 77, 105, 78, 106, 67, 95, 74, 102, 63, 91, 70, 98, 65, 93, 73, 101, 60, 88, 68, 96, 72, 100, 80, 108, 81, 109, 83, 111, 75, 103, 76, 104, 64, 92, 66, 94, 58, 86, 62, 90) L = (1, 60)(2, 65)(3, 68)(4, 71)(5, 72)(6, 73)(7, 57)(8, 63)(9, 61)(10, 70)(11, 58)(12, 79)(13, 80)(14, 59)(15, 81)(16, 82)(17, 69)(18, 62)(19, 67)(20, 74)(21, 64)(22, 66)(23, 83)(24, 84)(25, 77)(26, 75)(27, 78)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E20.242 Graph:: bipartite v = 3 e = 56 f = 15 degree seq :: [ 28^2, 56 ] E20.238 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, (Y3^-1 * Y1^-1)^2, (Y3^-1, Y1^-1), Y3^2 * Y1^2, (R * Y1)^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2 * Y1, Y1^-6 * 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 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 23, 51, 15, 43, 4, 32, 10, 38, 7, 35, 11, 39, 21, 49, 24, 52, 14, 42, 5, 33)(3, 31, 9, 37, 20, 48, 27, 55, 26, 54, 16, 44, 12, 40, 18, 46, 13, 41, 22, 50, 28, 56, 25, 53, 17, 45, 6, 34)(57, 85, 59, 87, 58, 86, 65, 93, 64, 92, 76, 104, 75, 103, 83, 111, 79, 107, 82, 110, 71, 99, 72, 100, 60, 88, 68, 96, 66, 94, 74, 102, 63, 91, 69, 97, 67, 95, 78, 106, 77, 105, 84, 112, 80, 108, 81, 109, 70, 98, 73, 101, 61, 89, 62, 90) L = (1, 60)(2, 66)(3, 68)(4, 70)(5, 71)(6, 72)(7, 57)(8, 63)(9, 74)(10, 61)(11, 58)(12, 73)(13, 59)(14, 79)(15, 80)(16, 81)(17, 82)(18, 62)(19, 67)(20, 69)(21, 64)(22, 65)(23, 77)(24, 75)(25, 83)(26, 84)(27, 78)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E20.245 Graph:: bipartite v = 3 e = 56 f = 15 degree seq :: [ 28^2, 56 ] E20.239 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3^-2, (Y1^-1 * Y3^-1)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, Y3 * Y2^4, Y1^2 * Y2 * Y1 * Y2, Y3^-1 * Y1 * Y2^2 * Y3^-1, Y2 * Y1^-1 * Y2 * Y3 * Y1^-2, Y3 * Y2 * Y3^2 * Y2 * Y1^-1, Y3^7, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 29, 2, 30, 8, 36, 21, 49, 27, 55, 18, 46, 4, 32, 10, 38, 7, 35, 12, 40, 24, 52, 13, 41, 17, 45, 5, 33)(3, 31, 9, 37, 20, 48, 6, 34, 11, 39, 23, 51, 14, 42, 25, 53, 16, 44, 19, 47, 26, 54, 22, 50, 28, 56, 15, 43)(57, 85, 59, 87, 69, 97, 78, 106, 63, 91, 72, 100, 74, 102, 79, 107, 64, 92, 76, 104, 61, 89, 71, 99, 80, 108, 82, 110, 66, 94, 81, 109, 83, 111, 67, 95, 58, 86, 65, 93, 73, 101, 84, 112, 68, 96, 75, 103, 60, 88, 70, 98, 77, 105, 62, 90) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 74)(6, 75)(7, 57)(8, 63)(9, 81)(10, 61)(11, 82)(12, 58)(13, 77)(14, 84)(15, 79)(16, 59)(17, 83)(18, 69)(19, 65)(20, 72)(21, 68)(22, 62)(23, 78)(24, 64)(25, 71)(26, 76)(27, 80)(28, 67)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E20.243 Graph:: bipartite v = 3 e = 56 f = 15 degree seq :: [ 28^2, 56 ] E20.240 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, (Y3^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2), (Y1^-1, Y2^-1), Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y2 * Y3^-1 * Y2^3, Y2 * Y1^-1 * Y2 * Y1^-2, Y3 * Y2 * Y1^-1 * Y3 * Y2, Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-2, Y1^-6 * Y3 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 13, 41, 25, 53, 18, 46, 4, 32, 10, 38, 7, 35, 12, 40, 24, 52, 21, 49, 17, 45, 5, 33)(3, 31, 9, 37, 23, 51, 19, 47, 28, 56, 22, 50, 14, 42, 26, 54, 16, 44, 27, 55, 20, 48, 6, 34, 11, 39, 15, 43)(57, 85, 59, 87, 69, 97, 75, 103, 60, 88, 70, 98, 68, 96, 83, 111, 73, 101, 67, 95, 58, 86, 65, 93, 81, 109, 84, 112, 66, 94, 82, 110, 80, 108, 76, 104, 61, 89, 71, 99, 64, 92, 79, 107, 74, 102, 78, 106, 63, 91, 72, 100, 77, 105, 62, 90) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 74)(6, 75)(7, 57)(8, 63)(9, 82)(10, 61)(11, 84)(12, 58)(13, 68)(14, 67)(15, 78)(16, 59)(17, 81)(18, 77)(19, 83)(20, 79)(21, 69)(22, 62)(23, 72)(24, 64)(25, 80)(26, 71)(27, 65)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E20.241 Graph:: bipartite v = 3 e = 56 f = 15 degree seq :: [ 28^2, 56 ] E20.241 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1^2 * Y3^-2, Y3^-1 * Y1 * Y2 * Y3^-1 * Y1, Y3^3 * Y1^4, Y3^7, Y1^-6 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 19, 47, 28, 56, 23, 51, 13, 41, 15, 43, 4, 32, 9, 37, 20, 48, 27, 55, 18, 46, 12, 40, 3, 31, 8, 36, 14, 42, 22, 50, 26, 54, 17, 45, 6, 34, 10, 38, 11, 39, 21, 49, 24, 52, 25, 53, 16, 44, 5, 33)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 67, 95)(61, 89, 68, 96)(62, 90, 69, 97)(63, 91, 70, 98)(65, 93, 77, 105)(66, 94, 71, 99)(72, 100, 74, 102)(73, 101, 79, 107)(75, 103, 78, 106)(76, 104, 80, 108)(81, 109, 83, 111)(82, 110, 84, 112) L = (1, 60)(2, 65)(3, 67)(4, 70)(5, 71)(6, 57)(7, 76)(8, 77)(9, 78)(10, 58)(11, 63)(12, 66)(13, 59)(14, 80)(15, 64)(16, 69)(17, 61)(18, 62)(19, 83)(20, 82)(21, 75)(22, 81)(23, 68)(24, 84)(25, 79)(26, 72)(27, 73)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E20.240 Graph:: bipartite v = 15 e = 56 f = 3 degree seq :: [ 4^14, 56 ] E20.242 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y1 * Y2 * Y1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-2 * Y3^-1 * Y2, (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, (R * Y2)^2, Y3^7, Y2 * Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-3, Y3^-1 * Y1^24 * Y3^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 15, 43, 14, 42, 18, 46, 24, 52, 28, 56, 20, 48, 25, 53, 19, 47, 13, 41, 4, 32, 9, 37, 3, 31, 8, 36, 6, 34, 10, 38, 16, 44, 23, 51, 22, 50, 26, 54, 27, 55, 21, 49, 12, 40, 17, 45, 11, 39, 5, 33)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 67, 95)(61, 89, 65, 93)(62, 90, 63, 91)(66, 94, 71, 99)(68, 96, 75, 103)(69, 97, 73, 101)(70, 98, 72, 100)(74, 102, 79, 107)(76, 104, 83, 111)(77, 105, 81, 109)(78, 106, 80, 108)(82, 110, 84, 112) L = (1, 60)(2, 65)(3, 67)(4, 68)(5, 69)(6, 57)(7, 59)(8, 61)(9, 73)(10, 58)(11, 75)(12, 76)(13, 77)(14, 62)(15, 64)(16, 63)(17, 81)(18, 66)(19, 83)(20, 78)(21, 84)(22, 70)(23, 71)(24, 72)(25, 82)(26, 74)(27, 80)(28, 79)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E20.237 Graph:: bipartite v = 15 e = 56 f = 3 degree seq :: [ 4^14, 56 ] E20.243 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y1^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2)^2, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3^7, Y2 * Y3^3 * Y1 * Y3^3 * Y1, (Y2 * Y3)^14, (Y3^-1 * Y1^-1)^28 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 15, 43, 12, 40, 17, 45, 24, 52, 28, 56, 22, 50, 26, 54, 19, 47, 13, 41, 6, 34, 10, 38, 3, 31, 8, 36, 4, 32, 9, 37, 16, 44, 23, 51, 20, 48, 25, 53, 27, 55, 21, 49, 14, 42, 18, 46, 11, 39, 5, 33)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 63, 91)(61, 89, 66, 94)(62, 90, 67, 95)(65, 93, 71, 99)(68, 96, 72, 100)(69, 97, 74, 102)(70, 98, 75, 103)(73, 101, 79, 107)(76, 104, 80, 108)(77, 105, 82, 110)(78, 106, 83, 111)(81, 109, 84, 112) L = (1, 60)(2, 65)(3, 63)(4, 68)(5, 64)(6, 57)(7, 72)(8, 71)(9, 73)(10, 58)(11, 59)(12, 76)(13, 61)(14, 62)(15, 79)(16, 80)(17, 81)(18, 66)(19, 67)(20, 78)(21, 69)(22, 70)(23, 84)(24, 83)(25, 82)(26, 74)(27, 75)(28, 77)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E20.239 Graph:: bipartite v = 15 e = 56 f = 3 degree seq :: [ 4^14, 56 ] E20.244 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y2 * Y1^-1 * Y2, (Y3^-1, Y1^-1), (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y1^-4 * Y3^-1, Y3^3 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 17, 45, 6, 34, 10, 38, 20, 48, 28, 56, 18, 46, 24, 52, 11, 39, 21, 49, 25, 53, 12, 40, 3, 31, 8, 36, 19, 47, 26, 54, 13, 41, 22, 50, 14, 42, 23, 51, 27, 55, 15, 43, 4, 32, 9, 37, 16, 44, 5, 33)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 67, 95)(61, 89, 68, 96)(62, 90, 69, 97)(63, 91, 75, 103)(65, 93, 77, 105)(66, 94, 78, 106)(70, 98, 76, 104)(71, 99, 80, 108)(72, 100, 81, 109)(73, 101, 82, 110)(74, 102, 83, 111)(79, 107, 84, 112) L = (1, 60)(2, 65)(3, 67)(4, 70)(5, 71)(6, 57)(7, 72)(8, 77)(9, 79)(10, 58)(11, 76)(12, 80)(13, 59)(14, 75)(15, 78)(16, 83)(17, 61)(18, 62)(19, 81)(20, 63)(21, 84)(22, 64)(23, 82)(24, 66)(25, 74)(26, 68)(27, 69)(28, 73)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E20.236 Graph:: bipartite v = 15 e = 56 f = 3 degree seq :: [ 4^14, 56 ] E20.245 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1, Y3^-1), Y2 * Y1^-1 * Y2 * Y1, Y1^4 * Y3^-1, Y2 * Y1^2 * Y3^3, Y3 * Y1 * Y3 * Y1 * Y3 * Y2, Y3^-3 * Y2 * Y1^-2, Y2 * Y3^-2 * Y1 * Y3^-2 * Y1, Y3^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 15, 43, 4, 32, 9, 37, 20, 48, 28, 56, 14, 42, 23, 51, 13, 41, 22, 50, 27, 55, 12, 40, 3, 31, 8, 36, 19, 47, 26, 54, 11, 39, 21, 49, 18, 46, 24, 52, 25, 53, 17, 45, 6, 34, 10, 38, 16, 44, 5, 33)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 67, 95)(61, 89, 68, 96)(62, 90, 69, 97)(63, 91, 75, 103)(65, 93, 77, 105)(66, 94, 78, 106)(70, 98, 81, 109)(71, 99, 82, 110)(72, 100, 83, 111)(73, 101, 79, 107)(74, 102, 76, 104)(80, 108, 84, 112) L = (1, 60)(2, 65)(3, 67)(4, 70)(5, 71)(6, 57)(7, 76)(8, 77)(9, 79)(10, 58)(11, 81)(12, 82)(13, 59)(14, 83)(15, 84)(16, 63)(17, 61)(18, 62)(19, 74)(20, 69)(21, 73)(22, 64)(23, 68)(24, 66)(25, 72)(26, 80)(27, 75)(28, 78)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E20.238 Graph:: bipartite v = 15 e = 56 f = 3 degree seq :: [ 4^14, 56 ] E20.246 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (Y2, Y3^-1), (Y1, Y3^-1), Y2^-2 * Y1 * Y2^-1, Y1 * Y3^-2 * Y2^-1, (R * Y1)^2, Y3^-1 * Y1 * Y2^-1 * Y3^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-3, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1^2 * Y3 * Y2^-1 * Y1^-2, (Y1^-1 * Y3^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 15, 43, 4, 32, 10, 38, 21, 49, 17, 45, 6, 34, 11, 39, 22, 50, 27, 55, 26, 54, 14, 42, 24, 52, 28, 56, 25, 53, 13, 41, 3, 31, 9, 37, 20, 48, 18, 46, 7, 35, 12, 40, 23, 51, 16, 44, 5, 33)(57, 85, 59, 87, 67, 95, 58, 86, 65, 93, 78, 106, 64, 92, 76, 104, 83, 111, 75, 103, 74, 102, 82, 110, 71, 99, 63, 91, 70, 98, 60, 88, 68, 96, 80, 108, 66, 94, 79, 107, 84, 112, 77, 105, 72, 100, 81, 109, 73, 101, 61, 89, 69, 97, 62, 90) L = (1, 60)(2, 66)(3, 68)(4, 67)(5, 71)(6, 70)(7, 57)(8, 77)(9, 79)(10, 78)(11, 80)(12, 58)(13, 63)(14, 59)(15, 62)(16, 75)(17, 82)(18, 61)(19, 73)(20, 72)(21, 83)(22, 84)(23, 64)(24, 65)(25, 74)(26, 69)(27, 81)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 4, 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 E20.235 Graph:: bipartite v = 2 e = 56 f = 16 degree seq :: [ 56^2 ] E20.247 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y1^-1), Y2^-2 * Y3^2, (Y2^-1, Y3^-1), (Y2 * Y3^-1)^2, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^3 * Y3, Y1^-1 * Y3^-4 * Y2^-1, Y2^-1 * Y1^-2 * Y3 * Y2^-1 * Y1^-1, Y3^3 * Y2 * Y1^-2, Y3 * Y2 * Y1^-1 * Y2^2 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 7, 35, 12, 40, 23, 51, 19, 47, 27, 55, 14, 42, 25, 53, 15, 43, 3, 31, 9, 37, 21, 49, 16, 44, 26, 54, 18, 46, 6, 34, 11, 39, 22, 50, 20, 48, 28, 56, 13, 41, 24, 52, 17, 45, 4, 32, 10, 38, 5, 33)(57, 85, 59, 87, 69, 97, 79, 107, 74, 102, 61, 89, 71, 99, 84, 112, 68, 96, 82, 110, 66, 94, 81, 109, 76, 104, 63, 91, 72, 100, 60, 88, 70, 98, 78, 106, 64, 92, 77, 105, 73, 101, 83, 111, 67, 95, 58, 86, 65, 93, 80, 108, 75, 103, 62, 90) L = (1, 60)(2, 66)(3, 70)(4, 69)(5, 73)(6, 72)(7, 57)(8, 61)(9, 81)(10, 80)(11, 82)(12, 58)(13, 78)(14, 79)(15, 83)(16, 59)(17, 84)(18, 77)(19, 63)(20, 62)(21, 71)(22, 74)(23, 64)(24, 76)(25, 75)(26, 65)(27, 68)(28, 67)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 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 E20.234 Graph:: bipartite v = 2 e = 56 f = 16 degree seq :: [ 56^2 ] E20.248 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^5, Y1^5, Y3^6 ] Map:: non-degenerate R = (1, 31, 4, 34, 12, 42, 22, 52, 13, 43, 5, 35)(2, 32, 7, 37, 16, 46, 25, 55, 17, 47, 8, 38)(3, 33, 10, 40, 20, 50, 28, 58, 21, 51, 11, 41)(6, 36, 14, 44, 23, 53, 29, 59, 24, 54, 15, 45)(9, 39, 18, 48, 26, 56, 30, 60, 27, 57, 19, 49)(61, 62, 66, 69, 63)(64, 70, 78, 74, 67)(65, 71, 79, 75, 68)(72, 76, 83, 86, 80)(73, 77, 84, 87, 81)(82, 88, 90, 89, 85)(91, 93, 99, 96, 92)(94, 97, 104, 108, 100)(95, 98, 105, 109, 101)(102, 110, 116, 113, 106)(103, 111, 117, 114, 107)(112, 115, 119, 120, 118) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^5 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E20.251 Graph:: simple bipartite v = 17 e = 60 f = 5 degree seq :: [ 5^12, 12^5 ] E20.249 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y2^-1, R * Y1 * R * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3^5, Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 31, 4, 34, 12, 42, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 18, 48, 8, 38)(3, 33, 10, 40, 21, 51, 22, 52, 11, 41)(6, 36, 15, 45, 25, 55, 26, 56, 16, 46)(9, 39, 19, 49, 27, 57, 28, 58, 20, 50)(14, 44, 23, 53, 29, 59, 30, 60, 24, 54)(61, 62, 66, 74, 69, 63)(64, 68, 75, 84, 79, 71)(65, 67, 76, 83, 80, 70)(72, 78, 85, 90, 87, 82)(73, 77, 86, 89, 88, 81)(91, 93, 99, 104, 96, 92)(94, 101, 109, 114, 105, 98)(95, 100, 110, 113, 106, 97)(102, 112, 117, 120, 115, 108)(103, 111, 118, 119, 116, 107) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20^6 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E20.252 Graph:: simple bipartite v = 16 e = 60 f = 6 degree seq :: [ 6^10, 10^6 ] E20.250 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 5, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y2 * Y1 * Y3, (R * Y3)^2, R * Y1 * R * Y2, Y3^5, Y1^6, (Y1^2 * Y2^-1)^2, Y2^6, Y3^2 * Y1^-1 * Y3^-2 * Y2^-1, Y3 * Y1^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 31, 4, 34, 14, 44, 19, 49, 7, 37)(2, 32, 6, 36, 18, 48, 24, 54, 10, 40)(3, 33, 12, 42, 25, 55, 15, 45, 5, 35)(8, 38, 9, 39, 23, 53, 29, 59, 17, 47)(11, 41, 16, 46, 28, 58, 26, 56, 13, 43)(20, 50, 21, 51, 27, 57, 30, 60, 22, 52)(61, 62, 68, 80, 71, 65)(63, 67, 66, 77, 81, 73)(64, 70, 69, 82, 76, 75)(72, 79, 78, 89, 87, 86)(74, 84, 83, 90, 88, 85)(91, 93, 101, 111, 98, 96)(92, 94, 95, 106, 110, 99)(97, 102, 103, 117, 107, 108)(100, 104, 105, 118, 112, 113)(109, 115, 116, 120, 119, 114) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20^6 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E20.253 Graph:: simple bipartite v = 16 e = 60 f = 6 degree seq :: [ 6^10, 10^6 ] E20.251 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^5, Y1^5, Y3^6 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 22, 52, 82, 112, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 16, 46, 76, 106, 25, 55, 85, 115, 17, 47, 77, 107, 8, 38, 68, 98)(3, 33, 63, 93, 10, 40, 70, 100, 20, 50, 80, 110, 28, 58, 88, 118, 21, 51, 81, 111, 11, 41, 71, 101)(6, 36, 66, 96, 14, 44, 74, 104, 23, 53, 83, 113, 29, 59, 89, 119, 24, 54, 84, 114, 15, 45, 75, 105)(9, 39, 69, 99, 18, 48, 78, 108, 26, 56, 86, 116, 30, 60, 90, 120, 27, 57, 87, 117, 19, 49, 79, 109) L = (1, 32)(2, 36)(3, 31)(4, 40)(5, 41)(6, 39)(7, 34)(8, 35)(9, 33)(10, 48)(11, 49)(12, 46)(13, 47)(14, 37)(15, 38)(16, 53)(17, 54)(18, 44)(19, 45)(20, 42)(21, 43)(22, 58)(23, 56)(24, 57)(25, 52)(26, 50)(27, 51)(28, 60)(29, 55)(30, 59)(61, 93)(62, 91)(63, 99)(64, 97)(65, 98)(66, 92)(67, 104)(68, 105)(69, 96)(70, 94)(71, 95)(72, 110)(73, 111)(74, 108)(75, 109)(76, 102)(77, 103)(78, 100)(79, 101)(80, 116)(81, 117)(82, 115)(83, 106)(84, 107)(85, 119)(86, 113)(87, 114)(88, 112)(89, 120)(90, 118) local type(s) :: { ( 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12 ) } Outer automorphisms :: reflexible Dual of E20.248 Transitivity :: VT+ Graph:: v = 5 e = 60 f = 17 degree seq :: [ 24^5 ] E20.252 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y2^-1, R * Y1 * R * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3^5, Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 18, 48, 78, 108, 8, 38, 68, 98)(3, 33, 63, 93, 10, 40, 70, 100, 21, 51, 81, 111, 22, 52, 82, 112, 11, 41, 71, 101)(6, 36, 66, 96, 15, 45, 75, 105, 25, 55, 85, 115, 26, 56, 86, 116, 16, 46, 76, 106)(9, 39, 69, 99, 19, 49, 79, 109, 27, 57, 87, 117, 28, 58, 88, 118, 20, 50, 80, 110)(14, 44, 74, 104, 23, 53, 83, 113, 29, 59, 89, 119, 30, 60, 90, 120, 24, 54, 84, 114) L = (1, 32)(2, 36)(3, 31)(4, 38)(5, 37)(6, 44)(7, 46)(8, 45)(9, 33)(10, 35)(11, 34)(12, 48)(13, 47)(14, 39)(15, 54)(16, 53)(17, 56)(18, 55)(19, 41)(20, 40)(21, 43)(22, 42)(23, 50)(24, 49)(25, 60)(26, 59)(27, 52)(28, 51)(29, 58)(30, 57)(61, 93)(62, 91)(63, 99)(64, 101)(65, 100)(66, 92)(67, 95)(68, 94)(69, 104)(70, 110)(71, 109)(72, 112)(73, 111)(74, 96)(75, 98)(76, 97)(77, 103)(78, 102)(79, 114)(80, 113)(81, 118)(82, 117)(83, 106)(84, 105)(85, 108)(86, 107)(87, 120)(88, 119)(89, 116)(90, 115) local type(s) :: { ( 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 E20.249 Transitivity :: VT+ Graph:: bipartite v = 6 e = 60 f = 16 degree seq :: [ 20^6 ] E20.253 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 5, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D10 (small group id <30, 2>) Aut = C6 x D10 (small group id <60, 10>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y2 * Y1 * Y3, (R * Y3)^2, R * Y1 * R * Y2, Y3^5, Y1^6, (Y1^2 * Y2^-1)^2, Y2^6, Y3^2 * Y1^-1 * Y3^-2 * Y2^-1, Y3 * Y1^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94, 14, 44, 74, 104, 19, 49, 79, 109, 7, 37, 67, 97)(2, 32, 62, 92, 6, 36, 66, 96, 18, 48, 78, 108, 24, 54, 84, 114, 10, 40, 70, 100)(3, 33, 63, 93, 12, 42, 72, 102, 25, 55, 85, 115, 15, 45, 75, 105, 5, 35, 65, 95)(8, 38, 68, 98, 9, 39, 69, 99, 23, 53, 83, 113, 29, 59, 89, 119, 17, 47, 77, 107)(11, 41, 71, 101, 16, 46, 76, 106, 28, 58, 88, 118, 26, 56, 86, 116, 13, 43, 73, 103)(20, 50, 80, 110, 21, 51, 81, 111, 27, 57, 87, 117, 30, 60, 90, 120, 22, 52, 82, 112) L = (1, 32)(2, 38)(3, 37)(4, 40)(5, 31)(6, 47)(7, 36)(8, 50)(9, 52)(10, 39)(11, 35)(12, 49)(13, 33)(14, 54)(15, 34)(16, 45)(17, 51)(18, 59)(19, 48)(20, 41)(21, 43)(22, 46)(23, 60)(24, 53)(25, 44)(26, 42)(27, 56)(28, 55)(29, 57)(30, 58)(61, 93)(62, 94)(63, 101)(64, 95)(65, 106)(66, 91)(67, 102)(68, 96)(69, 92)(70, 104)(71, 111)(72, 103)(73, 117)(74, 105)(75, 118)(76, 110)(77, 108)(78, 97)(79, 115)(80, 99)(81, 98)(82, 113)(83, 100)(84, 109)(85, 116)(86, 120)(87, 107)(88, 112)(89, 114)(90, 119) local type(s) :: { ( 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 E20.250 Transitivity :: VT+ Graph:: bipartite v = 6 e = 60 f = 16 degree seq :: [ 20^6 ] E20.254 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 6, 6}) Quotient :: dipole Aut^+ = C3 x D10 (small group id <30, 2>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^6 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 4, 34)(3, 33, 9, 39, 18, 48, 14, 44, 7, 37)(5, 35, 12, 42, 21, 51, 15, 45, 8, 38)(10, 40, 16, 46, 23, 53, 26, 56, 19, 49)(13, 43, 17, 47, 24, 54, 28, 58, 22, 52)(20, 50, 27, 57, 30, 60, 29, 59, 25, 55)(61, 91, 63, 93, 70, 100, 80, 110, 73, 103, 65, 95)(62, 92, 67, 97, 76, 106, 85, 115, 77, 107, 68, 98)(64, 94, 69, 99, 79, 109, 87, 117, 82, 112, 72, 102)(66, 96, 74, 104, 83, 113, 89, 119, 84, 114, 75, 105)(71, 101, 78, 108, 86, 116, 90, 120, 88, 118, 81, 111) 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) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 10^6, 12^5 ] E20.255 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 6, 6}) 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 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 11, 41, 4, 34)(3, 33, 9, 39, 18, 48, 14, 44, 7, 37)(5, 35, 12, 42, 21, 51, 15, 45, 8, 38)(10, 40, 16, 46, 23, 53, 26, 56, 19, 49)(13, 43, 17, 47, 24, 54, 28, 58, 22, 52)(20, 50, 27, 57, 30, 60, 29, 59, 25, 55)(61, 91, 63, 93, 70, 100, 80, 110, 73, 103, 65, 95)(62, 92, 67, 97, 76, 106, 85, 115, 77, 107, 68, 98)(64, 94, 69, 99, 79, 109, 87, 117, 82, 112, 72, 102)(66, 96, 74, 104, 83, 113, 89, 119, 84, 114, 75, 105)(71, 101, 78, 108, 86, 116, 90, 120, 88, 118, 81, 111) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 72)(6, 71)(7, 63)(8, 65)(9, 78)(10, 76)(11, 64)(12, 81)(13, 77)(14, 67)(15, 68)(16, 83)(17, 84)(18, 74)(19, 70)(20, 87)(21, 75)(22, 73)(23, 86)(24, 88)(25, 80)(26, 79)(27, 90)(28, 82)(29, 85)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E20.257 Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 10^6, 12^5 ] E20.256 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 6, 6}) 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^-1 * Y3^-1 * Y1^-1, Y1 * Y3^-2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 4, 34, 5, 35)(3, 33, 10, 40, 13, 43, 12, 42, 8, 38)(6, 36, 15, 45, 14, 44, 16, 46, 9, 39)(11, 41, 18, 48, 23, 53, 22, 52, 20, 50)(17, 47, 19, 49, 26, 56, 24, 54, 25, 55)(21, 51, 28, 58, 30, 60, 29, 59, 27, 57)(61, 91, 63, 93, 71, 101, 81, 111, 77, 107, 66, 96)(62, 92, 68, 98, 78, 108, 87, 117, 79, 109, 69, 99)(64, 94, 73, 103, 82, 112, 90, 120, 84, 114, 74, 104)(65, 95, 70, 100, 80, 110, 88, 118, 85, 115, 75, 105)(67, 97, 72, 102, 83, 113, 89, 119, 86, 116, 76, 106) L = (1, 64)(2, 65)(3, 72)(4, 62)(5, 67)(6, 76)(7, 61)(8, 73)(9, 74)(10, 68)(11, 82)(12, 70)(13, 63)(14, 66)(15, 69)(16, 75)(17, 84)(18, 80)(19, 85)(20, 83)(21, 89)(22, 78)(23, 71)(24, 79)(25, 86)(26, 77)(27, 90)(28, 87)(29, 88)(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) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 10^6, 12^5 ] E20.257 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 6, 6}) 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^-2 * Y1^-1, Y3 * Y1^-2, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 31, 2, 32, 4, 34, 7, 37, 5, 35)(3, 33, 10, 40, 12, 42, 13, 43, 8, 38)(6, 36, 15, 45, 16, 46, 14, 44, 9, 39)(11, 41, 18, 48, 22, 52, 23, 53, 20, 50)(17, 47, 19, 49, 24, 54, 26, 56, 25, 55)(21, 51, 28, 58, 29, 59, 30, 60, 27, 57)(61, 91, 63, 93, 71, 101, 81, 111, 77, 107, 66, 96)(62, 92, 68, 98, 78, 108, 87, 117, 79, 109, 69, 99)(64, 94, 73, 103, 82, 112, 90, 120, 84, 114, 74, 104)(65, 95, 70, 100, 80, 110, 88, 118, 85, 115, 75, 105)(67, 97, 72, 102, 83, 113, 89, 119, 86, 116, 76, 106) L = (1, 64)(2, 67)(3, 72)(4, 65)(5, 62)(6, 76)(7, 61)(8, 70)(9, 75)(10, 73)(11, 82)(12, 68)(13, 63)(14, 66)(15, 74)(16, 69)(17, 84)(18, 83)(19, 86)(20, 78)(21, 89)(22, 80)(23, 71)(24, 85)(25, 79)(26, 77)(27, 88)(28, 90)(29, 87)(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) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E20.255 Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 10^6, 12^5 ] E20.258 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 6, 6}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^5, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^6 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 4, 34)(3, 33, 7, 37, 14, 44, 20, 50, 10, 40)(5, 35, 8, 38, 15, 45, 21, 51, 12, 42)(9, 39, 16, 46, 23, 53, 27, 57, 19, 49)(13, 43, 17, 47, 24, 54, 28, 58, 22, 52)(18, 48, 25, 55, 29, 59, 30, 60, 26, 56)(61, 91, 63, 93, 69, 99, 78, 108, 73, 103, 65, 95)(62, 92, 67, 97, 76, 106, 85, 115, 77, 107, 68, 98)(64, 94, 70, 100, 79, 109, 86, 116, 82, 112, 72, 102)(66, 96, 74, 104, 83, 113, 89, 119, 84, 114, 75, 105)(71, 101, 80, 110, 87, 117, 90, 120, 88, 118, 81, 111) 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) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 10^6, 12^5 ] E20.259 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^-2 * Y3^-2, (Y2, Y3), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3^-4, (Y1^-1 * Y3 * Y2)^2, Y2^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 14, 44)(4, 34, 16, 46, 9, 39)(6, 36, 10, 40, 19, 49)(7, 37, 20, 50, 11, 41)(12, 42, 21, 51, 26, 56)(13, 43, 27, 57, 22, 52)(15, 45, 28, 58, 23, 53)(17, 47, 24, 54, 29, 59)(18, 48, 30, 60, 25, 55)(61, 91, 63, 93, 72, 102, 77, 107, 66, 96)(62, 92, 68, 98, 81, 111, 84, 114, 70, 100)(64, 94, 73, 103, 67, 97, 75, 105, 78, 108)(65, 95, 74, 104, 86, 116, 89, 119, 79, 109)(69, 99, 82, 112, 71, 101, 83, 113, 85, 115)(76, 106, 87, 117, 80, 110, 88, 118, 90, 120) L = (1, 64)(2, 69)(3, 73)(4, 77)(5, 76)(6, 78)(7, 61)(8, 82)(9, 84)(10, 85)(11, 62)(12, 67)(13, 66)(14, 87)(15, 63)(16, 89)(17, 75)(18, 72)(19, 90)(20, 65)(21, 71)(22, 70)(23, 68)(24, 83)(25, 81)(26, 80)(27, 79)(28, 74)(29, 88)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20^6 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E20.266 Graph:: simple bipartite v = 16 e = 60 f = 6 degree seq :: [ 6^10, 10^6 ] E20.260 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, Y2^-2 * Y1^2, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, (Y1^-1, Y3), Y3^2 * Y1^-1 * Y3 * Y1^-1, Y2^4 * Y1, Y3^-1 * Y1 * Y2 * Y3^-1 * Y2, (Y1^-1 * Y3^-1)^3, Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 19, 49, 5, 35)(3, 33, 9, 39, 20, 50, 6, 36, 11, 41)(4, 34, 10, 40, 25, 55, 24, 54, 17, 47)(7, 37, 12, 42, 16, 46, 28, 58, 21, 51)(13, 43, 26, 56, 23, 53, 22, 52, 30, 60)(14, 44, 18, 48, 29, 59, 15, 45, 27, 57)(61, 91, 63, 93, 68, 98, 80, 110, 65, 95, 71, 101, 62, 92, 69, 99, 79, 109, 66, 96)(64, 94, 75, 105, 85, 115, 74, 104, 77, 107, 89, 119, 70, 100, 87, 117, 84, 114, 78, 108)(67, 97, 83, 113, 76, 106, 90, 120, 81, 111, 86, 116, 72, 102, 82, 112, 88, 118, 73, 103) L = (1, 64)(2, 70)(3, 73)(4, 76)(5, 77)(6, 82)(7, 61)(8, 85)(9, 86)(10, 88)(11, 90)(12, 62)(13, 89)(14, 63)(15, 66)(16, 68)(17, 72)(18, 69)(19, 84)(20, 83)(21, 65)(22, 74)(23, 87)(24, 67)(25, 81)(26, 75)(27, 71)(28, 79)(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, 20, 6, 20, 6, 20, 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E20.264 Graph:: bipartite v = 9 e = 60 f = 13 degree seq :: [ 10^6, 20^3 ] E20.261 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-1, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^3 * Y1^-2, Y3^-1 * Y2 * R * Y2^-1 * R, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2, Y2 * Y3 * Y2 * Y3^-2, Y1^5, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 19, 49, 5, 35)(3, 33, 6, 36, 10, 40, 27, 57, 13, 43)(4, 34, 9, 39, 26, 56, 25, 55, 17, 47)(7, 37, 11, 41, 16, 46, 28, 58, 20, 50)(12, 42, 21, 51, 23, 53, 24, 54, 30, 60)(14, 44, 22, 52, 29, 59, 15, 45, 18, 48)(61, 91, 63, 93, 65, 95, 73, 103, 79, 109, 87, 117, 68, 98, 70, 100, 62, 92, 66, 96)(64, 94, 75, 105, 77, 107, 89, 119, 85, 115, 82, 112, 86, 116, 74, 104, 69, 99, 78, 108)(67, 97, 83, 113, 80, 110, 81, 111, 88, 118, 72, 102, 76, 106, 90, 120, 71, 101, 84, 114) L = (1, 64)(2, 69)(3, 72)(4, 76)(5, 77)(6, 81)(7, 61)(8, 86)(9, 88)(10, 83)(11, 62)(12, 89)(13, 90)(14, 63)(15, 87)(16, 68)(17, 71)(18, 73)(19, 85)(20, 65)(21, 75)(22, 66)(23, 78)(24, 74)(25, 67)(26, 80)(27, 84)(28, 79)(29, 70)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E20.265 Graph:: bipartite v = 9 e = 60 f = 13 degree seq :: [ 10^6, 20^3 ] E20.262 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^3 * Y1^-2, R * Y2 * Y3 * R * Y2^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1^5, Y3^-2 * Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 5, 35)(3, 33, 9, 39, 26, 56, 19, 49, 6, 36)(4, 34, 10, 40, 27, 57, 25, 55, 16, 46)(7, 37, 11, 41, 15, 45, 29, 59, 20, 50)(12, 42, 24, 54, 23, 53, 30, 60, 21, 51)(13, 43, 28, 58, 17, 47, 14, 44, 22, 52)(61, 91, 63, 93, 62, 92, 69, 99, 68, 98, 86, 116, 78, 108, 79, 109, 65, 95, 66, 96)(64, 94, 74, 104, 70, 100, 82, 112, 87, 117, 73, 103, 85, 115, 88, 118, 76, 106, 77, 107)(67, 97, 83, 113, 71, 101, 90, 120, 75, 105, 81, 111, 89, 119, 72, 102, 80, 110, 84, 114) L = (1, 64)(2, 70)(3, 72)(4, 75)(5, 76)(6, 81)(7, 61)(8, 87)(9, 84)(10, 89)(11, 62)(12, 77)(13, 63)(14, 79)(15, 68)(16, 71)(17, 86)(18, 85)(19, 90)(20, 65)(21, 88)(22, 66)(23, 82)(24, 74)(25, 67)(26, 83)(27, 80)(28, 69)(29, 78)(30, 73)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E20.263 Graph:: bipartite v = 9 e = 60 f = 13 degree seq :: [ 10^6, 20^3 ] E20.263 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3 * Y1^-2 * Y3 * Y2, Y1 * Y2 * Y1 * Y3^-2, Y1 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^2 * Y3^3, Y1^10, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 26, 56, 15, 45, 28, 58, 18, 48, 30, 60, 21, 51, 5, 35)(3, 33, 11, 41, 27, 57, 22, 52, 23, 53, 12, 42, 4, 34, 16, 46, 25, 55, 14, 44)(6, 36, 9, 39, 17, 47, 24, 54, 7, 37, 20, 50, 13, 43, 10, 40, 29, 59, 19, 49)(61, 91, 63, 93, 66, 96)(62, 92, 69, 99, 71, 101)(64, 94, 73, 103, 78, 108)(65, 95, 79, 109, 74, 104)(67, 97, 75, 105, 83, 113)(68, 98, 87, 117, 77, 107)(70, 100, 76, 106, 90, 120)(72, 102, 88, 118, 80, 110)(81, 111, 85, 115, 89, 119)(82, 112, 86, 116, 84, 114) L = (1, 64)(2, 70)(3, 73)(4, 77)(5, 80)(6, 78)(7, 61)(8, 85)(9, 76)(10, 82)(11, 90)(12, 62)(13, 68)(14, 88)(15, 63)(16, 86)(17, 81)(18, 87)(19, 72)(20, 71)(21, 83)(22, 65)(23, 66)(24, 74)(25, 67)(26, 79)(27, 89)(28, 69)(29, 75)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E20.262 Graph:: bipartite v = 13 e = 60 f = 9 degree seq :: [ 6^10, 20^3 ] E20.264 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^3, (R * Y2)^2, (Y3, Y2), Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y1^-2 * Y2^-1 * Y3, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2, Y2^-1 * Y1 * Y3 * Y1^-1 * Y3^-1, Y3^-5 * Y2^-1, (Y3^-1 * Y1^-1 * Y3^-1)^2, Y2^-1 * Y3 * Y1^8 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 25, 55, 28, 58, 30, 60, 26, 56, 14, 44, 5, 35)(3, 33, 11, 41, 4, 34, 15, 45, 23, 53, 24, 54, 21, 51, 18, 48, 19, 49, 12, 42)(6, 36, 9, 39, 13, 43, 10, 40, 16, 46, 29, 59, 27, 57, 20, 50, 7, 37, 17, 47)(61, 91, 63, 93, 66, 96)(62, 92, 69, 99, 71, 101)(64, 94, 73, 103, 68, 98)(65, 95, 77, 107, 72, 102)(67, 97, 74, 104, 79, 109)(70, 100, 75, 105, 82, 112)(76, 106, 85, 115, 83, 113)(78, 108, 86, 116, 80, 110)(81, 111, 87, 117, 90, 120)(84, 114, 88, 118, 89, 119) L = (1, 64)(2, 70)(3, 73)(4, 76)(5, 69)(6, 68)(7, 61)(8, 83)(9, 75)(10, 84)(11, 82)(12, 62)(13, 85)(14, 63)(15, 88)(16, 90)(17, 71)(18, 65)(19, 66)(20, 72)(21, 67)(22, 89)(23, 87)(24, 86)(25, 81)(26, 77)(27, 74)(28, 80)(29, 78)(30, 79)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E20.260 Graph:: bipartite v = 13 e = 60 f = 9 degree seq :: [ 6^10, 20^3 ] E20.265 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y2^-1, Y3), Y1 * Y3 * Y1 * Y2, Y1 * Y2^-1 * Y3 * Y1, (R * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3 * Y2, (Y3^-2 * Y1)^2, Y3^-5 * Y2^-1, (Y2^-1 * Y3)^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 27, 57, 29, 59, 25, 55, 26, 56, 17, 47, 5, 35)(3, 33, 11, 41, 19, 49, 12, 42, 21, 51, 30, 60, 28, 58, 16, 46, 4, 34, 14, 44)(6, 36, 9, 39, 7, 37, 20, 50, 23, 53, 24, 54, 15, 45, 18, 48, 13, 43, 10, 40)(61, 91, 63, 93, 66, 96)(62, 92, 69, 99, 71, 101)(64, 94, 73, 103, 77, 107)(65, 95, 70, 100, 74, 104)(67, 97, 68, 98, 79, 109)(72, 102, 82, 112, 80, 110)(75, 105, 85, 115, 88, 118)(76, 106, 86, 116, 78, 108)(81, 111, 83, 113, 87, 117)(84, 114, 90, 120, 89, 119) L = (1, 64)(2, 70)(3, 73)(4, 75)(5, 78)(6, 77)(7, 61)(8, 63)(9, 74)(10, 76)(11, 65)(12, 62)(13, 85)(14, 86)(15, 87)(16, 89)(17, 88)(18, 90)(19, 66)(20, 71)(21, 67)(22, 69)(23, 68)(24, 72)(25, 81)(26, 84)(27, 79)(28, 83)(29, 80)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E20.261 Graph:: bipartite v = 13 e = 60 f = 9 degree seq :: [ 6^10, 20^3 ] E20.266 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10, 10}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y1^-1, Y3^-1), Y1 * Y2^-2 * Y3^-1, Y3^-1 * Y1^-3, Y3^2 * Y1^-1 * Y3, Y2^2 * Y3 * Y1^-1, (R * Y3)^2, Y2 * Y3^-2 * Y2, (R * Y1)^2, (Y2 * Y1 * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 7, 37, 12, 42, 24, 54, 17, 47, 4, 34, 10, 40, 5, 35)(3, 33, 13, 43, 22, 52, 16, 46, 29, 59, 21, 51, 6, 36, 14, 44, 23, 53, 15, 45)(9, 39, 25, 55, 18, 48, 28, 58, 20, 50, 30, 60, 11, 41, 26, 56, 19, 49, 27, 57)(61, 91, 63, 93, 72, 102, 89, 119, 70, 100, 83, 113, 68, 98, 82, 112, 77, 107, 66, 96)(62, 92, 69, 99, 84, 114, 80, 110, 65, 95, 79, 109, 67, 97, 78, 108, 64, 94, 71, 101)(73, 103, 86, 116, 81, 111, 85, 115, 75, 105, 90, 120, 76, 106, 87, 117, 74, 104, 88, 118) L = (1, 64)(2, 70)(3, 74)(4, 72)(5, 77)(6, 76)(7, 61)(8, 65)(9, 86)(10, 84)(11, 88)(12, 62)(13, 83)(14, 89)(15, 66)(16, 63)(17, 67)(18, 87)(19, 90)(20, 85)(21, 82)(22, 75)(23, 81)(24, 68)(25, 79)(26, 80)(27, 71)(28, 69)(29, 73)(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 ) } Outer automorphisms :: reflexible Dual of E20.259 Graph:: bipartite v = 6 e = 60 f = 16 degree seq :: [ 20^6 ] E20.267 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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 * Y1 * Y2, Y1^3, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (Y2 * Y1^-1)^2, Y3^5, (Y3 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 6, 36, 9, 39)(4, 34, 8, 38, 14, 44)(7, 37, 10, 40, 16, 46)(11, 41, 17, 47, 21, 51)(12, 42, 15, 45, 20, 50)(13, 43, 19, 49, 25, 55)(18, 48, 22, 52, 27, 57)(23, 53, 28, 58, 30, 60)(24, 54, 26, 56, 29, 59)(61, 91, 63, 93, 65, 95, 69, 99, 62, 92, 66, 96)(64, 94, 72, 102, 74, 104, 80, 110, 68, 98, 75, 105)(67, 97, 71, 101, 76, 106, 81, 111, 70, 100, 77, 107)(73, 103, 84, 114, 85, 115, 89, 119, 79, 109, 86, 116)(78, 108, 83, 113, 87, 117, 90, 120, 82, 112, 88, 118) L = (1, 64)(2, 68)(3, 71)(4, 73)(5, 74)(6, 77)(7, 61)(8, 79)(9, 81)(10, 62)(11, 83)(12, 63)(13, 78)(14, 85)(15, 66)(16, 65)(17, 88)(18, 67)(19, 82)(20, 69)(21, 90)(22, 70)(23, 84)(24, 72)(25, 87)(26, 75)(27, 76)(28, 86)(29, 80)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 30, 12, 30, 12, 30 ), ( 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30 ) } Outer automorphisms :: reflexible Dual of E20.272 Graph:: bipartite v = 15 e = 60 f = 7 degree seq :: [ 6^10, 12^5 ] E20.268 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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^-1 * Y2^2, Y1^3, (Y2 * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y1)^2, (Y3^-1, Y1), (R * Y3)^2, Y3^5, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 6, 36)(4, 34, 9, 39, 14, 44)(7, 37, 10, 40, 16, 46)(11, 41, 19, 49, 17, 47)(12, 42, 20, 50, 15, 45)(13, 43, 21, 51, 25, 55)(18, 48, 22, 52, 27, 57)(23, 53, 29, 59, 28, 58)(24, 54, 30, 60, 26, 56)(61, 91, 63, 93, 62, 92, 68, 98, 65, 95, 66, 96)(64, 94, 72, 102, 69, 99, 80, 110, 74, 104, 75, 105)(67, 97, 71, 101, 70, 100, 79, 109, 76, 106, 77, 107)(73, 103, 84, 114, 81, 111, 90, 120, 85, 115, 86, 116)(78, 108, 83, 113, 82, 112, 89, 119, 87, 117, 88, 118) L = (1, 64)(2, 69)(3, 71)(4, 73)(5, 74)(6, 77)(7, 61)(8, 79)(9, 81)(10, 62)(11, 83)(12, 63)(13, 78)(14, 85)(15, 66)(16, 65)(17, 88)(18, 67)(19, 89)(20, 68)(21, 82)(22, 70)(23, 84)(24, 72)(25, 87)(26, 75)(27, 76)(28, 86)(29, 90)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 30, 12, 30, 12, 30 ), ( 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30 ) } Outer automorphisms :: reflexible Dual of E20.273 Graph:: bipartite v = 15 e = 60 f = 7 degree seq :: [ 6^10, 12^5 ] E20.269 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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 * Y1, Y1^3, (Y1 * Y2)^2, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, (Y1^-1, Y3), (R * Y1)^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-5, Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^2 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 6, 36)(4, 34, 9, 39, 15, 45)(7, 37, 10, 40, 17, 47)(11, 41, 19, 49, 18, 48)(12, 42, 16, 46, 13, 43)(14, 44, 21, 51, 28, 58)(20, 50, 22, 52, 27, 57)(23, 53, 30, 60, 29, 59)(24, 54, 26, 56, 25, 55)(61, 91, 63, 93, 62, 92, 68, 98, 65, 95, 66, 96)(64, 94, 73, 103, 69, 99, 72, 102, 75, 105, 76, 106)(67, 97, 79, 109, 70, 100, 78, 108, 77, 107, 71, 101)(74, 104, 86, 116, 81, 111, 85, 115, 88, 118, 84, 114)(80, 110, 89, 119, 82, 112, 83, 113, 87, 117, 90, 120) L = (1, 64)(2, 69)(3, 71)(4, 74)(5, 75)(6, 78)(7, 61)(8, 79)(9, 81)(10, 62)(11, 83)(12, 63)(13, 66)(14, 87)(15, 88)(16, 68)(17, 65)(18, 89)(19, 90)(20, 67)(21, 80)(22, 70)(23, 85)(24, 72)(25, 73)(26, 76)(27, 77)(28, 82)(29, 86)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 30, 12, 30, 12, 30 ), ( 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30 ) } Outer automorphisms :: reflexible Dual of E20.274 Graph:: bipartite v = 15 e = 60 f = 7 degree seq :: [ 6^10, 12^5 ] E20.270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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, Y3^2, Y1^-3 * Y3, Y1^-1 * Y3 * Y1 * Y3, Y2^2 * Y3 * Y1^-1, Y3 * Y2^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 4, 34, 9, 39, 5, 35)(3, 33, 11, 41, 6, 36, 12, 42, 15, 45, 13, 43)(8, 38, 16, 46, 10, 40, 17, 47, 14, 44, 18, 48)(19, 49, 25, 55, 20, 50, 26, 56, 21, 51, 27, 57)(22, 52, 28, 58, 23, 53, 29, 59, 24, 54, 30, 60)(61, 91, 63, 93, 69, 99, 75, 105, 67, 97, 66, 96)(62, 92, 68, 98, 65, 95, 74, 104, 64, 94, 70, 100)(71, 101, 79, 109, 73, 103, 81, 111, 72, 102, 80, 110)(76, 106, 82, 112, 78, 108, 84, 114, 77, 107, 83, 113)(85, 115, 90, 120, 87, 117, 89, 119, 86, 116, 88, 118) L = (1, 64)(2, 69)(3, 72)(4, 61)(5, 67)(6, 73)(7, 65)(8, 77)(9, 62)(10, 78)(11, 75)(12, 63)(13, 66)(14, 76)(15, 71)(16, 74)(17, 68)(18, 70)(19, 86)(20, 87)(21, 85)(22, 89)(23, 90)(24, 88)(25, 81)(26, 79)(27, 80)(28, 84)(29, 82)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E20.271 Graph:: bipartite v = 10 e = 60 f = 12 degree seq :: [ 12^10 ] E20.271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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, Y3^2, Y2^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, (Y2, Y1^-1), Y1 * Y2^-1 * Y3 * Y1 * Y3, Y2^-1 * Y1^5, (Y2 * Y1 * Y3)^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 19, 49, 12, 42, 3, 33, 8, 38, 20, 50, 30, 60, 18, 48, 6, 36, 10, 40, 22, 52, 17, 47, 5, 35)(4, 34, 13, 43, 26, 56, 24, 54, 9, 39, 11, 41, 25, 55, 29, 59, 21, 51, 23, 53, 15, 45, 16, 46, 28, 58, 27, 57, 14, 44)(61, 91, 63, 93, 66, 96)(62, 92, 68, 98, 70, 100)(64, 94, 71, 101, 75, 105)(65, 95, 72, 102, 78, 108)(67, 97, 80, 110, 82, 112)(69, 99, 83, 113, 74, 104)(73, 103, 85, 115, 76, 106)(77, 107, 79, 109, 90, 120)(81, 111, 87, 117, 84, 114)(86, 116, 89, 119, 88, 118) L = (1, 64)(2, 69)(3, 71)(4, 61)(5, 76)(6, 75)(7, 81)(8, 83)(9, 62)(10, 74)(11, 63)(12, 73)(13, 72)(14, 70)(15, 66)(16, 65)(17, 89)(18, 85)(19, 88)(20, 87)(21, 67)(22, 84)(23, 68)(24, 82)(25, 78)(26, 90)(27, 80)(28, 79)(29, 77)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12^6 ), ( 12^30 ) } Outer automorphisms :: reflexible Dual of E20.270 Graph:: bipartite v = 12 e = 60 f = 10 degree seq :: [ 6^10, 30^2 ] E20.272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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 * Y1^-2 * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, Y3^2 * Y2^3, Y2^-1 * Y3^-1 * Y1 * Y2^-2 * Y1^-1, Y1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y2^-1, Y3^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 16, 46, 5, 35)(3, 33, 13, 43, 4, 34, 12, 42, 23, 53, 11, 41)(6, 36, 18, 48, 24, 54, 9, 39, 7, 37, 10, 40)(14, 44, 29, 59, 15, 45, 28, 58, 17, 47, 30, 60)(19, 49, 26, 56, 21, 51, 27, 57, 20, 50, 25, 55)(61, 91, 63, 93, 74, 104, 81, 111, 84, 114, 68, 98, 64, 94, 75, 105, 80, 110, 67, 97, 76, 106, 83, 113, 77, 107, 79, 109, 66, 96)(62, 92, 69, 99, 85, 115, 90, 120, 73, 103, 82, 112, 70, 100, 86, 116, 89, 119, 72, 102, 65, 95, 78, 108, 87, 117, 88, 118, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 77)(5, 69)(6, 68)(7, 61)(8, 83)(9, 86)(10, 87)(11, 82)(12, 62)(13, 65)(14, 80)(15, 79)(16, 63)(17, 81)(18, 85)(19, 84)(20, 66)(21, 67)(22, 78)(23, 74)(24, 76)(25, 89)(26, 88)(27, 90)(28, 73)(29, 71)(30, 72)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E20.267 Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 12^5, 30^2 ] E20.273 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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^-1 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2^-1)^2, Y3^5, Y3^-5, Y3^2 * Y2^3, Y2 * Y3^-1 * Y1^4, Y3^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 17, 47, 5, 35)(3, 33, 13, 43, 23, 53, 11, 41, 4, 34, 12, 42)(6, 36, 18, 48, 7, 37, 10, 40, 24, 54, 9, 39)(14, 44, 29, 59, 16, 46, 30, 60, 15, 45, 28, 58)(19, 49, 26, 56, 20, 50, 25, 55, 21, 51, 27, 57)(61, 91, 63, 93, 74, 104, 81, 111, 84, 114, 77, 107, 64, 94, 75, 105, 80, 110, 67, 97, 68, 98, 83, 113, 76, 106, 79, 109, 66, 96)(62, 92, 69, 99, 85, 115, 90, 120, 73, 103, 65, 95, 70, 100, 86, 116, 89, 119, 72, 102, 82, 112, 78, 108, 87, 117, 88, 118, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 76)(5, 78)(6, 77)(7, 61)(8, 63)(9, 86)(10, 87)(11, 65)(12, 62)(13, 82)(14, 80)(15, 79)(16, 81)(17, 83)(18, 85)(19, 84)(20, 66)(21, 67)(22, 69)(23, 74)(24, 68)(25, 89)(26, 88)(27, 90)(28, 73)(29, 71)(30, 72)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E20.268 Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 12^5, 30^2 ] E20.274 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 6, 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^-2 * Y2^-1 * Y3, (Y2 * Y1)^2, Y1^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y2)^2, Y3 * Y1 * Y2 * Y1^-1, (Y3^-1, Y2^-1), Y2 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^3, Y3 * Y2 * Y3^3, Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^-2, Y3 * Y2^-1 * Y1^4 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 16, 46, 5, 35)(3, 33, 12, 42, 4, 34, 11, 41, 23, 53, 15, 45)(6, 36, 10, 40, 24, 54, 18, 48, 7, 37, 9, 39)(13, 43, 30, 60, 14, 44, 29, 59, 17, 47, 28, 58)(19, 49, 27, 57, 21, 51, 25, 55, 20, 50, 26, 56)(61, 91, 63, 93, 73, 103, 80, 110, 67, 97, 76, 106, 83, 113, 77, 107, 81, 111, 84, 114, 68, 98, 64, 94, 74, 104, 79, 109, 66, 96)(62, 92, 69, 99, 85, 115, 89, 119, 72, 102, 65, 95, 78, 108, 87, 117, 90, 120, 75, 105, 82, 112, 70, 100, 86, 116, 88, 118, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 69)(6, 68)(7, 61)(8, 83)(9, 86)(10, 87)(11, 82)(12, 62)(13, 79)(14, 81)(15, 65)(16, 63)(17, 80)(18, 85)(19, 84)(20, 66)(21, 67)(22, 78)(23, 73)(24, 76)(25, 88)(26, 90)(27, 89)(28, 75)(29, 71)(30, 72)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E20.269 Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 12^5, 30^2 ] E20.275 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 10, 15, 15}) Quotient :: edge^2 Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2, Y1), Y3 * Y2 * Y3 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-2, Y1^-3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 4, 34)(2, 32, 9, 39)(3, 33, 12, 42)(5, 35, 15, 45)(6, 36, 14, 44)(7, 37, 19, 49)(8, 38, 21, 51)(10, 40, 22, 52)(11, 41, 24, 54)(13, 43, 25, 55)(16, 46, 28, 58)(17, 47, 27, 57)(18, 48, 26, 56)(20, 50, 29, 59)(23, 53, 30, 60)(61, 62, 67, 77, 66, 70, 80, 71, 78, 83, 73, 63, 68, 76, 65)(64, 72, 84, 87, 75, 85, 89, 79, 88, 90, 82, 69, 81, 86, 74)(91, 93, 101, 107, 95, 103, 110, 97, 106, 113, 100, 92, 98, 108, 96)(94, 99, 109, 117, 104, 112, 119, 114, 116, 120, 115, 102, 111, 118, 105) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 40^4 ), ( 40^15 ) } Outer automorphisms :: reflexible Dual of E20.278 Graph:: simple bipartite v = 19 e = 60 f = 3 degree seq :: [ 4^15, 15^4 ] E20.276 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 10, 15, 15}) Quotient :: edge^2 Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y1^-1, Y2), (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y3 * Y2 * Y3^-1, Y2 * Y3 * Y1^-1 * Y3^-1, Y2^-2 * Y1 * Y3^2, Y2 * Y1^4, Y2 * Y1 * Y2^3, Y2^-1 * Y1^2 * Y3^-2, (Y3^-1 * Y2^-2)^2, Y3^10 ] Map:: non-degenerate R = (1, 31, 4, 34, 17, 47, 28, 58, 9, 39, 27, 57, 21, 51, 30, 60, 25, 55, 7, 37)(2, 32, 10, 40, 13, 43, 29, 59, 20, 50, 24, 54, 6, 36, 18, 48, 15, 45, 12, 42)(3, 33, 14, 44, 8, 38, 26, 56, 23, 53, 22, 52, 5, 35, 19, 49, 11, 41, 16, 46)(61, 62, 68, 81, 66, 71, 77, 73, 83, 85, 75, 63, 69, 80, 65)(64, 74, 89, 90, 79, 72, 88, 86, 84, 67, 76, 70, 87, 82, 78)(91, 93, 103, 111, 95, 105, 107, 98, 110, 115, 101, 92, 99, 113, 96)(94, 100, 116, 120, 108, 106, 118, 119, 112, 97, 102, 104, 117, 114, 109) 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) :: { ( 8^15 ), ( 8^20 ) } Outer automorphisms :: reflexible Dual of E20.277 Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 15^4, 20^3 ] E20.277 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 10, 15, 15}) Quotient :: loop^2 Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2, Y1), Y3 * Y2 * Y3 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-2, Y1^-3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94)(2, 32, 62, 92, 9, 39, 69, 99)(3, 33, 63, 93, 12, 42, 72, 102)(5, 35, 65, 95, 15, 45, 75, 105)(6, 36, 66, 96, 14, 44, 74, 104)(7, 37, 67, 97, 19, 49, 79, 109)(8, 38, 68, 98, 21, 51, 81, 111)(10, 40, 70, 100, 22, 52, 82, 112)(11, 41, 71, 101, 24, 54, 84, 114)(13, 43, 73, 103, 25, 55, 85, 115)(16, 46, 76, 106, 28, 58, 88, 118)(17, 47, 77, 107, 27, 57, 87, 117)(18, 48, 78, 108, 26, 56, 86, 116)(20, 50, 80, 110, 29, 59, 89, 119)(23, 53, 83, 113, 30, 60, 90, 120) L = (1, 32)(2, 37)(3, 38)(4, 42)(5, 31)(6, 40)(7, 47)(8, 46)(9, 51)(10, 50)(11, 48)(12, 54)(13, 33)(14, 34)(15, 55)(16, 35)(17, 36)(18, 53)(19, 58)(20, 41)(21, 56)(22, 39)(23, 43)(24, 57)(25, 59)(26, 44)(27, 45)(28, 60)(29, 49)(30, 52)(61, 93)(62, 98)(63, 101)(64, 99)(65, 103)(66, 91)(67, 106)(68, 108)(69, 109)(70, 92)(71, 107)(72, 111)(73, 110)(74, 112)(75, 94)(76, 113)(77, 95)(78, 96)(79, 117)(80, 97)(81, 118)(82, 119)(83, 100)(84, 116)(85, 102)(86, 120)(87, 104)(88, 105)(89, 114)(90, 115) local type(s) :: { ( 15, 20, 15, 20, 15, 20, 15, 20 ) } Outer automorphisms :: reflexible Dual of E20.276 Transitivity :: VT+ Graph:: v = 15 e = 60 f = 7 degree seq :: [ 8^15 ] E20.278 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 10, 15, 15}) Quotient :: loop^2 Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y1^-1, Y2), (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y3 * Y2 * Y3^-1, Y2 * Y3 * Y1^-1 * Y3^-1, Y2^-2 * Y1 * Y3^2, Y2 * Y1^4, Y2 * Y1 * Y2^3, Y2^-1 * Y1^2 * Y3^-2, (Y3^-1 * Y2^-2)^2, Y3^10 ] Map:: non-degenerate R = (1, 31, 61, 91, 4, 34, 64, 94, 17, 47, 77, 107, 28, 58, 88, 118, 9, 39, 69, 99, 27, 57, 87, 117, 21, 51, 81, 111, 30, 60, 90, 120, 25, 55, 85, 115, 7, 37, 67, 97)(2, 32, 62, 92, 10, 40, 70, 100, 13, 43, 73, 103, 29, 59, 89, 119, 20, 50, 80, 110, 24, 54, 84, 114, 6, 36, 66, 96, 18, 48, 78, 108, 15, 45, 75, 105, 12, 42, 72, 102)(3, 33, 63, 93, 14, 44, 74, 104, 8, 38, 68, 98, 26, 56, 86, 116, 23, 53, 83, 113, 22, 52, 82, 112, 5, 35, 65, 95, 19, 49, 79, 109, 11, 41, 71, 101, 16, 46, 76, 106) L = (1, 32)(2, 38)(3, 39)(4, 44)(5, 31)(6, 41)(7, 46)(8, 51)(9, 50)(10, 57)(11, 47)(12, 58)(13, 53)(14, 59)(15, 33)(16, 40)(17, 43)(18, 34)(19, 42)(20, 35)(21, 36)(22, 48)(23, 55)(24, 37)(25, 45)(26, 54)(27, 52)(28, 56)(29, 60)(30, 49)(61, 93)(62, 99)(63, 103)(64, 100)(65, 105)(66, 91)(67, 102)(68, 110)(69, 113)(70, 116)(71, 92)(72, 104)(73, 111)(74, 117)(75, 107)(76, 118)(77, 98)(78, 106)(79, 94)(80, 115)(81, 95)(82, 97)(83, 96)(84, 109)(85, 101)(86, 120)(87, 114)(88, 119)(89, 112)(90, 108) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E20.275 Transitivity :: VT+ Graph:: v = 3 e = 60 f = 19 degree seq :: [ 40^3 ] E20.279 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (Y3, Y2^-1), Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, Y3^-2 * Y2^3, Y3 * Y1^-1 * Y3^2 * Y1^-1, Y3^5, Y1 * Y2 * Y3^-1 * Y1 * Y2, Y2^2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 4, 34, 10, 40, 7, 37, 12, 42, 17, 47, 5, 35)(3, 33, 13, 43, 23, 53, 27, 57, 15, 45, 30, 60, 16, 46, 21, 51, 28, 58, 11, 41)(6, 36, 20, 50, 25, 55, 9, 39, 19, 49, 29, 59, 24, 54, 26, 56, 14, 44, 22, 52)(61, 91, 63, 93, 74, 104, 77, 107, 88, 118, 84, 114, 67, 97, 76, 106, 79, 109, 64, 94, 75, 105, 85, 115, 68, 98, 83, 113, 66, 96)(62, 92, 69, 99, 81, 111, 65, 95, 80, 110, 90, 120, 72, 102, 82, 112, 87, 117, 70, 100, 86, 116, 73, 103, 78, 108, 89, 119, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 77)(5, 78)(6, 79)(7, 61)(8, 67)(9, 86)(10, 65)(11, 87)(12, 62)(13, 90)(14, 85)(15, 88)(16, 63)(17, 68)(18, 72)(19, 74)(20, 89)(21, 73)(22, 69)(23, 76)(24, 66)(25, 84)(26, 80)(27, 81)(28, 83)(29, 82)(30, 71)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.287 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.280 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y3^-1 * Y2^-3, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y1 * Y2 * Y3^-1 * Y1^-1 * Y2, Y3^5, Y1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y3^-2 * Y1^8, (Y2^-1 * Y3)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 19, 49, 4, 34, 10, 40, 7, 37, 12, 42, 18, 48, 5, 35)(3, 33, 13, 43, 25, 55, 27, 57, 15, 45, 22, 52, 17, 47, 11, 41, 28, 58, 16, 46)(6, 36, 23, 53, 26, 56, 21, 51, 20, 50, 9, 39, 14, 44, 29, 59, 30, 60, 24, 54)(61, 91, 63, 93, 74, 104, 67, 97, 77, 107, 86, 116, 68, 98, 85, 115, 90, 120, 78, 108, 88, 118, 80, 110, 64, 94, 75, 105, 66, 96)(62, 92, 69, 99, 87, 117, 72, 102, 83, 113, 76, 106, 79, 109, 89, 119, 82, 112, 65, 95, 81, 111, 73, 103, 70, 100, 84, 114, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 78)(5, 79)(6, 80)(7, 61)(8, 67)(9, 84)(10, 65)(11, 73)(12, 62)(13, 82)(14, 66)(15, 88)(16, 87)(17, 63)(18, 68)(19, 72)(20, 90)(21, 89)(22, 76)(23, 69)(24, 81)(25, 77)(26, 74)(27, 71)(28, 85)(29, 83)(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) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.286 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.281 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-2, Y2^-1 * Y3 * Y2^-2, (Y3^-1, Y1^-1), (Y3, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^4, Y1 * Y2^-1 * Y3 * Y1 * Y2^-1, Y3^5, Y3 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 19, 49, 4, 34, 10, 40, 7, 37, 12, 42, 18, 48, 5, 35)(3, 33, 13, 43, 25, 55, 21, 51, 15, 45, 11, 41, 17, 47, 29, 59, 30, 60, 16, 46)(6, 36, 22, 52, 26, 56, 28, 58, 14, 44, 20, 50, 24, 54, 9, 39, 27, 57, 23, 53)(61, 91, 63, 93, 74, 104, 64, 94, 75, 105, 87, 117, 78, 108, 90, 120, 86, 116, 68, 98, 85, 115, 84, 114, 67, 97, 77, 107, 66, 96)(62, 92, 69, 99, 76, 106, 70, 100, 82, 112, 81, 111, 65, 95, 80, 110, 89, 119, 79, 109, 83, 113, 73, 103, 72, 102, 88, 118, 71, 101) L = (1, 64)(2, 70)(3, 75)(4, 78)(5, 79)(6, 74)(7, 61)(8, 67)(9, 82)(10, 65)(11, 76)(12, 62)(13, 71)(14, 87)(15, 90)(16, 81)(17, 63)(18, 68)(19, 72)(20, 83)(21, 89)(22, 80)(23, 88)(24, 66)(25, 77)(26, 84)(27, 86)(28, 69)(29, 73)(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) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.285 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.282 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-1, Y2^3 * Y1^2, Y1^2 * Y3^-3, Y1^10, (Y3 * Y2^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 16, 46, 26, 56, 29, 59, 30, 60, 24, 54, 15, 45, 5, 35)(3, 33, 9, 39, 12, 42, 23, 53, 27, 57, 22, 52, 25, 55, 14, 44, 20, 50, 8, 38)(4, 34, 11, 41, 17, 47, 7, 37, 18, 48, 19, 49, 28, 58, 21, 51, 10, 40, 13, 43)(61, 91, 63, 93, 70, 100, 75, 105, 80, 110, 88, 118, 90, 120, 85, 115, 78, 108, 86, 116, 87, 117, 77, 107, 66, 96, 72, 102, 64, 94)(62, 92, 67, 97, 74, 104, 65, 95, 71, 101, 82, 112, 84, 114, 73, 103, 83, 113, 89, 119, 81, 111, 69, 99, 76, 106, 79, 109, 68, 98) L = (1, 64)(2, 68)(3, 61)(4, 72)(5, 74)(6, 77)(7, 62)(8, 79)(9, 81)(10, 63)(11, 65)(12, 66)(13, 84)(14, 67)(15, 70)(16, 69)(17, 87)(18, 85)(19, 76)(20, 75)(21, 89)(22, 71)(23, 73)(24, 82)(25, 90)(26, 78)(27, 86)(28, 80)(29, 83)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.290 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.283 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y2^2 * Y3^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y3, (R * Y1)^2, (Y3 * Y1)^2, (R * Y2)^2, Y1^-1 * Y3 * Y1^-1 * Y2^-1, (R * Y3)^2, Y3^2 * Y1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^3, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 24, 54, 22, 52, 30, 60, 14, 44, 28, 58, 19, 49, 5, 35)(3, 33, 13, 43, 25, 55, 10, 40, 7, 37, 20, 50, 17, 47, 11, 41, 29, 59, 15, 45)(4, 34, 16, 46, 26, 56, 12, 42, 6, 36, 21, 51, 27, 57, 18, 48, 23, 53, 9, 39)(61, 91, 63, 93, 64, 94, 74, 104, 77, 107, 87, 117, 68, 98, 85, 115, 86, 116, 79, 109, 89, 119, 83, 113, 82, 112, 67, 97, 66, 96)(62, 92, 69, 99, 70, 100, 88, 118, 81, 111, 75, 105, 84, 114, 76, 106, 80, 110, 65, 95, 78, 108, 73, 103, 90, 120, 72, 102, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 73)(6, 63)(7, 61)(8, 86)(9, 88)(10, 81)(11, 69)(12, 62)(13, 72)(14, 87)(15, 76)(16, 65)(17, 68)(18, 90)(19, 83)(20, 78)(21, 84)(22, 66)(23, 67)(24, 80)(25, 79)(26, 89)(27, 85)(28, 75)(29, 82)(30, 71)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.289 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.284 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1 * Y2^-1 * Y3^-1 * Y1, Y1^-2 * Y2 * Y3, (R * Y3)^2, Y2 * Y3 * Y1^-2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y1^5, Y1 * Y2^-5 * Y1 * Y2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 29, 59, 28, 58, 30, 60, 27, 57, 18, 48, 5, 35)(3, 33, 13, 43, 23, 53, 19, 49, 26, 56, 11, 41, 21, 51, 10, 40, 7, 37, 15, 45)(4, 34, 16, 46, 14, 44, 12, 42, 25, 55, 9, 39, 24, 54, 20, 50, 6, 36, 17, 47)(61, 91, 63, 93, 74, 104, 89, 119, 86, 116, 84, 114, 78, 108, 67, 97, 64, 94, 68, 98, 83, 113, 85, 115, 90, 120, 81, 111, 66, 96)(62, 92, 69, 99, 75, 105, 88, 118, 77, 107, 79, 109, 65, 95, 72, 102, 70, 100, 82, 112, 80, 110, 73, 103, 87, 117, 76, 106, 71, 101) L = (1, 64)(2, 70)(3, 68)(4, 63)(5, 71)(6, 67)(7, 61)(8, 74)(9, 82)(10, 69)(11, 72)(12, 62)(13, 77)(14, 83)(15, 80)(16, 65)(17, 87)(18, 66)(19, 76)(20, 88)(21, 78)(22, 75)(23, 89)(24, 81)(25, 86)(26, 90)(27, 79)(28, 73)(29, 85)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.288 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.285 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, Y3^2 * Y1^3, Y3^5, Y3^-2 * Y1 * Y2 * Y1 * Y2, Y1 * Y3^-2 * Y2 * Y1 * Y2, Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y3, Y1^-1 * Y2 * Y1 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 20, 50, 27, 57, 16, 46, 4, 34, 9, 39, 19, 49, 6, 36, 10, 40, 22, 52, 15, 45, 18, 48, 5, 35)(3, 33, 11, 41, 24, 54, 30, 60, 17, 47, 26, 56, 12, 42, 21, 51, 29, 59, 14, 44, 25, 55, 8, 38, 23, 53, 28, 58, 13, 43)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 72, 102)(65, 95, 77, 107)(66, 96, 74, 104)(67, 97, 81, 111)(69, 99, 84, 114)(70, 100, 86, 116)(71, 101, 82, 112)(73, 103, 87, 117)(75, 105, 83, 113)(76, 106, 85, 115)(78, 108, 89, 119)(79, 109, 88, 118)(80, 110, 90, 120) L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 76)(6, 61)(7, 79)(8, 84)(9, 78)(10, 62)(11, 81)(12, 83)(13, 86)(14, 63)(15, 80)(16, 82)(17, 85)(18, 87)(19, 65)(20, 66)(21, 88)(22, 67)(23, 90)(24, 89)(25, 71)(26, 68)(27, 70)(28, 77)(29, 73)(30, 74)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.281 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.286 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3^5, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 4, 34, 9, 39, 20, 50, 15, 45, 23, 53, 30, 60, 18, 48, 24, 54, 17, 47, 6, 36, 10, 40, 5, 35)(3, 33, 11, 41, 25, 55, 12, 42, 16, 46, 29, 59, 27, 57, 19, 49, 22, 52, 28, 58, 21, 51, 8, 38, 14, 44, 26, 56, 13, 43)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 72, 102)(65, 95, 76, 106)(66, 96, 74, 104)(67, 97, 79, 109)(69, 99, 73, 103)(70, 100, 82, 112)(71, 101, 77, 107)(75, 105, 87, 117)(78, 108, 88, 118)(80, 110, 81, 111)(83, 113, 85, 115)(84, 114, 89, 119)(86, 116, 90, 120) L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 67)(6, 61)(7, 80)(8, 73)(9, 83)(10, 62)(11, 76)(12, 87)(13, 85)(14, 63)(15, 78)(16, 79)(17, 65)(18, 66)(19, 81)(20, 90)(21, 86)(22, 68)(23, 84)(24, 70)(25, 89)(26, 71)(27, 88)(28, 74)(29, 82)(30, 77)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.280 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.287 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-2 * Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y3 * Y1^-1 * Y2 * Y1^-1, Y3^5, Y1^-1 * Y3^-2 * Y1 * Y3^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 6, 36, 10, 40, 20, 50, 18, 48, 24, 54, 29, 59, 15, 45, 23, 53, 16, 46, 4, 34, 9, 39, 5, 35)(3, 33, 11, 41, 25, 55, 14, 44, 17, 47, 30, 60, 28, 58, 19, 49, 21, 51, 27, 57, 22, 52, 8, 38, 12, 42, 26, 56, 13, 43)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 72, 102)(65, 95, 77, 107)(66, 96, 74, 104)(67, 97, 79, 109)(69, 99, 81, 111)(70, 100, 73, 103)(71, 101, 76, 106)(75, 105, 87, 117)(78, 108, 88, 118)(80, 110, 82, 112)(83, 113, 90, 120)(84, 114, 85, 115)(86, 116, 89, 119) L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 76)(6, 61)(7, 65)(8, 81)(9, 83)(10, 62)(11, 86)(12, 87)(13, 68)(14, 63)(15, 78)(16, 89)(17, 71)(18, 66)(19, 77)(20, 67)(21, 90)(22, 79)(23, 84)(24, 70)(25, 73)(26, 82)(27, 88)(28, 74)(29, 80)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.279 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.288 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^2 * Y2 * Y1 * Y2 * Y1^2, Y2 * Y1^2 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-2, (Y3 * Y2)^10, (Y3^-1 * Y1^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35, 11, 41, 17, 47, 24, 54, 29, 59, 26, 56, 28, 58, 30, 60, 27, 57, 16, 46, 22, 52, 10, 40, 4, 34)(3, 33, 7, 37, 15, 45, 20, 50, 9, 39, 19, 49, 23, 53, 12, 42, 21, 51, 25, 55, 14, 44, 6, 36, 13, 43, 18, 48, 8, 38)(61, 91, 63, 93)(62, 92, 66, 96)(64, 94, 69, 99)(65, 95, 72, 102)(67, 97, 76, 106)(68, 98, 77, 107)(70, 100, 81, 111)(71, 101, 80, 110)(73, 103, 82, 112)(74, 104, 84, 114)(75, 105, 86, 116)(78, 108, 88, 118)(79, 109, 87, 117)(83, 113, 89, 119)(85, 115, 90, 120) L = (1, 62)(2, 65)(3, 67)(4, 61)(5, 71)(6, 73)(7, 75)(8, 63)(9, 79)(10, 64)(11, 77)(12, 81)(13, 78)(14, 66)(15, 80)(16, 82)(17, 84)(18, 68)(19, 83)(20, 69)(21, 85)(22, 70)(23, 72)(24, 89)(25, 74)(26, 88)(27, 76)(28, 90)(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) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.284 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.289 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-2 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y3 * Y2, Y1 * Y3^-7, (Y3 * Y2)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 8, 38, 18, 48, 23, 53, 30, 60, 25, 55, 24, 54, 27, 57, 28, 58, 14, 44, 15, 45, 4, 34, 5, 35)(3, 33, 9, 39, 12, 42, 22, 52, 16, 46, 29, 59, 26, 56, 17, 47, 13, 43, 20, 50, 21, 51, 7, 37, 19, 49, 10, 40, 11, 41)(61, 91, 63, 93)(62, 92, 67, 97)(64, 94, 73, 103)(65, 95, 76, 106)(66, 96, 77, 107)(68, 98, 82, 112)(69, 99, 74, 104)(70, 100, 84, 114)(71, 101, 78, 108)(72, 102, 85, 115)(75, 105, 79, 109)(80, 110, 87, 117)(81, 111, 83, 113)(86, 116, 90, 120)(88, 118, 89, 119) L = (1, 64)(2, 65)(3, 70)(4, 74)(5, 75)(6, 61)(7, 80)(8, 62)(9, 71)(10, 67)(11, 79)(12, 63)(13, 86)(14, 87)(15, 88)(16, 72)(17, 89)(18, 66)(19, 81)(20, 77)(21, 73)(22, 69)(23, 68)(24, 90)(25, 83)(26, 76)(27, 85)(28, 84)(29, 82)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.283 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.290 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y3^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y3^-1 * Y2, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y3^-1, Y1^-7 * Y3 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 19, 49, 27, 57, 28, 58, 15, 45, 4, 34, 6, 36, 9, 39, 20, 50, 25, 55, 30, 60, 17, 47, 5, 35)(3, 33, 10, 40, 14, 44, 22, 52, 16, 46, 29, 59, 26, 56, 11, 41, 13, 43, 24, 54, 23, 53, 8, 38, 21, 51, 18, 48, 12, 42)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 74, 104)(65, 95, 76, 106)(66, 96, 78, 108)(67, 97, 71, 101)(69, 99, 84, 114)(70, 100, 85, 115)(72, 102, 87, 117)(73, 103, 77, 107)(75, 105, 86, 116)(79, 109, 82, 112)(80, 110, 89, 119)(81, 111, 90, 120)(83, 113, 88, 118) L = (1, 64)(2, 66)(3, 71)(4, 65)(5, 75)(6, 61)(7, 69)(8, 82)(9, 62)(10, 73)(11, 72)(12, 86)(13, 63)(14, 84)(15, 77)(16, 68)(17, 88)(18, 89)(19, 80)(20, 67)(21, 76)(22, 83)(23, 74)(24, 70)(25, 79)(26, 78)(27, 85)(28, 90)(29, 81)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.282 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.291 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1 * Y3 * Y1, (Y2, Y3), (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y2^5 * Y1, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3^-2 * Y2^-2 ] 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, 84, 114, 69, 99, 62, 92, 67, 97, 79, 109, 76, 106, 65, 95)(64, 94, 72, 102, 87, 117, 78, 108, 83, 113, 68, 98, 80, 110, 89, 119, 86, 116, 75, 105)(66, 96, 73, 103, 82, 112, 90, 120, 85, 115, 70, 100, 81, 111, 74, 104, 88, 118, 77, 107) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 75)(6, 61)(7, 80)(8, 82)(9, 83)(10, 62)(11, 87)(12, 88)(13, 63)(14, 79)(15, 81)(16, 86)(17, 65)(18, 66)(19, 89)(20, 90)(21, 67)(22, 71)(23, 73)(24, 78)(25, 69)(26, 70)(27, 77)(28, 76)(29, 85)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30^4 ), ( 30^20 ) } Outer automorphisms :: reflexible Dual of E20.298 Graph:: bipartite v = 18 e = 60 f = 4 degree seq :: [ 4^15, 20^3 ] E20.292 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (Y1^-1, Y3^-1), (Y3^-1 * Y1^-1)^2, (Y2^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y3^-2 * Y1^-2, Y2 * Y1^2 * Y2^2, Y2^2 * Y3^-1 * Y2 * Y3^-1, Y1^4 * Y3^-1, Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 4, 34, 10, 40, 7, 37, 12, 42, 17, 47, 5, 35)(3, 33, 9, 39, 21, 51, 27, 57, 14, 44, 24, 54, 16, 46, 25, 55, 29, 59, 15, 45)(6, 36, 11, 41, 23, 53, 30, 60, 19, 49, 26, 56, 22, 52, 28, 58, 13, 43, 20, 50)(61, 91, 63, 93, 73, 103, 77, 107, 89, 119, 82, 112, 67, 97, 76, 106, 79, 109, 64, 94, 74, 104, 83, 113, 68, 98, 81, 111, 66, 96)(62, 92, 69, 99, 80, 110, 65, 95, 75, 105, 88, 118, 72, 102, 85, 115, 86, 116, 70, 100, 84, 114, 90, 120, 78, 108, 87, 117, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 67)(9, 84)(10, 65)(11, 86)(12, 62)(13, 83)(14, 89)(15, 87)(16, 63)(17, 68)(18, 72)(19, 73)(20, 90)(21, 76)(22, 66)(23, 82)(24, 75)(25, 69)(26, 80)(27, 85)(28, 71)(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) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.297 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.293 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, Y2^-3 * Y3^-1, Y1^2 * Y3^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, Y1^2 * Y3^-3, Y3^-2 * Y2 * Y3^2 * Y2^-1, (Y3 * Y2^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 4, 34, 10, 40, 7, 37, 12, 42, 17, 47, 5, 35)(3, 33, 9, 39, 21, 51, 28, 58, 14, 44, 24, 54, 16, 46, 25, 55, 27, 57, 15, 45)(6, 36, 11, 41, 22, 52, 30, 60, 19, 49, 26, 56, 13, 43, 23, 53, 29, 59, 20, 50)(61, 91, 63, 93, 73, 103, 67, 97, 76, 106, 82, 112, 68, 98, 81, 111, 89, 119, 77, 107, 87, 117, 79, 109, 64, 94, 74, 104, 66, 96)(62, 92, 69, 99, 83, 113, 72, 102, 85, 115, 90, 120, 78, 108, 88, 118, 80, 110, 65, 95, 75, 105, 86, 116, 70, 100, 84, 114, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 67)(9, 84)(10, 65)(11, 86)(12, 62)(13, 66)(14, 87)(15, 88)(16, 63)(17, 68)(18, 72)(19, 89)(20, 90)(21, 76)(22, 73)(23, 71)(24, 75)(25, 69)(26, 80)(27, 81)(28, 85)(29, 82)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.296 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.294 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-3, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2, Y3), (Y2^-1, Y1^-1), (R * Y3)^2, Y1^2 * Y3^2, (R * Y2)^2, Y3 * Y1^-4, Y3^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 4, 34, 10, 40, 7, 37, 12, 42, 17, 47, 5, 35)(3, 33, 9, 39, 21, 51, 30, 60, 14, 44, 24, 54, 16, 46, 25, 55, 29, 59, 15, 45)(6, 36, 11, 41, 22, 52, 28, 58, 13, 43, 23, 53, 20, 50, 26, 56, 27, 57, 19, 49)(61, 91, 63, 93, 73, 103, 64, 94, 74, 104, 87, 117, 77, 107, 89, 119, 82, 112, 68, 98, 81, 111, 80, 110, 67, 97, 76, 106, 66, 96)(62, 92, 69, 99, 83, 113, 70, 100, 84, 114, 79, 109, 65, 95, 75, 105, 88, 118, 78, 108, 90, 120, 86, 116, 72, 102, 85, 115, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 73)(7, 61)(8, 67)(9, 84)(10, 65)(11, 83)(12, 62)(13, 87)(14, 89)(15, 90)(16, 63)(17, 68)(18, 72)(19, 88)(20, 66)(21, 76)(22, 80)(23, 79)(24, 75)(25, 69)(26, 71)(27, 82)(28, 86)(29, 81)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.295 Graph:: bipartite v = 5 e = 60 f = 17 degree seq :: [ 20^3, 30^2 ] E20.295 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y2 * Y1 * Y2, Y1^3 * Y3^2, Y3^5, Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 18, 48, 23, 53, 15, 45, 4, 34, 9, 39, 17, 47, 6, 36, 10, 40, 20, 50, 14, 44, 16, 46, 5, 35)(3, 33, 8, 38, 19, 49, 28, 58, 30, 60, 25, 55, 11, 41, 21, 51, 27, 57, 13, 43, 22, 52, 29, 59, 24, 54, 26, 56, 12, 42)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 71, 101)(65, 95, 72, 102)(66, 96, 73, 103)(67, 97, 79, 109)(69, 99, 81, 111)(70, 100, 82, 112)(74, 104, 84, 114)(75, 105, 85, 115)(76, 106, 86, 116)(77, 107, 87, 117)(78, 108, 88, 118)(80, 110, 89, 119)(83, 113, 90, 120) L = (1, 64)(2, 69)(3, 71)(4, 74)(5, 75)(6, 61)(7, 77)(8, 81)(9, 76)(10, 62)(11, 84)(12, 85)(13, 63)(14, 78)(15, 80)(16, 83)(17, 65)(18, 66)(19, 87)(20, 67)(21, 86)(22, 68)(23, 70)(24, 88)(25, 89)(26, 90)(27, 72)(28, 73)(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) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.294 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.296 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y3, Y1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3^5, (Y1^-1 * Y3^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 4, 34, 9, 39, 18, 48, 14, 44, 21, 51, 26, 56, 16, 46, 22, 52, 15, 45, 6, 36, 10, 40, 5, 35)(3, 33, 8, 38, 17, 47, 11, 41, 19, 49, 27, 57, 23, 53, 28, 58, 30, 60, 25, 55, 29, 59, 24, 54, 13, 43, 20, 50, 12, 42)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 71, 101)(65, 95, 72, 102)(66, 96, 73, 103)(67, 97, 77, 107)(69, 99, 79, 109)(70, 100, 80, 110)(74, 104, 83, 113)(75, 105, 84, 114)(76, 106, 85, 115)(78, 108, 87, 117)(81, 111, 88, 118)(82, 112, 89, 119)(86, 116, 90, 120) L = (1, 64)(2, 69)(3, 71)(4, 74)(5, 67)(6, 61)(7, 78)(8, 79)(9, 81)(10, 62)(11, 83)(12, 77)(13, 63)(14, 76)(15, 65)(16, 66)(17, 87)(18, 86)(19, 88)(20, 68)(21, 82)(22, 70)(23, 85)(24, 72)(25, 73)(26, 75)(27, 90)(28, 89)(29, 80)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.293 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.297 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-3, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 6, 36, 10, 40, 18, 48, 16, 46, 22, 52, 26, 56, 14, 44, 21, 51, 15, 45, 4, 34, 9, 39, 5, 35)(3, 33, 8, 38, 17, 47, 13, 43, 20, 50, 27, 57, 25, 55, 29, 59, 30, 60, 23, 53, 28, 58, 24, 54, 11, 41, 19, 49, 12, 42)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 71, 101)(65, 95, 72, 102)(66, 96, 73, 103)(67, 97, 77, 107)(69, 99, 79, 109)(70, 100, 80, 110)(74, 104, 83, 113)(75, 105, 84, 114)(76, 106, 85, 115)(78, 108, 87, 117)(81, 111, 88, 118)(82, 112, 89, 119)(86, 116, 90, 120) L = (1, 64)(2, 69)(3, 71)(4, 74)(5, 75)(6, 61)(7, 65)(8, 79)(9, 81)(10, 62)(11, 83)(12, 84)(13, 63)(14, 76)(15, 86)(16, 66)(17, 72)(18, 67)(19, 88)(20, 68)(21, 82)(22, 70)(23, 85)(24, 90)(25, 73)(26, 78)(27, 77)(28, 89)(29, 80)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E20.292 Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.298 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 15, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, Y1^-1 * Y3^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^5 * Y2 * Y1^2, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 17, 47, 25, 55, 22, 52, 14, 44, 6, 36, 3, 33, 9, 39, 18, 48, 26, 56, 21, 51, 13, 43, 5, 35)(4, 34, 10, 40, 19, 49, 27, 57, 30, 60, 24, 54, 16, 46, 12, 42, 11, 41, 20, 50, 28, 58, 29, 59, 23, 53, 15, 45, 7, 37)(61, 91, 63, 93, 62, 92, 69, 99, 68, 98, 78, 108, 77, 107, 86, 116, 85, 115, 81, 111, 82, 112, 73, 103, 74, 104, 65, 95, 66, 96)(64, 94, 71, 101, 70, 100, 80, 110, 79, 109, 88, 118, 87, 117, 89, 119, 90, 120, 83, 113, 84, 114, 75, 105, 76, 106, 67, 97, 72, 102) L = (1, 64)(2, 70)(3, 71)(4, 62)(5, 67)(6, 72)(7, 61)(8, 79)(9, 80)(10, 68)(11, 69)(12, 63)(13, 75)(14, 76)(15, 65)(16, 66)(17, 87)(18, 88)(19, 77)(20, 78)(21, 83)(22, 84)(23, 73)(24, 74)(25, 90)(26, 89)(27, 85)(28, 86)(29, 81)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.291 Graph:: bipartite v = 4 e = 60 f = 18 degree seq :: [ 30^4 ] E20.299 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 6, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, (R * Y2)^2, (Y2^-1, Y3^-1), (Y1, Y3), (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), Y2^5, Y1^-1 * Y2^2 * Y3^-2, Y1 * Y2^-2 * Y3^2, Y3^4 * Y2 * Y1^-1, Y3^4 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 14, 44)(4, 34, 9, 39, 17, 47)(6, 36, 10, 40, 19, 49)(7, 37, 11, 41, 20, 50)(12, 42, 24, 54, 16, 46)(13, 43, 25, 55, 30, 60)(15, 45, 26, 56, 18, 48)(21, 51, 23, 53, 28, 58)(22, 52, 27, 57, 29, 59)(61, 91, 63, 93, 72, 102, 81, 111, 66, 96)(62, 92, 68, 98, 84, 114, 83, 113, 70, 100)(64, 94, 73, 103, 89, 119, 80, 110, 78, 108)(65, 95, 74, 104, 76, 106, 88, 118, 79, 109)(67, 97, 75, 105, 69, 99, 85, 115, 82, 112)(71, 101, 86, 116, 77, 107, 90, 120, 87, 117) L = (1, 64)(2, 69)(3, 73)(4, 76)(5, 77)(6, 78)(7, 61)(8, 85)(9, 72)(10, 75)(11, 62)(12, 89)(13, 88)(14, 90)(15, 63)(16, 87)(17, 84)(18, 74)(19, 86)(20, 65)(21, 80)(22, 66)(23, 67)(24, 82)(25, 81)(26, 68)(27, 70)(28, 71)(29, 79)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 60, 12, 60, 12, 60 ), ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) } Outer automorphisms :: reflexible Dual of E20.302 Graph:: simple bipartite v = 16 e = 60 f = 6 degree seq :: [ 6^10, 10^6 ] E20.300 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 6, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y1^-1), Y2^-1 * Y3 * Y1 * Y2^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^-3 * Y1^2, Y1^5, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1 * Y2^4 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 17, 47, 5, 35)(3, 33, 9, 39, 22, 52, 30, 60, 14, 44)(4, 34, 10, 40, 23, 53, 21, 51, 16, 46)(6, 36, 11, 41, 24, 54, 28, 58, 18, 48)(7, 37, 12, 42, 15, 45, 26, 56, 19, 49)(13, 43, 25, 55, 20, 50, 27, 57, 29, 59)(61, 91, 63, 93, 70, 100, 85, 115, 79, 109, 66, 96)(62, 92, 69, 99, 83, 113, 80, 110, 67, 97, 71, 101)(64, 94, 73, 103, 86, 116, 78, 108, 65, 95, 74, 104)(68, 98, 82, 112, 81, 111, 87, 117, 72, 102, 84, 114)(75, 105, 88, 118, 77, 107, 90, 120, 76, 106, 89, 119) L = (1, 64)(2, 70)(3, 73)(4, 75)(5, 76)(6, 74)(7, 61)(8, 83)(9, 85)(10, 86)(11, 63)(12, 62)(13, 88)(14, 89)(15, 68)(16, 72)(17, 81)(18, 90)(19, 65)(20, 66)(21, 67)(22, 80)(23, 79)(24, 69)(25, 78)(26, 77)(27, 71)(28, 82)(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) :: { ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible Dual of E20.301 Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 10^6, 12^5 ] E20.301 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 6, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^3, (Y1, Y3^-1), (R * Y2)^2, (R * Y3)^2, (Y3, Y2), (Y2^-1, Y1^-1), (R * Y1)^2, Y3^-1 * Y1^4, Y3 * Y1 * Y2^-1 * Y3 * Y1, Y2^-1 * Y1^2 * Y3^2, Y3^-2 * Y2^-1 * Y1^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 17, 47, 4, 34, 10, 40, 15, 45, 26, 56, 16, 46, 14, 44, 3, 33, 9, 39, 24, 54, 30, 60, 13, 43, 25, 55, 22, 52, 27, 57, 29, 59, 20, 50, 6, 36, 11, 41, 23, 53, 28, 58, 18, 48, 21, 51, 7, 37, 12, 42, 19, 49, 5, 35)(61, 91, 63, 93, 66, 96)(62, 92, 69, 99, 71, 101)(64, 94, 73, 103, 78, 108)(65, 95, 74, 104, 80, 110)(67, 97, 75, 105, 82, 112)(68, 98, 84, 114, 83, 113)(70, 100, 85, 115, 81, 111)(72, 102, 86, 116, 87, 117)(76, 106, 89, 119, 79, 109)(77, 107, 90, 120, 88, 118) L = (1, 64)(2, 70)(3, 73)(4, 76)(5, 77)(6, 78)(7, 61)(8, 75)(9, 85)(10, 74)(11, 81)(12, 62)(13, 89)(14, 90)(15, 63)(16, 84)(17, 86)(18, 79)(19, 68)(20, 88)(21, 65)(22, 66)(23, 67)(24, 82)(25, 80)(26, 69)(27, 71)(28, 72)(29, 83)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E20.300 Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 6^10, 60 ] E20.302 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 6, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2^-1 * Y1, (R * Y1)^2, (Y2, Y1^-1), (R * Y2)^2, Y3 * Y1^2 * Y2^-1, (R * Y3)^2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^2 * Y2^2 * Y1 * Y3, (Y2 * Y3^-1)^3, Y3 * Y2^-3 * Y3^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y1^6, Y3^2 * Y1^-1 * Y3^3 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 17, 47, 5, 35)(3, 33, 9, 39, 23, 53, 16, 46, 4, 34, 10, 40)(6, 36, 11, 41, 7, 37, 12, 42, 24, 54, 18, 48)(13, 43, 25, 55, 15, 45, 27, 57, 14, 44, 26, 56)(19, 49, 28, 58, 20, 50, 29, 59, 21, 51, 30, 60)(61, 91, 63, 93, 73, 103, 90, 120, 78, 108, 65, 95, 70, 100, 86, 116, 81, 111, 84, 114, 77, 107, 64, 94, 74, 104, 89, 119, 72, 102, 82, 112, 76, 106, 87, 117, 80, 110, 67, 97, 68, 98, 83, 113, 75, 105, 88, 118, 71, 101, 62, 92, 69, 99, 85, 115, 79, 109, 66, 96) L = (1, 64)(2, 70)(3, 74)(4, 75)(5, 76)(6, 77)(7, 61)(8, 63)(9, 86)(10, 87)(11, 65)(12, 62)(13, 89)(14, 88)(15, 90)(16, 85)(17, 83)(18, 82)(19, 84)(20, 66)(21, 67)(22, 69)(23, 73)(24, 68)(25, 81)(26, 80)(27, 79)(28, 78)(29, 71)(30, 72)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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, 6, 10, 6, 10, 6, 10, 6, 10 ) } Outer automorphisms :: reflexible Dual of E20.299 Graph:: bipartite v = 6 e = 60 f = 16 degree seq :: [ 12^5, 60 ] E20.303 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 6, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^3, (Y2^-1, Y3), (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), (Y1^-1, Y3^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y2^-1 * Y3^-5, Y3^-5 * Y2^-1, (Y2^-1 * Y3)^5, Y3^2 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-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, 31, 2, 32, 5, 35)(3, 33, 6, 36, 9, 39)(4, 34, 8, 38, 14, 44)(7, 37, 10, 40, 16, 46)(11, 41, 15, 45, 20, 50)(12, 42, 17, 47, 21, 51)(13, 43, 19, 49, 26, 56)(18, 48, 22, 52, 28, 58)(23, 53, 27, 57, 30, 60)(24, 54, 25, 55, 29, 59)(61, 91, 63, 93, 65, 95, 69, 99, 62, 92, 66, 96)(64, 94, 71, 101, 74, 104, 80, 110, 68, 98, 75, 105)(67, 97, 72, 102, 76, 106, 81, 111, 70, 100, 77, 107)(73, 103, 83, 113, 86, 116, 90, 120, 79, 109, 87, 117)(78, 108, 84, 114, 88, 118, 89, 119, 82, 112, 85, 115) L = (1, 64)(2, 68)(3, 71)(4, 73)(5, 74)(6, 75)(7, 61)(8, 79)(9, 80)(10, 62)(11, 83)(12, 63)(13, 85)(14, 86)(15, 87)(16, 65)(17, 66)(18, 67)(19, 89)(20, 90)(21, 69)(22, 70)(23, 78)(24, 72)(25, 77)(26, 84)(27, 82)(28, 76)(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, 10, 60, 10, 60, 10, 60, 10, 60 ) } Outer automorphisms :: reflexible Dual of E20.304 Graph:: bipartite v = 15 e = 60 f = 7 degree seq :: [ 6^10, 12^5 ] E20.304 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 6, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y2^-2, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3, (R * Y2)^2, (Y1^-1, Y3), (Y2^-1, Y1), (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3^3, Y1^-1 * Y3 * Y2 * Y3 * Y2, Y1^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 5, 35)(3, 33, 9, 39, 22, 52, 27, 57, 15, 45)(4, 34, 10, 40, 23, 53, 21, 51, 13, 43)(6, 36, 11, 41, 24, 54, 28, 58, 16, 46)(7, 37, 12, 42, 17, 47, 26, 56, 19, 49)(14, 44, 25, 55, 30, 60, 29, 59, 20, 50)(61, 91, 63, 93, 73, 103, 80, 110, 67, 97, 76, 106, 65, 95, 75, 105, 81, 111, 89, 119, 79, 109, 88, 118, 78, 108, 87, 117, 83, 113, 90, 120, 86, 116, 84, 114, 68, 98, 82, 112, 70, 100, 85, 115, 77, 107, 71, 101, 62, 92, 69, 99, 64, 94, 74, 104, 72, 102, 66, 96) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 73)(6, 69)(7, 61)(8, 83)(9, 85)(10, 86)(11, 82)(12, 62)(13, 72)(14, 71)(15, 80)(16, 63)(17, 68)(18, 81)(19, 65)(20, 66)(21, 67)(22, 90)(23, 79)(24, 87)(25, 84)(26, 78)(27, 89)(28, 75)(29, 76)(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) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E20.303 Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 10^6, 60 ] E20.305 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^10 * Y1^-1, (Y3 * Y2^-1)^30 ] Map:: R = (1, 31, 2, 32, 4, 34)(3, 33, 6, 36, 9, 39)(5, 35, 7, 37, 10, 40)(8, 38, 12, 42, 15, 45)(11, 41, 13, 43, 16, 46)(14, 44, 18, 48, 21, 51)(17, 47, 19, 49, 22, 52)(20, 50, 24, 54, 27, 57)(23, 53, 25, 55, 28, 58)(26, 56, 30, 60, 29, 59)(61, 91, 63, 93, 68, 98, 74, 104, 80, 110, 86, 116, 85, 115, 79, 109, 73, 103, 67, 97, 62, 92, 66, 96, 72, 102, 78, 108, 84, 114, 90, 120, 88, 118, 82, 112, 76, 106, 70, 100, 64, 94, 69, 99, 75, 105, 81, 111, 87, 117, 89, 119, 83, 113, 77, 107, 71, 101, 65, 95) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 6^10, 60 ] E20.306 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^10 * Y1, (Y3 * Y2^-1)^30 ] Map:: R = (1, 31, 2, 32, 4, 34)(3, 33, 6, 36, 9, 39)(5, 35, 7, 37, 10, 40)(8, 38, 12, 42, 15, 45)(11, 41, 13, 43, 16, 46)(14, 44, 18, 48, 21, 51)(17, 47, 19, 49, 22, 52)(20, 50, 24, 54, 27, 57)(23, 53, 25, 55, 28, 58)(26, 56, 29, 59, 30, 60)(61, 91, 63, 93, 68, 98, 74, 104, 80, 110, 86, 116, 88, 118, 82, 112, 76, 106, 70, 100, 64, 94, 69, 99, 75, 105, 81, 111, 87, 117, 90, 120, 85, 115, 79, 109, 73, 103, 67, 97, 62, 92, 66, 96, 72, 102, 78, 108, 84, 114, 89, 119, 83, 113, 77, 107, 71, 101, 65, 95) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 6^10, 60 ] E20.307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^10 * Y1, (Y3 * Y2^-1)^30 ] Map:: non-degenerate R = (1, 31, 2, 32, 4, 34)(3, 33, 6, 36, 9, 39)(5, 35, 7, 37, 10, 40)(8, 38, 12, 42, 15, 45)(11, 41, 13, 43, 16, 46)(14, 44, 18, 48, 21, 51)(17, 47, 19, 49, 22, 52)(20, 50, 24, 54, 27, 57)(23, 53, 25, 55, 28, 58)(26, 56, 29, 59, 30, 60)(61, 91, 63, 93, 68, 98, 74, 104, 80, 110, 86, 116, 88, 118, 82, 112, 76, 106, 70, 100, 64, 94, 69, 99, 75, 105, 81, 111, 87, 117, 90, 120, 85, 115, 79, 109, 73, 103, 67, 97, 62, 92, 66, 96, 72, 102, 78, 108, 84, 114, 89, 119, 83, 113, 77, 107, 71, 101, 65, 95) L = (1, 62)(2, 64)(3, 66)(4, 61)(5, 67)(6, 69)(7, 70)(8, 72)(9, 63)(10, 65)(11, 73)(12, 75)(13, 76)(14, 78)(15, 68)(16, 71)(17, 79)(18, 81)(19, 82)(20, 84)(21, 74)(22, 77)(23, 85)(24, 87)(25, 88)(26, 89)(27, 80)(28, 83)(29, 90)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 11 e = 60 f = 11 degree seq :: [ 6^10, 60 ] E20.308 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, (Y1^-1, Y2^-1), (Y2, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, Y2^2 * Y1 * Y2^3, Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 4, 34, 9, 39, 7, 37, 5, 35)(3, 33, 8, 38, 12, 42, 20, 50, 14, 44, 13, 43)(6, 36, 10, 40, 15, 45, 21, 51, 18, 48, 16, 46)(11, 41, 19, 49, 24, 54, 29, 59, 26, 56, 25, 55)(17, 47, 22, 52, 27, 57, 30, 60, 28, 58, 23, 53)(61, 91, 63, 93, 71, 101, 83, 113, 76, 106, 65, 95, 73, 103, 85, 115, 88, 118, 78, 108, 67, 97, 74, 104, 86, 116, 90, 120, 81, 111, 69, 99, 80, 110, 89, 119, 87, 117, 75, 105, 64, 94, 72, 102, 84, 114, 82, 112, 70, 100, 62, 92, 68, 98, 79, 109, 77, 107, 66, 96) L = (1, 64)(2, 69)(3, 72)(4, 67)(5, 62)(6, 75)(7, 61)(8, 80)(9, 65)(10, 81)(11, 84)(12, 74)(13, 68)(14, 63)(15, 78)(16, 70)(17, 87)(18, 66)(19, 89)(20, 73)(21, 76)(22, 90)(23, 82)(24, 86)(25, 79)(26, 71)(27, 88)(28, 77)(29, 85)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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, 4, 60, 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E20.309 Graph:: bipartite v = 6 e = 60 f = 16 degree seq :: [ 12^5, 60 ] E20.309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 30, 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, Y1 * Y2 * Y1^-1 * Y2, (R * Y3)^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y1)^2, (Y3, Y1), (R * Y2)^2, Y3^6, Y1^-2 * Y2 * Y3^-1 * Y1^-3 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 17, 47, 25, 55, 13, 43, 22, 52, 30, 60, 26, 56, 14, 44, 4, 34, 9, 39, 19, 49, 24, 54, 12, 42, 3, 33, 8, 38, 18, 48, 28, 58, 16, 46, 6, 36, 10, 40, 20, 50, 29, 59, 23, 53, 11, 41, 21, 51, 27, 57, 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, 88, 118)(79, 109, 87, 117)(80, 110, 90, 120)(86, 116, 89, 119) L = (1, 64)(2, 69)(3, 71)(4, 66)(5, 74)(6, 61)(7, 79)(8, 81)(9, 70)(10, 62)(11, 73)(12, 83)(13, 63)(14, 76)(15, 86)(16, 65)(17, 84)(18, 87)(19, 80)(20, 67)(21, 82)(22, 68)(23, 85)(24, 89)(25, 72)(26, 88)(27, 90)(28, 75)(29, 77)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 60, 12, 60 ), ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) } Outer automorphisms :: reflexible Dual of E20.308 Graph:: bipartite v = 16 e = 60 f = 6 degree seq :: [ 4^15, 60 ] E20.310 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = QD64 (small group id <64, 53>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-2 * Y2^-1, Y3^4, Y3^-1 * Y2^-1 * Y3 * Y2^-1, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y2^-1, Y3^-2 * Y2^2, Y1 * Y3^2 * Y1, (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * 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, 33, 4, 36, 8, 40, 7, 39)(2, 34, 10, 42, 5, 37, 12, 44)(3, 35, 14, 46, 6, 38, 16, 48)(9, 41, 18, 50, 11, 43, 20, 52)(13, 45, 22, 54, 15, 47, 24, 56)(17, 49, 26, 58, 19, 51, 28, 60)(21, 53, 30, 62, 23, 55, 32, 64)(25, 57, 29, 61, 27, 59, 31, 63)(65, 66, 72, 69)(67, 77, 70, 79)(68, 76, 71, 74)(73, 81, 75, 83)(78, 88, 80, 86)(82, 92, 84, 90)(85, 93, 87, 95)(89, 96, 91, 94)(97, 99, 104, 102)(98, 105, 101, 107)(100, 112, 103, 110)(106, 116, 108, 114)(109, 117, 111, 119)(113, 121, 115, 123)(118, 128, 120, 126)(122, 127, 124, 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) :: { ( 64^4 ), ( 64^8 ) } Outer automorphisms :: reflexible Dual of E20.313 Graph:: bipartite v = 24 e = 64 f = 2 degree seq :: [ 4^16, 8^8 ] E20.311 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = QD64 (small group id <64, 53>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y1, Y2^4, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3, Y2^2 * Y1^2, (R * Y3)^2, Y2 * Y1^-2 * Y2, R * Y1 * R * Y2, Y3^-1 * Y1 * Y2^-1 * Y3^-2, Y2^-1 * Y3^-1 * Y1 * Y3^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^2, Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 17, 49, 11, 43, 29, 61, 13, 45, 31, 63, 24, 56, 8, 40, 23, 55, 28, 60, 9, 41, 26, 58, 15, 47, 22, 54, 7, 39)(2, 34, 10, 42, 16, 48, 3, 35, 14, 46, 25, 57, 32, 64, 18, 50, 5, 37, 20, 52, 19, 51, 6, 38, 21, 53, 27, 59, 30, 62, 12, 44)(65, 66, 72, 69)(67, 77, 70, 79)(68, 76, 87, 82)(71, 74, 88, 84)(73, 89, 75, 91)(78, 93, 85, 90)(80, 95, 83, 86)(81, 94, 92, 96)(97, 99, 104, 102)(98, 105, 101, 107)(100, 112, 119, 115)(103, 110, 120, 117)(106, 124, 116, 113)(108, 122, 114, 125)(109, 126, 111, 128)(118, 121, 127, 123) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^4 ), ( 16^32 ) } Outer automorphisms :: reflexible Dual of E20.312 Graph:: bipartite v = 18 e = 64 f = 8 degree seq :: [ 4^16, 32^2 ] E20.312 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = QD64 (small group id <64, 53>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-2 * Y2^-1, Y3^4, Y3^-1 * Y2^-1 * Y3 * Y2^-1, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y2^-1, Y3^-2 * Y2^2, Y1 * Y3^2 * Y1, (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * 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, 33, 65, 97, 4, 36, 68, 100, 8, 40, 72, 104, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 5, 37, 69, 101, 12, 44, 76, 108)(3, 35, 67, 99, 14, 46, 78, 110, 6, 38, 70, 102, 16, 48, 80, 112)(9, 41, 73, 105, 18, 50, 82, 114, 11, 43, 75, 107, 20, 52, 84, 116)(13, 45, 77, 109, 22, 54, 86, 118, 15, 47, 79, 111, 24, 56, 88, 120)(17, 49, 81, 113, 26, 58, 90, 122, 19, 51, 83, 115, 28, 60, 92, 124)(21, 53, 85, 117, 30, 62, 94, 126, 23, 55, 87, 119, 32, 64, 96, 128)(25, 57, 89, 121, 29, 61, 93, 125, 27, 59, 91, 123, 31, 63, 95, 127) L = (1, 34)(2, 40)(3, 45)(4, 44)(5, 33)(6, 47)(7, 42)(8, 37)(9, 49)(10, 36)(11, 51)(12, 39)(13, 38)(14, 56)(15, 35)(16, 54)(17, 43)(18, 60)(19, 41)(20, 58)(21, 61)(22, 46)(23, 63)(24, 48)(25, 64)(26, 50)(27, 62)(28, 52)(29, 55)(30, 57)(31, 53)(32, 59)(65, 99)(66, 105)(67, 104)(68, 112)(69, 107)(70, 97)(71, 110)(72, 102)(73, 101)(74, 116)(75, 98)(76, 114)(77, 117)(78, 100)(79, 119)(80, 103)(81, 121)(82, 106)(83, 123)(84, 108)(85, 111)(86, 128)(87, 109)(88, 126)(89, 115)(90, 127)(91, 113)(92, 125)(93, 122)(94, 118)(95, 124)(96, 120) local type(s) :: { ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E20.311 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 18 degree seq :: [ 16^8 ] E20.313 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = QD64 (small group id <64, 53>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y1, Y2^4, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3, Y2^2 * Y1^2, (R * Y3)^2, Y2 * Y1^-2 * Y2, R * Y1 * R * Y2, Y3^-1 * Y1 * Y2^-1 * Y3^-2, Y2^-1 * Y3^-1 * Y1 * Y3^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^2, Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 17, 49, 81, 113, 11, 43, 75, 107, 29, 61, 93, 125, 13, 45, 77, 109, 31, 63, 95, 127, 24, 56, 88, 120, 8, 40, 72, 104, 23, 55, 87, 119, 28, 60, 92, 124, 9, 41, 73, 105, 26, 58, 90, 122, 15, 47, 79, 111, 22, 54, 86, 118, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 16, 48, 80, 112, 3, 35, 67, 99, 14, 46, 78, 110, 25, 57, 89, 121, 32, 64, 96, 128, 18, 50, 82, 114, 5, 37, 69, 101, 20, 52, 84, 116, 19, 51, 83, 115, 6, 38, 70, 102, 21, 53, 85, 117, 27, 59, 91, 123, 30, 62, 94, 126, 12, 44, 76, 108) L = (1, 34)(2, 40)(3, 45)(4, 44)(5, 33)(6, 47)(7, 42)(8, 37)(9, 57)(10, 56)(11, 59)(12, 55)(13, 38)(14, 61)(15, 35)(16, 63)(17, 62)(18, 36)(19, 54)(20, 39)(21, 58)(22, 48)(23, 50)(24, 52)(25, 43)(26, 46)(27, 41)(28, 64)(29, 53)(30, 60)(31, 51)(32, 49)(65, 99)(66, 105)(67, 104)(68, 112)(69, 107)(70, 97)(71, 110)(72, 102)(73, 101)(74, 124)(75, 98)(76, 122)(77, 126)(78, 120)(79, 128)(80, 119)(81, 106)(82, 125)(83, 100)(84, 113)(85, 103)(86, 121)(87, 115)(88, 117)(89, 127)(90, 114)(91, 118)(92, 116)(93, 108)(94, 111)(95, 123)(96, 109) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.310 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 24 degree seq :: [ 64^2 ] E20.314 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^4, Y1^4, (R * Y1)^2, Y3^-2 * Y2^-2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, R * Y2 * R * Y2^-1, Y3^-1 * Y1^2 * Y3^-1, Y2^4, Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y2^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, (Y3^-1 * Y1^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 6, 38, 9, 41)(4, 36, 15, 47, 7, 39, 16, 48)(10, 42, 19, 51, 12, 44, 20, 52)(13, 45, 21, 53, 14, 46, 22, 54)(17, 49, 25, 57, 18, 50, 26, 58)(23, 55, 31, 63, 24, 56, 32, 64)(27, 59, 30, 62, 28, 60, 29, 61)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 78, 110, 71, 103, 77, 109)(74, 106, 82, 114, 76, 108, 81, 113)(79, 111, 85, 117, 80, 112, 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, 74)(3, 77)(4, 72)(5, 76)(6, 78)(7, 65)(8, 71)(9, 81)(10, 69)(11, 82)(12, 66)(13, 70)(14, 67)(15, 87)(16, 88)(17, 75)(18, 73)(19, 91)(20, 92)(21, 93)(22, 94)(23, 80)(24, 79)(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, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E20.317 Graph:: bipartite v = 16 e = 64 f = 10 degree seq :: [ 8^16 ] E20.315 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, Y3^-2 * Y1^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-2 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, R * Y2 * R * Y2^-1, (R * Y1)^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3^-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, 7, 39, 16, 48)(10, 42, 19, 51, 12, 44, 20, 52)(13, 45, 21, 53, 14, 46, 22, 54)(17, 49, 25, 57, 18, 50, 26, 58)(23, 55, 31, 63, 24, 56, 32, 64)(27, 59, 29, 61, 28, 60, 30, 62)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 78, 110, 71, 103, 77, 109)(74, 106, 82, 114, 76, 108, 81, 113)(79, 111, 85, 117, 80, 112, 86, 118)(83, 115, 89, 121, 84, 116, 90, 122)(87, 119, 94, 126, 88, 120, 93, 125)(91, 123, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 72)(5, 76)(6, 78)(7, 65)(8, 71)(9, 81)(10, 69)(11, 82)(12, 66)(13, 70)(14, 67)(15, 87)(16, 88)(17, 75)(18, 73)(19, 91)(20, 92)(21, 93)(22, 94)(23, 80)(24, 79)(25, 96)(26, 95)(27, 84)(28, 83)(29, 86)(30, 85)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E20.316 Graph:: bipartite v = 16 e = 64 f = 10 degree seq :: [ 8^16 ] E20.316 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y3^4, Y3^2 * Y2^-2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3 * Y2 * Y3^-1, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, R * Y2 * R * Y2^-1, (R * Y3)^2, Y1^-1 * Y3 * Y1^2 * Y2^-1 * Y1^-1, Y1^-1 * Y2 * Y1 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 21, 53, 15, 47, 27, 59, 32, 64, 29, 61, 14, 46, 26, 58, 31, 63, 30, 62, 16, 48, 28, 60, 18, 50, 5, 37)(3, 35, 13, 45, 25, 57, 12, 44, 7, 39, 20, 52, 24, 56, 11, 43, 6, 38, 19, 51, 23, 55, 10, 42, 4, 36, 17, 49, 22, 54, 9, 41)(65, 97, 67, 99, 78, 110, 70, 102)(66, 98, 73, 105, 90, 122, 75, 107)(68, 100, 80, 112, 71, 103, 79, 111)(69, 101, 77, 109, 93, 125, 83, 115)(72, 104, 86, 118, 95, 127, 88, 120)(74, 106, 92, 124, 76, 108, 91, 123)(81, 113, 94, 126, 84, 116, 85, 117)(82, 114, 89, 121, 96, 128, 87, 119) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 81)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 85)(14, 71)(15, 70)(16, 67)(17, 93)(18, 86)(19, 94)(20, 69)(21, 83)(22, 96)(23, 95)(24, 82)(25, 72)(26, 76)(27, 75)(28, 73)(29, 84)(30, 77)(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) :: { ( 8^8 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E20.315 Graph:: bipartite v = 10 e = 64 f = 16 degree seq :: [ 8^8, 32^2 ] E20.317 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y2^2 * Y3^-2, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y3, Y3 * Y2^2 * Y3, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1 * Y3^-1 * Y1^-2, Y1^-1 * Y3^-1 * Y1^2 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 21, 53, 16, 48, 28, 60, 32, 64, 29, 61, 14, 46, 26, 58, 31, 63, 30, 62, 15, 47, 27, 59, 18, 50, 5, 37)(3, 35, 13, 45, 23, 55, 10, 42, 4, 36, 17, 49, 24, 56, 11, 43, 6, 38, 19, 51, 25, 57, 12, 44, 7, 39, 20, 52, 22, 54, 9, 41)(65, 97, 67, 99, 78, 110, 70, 102)(66, 98, 73, 105, 90, 122, 75, 107)(68, 100, 80, 112, 71, 103, 79, 111)(69, 101, 77, 109, 93, 125, 83, 115)(72, 104, 86, 118, 95, 127, 88, 120)(74, 106, 92, 124, 76, 108, 91, 123)(81, 113, 85, 117, 84, 116, 94, 126)(82, 114, 87, 119, 96, 128, 89, 121) L = (1, 68)(2, 74)(3, 79)(4, 78)(5, 81)(6, 80)(7, 65)(8, 87)(9, 91)(10, 90)(11, 92)(12, 66)(13, 94)(14, 71)(15, 70)(16, 67)(17, 93)(18, 88)(19, 85)(20, 69)(21, 77)(22, 82)(23, 95)(24, 96)(25, 72)(26, 76)(27, 75)(28, 73)(29, 84)(30, 83)(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) :: { ( 8^8 ), ( 8^32 ) } Outer automorphisms :: reflexible Dual of E20.314 Graph:: bipartite v = 10 e = 64 f = 16 degree seq :: [ 8^8, 32^2 ] E20.318 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), (R * Y1)^2, Y3^2 * Y2^-2 * Y3^-2 * Y1, Y3^-7 * Y2^-1 * Y3^-1, (Y2^-1 * Y3)^32 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 7, 39)(6, 38, 8, 40)(9, 41, 12, 44)(10, 42, 13, 45)(11, 43, 15, 47)(14, 46, 16, 48)(17, 49, 20, 52)(18, 50, 21, 53)(19, 51, 23, 55)(22, 54, 24, 56)(25, 57, 28, 60)(26, 58, 29, 61)(27, 59, 31, 63)(30, 62, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 73, 105, 71, 103, 76, 108)(70, 102, 74, 106, 72, 104, 77, 109)(75, 107, 81, 113, 79, 111, 84, 116)(78, 110, 82, 114, 80, 112, 85, 117)(83, 115, 89, 121, 87, 119, 92, 124)(86, 118, 90, 122, 88, 120, 93, 125)(91, 123, 94, 126, 95, 127, 96, 128) L = (1, 68)(2, 71)(3, 73)(4, 75)(5, 76)(6, 65)(7, 79)(8, 66)(9, 81)(10, 67)(11, 83)(12, 84)(13, 69)(14, 70)(15, 87)(16, 72)(17, 89)(18, 74)(19, 91)(20, 92)(21, 77)(22, 78)(23, 95)(24, 80)(25, 94)(26, 82)(27, 93)(28, 96)(29, 85)(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) :: { ( 64^4 ), ( 64^8 ) } Outer automorphisms :: reflexible Dual of E20.323 Graph:: bipartite v = 24 e = 64 f = 2 degree seq :: [ 4^16, 8^8 ] E20.319 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y2, Y1^-1), Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^8 * Y1, (Y3 * Y2^-1)^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 7, 39, 13, 45, 10, 42)(5, 37, 8, 40, 14, 46, 11, 43)(9, 41, 15, 47, 21, 53, 18, 50)(12, 44, 16, 48, 22, 54, 19, 51)(17, 49, 23, 55, 29, 61, 26, 58)(20, 52, 24, 56, 30, 62, 27, 59)(25, 57, 28, 60, 31, 63, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 96, 128, 94, 126, 86, 118, 78, 110, 70, 102, 77, 109, 85, 117, 93, 125, 95, 127, 88, 120, 80, 112, 72, 104, 66, 98, 71, 103, 79, 111, 87, 119, 92, 124, 84, 116, 76, 108, 69, 101) L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 68)(7, 77)(8, 78)(9, 79)(10, 67)(11, 69)(12, 80)(13, 74)(14, 75)(15, 85)(16, 86)(17, 87)(18, 73)(19, 76)(20, 88)(21, 82)(22, 83)(23, 93)(24, 94)(25, 92)(26, 81)(27, 84)(28, 95)(29, 90)(30, 91)(31, 96)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 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 E20.321 Graph:: bipartite v = 9 e = 64 f = 17 degree seq :: [ 8^8, 64 ] E20.320 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1^4, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^8 * Y1^-1, (Y3 * Y2^-1)^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 7, 39, 13, 45, 10, 42)(5, 37, 8, 40, 14, 46, 11, 43)(9, 41, 15, 47, 21, 53, 18, 50)(12, 44, 16, 48, 22, 54, 19, 51)(17, 49, 23, 55, 29, 61, 26, 58)(20, 52, 24, 56, 30, 62, 27, 59)(25, 57, 31, 63, 32, 64, 28, 60)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 88, 120, 80, 112, 72, 104, 66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 94, 126, 86, 118, 78, 110, 70, 102, 77, 109, 85, 117, 93, 125, 96, 128, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 92, 124, 84, 116, 76, 108, 69, 101) L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 68)(7, 77)(8, 78)(9, 79)(10, 67)(11, 69)(12, 80)(13, 74)(14, 75)(15, 85)(16, 86)(17, 87)(18, 73)(19, 76)(20, 88)(21, 82)(22, 83)(23, 93)(24, 94)(25, 95)(26, 81)(27, 84)(28, 89)(29, 90)(30, 91)(31, 96)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E20.322 Graph:: bipartite v = 9 e = 64 f = 17 degree seq :: [ 8^8, 64 ] E20.321 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^-1 * Y2 * Y1, Y1^-4 * Y3^-1 * Y1^-4, Y1^2 * Y3 * Y1^6, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 15, 47, 23, 55, 30, 62, 22, 54, 14, 46, 6, 38, 10, 42, 18, 50, 26, 58, 32, 64, 27, 59, 19, 51, 11, 43, 3, 35, 8, 40, 16, 48, 24, 56, 31, 63, 28, 60, 20, 52, 12, 44, 4, 36, 9, 41, 17, 49, 25, 57, 29, 61, 21, 53, 13, 45, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 70, 102)(69, 101, 75, 107)(71, 103, 80, 112)(73, 105, 74, 106)(76, 108, 78, 110)(77, 109, 83, 115)(79, 111, 88, 120)(81, 113, 82, 114)(84, 116, 86, 118)(85, 117, 91, 123)(87, 119, 95, 127)(89, 121, 90, 122)(92, 124, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 73)(3, 70)(4, 67)(5, 76)(6, 65)(7, 81)(8, 74)(9, 72)(10, 66)(11, 78)(12, 75)(13, 84)(14, 69)(15, 89)(16, 82)(17, 80)(18, 71)(19, 86)(20, 83)(21, 92)(22, 77)(23, 93)(24, 90)(25, 88)(26, 79)(27, 94)(28, 91)(29, 95)(30, 85)(31, 96)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) } Outer automorphisms :: reflexible Dual of E20.319 Graph:: bipartite v = 17 e = 64 f = 9 degree seq :: [ 4^16, 64 ] E20.322 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, (Y1, Y3), (R * Y3)^2, Y1^-4 * Y3 * Y1^-4, Y1^-3 * 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 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 15, 47, 23, 55, 28, 60, 20, 52, 12, 44, 4, 36, 9, 41, 17, 49, 25, 57, 32, 64, 27, 59, 19, 51, 11, 43, 3, 35, 8, 40, 16, 48, 24, 56, 31, 63, 30, 62, 22, 54, 14, 46, 6, 38, 10, 42, 18, 50, 26, 58, 29, 61, 21, 53, 13, 45, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 70, 102)(69, 101, 75, 107)(71, 103, 80, 112)(73, 105, 74, 106)(76, 108, 78, 110)(77, 109, 83, 115)(79, 111, 88, 120)(81, 113, 82, 114)(84, 116, 86, 118)(85, 117, 91, 123)(87, 119, 95, 127)(89, 121, 90, 122)(92, 124, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 73)(3, 70)(4, 67)(5, 76)(6, 65)(7, 81)(8, 74)(9, 72)(10, 66)(11, 78)(12, 75)(13, 84)(14, 69)(15, 89)(16, 82)(17, 80)(18, 71)(19, 86)(20, 83)(21, 92)(22, 77)(23, 96)(24, 90)(25, 88)(26, 79)(27, 94)(28, 91)(29, 87)(30, 85)(31, 93)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) } Outer automorphisms :: reflexible Dual of E20.320 Graph:: bipartite v = 17 e = 64 f = 9 degree seq :: [ 4^16, 64 ] E20.323 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, Y1^-2 * Y2^-1 * Y3^-1, (Y3^-1, Y2^-1), Y3 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2^2 * Y1 * Y3^-2, Y3^2 * Y2^2 * Y3 * Y1^-3, Y1^23 * Y2^-1, Y1 * Y2^25 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 29, 61, 25, 57, 17, 49, 4, 36, 10, 42, 6, 38, 11, 43, 20, 52, 30, 62, 27, 59, 13, 45, 22, 54, 16, 48, 23, 55, 18, 50, 24, 56, 32, 64, 26, 58, 15, 47, 3, 35, 9, 41, 7, 39, 12, 44, 21, 53, 31, 63, 28, 60, 14, 46, 5, 37)(65, 97, 67, 99, 77, 109, 89, 121, 95, 127, 88, 120, 75, 107, 66, 98, 73, 105, 86, 118, 81, 113, 92, 124, 96, 128, 84, 116, 72, 104, 71, 103, 80, 112, 68, 100, 78, 110, 90, 122, 94, 126, 83, 115, 76, 108, 87, 119, 74, 106, 69, 101, 79, 111, 91, 123, 93, 125, 85, 117, 82, 114, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 81)(6, 80)(7, 65)(8, 70)(9, 69)(10, 86)(11, 87)(12, 66)(13, 90)(14, 89)(15, 92)(16, 67)(17, 91)(18, 71)(19, 75)(20, 82)(21, 72)(22, 79)(23, 73)(24, 76)(25, 94)(26, 95)(27, 96)(28, 93)(29, 84)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E20.318 Graph:: bipartite v = 2 e = 64 f = 24 degree seq :: [ 64^2 ] E20.324 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 11, 11}) Quotient :: dipole Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^11, (Y3 * Y2^-1)^11 ] Map:: R = (1, 34, 2, 35, 4, 37)(3, 36, 6, 39, 9, 42)(5, 38, 7, 40, 10, 43)(8, 41, 12, 45, 15, 48)(11, 44, 13, 46, 16, 49)(14, 47, 18, 51, 21, 54)(17, 50, 19, 52, 22, 55)(20, 53, 24, 57, 27, 60)(23, 56, 25, 58, 28, 61)(26, 59, 30, 63, 32, 65)(29, 62, 31, 64, 33, 66)(67, 100, 69, 102, 74, 107, 80, 113, 86, 119, 92, 125, 95, 128, 89, 122, 83, 116, 77, 110, 71, 104)(68, 101, 72, 105, 78, 111, 84, 117, 90, 123, 96, 129, 97, 130, 91, 124, 85, 118, 79, 112, 73, 106)(70, 103, 75, 108, 81, 114, 87, 120, 93, 126, 98, 131, 99, 132, 94, 127, 88, 121, 82, 115, 76, 109) 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) :: { ( 6, 22, 6, 22, 6, 22 ), ( 6, 22, 6, 22, 6, 22, 6, 22, 6, 22, 6, 22, 6, 22, 6, 22, 6, 22, 6, 22, 6, 22 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 14 e = 66 f = 14 degree seq :: [ 6^11, 22^3 ] E20.325 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 4, 9}) Quotient :: edge^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = C4 x D18 (small group id <72, 5>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2^-2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, Y1 * Y2^2 * Y1, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y1^-1 * Y3^-4 * Y2^-1, (Y3 * Y1^-1 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 37, 4, 40, 17, 53, 29, 65, 13, 49, 9, 45, 25, 61, 22, 58, 7, 43)(2, 38, 10, 46, 26, 62, 33, 69, 19, 55, 6, 42, 21, 57, 28, 64, 12, 48)(3, 39, 14, 50, 30, 66, 18, 54, 5, 41, 20, 56, 34, 70, 32, 68, 16, 52)(8, 44, 23, 59, 35, 71, 31, 67, 15, 51, 11, 47, 27, 63, 36, 72, 24, 60)(73, 74, 80, 77)(75, 85, 78, 87)(76, 84, 95, 90)(79, 82, 96, 92)(81, 91, 83, 88)(86, 101, 93, 103)(89, 100, 107, 102)(94, 98, 108, 106)(97, 105, 99, 104)(109, 111, 116, 114)(110, 117, 113, 119)(112, 124, 131, 127)(115, 122, 132, 129)(118, 121, 128, 123)(120, 133, 126, 135)(125, 140, 143, 141)(130, 138, 144, 136)(134, 137, 142, 139) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 12^4 ), ( 12^18 ) } Outer automorphisms :: reflexible Dual of E20.328 Graph:: simple bipartite v = 22 e = 72 f = 12 degree seq :: [ 4^18, 18^4 ] E20.326 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 4, 4, 9}) Quotient :: edge^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = C4 x D18 (small group id <72, 5>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^4, Y2^2 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^2 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3, 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^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 4, 40, 7, 43)(2, 38, 10, 46, 12, 48)(3, 39, 14, 50, 16, 52)(5, 41, 19, 55, 17, 53)(6, 42, 20, 56, 18, 54)(8, 44, 21, 57, 22, 58)(9, 45, 24, 60, 26, 62)(11, 47, 28, 64, 27, 63)(13, 49, 30, 66, 32, 68)(15, 51, 34, 70, 33, 69)(23, 59, 35, 71, 31, 67)(25, 61, 36, 72, 29, 65)(73, 74, 80, 77)(75, 85, 78, 87)(76, 84, 93, 89)(79, 82, 94, 91)(81, 95, 83, 97)(86, 104, 92, 105)(88, 102, 90, 106)(96, 103, 100, 101)(98, 107, 99, 108)(109, 111, 116, 114)(110, 117, 113, 119)(112, 124, 129, 126)(115, 122, 130, 128)(118, 134, 127, 135)(120, 132, 125, 136)(121, 137, 123, 139)(131, 140, 133, 141)(138, 144, 142, 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) :: { ( 36^4 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E20.327 Graph:: simple bipartite v = 30 e = 72 f = 4 degree seq :: [ 4^18, 6^12 ] E20.327 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 4, 9}) Quotient :: loop^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = C4 x D18 (small group id <72, 5>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2^-2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, R * Y1 * R * Y2, Y1 * Y2^2 * Y1, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y1^-1 * Y3^-4 * Y2^-1, (Y3 * Y1^-1 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 17, 53, 89, 125, 29, 65, 101, 137, 13, 49, 85, 121, 9, 45, 81, 117, 25, 61, 97, 133, 22, 58, 94, 130, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 26, 62, 98, 134, 33, 69, 105, 141, 19, 55, 91, 127, 6, 42, 78, 114, 21, 57, 93, 129, 28, 64, 100, 136, 12, 48, 84, 120)(3, 39, 75, 111, 14, 50, 86, 122, 30, 66, 102, 138, 18, 54, 90, 126, 5, 41, 77, 113, 20, 56, 92, 128, 34, 70, 106, 142, 32, 68, 104, 140, 16, 52, 88, 124)(8, 44, 80, 116, 23, 59, 95, 131, 35, 71, 107, 143, 31, 67, 103, 139, 15, 51, 87, 123, 11, 47, 83, 119, 27, 63, 99, 135, 36, 72, 108, 144, 24, 60, 96, 132) L = (1, 38)(2, 44)(3, 49)(4, 48)(5, 37)(6, 51)(7, 46)(8, 41)(9, 55)(10, 60)(11, 52)(12, 59)(13, 42)(14, 65)(15, 39)(16, 45)(17, 64)(18, 40)(19, 47)(20, 43)(21, 67)(22, 62)(23, 54)(24, 56)(25, 69)(26, 72)(27, 68)(28, 71)(29, 57)(30, 53)(31, 50)(32, 61)(33, 63)(34, 58)(35, 66)(36, 70)(73, 111)(74, 117)(75, 116)(76, 124)(77, 119)(78, 109)(79, 122)(80, 114)(81, 113)(82, 121)(83, 110)(84, 133)(85, 128)(86, 132)(87, 118)(88, 131)(89, 140)(90, 135)(91, 112)(92, 123)(93, 115)(94, 138)(95, 127)(96, 129)(97, 126)(98, 137)(99, 120)(100, 130)(101, 142)(102, 144)(103, 134)(104, 143)(105, 125)(106, 139)(107, 141)(108, 136) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E20.326 Transitivity :: VT+ Graph:: bipartite v = 4 e = 72 f = 30 degree seq :: [ 36^4 ] E20.328 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 4, 4, 9}) Quotient :: loop^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = C4 x D18 (small group id <72, 5>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^4, Y2^2 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^2 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3, 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^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 12, 48, 84, 120)(3, 39, 75, 111, 14, 50, 86, 122, 16, 52, 88, 124)(5, 41, 77, 113, 19, 55, 91, 127, 17, 53, 89, 125)(6, 42, 78, 114, 20, 56, 92, 128, 18, 54, 90, 126)(8, 44, 80, 116, 21, 57, 93, 129, 22, 58, 94, 130)(9, 45, 81, 117, 24, 60, 96, 132, 26, 62, 98, 134)(11, 47, 83, 119, 28, 64, 100, 136, 27, 63, 99, 135)(13, 49, 85, 121, 30, 66, 102, 138, 32, 68, 104, 140)(15, 51, 87, 123, 34, 70, 106, 142, 33, 69, 105, 141)(23, 59, 95, 131, 35, 71, 107, 143, 31, 67, 103, 139)(25, 61, 97, 133, 36, 72, 108, 144, 29, 65, 101, 137) L = (1, 38)(2, 44)(3, 49)(4, 48)(5, 37)(6, 51)(7, 46)(8, 41)(9, 59)(10, 58)(11, 61)(12, 57)(13, 42)(14, 68)(15, 39)(16, 66)(17, 40)(18, 70)(19, 43)(20, 69)(21, 53)(22, 55)(23, 47)(24, 67)(25, 45)(26, 71)(27, 72)(28, 65)(29, 60)(30, 54)(31, 64)(32, 56)(33, 50)(34, 52)(35, 63)(36, 62)(73, 111)(74, 117)(75, 116)(76, 124)(77, 119)(78, 109)(79, 122)(80, 114)(81, 113)(82, 134)(83, 110)(84, 132)(85, 137)(86, 130)(87, 139)(88, 129)(89, 136)(90, 112)(91, 135)(92, 115)(93, 126)(94, 128)(95, 140)(96, 125)(97, 141)(98, 127)(99, 118)(100, 120)(101, 123)(102, 144)(103, 121)(104, 133)(105, 131)(106, 143)(107, 138)(108, 142) local type(s) :: { ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E20.325 Transitivity :: VT+ Graph:: bipartite v = 12 e = 72 f = 22 degree seq :: [ 12^12 ] E20.329 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1^-1 * Y3^3, (R * Y3)^2, (Y1^-1, Y3), (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 8, 44)(4, 40, 9, 45, 16, 52)(6, 42, 18, 54, 10, 46)(7, 43, 11, 47, 19, 55)(13, 49, 21, 57, 26, 62)(14, 50, 27, 63, 22, 58)(15, 51, 28, 64, 23, 59)(17, 53, 31, 67, 24, 60)(20, 56, 32, 68, 25, 61)(29, 65, 33, 69, 35, 71)(30, 66, 34, 70, 36, 72)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 80, 116, 93, 129, 82, 118)(76, 112, 87, 123, 101, 137, 89, 125)(77, 113, 84, 120, 98, 134, 90, 126)(79, 115, 86, 122, 102, 138, 92, 128)(81, 117, 95, 131, 105, 141, 96, 132)(83, 119, 94, 130, 106, 142, 97, 133)(88, 124, 100, 136, 107, 143, 103, 139)(91, 127, 99, 135, 108, 144, 104, 140) L = (1, 76)(2, 81)(3, 86)(4, 83)(5, 88)(6, 92)(7, 73)(8, 94)(9, 91)(10, 97)(11, 74)(12, 99)(13, 101)(14, 100)(15, 75)(16, 79)(17, 78)(18, 104)(19, 77)(20, 103)(21, 105)(22, 87)(23, 80)(24, 82)(25, 89)(26, 107)(27, 95)(28, 84)(29, 106)(30, 85)(31, 90)(32, 96)(33, 108)(34, 93)(35, 102)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8, 18, 8, 18, 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18 ) } Outer automorphisms :: reflexible Dual of E20.331 Graph:: simple bipartite v = 21 e = 72 f = 13 degree seq :: [ 6^12, 8^9 ] E20.330 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1^-1 * Y3^-3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^4, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 12, 48, 8, 44)(4, 40, 9, 45, 17, 53)(6, 42, 19, 55, 10, 46)(7, 43, 11, 47, 16, 52)(13, 49, 21, 57, 26, 62)(14, 50, 27, 63, 22, 58)(15, 51, 28, 64, 23, 59)(18, 54, 32, 68, 24, 60)(20, 56, 31, 67, 25, 61)(29, 65, 33, 69, 35, 71)(30, 66, 34, 70, 36, 72)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 80, 116, 93, 129, 82, 118)(76, 112, 87, 123, 101, 137, 90, 126)(77, 113, 84, 120, 98, 134, 91, 127)(79, 115, 86, 122, 102, 138, 92, 128)(81, 117, 95, 131, 105, 141, 96, 132)(83, 119, 94, 130, 106, 142, 97, 133)(88, 124, 99, 135, 108, 144, 103, 139)(89, 125, 100, 136, 107, 143, 104, 140) L = (1, 76)(2, 81)(3, 86)(4, 88)(5, 89)(6, 92)(7, 73)(8, 94)(9, 79)(10, 97)(11, 74)(12, 99)(13, 101)(14, 95)(15, 75)(16, 77)(17, 83)(18, 78)(19, 103)(20, 96)(21, 105)(22, 100)(23, 80)(24, 82)(25, 104)(26, 107)(27, 87)(28, 84)(29, 108)(30, 85)(31, 90)(32, 91)(33, 102)(34, 93)(35, 106)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8, 18, 8, 18, 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18 ) } Outer automorphisms :: reflexible Dual of E20.332 Graph:: simple bipartite v = 21 e = 72 f = 13 degree seq :: [ 6^12, 8^9 ] E20.331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y2 * Y1^-1 * Y2 * Y1, Y3 * Y1^-1 * Y3 * Y1, (R * Y2)^2, Y1^4, (R * Y1)^2, Y2 * Y3^-4 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 11, 47, 21, 57, 13, 49)(4, 40, 12, 48, 22, 58, 16, 52)(6, 42, 9, 45, 23, 59, 18, 54)(7, 43, 10, 46, 24, 60, 19, 55)(14, 50, 27, 63, 33, 69, 29, 65)(15, 51, 28, 64, 34, 70, 30, 66)(17, 53, 25, 61, 35, 71, 31, 67)(20, 56, 26, 62, 36, 72, 32, 68)(73, 109, 75, 111, 79, 115, 86, 122, 92, 128, 87, 123, 89, 125, 76, 112, 78, 114)(74, 110, 81, 117, 84, 120, 97, 133, 100, 136, 98, 134, 99, 135, 82, 118, 83, 119)(77, 113, 90, 126, 88, 124, 103, 139, 102, 138, 104, 140, 101, 137, 91, 127, 85, 121)(80, 116, 93, 129, 96, 132, 105, 141, 108, 144, 106, 142, 107, 143, 94, 130, 95, 131) L = (1, 76)(2, 82)(3, 78)(4, 87)(5, 91)(6, 89)(7, 73)(8, 94)(9, 83)(10, 98)(11, 99)(12, 74)(13, 101)(14, 75)(15, 86)(16, 77)(17, 92)(18, 85)(19, 104)(20, 79)(21, 95)(22, 106)(23, 107)(24, 80)(25, 81)(26, 97)(27, 100)(28, 84)(29, 102)(30, 88)(31, 90)(32, 103)(33, 93)(34, 105)(35, 108)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E20.329 Graph:: bipartite v = 13 e = 72 f = 21 degree seq :: [ 8^9, 18^4 ] E20.332 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1, (R * Y2^-1)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y1)^2, Y1^4, Y2^4 * Y3^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 11, 47, 21, 57, 14, 50)(4, 40, 12, 48, 22, 58, 16, 52)(6, 42, 9, 45, 23, 59, 18, 54)(7, 43, 10, 46, 24, 60, 19, 55)(13, 49, 28, 64, 33, 69, 29, 65)(15, 51, 27, 63, 34, 70, 30, 66)(17, 53, 26, 62, 35, 71, 31, 67)(20, 56, 25, 61, 36, 72, 32, 68)(73, 109, 75, 111, 85, 121, 89, 125, 76, 112, 79, 115, 87, 123, 92, 128, 78, 114)(74, 110, 81, 117, 97, 133, 99, 135, 82, 118, 84, 120, 98, 134, 100, 136, 83, 119)(77, 113, 90, 126, 104, 140, 102, 138, 91, 127, 88, 124, 103, 139, 101, 137, 86, 122)(80, 116, 93, 129, 105, 141, 107, 143, 94, 130, 96, 132, 106, 142, 108, 144, 95, 131) L = (1, 76)(2, 82)(3, 79)(4, 78)(5, 91)(6, 89)(7, 73)(8, 94)(9, 84)(10, 83)(11, 99)(12, 74)(13, 87)(14, 102)(15, 75)(16, 77)(17, 92)(18, 88)(19, 86)(20, 85)(21, 96)(22, 95)(23, 107)(24, 80)(25, 98)(26, 81)(27, 100)(28, 97)(29, 104)(30, 101)(31, 90)(32, 103)(33, 106)(34, 93)(35, 108)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 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 E20.330 Graph:: bipartite v = 13 e = 72 f = 21 degree seq :: [ 8^9, 18^4 ] E20.333 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^6 * Y2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 8, 44)(5, 41, 9, 45)(6, 42, 10, 46)(11, 47, 17, 53)(12, 48, 18, 54)(13, 49, 19, 55)(14, 50, 20, 56)(15, 51, 21, 57)(16, 52, 22, 58)(23, 59, 29, 65)(24, 60, 30, 66)(25, 61, 31, 67)(26, 62, 32, 68)(27, 63, 33, 69)(28, 64, 34, 70)(35, 71, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 86, 122)(78, 114, 84, 120, 87, 123)(80, 116, 89, 125, 92, 128)(82, 118, 90, 126, 93, 129)(85, 121, 95, 131, 98, 134)(88, 124, 96, 132, 99, 135)(91, 127, 101, 137, 104, 140)(94, 130, 102, 138, 105, 141)(97, 133, 100, 136, 107, 143)(103, 139, 106, 142, 108, 144) L = (1, 76)(2, 80)(3, 83)(4, 85)(5, 86)(6, 73)(7, 89)(8, 91)(9, 92)(10, 74)(11, 95)(12, 75)(13, 97)(14, 98)(15, 77)(16, 78)(17, 101)(18, 79)(19, 103)(20, 104)(21, 81)(22, 82)(23, 100)(24, 84)(25, 99)(26, 107)(27, 87)(28, 88)(29, 106)(30, 90)(31, 105)(32, 108)(33, 93)(34, 94)(35, 96)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 36^4 ), ( 36^6 ) } Outer automorphisms :: reflexible Dual of E20.338 Graph:: simple bipartite v = 30 e = 72 f = 4 degree seq :: [ 4^18, 6^12 ] E20.334 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, (Y3^-1 * Y1^-1)^2, (Y2, Y3), Y2^-6 * Y1, (Y2^3 * Y1)^2, (Y2^-3 * Y3)^2, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 7, 43)(6, 42, 10, 46, 16, 52)(11, 47, 19, 55, 25, 61)(12, 48, 20, 56, 14, 50)(15, 51, 21, 57, 18, 54)(17, 53, 22, 58, 28, 64)(23, 59, 31, 67, 29, 65)(24, 60, 32, 68, 26, 62)(27, 63, 33, 69, 30, 66)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 94, 130, 82, 118, 74, 110, 80, 116, 91, 127, 103, 139, 100, 136, 88, 124, 77, 113, 85, 121, 97, 133, 101, 137, 89, 125, 78, 114)(76, 112, 84, 120, 96, 132, 106, 142, 105, 141, 93, 129, 81, 117, 92, 128, 104, 140, 108, 144, 102, 138, 90, 126, 79, 115, 86, 122, 98, 134, 107, 143, 99, 135, 87, 123) L = (1, 76)(2, 81)(3, 84)(4, 74)(5, 79)(6, 87)(7, 73)(8, 92)(9, 77)(10, 93)(11, 96)(12, 80)(13, 86)(14, 75)(15, 82)(16, 90)(17, 99)(18, 78)(19, 104)(20, 85)(21, 88)(22, 105)(23, 106)(24, 91)(25, 98)(26, 83)(27, 94)(28, 102)(29, 107)(30, 89)(31, 108)(32, 97)(33, 100)(34, 103)(35, 95)(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) :: { ( 4, 36, 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E20.336 Graph:: bipartite v = 14 e = 72 f = 20 degree seq :: [ 6^12, 36^2 ] E20.335 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1^-1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^-6, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 7, 43)(6, 42, 10, 46, 16, 52)(11, 47, 19, 55, 25, 61)(12, 48, 20, 56, 14, 50)(15, 51, 21, 57, 18, 54)(17, 53, 22, 58, 28, 64)(23, 59, 29, 65, 33, 69)(24, 60, 31, 67, 26, 62)(27, 63, 32, 68, 30, 66)(34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 100, 136, 88, 124, 77, 113, 85, 121, 97, 133, 105, 141, 94, 130, 82, 118, 74, 110, 80, 116, 91, 127, 101, 137, 89, 125, 78, 114)(76, 112, 84, 120, 96, 132, 106, 142, 102, 138, 90, 126, 79, 115, 86, 122, 98, 134, 107, 143, 104, 140, 93, 129, 81, 117, 92, 128, 103, 139, 108, 144, 99, 135, 87, 123) L = (1, 76)(2, 81)(3, 84)(4, 74)(5, 79)(6, 87)(7, 73)(8, 92)(9, 77)(10, 93)(11, 96)(12, 80)(13, 86)(14, 75)(15, 82)(16, 90)(17, 99)(18, 78)(19, 103)(20, 85)(21, 88)(22, 104)(23, 106)(24, 91)(25, 98)(26, 83)(27, 94)(28, 102)(29, 108)(30, 89)(31, 97)(32, 100)(33, 107)(34, 101)(35, 95)(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, 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 E20.337 Graph:: bipartite v = 14 e = 72 f = 20 degree seq :: [ 6^12, 36^2 ] E20.336 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y2 * Y1^-1 * Y2 * Y1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-4, (Y1^-1 * Y3^-1)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 29, 65, 25, 61, 13, 49, 22, 58, 34, 70, 36, 72, 35, 71, 23, 59, 11, 47, 21, 57, 33, 69, 27, 63, 15, 51, 5, 41)(3, 39, 8, 44, 18, 54, 30, 66, 28, 64, 16, 52, 6, 42, 10, 46, 20, 56, 32, 68, 26, 62, 14, 50, 4, 40, 9, 45, 19, 55, 31, 67, 24, 60, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 95, 131)(87, 123, 96, 132)(88, 124, 97, 133)(89, 125, 102, 138)(91, 127, 105, 141)(92, 128, 106, 142)(98, 134, 107, 143)(99, 135, 103, 139)(100, 136, 101, 137)(104, 140, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 86)(6, 73)(7, 91)(8, 93)(9, 94)(10, 74)(11, 78)(12, 95)(13, 75)(14, 97)(15, 98)(16, 77)(17, 103)(18, 105)(19, 106)(20, 79)(21, 82)(22, 80)(23, 88)(24, 107)(25, 84)(26, 101)(27, 104)(28, 87)(29, 96)(30, 99)(31, 108)(32, 89)(33, 92)(34, 90)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 6, 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 E20.334 Graph:: bipartite v = 20 e = 72 f = 14 degree seq :: [ 4^18, 36^2 ] E20.337 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-3, Y2 * Y3 * Y2 * Y3^-1, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y1^-6, (Y1^-1 * Y3^-1)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 29, 65, 23, 59, 11, 47, 21, 57, 33, 69, 36, 72, 35, 71, 25, 61, 13, 49, 22, 58, 34, 70, 27, 63, 15, 51, 5, 41)(3, 39, 8, 44, 18, 54, 30, 66, 26, 62, 14, 50, 4, 40, 9, 45, 19, 55, 31, 67, 28, 64, 16, 52, 6, 42, 10, 46, 20, 56, 32, 68, 24, 60, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 95, 131)(87, 123, 96, 132)(88, 124, 97, 133)(89, 125, 102, 138)(91, 127, 105, 141)(92, 128, 106, 142)(98, 134, 101, 137)(99, 135, 104, 140)(100, 136, 107, 143)(103, 139, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 86)(6, 73)(7, 91)(8, 93)(9, 94)(10, 74)(11, 78)(12, 95)(13, 75)(14, 97)(15, 98)(16, 77)(17, 103)(18, 105)(19, 106)(20, 79)(21, 82)(22, 80)(23, 88)(24, 101)(25, 84)(26, 107)(27, 102)(28, 87)(29, 100)(30, 108)(31, 99)(32, 89)(33, 92)(34, 90)(35, 96)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E20.335 Graph:: bipartite v = 20 e = 72 f = 14 degree seq :: [ 4^18, 36^2 ] E20.338 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y2)^2, (R * Y3)^2, (Y1, Y3), Y3^2 * Y2^-2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1^-3, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-2, (Y1^-2 * Y3)^2, Y1 * Y3^3 * Y1^2, Y3^2 * Y2 * Y3 * Y2 * Y1^-1, Y3 * Y2^12 * Y1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 23, 59, 13, 49, 28, 64, 20, 56, 7, 43, 12, 48, 27, 63, 17, 53, 4, 40, 10, 46, 25, 61, 21, 57, 31, 67, 18, 54, 5, 41)(3, 39, 9, 45, 24, 60, 22, 58, 32, 68, 36, 72, 34, 70, 16, 52, 30, 66, 35, 71, 33, 69, 14, 50, 29, 65, 19, 55, 6, 42, 11, 47, 26, 62, 15, 51)(73, 109, 75, 111, 85, 121, 104, 140, 84, 120, 102, 138, 82, 118, 101, 137, 90, 126, 98, 134, 80, 116, 96, 132, 92, 128, 106, 142, 89, 125, 105, 141, 93, 129, 78, 114)(74, 110, 81, 117, 100, 136, 108, 144, 99, 135, 107, 143, 97, 133, 91, 127, 77, 113, 87, 123, 95, 131, 94, 130, 79, 115, 88, 124, 76, 112, 86, 122, 103, 139, 83, 119) L = (1, 76)(2, 82)(3, 86)(4, 85)(5, 89)(6, 88)(7, 73)(8, 97)(9, 101)(10, 100)(11, 102)(12, 74)(13, 103)(14, 104)(15, 105)(16, 75)(17, 95)(18, 99)(19, 106)(20, 77)(21, 79)(22, 78)(23, 93)(24, 91)(25, 92)(26, 107)(27, 80)(28, 90)(29, 108)(30, 81)(31, 84)(32, 83)(33, 94)(34, 87)(35, 96)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E20.333 Graph:: bipartite v = 4 e = 72 f = 30 degree seq :: [ 36^4 ] E20.339 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), Y2^4, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^5 * Y2^-1, Y2 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1, Y2^-1 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2 * Y1, (Y3^-1 * Y1)^10 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 18, 58)(8, 48, 23, 63)(10, 50, 27, 67)(11, 51, 20, 60)(12, 52, 21, 61)(13, 53, 22, 62)(15, 55, 24, 64)(16, 56, 25, 65)(17, 57, 26, 66)(19, 59, 28, 68)(29, 69, 38, 78)(30, 70, 39, 79)(31, 71, 37, 77)(32, 72, 35, 75)(33, 73, 36, 76)(34, 74, 40, 80)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 100, 140, 89, 129)(84, 124, 92, 132, 103, 143, 96, 136)(86, 126, 93, 133, 107, 147, 97, 137)(88, 128, 101, 141, 94, 134, 105, 145)(90, 130, 102, 142, 98, 138, 106, 146)(95, 135, 109, 149, 117, 157, 112, 152)(99, 139, 110, 150, 120, 160, 113, 153)(104, 144, 115, 155, 111, 151, 118, 158)(108, 148, 116, 156, 114, 154, 119, 159) L = (1, 84)(2, 88)(3, 92)(4, 95)(5, 96)(6, 81)(7, 101)(8, 104)(9, 105)(10, 82)(11, 103)(12, 109)(13, 83)(14, 111)(15, 110)(16, 112)(17, 85)(18, 100)(19, 86)(20, 94)(21, 115)(22, 87)(23, 117)(24, 116)(25, 118)(26, 89)(27, 91)(28, 90)(29, 120)(30, 93)(31, 119)(32, 99)(33, 97)(34, 98)(35, 114)(36, 102)(37, 113)(38, 108)(39, 106)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E20.350 Graph:: simple bipartite v = 30 e = 80 f = 12 degree seq :: [ 4^20, 8^10 ] E20.340 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y3^2, R^2, (Y2^-1, Y1^-1), (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (Y1^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 8, 48, 18, 58, 13, 53)(4, 44, 14, 54, 19, 59, 9, 49)(6, 46, 10, 50, 20, 60, 16, 56)(11, 51, 21, 61, 31, 71, 26, 66)(12, 52, 27, 67, 32, 72, 22, 62)(15, 55, 28, 68, 33, 73, 23, 63)(17, 57, 24, 64, 34, 74, 30, 70)(25, 65, 37, 77, 39, 79, 35, 75)(29, 69, 38, 78, 40, 80, 36, 76)(81, 121, 83, 123, 91, 131, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 104, 144, 90, 130)(84, 124, 92, 132, 105, 145, 109, 149, 95, 135)(85, 125, 93, 133, 106, 146, 110, 150, 96, 136)(87, 127, 98, 138, 111, 151, 114, 154, 100, 140)(89, 129, 102, 142, 115, 155, 116, 156, 103, 143)(94, 134, 107, 147, 117, 157, 118, 158, 108, 148)(99, 139, 112, 152, 119, 159, 120, 160, 113, 153) L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 105)(12, 83)(13, 107)(14, 85)(15, 86)(16, 108)(17, 109)(18, 112)(19, 87)(20, 113)(21, 115)(22, 88)(23, 90)(24, 116)(25, 91)(26, 117)(27, 93)(28, 96)(29, 97)(30, 118)(31, 119)(32, 98)(33, 100)(34, 120)(35, 101)(36, 104)(37, 106)(38, 110)(39, 111)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.345 Graph:: simple bipartite v = 18 e = 80 f = 24 degree seq :: [ 8^10, 10^8 ] E20.341 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^4, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 10, 50, 18, 58, 13, 53)(4, 44, 14, 54, 19, 59, 9, 49)(6, 46, 8, 48, 20, 60, 16, 56)(11, 51, 24, 64, 31, 71, 26, 66)(12, 52, 27, 67, 32, 72, 23, 63)(15, 55, 28, 68, 33, 73, 22, 62)(17, 57, 21, 61, 34, 74, 30, 70)(25, 65, 37, 77, 39, 79, 36, 76)(29, 69, 38, 78, 40, 80, 35, 75)(81, 121, 83, 123, 91, 131, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 104, 144, 90, 130)(84, 124, 92, 132, 105, 145, 109, 149, 95, 135)(85, 125, 96, 136, 110, 150, 106, 146, 93, 133)(87, 127, 98, 138, 111, 151, 114, 154, 100, 140)(89, 129, 102, 142, 115, 155, 116, 156, 103, 143)(94, 134, 108, 148, 118, 158, 117, 157, 107, 147)(99, 139, 112, 152, 119, 159, 120, 160, 113, 153) L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 105)(12, 83)(13, 107)(14, 85)(15, 86)(16, 108)(17, 109)(18, 112)(19, 87)(20, 113)(21, 115)(22, 88)(23, 90)(24, 116)(25, 91)(26, 117)(27, 93)(28, 96)(29, 97)(30, 118)(31, 119)(32, 98)(33, 100)(34, 120)(35, 101)(36, 104)(37, 106)(38, 110)(39, 111)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.346 Graph:: simple bipartite v = 18 e = 80 f = 24 degree seq :: [ 8^10, 10^8 ] E20.342 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3^-1), (Y3^-1 * Y2^-1)^2, Y1^4, (R * Y2^-1)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y2^-2 * Y3^-2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y3^-2 * Y2^3 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 22, 62, 15, 55)(4, 44, 17, 57, 23, 63, 12, 52)(6, 46, 9, 49, 24, 64, 20, 60)(7, 47, 21, 61, 25, 65, 10, 50)(13, 53, 29, 69, 36, 76, 31, 71)(14, 54, 32, 72, 37, 77, 27, 67)(16, 56, 33, 73, 38, 78, 30, 70)(18, 58, 26, 66, 39, 79, 35, 75)(19, 59, 34, 74, 40, 80, 28, 68)(81, 121, 83, 123, 93, 133, 98, 138, 86, 126)(82, 122, 89, 129, 106, 146, 109, 149, 91, 131)(84, 124, 94, 134, 87, 127, 96, 136, 99, 139)(85, 125, 100, 140, 115, 155, 111, 151, 95, 135)(88, 128, 102, 142, 116, 156, 119, 159, 104, 144)(90, 130, 107, 147, 92, 132, 108, 148, 110, 150)(97, 137, 114, 154, 113, 153, 101, 141, 112, 152)(103, 143, 117, 157, 105, 145, 118, 158, 120, 160) L = (1, 84)(2, 90)(3, 94)(4, 98)(5, 101)(6, 99)(7, 81)(8, 103)(9, 107)(10, 109)(11, 110)(12, 82)(13, 87)(14, 86)(15, 113)(16, 83)(17, 85)(18, 96)(19, 93)(20, 112)(21, 111)(22, 117)(23, 119)(24, 120)(25, 88)(26, 92)(27, 91)(28, 89)(29, 108)(30, 106)(31, 114)(32, 95)(33, 115)(34, 100)(35, 97)(36, 105)(37, 104)(38, 102)(39, 118)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.348 Graph:: simple bipartite v = 18 e = 80 f = 24 degree seq :: [ 8^10, 10^8 ] E20.343 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y3 * Y1)^2, (R * Y2)^2, (R * Y1)^2, Y1^4, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 15, 55)(4, 44, 16, 56, 22, 62, 12, 52)(6, 46, 9, 49, 23, 63, 17, 57)(7, 47, 18, 58, 24, 64, 10, 50)(13, 53, 27, 67, 34, 74, 30, 70)(14, 54, 31, 71, 35, 75, 28, 68)(19, 59, 25, 65, 36, 76, 32, 72)(20, 60, 33, 73, 37, 77, 26, 66)(29, 69, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 93, 133, 99, 139, 86, 126)(82, 122, 89, 129, 105, 145, 107, 147, 91, 131)(84, 124, 94, 134, 109, 149, 100, 140, 87, 127)(85, 125, 97, 137, 112, 152, 110, 150, 95, 135)(88, 128, 101, 141, 114, 154, 116, 156, 103, 143)(90, 130, 106, 146, 118, 158, 108, 148, 92, 132)(96, 136, 98, 138, 113, 153, 119, 159, 111, 151)(102, 142, 115, 155, 120, 160, 117, 157, 104, 144) L = (1, 84)(2, 90)(3, 94)(4, 83)(5, 98)(6, 87)(7, 81)(8, 102)(9, 106)(10, 89)(11, 92)(12, 82)(13, 109)(14, 93)(15, 96)(16, 85)(17, 113)(18, 97)(19, 100)(20, 86)(21, 115)(22, 101)(23, 104)(24, 88)(25, 118)(26, 105)(27, 108)(28, 91)(29, 99)(30, 111)(31, 95)(32, 119)(33, 112)(34, 120)(35, 114)(36, 117)(37, 103)(38, 107)(39, 110)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.347 Graph:: simple bipartite v = 18 e = 80 f = 24 degree seq :: [ 8^10, 10^8 ] E20.344 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, (Y1^-1 * Y3^-1)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2^5, (Y3 * Y2^-1)^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 14, 54)(4, 44, 16, 56, 22, 62, 12, 52)(6, 46, 9, 49, 23, 63, 18, 58)(7, 47, 19, 59, 24, 64, 10, 50)(13, 53, 28, 68, 34, 74, 29, 69)(15, 55, 31, 71, 35, 75, 27, 67)(17, 57, 32, 72, 36, 76, 26, 66)(20, 60, 25, 65, 37, 77, 33, 73)(30, 70, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 93, 133, 100, 140, 86, 126)(82, 122, 89, 129, 105, 145, 108, 148, 91, 131)(84, 124, 87, 127, 95, 135, 110, 150, 97, 137)(85, 125, 98, 138, 113, 153, 109, 149, 94, 134)(88, 128, 101, 141, 114, 154, 117, 157, 103, 143)(90, 130, 92, 132, 106, 146, 118, 158, 107, 147)(96, 136, 112, 152, 119, 159, 111, 151, 99, 139)(102, 142, 104, 144, 115, 155, 120, 160, 116, 156) L = (1, 84)(2, 90)(3, 87)(4, 86)(5, 99)(6, 97)(7, 81)(8, 102)(9, 92)(10, 91)(11, 107)(12, 82)(13, 95)(14, 111)(15, 83)(16, 85)(17, 100)(18, 96)(19, 94)(20, 110)(21, 104)(22, 103)(23, 116)(24, 88)(25, 106)(26, 89)(27, 108)(28, 118)(29, 119)(30, 93)(31, 109)(32, 98)(33, 112)(34, 115)(35, 101)(36, 117)(37, 120)(38, 105)(39, 113)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.349 Graph:: simple bipartite v = 18 e = 80 f = 24 degree seq :: [ 8^10, 10^8 ] E20.345 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-5, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y1 * Y3 * Y2 * Y3, Y1^-1 * Y3 * Y2 * Y3 * Y1 * Y2, (Y1^-1 * Y2 * Y1 * Y2)^2, (Y2 * Y3)^4, Y2 * Y3 * Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 16, 56, 13, 53, 4, 44, 8, 48, 18, 58, 15, 55, 5, 45)(3, 43, 9, 49, 17, 57, 31, 71, 25, 65, 10, 50, 22, 62, 32, 72, 27, 67, 11, 51)(7, 47, 19, 59, 30, 70, 28, 68, 12, 52, 20, 60, 33, 73, 29, 69, 14, 54, 21, 61)(23, 63, 34, 74, 39, 79, 37, 77, 24, 64, 35, 75, 40, 80, 38, 78, 26, 66, 36, 76)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 92, 132)(85, 125, 94, 134)(86, 126, 97, 137)(88, 128, 102, 142)(89, 129, 103, 143)(90, 130, 104, 144)(91, 131, 106, 146)(93, 133, 105, 145)(95, 135, 107, 147)(96, 136, 110, 150)(98, 138, 113, 153)(99, 139, 114, 154)(100, 140, 115, 155)(101, 141, 116, 156)(108, 148, 117, 157)(109, 149, 118, 158)(111, 151, 119, 159)(112, 152, 120, 160) L = (1, 84)(2, 88)(3, 90)(4, 81)(5, 93)(6, 98)(7, 100)(8, 82)(9, 102)(10, 83)(11, 105)(12, 101)(13, 85)(14, 108)(15, 96)(16, 95)(17, 112)(18, 86)(19, 113)(20, 87)(21, 92)(22, 89)(23, 115)(24, 116)(25, 91)(26, 117)(27, 111)(28, 94)(29, 110)(30, 109)(31, 107)(32, 97)(33, 99)(34, 120)(35, 103)(36, 104)(37, 106)(38, 119)(39, 118)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E20.340 Graph:: bipartite v = 24 e = 80 f = 18 degree seq :: [ 4^20, 20^4 ] E20.346 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * R)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-5, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y1^-1 * R * Y2 * R, (Y1^-1 * Y3 * Y2)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, (R * Y2)^4, (Y2 * R * Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 16, 56, 13, 53, 4, 44, 8, 48, 18, 58, 15, 55, 5, 45)(3, 43, 9, 49, 23, 63, 31, 71, 22, 62, 10, 50, 25, 65, 32, 72, 17, 57, 11, 51)(7, 47, 19, 59, 14, 54, 29, 69, 33, 73, 20, 60, 12, 52, 28, 68, 30, 70, 21, 61)(24, 64, 34, 74, 27, 67, 36, 76, 40, 80, 37, 77, 26, 66, 35, 75, 39, 79, 38, 78)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 92, 132)(85, 125, 94, 134)(86, 126, 97, 137)(88, 128, 102, 142)(89, 129, 104, 144)(90, 130, 106, 146)(91, 131, 107, 147)(93, 133, 105, 145)(95, 135, 103, 143)(96, 136, 110, 150)(98, 138, 113, 153)(99, 139, 114, 154)(100, 140, 115, 155)(101, 141, 116, 156)(108, 148, 117, 157)(109, 149, 118, 158)(111, 151, 119, 159)(112, 152, 120, 160) L = (1, 84)(2, 88)(3, 90)(4, 81)(5, 93)(6, 98)(7, 100)(8, 82)(9, 105)(10, 83)(11, 102)(12, 99)(13, 85)(14, 108)(15, 96)(16, 95)(17, 111)(18, 86)(19, 92)(20, 87)(21, 113)(22, 91)(23, 112)(24, 117)(25, 89)(26, 114)(27, 115)(28, 94)(29, 110)(30, 109)(31, 97)(32, 103)(33, 101)(34, 106)(35, 107)(36, 119)(37, 104)(38, 120)(39, 116)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E20.341 Graph:: bipartite v = 24 e = 80 f = 18 degree seq :: [ 4^20, 20^4 ] E20.347 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y1^-1)^4, (Y3 * Y2)^4, (Y3^-1 * Y1^-1)^5, Y1^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 5, 45, 11, 51, 20, 60, 29, 69, 28, 68, 19, 59, 10, 50, 4, 44)(3, 43, 7, 47, 15, 55, 25, 65, 33, 73, 37, 77, 30, 70, 22, 62, 12, 52, 8, 48)(6, 46, 13, 53, 9, 49, 18, 58, 27, 67, 35, 75, 36, 76, 31, 71, 21, 61, 14, 54)(16, 56, 23, 63, 17, 57, 24, 64, 32, 72, 38, 78, 40, 80, 39, 79, 34, 74, 26, 66)(81, 121, 83, 123)(82, 122, 86, 126)(84, 124, 89, 129)(85, 125, 92, 132)(87, 127, 96, 136)(88, 128, 97, 137)(90, 130, 95, 135)(91, 131, 101, 141)(93, 133, 103, 143)(94, 134, 104, 144)(98, 138, 106, 146)(99, 139, 107, 147)(100, 140, 110, 150)(102, 142, 112, 152)(105, 145, 114, 154)(108, 148, 113, 153)(109, 149, 116, 156)(111, 151, 118, 158)(115, 155, 119, 159)(117, 157, 120, 160) L = (1, 82)(2, 85)(3, 87)(4, 81)(5, 91)(6, 93)(7, 95)(8, 83)(9, 98)(10, 84)(11, 100)(12, 88)(13, 89)(14, 86)(15, 105)(16, 103)(17, 104)(18, 107)(19, 90)(20, 109)(21, 94)(22, 92)(23, 97)(24, 112)(25, 113)(26, 96)(27, 115)(28, 99)(29, 108)(30, 102)(31, 101)(32, 118)(33, 117)(34, 106)(35, 116)(36, 111)(37, 110)(38, 120)(39, 114)(40, 119)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E20.343 Graph:: bipartite v = 24 e = 80 f = 18 degree seq :: [ 4^20, 20^4 ] E20.348 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * R)^2, (Y1^-1 * R)^2, (Y3, Y1^-1), Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^2, (Y2 * Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1, Y3^-1 * Y2 * Y1^-1 * R * Y2 * R, (Y2 * R * Y2 * Y1^-1)^2, (Y1^-1 * Y2)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 6, 46, 10, 50, 20, 60, 16, 56, 4, 44, 9, 49, 5, 45)(3, 43, 11, 51, 25, 65, 14, 54, 28, 68, 33, 73, 26, 66, 12, 52, 19, 59, 13, 53)(8, 48, 21, 61, 17, 57, 24, 64, 15, 55, 32, 72, 34, 74, 22, 62, 18, 58, 23, 63)(27, 67, 35, 75, 30, 70, 37, 77, 29, 69, 36, 76, 40, 80, 39, 79, 31, 71, 38, 78)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 95, 135)(85, 125, 97, 137)(86, 126, 98, 138)(87, 127, 99, 139)(89, 129, 105, 145)(90, 130, 106, 146)(91, 131, 107, 147)(92, 132, 109, 149)(93, 133, 110, 150)(94, 134, 111, 151)(96, 136, 108, 148)(100, 140, 114, 154)(101, 141, 115, 155)(102, 142, 116, 156)(103, 143, 117, 157)(104, 144, 118, 158)(112, 152, 119, 159)(113, 153, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 90)(5, 96)(6, 81)(7, 85)(8, 102)(9, 100)(10, 82)(11, 99)(12, 108)(13, 106)(14, 83)(15, 101)(16, 86)(17, 103)(18, 112)(19, 113)(20, 87)(21, 98)(22, 95)(23, 114)(24, 88)(25, 93)(26, 94)(27, 119)(28, 91)(29, 115)(30, 118)(31, 116)(32, 97)(33, 105)(34, 104)(35, 111)(36, 110)(37, 107)(38, 120)(39, 109)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E20.342 Graph:: bipartite v = 24 e = 80 f = 18 degree seq :: [ 4^20, 20^4 ] E20.349 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), Y3^-3 * Y1^-1, Y1^2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1^2 * Y2 * Y1^-1, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y2 * R * Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 4, 44, 9, 49, 20, 60, 16, 56, 6, 46, 10, 50, 5, 45)(3, 43, 11, 51, 26, 66, 12, 52, 28, 68, 33, 73, 25, 65, 14, 54, 19, 59, 13, 53)(8, 48, 21, 61, 17, 57, 22, 62, 18, 58, 32, 72, 34, 74, 24, 64, 15, 55, 23, 63)(27, 67, 35, 75, 30, 70, 37, 77, 31, 71, 38, 78, 40, 80, 39, 79, 29, 69, 36, 76)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 95, 135)(85, 125, 97, 137)(86, 126, 98, 138)(87, 127, 99, 139)(89, 129, 105, 145)(90, 130, 106, 146)(91, 131, 107, 147)(92, 132, 109, 149)(93, 133, 110, 150)(94, 134, 111, 151)(96, 136, 108, 148)(100, 140, 114, 154)(101, 141, 115, 155)(102, 142, 116, 156)(103, 143, 117, 157)(104, 144, 118, 158)(112, 152, 119, 159)(113, 153, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 96)(5, 87)(6, 81)(7, 100)(8, 102)(9, 86)(10, 82)(11, 108)(12, 105)(13, 106)(14, 83)(15, 101)(16, 85)(17, 112)(18, 104)(19, 91)(20, 90)(21, 98)(22, 114)(23, 97)(24, 88)(25, 93)(26, 113)(27, 117)(28, 94)(29, 115)(30, 118)(31, 119)(32, 95)(33, 99)(34, 103)(35, 111)(36, 110)(37, 120)(38, 109)(39, 107)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E20.344 Graph:: bipartite v = 24 e = 80 f = 18 degree seq :: [ 4^20, 20^4 ] E20.350 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y1^-1)^2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y1)^2, (Y2, Y1^-1), (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, Y3^-4 * Y1, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-3 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^4 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 8, 48, 13, 53, 5, 45)(3, 43, 9, 49, 6, 46, 11, 51, 15, 55)(4, 44, 10, 50, 25, 65, 32, 72, 19, 59)(7, 47, 12, 52, 26, 66, 33, 73, 20, 60)(14, 54, 27, 67, 21, 61, 31, 71, 23, 63)(16, 56, 28, 68, 22, 62, 17, 57, 29, 69)(18, 58, 30, 70, 39, 79, 37, 77, 24, 64)(34, 74, 38, 78, 36, 76, 40, 80, 35, 75)(81, 121, 83, 123, 93, 133, 91, 131, 82, 122, 89, 129, 85, 125, 95, 135, 88, 128, 86, 126)(84, 124, 97, 137, 112, 152, 108, 148, 90, 130, 109, 149, 99, 139, 102, 142, 105, 145, 96, 136)(87, 127, 101, 141, 113, 153, 94, 134, 92, 132, 111, 151, 100, 140, 107, 147, 106, 146, 103, 143)(98, 138, 114, 154, 117, 157, 120, 160, 110, 150, 118, 158, 104, 144, 115, 155, 119, 159, 116, 156) L = (1, 84)(2, 90)(3, 94)(4, 98)(5, 99)(6, 101)(7, 81)(8, 105)(9, 107)(10, 110)(11, 111)(12, 82)(13, 112)(14, 114)(15, 103)(16, 83)(17, 91)(18, 92)(19, 104)(20, 85)(21, 116)(22, 86)(23, 115)(24, 87)(25, 119)(26, 88)(27, 118)(28, 89)(29, 95)(30, 106)(31, 120)(32, 117)(33, 93)(34, 108)(35, 96)(36, 97)(37, 100)(38, 102)(39, 113)(40, 109)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 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 E20.339 Graph:: bipartite v = 12 e = 80 f = 30 degree seq :: [ 10^8, 20^4 ] E20.351 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ 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^-1 * Y1)^2, Y2^-1 * Y1 * Y3 * Y1 * Y3, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 13, 53)(10, 50, 12, 52)(11, 51, 23, 63)(15, 55, 28, 68)(16, 56, 22, 62)(17, 57, 20, 60)(18, 58, 33, 73)(21, 61, 26, 66)(24, 64, 25, 65)(27, 67, 35, 75)(29, 69, 31, 71)(30, 70, 36, 76)(32, 72, 34, 74)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 103, 143, 89, 129)(84, 124, 95, 135, 110, 150, 105, 145, 92, 132)(86, 126, 98, 138, 112, 152, 106, 146, 93, 133)(88, 128, 101, 141, 114, 154, 113, 153, 99, 139)(90, 130, 104, 144, 116, 156, 108, 148, 94, 134)(96, 136, 107, 147, 117, 157, 119, 159, 111, 151)(102, 142, 109, 149, 118, 158, 120, 160, 115, 155) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 99)(8, 102)(9, 101)(10, 82)(11, 105)(12, 107)(13, 83)(14, 87)(15, 111)(16, 86)(17, 110)(18, 85)(19, 109)(20, 113)(21, 115)(22, 90)(23, 114)(24, 89)(25, 117)(26, 91)(27, 93)(28, 100)(29, 94)(30, 119)(31, 98)(32, 97)(33, 118)(34, 120)(35, 104)(36, 103)(37, 106)(38, 108)(39, 112)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E20.358 Graph:: simple bipartite v = 28 e = 80 f = 14 degree seq :: [ 4^20, 10^8 ] E20.352 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, R * Y2 * R * Y2^-1, Y1 * Y2^-1 * Y3 * Y1 * Y3, Y2^5 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 18, 58)(10, 50, 15, 55)(11, 51, 24, 64)(12, 52, 27, 67)(13, 53, 29, 69)(16, 56, 23, 63)(17, 57, 20, 60)(21, 61, 33, 73)(22, 62, 31, 71)(25, 65, 35, 75)(26, 66, 34, 74)(28, 68, 30, 70)(32, 72, 36, 76)(37, 77, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 104, 144, 89, 129)(84, 124, 95, 135, 111, 151, 105, 145, 92, 132)(86, 126, 98, 138, 113, 153, 106, 146, 93, 133)(88, 128, 99, 139, 109, 149, 114, 154, 101, 141)(90, 130, 94, 134, 107, 147, 115, 155, 102, 142)(96, 136, 108, 148, 117, 157, 119, 159, 112, 152)(103, 143, 116, 156, 120, 160, 118, 158, 110, 150) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 103)(9, 99)(10, 82)(11, 105)(12, 108)(13, 83)(14, 89)(15, 112)(16, 86)(17, 111)(18, 85)(19, 110)(20, 114)(21, 116)(22, 87)(23, 90)(24, 109)(25, 117)(26, 91)(27, 104)(28, 93)(29, 118)(30, 94)(31, 119)(32, 98)(33, 97)(34, 120)(35, 100)(36, 102)(37, 106)(38, 107)(39, 113)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E20.359 Graph:: simple bipartite v = 28 e = 80 f = 14 degree seq :: [ 4^20, 10^8 ] E20.353 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3, Y3^4, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, (Y2^-1 * Y1)^2, Y2^5, (Y3^-1 * Y1 * Y3^-1)^2, (Y3^-1 * Y2^-1 * Y1)^2, Y3^-1 * Y1 * Y2^2 * Y3^-1 * Y1, Y2^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 23, 63)(10, 50, 28, 68)(11, 51, 26, 66)(12, 52, 22, 62)(13, 53, 21, 61)(15, 55, 30, 70)(16, 56, 25, 65)(17, 57, 20, 60)(18, 58, 35, 75)(24, 64, 34, 74)(27, 67, 32, 72)(29, 69, 38, 78)(31, 71, 40, 80)(33, 73, 36, 76)(37, 77, 39, 79)(81, 121, 83, 123, 91, 131, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 106, 146, 89, 129)(84, 124, 95, 135, 112, 152, 108, 148, 92, 132)(86, 126, 98, 138, 114, 154, 103, 143, 93, 133)(88, 128, 104, 144, 115, 155, 99, 139, 101, 141)(90, 130, 107, 147, 110, 150, 94, 134, 102, 142)(96, 136, 109, 149, 117, 157, 120, 160, 113, 153)(105, 145, 116, 156, 111, 151, 119, 159, 118, 158) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 105)(9, 104)(10, 82)(11, 108)(12, 109)(13, 83)(14, 100)(15, 113)(16, 86)(17, 112)(18, 85)(19, 111)(20, 99)(21, 116)(22, 87)(23, 91)(24, 118)(25, 90)(26, 115)(27, 89)(28, 117)(29, 93)(30, 106)(31, 94)(32, 120)(33, 98)(34, 97)(35, 119)(36, 102)(37, 103)(38, 107)(39, 110)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E20.357 Graph:: simple bipartite v = 28 e = 80 f = 14 degree seq :: [ 4^20, 10^8 ] E20.354 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2 * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3^4, (R * Y3)^2, Y2^5, Y2^-1 * Y3 * Y1 * Y3 * Y2 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 23, 63)(10, 50, 28, 68)(11, 51, 26, 66)(12, 52, 31, 71)(13, 53, 33, 73)(15, 55, 27, 67)(16, 56, 25, 65)(17, 57, 20, 60)(18, 58, 24, 64)(21, 61, 30, 70)(22, 62, 29, 69)(32, 72, 38, 78)(34, 74, 39, 79)(35, 75, 36, 76)(37, 77, 40, 80)(81, 121, 83, 123, 91, 131, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 106, 146, 89, 129)(84, 124, 95, 135, 108, 148, 109, 149, 92, 132)(86, 126, 98, 138, 103, 143, 110, 150, 93, 133)(88, 128, 104, 144, 99, 139, 113, 153, 101, 141)(90, 130, 107, 147, 94, 134, 111, 151, 102, 142)(96, 136, 112, 152, 119, 159, 117, 157, 115, 155)(105, 145, 116, 156, 120, 160, 114, 154, 118, 158) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 105)(9, 104)(10, 82)(11, 109)(12, 112)(13, 83)(14, 106)(15, 115)(16, 86)(17, 108)(18, 85)(19, 114)(20, 113)(21, 116)(22, 87)(23, 97)(24, 118)(25, 90)(26, 99)(27, 89)(28, 117)(29, 119)(30, 91)(31, 100)(32, 93)(33, 120)(34, 94)(35, 98)(36, 102)(37, 103)(38, 107)(39, 110)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E20.360 Graph:: simple bipartite v = 28 e = 80 f = 14 degree seq :: [ 4^20, 10^8 ] E20.355 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^4, Y2^5, Y3^-2 * Y1 * Y3^2 * Y1, Y3 * Y2^-2 * Y1 * Y3 * Y1, (Y3^-1 * Y2 * Y1)^2 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 14, 54)(5, 45, 9, 49)(6, 46, 19, 59)(8, 48, 24, 64)(10, 50, 29, 69)(11, 51, 21, 61)(12, 52, 32, 72)(13, 53, 26, 66)(15, 55, 25, 65)(16, 56, 23, 63)(17, 57, 27, 67)(18, 58, 37, 77)(20, 60, 30, 70)(22, 62, 36, 76)(28, 68, 31, 71)(33, 73, 38, 78)(34, 74, 39, 79)(35, 75, 40, 80)(81, 121, 83, 123, 91, 131, 97, 137, 85, 125)(82, 122, 87, 127, 101, 141, 107, 147, 89, 129)(84, 124, 92, 132, 111, 151, 109, 149, 96, 136)(86, 126, 93, 133, 104, 144, 116, 156, 98, 138)(88, 128, 102, 142, 117, 157, 99, 139, 106, 146)(90, 130, 103, 143, 94, 134, 112, 152, 108, 148)(95, 135, 100, 140, 113, 153, 119, 159, 115, 155)(105, 145, 110, 150, 118, 158, 114, 154, 120, 160) L = (1, 84)(2, 88)(3, 92)(4, 95)(5, 96)(6, 81)(7, 102)(8, 105)(9, 106)(10, 82)(11, 111)(12, 100)(13, 83)(14, 101)(15, 98)(16, 115)(17, 109)(18, 85)(19, 114)(20, 86)(21, 117)(22, 110)(23, 87)(24, 91)(25, 108)(26, 120)(27, 99)(28, 89)(29, 119)(30, 90)(31, 113)(32, 107)(33, 93)(34, 94)(35, 116)(36, 97)(37, 118)(38, 103)(39, 104)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E20.356 Graph:: simple bipartite v = 28 e = 80 f = 14 degree seq :: [ 4^20, 10^8 ] E20.356 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y3^2, R^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y2)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^4, Y2^-5 * Y3 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 11, 51, 18, 58, 8, 48)(4, 44, 14, 54, 19, 59, 9, 49)(6, 46, 16, 56, 20, 60, 10, 50)(12, 52, 21, 61, 31, 71, 25, 65)(13, 53, 22, 62, 32, 72, 26, 66)(15, 55, 23, 63, 33, 73, 29, 69)(17, 57, 24, 64, 34, 74, 30, 70)(27, 67, 37, 77, 39, 79, 35, 75)(28, 68, 38, 78, 40, 80, 36, 76)(81, 121, 83, 123, 92, 132, 107, 147, 95, 135, 84, 124, 93, 133, 108, 148, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 115, 155, 103, 143, 89, 129, 102, 142, 116, 156, 104, 144, 90, 130)(85, 125, 91, 131, 105, 145, 117, 157, 109, 149, 94, 134, 106, 146, 118, 158, 110, 150, 96, 136)(87, 127, 98, 138, 111, 151, 119, 159, 113, 153, 99, 139, 112, 152, 120, 160, 114, 154, 100, 140) L = (1, 84)(2, 89)(3, 93)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 106)(12, 108)(13, 83)(14, 85)(15, 86)(16, 109)(17, 107)(18, 112)(19, 87)(20, 113)(21, 116)(22, 88)(23, 90)(24, 115)(25, 118)(26, 91)(27, 97)(28, 92)(29, 96)(30, 117)(31, 120)(32, 98)(33, 100)(34, 119)(35, 104)(36, 101)(37, 110)(38, 105)(39, 114)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E20.355 Graph:: bipartite v = 14 e = 80 f = 28 degree seq :: [ 8^10, 20^4 ] E20.357 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y3 * Y2^-1 * Y3 * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1^-1)^2, Y1^4, (Y1^-1 * Y2^-1)^2, Y3 * Y2^-5 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 11, 51, 18, 58, 10, 50)(4, 44, 14, 54, 19, 59, 9, 49)(6, 46, 16, 56, 20, 60, 8, 48)(12, 52, 24, 64, 31, 71, 26, 66)(13, 53, 23, 63, 32, 72, 25, 65)(15, 55, 22, 62, 33, 73, 29, 69)(17, 57, 21, 61, 34, 74, 30, 70)(27, 67, 38, 78, 39, 79, 36, 76)(28, 68, 37, 77, 40, 80, 35, 75)(81, 121, 83, 123, 92, 132, 107, 147, 95, 135, 84, 124, 93, 133, 108, 148, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 115, 155, 103, 143, 89, 129, 102, 142, 116, 156, 104, 144, 90, 130)(85, 125, 96, 136, 110, 150, 117, 157, 105, 145, 94, 134, 109, 149, 118, 158, 106, 146, 91, 131)(87, 127, 98, 138, 111, 151, 119, 159, 113, 153, 99, 139, 112, 152, 120, 160, 114, 154, 100, 140) L = (1, 84)(2, 89)(3, 93)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 105)(12, 108)(13, 83)(14, 85)(15, 86)(16, 109)(17, 107)(18, 112)(19, 87)(20, 113)(21, 116)(22, 88)(23, 90)(24, 115)(25, 91)(26, 117)(27, 97)(28, 92)(29, 96)(30, 118)(31, 120)(32, 98)(33, 100)(34, 119)(35, 104)(36, 101)(37, 106)(38, 110)(39, 114)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E20.353 Graph:: bipartite v = 14 e = 80 f = 28 degree seq :: [ 8^10, 20^4 ] E20.358 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y1^-1 * Y2 * Y1^-1 * Y3^-1, Y1^4, Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y2^10, (Y3 * Y2^-1)^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 5, 45)(3, 43, 9, 49, 13, 53, 8, 48)(4, 44, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 36, 76, 33, 73)(28, 68, 31, 71, 37, 77, 35, 75)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 108, 148, 100, 140, 92, 132, 84, 124)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(85, 125, 91, 131, 99, 139, 107, 147, 115, 155, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134) L = (1, 84)(2, 88)(3, 81)(4, 92)(5, 89)(6, 94)(7, 82)(8, 96)(9, 97)(10, 83)(11, 85)(12, 100)(13, 86)(14, 102)(15, 87)(16, 104)(17, 105)(18, 90)(19, 91)(20, 108)(21, 93)(22, 110)(23, 95)(24, 112)(25, 113)(26, 98)(27, 99)(28, 114)(29, 101)(30, 117)(31, 103)(32, 118)(33, 119)(34, 106)(35, 107)(36, 109)(37, 120)(38, 111)(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, 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 E20.351 Graph:: bipartite v = 14 e = 80 f = 28 degree seq :: [ 8^10, 20^4 ] E20.359 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^-3 * Y3, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^-1 * Y3^-3 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 21, 61, 11, 51)(4, 44, 17, 57, 22, 62, 12, 52)(6, 46, 19, 59, 23, 63, 9, 49)(7, 47, 20, 60, 24, 64, 10, 50)(14, 54, 27, 67, 34, 74, 30, 70)(15, 55, 28, 68, 35, 75, 31, 71)(16, 56, 25, 65, 36, 76, 29, 69)(18, 58, 26, 66, 37, 77, 33, 73)(32, 72, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 94, 134, 84, 124, 95, 135, 112, 152, 98, 138, 87, 127, 96, 136, 86, 126)(82, 122, 89, 129, 105, 145, 90, 130, 106, 146, 118, 158, 108, 148, 92, 132, 107, 147, 91, 131)(85, 125, 99, 139, 109, 149, 100, 140, 113, 153, 119, 159, 111, 151, 97, 137, 110, 150, 93, 133)(88, 128, 101, 141, 114, 154, 102, 142, 115, 155, 120, 160, 117, 157, 104, 144, 116, 156, 103, 143) L = (1, 84)(2, 90)(3, 95)(4, 98)(5, 100)(6, 94)(7, 81)(8, 102)(9, 106)(10, 108)(11, 105)(12, 82)(13, 109)(14, 112)(15, 87)(16, 83)(17, 85)(18, 86)(19, 113)(20, 111)(21, 115)(22, 117)(23, 114)(24, 88)(25, 118)(26, 92)(27, 89)(28, 91)(29, 119)(30, 99)(31, 93)(32, 96)(33, 97)(34, 120)(35, 104)(36, 101)(37, 103)(38, 107)(39, 110)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E20.352 Graph:: bipartite v = 14 e = 80 f = 28 degree seq :: [ 8^10, 20^4 ] E20.360 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 5, 10}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2 * Y3^-1, (Y2 * Y1^-1)^2, (R * Y3)^2, Y1^4, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, Y2^-2 * Y3^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 21, 61, 11, 51)(4, 44, 17, 57, 22, 62, 12, 52)(6, 46, 19, 59, 23, 63, 9, 49)(7, 47, 20, 60, 24, 64, 10, 50)(14, 54, 26, 66, 34, 74, 30, 70)(15, 55, 25, 65, 35, 75, 31, 71)(16, 56, 28, 68, 36, 76, 29, 69)(18, 58, 27, 67, 37, 77, 33, 73)(32, 72, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 94, 134, 87, 127, 96, 136, 112, 152, 98, 138, 84, 124, 95, 135, 86, 126)(82, 122, 89, 129, 105, 145, 92, 132, 107, 147, 118, 158, 108, 148, 90, 130, 106, 146, 91, 131)(85, 125, 99, 139, 111, 151, 97, 137, 113, 153, 119, 159, 109, 149, 100, 140, 110, 150, 93, 133)(88, 128, 101, 141, 114, 154, 104, 144, 116, 156, 120, 160, 117, 157, 102, 142, 115, 155, 103, 143) L = (1, 84)(2, 90)(3, 95)(4, 96)(5, 100)(6, 98)(7, 81)(8, 102)(9, 106)(10, 107)(11, 108)(12, 82)(13, 109)(14, 86)(15, 112)(16, 83)(17, 85)(18, 87)(19, 110)(20, 113)(21, 115)(22, 116)(23, 117)(24, 88)(25, 91)(26, 118)(27, 89)(28, 92)(29, 97)(30, 119)(31, 93)(32, 94)(33, 99)(34, 103)(35, 120)(36, 101)(37, 104)(38, 105)(39, 111)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 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 E20.354 Graph:: bipartite v = 14 e = 80 f = 28 degree seq :: [ 8^10, 20^4 ] E20.361 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 20}) Quotient :: dipole Aut^+ = C5 : Q8 (small group id <40, 4>) Aut = (C20 x C2) : C2 (small group id <80, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^4 * Y2 * Y3^4 * Y2^-1, Y3^-10 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 5, 45)(4, 44, 7, 47)(6, 46, 8, 48)(9, 49, 13, 53)(10, 50, 12, 52)(11, 51, 15, 55)(14, 54, 16, 56)(17, 57, 21, 61)(18, 58, 20, 60)(19, 59, 23, 63)(22, 62, 24, 64)(25, 65, 29, 69)(26, 66, 28, 68)(27, 67, 31, 71)(30, 70, 32, 72)(33, 73, 37, 77)(34, 74, 36, 76)(35, 75, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 82, 122, 85, 125)(84, 124, 90, 130, 87, 127, 92, 132)(86, 126, 89, 129, 88, 128, 93, 133)(91, 131, 98, 138, 95, 135, 100, 140)(94, 134, 97, 137, 96, 136, 101, 141)(99, 139, 106, 146, 103, 143, 108, 148)(102, 142, 105, 145, 104, 144, 109, 149)(107, 147, 114, 154, 111, 151, 116, 156)(110, 150, 113, 153, 112, 152, 117, 157)(115, 155, 120, 160, 118, 158, 119, 159) L = (1, 84)(2, 87)(3, 89)(4, 91)(5, 93)(6, 81)(7, 95)(8, 82)(9, 97)(10, 83)(11, 99)(12, 85)(13, 101)(14, 86)(15, 103)(16, 88)(17, 105)(18, 90)(19, 107)(20, 92)(21, 109)(22, 94)(23, 111)(24, 96)(25, 113)(26, 98)(27, 115)(28, 100)(29, 117)(30, 102)(31, 118)(32, 104)(33, 119)(34, 106)(35, 112)(36, 108)(37, 120)(38, 110)(39, 116)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 40, 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E20.362 Graph:: bipartite v = 30 e = 80 f = 12 degree seq :: [ 4^20, 8^10 ] E20.362 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 20}) Quotient :: dipole Aut^+ = C5 : Q8 (small group id <40, 4>) Aut = (C20 x C2) : C2 (small group id <80, 38>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y2)^2, Y2 * Y3^-1 * Y1^2, Y3 * Y1^-1 * Y3 * Y1, Y2^-1 * Y3 * Y1^-2, (R * Y3)^2, (Y3, Y2^-1), Y2^2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, Y3^2 * Y2 * Y1 * Y2^3 * Y1^-1, Y3^-2 * Y2^-3 * Y3^-1 * Y2^-4 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 4, 44, 12, 52)(6, 46, 9, 49, 7, 47, 10, 50)(13, 53, 19, 59, 14, 54, 20, 60)(15, 55, 17, 57, 16, 56, 18, 58)(21, 61, 27, 67, 22, 62, 28, 68)(23, 63, 25, 65, 24, 64, 26, 66)(29, 69, 35, 75, 30, 70, 36, 76)(31, 71, 33, 73, 32, 72, 34, 74)(37, 77, 40, 80, 38, 78, 39, 79)(81, 121, 83, 123, 93, 133, 101, 141, 109, 149, 117, 157, 112, 152, 104, 144, 96, 136, 87, 127, 88, 128, 84, 124, 94, 134, 102, 142, 110, 150, 118, 158, 111, 151, 103, 143, 95, 135, 86, 126)(82, 122, 89, 129, 97, 137, 105, 145, 113, 153, 119, 159, 116, 156, 108, 148, 100, 140, 92, 132, 85, 125, 90, 130, 98, 138, 106, 146, 114, 154, 120, 160, 115, 155, 107, 147, 99, 139, 91, 131) L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 89)(6, 88)(7, 81)(8, 83)(9, 98)(10, 97)(11, 85)(12, 82)(13, 102)(14, 101)(15, 87)(16, 86)(17, 106)(18, 105)(19, 92)(20, 91)(21, 110)(22, 109)(23, 96)(24, 95)(25, 114)(26, 113)(27, 100)(28, 99)(29, 118)(30, 117)(31, 104)(32, 103)(33, 120)(34, 119)(35, 108)(36, 107)(37, 111)(38, 112)(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, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E20.361 Graph:: bipartite v = 12 e = 80 f = 30 degree seq :: [ 8^10, 40^2 ] E20.363 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 40, 40}) Quotient :: dipole Aut^+ = C40 (small group id <40, 2>) Aut = D80 (small group id <80, 7>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^20 * Y1, (Y3 * Y2^-1)^40 ] Map:: R = (1, 41, 2, 42)(3, 43, 5, 45)(4, 44, 6, 46)(7, 47, 9, 49)(8, 48, 10, 50)(11, 51, 13, 53)(12, 52, 14, 54)(15, 55, 17, 57)(16, 56, 18, 58)(19, 59, 21, 61)(20, 60, 22, 62)(23, 63, 25, 65)(24, 64, 26, 66)(27, 67, 29, 69)(28, 68, 30, 70)(31, 71, 33, 73)(32, 72, 34, 74)(35, 75, 37, 77)(36, 76, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 87, 127, 91, 131, 95, 135, 99, 139, 103, 143, 107, 147, 111, 151, 115, 155, 119, 159, 118, 158, 114, 154, 110, 150, 106, 146, 102, 142, 98, 138, 94, 134, 90, 130, 86, 126, 82, 122, 85, 125, 89, 129, 93, 133, 97, 137, 101, 141, 105, 145, 109, 149, 113, 153, 117, 157, 120, 160, 116, 156, 112, 152, 108, 148, 104, 144, 100, 140, 96, 136, 92, 132, 88, 128, 84, 124) 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, 80, 4, 80 ), ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 21 e = 80 f = 21 degree seq :: [ 4^20, 80 ] E20.364 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^20, (T2^-1 * T1^-1)^41 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(42, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 82, 81, 78, 77, 74, 73, 70, 69, 66, 65, 62, 61, 58, 57, 54, 53, 50, 49, 46, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.386 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.365 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T2^-20 * T1 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(42, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 67, 70, 71, 74, 75, 78, 79, 82, 80, 81, 76, 77, 72, 73, 68, 69, 64, 65, 60, 61, 56, 57, 52, 53, 48, 49, 44, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.383 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.366 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^13, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 40, 34, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 36, 41, 35, 29, 23, 17, 11, 5)(42, 43, 47, 44, 48, 53, 50, 54, 59, 56, 60, 65, 62, 66, 71, 68, 72, 77, 74, 78, 82, 80, 81, 76, 79, 75, 70, 73, 69, 64, 67, 63, 58, 61, 57, 52, 55, 51, 46, 49, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.388 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.367 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-13 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 36, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 34, 40, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 41, 35, 29, 23, 17, 11, 5)(42, 43, 47, 46, 49, 53, 52, 55, 59, 58, 61, 65, 64, 67, 71, 70, 73, 77, 76, 79, 80, 82, 81, 74, 78, 75, 68, 72, 69, 62, 66, 63, 56, 60, 57, 50, 54, 51, 44, 48, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.384 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.368 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^9, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 36, 28, 20, 12, 4, 10, 18, 26, 34, 40, 41, 35, 27, 19, 11, 6, 14, 22, 30, 38, 39, 32, 24, 16, 8, 2, 7, 15, 23, 31, 37, 29, 21, 13, 5)(42, 43, 47, 51, 44, 48, 55, 59, 50, 56, 63, 67, 58, 64, 71, 75, 66, 72, 79, 81, 74, 78, 80, 82, 77, 70, 73, 76, 69, 62, 65, 68, 61, 54, 57, 60, 53, 46, 49, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.390 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.369 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1 * T2 * T1^3, T2^-1 * T1 * T2^-9, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 38, 30, 22, 14, 6, 11, 19, 27, 35, 40, 41, 36, 28, 20, 12, 4, 10, 18, 26, 34, 37, 29, 21, 13, 5)(42, 43, 47, 53, 46, 49, 55, 61, 54, 57, 63, 69, 62, 65, 71, 77, 70, 73, 79, 82, 78, 74, 80, 81, 75, 66, 72, 76, 67, 58, 64, 68, 59, 50, 56, 60, 51, 44, 48, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.385 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.370 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T2 * T1 * T2^7, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 32, 22, 12, 4, 10, 20, 30, 38, 39, 31, 21, 11, 14, 24, 34, 40, 41, 36, 26, 16, 6, 15, 25, 35, 37, 28, 18, 8, 2, 7, 17, 27, 33, 23, 13, 5)(42, 43, 47, 55, 51, 44, 48, 56, 65, 61, 50, 58, 66, 75, 71, 60, 68, 76, 81, 79, 70, 74, 78, 82, 80, 73, 64, 69, 77, 72, 63, 54, 59, 67, 62, 53, 46, 49, 57, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.391 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.371 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^2 * T2^-1 * T1^-2, T1^5 * T2, T2^-8 * T1, T2^-1 * T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 28, 18, 8, 2, 7, 17, 27, 37, 36, 26, 16, 6, 15, 25, 35, 41, 40, 34, 24, 14, 11, 21, 31, 38, 39, 32, 22, 12, 4, 10, 20, 30, 33, 23, 13, 5)(42, 43, 47, 55, 53, 46, 49, 57, 65, 63, 54, 59, 67, 75, 73, 64, 69, 77, 81, 80, 74, 70, 78, 82, 79, 71, 60, 68, 76, 72, 61, 50, 58, 66, 62, 51, 44, 48, 56, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.387 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.372 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-1 * T1^6, T2^6 * T1^-1 * T2, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 19, 30, 18, 8, 2, 7, 17, 29, 38, 28, 16, 6, 15, 27, 37, 40, 33, 22, 14, 26, 36, 41, 34, 23, 11, 21, 32, 39, 35, 24, 12, 4, 10, 20, 31, 25, 13, 5)(42, 43, 47, 55, 62, 51, 44, 48, 56, 67, 73, 61, 50, 58, 68, 77, 80, 72, 60, 70, 78, 82, 76, 66, 71, 79, 81, 75, 65, 54, 59, 69, 74, 64, 53, 46, 49, 57, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.392 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.373 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-1 * T1^2 * T2 * T1^-2, T1^3 * T2 * T1^3, T2^-5 * T1^-1 * 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 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 24, 12, 4, 10, 20, 32, 39, 35, 23, 11, 21, 33, 40, 36, 26, 14, 22, 34, 41, 38, 28, 16, 6, 15, 27, 37, 30, 18, 8, 2, 7, 17, 29, 25, 13, 5)(42, 43, 47, 55, 64, 53, 46, 49, 57, 67, 76, 65, 54, 59, 69, 77, 80, 72, 66, 71, 79, 81, 73, 60, 70, 78, 82, 74, 61, 50, 58, 68, 75, 62, 51, 44, 48, 56, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.389 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.374 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-2 * T2, T2^4 * T1^5, T2^-1 * T1 * T2^-1 * T1^2 * T2^-3 * T1, T2^41, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 26, 40, 24, 12, 4, 10, 20, 34, 28, 14, 27, 39, 23, 11, 21, 35, 30, 16, 6, 15, 29, 38, 22, 36, 32, 18, 8, 2, 7, 17, 31, 37, 41, 25, 13, 5)(42, 43, 47, 55, 67, 82, 77, 62, 51, 44, 48, 56, 68, 81, 66, 73, 76, 61, 50, 58, 70, 80, 65, 54, 59, 71, 75, 60, 72, 79, 64, 53, 46, 49, 57, 69, 74, 78, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.393 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.375 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T1^-1 * T2 * T1^-1 * T2^3 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-7 * T2^-1, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 36, 38, 41, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 35, 39, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 37, 34, 40, 31, 22, 25, 13, 5)(42, 43, 47, 55, 67, 75, 82, 74, 66, 62, 51, 44, 48, 56, 68, 76, 81, 73, 65, 54, 59, 61, 50, 58, 69, 77, 80, 72, 64, 53, 46, 49, 57, 60, 70, 78, 79, 71, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.397 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.376 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1^-1, T2^-1), T2^3 * T1 * T2 * T1^2, T1^-8 * T2^3, T2^11 * T1^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 32, 39, 34, 37, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 33, 40, 35, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 38, 41, 36, 27, 14, 25, 13, 5)(42, 43, 47, 55, 67, 75, 79, 71, 60, 64, 53, 46, 49, 57, 68, 76, 80, 72, 61, 50, 58, 65, 54, 59, 69, 77, 81, 73, 62, 51, 44, 48, 56, 66, 70, 78, 82, 74, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.394 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.377 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2, T1), (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T2^3 * T1^-2 * T2^4, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-2 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 30, 16, 6, 15, 29, 22, 36, 41, 38, 26, 24, 12, 4, 10, 20, 34, 32, 18, 8, 2, 7, 17, 31, 40, 39, 28, 14, 27, 23, 11, 21, 35, 37, 25, 13, 5)(42, 43, 47, 55, 67, 66, 73, 74, 81, 77, 62, 51, 44, 48, 56, 68, 65, 54, 59, 71, 80, 82, 76, 61, 50, 58, 70, 64, 53, 46, 49, 57, 69, 79, 78, 75, 60, 72, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.398 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.378 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2 * T1^-1 * T2^2 * T1^-2, T1 * T2 * T1 * T2^6, T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 35, 23, 11, 21, 28, 14, 27, 39, 40, 32, 18, 8, 2, 7, 17, 31, 36, 24, 12, 4, 10, 20, 26, 38, 41, 34, 22, 30, 16, 6, 15, 29, 37, 25, 13, 5)(42, 43, 47, 55, 67, 60, 72, 78, 81, 75, 64, 53, 46, 49, 57, 69, 61, 50, 58, 70, 80, 82, 76, 65, 54, 59, 71, 62, 51, 44, 48, 56, 68, 79, 74, 77, 66, 73, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.395 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.379 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T2 * T1 * T2^2 * T1, T1^-5 * T2 * T1^-8, T1^-1 * T2^19 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 30, 35, 37, 38, 40, 33, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 36, 41, 39, 32, 34, 27, 20, 22, 15, 6, 13, 5)(42, 43, 47, 55, 61, 67, 73, 79, 77, 71, 65, 59, 51, 44, 48, 54, 57, 63, 69, 75, 81, 82, 76, 70, 64, 58, 50, 53, 46, 49, 56, 62, 68, 74, 80, 78, 72, 66, 60, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.399 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.380 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^2 * T1^-1, T1^-4 * T2^-1 * T1^-9, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 34, 32, 39, 41, 36, 29, 31, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 33, 40, 38, 35, 37, 30, 23, 25, 18, 11, 13, 5)(42, 43, 47, 55, 61, 67, 73, 79, 77, 71, 65, 59, 53, 46, 49, 50, 57, 63, 69, 75, 81, 82, 78, 72, 66, 60, 54, 51, 44, 48, 56, 62, 68, 74, 80, 76, 70, 64, 58, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.396 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.381 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T1^-1 * T2^-1 * T1^-1 * T2^-4, T2^2 * T1^-1 * T2 * T1^-6, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-3 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 23, 11, 21, 32, 36, 41, 34, 39, 28, 14, 27, 30, 18, 8, 2, 7, 17, 24, 12, 4, 10, 20, 31, 35, 22, 33, 38, 26, 37, 40, 29, 16, 6, 15, 25, 13, 5)(42, 43, 47, 55, 67, 77, 72, 60, 65, 54, 59, 70, 80, 74, 62, 51, 44, 48, 56, 68, 78, 82, 76, 64, 53, 46, 49, 57, 69, 79, 73, 61, 50, 58, 66, 71, 81, 75, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.401 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.382 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {41, 41, 41}) Quotient :: edge Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-4 * T1, T1^3 * T2^-3 * T1^-1 * T2^-2, T2^-1 * T1^-1 * T2^-1 * T1^-6 * T2^-1, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 29, 40, 38, 26, 37, 33, 22, 31, 35, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 30, 28, 14, 27, 39, 32, 41, 36, 34, 23, 11, 21, 25, 13, 5)(42, 43, 47, 55, 67, 77, 76, 66, 61, 50, 58, 70, 80, 74, 64, 53, 46, 49, 57, 69, 79, 82, 72, 62, 51, 44, 48, 56, 68, 78, 75, 65, 54, 59, 60, 71, 81, 73, 63, 52, 45) L = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.400 Transitivity :: ET+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.383 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1, (F * T1)^2, (F * T2)^2, T2^41, T1^41, (T2^-1 * T1^-1)^41 ] Map:: non-degenerate R = (1, 42, 2, 43, 6, 47, 14, 55, 26, 67, 34, 75, 41, 82, 33, 74, 25, 66, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 27, 68, 35, 76, 40, 81, 32, 73, 24, 65, 13, 54, 18, 59, 20, 61, 9, 50, 17, 58, 28, 69, 36, 77, 39, 80, 31, 72, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 19, 60, 29, 70, 37, 78, 38, 79, 30, 71, 22, 63, 11, 52, 4, 45) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 67)(15, 68)(16, 60)(17, 69)(18, 61)(19, 70)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 62)(26, 75)(27, 76)(28, 77)(29, 78)(30, 63)(31, 64)(32, 65)(33, 66)(34, 82)(35, 81)(36, 80)(37, 79)(38, 71)(39, 72)(40, 73)(41, 74) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.365 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.384 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^20, (T2^-1 * T1^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 7, 48, 11, 52, 15, 56, 19, 60, 23, 64, 27, 68, 31, 72, 35, 76, 39, 80, 40, 81, 36, 77, 32, 73, 28, 69, 24, 65, 20, 61, 16, 57, 12, 53, 8, 49, 4, 45, 2, 43, 6, 47, 10, 51, 14, 55, 18, 59, 22, 63, 26, 67, 30, 71, 34, 75, 38, 79, 41, 82, 37, 78, 33, 74, 29, 70, 25, 66, 21, 62, 17, 58, 13, 54, 9, 50, 5, 46) L = (1, 43)(2, 44)(3, 47)(4, 42)(5, 45)(6, 48)(7, 51)(8, 46)(9, 49)(10, 52)(11, 55)(12, 50)(13, 53)(14, 56)(15, 59)(16, 54)(17, 57)(18, 60)(19, 63)(20, 58)(21, 61)(22, 64)(23, 67)(24, 62)(25, 65)(26, 68)(27, 71)(28, 66)(29, 69)(30, 72)(31, 75)(32, 70)(33, 73)(34, 76)(35, 79)(36, 74)(37, 77)(38, 80)(39, 82)(40, 78)(41, 81) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.367 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.385 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^13, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 15, 56, 21, 62, 27, 68, 33, 74, 39, 80, 38, 79, 32, 73, 26, 67, 20, 61, 14, 55, 8, 49, 2, 43, 7, 48, 13, 54, 19, 60, 25, 66, 31, 72, 37, 78, 40, 81, 34, 75, 28, 69, 22, 63, 16, 57, 10, 51, 4, 45, 6, 47, 12, 53, 18, 59, 24, 65, 30, 71, 36, 77, 41, 82, 35, 76, 29, 70, 23, 64, 17, 58, 11, 52, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 44)(7, 53)(8, 45)(9, 54)(10, 46)(11, 55)(12, 50)(13, 59)(14, 51)(15, 60)(16, 52)(17, 61)(18, 56)(19, 65)(20, 57)(21, 66)(22, 58)(23, 67)(24, 62)(25, 71)(26, 63)(27, 72)(28, 64)(29, 73)(30, 68)(31, 77)(32, 69)(33, 78)(34, 70)(35, 79)(36, 74)(37, 82)(38, 75)(39, 81)(40, 76)(41, 80) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.369 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.386 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-13 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 15, 56, 21, 62, 27, 68, 33, 74, 39, 80, 36, 77, 30, 71, 24, 65, 18, 59, 12, 53, 6, 47, 4, 45, 10, 51, 16, 57, 22, 63, 28, 69, 34, 75, 40, 81, 38, 79, 32, 73, 26, 67, 20, 61, 14, 55, 8, 49, 2, 43, 7, 48, 13, 54, 19, 60, 25, 66, 31, 72, 37, 78, 41, 82, 35, 76, 29, 70, 23, 64, 17, 58, 11, 52, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 46)(7, 45)(8, 53)(9, 54)(10, 44)(11, 55)(12, 52)(13, 51)(14, 59)(15, 60)(16, 50)(17, 61)(18, 58)(19, 57)(20, 65)(21, 66)(22, 56)(23, 67)(24, 64)(25, 63)(26, 71)(27, 72)(28, 62)(29, 73)(30, 70)(31, 69)(32, 77)(33, 78)(34, 68)(35, 79)(36, 76)(37, 75)(38, 80)(39, 82)(40, 74)(41, 81) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.364 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.387 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^9, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 17, 58, 25, 66, 33, 74, 36, 77, 28, 69, 20, 61, 12, 53, 4, 45, 10, 51, 18, 59, 26, 67, 34, 75, 40, 81, 41, 82, 35, 76, 27, 68, 19, 60, 11, 52, 6, 47, 14, 55, 22, 63, 30, 71, 38, 79, 39, 80, 32, 73, 24, 65, 16, 57, 8, 49, 2, 43, 7, 48, 15, 56, 23, 64, 31, 72, 37, 78, 29, 70, 21, 62, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 51)(7, 55)(8, 52)(9, 56)(10, 44)(11, 45)(12, 46)(13, 57)(14, 59)(15, 63)(16, 60)(17, 64)(18, 50)(19, 53)(20, 54)(21, 65)(22, 67)(23, 71)(24, 68)(25, 72)(26, 58)(27, 61)(28, 62)(29, 73)(30, 75)(31, 79)(32, 76)(33, 78)(34, 66)(35, 69)(36, 70)(37, 80)(38, 81)(39, 82)(40, 74)(41, 77) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.371 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.388 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1 * T2 * T1^3, T2^-1 * T1 * T2^-9, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 17, 58, 25, 66, 33, 74, 32, 73, 24, 65, 16, 57, 8, 49, 2, 43, 7, 48, 15, 56, 23, 64, 31, 72, 39, 80, 38, 79, 30, 71, 22, 63, 14, 55, 6, 47, 11, 52, 19, 60, 27, 68, 35, 76, 40, 81, 41, 82, 36, 77, 28, 69, 20, 61, 12, 53, 4, 45, 10, 51, 18, 59, 26, 67, 34, 75, 37, 78, 29, 70, 21, 62, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 53)(7, 52)(8, 55)(9, 56)(10, 44)(11, 45)(12, 46)(13, 57)(14, 61)(15, 60)(16, 63)(17, 64)(18, 50)(19, 51)(20, 54)(21, 65)(22, 69)(23, 68)(24, 71)(25, 72)(26, 58)(27, 59)(28, 62)(29, 73)(30, 77)(31, 76)(32, 79)(33, 80)(34, 66)(35, 67)(36, 70)(37, 74)(38, 82)(39, 81)(40, 75)(41, 78) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.366 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.389 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T2 * T1 * T2^7, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 29, 70, 32, 73, 22, 63, 12, 53, 4, 45, 10, 51, 20, 61, 30, 71, 38, 79, 39, 80, 31, 72, 21, 62, 11, 52, 14, 55, 24, 65, 34, 75, 40, 81, 41, 82, 36, 77, 26, 67, 16, 57, 6, 47, 15, 56, 25, 66, 35, 76, 37, 78, 28, 69, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 27, 68, 33, 74, 23, 64, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 51)(15, 65)(16, 52)(17, 66)(18, 67)(19, 68)(20, 50)(21, 53)(22, 54)(23, 69)(24, 61)(25, 75)(26, 62)(27, 76)(28, 77)(29, 74)(30, 60)(31, 63)(32, 64)(33, 78)(34, 71)(35, 81)(36, 72)(37, 82)(38, 70)(39, 73)(40, 79)(41, 80) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.373 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.390 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^2 * T2^-1 * T1^-2, T1^5 * T2, T2^-8 * T1, T2^-1 * T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 29, 70, 28, 69, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 27, 68, 37, 78, 36, 77, 26, 67, 16, 57, 6, 47, 15, 56, 25, 66, 35, 76, 41, 82, 40, 81, 34, 75, 24, 65, 14, 55, 11, 52, 21, 62, 31, 72, 38, 79, 39, 80, 32, 73, 22, 63, 12, 53, 4, 45, 10, 51, 20, 61, 30, 71, 33, 74, 23, 64, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 53)(15, 52)(16, 65)(17, 66)(18, 67)(19, 68)(20, 50)(21, 51)(22, 54)(23, 69)(24, 63)(25, 62)(26, 75)(27, 76)(28, 77)(29, 78)(30, 60)(31, 61)(32, 64)(33, 70)(34, 73)(35, 72)(36, 81)(37, 82)(38, 71)(39, 74)(40, 80)(41, 79) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.368 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.391 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-1 * T1^2 * T2 * T1^-2, T1^3 * T2 * T1^3, T2^-5 * T1^-1 * 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 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^3 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 31, 72, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 32, 73, 39, 80, 35, 76, 23, 64, 11, 52, 21, 62, 33, 74, 40, 81, 36, 77, 26, 67, 14, 55, 22, 63, 34, 75, 41, 82, 38, 79, 28, 69, 16, 57, 6, 47, 15, 56, 27, 68, 37, 78, 30, 71, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 29, 70, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 64)(15, 63)(16, 67)(17, 68)(18, 69)(19, 70)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 71)(26, 76)(27, 75)(28, 77)(29, 78)(30, 79)(31, 66)(32, 60)(33, 61)(34, 62)(35, 65)(36, 80)(37, 82)(38, 81)(39, 72)(40, 73)(41, 74) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.370 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.392 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-4 * T1^-1 * T2^-2, T1^-1 * T2^-1 * T1^-6, T1^2 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-3 * T1, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 32, 73, 35, 76, 23, 64, 11, 52, 21, 62, 33, 74, 40, 81, 36, 77, 26, 67, 22, 63, 34, 75, 41, 82, 38, 79, 28, 69, 14, 55, 27, 68, 37, 78, 39, 80, 30, 71, 16, 57, 6, 47, 15, 56, 29, 70, 31, 72, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 67)(15, 68)(16, 69)(17, 70)(18, 71)(19, 66)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 72)(26, 64)(27, 63)(28, 77)(29, 78)(30, 79)(31, 80)(32, 60)(33, 61)(34, 62)(35, 65)(36, 76)(37, 75)(38, 81)(39, 82)(40, 73)(41, 74) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.372 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.393 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-2 * T1 * T2^2, T2 * T1 * T2^4, T1 * T2^-1 * T1^7, T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 12, 53, 4, 45, 10, 51, 20, 61, 29, 70, 23, 64, 11, 52, 21, 62, 30, 71, 37, 78, 33, 74, 22, 63, 31, 72, 38, 79, 41, 82, 39, 80, 32, 73, 24, 65, 34, 75, 40, 81, 36, 77, 26, 67, 14, 55, 25, 66, 35, 76, 28, 69, 16, 57, 6, 47, 15, 56, 27, 68, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 65)(15, 66)(16, 67)(17, 68)(18, 69)(19, 54)(20, 50)(21, 51)(22, 52)(23, 53)(24, 72)(25, 75)(26, 73)(27, 76)(28, 77)(29, 60)(30, 61)(31, 62)(32, 63)(33, 64)(34, 79)(35, 81)(36, 80)(37, 70)(38, 71)(39, 74)(40, 82)(41, 78) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.374 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.394 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1), T2 * T1 * T2^3, T1^-1 * T2 * T1^-9, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 12, 53, 4, 45, 10, 51, 18, 59, 21, 62, 11, 52, 19, 60, 26, 67, 29, 70, 20, 61, 27, 68, 34, 75, 37, 78, 28, 69, 35, 76, 40, 81, 41, 82, 36, 77, 30, 71, 38, 79, 39, 80, 32, 73, 22, 63, 31, 72, 33, 74, 24, 65, 14, 55, 23, 64, 25, 66, 16, 57, 6, 47, 15, 56, 17, 58, 8, 49, 2, 43, 7, 48, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 54)(10, 44)(11, 45)(12, 46)(13, 58)(14, 63)(15, 64)(16, 65)(17, 66)(18, 50)(19, 51)(20, 52)(21, 53)(22, 71)(23, 72)(24, 73)(25, 74)(26, 59)(27, 60)(28, 61)(29, 62)(30, 76)(31, 79)(32, 77)(33, 80)(34, 67)(35, 68)(36, 69)(37, 70)(38, 81)(39, 82)(40, 75)(41, 78) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.376 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.395 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T1^-1 * T2 * T1^-1 * T2^3 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-7 * T2^-1, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 14, 55, 27, 68, 36, 77, 38, 79, 41, 82, 32, 73, 23, 64, 11, 52, 21, 62, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 29, 70, 26, 67, 35, 76, 39, 80, 30, 71, 33, 74, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 16, 57, 6, 47, 15, 56, 28, 69, 37, 78, 34, 75, 40, 81, 31, 72, 22, 63, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 67)(15, 68)(16, 60)(17, 69)(18, 61)(19, 70)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 62)(26, 75)(27, 76)(28, 77)(29, 78)(30, 63)(31, 64)(32, 65)(33, 66)(34, 82)(35, 81)(36, 80)(37, 79)(38, 71)(39, 72)(40, 73)(41, 74) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.378 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.396 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2, T1), (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T2^3 * T1^-2 * T2^4, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-2 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 33, 74, 30, 71, 16, 57, 6, 47, 15, 56, 29, 70, 22, 63, 36, 77, 41, 82, 38, 79, 26, 67, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 34, 75, 32, 73, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 31, 72, 40, 81, 39, 80, 28, 69, 14, 55, 27, 68, 23, 64, 11, 52, 21, 62, 35, 76, 37, 78, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 67)(15, 68)(16, 69)(17, 70)(18, 71)(19, 72)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 73)(26, 66)(27, 65)(28, 79)(29, 64)(30, 80)(31, 63)(32, 74)(33, 81)(34, 60)(35, 61)(36, 62)(37, 75)(38, 78)(39, 82)(40, 77)(41, 76) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.380 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.397 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2 * T1^-1 * T2^2 * T1^-2, T1 * T2 * T1 * T2^6, T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^4 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 33, 74, 35, 76, 23, 64, 11, 52, 21, 62, 28, 69, 14, 55, 27, 68, 39, 80, 40, 81, 32, 73, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 31, 72, 36, 77, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 26, 67, 38, 79, 41, 82, 34, 75, 22, 63, 30, 71, 16, 57, 6, 47, 15, 56, 29, 70, 37, 78, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 67)(15, 68)(16, 69)(17, 70)(18, 71)(19, 72)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 73)(26, 60)(27, 79)(28, 61)(29, 80)(30, 62)(31, 78)(32, 63)(33, 77)(34, 64)(35, 65)(36, 66)(37, 81)(38, 74)(39, 82)(40, 75)(41, 76) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.375 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.398 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^2 * T1^-1, T1^-4 * T2^-1 * T1^-9, (T1^-1 * T2^-1)^41 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 6, 47, 15, 56, 22, 63, 20, 61, 27, 68, 34, 75, 32, 73, 39, 80, 41, 82, 36, 77, 29, 70, 31, 72, 24, 65, 17, 58, 19, 60, 12, 53, 4, 45, 10, 51, 8, 49, 2, 43, 7, 48, 16, 57, 14, 55, 21, 62, 28, 69, 26, 67, 33, 74, 40, 81, 38, 79, 35, 76, 37, 78, 30, 71, 23, 64, 25, 66, 18, 59, 11, 52, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 50)(9, 57)(10, 44)(11, 45)(12, 46)(13, 51)(14, 61)(15, 62)(16, 63)(17, 52)(18, 53)(19, 54)(20, 67)(21, 68)(22, 69)(23, 58)(24, 59)(25, 60)(26, 73)(27, 74)(28, 75)(29, 64)(30, 65)(31, 66)(32, 79)(33, 80)(34, 81)(35, 70)(36, 71)(37, 72)(38, 77)(39, 76)(40, 82)(41, 78) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.377 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.399 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^-13 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 4, 45, 10, 51, 15, 56, 11, 52, 16, 57, 21, 62, 17, 58, 22, 63, 27, 68, 23, 64, 28, 69, 33, 74, 29, 70, 34, 75, 39, 80, 35, 76, 40, 81, 36, 77, 41, 82, 38, 79, 30, 71, 37, 78, 32, 73, 24, 65, 31, 72, 26, 67, 18, 59, 25, 66, 20, 61, 12, 53, 19, 60, 14, 55, 6, 47, 13, 54, 8, 49, 2, 43, 7, 48, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 53)(7, 54)(8, 55)(9, 46)(10, 44)(11, 45)(12, 59)(13, 60)(14, 61)(15, 50)(16, 51)(17, 52)(18, 65)(19, 66)(20, 67)(21, 56)(22, 57)(23, 58)(24, 71)(25, 72)(26, 73)(27, 62)(28, 63)(29, 64)(30, 77)(31, 78)(32, 79)(33, 68)(34, 69)(35, 70)(36, 80)(37, 82)(38, 81)(39, 74)(40, 75)(41, 76) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.379 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.400 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-3 * T2 * T1^-1 * T2^2, T1^-1 * T2^-1 * T1^-1 * T2^-7 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 29, 70, 37, 78, 38, 79, 30, 71, 22, 63, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 28, 69, 36, 77, 39, 80, 31, 72, 23, 64, 11, 52, 21, 62, 16, 57, 6, 47, 15, 56, 27, 68, 35, 76, 40, 81, 32, 73, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 14, 55, 26, 67, 34, 75, 41, 82, 33, 74, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 60)(15, 67)(16, 61)(17, 68)(18, 62)(19, 69)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 63)(26, 70)(27, 75)(28, 76)(29, 77)(30, 64)(31, 65)(32, 66)(33, 71)(34, 78)(35, 82)(36, 81)(37, 80)(38, 72)(39, 73)(40, 74)(41, 79) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.382 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.401 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {41, 41, 41}) Quotient :: loop Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2, T1^-1), (F * T1)^2, T1^-1 * T2^-1 * T1^-1 * T2^-4 * T1^-1, T1^3 * T2^-2 * T1^4, T2^-1 * T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^3 * T1^-2 ] Map:: non-degenerate R = (1, 42, 3, 44, 9, 50, 19, 60, 33, 74, 22, 63, 36, 77, 26, 67, 38, 79, 32, 73, 18, 59, 8, 49, 2, 43, 7, 48, 17, 58, 31, 72, 23, 64, 11, 52, 21, 62, 35, 76, 41, 82, 39, 80, 30, 71, 16, 57, 6, 47, 15, 56, 29, 70, 24, 65, 12, 53, 4, 45, 10, 51, 20, 61, 34, 75, 40, 81, 37, 78, 28, 69, 14, 55, 27, 68, 25, 66, 13, 54, 5, 46) L = (1, 43)(2, 47)(3, 48)(4, 42)(5, 49)(6, 55)(7, 56)(8, 57)(9, 58)(10, 44)(11, 45)(12, 46)(13, 59)(14, 67)(15, 68)(16, 69)(17, 70)(18, 71)(19, 72)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 73)(26, 76)(27, 79)(28, 77)(29, 66)(30, 78)(31, 65)(32, 80)(33, 64)(34, 60)(35, 61)(36, 62)(37, 63)(38, 82)(39, 81)(40, 74)(41, 75) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.381 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.402 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^20 * Y2, Y2 * Y1^-20 ] Map:: R = (1, 42, 2, 43, 6, 47, 10, 51, 14, 55, 18, 59, 22, 63, 26, 67, 30, 71, 34, 75, 38, 79, 40, 81, 36, 77, 32, 73, 28, 69, 24, 65, 20, 61, 16, 57, 12, 53, 8, 49, 3, 44, 5, 46, 7, 48, 11, 52, 15, 56, 19, 60, 23, 64, 27, 68, 31, 72, 35, 76, 39, 80, 41, 82, 37, 78, 33, 74, 29, 70, 25, 66, 21, 62, 17, 58, 13, 54, 9, 50, 4, 45)(83, 124, 85, 126, 86, 127, 90, 131, 91, 132, 94, 135, 95, 136, 98, 139, 99, 140, 102, 143, 103, 144, 106, 147, 107, 148, 110, 151, 111, 152, 114, 155, 115, 156, 118, 159, 119, 160, 122, 163, 123, 164, 120, 161, 121, 162, 116, 157, 117, 158, 112, 153, 113, 154, 108, 149, 109, 150, 104, 145, 105, 146, 100, 141, 101, 142, 96, 137, 97, 138, 92, 133, 93, 134, 88, 129, 89, 130, 84, 125, 87, 128) L = (1, 86)(2, 83)(3, 90)(4, 91)(5, 85)(6, 84)(7, 87)(8, 94)(9, 95)(10, 88)(11, 89)(12, 98)(13, 99)(14, 92)(15, 93)(16, 102)(17, 103)(18, 96)(19, 97)(20, 106)(21, 107)(22, 100)(23, 101)(24, 110)(25, 111)(26, 104)(27, 105)(28, 114)(29, 115)(30, 108)(31, 109)(32, 118)(33, 119)(34, 112)(35, 113)(36, 122)(37, 123)(38, 116)(39, 117)(40, 120)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.421 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.403 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2^-1 * Y3^9 * Y2^-1 * Y3^-10, Y1^10 * Y2 * Y1 * Y3^-9, Y2 * Y3^-20, (Y3 * Y2^-1)^41 ] Map:: R = (1, 42, 2, 43, 6, 47, 10, 51, 14, 55, 18, 59, 22, 63, 26, 67, 30, 71, 34, 75, 38, 79, 41, 82, 37, 78, 33, 74, 29, 70, 25, 66, 21, 62, 17, 58, 13, 54, 9, 50, 5, 46, 3, 44, 7, 48, 11, 52, 15, 56, 19, 60, 23, 64, 27, 68, 31, 72, 35, 76, 39, 80, 40, 81, 36, 77, 32, 73, 28, 69, 24, 65, 20, 61, 16, 57, 12, 53, 8, 49, 4, 45)(83, 124, 85, 126, 84, 125, 89, 130, 88, 129, 93, 134, 92, 133, 97, 138, 96, 137, 101, 142, 100, 141, 105, 146, 104, 145, 109, 150, 108, 149, 113, 154, 112, 153, 117, 158, 116, 157, 121, 162, 120, 161, 122, 163, 123, 164, 118, 159, 119, 160, 114, 155, 115, 156, 110, 151, 111, 152, 106, 147, 107, 148, 102, 143, 103, 144, 98, 139, 99, 140, 94, 135, 95, 136, 90, 131, 91, 132, 86, 127, 87, 128) L = (1, 86)(2, 83)(3, 87)(4, 90)(5, 91)(6, 84)(7, 85)(8, 94)(9, 95)(10, 88)(11, 89)(12, 98)(13, 99)(14, 92)(15, 93)(16, 102)(17, 103)(18, 96)(19, 97)(20, 106)(21, 107)(22, 100)(23, 101)(24, 110)(25, 111)(26, 104)(27, 105)(28, 114)(29, 115)(30, 108)(31, 109)(32, 118)(33, 119)(34, 112)(35, 113)(36, 122)(37, 123)(38, 116)(39, 117)(40, 121)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.433 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2^-3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^6 * Y2^-2 * Y3^-7, Y1^-1 * Y2^-1 * Y1^-13, Y1^-1 * Y2^-1 * Y3^5 * Y2^2 * Y3^5 * Y2^2 * Y3^5 * Y2^2 * Y3^5 * Y2^2 * Y3^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 42, 2, 43, 6, 47, 12, 53, 18, 59, 24, 65, 30, 71, 36, 77, 39, 80, 33, 74, 27, 68, 21, 62, 15, 56, 9, 50, 5, 46, 8, 49, 14, 55, 20, 61, 26, 67, 32, 73, 38, 79, 40, 81, 34, 75, 28, 69, 22, 63, 16, 57, 10, 51, 3, 44, 7, 48, 13, 54, 19, 60, 25, 66, 31, 72, 37, 78, 41, 82, 35, 76, 29, 70, 23, 64, 17, 58, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 86, 127, 92, 133, 97, 138, 93, 134, 98, 139, 103, 144, 99, 140, 104, 145, 109, 150, 105, 146, 110, 151, 115, 156, 111, 152, 116, 157, 121, 162, 117, 158, 122, 163, 118, 159, 123, 164, 120, 161, 112, 153, 119, 160, 114, 155, 106, 147, 113, 154, 108, 149, 100, 141, 107, 148, 102, 143, 94, 135, 101, 142, 96, 137, 88, 129, 95, 136, 90, 131, 84, 125, 89, 130, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 91)(6, 84)(7, 85)(8, 87)(9, 97)(10, 98)(11, 99)(12, 88)(13, 89)(14, 90)(15, 103)(16, 104)(17, 105)(18, 94)(19, 95)(20, 96)(21, 109)(22, 110)(23, 111)(24, 100)(25, 101)(26, 102)(27, 115)(28, 116)(29, 117)(30, 106)(31, 107)(32, 108)(33, 121)(34, 122)(35, 123)(36, 112)(37, 113)(38, 114)(39, 118)(40, 120)(41, 119)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.439 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, Y2^-2 * Y3^-1 * Y2^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, Y2^-1 * Y1^5 * Y3^-2 * Y1^7, Y3^-1 * Y1 * Y2 * Y3^6 * Y2 * Y3^6 * Y2 * Y3^5 * Y2, (Y3 * Y2^-1)^41 ] Map:: R = (1, 42, 2, 43, 6, 47, 12, 53, 18, 59, 24, 65, 30, 71, 36, 77, 39, 80, 33, 74, 27, 68, 21, 62, 15, 56, 9, 50, 3, 44, 7, 48, 13, 54, 19, 60, 25, 66, 31, 72, 37, 78, 41, 82, 35, 76, 29, 70, 23, 64, 17, 58, 11, 52, 5, 46, 8, 49, 14, 55, 20, 61, 26, 67, 32, 73, 38, 79, 40, 81, 34, 75, 28, 69, 22, 63, 16, 57, 10, 51, 4, 45)(83, 124, 85, 126, 90, 131, 84, 125, 89, 130, 96, 137, 88, 129, 95, 136, 102, 143, 94, 135, 101, 142, 108, 149, 100, 141, 107, 148, 114, 155, 106, 147, 113, 154, 120, 161, 112, 153, 119, 160, 122, 163, 118, 159, 123, 164, 116, 157, 121, 162, 117, 158, 110, 151, 115, 156, 111, 152, 104, 145, 109, 150, 105, 146, 98, 139, 103, 144, 99, 140, 92, 133, 97, 138, 93, 134, 86, 127, 91, 132, 87, 128) L = (1, 86)(2, 83)(3, 91)(4, 92)(5, 93)(6, 84)(7, 85)(8, 87)(9, 97)(10, 98)(11, 99)(12, 88)(13, 89)(14, 90)(15, 103)(16, 104)(17, 105)(18, 94)(19, 95)(20, 96)(21, 109)(22, 110)(23, 111)(24, 100)(25, 101)(26, 102)(27, 115)(28, 116)(29, 117)(30, 106)(31, 107)(32, 108)(33, 121)(34, 122)(35, 123)(36, 112)(37, 113)(38, 114)(39, 118)(40, 120)(41, 119)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.430 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (Y2^-1, Y1), (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^2 * Y3^-1 * Y2^2, Y1^-10 * Y2, Y2 * Y3^3 * Y2 * Y3^4 * Y2 * Y3^4 * Y2 * Y3^4 * Y2 * Y3^4 * Y2, Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2^2 * Y3 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 22, 63, 30, 71, 35, 76, 27, 68, 19, 60, 10, 51, 3, 44, 7, 48, 15, 56, 23, 64, 31, 72, 38, 79, 40, 81, 34, 75, 26, 67, 18, 59, 9, 50, 13, 54, 17, 58, 25, 66, 33, 74, 39, 80, 41, 82, 37, 78, 29, 70, 21, 62, 12, 53, 5, 46, 8, 49, 16, 57, 24, 65, 32, 73, 36, 77, 28, 69, 20, 61, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 94, 135, 86, 127, 92, 133, 100, 141, 103, 144, 93, 134, 101, 142, 108, 149, 111, 152, 102, 143, 109, 150, 116, 157, 119, 160, 110, 151, 117, 158, 122, 163, 123, 164, 118, 159, 112, 153, 120, 161, 121, 162, 114, 155, 104, 145, 113, 154, 115, 156, 106, 147, 96, 137, 105, 146, 107, 148, 98, 139, 88, 129, 97, 138, 99, 140, 90, 131, 84, 125, 89, 130, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 100)(10, 101)(11, 102)(12, 103)(13, 91)(14, 88)(15, 89)(16, 90)(17, 95)(18, 108)(19, 109)(20, 110)(21, 111)(22, 96)(23, 97)(24, 98)(25, 99)(26, 116)(27, 117)(28, 118)(29, 119)(30, 104)(31, 105)(32, 106)(33, 107)(34, 122)(35, 112)(36, 114)(37, 123)(38, 113)(39, 115)(40, 120)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.434 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (Y2, Y3^-1), Y2^-1 * Y1 * Y2^-3, Y2 * Y3^-1 * Y1^6 * Y3^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 22, 63, 30, 71, 36, 77, 28, 69, 20, 61, 12, 53, 5, 46, 8, 49, 16, 57, 24, 65, 32, 73, 38, 79, 41, 82, 37, 78, 29, 70, 21, 62, 13, 54, 9, 50, 17, 58, 25, 66, 33, 74, 39, 80, 40, 81, 34, 75, 26, 67, 18, 59, 10, 51, 3, 44, 7, 48, 15, 56, 23, 64, 31, 72, 35, 76, 27, 68, 19, 60, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 90, 131, 84, 125, 89, 130, 99, 140, 98, 139, 88, 129, 97, 138, 107, 148, 106, 147, 96, 137, 105, 146, 115, 156, 114, 155, 104, 145, 113, 154, 121, 162, 120, 161, 112, 153, 117, 158, 122, 163, 123, 164, 118, 159, 109, 150, 116, 157, 119, 160, 110, 151, 101, 142, 108, 149, 111, 152, 102, 143, 93, 134, 100, 141, 103, 144, 94, 135, 86, 127, 92, 133, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 95)(10, 100)(11, 101)(12, 102)(13, 103)(14, 88)(15, 89)(16, 90)(17, 91)(18, 108)(19, 109)(20, 110)(21, 111)(22, 96)(23, 97)(24, 98)(25, 99)(26, 116)(27, 117)(28, 118)(29, 119)(30, 104)(31, 105)(32, 106)(33, 107)(34, 122)(35, 113)(36, 112)(37, 123)(38, 114)(39, 115)(40, 121)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.428 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.408 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3 * Y2^-2 * Y3^-1 * Y2^2, Y3 * Y2^-5, Y1^2 * Y2^-1 * Y1^2 * Y3^-4, Y3 * Y2 * Y3^7, Y1^5 * Y3^-1 * Y2^-1 * Y3^-2, Y3^-2 * Y2^-2 * Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-3 * Y2, Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^3 * Y2^-1 * Y3 * Y2 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 24, 65, 31, 72, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 25, 66, 34, 75, 38, 79, 30, 71, 20, 61, 9, 50, 17, 58, 27, 68, 35, 76, 40, 81, 41, 82, 37, 78, 29, 70, 19, 60, 13, 54, 18, 59, 28, 69, 36, 77, 39, 80, 33, 74, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 26, 67, 32, 73, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 94, 135, 86, 127, 92, 133, 102, 143, 111, 152, 105, 146, 93, 134, 103, 144, 112, 153, 119, 160, 115, 156, 104, 145, 113, 154, 120, 161, 123, 164, 121, 162, 114, 155, 106, 147, 116, 157, 122, 163, 118, 159, 108, 149, 96, 137, 107, 148, 117, 158, 110, 151, 98, 139, 88, 129, 97, 138, 109, 150, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 101)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 111)(20, 112)(21, 113)(22, 114)(23, 115)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 119)(30, 120)(31, 106)(32, 108)(33, 121)(34, 107)(35, 109)(36, 110)(37, 123)(38, 116)(39, 118)(40, 117)(41, 122)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.429 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.409 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y2 * Y3^2 * Y2^-1 * Y1^2, Y2^3 * Y1^-1 * Y2^2, Y1^3 * Y2 * Y1^2 * Y3^-3, Y3 * Y2^-1 * Y3^4 * 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, 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 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 24, 65, 32, 73, 22, 63, 12, 53, 5, 46, 8, 49, 16, 57, 26, 67, 34, 75, 39, 80, 33, 74, 23, 64, 13, 54, 18, 59, 28, 69, 36, 77, 40, 81, 41, 82, 37, 78, 29, 70, 19, 60, 9, 50, 17, 58, 27, 68, 35, 76, 38, 79, 30, 71, 20, 61, 10, 51, 3, 44, 7, 48, 15, 56, 25, 66, 31, 72, 21, 62, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 110, 151, 98, 139, 88, 129, 97, 138, 109, 150, 118, 159, 108, 149, 96, 137, 107, 148, 117, 158, 122, 163, 116, 157, 106, 147, 113, 154, 120, 161, 123, 164, 121, 162, 114, 155, 103, 144, 112, 153, 119, 160, 115, 156, 104, 145, 93, 134, 102, 143, 111, 152, 105, 146, 94, 135, 86, 127, 92, 133, 101, 142, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 101)(10, 102)(11, 103)(12, 104)(13, 105)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 111)(20, 112)(21, 113)(22, 114)(23, 115)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 119)(30, 120)(31, 107)(32, 106)(33, 121)(34, 108)(35, 109)(36, 110)(37, 123)(38, 117)(39, 116)(40, 118)(41, 122)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.426 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.410 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), Y2^-5 * Y1^-1 * Y2^-1, Y2^2 * Y3 * Y1^-1 * Y2^-2 * Y3^-2, Y3 * Y2^-1 * Y3^2 * Y1^-4, Y2^2 * Y3^3 * Y2^-2 * Y1 * Y3^-2, Y1^3 * Y2^-1 * Y1 * Y2^-1 * Y3^-2 * Y2^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 26, 67, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 28, 69, 36, 77, 35, 76, 24, 65, 13, 54, 18, 59, 30, 71, 38, 79, 40, 81, 32, 73, 19, 60, 25, 66, 31, 72, 39, 80, 41, 82, 33, 74, 20, 61, 9, 50, 17, 58, 29, 70, 37, 78, 34, 75, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 27, 68, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 114, 155, 117, 158, 105, 146, 93, 134, 103, 144, 115, 156, 122, 163, 118, 159, 108, 149, 104, 145, 116, 157, 123, 164, 120, 161, 110, 151, 96, 137, 109, 150, 119, 160, 121, 162, 112, 153, 98, 139, 88, 129, 97, 138, 111, 152, 113, 154, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 114)(20, 115)(21, 116)(22, 109)(23, 108)(24, 117)(25, 101)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 107)(32, 122)(33, 123)(34, 119)(35, 118)(36, 110)(37, 111)(38, 112)(39, 113)(40, 120)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.427 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.411 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^2 * Y3 * Y2^4, Y3^-5 * Y2^-1 * Y3^-2, Y1 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 26, 67, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 27, 68, 36, 77, 32, 73, 20, 61, 9, 50, 17, 58, 29, 70, 37, 78, 41, 82, 35, 76, 25, 66, 19, 60, 31, 72, 39, 80, 40, 81, 34, 75, 24, 65, 13, 54, 18, 59, 30, 71, 38, 79, 33, 74, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 28, 69, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 113, 154, 112, 153, 98, 139, 88, 129, 97, 138, 111, 152, 121, 162, 120, 161, 110, 151, 96, 137, 109, 150, 119, 160, 122, 163, 115, 156, 104, 145, 108, 149, 118, 159, 123, 164, 116, 157, 105, 146, 93, 134, 103, 144, 114, 155, 117, 158, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 107)(20, 114)(21, 108)(22, 110)(23, 115)(24, 116)(25, 117)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 118)(33, 120)(34, 122)(35, 123)(36, 109)(37, 111)(38, 112)(39, 113)(40, 121)(41, 119)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.425 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.412 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^-1 * Y3^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, Y1^3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y3, Y1 * Y2 * Y1^2 * Y2^3 * Y1 * Y3^-1, Y2^-2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-3, Y2^3 * Y1 * Y2 * Y1 * Y3^-3, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y1 * Y3^-2, Y2^-1 * Y1^2 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-2, Y3 * Y2^-2 * Y1^4 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2 * Y1^2 * Y2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y2^-1 * Y3^2 * 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 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 26, 67, 41, 82, 36, 77, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 27, 68, 40, 81, 25, 66, 32, 73, 35, 76, 20, 61, 9, 50, 17, 58, 29, 70, 39, 80, 24, 65, 13, 54, 18, 59, 30, 71, 34, 75, 19, 60, 31, 72, 38, 79, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 28, 69, 33, 74, 37, 78, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 115, 156, 108, 149, 122, 163, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 116, 157, 110, 151, 96, 137, 109, 150, 121, 162, 105, 146, 93, 134, 103, 144, 117, 158, 112, 153, 98, 139, 88, 129, 97, 138, 111, 152, 120, 161, 104, 145, 118, 159, 114, 155, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 113, 154, 119, 160, 123, 164, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 116)(20, 117)(21, 118)(22, 119)(23, 120)(24, 121)(25, 122)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 107)(33, 110)(34, 112)(35, 114)(36, 123)(37, 115)(38, 113)(39, 111)(40, 109)(41, 108)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.424 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.413 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y1 * Y2^-1 * Y3 * Y2, (R * Y2)^2, Y3^-2 * Y2^-1 * Y3^2 * Y2, Y1^3 * Y2 * Y3^-1 * Y2^2, Y2^-1 * Y3^-2 * Y2^-3 * Y3^-1 * Y2^-4, Y2^13 * Y1^-1 * Y2 * Y3^-1 * Y2^-3 * Y3^-1, Y2^-20 * Y1 * Y2 * Y3^-1, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 25, 66, 28, 69, 35, 76, 37, 78, 40, 81, 31, 72, 20, 61, 9, 50, 17, 58, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 26, 67, 33, 74, 36, 77, 38, 79, 29, 70, 32, 73, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 24, 65, 13, 54, 18, 59, 27, 68, 34, 75, 41, 82, 39, 80, 30, 71, 19, 60, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 111, 152, 119, 160, 116, 157, 108, 149, 96, 137, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 112, 153, 120, 161, 117, 158, 109, 150, 98, 139, 88, 129, 97, 138, 105, 146, 93, 134, 103, 144, 113, 154, 121, 162, 118, 159, 110, 151, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 104, 145, 114, 155, 122, 163, 123, 164, 115, 156, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 112)(20, 113)(21, 114)(22, 101)(23, 99)(24, 97)(25, 96)(26, 98)(27, 100)(28, 107)(29, 120)(30, 121)(31, 122)(32, 111)(33, 108)(34, 109)(35, 110)(36, 115)(37, 117)(38, 118)(39, 123)(40, 119)(41, 116)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.423 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.414 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y1^-1, Y2), (R * Y2)^2, Y3 * Y1^-2 * Y2^3 * Y3, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y2^8 * Y1 * Y3^-2, Y2 * Y1^-15, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 42, 2, 43, 6, 47, 14, 55, 19, 60, 28, 69, 35, 76, 41, 82, 38, 79, 31, 72, 24, 65, 13, 54, 18, 59, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 26, 67, 29, 70, 36, 77, 40, 81, 33, 74, 30, 71, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 20, 61, 9, 50, 17, 58, 27, 68, 34, 75, 37, 78, 39, 80, 32, 73, 25, 66, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 111, 152, 119, 160, 120, 161, 112, 153, 104, 145, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 110, 151, 118, 159, 121, 162, 113, 154, 105, 146, 93, 134, 103, 144, 98, 139, 88, 129, 97, 138, 109, 150, 117, 158, 122, 163, 114, 155, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 96, 137, 108, 149, 116, 157, 123, 164, 115, 156, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 96)(20, 98)(21, 100)(22, 107)(23, 112)(24, 113)(25, 114)(26, 97)(27, 99)(28, 101)(29, 108)(30, 115)(31, 120)(32, 121)(33, 122)(34, 109)(35, 110)(36, 111)(37, 116)(38, 123)(39, 119)(40, 118)(41, 117)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.437 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.415 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1), (Y3^-1, Y2^-1), (R * Y2)^2, Y2 * Y3^-2 * Y2^-1 * Y1^-2, Y2^-3 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1, Y1^3 * Y2 * Y1 * Y2 * Y1 * Y3^-2, Y2 * Y1 * Y2 * Y1^2 * Y3^-4, Y3^-20 * Y1^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2, Y2^-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 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 26, 67, 36, 77, 24, 65, 13, 54, 18, 59, 30, 71, 19, 60, 31, 72, 39, 80, 40, 81, 33, 74, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 27, 68, 35, 76, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 28, 69, 38, 79, 41, 82, 37, 78, 25, 66, 32, 73, 20, 61, 9, 50, 17, 58, 29, 70, 34, 75, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 110, 151, 96, 137, 109, 150, 116, 157, 122, 163, 119, 160, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 112, 153, 98, 139, 88, 129, 97, 138, 111, 152, 121, 162, 123, 164, 118, 159, 105, 146, 93, 134, 103, 144, 114, 155, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 113, 154, 120, 161, 108, 149, 117, 158, 104, 145, 115, 156, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 112)(20, 114)(21, 115)(22, 116)(23, 117)(24, 118)(25, 119)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 107)(33, 122)(34, 111)(35, 109)(36, 108)(37, 123)(38, 110)(39, 113)(40, 121)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.435 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.416 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^-1 * Y1^-1, Y1^-1 * Y3^-1, Y3 * Y2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-3 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-4, Y1^5 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y3 * Y2 * Y3^23, Y2 * Y3 * Y2 * Y3 * Y2^2 * Y3^2 * Y2^2 * Y3^2 * Y2^2 * Y3^2 * Y2^2 * Y3^2 * Y2^2 * Y3^2 * Y2^2 * Y3^2 * Y2^2 * Y3, 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 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^2 * Y3 * Y1^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 26, 67, 35, 76, 20, 61, 9, 50, 17, 58, 29, 70, 25, 66, 32, 73, 39, 80, 40, 81, 33, 74, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 28, 69, 36, 77, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 27, 68, 38, 79, 41, 82, 34, 75, 19, 60, 31, 72, 24, 65, 13, 54, 18, 59, 30, 71, 37, 78, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 115, 156, 104, 145, 118, 159, 108, 149, 120, 161, 114, 155, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 113, 154, 105, 146, 93, 134, 103, 144, 117, 158, 123, 164, 121, 162, 112, 153, 98, 139, 88, 129, 97, 138, 111, 152, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 116, 157, 122, 163, 119, 160, 110, 151, 96, 137, 109, 150, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 116)(20, 117)(21, 118)(22, 119)(23, 115)(24, 113)(25, 111)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 107)(33, 122)(34, 123)(35, 108)(36, 110)(37, 112)(38, 109)(39, 114)(40, 121)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.438 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.417 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y2, Y3^-1), Y2 * Y3 * Y2 * Y3^2, Y2^-1 * Y1^2 * Y3^-1 * Y2^-1, Y2^-1 * Y3 * Y2^-12, Y1^41, 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 ] Map:: R = (1, 42, 2, 43, 6, 47, 9, 50, 15, 56, 20, 61, 22, 63, 27, 68, 32, 73, 34, 75, 39, 80, 41, 82, 36, 77, 31, 72, 29, 70, 24, 65, 19, 60, 17, 58, 12, 53, 5, 46, 8, 49, 10, 51, 3, 44, 7, 48, 14, 55, 16, 57, 21, 62, 26, 67, 28, 69, 33, 74, 38, 79, 40, 81, 37, 78, 35, 76, 30, 71, 25, 66, 23, 64, 18, 59, 13, 54, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 98, 139, 104, 145, 110, 151, 116, 157, 122, 163, 118, 159, 112, 153, 106, 147, 100, 141, 94, 135, 86, 127, 92, 133, 88, 129, 96, 137, 102, 143, 108, 149, 114, 155, 120, 161, 123, 164, 117, 158, 111, 152, 105, 146, 99, 140, 93, 134, 90, 131, 84, 125, 89, 130, 97, 138, 103, 144, 109, 150, 115, 156, 121, 162, 119, 160, 113, 154, 107, 148, 101, 142, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 88)(10, 90)(11, 95)(12, 99)(13, 100)(14, 89)(15, 91)(16, 96)(17, 101)(18, 105)(19, 106)(20, 97)(21, 98)(22, 102)(23, 107)(24, 111)(25, 112)(26, 103)(27, 104)(28, 108)(29, 113)(30, 117)(31, 118)(32, 109)(33, 110)(34, 114)(35, 119)(36, 123)(37, 122)(38, 115)(39, 116)(40, 120)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.436 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.418 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, Y1^-1 * Y3^-1, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), Y2 * Y1 * Y2 * Y1^2, Y2^11 * Y1^-1 * Y2^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 13, 54, 15, 56, 20, 61, 25, 66, 27, 68, 32, 73, 37, 78, 39, 80, 41, 82, 35, 76, 28, 69, 30, 71, 23, 64, 16, 57, 18, 59, 10, 51, 3, 44, 7, 48, 12, 53, 5, 46, 8, 49, 14, 55, 19, 60, 21, 62, 26, 67, 31, 72, 33, 74, 38, 79, 40, 81, 34, 75, 36, 77, 29, 70, 22, 63, 24, 65, 17, 58, 9, 50, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 98, 139, 104, 145, 110, 151, 116, 157, 121, 162, 115, 156, 109, 150, 103, 144, 97, 138, 90, 131, 84, 125, 89, 130, 93, 134, 100, 141, 106, 147, 112, 153, 118, 159, 123, 164, 120, 161, 114, 155, 108, 149, 102, 143, 96, 137, 88, 129, 94, 135, 86, 127, 92, 133, 99, 140, 105, 146, 111, 152, 117, 158, 122, 163, 119, 160, 113, 154, 107, 148, 101, 142, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 99)(10, 100)(11, 91)(12, 89)(13, 88)(14, 90)(15, 95)(16, 105)(17, 106)(18, 98)(19, 96)(20, 97)(21, 101)(22, 111)(23, 112)(24, 104)(25, 102)(26, 103)(27, 107)(28, 117)(29, 118)(30, 110)(31, 108)(32, 109)(33, 113)(34, 122)(35, 123)(36, 116)(37, 114)(38, 115)(39, 119)(40, 120)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.422 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.419 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y3)^2, Y3 * Y2 * Y3^2 * Y2 * Y1^-2, Y2^-2 * Y1^2 * Y3^-3, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-5, Y2^-4 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 20, 61, 9, 50, 17, 58, 27, 68, 36, 77, 41, 82, 30, 71, 38, 79, 34, 75, 25, 66, 29, 70, 32, 73, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 26, 67, 31, 72, 19, 60, 28, 69, 37, 78, 35, 76, 39, 80, 40, 81, 33, 74, 24, 65, 13, 54, 18, 59, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 112, 153, 122, 163, 114, 155, 104, 145, 98, 139, 88, 129, 97, 138, 109, 150, 119, 160, 116, 157, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 113, 154, 123, 164, 121, 162, 111, 152, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 110, 151, 120, 161, 115, 156, 105, 146, 93, 134, 103, 144, 96, 137, 108, 149, 118, 159, 117, 158, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 113)(20, 96)(21, 98)(22, 100)(23, 114)(24, 115)(25, 116)(26, 97)(27, 99)(28, 101)(29, 107)(30, 123)(31, 108)(32, 111)(33, 122)(34, 120)(35, 119)(36, 109)(37, 110)(38, 112)(39, 117)(40, 121)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.431 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.420 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1), (R * Y1)^2, (R * Y2)^2, Y1^2 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^2 * Y3 * Y2 * Y3 * Y2^4 * Y1^-1, Y2 * Y3^18, Y3^9 * Y2^-20, 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 ] Map:: R = (1, 42, 2, 43, 6, 47, 14, 55, 24, 65, 13, 54, 18, 59, 27, 68, 36, 77, 41, 82, 35, 76, 39, 80, 31, 72, 19, 60, 28, 69, 33, 74, 21, 62, 10, 51, 3, 44, 7, 48, 15, 56, 23, 64, 12, 53, 5, 46, 8, 49, 16, 57, 26, 67, 34, 75, 25, 66, 29, 70, 37, 78, 30, 71, 38, 79, 40, 81, 32, 73, 20, 61, 9, 50, 17, 58, 22, 63, 11, 52, 4, 45)(83, 124, 85, 126, 91, 132, 101, 142, 112, 153, 118, 159, 108, 149, 96, 137, 105, 146, 93, 134, 103, 144, 114, 155, 121, 162, 111, 152, 100, 141, 90, 131, 84, 125, 89, 130, 99, 140, 110, 151, 120, 161, 123, 164, 116, 157, 106, 147, 94, 135, 86, 127, 92, 133, 102, 143, 113, 154, 119, 160, 109, 150, 98, 139, 88, 129, 97, 138, 104, 145, 115, 156, 122, 163, 117, 158, 107, 148, 95, 136, 87, 128) L = (1, 86)(2, 83)(3, 92)(4, 93)(5, 94)(6, 84)(7, 85)(8, 87)(9, 102)(10, 103)(11, 104)(12, 105)(13, 106)(14, 88)(15, 89)(16, 90)(17, 91)(18, 95)(19, 113)(20, 114)(21, 115)(22, 99)(23, 97)(24, 96)(25, 116)(26, 98)(27, 100)(28, 101)(29, 107)(30, 119)(31, 121)(32, 122)(33, 110)(34, 108)(35, 123)(36, 109)(37, 111)(38, 112)(39, 117)(40, 120)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.432 Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.421 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2^41, (Y3 * Y2^-1)^41, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 86, 127, 88, 129, 90, 131, 92, 133, 94, 135, 96, 137, 100, 141, 98, 139, 99, 140, 101, 142, 102, 143, 103, 144, 104, 145, 105, 146, 106, 147, 110, 151, 108, 149, 109, 150, 111, 152, 112, 153, 113, 154, 114, 155, 115, 156, 116, 157, 120, 161, 118, 159, 119, 160, 121, 162, 122, 163, 123, 164, 117, 158, 107, 148, 97, 138, 95, 136, 93, 134, 91, 132, 89, 130, 87, 128, 85, 126) L = (1, 85)(2, 83)(3, 87)(4, 84)(5, 89)(6, 86)(7, 91)(8, 88)(9, 93)(10, 90)(11, 95)(12, 92)(13, 97)(14, 94)(15, 107)(16, 100)(17, 98)(18, 96)(19, 99)(20, 101)(21, 102)(22, 103)(23, 104)(24, 105)(25, 117)(26, 110)(27, 108)(28, 106)(29, 109)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 123)(36, 120)(37, 118)(38, 116)(39, 119)(40, 121)(41, 122)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.402 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.422 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-20, (Y3^-1 * Y1^-1)^41, (Y3 * Y2^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 87, 128, 88, 129, 91, 132, 92, 133, 95, 136, 96, 137, 99, 140, 100, 141, 103, 144, 104, 145, 107, 148, 108, 149, 111, 152, 112, 153, 115, 156, 116, 157, 119, 160, 120, 161, 123, 164, 121, 162, 122, 163, 117, 158, 118, 159, 113, 154, 114, 155, 109, 150, 110, 151, 105, 146, 106, 147, 101, 142, 102, 143, 97, 138, 98, 139, 93, 134, 94, 135, 89, 130, 90, 131, 85, 126, 86, 127) L = (1, 85)(2, 86)(3, 89)(4, 90)(5, 83)(6, 84)(7, 93)(8, 94)(9, 87)(10, 88)(11, 97)(12, 98)(13, 91)(14, 92)(15, 101)(16, 102)(17, 95)(18, 96)(19, 105)(20, 106)(21, 99)(22, 100)(23, 109)(24, 110)(25, 103)(26, 104)(27, 113)(28, 114)(29, 107)(30, 108)(31, 117)(32, 118)(33, 111)(34, 112)(35, 121)(36, 122)(37, 115)(38, 116)(39, 120)(40, 123)(41, 119)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.418 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.423 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-1 * Y2^-3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-13, (Y3^-1 * Y1^-1)^41, (Y3 * Y2^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 87, 128, 90, 131, 94, 135, 93, 134, 96, 137, 100, 141, 99, 140, 102, 143, 106, 147, 105, 146, 108, 149, 112, 153, 111, 152, 114, 155, 118, 159, 117, 158, 120, 161, 121, 162, 123, 164, 122, 163, 115, 156, 119, 160, 116, 157, 109, 150, 113, 154, 110, 151, 103, 144, 107, 148, 104, 145, 97, 138, 101, 142, 98, 139, 91, 132, 95, 136, 92, 133, 85, 126, 89, 130, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 86)(7, 95)(8, 84)(9, 97)(10, 98)(11, 87)(12, 88)(13, 101)(14, 90)(15, 103)(16, 104)(17, 93)(18, 94)(19, 107)(20, 96)(21, 109)(22, 110)(23, 99)(24, 100)(25, 113)(26, 102)(27, 115)(28, 116)(29, 105)(30, 106)(31, 119)(32, 108)(33, 121)(34, 122)(35, 111)(36, 112)(37, 123)(38, 114)(39, 118)(40, 120)(41, 117)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.413 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.424 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3 * Y2^4, Y3^-1 * Y2 * Y3^-9, (Y2^-1 * Y3)^41, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 94, 135, 87, 128, 90, 131, 96, 137, 102, 143, 95, 136, 98, 139, 104, 145, 110, 151, 103, 144, 106, 147, 112, 153, 118, 159, 111, 152, 114, 155, 120, 161, 123, 164, 119, 160, 115, 156, 121, 162, 122, 163, 116, 157, 107, 148, 113, 154, 117, 158, 108, 149, 99, 140, 105, 146, 109, 150, 100, 141, 91, 132, 97, 138, 101, 142, 92, 133, 85, 126, 89, 130, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 93)(7, 97)(8, 84)(9, 99)(10, 100)(11, 101)(12, 86)(13, 87)(14, 88)(15, 105)(16, 90)(17, 107)(18, 108)(19, 109)(20, 94)(21, 95)(22, 96)(23, 113)(24, 98)(25, 115)(26, 116)(27, 117)(28, 102)(29, 103)(30, 104)(31, 121)(32, 106)(33, 114)(34, 119)(35, 122)(36, 110)(37, 111)(38, 112)(39, 120)(40, 123)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.412 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.425 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3 * Y2^2 * Y3^-1 * Y2^-2, Y3^-1 * Y2^-5, Y3^-8 * Y2, Y2^-2 * Y3^-2 * Y2 * Y3^-1 * Y2^2 * Y3^-5, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^4, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 94, 135, 87, 128, 90, 131, 98, 139, 106, 147, 104, 145, 95, 136, 100, 141, 108, 149, 116, 157, 114, 155, 105, 146, 110, 151, 118, 159, 122, 163, 121, 162, 115, 156, 111, 152, 119, 160, 123, 164, 120, 161, 112, 153, 101, 142, 109, 150, 117, 158, 113, 154, 102, 143, 91, 132, 99, 140, 107, 148, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 93)(15, 107)(16, 88)(17, 109)(18, 90)(19, 111)(20, 112)(21, 113)(22, 94)(23, 95)(24, 96)(25, 117)(26, 98)(27, 119)(28, 100)(29, 110)(30, 115)(31, 120)(32, 104)(33, 105)(34, 106)(35, 123)(36, 108)(37, 118)(38, 121)(39, 114)(40, 116)(41, 122)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.411 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.426 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^-1 * Y2^2 * Y3 * Y2^-2, Y2^3 * Y3 * Y2^3, Y3^-5 * Y2^-1 * Y3^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 108, 149, 117, 158, 106, 147, 95, 136, 100, 141, 110, 151, 118, 159, 121, 162, 113, 154, 107, 148, 112, 153, 120, 161, 122, 163, 114, 155, 101, 142, 111, 152, 119, 160, 123, 164, 115, 156, 102, 143, 91, 132, 99, 140, 109, 150, 116, 157, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 104)(15, 109)(16, 88)(17, 111)(18, 90)(19, 113)(20, 114)(21, 115)(22, 116)(23, 93)(24, 94)(25, 95)(26, 96)(27, 119)(28, 98)(29, 107)(30, 100)(31, 106)(32, 121)(33, 122)(34, 123)(35, 105)(36, 108)(37, 112)(38, 110)(39, 117)(40, 118)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.409 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.427 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-4 * Y2^-1 * Y3^-2, Y2^-1 * Y3^-1 * Y2^-6, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-3 * Y2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 108, 149, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 110, 151, 118, 159, 117, 158, 106, 147, 95, 136, 100, 141, 112, 153, 120, 161, 122, 163, 114, 155, 101, 142, 107, 148, 113, 154, 121, 162, 123, 164, 115, 156, 102, 143, 91, 132, 99, 140, 111, 152, 119, 160, 116, 157, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 109, 150, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 109)(15, 111)(16, 88)(17, 107)(18, 90)(19, 106)(20, 114)(21, 115)(22, 116)(23, 93)(24, 94)(25, 95)(26, 104)(27, 119)(28, 96)(29, 113)(30, 98)(31, 100)(32, 117)(33, 122)(34, 123)(35, 105)(36, 108)(37, 121)(38, 110)(39, 112)(40, 118)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.410 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.428 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2^-1), Y2^-1 * Y3^2 * Y2 * Y3^-2, Y3^3 * Y2^-1 * Y3^2, Y2^3 * Y3 * Y2^5, Y2^2 * Y3^-1 * Y2^3 * Y3^2 * Y2 * Y3 * Y2^2 * Y3^-1, Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^-2, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 106, 147, 114, 155, 104, 145, 94, 135, 87, 128, 90, 131, 98, 139, 108, 149, 116, 157, 121, 162, 115, 156, 105, 146, 95, 136, 100, 141, 110, 151, 118, 159, 122, 163, 123, 164, 119, 160, 111, 152, 101, 142, 91, 132, 99, 140, 109, 150, 117, 158, 120, 161, 112, 153, 102, 143, 92, 133, 85, 126, 89, 130, 97, 138, 107, 148, 113, 154, 103, 144, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 100)(10, 101)(11, 102)(12, 86)(13, 87)(14, 107)(15, 109)(16, 88)(17, 110)(18, 90)(19, 95)(20, 111)(21, 112)(22, 93)(23, 94)(24, 113)(25, 117)(26, 96)(27, 118)(28, 98)(29, 105)(30, 119)(31, 120)(32, 103)(33, 104)(34, 106)(35, 122)(36, 108)(37, 115)(38, 123)(39, 114)(40, 116)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.407 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.429 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^5 * Y3^-4, Y3^2 * Y2^2 * Y3^3 * Y2^2, Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^-3 * Y3 * Y2^-3, Y2 * Y3^32, Y2 * Y3^32, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 108, 149, 115, 156, 120, 161, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 110, 151, 116, 157, 101, 142, 113, 154, 121, 162, 106, 147, 95, 136, 100, 141, 112, 153, 117, 158, 102, 143, 91, 132, 99, 140, 111, 152, 122, 163, 107, 148, 114, 155, 118, 159, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 109, 150, 123, 164, 119, 160, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 109)(15, 111)(16, 88)(17, 113)(18, 90)(19, 115)(20, 116)(21, 117)(22, 118)(23, 93)(24, 94)(25, 95)(26, 123)(27, 122)(28, 96)(29, 121)(30, 98)(31, 120)(32, 100)(33, 119)(34, 108)(35, 110)(36, 112)(37, 114)(38, 104)(39, 105)(40, 106)(41, 107)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.408 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.430 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), Y3^-4 * Y2, Y2^5 * Y3 * Y2^5, Y2^-3 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-3 * Y3, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 104, 145, 112, 153, 118, 159, 110, 151, 102, 143, 94, 135, 87, 128, 90, 131, 98, 139, 106, 147, 114, 155, 120, 161, 123, 164, 119, 160, 111, 152, 103, 144, 95, 136, 91, 132, 99, 140, 107, 148, 115, 156, 121, 162, 122, 163, 116, 157, 108, 149, 100, 141, 92, 133, 85, 126, 89, 130, 97, 138, 105, 146, 113, 154, 117, 158, 109, 150, 101, 142, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 90)(10, 95)(11, 100)(12, 86)(13, 87)(14, 105)(15, 107)(16, 88)(17, 98)(18, 103)(19, 108)(20, 93)(21, 94)(22, 113)(23, 115)(24, 96)(25, 106)(26, 111)(27, 116)(28, 101)(29, 102)(30, 117)(31, 121)(32, 104)(33, 114)(34, 119)(35, 122)(36, 109)(37, 110)(38, 112)(39, 120)(40, 123)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.405 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.431 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^2 * Y2 * Y3 * Y2^2 * Y3, Y3^2 * Y2^-1 * Y3 * Y2^-7, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^4, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 108, 149, 116, 157, 120, 161, 112, 153, 101, 142, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 109, 150, 117, 158, 121, 162, 113, 154, 102, 143, 91, 132, 99, 140, 106, 147, 95, 136, 100, 141, 110, 151, 118, 159, 122, 163, 114, 155, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 107, 148, 111, 152, 119, 160, 123, 164, 115, 156, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 107)(15, 106)(16, 88)(17, 105)(18, 90)(19, 104)(20, 112)(21, 113)(22, 114)(23, 93)(24, 94)(25, 95)(26, 111)(27, 96)(28, 98)(29, 100)(30, 115)(31, 120)(32, 121)(33, 122)(34, 119)(35, 108)(36, 109)(37, 110)(38, 123)(39, 116)(40, 117)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.419 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.432 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^-2 * Y3 * Y2^-1 * Y3^2 * Y2^-2, Y3 * Y2 * Y3^6 * Y2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 108, 149, 101, 142, 113, 154, 119, 160, 122, 163, 116, 157, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 110, 151, 102, 143, 91, 132, 99, 140, 111, 152, 121, 162, 123, 164, 117, 158, 106, 147, 95, 136, 100, 141, 112, 153, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 109, 150, 120, 161, 115, 156, 118, 159, 107, 148, 114, 155, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 109)(15, 111)(16, 88)(17, 113)(18, 90)(19, 115)(20, 108)(21, 110)(22, 112)(23, 93)(24, 94)(25, 95)(26, 120)(27, 121)(28, 96)(29, 119)(30, 98)(31, 118)(32, 100)(33, 117)(34, 104)(35, 105)(36, 106)(37, 107)(38, 123)(39, 122)(40, 114)(41, 116)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.420 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.433 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y3^-1 * Y2 * Y3^-2 * Y2, Y2^-5 * Y3^-1 * Y2^-8, Y2^-1 * Y3^-19, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 102, 143, 108, 149, 114, 155, 120, 161, 118, 159, 112, 153, 106, 147, 100, 141, 94, 135, 87, 128, 90, 131, 91, 132, 98, 139, 104, 145, 110, 151, 116, 157, 122, 163, 123, 164, 119, 160, 113, 154, 107, 148, 101, 142, 95, 136, 92, 133, 85, 126, 89, 130, 97, 138, 103, 144, 109, 150, 115, 156, 121, 162, 117, 158, 111, 152, 105, 146, 99, 140, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 98)(8, 84)(9, 88)(10, 90)(11, 95)(12, 86)(13, 87)(14, 103)(15, 104)(16, 96)(17, 101)(18, 93)(19, 94)(20, 109)(21, 110)(22, 102)(23, 107)(24, 99)(25, 100)(26, 115)(27, 116)(28, 108)(29, 113)(30, 105)(31, 106)(32, 121)(33, 122)(34, 114)(35, 119)(36, 111)(37, 112)(38, 117)(39, 123)(40, 120)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.403 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.434 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^14 * Y3, (Y3 * Y2^-1)^41, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 94, 135, 100, 141, 106, 147, 112, 153, 118, 159, 121, 162, 115, 156, 109, 150, 103, 144, 97, 138, 91, 132, 87, 128, 90, 131, 96, 137, 102, 143, 108, 149, 114, 155, 120, 161, 122, 163, 116, 157, 110, 151, 104, 145, 98, 139, 92, 133, 85, 126, 89, 130, 95, 136, 101, 142, 107, 148, 113, 154, 119, 160, 123, 164, 117, 158, 111, 152, 105, 146, 99, 140, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 95)(7, 87)(8, 84)(9, 86)(10, 97)(11, 98)(12, 101)(13, 90)(14, 88)(15, 93)(16, 103)(17, 104)(18, 107)(19, 96)(20, 94)(21, 99)(22, 109)(23, 110)(24, 113)(25, 102)(26, 100)(27, 105)(28, 115)(29, 116)(30, 119)(31, 108)(32, 106)(33, 111)(34, 121)(35, 122)(36, 123)(37, 114)(38, 112)(39, 117)(40, 118)(41, 120)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.406 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.435 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y2^-1, Y3), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y2^3 * Y3 * Y2 * Y3^2, Y2^-1 * Y3 * Y2^-1 * Y3^7 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 107, 148, 110, 151, 117, 158, 119, 160, 122, 163, 113, 154, 102, 143, 91, 132, 99, 140, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 108, 149, 115, 156, 118, 159, 120, 161, 111, 152, 114, 155, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 106, 147, 95, 136, 100, 141, 109, 150, 116, 157, 123, 164, 121, 162, 112, 153, 101, 142, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 106)(15, 105)(16, 88)(17, 104)(18, 90)(19, 111)(20, 112)(21, 113)(22, 114)(23, 93)(24, 94)(25, 95)(26, 96)(27, 98)(28, 100)(29, 119)(30, 120)(31, 121)(32, 122)(33, 107)(34, 108)(35, 109)(36, 110)(37, 116)(38, 117)(39, 118)(40, 123)(41, 115)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.415 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.436 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2), Y3 * Y2^-1 * Y3^4 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-6 * 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^-2 * Y3 * Y2^-3 * Y3^-1 * Y2^-2, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 108, 149, 118, 159, 117, 158, 107, 148, 102, 143, 91, 132, 99, 140, 111, 152, 121, 162, 115, 156, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 110, 151, 120, 161, 123, 164, 113, 154, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 109, 150, 119, 160, 116, 157, 106, 147, 95, 136, 100, 141, 101, 142, 112, 153, 122, 163, 114, 155, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 109)(15, 111)(16, 88)(17, 112)(18, 90)(19, 98)(20, 100)(21, 107)(22, 113)(23, 93)(24, 94)(25, 95)(26, 119)(27, 121)(28, 96)(29, 122)(30, 110)(31, 117)(32, 123)(33, 104)(34, 105)(35, 106)(36, 116)(37, 115)(38, 108)(39, 114)(40, 120)(41, 118)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.417 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.437 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y2^-1), (R * Y2)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-4 * Y2^-1, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^5, Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^4 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^4, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 108, 149, 117, 158, 102, 143, 91, 132, 99, 140, 111, 152, 107, 148, 114, 155, 121, 162, 122, 163, 115, 156, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 110, 151, 118, 159, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 109, 150, 120, 161, 123, 164, 116, 157, 101, 142, 113, 154, 106, 147, 95, 136, 100, 141, 112, 153, 119, 160, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 109)(15, 111)(16, 88)(17, 113)(18, 90)(19, 115)(20, 116)(21, 117)(22, 118)(23, 93)(24, 94)(25, 95)(26, 120)(27, 107)(28, 96)(29, 106)(30, 98)(31, 105)(32, 100)(33, 104)(34, 122)(35, 123)(36, 108)(37, 110)(38, 114)(39, 112)(40, 119)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.414 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.438 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y3^-2 * Y2^5, Y3^5 * Y2 * Y3 * Y2^2 * Y3, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^2, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 96, 137, 102, 143, 91, 132, 99, 140, 109, 150, 118, 159, 123, 164, 112, 153, 120, 161, 116, 157, 107, 148, 111, 152, 114, 155, 105, 146, 94, 135, 87, 128, 90, 131, 98, 139, 103, 144, 92, 133, 85, 126, 89, 130, 97, 138, 108, 149, 113, 154, 101, 142, 110, 151, 119, 160, 117, 158, 121, 162, 122, 163, 115, 156, 106, 147, 95, 136, 100, 141, 104, 145, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 97)(7, 99)(8, 84)(9, 101)(10, 102)(11, 103)(12, 86)(13, 87)(14, 108)(15, 109)(16, 88)(17, 110)(18, 90)(19, 112)(20, 113)(21, 96)(22, 98)(23, 93)(24, 94)(25, 95)(26, 118)(27, 119)(28, 120)(29, 100)(30, 122)(31, 123)(32, 104)(33, 105)(34, 106)(35, 107)(36, 117)(37, 116)(38, 115)(39, 111)(40, 114)(41, 121)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.416 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.439 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {41, 41, 41}) Quotient :: dipole Aut^+ = C41 (small group id <41, 1>) Aut = D82 (small group id <82, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^11 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^41 ] Map:: R = (1, 42)(2, 43)(3, 44)(4, 45)(5, 46)(6, 47)(7, 48)(8, 49)(9, 50)(10, 51)(11, 52)(12, 53)(13, 54)(14, 55)(15, 56)(16, 57)(17, 58)(18, 59)(19, 60)(20, 61)(21, 62)(22, 63)(23, 64)(24, 65)(25, 66)(26, 67)(27, 68)(28, 69)(29, 70)(30, 71)(31, 72)(32, 73)(33, 74)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 82)(83, 124, 84, 125, 88, 129, 91, 132, 97, 138, 102, 143, 104, 145, 109, 150, 114, 155, 116, 157, 121, 162, 123, 164, 118, 159, 113, 154, 111, 152, 106, 147, 101, 142, 99, 140, 94, 135, 87, 128, 90, 131, 92, 133, 85, 126, 89, 130, 96, 137, 98, 139, 103, 144, 108, 149, 110, 151, 115, 156, 120, 161, 122, 163, 119, 160, 117, 158, 112, 153, 107, 148, 105, 146, 100, 141, 95, 136, 93, 134, 86, 127) L = (1, 85)(2, 89)(3, 91)(4, 92)(5, 83)(6, 96)(7, 97)(8, 84)(9, 98)(10, 88)(11, 90)(12, 86)(13, 87)(14, 102)(15, 103)(16, 104)(17, 93)(18, 94)(19, 95)(20, 108)(21, 109)(22, 110)(23, 99)(24, 100)(25, 101)(26, 114)(27, 115)(28, 116)(29, 105)(30, 106)(31, 107)(32, 120)(33, 121)(34, 122)(35, 111)(36, 112)(37, 113)(38, 123)(39, 119)(40, 118)(41, 117)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.404 Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.440 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y2 * Y1^2 * Y3 * Y2 * Y1^-2 * Y3, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y1^3 * Y2 * Y1^-3, Y1 * Y3 * Y1^2 * Y2 * Y1^4 ] Map:: R = (1, 44, 2, 47, 5, 53, 11, 65, 23, 76, 34, 83, 41, 74, 32, 58, 16, 70, 28, 81, 39, 84, 42, 75, 33, 59, 17, 71, 29, 82, 40, 73, 31, 80, 38, 64, 22, 52, 10, 46, 4, 43)(3, 49, 7, 57, 15, 66, 24, 79, 37, 63, 21, 72, 30, 56, 14, 48, 6, 55, 13, 69, 27, 78, 36, 62, 20, 51, 9, 61, 19, 68, 26, 54, 12, 67, 25, 77, 35, 60, 18, 50, 8, 45) 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, 36)(25, 39)(26, 40)(27, 38)(30, 41)(37, 42)(43, 45)(44, 48)(46, 51)(47, 54)(49, 58)(50, 59)(52, 63)(53, 66)(55, 70)(56, 71)(57, 73)(60, 76)(61, 74)(62, 75)(64, 77)(65, 78)(67, 81)(68, 82)(69, 80)(72, 83)(79, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.441 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) 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 * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y3, (Y1^-3 * Y2)^2, Y1^-4 * Y3 * Y1^2 * Y2 * Y1^-1 ] Map:: R = (1, 44, 2, 47, 5, 53, 11, 65, 23, 74, 32, 83, 41, 76, 34, 59, 17, 71, 29, 82, 40, 84, 42, 75, 33, 58, 16, 70, 28, 81, 39, 77, 35, 80, 38, 64, 22, 52, 10, 46, 4, 43)(3, 49, 7, 57, 15, 73, 31, 68, 26, 54, 12, 67, 25, 62, 20, 51, 9, 61, 19, 78, 36, 72, 30, 56, 14, 48, 6, 55, 13, 69, 27, 63, 21, 79, 37, 66, 24, 60, 18, 50, 8, 45) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 36)(25, 39)(26, 40)(27, 41)(30, 38)(37, 42)(43, 45)(44, 48)(46, 51)(47, 54)(49, 58)(50, 59)(52, 63)(53, 66)(55, 70)(56, 71)(57, 74)(60, 77)(61, 75)(62, 76)(64, 73)(65, 78)(67, 81)(68, 82)(69, 83)(72, 80)(79, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.442 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) 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, R * Y3 * R * Y2, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y1^-2, Y2 * Y1^-2 * Y3 * Y1^2, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y3, Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1, (Y2 * Y3)^7 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 52, 10, 62, 20, 75, 33, 82, 40, 84, 42, 69, 27, 80, 38, 72, 30, 70, 28, 81, 39, 66, 24, 79, 37, 83, 41, 67, 25, 74, 32, 55, 13, 59, 17, 47, 5, 43)(3, 51, 9, 56, 14, 46, 4, 54, 12, 60, 18, 73, 31, 77, 35, 57, 15, 76, 34, 78, 36, 58, 16, 63, 21, 49, 7, 61, 19, 65, 23, 50, 8, 64, 22, 68, 26, 71, 29, 53, 11, 45) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 18)(8, 17)(9, 24)(10, 26)(11, 27)(12, 30)(14, 33)(16, 32)(19, 37)(20, 36)(21, 38)(22, 28)(23, 40)(25, 29)(31, 41)(34, 39)(35, 42)(43, 46)(44, 50)(45, 52)(47, 58)(48, 57)(49, 62)(51, 67)(53, 70)(54, 66)(55, 73)(56, 69)(59, 71)(60, 75)(61, 74)(63, 81)(64, 79)(65, 80)(68, 82)(72, 77)(76, 83)(78, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.443 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.443 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) 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, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y3 * Y1^3, Y3 * Y1^-2 * Y2 * Y1^2, Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, Y3 * Y1 * Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y1^-1, (Y3 * Y2)^7 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 55, 13, 64, 22, 71, 29, 81, 39, 84, 42, 70, 28, 80, 38, 67, 25, 74, 32, 82, 40, 66, 24, 79, 37, 83, 41, 72, 30, 69, 27, 52, 10, 59, 17, 47, 5, 43)(3, 51, 9, 60, 18, 68, 26, 78, 36, 58, 16, 77, 35, 76, 34, 57, 15, 65, 23, 50, 8, 63, 21, 62, 20, 49, 7, 61, 19, 73, 31, 75, 33, 56, 14, 46, 4, 54, 12, 53, 11, 45) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 16)(8, 22)(9, 24)(10, 26)(11, 28)(12, 30)(14, 32)(17, 33)(18, 29)(19, 37)(20, 38)(21, 27)(23, 40)(25, 36)(31, 39)(34, 42)(35, 41)(43, 46)(44, 50)(45, 52)(47, 58)(48, 60)(49, 59)(51, 67)(53, 71)(54, 66)(55, 73)(56, 70)(57, 69)(61, 74)(62, 81)(63, 79)(64, 76)(65, 80)(68, 83)(72, 75)(77, 82)(78, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.442 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.444 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-2 * Y1 * Y3^3 * Y1 * Y3^-1, Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3^-1, Y3^3 * Y1 * Y3^2 * Y1 * Y3^2 ] Map:: R = (1, 43, 3, 45, 8, 50, 18, 60, 35, 77, 29, 71, 40, 82, 24, 66, 11, 53, 23, 65, 39, 81, 42, 84, 28, 70, 13, 55, 27, 69, 41, 83, 25, 67, 38, 80, 22, 64, 10, 52, 4, 46)(2, 44, 5, 47, 12, 54, 26, 68, 37, 79, 21, 63, 32, 74, 16, 58, 7, 49, 15, 57, 31, 73, 36, 78, 20, 62, 9, 51, 19, 61, 34, 76, 17, 59, 33, 75, 30, 72, 14, 56, 6, 48)(85, 86)(87, 91)(88, 93)(89, 95)(90, 97)(92, 101)(94, 105)(96, 109)(98, 113)(99, 107)(100, 111)(102, 110)(103, 108)(104, 112)(106, 114)(115, 122)(116, 124)(117, 123)(118, 125)(119, 120)(121, 126)(127, 128)(129, 133)(130, 135)(131, 137)(132, 139)(134, 143)(136, 147)(138, 151)(140, 155)(141, 149)(142, 153)(144, 152)(145, 150)(146, 154)(148, 156)(157, 164)(158, 166)(159, 165)(160, 167)(161, 162)(163, 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) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.450 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.445 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, (Y3^-2 * Y1 * Y3^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-3 * Y1 * Y3^2 * Y1 * Y3^-2 ] Map:: R = (1, 43, 3, 45, 8, 50, 18, 60, 35, 77, 25, 67, 41, 83, 28, 70, 13, 55, 27, 69, 42, 84, 40, 82, 24, 66, 11, 53, 23, 65, 39, 81, 29, 71, 38, 80, 22, 64, 10, 52, 4, 46)(2, 44, 5, 47, 12, 54, 26, 68, 34, 76, 17, 59, 33, 75, 20, 62, 9, 51, 19, 61, 36, 78, 32, 74, 16, 58, 7, 49, 15, 57, 31, 73, 21, 63, 37, 79, 30, 72, 14, 56, 6, 48)(85, 86)(87, 91)(88, 93)(89, 95)(90, 97)(92, 101)(94, 105)(96, 109)(98, 113)(99, 107)(100, 111)(102, 114)(103, 108)(104, 112)(106, 110)(115, 125)(116, 122)(117, 123)(118, 126)(119, 120)(121, 124)(127, 128)(129, 133)(130, 135)(131, 137)(132, 139)(134, 143)(136, 147)(138, 151)(140, 155)(141, 149)(142, 153)(144, 156)(145, 150)(146, 154)(148, 152)(157, 167)(158, 164)(159, 165)(160, 168)(161, 162)(163, 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) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.451 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.446 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1 * Y3^3, Y2 * Y3^2 * Y1 * Y3^-2, Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2, Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3, Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y1, (Y1 * Y2)^7 ] Map:: R = (1, 43, 4, 46, 14, 56, 6, 48, 19, 61, 29, 71, 37, 79, 42, 84, 22, 64, 41, 83, 27, 69, 23, 65, 39, 81, 20, 62, 38, 80, 40, 82, 21, 63, 26, 68, 9, 51, 17, 59, 5, 47)(2, 44, 7, 49, 11, 53, 3, 45, 10, 52, 28, 70, 25, 67, 35, 77, 15, 57, 34, 76, 36, 78, 16, 58, 31, 73, 12, 54, 30, 72, 33, 75, 13, 55, 32, 74, 18, 60, 24, 66, 8, 50)(85, 86)(87, 93)(88, 96)(89, 99)(90, 102)(91, 104)(92, 106)(94, 111)(95, 113)(97, 101)(98, 112)(100, 110)(103, 120)(105, 108)(107, 116)(109, 124)(114, 122)(115, 125)(117, 121)(118, 123)(119, 126)(127, 129)(128, 132)(130, 139)(131, 142)(133, 147)(134, 149)(135, 151)(136, 146)(137, 148)(138, 145)(140, 141)(143, 150)(144, 163)(152, 156)(153, 161)(154, 155)(157, 165)(158, 164)(159, 167)(160, 166)(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) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.453 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.447 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y3^-3 * Y2, Y1 * Y3^2 * Y2 * Y3^-2, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1, (Y2 * Y1)^7 ] Map:: R = (1, 43, 4, 46, 14, 56, 9, 51, 26, 68, 24, 66, 42, 84, 41, 83, 23, 65, 40, 82, 21, 63, 28, 70, 39, 81, 20, 62, 38, 80, 37, 79, 27, 69, 19, 61, 6, 48, 17, 59, 5, 47)(2, 44, 7, 49, 22, 64, 18, 60, 36, 78, 16, 58, 35, 77, 34, 76, 15, 57, 33, 75, 13, 55, 32, 74, 31, 73, 12, 54, 30, 72, 25, 67, 29, 71, 11, 53, 3, 45, 10, 52, 8, 50)(85, 86)(87, 93)(88, 96)(89, 99)(90, 102)(91, 104)(92, 107)(94, 111)(95, 112)(97, 110)(98, 100)(101, 113)(103, 116)(105, 120)(106, 108)(109, 126)(114, 122)(115, 124)(117, 123)(118, 125)(119, 121)(127, 129)(128, 132)(130, 139)(131, 142)(133, 147)(134, 150)(135, 151)(136, 146)(137, 149)(138, 143)(140, 148)(141, 145)(144, 163)(152, 160)(153, 155)(154, 156)(157, 168)(158, 164)(159, 166)(161, 165)(162, 167) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.452 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.448 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2, Y1), (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2, Y2^-3 * Y1^-3, (Y3 * Y1 * Y2^-1)^2, Y2^-5 * Y1^2, Y1 * Y3 * Y2^2 * Y3 * Y1^-1 * Y2^2, Y1^8 * Y2, Y1^2 * Y3 * Y1^-1 * Y2 * Y1^-2 * Y3 * Y2^-1, Y1^13 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 43, 4, 46)(2, 44, 9, 51)(3, 45, 12, 54)(5, 47, 14, 56)(6, 48, 15, 57)(7, 49, 21, 63)(8, 50, 24, 66)(10, 52, 25, 67)(11, 53, 28, 70)(13, 55, 30, 72)(16, 58, 32, 74)(17, 59, 33, 75)(18, 60, 34, 76)(19, 61, 35, 77)(20, 62, 36, 78)(22, 64, 37, 79)(23, 65, 38, 80)(26, 68, 39, 81)(27, 69, 40, 82)(29, 71, 41, 83)(31, 73, 42, 84)(85, 86, 91, 103, 113, 95, 107, 101, 90, 94, 106, 115, 97, 87, 92, 104, 102, 110, 111, 100, 89)(88, 98, 116, 124, 123, 118, 120, 108, 96, 114, 126, 121, 109, 99, 117, 122, 112, 125, 119, 105, 93)(127, 129, 137, 153, 148, 133, 146, 143, 131, 139, 155, 152, 136, 128, 134, 149, 142, 157, 145, 144, 132)(130, 141, 160, 161, 168, 158, 164, 150, 135, 151, 165, 167, 156, 140, 159, 162, 147, 163, 166, 154, 138) 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 ), ( 8^21 ) } Outer automorphisms :: reflexible Dual of E20.454 Graph:: simple bipartite v = 25 e = 84 f = 21 degree seq :: [ 4^21, 21^4 ] E20.449 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = C7 x S3 (small group id <42, 3>) Aut = C14 x S3 (small group id <84, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y1 * Y2, (R * Y3)^2, R * Y2 * R * Y1, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2^3 * Y3 * Y2^-3, Y1 * Y3 * Y1^-3 * Y3 * Y2^-2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y1 * Y2^-2 * Y3 * Y1^-2, Y1^2 * Y3 * Y1 * Y2^-4 * Y3 ] Map:: non-degenerate R = (1, 43, 4, 46)(2, 44, 6, 48)(3, 45, 8, 50)(5, 47, 12, 54)(7, 49, 16, 58)(9, 51, 20, 62)(10, 52, 22, 64)(11, 53, 24, 66)(13, 55, 28, 70)(14, 56, 30, 72)(15, 57, 32, 74)(17, 59, 34, 76)(18, 60, 36, 78)(19, 61, 37, 79)(21, 63, 38, 80)(23, 65, 35, 77)(25, 67, 39, 81)(26, 68, 40, 82)(27, 69, 31, 73)(29, 71, 41, 83)(33, 75, 42, 84)(85, 86, 89, 95, 107, 122, 125, 118, 104, 112, 123, 126, 120, 106, 114, 124, 121, 115, 99, 91, 87)(88, 93, 103, 108, 117, 100, 113, 98, 90, 97, 111, 119, 102, 92, 101, 110, 96, 109, 116, 105, 94)(127, 129, 133, 141, 157, 163, 166, 156, 148, 162, 168, 165, 154, 146, 160, 167, 164, 149, 137, 131, 128)(130, 136, 147, 158, 151, 138, 152, 143, 134, 144, 161, 153, 139, 132, 140, 155, 142, 159, 150, 145, 135) 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 ), ( 8^21 ) } Outer automorphisms :: reflexible Dual of E20.455 Graph:: simple bipartite v = 25 e = 84 f = 21 degree seq :: [ 4^21, 21^4 ] E20.450 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-2 * Y1 * Y3^3 * Y1 * Y3^-1, Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3^-1, Y3^3 * Y1 * Y3^2 * Y1 * Y3^2 ] Map:: R = (1, 43, 85, 127, 3, 45, 87, 129, 8, 50, 92, 134, 18, 60, 102, 144, 35, 77, 119, 161, 29, 71, 113, 155, 40, 82, 124, 166, 24, 66, 108, 150, 11, 53, 95, 137, 23, 65, 107, 149, 39, 81, 123, 165, 42, 84, 126, 168, 28, 70, 112, 154, 13, 55, 97, 139, 27, 69, 111, 153, 41, 83, 125, 167, 25, 67, 109, 151, 38, 80, 122, 164, 22, 64, 106, 148, 10, 52, 94, 136, 4, 46, 88, 130)(2, 44, 86, 128, 5, 47, 89, 131, 12, 54, 96, 138, 26, 68, 110, 152, 37, 79, 121, 163, 21, 63, 105, 147, 32, 74, 116, 158, 16, 58, 100, 142, 7, 49, 91, 133, 15, 57, 99, 141, 31, 73, 115, 157, 36, 78, 120, 162, 20, 62, 104, 146, 9, 51, 93, 135, 19, 61, 103, 145, 34, 76, 118, 160, 17, 59, 101, 143, 33, 75, 117, 159, 30, 72, 114, 156, 14, 56, 98, 140, 6, 48, 90, 132) L = (1, 44)(2, 43)(3, 49)(4, 51)(5, 53)(6, 55)(7, 45)(8, 59)(9, 46)(10, 63)(11, 47)(12, 67)(13, 48)(14, 71)(15, 65)(16, 69)(17, 50)(18, 68)(19, 66)(20, 70)(21, 52)(22, 72)(23, 57)(24, 61)(25, 54)(26, 60)(27, 58)(28, 62)(29, 56)(30, 64)(31, 80)(32, 82)(33, 81)(34, 83)(35, 78)(36, 77)(37, 84)(38, 73)(39, 75)(40, 74)(41, 76)(42, 79)(85, 128)(86, 127)(87, 133)(88, 135)(89, 137)(90, 139)(91, 129)(92, 143)(93, 130)(94, 147)(95, 131)(96, 151)(97, 132)(98, 155)(99, 149)(100, 153)(101, 134)(102, 152)(103, 150)(104, 154)(105, 136)(106, 156)(107, 141)(108, 145)(109, 138)(110, 144)(111, 142)(112, 146)(113, 140)(114, 148)(115, 164)(116, 166)(117, 165)(118, 167)(119, 162)(120, 161)(121, 168)(122, 157)(123, 159)(124, 158)(125, 160)(126, 163) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.444 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.451 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, (Y3^-2 * Y1 * Y3^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-3 * Y1 * Y3^2 * Y1 * Y3^-2 ] Map:: R = (1, 43, 85, 127, 3, 45, 87, 129, 8, 50, 92, 134, 18, 60, 102, 144, 35, 77, 119, 161, 25, 67, 109, 151, 41, 83, 125, 167, 28, 70, 112, 154, 13, 55, 97, 139, 27, 69, 111, 153, 42, 84, 126, 168, 40, 82, 124, 166, 24, 66, 108, 150, 11, 53, 95, 137, 23, 65, 107, 149, 39, 81, 123, 165, 29, 71, 113, 155, 38, 80, 122, 164, 22, 64, 106, 148, 10, 52, 94, 136, 4, 46, 88, 130)(2, 44, 86, 128, 5, 47, 89, 131, 12, 54, 96, 138, 26, 68, 110, 152, 34, 76, 118, 160, 17, 59, 101, 143, 33, 75, 117, 159, 20, 62, 104, 146, 9, 51, 93, 135, 19, 61, 103, 145, 36, 78, 120, 162, 32, 74, 116, 158, 16, 58, 100, 142, 7, 49, 91, 133, 15, 57, 99, 141, 31, 73, 115, 157, 21, 63, 105, 147, 37, 79, 121, 163, 30, 72, 114, 156, 14, 56, 98, 140, 6, 48, 90, 132) L = (1, 44)(2, 43)(3, 49)(4, 51)(5, 53)(6, 55)(7, 45)(8, 59)(9, 46)(10, 63)(11, 47)(12, 67)(13, 48)(14, 71)(15, 65)(16, 69)(17, 50)(18, 72)(19, 66)(20, 70)(21, 52)(22, 68)(23, 57)(24, 61)(25, 54)(26, 64)(27, 58)(28, 62)(29, 56)(30, 60)(31, 83)(32, 80)(33, 81)(34, 84)(35, 78)(36, 77)(37, 82)(38, 74)(39, 75)(40, 79)(41, 73)(42, 76)(85, 128)(86, 127)(87, 133)(88, 135)(89, 137)(90, 139)(91, 129)(92, 143)(93, 130)(94, 147)(95, 131)(96, 151)(97, 132)(98, 155)(99, 149)(100, 153)(101, 134)(102, 156)(103, 150)(104, 154)(105, 136)(106, 152)(107, 141)(108, 145)(109, 138)(110, 148)(111, 142)(112, 146)(113, 140)(114, 144)(115, 167)(116, 164)(117, 165)(118, 168)(119, 162)(120, 161)(121, 166)(122, 158)(123, 159)(124, 163)(125, 157)(126, 160) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.445 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.452 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1 * Y3^3, Y2 * Y3^2 * Y1 * Y3^-2, Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2, Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3, Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y1, (Y1 * Y2)^7 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 14, 56, 98, 140, 6, 48, 90, 132, 19, 61, 103, 145, 29, 71, 113, 155, 37, 79, 121, 163, 42, 84, 126, 168, 22, 64, 106, 148, 41, 83, 125, 167, 27, 69, 111, 153, 23, 65, 107, 149, 39, 81, 123, 165, 20, 62, 104, 146, 38, 80, 122, 164, 40, 82, 124, 166, 21, 63, 105, 147, 26, 68, 110, 152, 9, 51, 93, 135, 17, 59, 101, 143, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 28, 70, 112, 154, 25, 67, 109, 151, 35, 77, 119, 161, 15, 57, 99, 141, 34, 76, 118, 160, 36, 78, 120, 162, 16, 58, 100, 142, 31, 73, 115, 157, 12, 54, 96, 138, 30, 72, 114, 156, 33, 75, 117, 159, 13, 55, 97, 139, 32, 74, 116, 158, 18, 60, 102, 144, 24, 66, 108, 150, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 54)(5, 57)(6, 60)(7, 62)(8, 64)(9, 45)(10, 69)(11, 71)(12, 46)(13, 59)(14, 70)(15, 47)(16, 68)(17, 55)(18, 48)(19, 78)(20, 49)(21, 66)(22, 50)(23, 74)(24, 63)(25, 82)(26, 58)(27, 52)(28, 56)(29, 53)(30, 80)(31, 83)(32, 65)(33, 79)(34, 81)(35, 84)(36, 61)(37, 75)(38, 72)(39, 76)(40, 67)(41, 73)(42, 77)(85, 129)(86, 132)(87, 127)(88, 139)(89, 142)(90, 128)(91, 147)(92, 149)(93, 151)(94, 146)(95, 148)(96, 145)(97, 130)(98, 141)(99, 140)(100, 131)(101, 150)(102, 163)(103, 138)(104, 136)(105, 133)(106, 137)(107, 134)(108, 143)(109, 135)(110, 156)(111, 161)(112, 155)(113, 154)(114, 152)(115, 165)(116, 164)(117, 167)(118, 166)(119, 153)(120, 168)(121, 144)(122, 158)(123, 157)(124, 160)(125, 159)(126, 162) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.447 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.453 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y3^-3 * Y2, Y1 * Y3^2 * Y2 * Y3^-2, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1, (Y2 * Y1)^7 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 14, 56, 98, 140, 9, 51, 93, 135, 26, 68, 110, 152, 24, 66, 108, 150, 42, 84, 126, 168, 41, 83, 125, 167, 23, 65, 107, 149, 40, 82, 124, 166, 21, 63, 105, 147, 28, 70, 112, 154, 39, 81, 123, 165, 20, 62, 104, 146, 38, 80, 122, 164, 37, 79, 121, 163, 27, 69, 111, 153, 19, 61, 103, 145, 6, 48, 90, 132, 17, 59, 101, 143, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 22, 64, 106, 148, 18, 60, 102, 144, 36, 78, 120, 162, 16, 58, 100, 142, 35, 77, 119, 161, 34, 76, 118, 160, 15, 57, 99, 141, 33, 75, 117, 159, 13, 55, 97, 139, 32, 74, 116, 158, 31, 73, 115, 157, 12, 54, 96, 138, 30, 72, 114, 156, 25, 67, 109, 151, 29, 71, 113, 155, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 54)(5, 57)(6, 60)(7, 62)(8, 65)(9, 45)(10, 69)(11, 70)(12, 46)(13, 68)(14, 58)(15, 47)(16, 56)(17, 71)(18, 48)(19, 74)(20, 49)(21, 78)(22, 66)(23, 50)(24, 64)(25, 84)(26, 55)(27, 52)(28, 53)(29, 59)(30, 80)(31, 82)(32, 61)(33, 81)(34, 83)(35, 79)(36, 63)(37, 77)(38, 72)(39, 75)(40, 73)(41, 76)(42, 67)(85, 129)(86, 132)(87, 127)(88, 139)(89, 142)(90, 128)(91, 147)(92, 150)(93, 151)(94, 146)(95, 149)(96, 143)(97, 130)(98, 148)(99, 145)(100, 131)(101, 138)(102, 163)(103, 141)(104, 136)(105, 133)(106, 140)(107, 137)(108, 134)(109, 135)(110, 160)(111, 155)(112, 156)(113, 153)(114, 154)(115, 168)(116, 164)(117, 166)(118, 152)(119, 165)(120, 167)(121, 144)(122, 158)(123, 161)(124, 159)(125, 162)(126, 157) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.446 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.454 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2, Y1), (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2, Y2^-3 * Y1^-3, (Y3 * Y1 * Y2^-1)^2, Y2^-5 * Y1^2, Y1 * Y3 * Y2^2 * Y3 * Y1^-1 * Y2^2, Y1^8 * Y2, Y1^2 * Y3 * Y1^-1 * Y2 * Y1^-2 * Y3 * Y2^-1, Y1^13 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 43, 85, 127, 4, 46, 88, 130)(2, 44, 86, 128, 9, 51, 93, 135)(3, 45, 87, 129, 12, 54, 96, 138)(5, 47, 89, 131, 14, 56, 98, 140)(6, 48, 90, 132, 15, 57, 99, 141)(7, 49, 91, 133, 21, 63, 105, 147)(8, 50, 92, 134, 24, 66, 108, 150)(10, 52, 94, 136, 25, 67, 109, 151)(11, 53, 95, 137, 28, 70, 112, 154)(13, 55, 97, 139, 30, 72, 114, 156)(16, 58, 100, 142, 32, 74, 116, 158)(17, 59, 101, 143, 33, 75, 117, 159)(18, 60, 102, 144, 34, 76, 118, 160)(19, 61, 103, 145, 35, 77, 119, 161)(20, 62, 104, 146, 36, 78, 120, 162)(22, 64, 106, 148, 37, 79, 121, 163)(23, 65, 107, 149, 38, 80, 122, 164)(26, 68, 110, 152, 39, 81, 123, 165)(27, 69, 111, 153, 40, 82, 124, 166)(29, 71, 113, 155, 41, 83, 125, 167)(31, 73, 115, 157, 42, 84, 126, 168) L = (1, 44)(2, 49)(3, 50)(4, 56)(5, 43)(6, 52)(7, 61)(8, 62)(9, 46)(10, 64)(11, 65)(12, 72)(13, 45)(14, 74)(15, 75)(16, 47)(17, 48)(18, 68)(19, 71)(20, 60)(21, 51)(22, 73)(23, 59)(24, 54)(25, 57)(26, 69)(27, 58)(28, 83)(29, 53)(30, 84)(31, 55)(32, 82)(33, 80)(34, 78)(35, 63)(36, 66)(37, 67)(38, 70)(39, 76)(40, 81)(41, 77)(42, 79)(85, 129)(86, 134)(87, 137)(88, 141)(89, 139)(90, 127)(91, 146)(92, 149)(93, 151)(94, 128)(95, 153)(96, 130)(97, 155)(98, 159)(99, 160)(100, 157)(101, 131)(102, 132)(103, 144)(104, 143)(105, 163)(106, 133)(107, 142)(108, 135)(109, 165)(110, 136)(111, 148)(112, 138)(113, 152)(114, 140)(115, 145)(116, 164)(117, 162)(118, 161)(119, 168)(120, 147)(121, 166)(122, 150)(123, 167)(124, 154)(125, 156)(126, 158) local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21 ) } Outer automorphisms :: reflexible Dual of E20.448 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 25 degree seq :: [ 8^21 ] E20.455 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = C7 x S3 (small group id <42, 3>) Aut = C14 x S3 (small group id <84, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y1 * Y2, (R * Y3)^2, R * Y2 * R * Y1, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2^3 * Y3 * Y2^-3, Y1 * Y3 * Y1^-3 * Y3 * Y2^-2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y1 * Y2^-2 * Y3 * Y1^-2, Y1^2 * Y3 * Y1 * Y2^-4 * Y3 ] 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, 16, 58, 100, 142)(9, 51, 93, 135, 20, 62, 104, 146)(10, 52, 94, 136, 22, 64, 106, 148)(11, 53, 95, 137, 24, 66, 108, 150)(13, 55, 97, 139, 28, 70, 112, 154)(14, 56, 98, 140, 30, 72, 114, 156)(15, 57, 99, 141, 32, 74, 116, 158)(17, 59, 101, 143, 34, 76, 118, 160)(18, 60, 102, 144, 36, 78, 120, 162)(19, 61, 103, 145, 37, 79, 121, 163)(21, 63, 105, 147, 38, 80, 122, 164)(23, 65, 107, 149, 35, 77, 119, 161)(25, 67, 109, 151, 39, 81, 123, 165)(26, 68, 110, 152, 40, 82, 124, 166)(27, 69, 111, 153, 31, 73, 115, 157)(29, 71, 113, 155, 41, 83, 125, 167)(33, 75, 117, 159, 42, 84, 126, 168) L = (1, 44)(2, 47)(3, 43)(4, 51)(5, 53)(6, 55)(7, 45)(8, 59)(9, 61)(10, 46)(11, 65)(12, 67)(13, 69)(14, 48)(15, 49)(16, 71)(17, 68)(18, 50)(19, 66)(20, 70)(21, 52)(22, 72)(23, 80)(24, 75)(25, 74)(26, 54)(27, 77)(28, 81)(29, 56)(30, 82)(31, 57)(32, 63)(33, 58)(34, 62)(35, 60)(36, 64)(37, 73)(38, 83)(39, 84)(40, 79)(41, 76)(42, 78)(85, 129)(86, 127)(87, 133)(88, 136)(89, 128)(90, 140)(91, 141)(92, 144)(93, 130)(94, 147)(95, 131)(96, 152)(97, 132)(98, 155)(99, 157)(100, 159)(101, 134)(102, 161)(103, 135)(104, 160)(105, 158)(106, 162)(107, 137)(108, 145)(109, 138)(110, 143)(111, 139)(112, 146)(113, 142)(114, 148)(115, 163)(116, 151)(117, 150)(118, 167)(119, 153)(120, 168)(121, 166)(122, 149)(123, 154)(124, 156)(125, 164)(126, 165) local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21 ) } Outer automorphisms :: reflexible Dual of E20.449 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 25 degree seq :: [ 8^21 ] E20.456 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^3 * Y1 * Y2^-2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^3 * Y1 * Y2^2 * Y1 * Y2^2, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 9, 51)(5, 47, 11, 53)(6, 48, 13, 55)(8, 50, 17, 59)(10, 52, 21, 63)(12, 54, 25, 67)(14, 56, 29, 71)(15, 57, 23, 65)(16, 58, 27, 69)(18, 60, 26, 68)(19, 61, 24, 66)(20, 62, 28, 70)(22, 64, 30, 72)(31, 73, 38, 80)(32, 74, 40, 82)(33, 75, 39, 81)(34, 76, 41, 83)(35, 77, 36, 78)(37, 79, 42, 84)(85, 127, 87, 129, 92, 134, 102, 144, 119, 161, 113, 155, 124, 166, 108, 150, 95, 137, 107, 149, 123, 165, 126, 168, 112, 154, 97, 139, 111, 153, 125, 167, 109, 151, 122, 164, 106, 148, 94, 136, 88, 130)(86, 128, 89, 131, 96, 138, 110, 152, 121, 163, 105, 147, 116, 158, 100, 142, 91, 133, 99, 141, 115, 157, 120, 162, 104, 146, 93, 135, 103, 145, 118, 160, 101, 143, 117, 159, 114, 156, 98, 140, 90, 132) 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, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.457 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1 * Y2^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^-3 * Y1 * Y2^2 * Y1 * Y2^-2, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 9, 51)(5, 47, 11, 53)(6, 48, 13, 55)(8, 50, 17, 59)(10, 52, 21, 63)(12, 54, 25, 67)(14, 56, 29, 71)(15, 57, 23, 65)(16, 58, 27, 69)(18, 60, 30, 72)(19, 61, 24, 66)(20, 62, 28, 70)(22, 64, 26, 68)(31, 73, 41, 83)(32, 74, 38, 80)(33, 75, 39, 81)(34, 76, 42, 84)(35, 77, 36, 78)(37, 79, 40, 82)(85, 127, 87, 129, 92, 134, 102, 144, 119, 161, 109, 151, 125, 167, 112, 154, 97, 139, 111, 153, 126, 168, 124, 166, 108, 150, 95, 137, 107, 149, 123, 165, 113, 155, 122, 164, 106, 148, 94, 136, 88, 130)(86, 128, 89, 131, 96, 138, 110, 152, 118, 160, 101, 143, 117, 159, 104, 146, 93, 135, 103, 145, 120, 162, 116, 158, 100, 142, 91, 133, 99, 141, 115, 157, 105, 147, 121, 163, 114, 156, 98, 140, 90, 132) 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, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.458 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y2)^2, (Y3, Y2), (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y2^-1 * Y1, Y3^-1 * Y2^-7, 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 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 10, 52)(5, 47, 16, 58)(6, 48, 8, 50)(7, 49, 14, 56)(9, 51, 15, 57)(12, 54, 24, 66)(13, 55, 20, 62)(17, 59, 30, 72)(18, 60, 22, 64)(19, 61, 26, 68)(21, 63, 32, 74)(23, 65, 27, 69)(25, 67, 33, 75)(28, 70, 29, 71)(31, 73, 34, 76)(35, 77, 38, 80)(36, 78, 39, 81)(37, 79, 41, 83)(40, 82, 42, 84)(85, 127, 87, 129, 96, 138, 109, 151, 121, 163, 116, 158, 102, 144, 90, 132, 98, 140, 111, 153, 123, 165, 124, 166, 112, 154, 99, 141, 88, 130, 97, 139, 110, 152, 122, 164, 115, 157, 101, 143, 89, 131)(86, 128, 91, 133, 103, 145, 117, 159, 126, 168, 114, 156, 106, 148, 94, 136, 95, 137, 107, 149, 119, 161, 125, 167, 113, 155, 100, 142, 92, 134, 104, 146, 108, 150, 120, 162, 118, 160, 105, 147, 93, 135) L = (1, 88)(2, 92)(3, 97)(4, 90)(5, 99)(6, 85)(7, 104)(8, 94)(9, 100)(10, 86)(11, 91)(12, 110)(13, 98)(14, 87)(15, 102)(16, 106)(17, 112)(18, 89)(19, 108)(20, 95)(21, 113)(22, 93)(23, 103)(24, 107)(25, 122)(26, 111)(27, 96)(28, 116)(29, 114)(30, 105)(31, 124)(32, 101)(33, 120)(34, 125)(35, 117)(36, 119)(37, 115)(38, 123)(39, 109)(40, 121)(41, 126)(42, 118)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.459 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1, Y3^-1), (Y1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y2^2 * Y1, Y1 * Y2 * Y1 * Y2^-1 * Y3^-2, Y2^-4 * Y3 * Y2^-2 ] 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, 27, 69)(12, 54, 26, 68)(13, 55, 23, 65)(14, 56, 28, 70)(15, 57, 30, 72)(16, 58, 22, 64)(18, 60, 24, 66)(19, 61, 29, 71)(20, 62, 25, 67)(31, 73, 40, 82)(32, 74, 41, 83)(33, 75, 42, 84)(34, 76, 37, 79)(35, 77, 38, 80)(36, 78, 39, 81)(85, 127, 87, 129, 96, 138, 115, 157, 120, 162, 100, 142, 88, 130, 97, 139, 111, 153, 104, 146, 117, 159, 119, 161, 99, 141, 105, 147, 103, 145, 90, 132, 98, 140, 116, 158, 118, 160, 102, 144, 89, 131)(86, 128, 91, 133, 106, 148, 121, 163, 126, 168, 110, 152, 92, 134, 107, 149, 101, 143, 114, 156, 123, 165, 125, 167, 109, 151, 95, 137, 113, 155, 94, 136, 108, 150, 122, 164, 124, 166, 112, 154, 93, 135) L = (1, 88)(2, 92)(3, 97)(4, 99)(5, 100)(6, 85)(7, 107)(8, 109)(9, 110)(10, 86)(11, 112)(12, 111)(13, 105)(14, 87)(15, 118)(16, 119)(17, 113)(18, 120)(19, 89)(20, 90)(21, 102)(22, 101)(23, 95)(24, 91)(25, 124)(26, 125)(27, 103)(28, 126)(29, 93)(30, 94)(31, 104)(32, 96)(33, 98)(34, 115)(35, 116)(36, 117)(37, 114)(38, 106)(39, 108)(40, 121)(41, 122)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.463 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.460 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3 * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^2 * Y2^3, Y3 * Y1 * Y2 * Y1 * Y2^-1, Y3^7, Y3^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] 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, 14, 56)(9, 51, 16, 58)(12, 54, 29, 71)(13, 55, 28, 70)(15, 57, 26, 68)(18, 60, 37, 79)(19, 61, 35, 77)(20, 62, 23, 65)(21, 63, 39, 81)(22, 64, 31, 73)(24, 66, 41, 83)(25, 67, 33, 75)(27, 69, 30, 72)(32, 74, 42, 84)(34, 76, 36, 78)(38, 80, 40, 82)(85, 127, 87, 129, 96, 138, 104, 146, 115, 157, 123, 165, 116, 158, 118, 160, 100, 142, 88, 130, 97, 139, 103, 145, 90, 132, 98, 140, 114, 156, 122, 164, 125, 167, 117, 159, 99, 141, 102, 144, 89, 131)(86, 128, 91, 133, 105, 147, 110, 152, 112, 154, 113, 155, 124, 166, 120, 162, 101, 143, 92, 134, 106, 148, 109, 151, 94, 136, 95, 137, 111, 153, 126, 168, 121, 163, 119, 161, 107, 149, 108, 150, 93, 135) L = (1, 88)(2, 92)(3, 97)(4, 99)(5, 100)(6, 85)(7, 106)(8, 107)(9, 101)(10, 86)(11, 91)(12, 103)(13, 102)(14, 87)(15, 116)(16, 117)(17, 119)(18, 118)(19, 89)(20, 90)(21, 109)(22, 108)(23, 124)(24, 120)(25, 93)(26, 94)(27, 105)(28, 95)(29, 111)(30, 96)(31, 98)(32, 122)(33, 123)(34, 125)(35, 113)(36, 121)(37, 112)(38, 104)(39, 114)(40, 126)(41, 115)(42, 110)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.461 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-2 * Y2^3, Y1 * Y3 * Y2 * Y1 * Y2^-1, Y3^-7, Y3^7 ] 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, 13, 55)(9, 51, 19, 61)(12, 54, 29, 71)(14, 56, 28, 70)(15, 57, 26, 68)(16, 58, 33, 75)(18, 60, 35, 77)(20, 62, 23, 65)(21, 63, 39, 81)(22, 64, 31, 73)(24, 66, 37, 79)(25, 67, 41, 83)(27, 69, 30, 72)(32, 74, 42, 84)(34, 76, 36, 78)(38, 80, 40, 82)(85, 127, 87, 129, 96, 138, 99, 141, 115, 157, 123, 165, 122, 164, 120, 162, 103, 145, 90, 132, 98, 140, 100, 142, 88, 130, 97, 139, 114, 156, 116, 158, 125, 167, 121, 163, 104, 146, 102, 144, 89, 131)(86, 128, 91, 133, 105, 147, 107, 149, 112, 154, 113, 155, 126, 168, 118, 160, 101, 143, 94, 136, 106, 148, 108, 150, 92, 134, 95, 137, 111, 153, 124, 166, 119, 161, 117, 159, 110, 152, 109, 151, 93, 135) L = (1, 88)(2, 92)(3, 97)(4, 99)(5, 100)(6, 85)(7, 95)(8, 107)(9, 108)(10, 86)(11, 112)(12, 114)(13, 115)(14, 87)(15, 116)(16, 96)(17, 93)(18, 98)(19, 89)(20, 90)(21, 111)(22, 91)(23, 124)(24, 105)(25, 106)(26, 94)(27, 113)(28, 119)(29, 117)(30, 123)(31, 125)(32, 122)(33, 101)(34, 109)(35, 118)(36, 102)(37, 103)(38, 104)(39, 121)(40, 126)(41, 120)(42, 110)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.462 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.462 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (Y1 * Y3)^2, Y3 * Y2^-3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3 * Y2^2 * Y1 * Y2^-2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3 * Y2, Y3^7, Y1 * Y2 * Y3^-1 * Y1 * Y3^2 * Y2^-1 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 10, 52)(5, 47, 16, 58)(6, 48, 8, 50)(7, 49, 19, 61)(9, 51, 24, 66)(12, 54, 31, 73)(13, 55, 30, 72)(14, 56, 28, 70)(15, 57, 26, 68)(17, 59, 37, 79)(18, 60, 23, 65)(20, 62, 32, 74)(21, 63, 41, 83)(22, 64, 34, 76)(25, 67, 42, 84)(27, 69, 39, 81)(29, 71, 35, 77)(33, 75, 38, 80)(36, 78, 40, 82)(85, 127, 87, 129, 96, 138, 88, 130, 97, 139, 116, 158, 99, 141, 117, 159, 108, 150, 119, 161, 125, 167, 126, 168, 124, 166, 103, 145, 123, 165, 102, 144, 118, 160, 101, 143, 90, 132, 98, 140, 89, 131)(86, 128, 91, 133, 104, 146, 92, 134, 105, 147, 115, 157, 107, 149, 122, 164, 100, 142, 120, 162, 114, 156, 121, 163, 113, 155, 95, 137, 111, 153, 110, 152, 112, 154, 109, 151, 94, 136, 106, 148, 93, 135) L = (1, 88)(2, 92)(3, 97)(4, 99)(5, 96)(6, 85)(7, 105)(8, 107)(9, 104)(10, 86)(11, 112)(12, 116)(13, 117)(14, 87)(15, 119)(16, 121)(17, 89)(18, 90)(19, 118)(20, 115)(21, 122)(22, 91)(23, 120)(24, 126)(25, 93)(26, 94)(27, 109)(28, 106)(29, 110)(30, 95)(31, 100)(32, 108)(33, 125)(34, 98)(35, 124)(36, 113)(37, 111)(38, 114)(39, 101)(40, 102)(41, 103)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.461 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.463 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-3, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y3 * Y2 * Y1 * Y2^2 * Y1 * Y3, Y3^-1 * Y1 * Y3 * Y2 * Y3 * Y1 * Y2^-1, Y1 * Y2 * Y3^-2 * Y2 * Y1 * Y2, Y1 * Y2 * Y3^3 * Y1 * Y2^-1, Y3^7, Y1 * Y3^-1 * Y2^-1 * Y1 * Y3 * Y2^-2, (Y3 * Y2^-1)^21 ] 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, 19, 61)(9, 51, 25, 67)(12, 54, 31, 73)(13, 55, 30, 72)(14, 56, 28, 70)(15, 57, 26, 68)(16, 58, 37, 79)(18, 60, 23, 65)(20, 62, 32, 74)(21, 63, 33, 75)(22, 64, 41, 83)(24, 66, 42, 84)(27, 69, 36, 78)(29, 71, 40, 82)(34, 76, 39, 81)(35, 77, 38, 80)(85, 127, 87, 129, 96, 138, 90, 132, 98, 140, 116, 158, 102, 144, 118, 160, 109, 151, 124, 166, 125, 167, 126, 168, 119, 161, 103, 145, 120, 162, 99, 141, 117, 159, 100, 142, 88, 130, 97, 139, 89, 131)(86, 128, 91, 133, 104, 146, 94, 136, 106, 148, 115, 157, 110, 152, 123, 165, 101, 143, 122, 164, 112, 154, 121, 163, 113, 155, 95, 137, 111, 153, 107, 149, 114, 156, 108, 150, 92, 134, 105, 147, 93, 135) L = (1, 88)(2, 92)(3, 97)(4, 99)(5, 100)(6, 85)(7, 105)(8, 107)(9, 108)(10, 86)(11, 112)(12, 89)(13, 117)(14, 87)(15, 119)(16, 120)(17, 115)(18, 90)(19, 125)(20, 93)(21, 114)(22, 91)(23, 113)(24, 111)(25, 116)(26, 94)(27, 121)(28, 123)(29, 122)(30, 95)(31, 104)(32, 96)(33, 103)(34, 98)(35, 124)(36, 126)(37, 101)(38, 110)(39, 106)(40, 102)(41, 118)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.459 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.464 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) 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, Y1 * Y2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y2^-1 * Y3 * Y2^-3, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1 * Y3 * Y2^3 * Y1^-2 * Y3 * Y2^-1, Y1^3 * Y3 * Y1^-2 * Y3 * Y2^-2, Y2^21, Y1^21 ] Map:: non-degenerate R = (1, 43, 4, 46)(2, 44, 6, 48)(3, 45, 8, 50)(5, 47, 12, 54)(7, 49, 16, 58)(9, 51, 20, 62)(10, 52, 22, 64)(11, 53, 24, 66)(13, 55, 28, 70)(14, 56, 30, 72)(15, 57, 32, 74)(17, 59, 35, 77)(18, 60, 36, 78)(19, 61, 37, 79)(21, 63, 38, 80)(23, 65, 34, 76)(25, 67, 39, 81)(26, 68, 40, 82)(27, 69, 41, 83)(29, 71, 31, 73)(33, 75, 42, 84)(85, 86, 89, 95, 107, 121, 125, 120, 106, 114, 124, 126, 119, 104, 112, 123, 122, 115, 99, 91, 87)(88, 93, 103, 116, 110, 96, 109, 102, 92, 101, 118, 113, 98, 90, 97, 111, 100, 117, 108, 105, 94)(127, 129, 133, 141, 157, 164, 165, 154, 146, 161, 168, 166, 156, 148, 162, 167, 163, 149, 137, 131, 128)(130, 136, 147, 150, 159, 142, 153, 139, 132, 140, 155, 160, 143, 134, 144, 151, 138, 152, 158, 145, 135) 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 ), ( 8^21 ) } Outer automorphisms :: reflexible Dual of E20.465 Graph:: simple bipartite v = 25 e = 84 f = 21 degree seq :: [ 4^21, 21^4 ] E20.465 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) 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, Y1 * Y2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y2^-1 * Y3 * Y2^-3, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1 * Y3 * Y2^3 * Y1^-2 * Y3 * Y2^-1, Y1^3 * Y3 * Y1^-2 * Y3 * Y2^-2, Y2^21, Y1^21 ] 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, 16, 58, 100, 142)(9, 51, 93, 135, 20, 62, 104, 146)(10, 52, 94, 136, 22, 64, 106, 148)(11, 53, 95, 137, 24, 66, 108, 150)(13, 55, 97, 139, 28, 70, 112, 154)(14, 56, 98, 140, 30, 72, 114, 156)(15, 57, 99, 141, 32, 74, 116, 158)(17, 59, 101, 143, 35, 77, 119, 161)(18, 60, 102, 144, 36, 78, 120, 162)(19, 61, 103, 145, 37, 79, 121, 163)(21, 63, 105, 147, 38, 80, 122, 164)(23, 65, 107, 149, 34, 76, 118, 160)(25, 67, 109, 151, 39, 81, 123, 165)(26, 68, 110, 152, 40, 82, 124, 166)(27, 69, 111, 153, 41, 83, 125, 167)(29, 71, 113, 155, 31, 73, 115, 157)(33, 75, 117, 159, 42, 84, 126, 168) L = (1, 44)(2, 47)(3, 43)(4, 51)(5, 53)(6, 55)(7, 45)(8, 59)(9, 61)(10, 46)(11, 65)(12, 67)(13, 69)(14, 48)(15, 49)(16, 75)(17, 76)(18, 50)(19, 74)(20, 70)(21, 52)(22, 72)(23, 79)(24, 63)(25, 60)(26, 54)(27, 58)(28, 81)(29, 56)(30, 82)(31, 57)(32, 68)(33, 66)(34, 71)(35, 62)(36, 64)(37, 83)(38, 73)(39, 80)(40, 84)(41, 78)(42, 77)(85, 129)(86, 127)(87, 133)(88, 136)(89, 128)(90, 140)(91, 141)(92, 144)(93, 130)(94, 147)(95, 131)(96, 152)(97, 132)(98, 155)(99, 157)(100, 153)(101, 134)(102, 151)(103, 135)(104, 161)(105, 150)(106, 162)(107, 137)(108, 159)(109, 138)(110, 158)(111, 139)(112, 146)(113, 160)(114, 148)(115, 164)(116, 145)(117, 142)(118, 143)(119, 168)(120, 167)(121, 149)(122, 165)(123, 154)(124, 156)(125, 163)(126, 166) local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21 ) } Outer automorphisms :: reflexible Dual of E20.464 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 25 degree seq :: [ 8^21 ] E20.466 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^21 ] Map:: R = (1, 44, 2, 47, 5, 51, 9, 55, 13, 59, 17, 63, 21, 67, 25, 71, 29, 75, 33, 79, 37, 82, 40, 78, 36, 74, 32, 70, 28, 66, 24, 62, 20, 58, 16, 54, 12, 50, 8, 46, 4, 43)(3, 49, 7, 53, 11, 57, 15, 61, 19, 65, 23, 69, 27, 73, 31, 77, 35, 81, 39, 84, 42, 83, 41, 80, 38, 76, 34, 72, 30, 68, 26, 64, 22, 60, 18, 56, 14, 52, 10, 48, 6, 45) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 34)(32, 35)(33, 38)(36, 39)(37, 41)(40, 42)(43, 45)(44, 48)(46, 49)(47, 52)(50, 53)(51, 56)(54, 57)(55, 60)(58, 61)(59, 64)(62, 65)(63, 68)(66, 69)(67, 72)(70, 73)(71, 76)(74, 77)(75, 80)(78, 81)(79, 83)(82, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.467 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, (Y3 * Y2)^3, Y1^2 * Y2 * Y1^-5 * Y3, Y1^2 * Y3 * Y1^-2 * Y2 * Y3 * Y1^-3 * Y2, Y1 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y1^2 * 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 * Y3 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 56, 14, 67, 25, 77, 35, 65, 23, 54, 12, 60, 18, 71, 29, 80, 38, 83, 41, 74, 32, 62, 20, 52, 10, 59, 17, 70, 28, 78, 36, 66, 24, 55, 13, 47, 5, 43)(3, 51, 9, 61, 19, 73, 31, 82, 40, 81, 39, 72, 30, 63, 21, 75, 33, 84, 42, 79, 37, 69, 27, 58, 16, 50, 8, 46, 4, 53, 11, 64, 22, 76, 34, 68, 26, 57, 15, 49, 7, 45) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 29)(17, 30)(20, 33)(22, 35)(24, 31)(25, 34)(27, 38)(28, 39)(32, 42)(36, 40)(37, 41)(43, 46)(44, 50)(45, 52)(47, 53)(48, 58)(49, 59)(51, 62)(54, 63)(55, 64)(56, 69)(57, 70)(60, 72)(61, 74)(65, 75)(66, 76)(67, 79)(68, 78)(71, 81)(73, 83)(77, 84)(80, 82) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.468 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1 * Y3 * Y1^-2 * Y2, (Y2 * Y3)^7, Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 52, 10, 57, 15, 62, 20, 64, 22, 69, 27, 74, 32, 76, 34, 81, 39, 84, 42, 79, 37, 77, 35, 72, 30, 67, 25, 65, 23, 60, 18, 54, 12, 55, 13, 47, 5, 43)(3, 51, 9, 50, 8, 46, 4, 53, 11, 59, 17, 61, 19, 66, 24, 71, 29, 73, 31, 78, 36, 83, 41, 82, 40, 80, 38, 75, 33, 70, 28, 68, 26, 63, 21, 58, 16, 56, 14, 49, 7, 45) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 13)(10, 16)(11, 18)(15, 21)(17, 23)(19, 25)(20, 26)(22, 28)(24, 30)(27, 33)(29, 35)(31, 37)(32, 38)(34, 40)(36, 42)(39, 41)(43, 46)(44, 50)(45, 52)(47, 53)(48, 51)(49, 57)(54, 61)(55, 59)(56, 62)(58, 64)(60, 66)(63, 69)(65, 71)(67, 73)(68, 74)(70, 76)(72, 78)(75, 81)(77, 83)(79, 82)(80, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.471 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.469 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, (R * Y1)^2, R * Y3 * R * Y2, (Y2 * Y1)^2, Y3 * Y1 * Y2 * Y1^-3, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 56, 14, 54, 12, 60, 18, 66, 24, 73, 31, 72, 30, 76, 34, 82, 40, 84, 42, 78, 36, 71, 29, 75, 33, 69, 27, 62, 20, 52, 10, 59, 17, 55, 13, 47, 5, 43)(3, 51, 9, 61, 19, 67, 25, 63, 21, 70, 28, 77, 35, 83, 41, 79, 37, 80, 38, 81, 39, 74, 32, 68, 26, 64, 22, 65, 23, 58, 16, 50, 8, 46, 4, 53, 11, 57, 15, 49, 7, 45) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 14)(13, 19)(16, 24)(17, 25)(20, 28)(22, 30)(23, 31)(26, 34)(27, 35)(29, 37)(32, 40)(33, 41)(36, 38)(39, 42)(43, 46)(44, 50)(45, 52)(47, 53)(48, 58)(49, 59)(51, 62)(54, 64)(55, 57)(56, 65)(60, 68)(61, 69)(63, 71)(66, 74)(67, 75)(70, 78)(72, 80)(73, 81)(76, 79)(77, 84)(82, 83) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.470 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.470 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2 * Y1)^2, Y1 * Y2 * Y1^-2 * Y3, (Y3 * Y2)^7, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 54, 12, 57, 15, 62, 20, 67, 25, 69, 27, 74, 32, 79, 37, 81, 39, 83, 41, 78, 36, 76, 34, 71, 29, 66, 24, 64, 22, 59, 17, 52, 10, 55, 13, 47, 5, 43)(3, 51, 9, 58, 16, 60, 18, 65, 23, 70, 28, 72, 30, 77, 35, 82, 40, 84, 42, 80, 38, 75, 33, 73, 31, 68, 26, 63, 21, 61, 19, 56, 14, 50, 8, 46, 4, 53, 11, 49, 7, 45) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 11)(8, 15)(10, 18)(13, 16)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 35)(31, 37)(33, 39)(34, 40)(36, 42)(38, 41)(43, 46)(44, 50)(45, 52)(47, 53)(48, 56)(49, 55)(51, 59)(54, 61)(57, 63)(58, 64)(60, 66)(62, 68)(65, 71)(67, 73)(69, 75)(70, 76)(72, 78)(74, 80)(77, 83)(79, 84)(81, 82) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.469 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.471 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 21, 21}) Quotient :: halfedge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2, (Y3 * Y1^3)^2, Y1^10 * Y2 * Y3 ] Map:: non-degenerate R = (1, 44, 2, 48, 6, 56, 14, 64, 22, 72, 30, 80, 38, 78, 36, 70, 28, 62, 20, 54, 12, 52, 10, 59, 17, 67, 25, 75, 33, 83, 41, 79, 37, 71, 29, 63, 21, 55, 13, 47, 5, 43)(3, 51, 9, 60, 18, 68, 26, 76, 34, 84, 42, 82, 40, 74, 32, 66, 24, 58, 16, 50, 8, 46, 4, 53, 11, 61, 19, 69, 27, 77, 35, 81, 39, 73, 31, 65, 23, 57, 15, 49, 7, 45) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 10)(11, 20)(13, 18)(14, 23)(16, 17)(19, 28)(21, 26)(22, 31)(24, 25)(27, 36)(29, 34)(30, 39)(32, 33)(35, 38)(37, 42)(40, 41)(43, 46)(44, 50)(45, 52)(47, 53)(48, 58)(49, 59)(51, 54)(55, 61)(56, 66)(57, 67)(60, 62)(63, 69)(64, 74)(65, 75)(68, 70)(71, 77)(72, 82)(73, 83)(76, 78)(79, 81)(80, 84) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.468 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.472 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^21 ] Map:: R = (1, 43, 3, 45, 7, 49, 11, 53, 15, 57, 19, 61, 23, 65, 27, 69, 31, 73, 35, 77, 39, 81, 40, 82, 36, 78, 32, 74, 28, 70, 24, 66, 20, 62, 16, 58, 12, 54, 8, 50, 4, 46)(2, 44, 5, 47, 9, 51, 13, 55, 17, 59, 21, 63, 25, 67, 29, 71, 33, 75, 37, 79, 41, 83, 42, 84, 38, 80, 34, 76, 30, 72, 26, 68, 22, 64, 18, 60, 14, 56, 10, 52, 6, 48)(85, 86)(87, 90)(88, 89)(91, 94)(92, 93)(95, 98)(96, 97)(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)(129, 132)(130, 131)(133, 136)(134, 135)(137, 140)(138, 139)(141, 144)(142, 143)(145, 148)(146, 147)(149, 152)(150, 151)(153, 156)(154, 155)(157, 160)(158, 159)(161, 164)(162, 163)(165, 168)(166, 167) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.479 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.473 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y1 * Y3^3 * Y2, (Y1 * Y2)^7, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 43, 4, 46, 12, 54, 6, 48, 15, 57, 22, 64, 20, 62, 27, 69, 34, 76, 32, 74, 39, 81, 41, 83, 35, 77, 37, 79, 30, 72, 23, 65, 25, 67, 18, 60, 9, 51, 13, 55, 5, 47)(2, 44, 7, 49, 11, 53, 3, 45, 10, 52, 19, 61, 17, 59, 24, 66, 31, 73, 29, 71, 36, 78, 42, 84, 38, 80, 40, 82, 33, 75, 26, 68, 28, 70, 21, 63, 14, 56, 16, 58, 8, 50)(85, 86)(87, 93)(88, 92)(89, 91)(90, 98)(94, 102)(95, 97)(96, 100)(99, 105)(101, 107)(103, 109)(104, 110)(106, 112)(108, 114)(111, 117)(113, 119)(115, 121)(116, 122)(118, 124)(120, 125)(123, 126)(127, 129)(128, 132)(130, 137)(131, 136)(133, 138)(134, 141)(135, 143)(139, 145)(140, 146)(142, 148)(144, 150)(147, 153)(149, 155)(151, 157)(152, 158)(154, 160)(156, 162)(159, 165)(161, 164)(163, 168)(166, 167) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.484 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.474 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y2 * Y3)^2, (Y2 * Y1)^3, Y2 * Y3^-7 * Y1, Y1 * Y3^-3 * Y2 * Y1 * Y3^-4 * Y2, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ] Map:: R = (1, 43, 4, 46, 12, 54, 23, 65, 35, 77, 28, 70, 16, 58, 6, 48, 15, 57, 27, 69, 39, 81, 41, 83, 32, 74, 20, 62, 9, 51, 19, 61, 31, 73, 36, 78, 24, 66, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 29, 71, 34, 76, 22, 64, 11, 53, 3, 45, 10, 52, 21, 63, 33, 75, 42, 84, 38, 80, 26, 68, 14, 56, 25, 67, 37, 79, 40, 82, 30, 72, 18, 60, 8, 50)(85, 86)(87, 93)(88, 92)(89, 91)(90, 98)(94, 104)(95, 103)(96, 102)(97, 101)(99, 110)(100, 109)(105, 116)(106, 115)(107, 114)(108, 113)(111, 122)(112, 121)(117, 125)(118, 120)(119, 124)(123, 126)(127, 129)(128, 132)(130, 137)(131, 136)(133, 142)(134, 141)(135, 140)(138, 148)(139, 147)(143, 154)(144, 153)(145, 152)(146, 151)(149, 160)(150, 159)(155, 161)(156, 165)(157, 164)(158, 163)(162, 168)(166, 167) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.481 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.475 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3^-3 * Y2, (Y2 * Y1)^7 ] Map:: R = (1, 43, 4, 46, 12, 54, 9, 51, 18, 60, 25, 67, 23, 65, 30, 72, 37, 79, 35, 77, 41, 83, 39, 81, 32, 74, 34, 76, 27, 69, 20, 62, 22, 64, 15, 57, 6, 48, 13, 55, 5, 47)(2, 44, 7, 49, 16, 58, 14, 56, 21, 63, 28, 70, 26, 68, 33, 75, 40, 82, 38, 80, 42, 84, 36, 78, 29, 71, 31, 73, 24, 66, 17, 59, 19, 61, 11, 53, 3, 45, 10, 52, 8, 50)(85, 86)(87, 93)(88, 92)(89, 91)(90, 98)(94, 96)(95, 102)(97, 100)(99, 105)(101, 107)(103, 109)(104, 110)(106, 112)(108, 114)(111, 117)(113, 119)(115, 121)(116, 122)(118, 124)(120, 125)(123, 126)(127, 129)(128, 132)(130, 137)(131, 136)(133, 141)(134, 139)(135, 143)(138, 145)(140, 146)(142, 148)(144, 150)(147, 153)(149, 155)(151, 157)(152, 158)(154, 160)(156, 162)(159, 165)(161, 164)(163, 168)(166, 167) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.483 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.476 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3^-8 * Y1 * Y3^2 * Y2 ] Map:: R = (1, 43, 4, 46, 12, 54, 20, 62, 28, 70, 36, 78, 38, 80, 30, 72, 22, 64, 14, 56, 6, 48, 9, 51, 17, 59, 25, 67, 33, 75, 41, 83, 37, 79, 29, 71, 21, 63, 13, 55, 5, 47)(2, 44, 7, 49, 15, 57, 23, 65, 31, 73, 39, 81, 35, 77, 27, 69, 19, 61, 11, 53, 3, 45, 10, 52, 18, 60, 26, 68, 34, 76, 42, 84, 40, 82, 32, 74, 24, 66, 16, 58, 8, 50)(85, 86)(87, 93)(88, 92)(89, 91)(90, 94)(95, 101)(96, 100)(97, 99)(98, 102)(103, 109)(104, 108)(105, 107)(106, 110)(111, 117)(112, 116)(113, 115)(114, 118)(119, 125)(120, 124)(121, 123)(122, 126)(127, 129)(128, 132)(130, 137)(131, 136)(133, 140)(134, 135)(138, 145)(139, 144)(141, 148)(142, 143)(146, 153)(147, 152)(149, 156)(150, 151)(154, 161)(155, 160)(157, 164)(158, 159)(162, 165)(163, 168)(166, 167) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.482 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.477 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y2 * Y3^-3 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^21 ] Map:: R = (1, 43, 4, 46, 12, 54, 16, 58, 6, 48, 15, 57, 26, 68, 33, 75, 23, 65, 32, 74, 40, 82, 42, 84, 37, 79, 27, 69, 36, 78, 30, 72, 21, 63, 9, 51, 20, 62, 13, 55, 5, 47)(2, 44, 7, 49, 17, 59, 11, 53, 3, 45, 10, 52, 22, 64, 29, 71, 19, 61, 28, 70, 38, 80, 41, 83, 35, 77, 31, 73, 39, 81, 34, 76, 25, 67, 14, 56, 24, 66, 18, 60, 8, 50)(85, 86)(87, 93)(88, 92)(89, 91)(90, 98)(94, 105)(95, 104)(96, 102)(97, 101)(99, 109)(100, 108)(103, 111)(106, 114)(107, 115)(110, 118)(112, 121)(113, 120)(116, 119)(117, 123)(122, 126)(124, 125)(127, 129)(128, 132)(130, 137)(131, 136)(133, 142)(134, 141)(135, 145)(138, 143)(139, 148)(140, 149)(144, 152)(146, 155)(147, 154)(150, 159)(151, 158)(153, 161)(156, 164)(157, 163)(160, 166)(162, 167)(165, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.480 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.478 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 21, 21}) Quotient :: edge^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y2^21, Y1^21 ] Map:: non-degenerate R = (1, 43, 4, 46)(2, 44, 6, 48)(3, 45, 8, 50)(5, 47, 10, 52)(7, 49, 12, 54)(9, 51, 14, 56)(11, 53, 16, 58)(13, 55, 18, 60)(15, 57, 20, 62)(17, 59, 22, 64)(19, 61, 24, 66)(21, 63, 26, 68)(23, 65, 28, 70)(25, 67, 30, 72)(27, 69, 32, 74)(29, 71, 34, 76)(31, 73, 36, 78)(33, 75, 38, 80)(35, 77, 40, 82)(37, 79, 41, 83)(39, 81, 42, 84)(85, 86, 89, 93, 97, 101, 105, 109, 113, 117, 121, 123, 119, 115, 111, 107, 103, 99, 95, 91, 87)(88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 126, 125, 122, 118, 114, 110, 106, 102, 98, 94, 90)(127, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 163, 159, 155, 151, 147, 143, 139, 135, 131, 128)(130, 132, 136, 140, 144, 148, 152, 156, 160, 164, 167, 168, 166, 162, 158, 154, 150, 146, 142, 138, 134) 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 ), ( 8^21 ) } Outer automorphisms :: reflexible Dual of E20.485 Graph:: simple bipartite v = 25 e = 84 f = 21 degree seq :: [ 4^21, 21^4 ] E20.479 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^21 ] Map:: R = (1, 43, 85, 127, 3, 45, 87, 129, 7, 49, 91, 133, 11, 53, 95, 137, 15, 57, 99, 141, 19, 61, 103, 145, 23, 65, 107, 149, 27, 69, 111, 153, 31, 73, 115, 157, 35, 77, 119, 161, 39, 81, 123, 165, 40, 82, 124, 166, 36, 78, 120, 162, 32, 74, 116, 158, 28, 70, 112, 154, 24, 66, 108, 150, 20, 62, 104, 146, 16, 58, 100, 142, 12, 54, 96, 138, 8, 50, 92, 134, 4, 46, 88, 130)(2, 44, 86, 128, 5, 47, 89, 131, 9, 51, 93, 135, 13, 55, 97, 139, 17, 59, 101, 143, 21, 63, 105, 147, 25, 67, 109, 151, 29, 71, 113, 155, 33, 75, 117, 159, 37, 79, 121, 163, 41, 83, 125, 167, 42, 84, 126, 168, 38, 80, 122, 164, 34, 76, 118, 160, 30, 72, 114, 156, 26, 68, 110, 152, 22, 64, 106, 148, 18, 60, 102, 144, 14, 56, 98, 140, 10, 52, 94, 136, 6, 48, 90, 132) L = (1, 44)(2, 43)(3, 48)(4, 47)(5, 46)(6, 45)(7, 52)(8, 51)(9, 50)(10, 49)(11, 56)(12, 55)(13, 54)(14, 53)(15, 60)(16, 59)(17, 58)(18, 57)(19, 64)(20, 63)(21, 62)(22, 61)(23, 68)(24, 67)(25, 66)(26, 65)(27, 72)(28, 71)(29, 70)(30, 69)(31, 76)(32, 75)(33, 74)(34, 73)(35, 80)(36, 79)(37, 78)(38, 77)(39, 84)(40, 83)(41, 82)(42, 81)(85, 128)(86, 127)(87, 132)(88, 131)(89, 130)(90, 129)(91, 136)(92, 135)(93, 134)(94, 133)(95, 140)(96, 139)(97, 138)(98, 137)(99, 144)(100, 143)(101, 142)(102, 141)(103, 148)(104, 147)(105, 146)(106, 145)(107, 152)(108, 151)(109, 150)(110, 149)(111, 156)(112, 155)(113, 154)(114, 153)(115, 160)(116, 159)(117, 158)(118, 157)(119, 164)(120, 163)(121, 162)(122, 161)(123, 168)(124, 167)(125, 166)(126, 165) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.472 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.480 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y1 * Y3^3 * Y2, (Y1 * Y2)^7, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 12, 54, 96, 138, 6, 48, 90, 132, 15, 57, 99, 141, 22, 64, 106, 148, 20, 62, 104, 146, 27, 69, 111, 153, 34, 76, 118, 160, 32, 74, 116, 158, 39, 81, 123, 165, 41, 83, 125, 167, 35, 77, 119, 161, 37, 79, 121, 163, 30, 72, 114, 156, 23, 65, 107, 149, 25, 67, 109, 151, 18, 60, 102, 144, 9, 51, 93, 135, 13, 55, 97, 139, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 19, 61, 103, 145, 17, 59, 101, 143, 24, 66, 108, 150, 31, 73, 115, 157, 29, 71, 113, 155, 36, 78, 120, 162, 42, 84, 126, 168, 38, 80, 122, 164, 40, 82, 124, 166, 33, 75, 117, 159, 26, 68, 110, 152, 28, 70, 112, 154, 21, 63, 105, 147, 14, 56, 98, 140, 16, 58, 100, 142, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 50)(5, 49)(6, 56)(7, 47)(8, 46)(9, 45)(10, 60)(11, 55)(12, 58)(13, 53)(14, 48)(15, 63)(16, 54)(17, 65)(18, 52)(19, 67)(20, 68)(21, 57)(22, 70)(23, 59)(24, 72)(25, 61)(26, 62)(27, 75)(28, 64)(29, 77)(30, 66)(31, 79)(32, 80)(33, 69)(34, 82)(35, 71)(36, 83)(37, 73)(38, 74)(39, 84)(40, 76)(41, 78)(42, 81)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 138)(92, 141)(93, 143)(94, 131)(95, 130)(96, 133)(97, 145)(98, 146)(99, 134)(100, 148)(101, 135)(102, 150)(103, 139)(104, 140)(105, 153)(106, 142)(107, 155)(108, 144)(109, 157)(110, 158)(111, 147)(112, 160)(113, 149)(114, 162)(115, 151)(116, 152)(117, 165)(118, 154)(119, 164)(120, 156)(121, 168)(122, 161)(123, 159)(124, 167)(125, 166)(126, 163) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.477 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.481 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y2 * Y3)^2, (Y2 * Y1)^3, Y2 * Y3^-7 * Y1, Y1 * Y3^-3 * Y2 * Y1 * Y3^-4 * Y2, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 12, 54, 96, 138, 23, 65, 107, 149, 35, 77, 119, 161, 28, 70, 112, 154, 16, 58, 100, 142, 6, 48, 90, 132, 15, 57, 99, 141, 27, 69, 111, 153, 39, 81, 123, 165, 41, 83, 125, 167, 32, 74, 116, 158, 20, 62, 104, 146, 9, 51, 93, 135, 19, 61, 103, 145, 31, 73, 115, 157, 36, 78, 120, 162, 24, 66, 108, 150, 13, 55, 97, 139, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 17, 59, 101, 143, 29, 71, 113, 155, 34, 76, 118, 160, 22, 64, 106, 148, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 21, 63, 105, 147, 33, 75, 117, 159, 42, 84, 126, 168, 38, 80, 122, 164, 26, 68, 110, 152, 14, 56, 98, 140, 25, 67, 109, 151, 37, 79, 121, 163, 40, 82, 124, 166, 30, 72, 114, 156, 18, 60, 102, 144, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 50)(5, 49)(6, 56)(7, 47)(8, 46)(9, 45)(10, 62)(11, 61)(12, 60)(13, 59)(14, 48)(15, 68)(16, 67)(17, 55)(18, 54)(19, 53)(20, 52)(21, 74)(22, 73)(23, 72)(24, 71)(25, 58)(26, 57)(27, 80)(28, 79)(29, 66)(30, 65)(31, 64)(32, 63)(33, 83)(34, 78)(35, 82)(36, 76)(37, 70)(38, 69)(39, 84)(40, 77)(41, 75)(42, 81)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 142)(92, 141)(93, 140)(94, 131)(95, 130)(96, 148)(97, 147)(98, 135)(99, 134)(100, 133)(101, 154)(102, 153)(103, 152)(104, 151)(105, 139)(106, 138)(107, 160)(108, 159)(109, 146)(110, 145)(111, 144)(112, 143)(113, 161)(114, 165)(115, 164)(116, 163)(117, 150)(118, 149)(119, 155)(120, 168)(121, 158)(122, 157)(123, 156)(124, 167)(125, 166)(126, 162) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.474 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.482 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3^-3 * Y2, (Y2 * Y1)^7 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 12, 54, 96, 138, 9, 51, 93, 135, 18, 60, 102, 144, 25, 67, 109, 151, 23, 65, 107, 149, 30, 72, 114, 156, 37, 79, 121, 163, 35, 77, 119, 161, 41, 83, 125, 167, 39, 81, 123, 165, 32, 74, 116, 158, 34, 76, 118, 160, 27, 69, 111, 153, 20, 62, 104, 146, 22, 64, 106, 148, 15, 57, 99, 141, 6, 48, 90, 132, 13, 55, 97, 139, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 16, 58, 100, 142, 14, 56, 98, 140, 21, 63, 105, 147, 28, 70, 112, 154, 26, 68, 110, 152, 33, 75, 117, 159, 40, 82, 124, 166, 38, 80, 122, 164, 42, 84, 126, 168, 36, 78, 120, 162, 29, 71, 113, 155, 31, 73, 115, 157, 24, 66, 108, 150, 17, 59, 101, 143, 19, 61, 103, 145, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 50)(5, 49)(6, 56)(7, 47)(8, 46)(9, 45)(10, 54)(11, 60)(12, 52)(13, 58)(14, 48)(15, 63)(16, 55)(17, 65)(18, 53)(19, 67)(20, 68)(21, 57)(22, 70)(23, 59)(24, 72)(25, 61)(26, 62)(27, 75)(28, 64)(29, 77)(30, 66)(31, 79)(32, 80)(33, 69)(34, 82)(35, 71)(36, 83)(37, 73)(38, 74)(39, 84)(40, 76)(41, 78)(42, 81)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 141)(92, 139)(93, 143)(94, 131)(95, 130)(96, 145)(97, 134)(98, 146)(99, 133)(100, 148)(101, 135)(102, 150)(103, 138)(104, 140)(105, 153)(106, 142)(107, 155)(108, 144)(109, 157)(110, 158)(111, 147)(112, 160)(113, 149)(114, 162)(115, 151)(116, 152)(117, 165)(118, 154)(119, 164)(120, 156)(121, 168)(122, 161)(123, 159)(124, 167)(125, 166)(126, 163) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.476 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.483 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3^-8 * Y1 * Y3^2 * Y2 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 12, 54, 96, 138, 20, 62, 104, 146, 28, 70, 112, 154, 36, 78, 120, 162, 38, 80, 122, 164, 30, 72, 114, 156, 22, 64, 106, 148, 14, 56, 98, 140, 6, 48, 90, 132, 9, 51, 93, 135, 17, 59, 101, 143, 25, 67, 109, 151, 33, 75, 117, 159, 41, 83, 125, 167, 37, 79, 121, 163, 29, 71, 113, 155, 21, 63, 105, 147, 13, 55, 97, 139, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 15, 57, 99, 141, 23, 65, 107, 149, 31, 73, 115, 157, 39, 81, 123, 165, 35, 77, 119, 161, 27, 69, 111, 153, 19, 61, 103, 145, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 18, 60, 102, 144, 26, 68, 110, 152, 34, 76, 118, 160, 42, 84, 126, 168, 40, 82, 124, 166, 32, 74, 116, 158, 24, 66, 108, 150, 16, 58, 100, 142, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 50)(5, 49)(6, 52)(7, 47)(8, 46)(9, 45)(10, 48)(11, 59)(12, 58)(13, 57)(14, 60)(15, 55)(16, 54)(17, 53)(18, 56)(19, 67)(20, 66)(21, 65)(22, 68)(23, 63)(24, 62)(25, 61)(26, 64)(27, 75)(28, 74)(29, 73)(30, 76)(31, 71)(32, 70)(33, 69)(34, 72)(35, 83)(36, 82)(37, 81)(38, 84)(39, 79)(40, 78)(41, 77)(42, 80)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 140)(92, 135)(93, 134)(94, 131)(95, 130)(96, 145)(97, 144)(98, 133)(99, 148)(100, 143)(101, 142)(102, 139)(103, 138)(104, 153)(105, 152)(106, 141)(107, 156)(108, 151)(109, 150)(110, 147)(111, 146)(112, 161)(113, 160)(114, 149)(115, 164)(116, 159)(117, 158)(118, 155)(119, 154)(120, 165)(121, 168)(122, 157)(123, 162)(124, 167)(125, 166)(126, 163) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.475 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.484 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y2 * Y3^-3 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^21 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 12, 54, 96, 138, 16, 58, 100, 142, 6, 48, 90, 132, 15, 57, 99, 141, 26, 68, 110, 152, 33, 75, 117, 159, 23, 65, 107, 149, 32, 74, 116, 158, 40, 82, 124, 166, 42, 84, 126, 168, 37, 79, 121, 163, 27, 69, 111, 153, 36, 78, 120, 162, 30, 72, 114, 156, 21, 63, 105, 147, 9, 51, 93, 135, 20, 62, 104, 146, 13, 55, 97, 139, 5, 47, 89, 131)(2, 44, 86, 128, 7, 49, 91, 133, 17, 59, 101, 143, 11, 53, 95, 137, 3, 45, 87, 129, 10, 52, 94, 136, 22, 64, 106, 148, 29, 71, 113, 155, 19, 61, 103, 145, 28, 70, 112, 154, 38, 80, 122, 164, 41, 83, 125, 167, 35, 77, 119, 161, 31, 73, 115, 157, 39, 81, 123, 165, 34, 76, 118, 160, 25, 67, 109, 151, 14, 56, 98, 140, 24, 66, 108, 150, 18, 60, 102, 144, 8, 50, 92, 134) L = (1, 44)(2, 43)(3, 51)(4, 50)(5, 49)(6, 56)(7, 47)(8, 46)(9, 45)(10, 63)(11, 62)(12, 60)(13, 59)(14, 48)(15, 67)(16, 66)(17, 55)(18, 54)(19, 69)(20, 53)(21, 52)(22, 72)(23, 73)(24, 58)(25, 57)(26, 76)(27, 61)(28, 79)(29, 78)(30, 64)(31, 65)(32, 77)(33, 81)(34, 68)(35, 74)(36, 71)(37, 70)(38, 84)(39, 75)(40, 83)(41, 82)(42, 80)(85, 129)(86, 132)(87, 127)(88, 137)(89, 136)(90, 128)(91, 142)(92, 141)(93, 145)(94, 131)(95, 130)(96, 143)(97, 148)(98, 149)(99, 134)(100, 133)(101, 138)(102, 152)(103, 135)(104, 155)(105, 154)(106, 139)(107, 140)(108, 159)(109, 158)(110, 144)(111, 161)(112, 147)(113, 146)(114, 164)(115, 163)(116, 151)(117, 150)(118, 166)(119, 153)(120, 167)(121, 157)(122, 156)(123, 168)(124, 160)(125, 162)(126, 165) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.473 Transitivity :: VT+ Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.485 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 21, 21}) Quotient :: loop^2 Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y2^21, Y1^21 ] 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, 10, 52, 94, 136)(7, 49, 91, 133, 12, 54, 96, 138)(9, 51, 93, 135, 14, 56, 98, 140)(11, 53, 95, 137, 16, 58, 100, 142)(13, 55, 97, 139, 18, 60, 102, 144)(15, 57, 99, 141, 20, 62, 104, 146)(17, 59, 101, 143, 22, 64, 106, 148)(19, 61, 103, 145, 24, 66, 108, 150)(21, 63, 105, 147, 26, 68, 110, 152)(23, 65, 107, 149, 28, 70, 112, 154)(25, 67, 109, 151, 30, 72, 114, 156)(27, 69, 111, 153, 32, 74, 116, 158)(29, 71, 113, 155, 34, 76, 118, 160)(31, 73, 115, 157, 36, 78, 120, 162)(33, 75, 117, 159, 38, 80, 122, 164)(35, 77, 119, 161, 40, 82, 124, 166)(37, 79, 121, 163, 41, 83, 125, 167)(39, 81, 123, 165, 42, 84, 126, 168) L = (1, 44)(2, 47)(3, 43)(4, 50)(5, 51)(6, 46)(7, 45)(8, 54)(9, 55)(10, 48)(11, 49)(12, 58)(13, 59)(14, 52)(15, 53)(16, 62)(17, 63)(18, 56)(19, 57)(20, 66)(21, 67)(22, 60)(23, 61)(24, 70)(25, 71)(26, 64)(27, 65)(28, 74)(29, 75)(30, 68)(31, 69)(32, 78)(33, 79)(34, 72)(35, 73)(36, 82)(37, 81)(38, 76)(39, 77)(40, 84)(41, 80)(42, 83)(85, 129)(86, 127)(87, 133)(88, 132)(89, 128)(90, 136)(91, 137)(92, 130)(93, 131)(94, 140)(95, 141)(96, 134)(97, 135)(98, 144)(99, 145)(100, 138)(101, 139)(102, 148)(103, 149)(104, 142)(105, 143)(106, 152)(107, 153)(108, 146)(109, 147)(110, 156)(111, 157)(112, 150)(113, 151)(114, 160)(115, 161)(116, 154)(117, 155)(118, 164)(119, 165)(120, 158)(121, 159)(122, 167)(123, 163)(124, 162)(125, 168)(126, 166) local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21 ) } Outer automorphisms :: reflexible Dual of E20.478 Transitivity :: VT+ Graph:: v = 21 e = 84 f = 25 degree seq :: [ 8^21 ] E20.486 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^21, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44)(3, 45, 5, 47)(4, 46, 6, 48)(7, 49, 9, 51)(8, 50, 10, 52)(11, 53, 13, 55)(12, 54, 14, 56)(15, 57, 17, 59)(16, 58, 18, 60)(19, 61, 21, 63)(20, 62, 22, 64)(23, 65, 25, 67)(24, 66, 26, 68)(27, 69, 29, 71)(28, 70, 30, 72)(31, 73, 33, 75)(32, 74, 34, 76)(35, 77, 37, 79)(36, 78, 38, 80)(39, 81, 41, 83)(40, 82, 42, 84)(85, 127, 87, 129, 91, 133, 95, 137, 99, 141, 103, 145, 107, 149, 111, 153, 115, 157, 119, 161, 123, 165, 124, 166, 120, 162, 116, 158, 112, 154, 108, 150, 104, 146, 100, 142, 96, 138, 92, 134, 88, 130)(86, 128, 89, 131, 93, 135, 97, 139, 101, 143, 105, 147, 109, 151, 113, 155, 117, 159, 121, 163, 125, 167, 126, 168, 122, 164, 118, 160, 114, 156, 110, 152, 106, 148, 102, 144, 98, 140, 94, 136, 90, 132) 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, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.487 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^21, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44)(3, 45, 6, 48)(4, 46, 5, 47)(7, 49, 10, 52)(8, 50, 9, 51)(11, 53, 14, 56)(12, 54, 13, 55)(15, 57, 18, 60)(16, 58, 17, 59)(19, 61, 22, 64)(20, 62, 21, 63)(23, 65, 26, 68)(24, 66, 25, 67)(27, 69, 30, 72)(28, 70, 29, 71)(31, 73, 34, 76)(32, 74, 33, 75)(35, 77, 38, 80)(36, 78, 37, 79)(39, 81, 42, 84)(40, 82, 41, 83)(85, 127, 87, 129, 91, 133, 95, 137, 99, 141, 103, 145, 107, 149, 111, 153, 115, 157, 119, 161, 123, 165, 124, 166, 120, 162, 116, 158, 112, 154, 108, 150, 104, 146, 100, 142, 96, 138, 92, 134, 88, 130)(86, 128, 89, 131, 93, 135, 97, 139, 101, 143, 105, 147, 109, 151, 113, 155, 117, 159, 121, 163, 125, 167, 126, 168, 122, 164, 118, 160, 114, 156, 110, 152, 106, 148, 102, 144, 98, 140, 94, 136, 90, 132) 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, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.488 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y2^-7, (Y2^-1 * Y3)^21 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 21, 63)(12, 54, 22, 64)(13, 55, 20, 62)(14, 56, 19, 61)(15, 57, 17, 59)(16, 58, 18, 60)(23, 65, 33, 75)(24, 66, 34, 76)(25, 67, 32, 74)(26, 68, 31, 73)(27, 69, 29, 71)(28, 70, 30, 72)(35, 77, 40, 82)(36, 78, 39, 81)(37, 79, 42, 84)(38, 80, 41, 83)(85, 127, 87, 129, 95, 137, 107, 149, 119, 161, 112, 154, 100, 142, 90, 132, 97, 139, 109, 151, 121, 163, 122, 164, 110, 152, 98, 140, 88, 130, 96, 138, 108, 150, 120, 162, 111, 153, 99, 141, 89, 131)(86, 128, 91, 133, 101, 143, 113, 155, 123, 165, 118, 160, 106, 148, 94, 136, 103, 145, 115, 157, 125, 167, 126, 168, 116, 158, 104, 146, 92, 134, 102, 144, 114, 156, 124, 166, 117, 159, 105, 147, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 90)(5, 98)(6, 85)(7, 102)(8, 94)(9, 104)(10, 86)(11, 108)(12, 97)(13, 87)(14, 100)(15, 110)(16, 89)(17, 114)(18, 103)(19, 91)(20, 106)(21, 116)(22, 93)(23, 120)(24, 109)(25, 95)(26, 112)(27, 122)(28, 99)(29, 124)(30, 115)(31, 101)(32, 118)(33, 126)(34, 105)(35, 111)(36, 121)(37, 107)(38, 119)(39, 117)(40, 125)(41, 113)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.489 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (Y2, Y3), (R * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^-3 * Y3^-3, Y3^-1 * Y2^6, Y3^7, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 24, 66)(12, 54, 25, 67)(13, 55, 23, 65)(14, 56, 26, 68)(15, 57, 21, 63)(16, 58, 19, 61)(17, 59, 20, 62)(18, 60, 22, 64)(27, 69, 40, 82)(28, 70, 38, 80)(29, 71, 42, 84)(30, 72, 36, 78)(31, 73, 41, 83)(32, 74, 35, 77)(33, 75, 39, 81)(34, 76, 37, 79)(85, 127, 87, 129, 95, 137, 111, 153, 118, 160, 99, 141, 88, 130, 96, 138, 112, 154, 102, 144, 115, 157, 117, 159, 98, 140, 114, 156, 101, 143, 90, 132, 97, 139, 113, 155, 116, 158, 100, 142, 89, 131)(86, 128, 91, 133, 103, 145, 119, 161, 126, 168, 107, 149, 92, 134, 104, 146, 120, 162, 110, 152, 123, 165, 125, 167, 106, 148, 122, 164, 109, 151, 94, 136, 105, 147, 121, 163, 124, 166, 108, 150, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 112)(12, 114)(13, 87)(14, 116)(15, 117)(16, 118)(17, 89)(18, 90)(19, 120)(20, 122)(21, 91)(22, 124)(23, 125)(24, 126)(25, 93)(26, 94)(27, 102)(28, 101)(29, 95)(30, 100)(31, 97)(32, 111)(33, 113)(34, 115)(35, 110)(36, 109)(37, 103)(38, 108)(39, 105)(40, 119)(41, 121)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.493 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.490 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y3^2 * Y2^3, Y3^7, Y3^7, Y3 * Y2^-1 * Y3^3 * Y2^-2 * Y3, (Y2^-1 * Y3)^21 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 24, 66)(12, 54, 25, 67)(13, 55, 23, 65)(14, 56, 26, 68)(15, 57, 21, 63)(16, 58, 19, 61)(17, 59, 20, 62)(18, 60, 22, 64)(27, 69, 37, 79)(28, 70, 36, 78)(29, 71, 38, 80)(30, 72, 34, 76)(31, 73, 33, 75)(32, 74, 35, 77)(39, 81, 42, 84)(40, 82, 41, 83)(85, 127, 87, 129, 95, 137, 102, 144, 112, 154, 123, 165, 113, 155, 115, 157, 99, 141, 88, 130, 96, 138, 101, 143, 90, 132, 97, 139, 111, 153, 116, 158, 124, 166, 114, 156, 98, 140, 100, 142, 89, 131)(86, 128, 91, 133, 103, 145, 110, 152, 118, 160, 125, 167, 119, 161, 121, 163, 107, 149, 92, 134, 104, 146, 109, 151, 94, 136, 105, 147, 117, 159, 122, 164, 126, 168, 120, 162, 106, 148, 108, 150, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 101)(12, 100)(13, 87)(14, 113)(15, 114)(16, 115)(17, 89)(18, 90)(19, 109)(20, 108)(21, 91)(22, 119)(23, 120)(24, 121)(25, 93)(26, 94)(27, 95)(28, 97)(29, 116)(30, 123)(31, 124)(32, 102)(33, 103)(34, 105)(35, 122)(36, 125)(37, 126)(38, 110)(39, 111)(40, 112)(41, 117)(42, 118)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.491 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y3^-2 * Y2^3, Y3^-7, Y3^7, Y3^7, Y3^-2 * Y2^-1 * Y3^-3 * Y2^-2 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 24, 66)(12, 54, 25, 67)(13, 55, 23, 65)(14, 56, 26, 68)(15, 57, 21, 63)(16, 58, 19, 61)(17, 59, 20, 62)(18, 60, 22, 64)(27, 69, 36, 78)(28, 70, 37, 79)(29, 71, 38, 80)(30, 72, 33, 75)(31, 73, 34, 76)(32, 74, 35, 77)(39, 81, 42, 84)(40, 82, 41, 83)(85, 127, 87, 129, 95, 137, 98, 140, 112, 154, 123, 165, 116, 158, 114, 156, 101, 143, 90, 132, 97, 139, 99, 141, 88, 130, 96, 138, 111, 153, 113, 155, 124, 166, 115, 157, 102, 144, 100, 142, 89, 131)(86, 128, 91, 133, 103, 145, 106, 148, 118, 160, 125, 167, 122, 164, 120, 162, 109, 151, 94, 136, 105, 147, 107, 149, 92, 134, 104, 146, 117, 159, 119, 161, 126, 168, 121, 163, 110, 152, 108, 150, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 111)(12, 112)(13, 87)(14, 113)(15, 95)(16, 97)(17, 89)(18, 90)(19, 117)(20, 118)(21, 91)(22, 119)(23, 103)(24, 105)(25, 93)(26, 94)(27, 123)(28, 124)(29, 116)(30, 100)(31, 101)(32, 102)(33, 125)(34, 126)(35, 122)(36, 108)(37, 109)(38, 110)(39, 115)(40, 114)(41, 121)(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, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.492 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.492 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-3, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^7 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 19, 61)(12, 54, 21, 63)(13, 55, 17, 59)(14, 56, 22, 64)(15, 57, 18, 60)(16, 58, 20, 62)(23, 65, 31, 73)(24, 66, 33, 75)(25, 67, 29, 71)(26, 68, 34, 76)(27, 69, 30, 72)(28, 70, 32, 74)(35, 77, 41, 83)(36, 78, 42, 84)(37, 79, 39, 81)(38, 80, 40, 82)(85, 127, 87, 129, 95, 137, 88, 130, 96, 138, 107, 149, 98, 140, 108, 150, 119, 161, 110, 152, 120, 162, 122, 164, 112, 154, 121, 163, 111, 153, 100, 142, 109, 151, 99, 141, 90, 132, 97, 139, 89, 131)(86, 128, 91, 133, 101, 143, 92, 134, 102, 144, 113, 155, 104, 146, 114, 156, 123, 165, 116, 158, 124, 166, 126, 168, 118, 160, 125, 167, 117, 159, 106, 148, 115, 157, 105, 147, 94, 136, 103, 145, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 95)(6, 85)(7, 102)(8, 104)(9, 101)(10, 86)(11, 107)(12, 108)(13, 87)(14, 110)(15, 89)(16, 90)(17, 113)(18, 114)(19, 91)(20, 116)(21, 93)(22, 94)(23, 119)(24, 120)(25, 97)(26, 112)(27, 99)(28, 100)(29, 123)(30, 124)(31, 103)(32, 118)(33, 105)(34, 106)(35, 122)(36, 121)(37, 109)(38, 111)(39, 126)(40, 125)(41, 115)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.491 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.493 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3 * Y3^-1, (Y2, Y3^-1), (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 18, 60)(12, 54, 17, 59)(13, 55, 21, 63)(14, 56, 22, 64)(15, 57, 19, 61)(16, 58, 20, 62)(23, 65, 30, 72)(24, 66, 29, 71)(25, 67, 33, 75)(26, 68, 34, 76)(27, 69, 31, 73)(28, 70, 32, 74)(35, 77, 40, 82)(36, 78, 39, 81)(37, 79, 42, 84)(38, 80, 41, 83)(85, 127, 87, 129, 95, 137, 90, 132, 97, 139, 107, 149, 100, 142, 109, 151, 119, 161, 112, 154, 121, 163, 122, 164, 110, 152, 120, 162, 111, 153, 98, 140, 108, 150, 99, 141, 88, 130, 96, 138, 89, 131)(86, 128, 91, 133, 101, 143, 94, 136, 103, 145, 113, 155, 106, 148, 115, 157, 123, 165, 118, 160, 125, 167, 126, 168, 116, 158, 124, 166, 117, 159, 104, 146, 114, 156, 105, 147, 92, 134, 102, 144, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 102)(8, 104)(9, 105)(10, 86)(11, 89)(12, 108)(13, 87)(14, 110)(15, 111)(16, 90)(17, 93)(18, 114)(19, 91)(20, 116)(21, 117)(22, 94)(23, 95)(24, 120)(25, 97)(26, 112)(27, 122)(28, 100)(29, 101)(30, 124)(31, 103)(32, 118)(33, 126)(34, 106)(35, 107)(36, 121)(37, 109)(38, 119)(39, 113)(40, 125)(41, 115)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.489 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.494 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^21, (Y3 * Y2^-1)^21 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 6, 48)(4, 46, 5, 47)(7, 49, 10, 52)(8, 50, 9, 51)(11, 53, 14, 56)(12, 54, 13, 55)(15, 57, 18, 60)(16, 58, 17, 59)(19, 61, 22, 64)(20, 62, 21, 63)(23, 65, 26, 68)(24, 66, 25, 67)(27, 69, 30, 72)(28, 70, 29, 71)(31, 73, 34, 76)(32, 74, 33, 75)(35, 77, 38, 80)(36, 78, 37, 79)(39, 81, 42, 84)(40, 82, 41, 83)(85, 127, 87, 129, 91, 133, 95, 137, 99, 141, 103, 145, 107, 149, 111, 153, 115, 157, 119, 161, 123, 165, 124, 166, 120, 162, 116, 158, 112, 154, 108, 150, 104, 146, 100, 142, 96, 138, 92, 134, 88, 130)(86, 128, 89, 131, 93, 135, 97, 139, 101, 143, 105, 147, 109, 151, 113, 155, 117, 159, 121, 163, 125, 167, 126, 168, 122, 164, 118, 160, 114, 156, 110, 152, 106, 148, 102, 144, 98, 140, 94, 136, 90, 132) L = (1, 88)(2, 90)(3, 85)(4, 92)(5, 86)(6, 94)(7, 87)(8, 96)(9, 89)(10, 98)(11, 91)(12, 100)(13, 93)(14, 102)(15, 95)(16, 104)(17, 97)(18, 106)(19, 99)(20, 108)(21, 101)(22, 110)(23, 103)(24, 112)(25, 105)(26, 114)(27, 107)(28, 116)(29, 109)(30, 118)(31, 111)(32, 120)(33, 113)(34, 122)(35, 115)(36, 124)(37, 117)(38, 126)(39, 119)(40, 123)(41, 121)(42, 125)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.498 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.495 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^10 * Y2 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 17, 59)(12, 54, 18, 60)(13, 55, 15, 57)(14, 56, 16, 58)(19, 61, 25, 67)(20, 62, 26, 68)(21, 63, 23, 65)(22, 64, 24, 66)(27, 69, 33, 75)(28, 70, 34, 76)(29, 71, 31, 73)(30, 72, 32, 74)(35, 77, 41, 83)(36, 78, 42, 84)(37, 79, 39, 81)(38, 80, 40, 82)(85, 127, 87, 129, 88, 130, 95, 137, 96, 138, 103, 145, 104, 146, 111, 153, 112, 154, 119, 161, 120, 162, 122, 164, 121, 163, 114, 156, 113, 155, 106, 148, 105, 147, 98, 140, 97, 139, 90, 132, 89, 131)(86, 128, 91, 133, 92, 134, 99, 141, 100, 142, 107, 149, 108, 150, 115, 157, 116, 158, 123, 165, 124, 166, 126, 168, 125, 167, 118, 160, 117, 159, 110, 152, 109, 151, 102, 144, 101, 143, 94, 136, 93, 135) L = (1, 88)(2, 92)(3, 95)(4, 96)(5, 87)(6, 85)(7, 99)(8, 100)(9, 91)(10, 86)(11, 103)(12, 104)(13, 89)(14, 90)(15, 107)(16, 108)(17, 93)(18, 94)(19, 111)(20, 112)(21, 97)(22, 98)(23, 115)(24, 116)(25, 101)(26, 102)(27, 119)(28, 120)(29, 105)(30, 106)(31, 123)(32, 124)(33, 109)(34, 110)(35, 122)(36, 121)(37, 113)(38, 114)(39, 126)(40, 125)(41, 117)(42, 118)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.496 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3 * Y2^4, Y3^-1 * Y2 * Y3^-4, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 24, 66)(12, 54, 25, 67)(13, 55, 23, 65)(14, 56, 26, 68)(15, 57, 21, 63)(16, 58, 19, 61)(17, 59, 20, 62)(18, 60, 22, 64)(27, 69, 37, 79)(28, 70, 38, 80)(29, 71, 36, 78)(30, 72, 35, 77)(31, 73, 33, 75)(32, 74, 34, 76)(39, 81, 42, 84)(40, 82, 41, 83)(85, 127, 87, 129, 95, 137, 101, 143, 90, 132, 97, 139, 111, 153, 116, 158, 102, 144, 113, 155, 123, 165, 124, 166, 114, 156, 98, 140, 112, 154, 115, 157, 99, 141, 88, 130, 96, 138, 100, 142, 89, 131)(86, 128, 91, 133, 103, 145, 109, 151, 94, 136, 105, 147, 117, 159, 122, 164, 110, 152, 119, 161, 125, 167, 126, 168, 120, 162, 106, 148, 118, 160, 121, 163, 107, 149, 92, 134, 104, 146, 108, 150, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 100)(12, 112)(13, 87)(14, 113)(15, 114)(16, 115)(17, 89)(18, 90)(19, 108)(20, 118)(21, 91)(22, 119)(23, 120)(24, 121)(25, 93)(26, 94)(27, 95)(28, 123)(29, 97)(30, 102)(31, 124)(32, 101)(33, 103)(34, 125)(35, 105)(36, 110)(37, 126)(38, 109)(39, 111)(40, 116)(41, 117)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.497 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.497 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y3 * Y2 * Y3^3, Y3 * Y2^-5, Y2^2 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 24, 66)(12, 54, 25, 67)(13, 55, 23, 65)(14, 56, 26, 68)(15, 57, 21, 63)(16, 58, 19, 61)(17, 59, 20, 62)(18, 60, 22, 64)(27, 69, 35, 77)(28, 70, 38, 80)(29, 71, 33, 75)(30, 72, 37, 79)(31, 73, 36, 78)(32, 74, 34, 76)(39, 81, 42, 84)(40, 82, 41, 83)(85, 127, 87, 129, 95, 137, 111, 153, 99, 141, 88, 130, 96, 138, 112, 154, 123, 165, 115, 157, 98, 140, 102, 144, 114, 156, 124, 166, 116, 158, 101, 143, 90, 132, 97, 139, 113, 155, 100, 142, 89, 131)(86, 128, 91, 133, 103, 145, 117, 159, 107, 149, 92, 134, 104, 146, 118, 160, 125, 167, 121, 163, 106, 148, 110, 152, 120, 162, 126, 168, 122, 164, 109, 151, 94, 136, 105, 147, 119, 161, 108, 150, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 112)(12, 102)(13, 87)(14, 101)(15, 115)(16, 111)(17, 89)(18, 90)(19, 118)(20, 110)(21, 91)(22, 109)(23, 121)(24, 117)(25, 93)(26, 94)(27, 123)(28, 114)(29, 95)(30, 97)(31, 116)(32, 100)(33, 125)(34, 120)(35, 103)(36, 105)(37, 122)(38, 108)(39, 124)(40, 113)(41, 126)(42, 119)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.496 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.498 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 21, 21}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y2^-10 * Y3^-1 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 17, 59)(12, 54, 18, 60)(13, 55, 15, 57)(14, 56, 16, 58)(19, 61, 25, 67)(20, 62, 26, 68)(21, 63, 23, 65)(22, 64, 24, 66)(27, 69, 33, 75)(28, 70, 34, 76)(29, 71, 31, 73)(30, 72, 32, 74)(35, 77, 41, 83)(36, 78, 42, 84)(37, 79, 39, 81)(38, 80, 40, 82)(85, 127, 87, 129, 95, 137, 103, 145, 111, 153, 119, 161, 122, 164, 114, 156, 106, 148, 98, 140, 90, 132, 88, 130, 96, 138, 104, 146, 112, 154, 120, 162, 121, 163, 113, 155, 105, 147, 97, 139, 89, 131)(86, 128, 91, 133, 99, 141, 107, 149, 115, 157, 123, 165, 126, 168, 118, 160, 110, 152, 102, 144, 94, 136, 92, 134, 100, 142, 108, 150, 116, 158, 124, 166, 125, 167, 117, 159, 109, 151, 101, 143, 93, 135) L = (1, 88)(2, 92)(3, 96)(4, 87)(5, 90)(6, 85)(7, 100)(8, 91)(9, 94)(10, 86)(11, 104)(12, 95)(13, 98)(14, 89)(15, 108)(16, 99)(17, 102)(18, 93)(19, 112)(20, 103)(21, 106)(22, 97)(23, 116)(24, 107)(25, 110)(26, 101)(27, 120)(28, 111)(29, 114)(30, 105)(31, 124)(32, 115)(33, 118)(34, 109)(35, 121)(36, 119)(37, 122)(38, 113)(39, 125)(40, 123)(41, 126)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.494 Graph:: bipartite v = 23 e = 84 f = 23 degree seq :: [ 4^21, 42^2 ] E20.499 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T2)^2, (F * T1)^2, T1^2 * T2^-2, T2^20 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 6, 12, 15, 20, 23, 28, 31, 36, 39, 42, 37, 34, 29, 26, 21, 18, 13, 10, 4, 8, 2, 7, 11, 16, 19, 24, 27, 32, 35, 40, 41, 38, 33, 30, 25, 22, 17, 14, 9, 5)(43, 44, 48, 53, 57, 61, 65, 69, 73, 77, 81, 83, 79, 75, 71, 67, 63, 59, 55, 51, 46)(45, 49, 54, 58, 62, 66, 70, 74, 78, 82, 84, 80, 76, 72, 68, 64, 60, 56, 52, 47, 50) 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) :: { ( 84^21 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.510 Transitivity :: ET+ Graph:: bipartite v = 3 e = 42 f = 1 degree seq :: [ 21^2, 42 ] E20.500 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 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, T1), T2^-4 * T1, T1 * T2 * T1^9 * T2, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 33, 32, 22, 31, 41, 40, 30, 39, 35, 42, 38, 36, 27, 34, 37, 28, 19, 26, 29, 20, 11, 18, 21, 12, 4, 10, 13, 5)(43, 44, 48, 56, 64, 72, 80, 79, 71, 63, 55, 51, 59, 67, 75, 83, 77, 69, 61, 53, 46)(45, 49, 57, 65, 73, 81, 78, 70, 62, 54, 47, 50, 58, 66, 74, 82, 84, 76, 68, 60, 52) 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) :: { ( 84^21 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.509 Transitivity :: ET+ Graph:: bipartite v = 3 e = 42 f = 1 degree seq :: [ 21^2, 42 ] E20.501 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, T1 * T2^2, (F * T1)^2, (F * T2)^2, T1^21 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 42, 38, 39, 34, 35, 30, 31, 26, 27, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(43, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 83, 79, 75, 71, 67, 63, 59, 55, 51, 46)(45, 47, 49, 53, 57, 61, 65, 69, 73, 77, 81, 84, 82, 78, 74, 70, 66, 62, 58, 54, 50) 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) :: { ( 84^21 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.508 Transitivity :: ET+ Graph:: bipartite v = 3 e = 42 f = 1 degree seq :: [ 21^2, 42 ] E20.502 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^-6 * T1^3, T2^4 * T1^5, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 28, 14, 27, 39, 23, 11, 21, 35, 32, 18, 8, 2, 7, 17, 31, 37, 42, 26, 40, 24, 12, 4, 10, 20, 34, 30, 16, 6, 15, 29, 38, 22, 36, 41, 25, 13, 5)(43, 44, 48, 56, 68, 83, 77, 62, 51, 59, 71, 81, 66, 55, 60, 72, 75, 79, 64, 53, 46)(45, 49, 57, 69, 82, 67, 74, 76, 61, 73, 80, 65, 54, 47, 50, 58, 70, 84, 78, 63, 52) 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) :: { ( 84^21 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.507 Transitivity :: ET+ Graph:: bipartite v = 3 e = 42 f = 1 degree seq :: [ 21^2, 42 ] E20.503 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-2 * T1^-4, T2^-10 * T1, T1 * T2^-1 * T1 * T2^-3 * T1^2 * T2^-4 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 27, 35, 34, 26, 18, 8, 2, 7, 17, 25, 33, 41, 40, 32, 24, 16, 6, 15, 11, 21, 29, 37, 42, 39, 31, 23, 14, 12, 4, 10, 20, 28, 36, 38, 30, 22, 13, 5)(43, 44, 48, 56, 55, 60, 66, 73, 72, 76, 82, 84, 78, 69, 75, 71, 62, 51, 59, 53, 46)(45, 49, 57, 54, 47, 50, 58, 65, 64, 68, 74, 81, 80, 77, 83, 79, 70, 61, 67, 63, 52) 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) :: { ( 84^21 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.506 Transitivity :: ET+ Graph:: bipartite v = 3 e = 42 f = 1 degree seq :: [ 21^2, 42 ] E20.504 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-1 * T1^-5, T2^-1 * T1 * T2^-7 * T1, T1^-1 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 36, 26, 16, 6, 15, 25, 35, 42, 40, 32, 22, 12, 4, 10, 20, 30, 38, 28, 18, 8, 2, 7, 17, 27, 37, 41, 34, 24, 14, 11, 21, 31, 39, 33, 23, 13, 5)(43, 44, 48, 56, 54, 47, 50, 58, 66, 64, 55, 60, 68, 76, 74, 65, 70, 78, 83, 82, 75, 80, 71, 79, 84, 81, 72, 61, 69, 77, 73, 62, 51, 59, 67, 63, 52, 45, 49, 57, 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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.512 Transitivity :: ET+ Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.505 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {21, 42, 42}) Quotient :: edge Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^-1 * T2^-1 * T1^-1 * T2^-3, T2^2 * T1^-1 * T2 * T1^-8, T1^-3 * T2^15 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 35, 30, 37, 41, 31, 40, 34, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 36, 39, 38, 42, 33, 23, 32, 26, 16, 6, 15, 13, 5)(43, 44, 48, 56, 65, 73, 81, 77, 69, 61, 54, 47, 50, 58, 67, 75, 83, 78, 70, 62, 51, 59, 55, 60, 68, 76, 84, 79, 71, 63, 52, 45, 49, 57, 66, 74, 82, 80, 72, 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) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.511 Transitivity :: ET+ Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.506 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T2)^2, (F * T1)^2, T1^2 * T2^-2, T2^20 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 43, 3, 45, 6, 48, 12, 54, 15, 57, 20, 62, 23, 65, 28, 70, 31, 73, 36, 78, 39, 81, 42, 84, 37, 79, 34, 76, 29, 71, 26, 68, 21, 63, 18, 60, 13, 55, 10, 52, 4, 46, 8, 50, 2, 44, 7, 49, 11, 53, 16, 58, 19, 61, 24, 66, 27, 69, 32, 74, 35, 77, 40, 82, 41, 83, 38, 80, 33, 75, 30, 72, 25, 67, 22, 64, 17, 59, 14, 56, 9, 51, 5, 47) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 53)(7, 54)(8, 45)(9, 46)(10, 47)(11, 57)(12, 58)(13, 51)(14, 52)(15, 61)(16, 62)(17, 55)(18, 56)(19, 65)(20, 66)(21, 59)(22, 60)(23, 69)(24, 70)(25, 63)(26, 64)(27, 73)(28, 74)(29, 67)(30, 68)(31, 77)(32, 78)(33, 71)(34, 72)(35, 81)(36, 82)(37, 75)(38, 76)(39, 83)(40, 84)(41, 79)(42, 80) local type(s) :: { ( 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42 ) } Outer automorphisms :: reflexible Dual of E20.503 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 3 degree seq :: [ 84 ] E20.507 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 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, T1), T2^-4 * T1, T1 * T2 * T1^9 * T2, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 8, 50, 2, 44, 7, 49, 17, 59, 16, 58, 6, 48, 15, 57, 25, 67, 24, 66, 14, 56, 23, 65, 33, 75, 32, 74, 22, 64, 31, 73, 41, 83, 40, 82, 30, 72, 39, 81, 35, 77, 42, 84, 38, 80, 36, 78, 27, 69, 34, 76, 37, 79, 28, 70, 19, 61, 26, 68, 29, 71, 20, 62, 11, 53, 18, 60, 21, 63, 12, 54, 4, 46, 10, 52, 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, 51)(14, 64)(15, 65)(16, 66)(17, 67)(18, 52)(19, 53)(20, 54)(21, 55)(22, 72)(23, 73)(24, 74)(25, 75)(26, 60)(27, 61)(28, 62)(29, 63)(30, 80)(31, 81)(32, 82)(33, 83)(34, 68)(35, 69)(36, 70)(37, 71)(38, 79)(39, 78)(40, 84)(41, 77)(42, 76) local type(s) :: { ( 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42 ) } Outer automorphisms :: reflexible Dual of E20.502 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 3 degree seq :: [ 84 ] E20.508 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, T1 * T2^2, (F * T1)^2, (F * T2)^2, T1^21 ] Map:: non-degenerate R = (1, 43, 3, 45, 4, 46, 8, 50, 9, 51, 12, 54, 13, 55, 16, 58, 17, 59, 20, 62, 21, 63, 24, 66, 25, 67, 28, 70, 29, 71, 32, 74, 33, 75, 36, 78, 37, 79, 40, 82, 41, 83, 42, 84, 38, 80, 39, 81, 34, 76, 35, 77, 30, 72, 31, 73, 26, 68, 27, 69, 22, 64, 23, 65, 18, 60, 19, 61, 14, 56, 15, 57, 10, 52, 11, 53, 6, 48, 7, 49, 2, 44, 5, 47) L = (1, 44)(2, 48)(3, 47)(4, 43)(5, 49)(6, 52)(7, 53)(8, 45)(9, 46)(10, 56)(11, 57)(12, 50)(13, 51)(14, 60)(15, 61)(16, 54)(17, 55)(18, 64)(19, 65)(20, 58)(21, 59)(22, 68)(23, 69)(24, 62)(25, 63)(26, 72)(27, 73)(28, 66)(29, 67)(30, 76)(31, 77)(32, 70)(33, 71)(34, 80)(35, 81)(36, 74)(37, 75)(38, 83)(39, 84)(40, 78)(41, 79)(42, 82) local type(s) :: { ( 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42 ) } Outer automorphisms :: reflexible Dual of E20.501 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 3 degree seq :: [ 84 ] E20.509 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^-6 * T1^3, T2^4 * T1^5, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 33, 75, 28, 70, 14, 56, 27, 69, 39, 81, 23, 65, 11, 53, 21, 63, 35, 77, 32, 74, 18, 60, 8, 50, 2, 44, 7, 49, 17, 59, 31, 73, 37, 79, 42, 84, 26, 68, 40, 82, 24, 66, 12, 54, 4, 46, 10, 52, 20, 62, 34, 76, 30, 72, 16, 58, 6, 48, 15, 57, 29, 71, 38, 80, 22, 64, 36, 78, 41, 83, 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, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 74)(26, 83)(27, 82)(28, 84)(29, 81)(30, 75)(31, 80)(32, 76)(33, 79)(34, 61)(35, 62)(36, 63)(37, 64)(38, 65)(39, 66)(40, 67)(41, 77)(42, 78) local type(s) :: { ( 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42 ) } Outer automorphisms :: reflexible Dual of E20.500 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 3 degree seq :: [ 84 ] E20.510 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-2 * T1^-4, T2^-10 * T1, T1 * T2^-1 * T1 * T2^-3 * T1^2 * T2^-4 * T1 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 19, 61, 27, 69, 35, 77, 34, 76, 26, 68, 18, 60, 8, 50, 2, 44, 7, 49, 17, 59, 25, 67, 33, 75, 41, 83, 40, 82, 32, 74, 24, 66, 16, 58, 6, 48, 15, 57, 11, 53, 21, 63, 29, 71, 37, 79, 42, 84, 39, 81, 31, 73, 23, 65, 14, 56, 12, 54, 4, 46, 10, 52, 20, 62, 28, 70, 36, 78, 38, 80, 30, 72, 22, 64, 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, 55)(15, 54)(16, 65)(17, 53)(18, 66)(19, 67)(20, 51)(21, 52)(22, 68)(23, 64)(24, 73)(25, 63)(26, 74)(27, 75)(28, 61)(29, 62)(30, 76)(31, 72)(32, 81)(33, 71)(34, 82)(35, 83)(36, 69)(37, 70)(38, 77)(39, 80)(40, 84)(41, 79)(42, 78) local type(s) :: { ( 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42, 21, 42 ) } Outer automorphisms :: reflexible Dual of E20.499 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 42 f = 3 degree seq :: [ 84 ] E20.511 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, (T2, T1^-1), (F * T2)^2, T2^-1 * T1^2 * T2^-1, (F * T1)^2, T1 * T2^-9 * T1^-1 * T2^9, T2^10 * T1 * T2^9 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 43, 3, 45, 6, 48, 12, 54, 15, 57, 20, 62, 23, 65, 28, 70, 31, 73, 36, 78, 39, 81, 41, 83, 38, 80, 33, 75, 30, 72, 25, 67, 22, 64, 17, 59, 14, 56, 9, 51, 5, 47)(2, 44, 7, 49, 11, 53, 16, 58, 19, 61, 24, 66, 27, 69, 32, 74, 35, 77, 40, 82, 42, 84, 37, 79, 34, 76, 29, 71, 26, 68, 21, 63, 18, 60, 13, 55, 10, 52, 4, 46, 8, 50) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 53)(7, 54)(8, 45)(9, 46)(10, 47)(11, 57)(12, 58)(13, 51)(14, 52)(15, 61)(16, 62)(17, 55)(18, 56)(19, 65)(20, 66)(21, 59)(22, 60)(23, 69)(24, 70)(25, 63)(26, 64)(27, 73)(28, 74)(29, 67)(30, 68)(31, 77)(32, 78)(33, 71)(34, 72)(35, 81)(36, 82)(37, 75)(38, 76)(39, 84)(40, 83)(41, 79)(42, 80) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.505 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.512 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {21, 42, 42}) Quotient :: loop Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-3, T1 * T2 * T1 * T2^9, (T1^-1 * T2^-1)^42 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 17, 59, 25, 67, 33, 75, 41, 83, 35, 77, 27, 69, 19, 61, 11, 53, 6, 48, 14, 56, 22, 64, 30, 72, 38, 80, 37, 79, 29, 71, 21, 63, 13, 55, 5, 47)(2, 44, 7, 49, 15, 57, 23, 65, 31, 73, 39, 81, 36, 78, 28, 70, 20, 62, 12, 54, 4, 46, 10, 52, 18, 60, 26, 68, 34, 76, 42, 84, 40, 82, 32, 74, 24, 66, 16, 58, 8, 50) L = (1, 44)(2, 48)(3, 49)(4, 43)(5, 50)(6, 52)(7, 56)(8, 53)(9, 57)(10, 45)(11, 46)(12, 47)(13, 58)(14, 60)(15, 64)(16, 61)(17, 65)(18, 51)(19, 54)(20, 55)(21, 66)(22, 68)(23, 72)(24, 69)(25, 73)(26, 59)(27, 62)(28, 63)(29, 74)(30, 76)(31, 80)(32, 77)(33, 81)(34, 67)(35, 70)(36, 71)(37, 82)(38, 84)(39, 79)(40, 83)(41, 78)(42, 75) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible Dual of E20.504 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.513 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2^-2 * Y3^-2, (Y2^-1 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-2 * Y1^8 * Y2^2 * Y3^-9, Y3^-2 * Y1^19, Y3^-2 * Y2^40, Y3 * Y1^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 43, 2, 44, 6, 48, 11, 53, 15, 57, 19, 61, 23, 65, 27, 69, 31, 73, 35, 77, 39, 81, 41, 83, 37, 79, 33, 75, 29, 71, 25, 67, 21, 63, 17, 59, 13, 55, 9, 51, 4, 46)(3, 45, 7, 49, 12, 54, 16, 58, 20, 62, 24, 66, 28, 70, 32, 74, 36, 78, 40, 82, 42, 84, 38, 80, 34, 76, 30, 72, 26, 68, 22, 64, 18, 60, 14, 56, 10, 52, 5, 47, 8, 50)(85, 127, 87, 129, 90, 132, 96, 138, 99, 141, 104, 146, 107, 149, 112, 154, 115, 157, 120, 162, 123, 165, 126, 168, 121, 163, 118, 160, 113, 155, 110, 152, 105, 147, 102, 144, 97, 139, 94, 136, 88, 130, 92, 134, 86, 128, 91, 133, 95, 137, 100, 142, 103, 145, 108, 150, 111, 153, 116, 158, 119, 161, 124, 166, 125, 167, 122, 164, 117, 159, 114, 156, 109, 151, 106, 148, 101, 143, 98, 140, 93, 135, 89, 131) L = (1, 88)(2, 85)(3, 92)(4, 93)(5, 94)(6, 86)(7, 87)(8, 89)(9, 97)(10, 98)(11, 90)(12, 91)(13, 101)(14, 102)(15, 95)(16, 96)(17, 105)(18, 106)(19, 99)(20, 100)(21, 109)(22, 110)(23, 103)(24, 104)(25, 113)(26, 114)(27, 107)(28, 108)(29, 117)(30, 118)(31, 111)(32, 112)(33, 121)(34, 122)(35, 115)(36, 116)(37, 125)(38, 126)(39, 119)(40, 120)(41, 123)(42, 124)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 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, 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, 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, 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, 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 E20.526 Graph:: bipartite v = 3 e = 84 f = 43 degree seq :: [ 42^2, 84 ] E20.514 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 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, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^21, Y1^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 10, 52, 14, 56, 18, 60, 22, 64, 26, 68, 30, 72, 34, 76, 38, 80, 41, 83, 37, 79, 33, 75, 29, 71, 25, 67, 21, 63, 17, 59, 13, 55, 9, 51, 4, 46)(3, 45, 5, 47, 7, 49, 11, 53, 15, 57, 19, 61, 23, 65, 27, 69, 31, 73, 35, 77, 39, 81, 42, 84, 40, 82, 36, 78, 32, 74, 28, 70, 24, 66, 20, 62, 16, 58, 12, 54, 8, 50)(85, 127, 87, 129, 88, 130, 92, 134, 93, 135, 96, 138, 97, 139, 100, 142, 101, 143, 104, 146, 105, 147, 108, 150, 109, 151, 112, 154, 113, 155, 116, 158, 117, 159, 120, 162, 121, 163, 124, 166, 125, 167, 126, 168, 122, 164, 123, 165, 118, 160, 119, 161, 114, 156, 115, 157, 110, 152, 111, 153, 106, 148, 107, 149, 102, 144, 103, 145, 98, 140, 99, 141, 94, 136, 95, 137, 90, 132, 91, 133, 86, 128, 89, 131) L = (1, 88)(2, 85)(3, 92)(4, 93)(5, 87)(6, 86)(7, 89)(8, 96)(9, 97)(10, 90)(11, 91)(12, 100)(13, 101)(14, 94)(15, 95)(16, 104)(17, 105)(18, 98)(19, 99)(20, 108)(21, 109)(22, 102)(23, 103)(24, 112)(25, 113)(26, 106)(27, 107)(28, 116)(29, 117)(30, 110)(31, 111)(32, 120)(33, 121)(34, 114)(35, 115)(36, 124)(37, 125)(38, 118)(39, 119)(40, 126)(41, 122)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 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, 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, 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, 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, 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 E20.524 Graph:: bipartite v = 3 e = 84 f = 43 degree seq :: [ 42^2, 84 ] E20.515 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y2^-1 * Y1 * Y2^-3, Y2 * Y1 * Y2 * Y1^9, Y3^5 * Y2^-1 * Y3 * Y2^-1 * Y1^-4, Y1^5 * Y2^-1 * Y1 * Y3^-5 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 43, 2, 44, 6, 48, 14, 56, 22, 64, 30, 72, 38, 80, 37, 79, 29, 71, 21, 63, 13, 55, 9, 51, 17, 59, 25, 67, 33, 75, 41, 83, 35, 77, 27, 69, 19, 61, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 23, 65, 31, 73, 39, 81, 36, 78, 28, 70, 20, 62, 12, 54, 5, 47, 8, 50, 16, 58, 24, 66, 32, 74, 40, 82, 42, 84, 34, 76, 26, 68, 18, 60, 10, 52)(85, 127, 87, 129, 93, 135, 92, 134, 86, 128, 91, 133, 101, 143, 100, 142, 90, 132, 99, 141, 109, 151, 108, 150, 98, 140, 107, 149, 117, 159, 116, 158, 106, 148, 115, 157, 125, 167, 124, 166, 114, 156, 123, 165, 119, 161, 126, 168, 122, 164, 120, 162, 111, 153, 118, 160, 121, 163, 112, 154, 103, 145, 110, 152, 113, 155, 104, 146, 95, 137, 102, 144, 105, 147, 96, 138, 88, 130, 94, 136, 97, 139, 89, 131) L = (1, 88)(2, 85)(3, 94)(4, 95)(5, 96)(6, 86)(7, 87)(8, 89)(9, 97)(10, 102)(11, 103)(12, 104)(13, 105)(14, 90)(15, 91)(16, 92)(17, 93)(18, 110)(19, 111)(20, 112)(21, 113)(22, 98)(23, 99)(24, 100)(25, 101)(26, 118)(27, 119)(28, 120)(29, 121)(30, 106)(31, 107)(32, 108)(33, 109)(34, 126)(35, 125)(36, 123)(37, 122)(38, 114)(39, 115)(40, 116)(41, 117)(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, 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, 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, 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, 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, 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 E20.525 Graph:: bipartite v = 3 e = 84 f = 43 degree seq :: [ 42^2, 84 ] E20.516 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 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, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2^2 * Y1 * Y2^-2 * Y1^-2, Y2^4 * Y1^5, Y2 * Y3^2 * Y2^3 * Y3 * Y2^2, Y1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-3, Y1 * Y2^-1 * Y1^2 * Y2^-5, Y2^-1 * Y1^-1 * Y2 * Y1^-3 * Y2 * Y1^-3 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-3 * Y2 * Y1^-3 * Y2 * Y1^-1, Y3^21, Y3 * Y1^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 26, 68, 41, 83, 35, 77, 20, 62, 9, 51, 17, 59, 29, 71, 39, 81, 24, 66, 13, 55, 18, 60, 30, 72, 33, 75, 37, 79, 22, 64, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 27, 69, 40, 82, 25, 67, 32, 74, 34, 76, 19, 61, 31, 73, 38, 80, 23, 65, 12, 54, 5, 47, 8, 50, 16, 58, 28, 70, 42, 84, 36, 78, 21, 63, 10, 52)(85, 127, 87, 129, 93, 135, 103, 145, 117, 159, 112, 154, 98, 140, 111, 153, 123, 165, 107, 149, 95, 137, 105, 147, 119, 161, 116, 158, 102, 144, 92, 134, 86, 128, 91, 133, 101, 143, 115, 157, 121, 163, 126, 168, 110, 152, 124, 166, 108, 150, 96, 138, 88, 130, 94, 136, 104, 146, 118, 160, 114, 156, 100, 142, 90, 132, 99, 141, 113, 155, 122, 164, 106, 148, 120, 162, 125, 167, 109, 151, 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, 106)(12, 107)(13, 108)(14, 90)(15, 91)(16, 92)(17, 93)(18, 97)(19, 118)(20, 119)(21, 120)(22, 121)(23, 122)(24, 123)(25, 124)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 109)(33, 114)(34, 116)(35, 125)(36, 126)(37, 117)(38, 115)(39, 113)(40, 111)(41, 110)(42, 112)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 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, 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, 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, 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, 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 E20.523 Graph:: bipartite v = 3 e = 84 f = 43 degree seq :: [ 42^2, 84 ] E20.517 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), (R * Y2)^2, (Y2, Y1^-1), Y2 * Y1 * Y2 * Y1^3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-9, Y1^2 * Y2^-1 * Y1 * Y2^-3 * Y3^-2 * Y2^-4, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 13, 55, 18, 60, 24, 66, 31, 73, 30, 72, 34, 76, 40, 82, 42, 84, 36, 78, 27, 69, 33, 75, 29, 71, 20, 62, 9, 51, 17, 59, 11, 53, 4, 46)(3, 45, 7, 49, 15, 57, 12, 54, 5, 47, 8, 50, 16, 58, 23, 65, 22, 64, 26, 68, 32, 74, 39, 81, 38, 80, 35, 77, 41, 83, 37, 79, 28, 70, 19, 61, 25, 67, 21, 63, 10, 52)(85, 127, 87, 129, 93, 135, 103, 145, 111, 153, 119, 161, 118, 160, 110, 152, 102, 144, 92, 134, 86, 128, 91, 133, 101, 143, 109, 151, 117, 159, 125, 167, 124, 166, 116, 158, 108, 150, 100, 142, 90, 132, 99, 141, 95, 137, 105, 147, 113, 155, 121, 163, 126, 168, 123, 165, 115, 157, 107, 149, 98, 140, 96, 138, 88, 130, 94, 136, 104, 146, 112, 154, 120, 162, 122, 164, 114, 156, 106, 148, 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, 101)(12, 99)(13, 98)(14, 90)(15, 91)(16, 92)(17, 93)(18, 97)(19, 112)(20, 113)(21, 109)(22, 107)(23, 100)(24, 102)(25, 103)(26, 106)(27, 120)(28, 121)(29, 117)(30, 115)(31, 108)(32, 110)(33, 111)(34, 114)(35, 122)(36, 126)(37, 125)(38, 123)(39, 116)(40, 118)(41, 119)(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, 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, 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, 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, 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, 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 E20.522 Graph:: bipartite v = 3 e = 84 f = 43 degree seq :: [ 42^2, 84 ] E20.518 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y2^-2 * Y1 * Y2^2, Y2^-3 * Y1^-1 * Y2^-2, Y2 * Y1^-1 * Y2 * Y1^-7, (Y3^-1 * Y1^-1)^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 24, 66, 34, 76, 30, 72, 20, 62, 9, 51, 17, 59, 27, 69, 37, 79, 42, 84, 40, 82, 33, 75, 23, 65, 12, 54, 5, 47, 8, 50, 16, 58, 26, 68, 36, 78, 31, 73, 21, 63, 10, 52, 3, 45, 7, 49, 15, 57, 25, 67, 35, 77, 41, 83, 39, 81, 29, 71, 19, 61, 13, 55, 18, 60, 28, 70, 38, 80, 32, 74, 22, 64, 11, 53, 4, 46)(85, 127, 87, 129, 93, 135, 103, 145, 96, 138, 88, 130, 94, 136, 104, 146, 113, 155, 107, 149, 95, 137, 105, 147, 114, 156, 123, 165, 117, 159, 106, 148, 115, 157, 118, 160, 125, 167, 124, 166, 116, 158, 120, 162, 108, 150, 119, 161, 126, 168, 122, 164, 110, 152, 98, 140, 109, 151, 121, 163, 112, 154, 100, 142, 90, 132, 99, 141, 111, 153, 102, 144, 92, 134, 86, 128, 91, 133, 101, 143, 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, 109)(15, 111)(16, 90)(17, 97)(18, 92)(19, 96)(20, 113)(21, 114)(22, 115)(23, 95)(24, 119)(25, 121)(26, 98)(27, 102)(28, 100)(29, 107)(30, 123)(31, 118)(32, 120)(33, 106)(34, 125)(35, 126)(36, 108)(37, 112)(38, 110)(39, 117)(40, 116)(41, 124)(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, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.521 Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.519 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 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, Y1), Y1^-1 * Y2^-1 * Y1^-3 * Y2^-1, Y2^8 * Y1^-1 * Y2 * Y1^-2, (Y3^-1 * Y1^-1)^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 13, 55, 18, 60, 24, 66, 31, 73, 30, 72, 34, 76, 40, 82, 35, 77, 41, 83, 37, 79, 28, 70, 19, 61, 25, 67, 21, 63, 10, 52, 3, 45, 7, 49, 15, 57, 12, 54, 5, 47, 8, 50, 16, 58, 23, 65, 22, 64, 26, 68, 32, 74, 39, 81, 38, 80, 42, 84, 36, 78, 27, 69, 33, 75, 29, 71, 20, 62, 9, 51, 17, 59, 11, 53, 4, 46)(85, 127, 87, 129, 93, 135, 103, 145, 111, 153, 119, 161, 123, 165, 115, 157, 107, 149, 98, 140, 96, 138, 88, 130, 94, 136, 104, 146, 112, 154, 120, 162, 124, 166, 116, 158, 108, 150, 100, 142, 90, 132, 99, 141, 95, 137, 105, 147, 113, 155, 121, 163, 126, 168, 118, 160, 110, 152, 102, 144, 92, 134, 86, 128, 91, 133, 101, 143, 109, 151, 117, 159, 125, 167, 122, 164, 114, 156, 106, 148, 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, 96)(15, 95)(16, 90)(17, 109)(18, 92)(19, 111)(20, 112)(21, 113)(22, 97)(23, 98)(24, 100)(25, 117)(26, 102)(27, 119)(28, 120)(29, 121)(30, 106)(31, 107)(32, 108)(33, 125)(34, 110)(35, 123)(36, 124)(37, 126)(38, 114)(39, 115)(40, 116)(41, 122)(42, 118)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.520 Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.520 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-2 * Y2^-2, Y3^-2 * Y2^8 * Y3^-1 * Y2 * Y3^-9, Y3^-2 * Y2^19, (Y3^-1 * Y1^-1)^42, (Y3 * Y2^-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, 95, 137, 99, 141, 103, 145, 107, 149, 111, 153, 115, 157, 119, 161, 123, 165, 125, 167, 122, 164, 117, 159, 114, 156, 109, 151, 106, 148, 101, 143, 98, 140, 93, 135, 88, 130)(87, 129, 91, 133, 89, 131, 92, 134, 96, 138, 100, 142, 104, 146, 108, 150, 112, 154, 116, 158, 120, 162, 124, 166, 126, 168, 121, 163, 118, 160, 113, 155, 110, 152, 105, 147, 102, 144, 97, 139, 94, 136) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 89)(7, 88)(8, 86)(9, 97)(10, 98)(11, 92)(12, 90)(13, 101)(14, 102)(15, 96)(16, 95)(17, 105)(18, 106)(19, 100)(20, 99)(21, 109)(22, 110)(23, 104)(24, 103)(25, 113)(26, 114)(27, 108)(28, 107)(29, 117)(30, 118)(31, 112)(32, 111)(33, 121)(34, 122)(35, 116)(36, 115)(37, 125)(38, 126)(39, 120)(40, 119)(41, 124)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.519 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.521 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, Y3 * Y2 * Y3^3, Y2^-1 * Y3 * Y2^-4 * Y3 * Y2^-5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (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, 106, 148, 114, 156, 122, 164, 118, 160, 110, 152, 102, 144, 93, 135, 97, 139, 101, 143, 109, 151, 117, 159, 125, 167, 120, 162, 112, 154, 104, 146, 95, 137, 88, 130)(87, 129, 91, 133, 99, 141, 107, 149, 115, 157, 123, 165, 126, 168, 121, 163, 113, 155, 105, 147, 96, 138, 89, 131, 92, 134, 100, 142, 108, 150, 116, 158, 124, 166, 119, 161, 111, 153, 103, 145, 94, 136) L = (1, 87)(2, 91)(3, 93)(4, 94)(5, 85)(6, 99)(7, 97)(8, 86)(9, 96)(10, 102)(11, 103)(12, 88)(13, 89)(14, 107)(15, 101)(16, 90)(17, 92)(18, 105)(19, 110)(20, 111)(21, 95)(22, 115)(23, 109)(24, 98)(25, 100)(26, 113)(27, 118)(28, 119)(29, 104)(30, 123)(31, 117)(32, 106)(33, 108)(34, 121)(35, 122)(36, 124)(37, 112)(38, 126)(39, 125)(40, 114)(41, 116)(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) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.518 Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.522 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, (Y3, Y1^-1), (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^10 * Y1 * Y3^9 * Y1, (Y3 * Y2^-1)^21, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 43, 2, 44, 6, 48, 11, 53, 15, 57, 19, 61, 23, 65, 27, 69, 31, 73, 35, 77, 39, 81, 42, 84, 38, 80, 34, 76, 30, 72, 26, 68, 22, 64, 18, 60, 14, 56, 10, 52, 5, 47, 8, 50, 3, 45, 7, 49, 12, 54, 16, 58, 20, 62, 24, 66, 28, 70, 32, 74, 36, 78, 40, 82, 41, 83, 37, 79, 33, 75, 29, 71, 25, 67, 21, 63, 17, 59, 13, 55, 9, 51, 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, 90)(4, 92)(5, 85)(6, 96)(7, 95)(8, 86)(9, 89)(10, 88)(11, 100)(12, 99)(13, 94)(14, 93)(15, 104)(16, 103)(17, 98)(18, 97)(19, 108)(20, 107)(21, 102)(22, 101)(23, 112)(24, 111)(25, 106)(26, 105)(27, 116)(28, 115)(29, 110)(30, 109)(31, 120)(32, 119)(33, 114)(34, 113)(35, 124)(36, 123)(37, 118)(38, 117)(39, 125)(40, 126)(41, 122)(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) :: { ( 42, 84 ), ( 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84 ) } Outer automorphisms :: reflexible Dual of E20.517 Graph:: bipartite v = 43 e = 84 f = 3 degree seq :: [ 2^42, 84 ] E20.523 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 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, (Y1, Y3^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1 * Y3^9, (Y3 * Y2^-1)^21, (Y1^-1 * Y3^-1)^42 ] Map:: R = (1, 43, 2, 44, 6, 48, 10, 52, 3, 45, 7, 49, 14, 56, 18, 60, 9, 51, 15, 57, 22, 64, 26, 68, 17, 59, 23, 65, 30, 72, 34, 76, 25, 67, 31, 73, 38, 80, 42, 84, 33, 75, 39, 81, 37, 79, 40, 82, 41, 83, 36, 78, 29, 71, 32, 74, 35, 77, 28, 70, 21, 63, 24, 66, 27, 69, 20, 62, 13, 55, 16, 58, 19, 61, 12, 54, 5, 47, 8, 50, 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, 98)(7, 99)(8, 86)(9, 101)(10, 102)(11, 90)(12, 88)(13, 89)(14, 106)(15, 107)(16, 92)(17, 109)(18, 110)(19, 95)(20, 96)(21, 97)(22, 114)(23, 115)(24, 100)(25, 117)(26, 118)(27, 103)(28, 104)(29, 105)(30, 122)(31, 123)(32, 108)(33, 125)(34, 126)(35, 111)(36, 112)(37, 113)(38, 121)(39, 120)(40, 116)(41, 119)(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) :: { ( 42, 84 ), ( 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84 ) } Outer automorphisms :: reflexible Dual of E20.516 Graph:: bipartite v = 43 e = 84 f = 3 degree seq :: [ 2^42, 84 ] E20.524 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^21, (Y3^10 * Y1^-1)^2, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44, 5, 47, 6, 48, 9, 51, 10, 52, 13, 55, 14, 56, 17, 59, 18, 60, 21, 63, 22, 64, 25, 67, 26, 68, 29, 71, 30, 72, 33, 75, 34, 76, 37, 79, 38, 80, 41, 83, 42, 84, 39, 81, 40, 82, 35, 77, 36, 78, 31, 73, 32, 74, 27, 69, 28, 70, 23, 65, 24, 66, 19, 61, 20, 62, 15, 57, 16, 58, 11, 53, 12, 54, 7, 49, 8, 50, 3, 45, 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, 88)(3, 91)(4, 92)(5, 85)(6, 86)(7, 95)(8, 96)(9, 89)(10, 90)(11, 99)(12, 100)(13, 93)(14, 94)(15, 103)(16, 104)(17, 97)(18, 98)(19, 107)(20, 108)(21, 101)(22, 102)(23, 111)(24, 112)(25, 105)(26, 106)(27, 115)(28, 116)(29, 109)(30, 110)(31, 119)(32, 120)(33, 113)(34, 114)(35, 123)(36, 124)(37, 117)(38, 118)(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) :: { ( 42, 84 ), ( 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84 ) } Outer automorphisms :: reflexible Dual of E20.514 Graph:: bipartite v = 43 e = 84 f = 3 degree seq :: [ 2^42, 84 ] E20.525 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 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, (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^4 * Y3^5, Y1^6 * Y3^-3, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 26, 68, 34, 76, 19, 61, 31, 73, 39, 81, 24, 66, 13, 55, 18, 60, 30, 72, 36, 78, 21, 63, 10, 52, 3, 45, 7, 49, 15, 57, 27, 69, 41, 83, 42, 84, 33, 75, 38, 80, 23, 65, 12, 54, 5, 47, 8, 50, 16, 58, 28, 70, 35, 77, 20, 62, 9, 51, 17, 59, 29, 71, 40, 82, 25, 67, 32, 74, 37, 79, 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, 111)(15, 113)(16, 90)(17, 115)(18, 92)(19, 117)(20, 118)(21, 119)(22, 120)(23, 95)(24, 96)(25, 97)(26, 125)(27, 124)(28, 98)(29, 123)(30, 100)(31, 122)(32, 102)(33, 121)(34, 126)(35, 110)(36, 112)(37, 114)(38, 106)(39, 107)(40, 108)(41, 109)(42, 116)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 42, 84 ), ( 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84 ) } Outer automorphisms :: reflexible Dual of E20.515 Graph:: bipartite v = 43 e = 84 f = 3 degree seq :: [ 2^42, 84 ] E20.526 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {21, 42, 42}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3^-4, (R * Y2 * Y3^-1)^2, Y1^10 * Y3^-1, (Y3 * Y2^-1)^21 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 23, 65, 31, 73, 37, 79, 29, 71, 21, 63, 10, 52, 3, 45, 7, 49, 15, 57, 24, 66, 32, 74, 39, 81, 42, 84, 36, 78, 28, 70, 20, 62, 9, 51, 17, 59, 13, 55, 18, 60, 26, 68, 34, 76, 40, 82, 41, 83, 35, 77, 27, 69, 19, 61, 12, 54, 5, 47, 8, 50, 16, 58, 25, 67, 33, 75, 38, 80, 30, 72, 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, 108)(15, 97)(16, 90)(17, 96)(18, 92)(19, 95)(20, 111)(21, 112)(22, 113)(23, 116)(24, 102)(25, 98)(26, 100)(27, 106)(28, 119)(29, 120)(30, 121)(31, 123)(32, 110)(33, 107)(34, 109)(35, 114)(36, 125)(37, 126)(38, 115)(39, 118)(40, 117)(41, 122)(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) :: { ( 42, 84 ), ( 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84, 42, 84 ) } Outer automorphisms :: reflexible Dual of E20.513 Graph:: bipartite v = 43 e = 84 f = 3 degree seq :: [ 2^42, 84 ] E20.527 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (Y3 * Y1)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, R * Y2 * R * Y3, Y1^-9 * Y2 * Y1^2 * Y3, Y1^5 * Y2 * Y1^-6 * Y3 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 57, 13, 65, 21, 73, 29, 81, 37, 86, 42, 78, 34, 70, 26, 62, 18, 54, 10, 60, 16, 68, 24, 76, 32, 84, 40, 88, 44, 80, 36, 72, 28, 64, 20, 56, 12, 49, 5, 45)(3, 53, 9, 61, 17, 69, 25, 77, 33, 85, 41, 83, 39, 75, 31, 67, 23, 59, 15, 52, 8, 48, 4, 55, 11, 63, 19, 71, 27, 79, 35, 87, 43, 82, 38, 74, 30, 66, 22, 58, 14, 51, 7, 47) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 25)(21, 30)(23, 32)(27, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 41)(37, 43)(39, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 59)(51, 60)(53, 62)(56, 63)(57, 67)(58, 68)(61, 70)(64, 71)(65, 75)(66, 76)(69, 78)(72, 79)(73, 83)(74, 84)(77, 86)(80, 87)(81, 85)(82, 88) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.532 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.528 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^2, Y2 * Y3 * Y2 * Y1^-4 * Y3, Y1^3 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-2 * Y2, Y1^15 * Y2 * Y1^2 * Y3, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 70, 26, 81, 37, 86, 42, 78, 34, 64, 20, 54, 10, 61, 17, 73, 29, 67, 23, 56, 12, 62, 18, 74, 30, 83, 39, 88, 44, 80, 36, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 77, 33, 85, 41, 82, 38, 72, 28, 60, 16, 52, 8, 48, 4, 55, 11, 66, 22, 75, 31, 65, 21, 79, 35, 87, 43, 84, 40, 76, 32, 68, 24, 71, 27, 59, 15, 51, 7, 47) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 29)(24, 26)(25, 33)(28, 39)(32, 37)(34, 43)(36, 41)(38, 44)(40, 42)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 72)(59, 73)(62, 76)(63, 78)(65, 80)(67, 71)(69, 75)(70, 82)(74, 84)(77, 86)(79, 88)(81, 85)(83, 87) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.536 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.529 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y3, Y1^3 * Y3 * Y1^-4 * Y2, Y1^3 * Y3 * Y2 * Y1^2 * Y3 * Y2 * Y1^2 * Y2 * Y3, (Y2 * Y1 * Y3)^11 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 70, 26, 77, 33, 64, 20, 54, 10, 61, 17, 73, 29, 83, 39, 88, 44, 87, 43, 80, 36, 67, 23, 56, 12, 62, 18, 74, 30, 81, 37, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 76, 32, 72, 28, 60, 16, 52, 8, 48, 4, 55, 11, 66, 22, 79, 35, 86, 42, 84, 40, 75, 31, 68, 24, 65, 21, 78, 34, 85, 41, 82, 38, 71, 27, 59, 15, 51, 7, 47) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 24)(20, 34)(22, 36)(25, 32)(26, 38)(28, 37)(29, 31)(33, 41)(35, 43)(39, 40)(42, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 72)(59, 73)(62, 75)(63, 77)(65, 67)(69, 79)(70, 76)(71, 83)(74, 84)(78, 80)(81, 86)(82, 88)(85, 87) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.535 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.530 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y1^-1 * Y2 * Y3 * Y1^-4, Y1^2 * Y3 * Y1^-3 * Y2, Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1, (Y2 * Y1 * Y3)^11 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 64, 20, 54, 10, 61, 17, 71, 27, 80, 36, 84, 40, 75, 31, 82, 38, 79, 35, 83, 39, 86, 42, 77, 33, 67, 23, 56, 12, 62, 18, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 60, 16, 52, 8, 48, 4, 55, 11, 66, 22, 76, 32, 73, 29, 68, 24, 78, 34, 85, 41, 88, 44, 87, 43, 81, 37, 72, 28, 65, 21, 74, 30, 70, 26, 59, 15, 51, 7, 47) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 25)(17, 28)(20, 30)(22, 33)(24, 35)(27, 37)(29, 39)(31, 41)(32, 42)(34, 38)(36, 43)(40, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 63)(59, 71)(62, 73)(65, 75)(67, 78)(69, 76)(70, 80)(72, 82)(74, 84)(77, 85)(79, 81)(83, 87)(86, 88) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.534 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.531 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y3)^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y1^2 * Y3 * Y1^-1 * Y2, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 54, 10, 59, 15, 64, 20, 66, 22, 71, 27, 76, 32, 78, 34, 83, 39, 88, 44, 86, 42, 81, 37, 79, 35, 74, 30, 69, 25, 67, 23, 62, 18, 56, 12, 57, 13, 49, 5, 45)(3, 53, 9, 52, 8, 48, 4, 55, 11, 61, 17, 63, 19, 68, 24, 73, 29, 75, 31, 80, 36, 85, 41, 87, 43, 84, 40, 82, 38, 77, 33, 72, 28, 70, 26, 65, 21, 60, 16, 58, 14, 51, 7, 47) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 13)(10, 16)(11, 18)(15, 21)(17, 23)(19, 25)(20, 26)(22, 28)(24, 30)(27, 33)(29, 35)(31, 37)(32, 38)(34, 40)(36, 42)(39, 43)(41, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 53)(51, 59)(56, 63)(57, 61)(58, 64)(60, 66)(62, 68)(65, 71)(67, 73)(69, 75)(70, 76)(72, 78)(74, 80)(77, 83)(79, 85)(81, 87)(82, 88)(84, 86) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.533 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.532 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y1^-1 * Y2)^2, Y1^11 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 57, 13, 65, 21, 73, 29, 80, 36, 72, 28, 64, 20, 56, 12, 49, 5, 45)(3, 53, 9, 61, 17, 69, 25, 77, 33, 84, 40, 81, 37, 74, 30, 66, 22, 58, 14, 51, 7, 47)(4, 55, 11, 63, 19, 71, 27, 79, 35, 86, 42, 82, 38, 75, 31, 67, 23, 59, 15, 52, 8, 48)(10, 60, 16, 68, 24, 76, 32, 83, 39, 87, 43, 88, 44, 85, 41, 78, 34, 70, 26, 62, 18, 54) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 25)(21, 30)(23, 32)(27, 34)(28, 33)(29, 37)(31, 39)(35, 41)(36, 40)(38, 43)(42, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 59)(51, 60)(53, 62)(56, 63)(57, 67)(58, 68)(61, 70)(64, 71)(65, 75)(66, 76)(69, 78)(72, 79)(73, 82)(74, 83)(77, 85)(80, 86)(81, 87)(84, 88) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.527 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.533 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3 * Y1)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y3 * Y1^-3 * Y2 * Y3 * Y2, Y1^11, Y1^11 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 70, 26, 78, 34, 85, 41, 77, 33, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 68, 24, 76, 32, 84, 40, 86, 42, 79, 35, 71, 27, 59, 15, 51, 7, 47)(4, 55, 11, 66, 22, 74, 30, 82, 38, 88, 44, 81, 37, 73, 29, 65, 21, 60, 16, 52, 8, 48)(10, 61, 17, 72, 28, 80, 36, 87, 43, 83, 39, 75, 31, 67, 23, 56, 12, 62, 18, 64, 20, 54) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 20)(17, 29)(22, 31)(24, 25)(26, 35)(28, 37)(30, 39)(32, 33)(34, 42)(36, 44)(38, 43)(40, 41)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 65)(59, 72)(62, 63)(67, 76)(69, 74)(70, 73)(71, 80)(75, 84)(77, 82)(78, 81)(79, 87)(83, 86)(85, 88) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.531 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.534 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3 * Y1)^2, (Y1^-2 * Y3)^2, Y2 * Y3 * Y2 * Y3 * Y1^3, Y2 * Y1^-1 * Y3 * Y2 * Y1^-2 * Y3, Y1^11, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 70, 26, 78, 34, 85, 41, 77, 33, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 74, 30, 82, 38, 88, 44, 81, 37, 73, 29, 68, 24, 59, 15, 51, 7, 47)(4, 55, 11, 66, 22, 65, 21, 76, 32, 84, 40, 86, 42, 79, 35, 71, 27, 60, 16, 52, 8, 48)(10, 61, 17, 67, 23, 56, 12, 62, 18, 72, 28, 80, 36, 87, 43, 83, 39, 75, 31, 64, 20, 54) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 24)(16, 28)(17, 22)(20, 32)(25, 30)(26, 29)(27, 36)(31, 40)(33, 38)(34, 37)(35, 43)(39, 42)(41, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 71)(59, 67)(62, 73)(63, 75)(65, 69)(70, 79)(72, 81)(74, 83)(76, 77)(78, 86)(80, 88)(82, 87)(84, 85) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.530 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.535 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^2 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-1 * Y3, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y1^5 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 70, 26, 84, 40, 80, 36, 85, 41, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 77, 33, 88, 44, 76, 32, 68, 24, 83, 39, 71, 27, 59, 15, 51, 7, 47)(4, 55, 11, 66, 22, 81, 37, 75, 31, 65, 21, 79, 35, 86, 42, 72, 28, 60, 16, 52, 8, 48)(10, 61, 17, 73, 29, 82, 38, 67, 23, 56, 12, 62, 18, 74, 30, 87, 43, 78, 34, 64, 20, 54) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 39)(28, 43)(29, 37)(32, 36)(34, 42)(41, 44)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 72)(59, 73)(62, 76)(63, 78)(65, 80)(67, 83)(69, 81)(70, 86)(71, 82)(74, 88)(75, 85)(77, 87)(79, 84) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.529 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.536 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 11, 22}) Quotient :: halfedge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y2)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1)^2, Y1^-2 * Y2 * Y3 * Y1^2 * Y3 * Y2, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y3 * Y1^-2 * Y2 * Y3 * Y1^-3 * Y2 ] Map:: non-degenerate R = (1, 46, 2, 50, 6, 58, 14, 70, 26, 80, 36, 84, 40, 85, 41, 69, 25, 57, 13, 49, 5, 45)(3, 53, 9, 63, 19, 77, 33, 76, 32, 68, 24, 83, 39, 86, 42, 71, 27, 59, 15, 51, 7, 47)(4, 55, 11, 66, 22, 81, 37, 88, 44, 75, 31, 65, 21, 79, 35, 72, 28, 60, 16, 52, 8, 48)(10, 61, 17, 73, 29, 87, 43, 82, 38, 67, 23, 56, 12, 62, 18, 74, 30, 78, 34, 64, 20, 54) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 42)(28, 34)(29, 44)(32, 41)(36, 39)(37, 43)(45, 48)(46, 52)(47, 54)(49, 55)(50, 60)(51, 61)(53, 64)(56, 68)(57, 66)(58, 72)(59, 73)(62, 76)(63, 78)(65, 80)(67, 83)(69, 81)(70, 79)(71, 87)(74, 77)(75, 84)(82, 86)(85, 88) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.528 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.537 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y3^11, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 45, 4, 48, 11, 55, 19, 63, 27, 71, 35, 79, 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)(3, 47, 9, 53, 17, 61, 25, 69, 33, 77, 41, 85, 42, 86, 34, 78, 26, 70, 18, 62, 10, 54)(6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 43, 87, 44, 88, 38, 82, 30, 74, 22, 66, 14, 58)(89, 90)(91, 94)(92, 96)(93, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 110)(106, 109)(107, 112)(108, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 126)(122, 125)(123, 128)(124, 127)(129, 132)(130, 131)(133, 135)(134, 138)(136, 142)(137, 141)(139, 146)(140, 145)(143, 150)(144, 149)(147, 154)(148, 153)(151, 158)(152, 157)(155, 162)(156, 161)(159, 166)(160, 165)(163, 170)(164, 169)(167, 174)(168, 173)(171, 176)(172, 175) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.552 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.538 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-2, Y3^11, (Y3^-4 * Y2 * Y1)^2, (Y3 * Y1 * Y2)^22 ] Map:: R = (1, 45, 4, 48, 12, 56, 24, 68, 32, 76, 40, 84, 41, 85, 33, 77, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 19, 63, 29, 73, 37, 81, 44, 88, 36, 80, 28, 72, 18, 62, 8, 52)(3, 47, 10, 54, 22, 66, 31, 75, 39, 83, 42, 86, 34, 78, 26, 70, 14, 58, 23, 67, 11, 55)(6, 50, 15, 59, 27, 71, 35, 79, 43, 87, 38, 82, 30, 74, 21, 65, 9, 53, 20, 64, 16, 60)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 114)(104, 111)(107, 113)(110, 118)(112, 116)(115, 122)(117, 121)(119, 126)(120, 124)(123, 130)(125, 129)(127, 131)(128, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 156)(149, 152)(150, 159)(153, 161)(157, 163)(158, 164)(160, 167)(162, 169)(165, 171)(166, 172)(168, 175)(170, 176)(173, 174) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.555 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.539 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y3^3 * Y1, Y3^11, Y2 * Y3^-1 * Y1 * Y3^2 * Y2 * Y3^-5 * Y1, (Y3 * Y1 * Y2)^22 ] Map:: R = (1, 45, 4, 48, 12, 56, 24, 68, 32, 76, 40, 84, 41, 85, 33, 77, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 28, 72, 36, 80, 44, 88, 37, 81, 29, 73, 19, 63, 18, 62, 8, 52)(3, 47, 10, 54, 22, 66, 14, 58, 26, 70, 34, 78, 42, 86, 39, 83, 31, 75, 23, 67, 11, 55)(6, 50, 15, 59, 21, 65, 9, 53, 20, 64, 30, 74, 38, 82, 43, 87, 35, 79, 27, 71, 16, 60)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 110)(104, 114)(107, 112)(111, 118)(113, 116)(115, 122)(117, 120)(119, 126)(121, 124)(123, 130)(125, 128)(127, 131)(129, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 157)(149, 159)(150, 153)(152, 161)(156, 163)(158, 165)(160, 167)(162, 169)(164, 171)(166, 173)(168, 175)(170, 176)(172, 174) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.556 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.540 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-4, Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y3^-4 * Y1, Y3^11 ] Map:: R = (1, 45, 4, 48, 12, 56, 24, 68, 40, 84, 33, 77, 26, 70, 41, 85, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 44, 88, 35, 79, 19, 63, 34, 78, 32, 76, 18, 62, 8, 52)(3, 47, 10, 54, 22, 66, 38, 82, 28, 72, 14, 58, 27, 71, 42, 86, 39, 83, 23, 67, 11, 55)(6, 50, 15, 59, 29, 73, 37, 81, 21, 65, 9, 53, 20, 64, 36, 80, 43, 87, 30, 74, 16, 60)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 116)(104, 115)(107, 121)(110, 125)(111, 124)(112, 120)(113, 119)(114, 123)(117, 126)(118, 130)(122, 128)(127, 131)(129, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 158)(149, 162)(150, 161)(152, 167)(153, 166)(156, 171)(157, 170)(159, 165)(160, 173)(163, 175)(164, 169)(168, 176)(172, 174) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.553 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.541 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, (R * Y3)^2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^2 * Y2 * Y1 * Y3 * Y2 * Y3^-1, Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^2 * Y1 * Y2 * Y3^4 * Y1, Y3^11 ] Map:: R = (1, 45, 4, 48, 12, 56, 24, 68, 40, 84, 26, 70, 33, 77, 41, 85, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 35, 79, 19, 63, 34, 78, 44, 88, 32, 76, 18, 62, 8, 52)(3, 47, 10, 54, 22, 66, 38, 82, 42, 86, 28, 72, 14, 58, 27, 71, 39, 83, 23, 67, 11, 55)(6, 50, 15, 59, 29, 73, 43, 87, 37, 81, 21, 65, 9, 53, 20, 64, 36, 80, 30, 74, 16, 60)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 116)(104, 115)(107, 121)(110, 125)(111, 124)(112, 120)(113, 119)(114, 122)(117, 130)(118, 127)(123, 129)(126, 131)(128, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 158)(149, 162)(150, 161)(152, 167)(153, 166)(156, 171)(157, 170)(159, 172)(160, 165)(163, 168)(164, 175)(169, 176)(173, 174) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.554 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.542 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, (Y3 * Y1)^2, Y3^-5 * Y1 * Y2 * Y3^-6, 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 ] Map:: R = (1, 45, 4, 48, 11, 55, 19, 63, 27, 71, 35, 79, 43, 87, 38, 82, 30, 74, 22, 66, 14, 58, 6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 44, 88, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49)(2, 46, 7, 51, 15, 59, 23, 67, 31, 75, 39, 83, 42, 86, 34, 78, 26, 70, 18, 62, 10, 54, 3, 47, 9, 53, 17, 61, 25, 69, 33, 77, 41, 85, 40, 84, 32, 76, 24, 68, 16, 60, 8, 52)(89, 90)(91, 94)(92, 96)(93, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 110)(106, 109)(107, 112)(108, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 126)(122, 125)(123, 128)(124, 127)(129, 131)(130, 132)(133, 135)(134, 138)(136, 142)(137, 141)(139, 146)(140, 145)(143, 150)(144, 149)(147, 154)(148, 153)(151, 158)(152, 157)(155, 162)(156, 161)(159, 166)(160, 165)(163, 170)(164, 169)(167, 174)(168, 173)(171, 175)(172, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.547 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.543 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, Y3^2 * Y2 * Y3^-2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3^22, Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 45, 4, 48, 12, 56, 24, 68, 26, 70, 38, 82, 44, 88, 35, 79, 21, 65, 9, 53, 20, 64, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 40, 84, 42, 86, 33, 77, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 19, 63, 34, 78, 43, 87, 39, 83, 28, 72, 14, 58, 27, 71, 23, 67, 11, 55, 3, 47, 10, 54, 22, 66, 36, 80, 41, 85, 37, 81, 32, 76, 18, 62, 8, 52)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 116)(104, 115)(107, 121)(110, 123)(111, 118)(112, 120)(113, 119)(114, 125)(117, 127)(122, 130)(124, 132)(126, 129)(128, 131)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 158)(149, 162)(150, 161)(152, 163)(153, 166)(156, 159)(157, 168)(160, 170)(164, 172)(165, 173)(167, 175)(169, 174)(171, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.550 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.544 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^7 * Y1, (Y3 * Y1 * Y2)^11 ] Map:: R = (1, 45, 4, 48, 12, 56, 24, 68, 36, 80, 33, 77, 21, 65, 9, 53, 20, 64, 32, 76, 42, 86, 44, 88, 39, 83, 28, 72, 16, 60, 6, 50, 15, 59, 27, 71, 37, 81, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 29, 73, 40, 84, 38, 82, 26, 70, 14, 58, 19, 63, 31, 75, 41, 85, 43, 87, 35, 79, 23, 67, 11, 55, 3, 47, 10, 54, 22, 66, 34, 78, 30, 74, 18, 62, 8, 52)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 114)(104, 107)(110, 121)(111, 120)(112, 118)(113, 117)(115, 126)(116, 119)(122, 124)(123, 130)(125, 128)(127, 129)(131, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 152)(149, 160)(150, 159)(153, 163)(156, 167)(157, 166)(158, 164)(161, 171)(162, 169)(165, 173)(168, 175)(170, 174)(172, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.551 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.545 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y2 * Y3^5 * Y1, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y2 * Y1 * Y3^3 * Y2 * Y1 * Y3^3 * Y2 * Y1 * Y3 ] Map:: R = (1, 45, 4, 48, 12, 56, 24, 68, 21, 65, 9, 53, 20, 64, 34, 78, 42, 86, 41, 85, 31, 75, 38, 82, 26, 70, 37, 81, 40, 84, 29, 73, 16, 60, 6, 50, 15, 59, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 30, 74, 28, 72, 14, 58, 27, 71, 39, 83, 44, 88, 43, 87, 36, 80, 33, 77, 19, 63, 32, 76, 35, 79, 23, 67, 11, 55, 3, 47, 10, 54, 22, 66, 18, 62, 8, 52)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 109)(99, 108)(100, 106)(101, 105)(103, 116)(104, 115)(107, 119)(110, 112)(111, 122)(113, 118)(114, 124)(117, 127)(120, 129)(121, 126)(123, 130)(125, 131)(128, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 148)(140, 147)(141, 151)(144, 155)(145, 154)(146, 158)(149, 161)(150, 157)(152, 165)(153, 164)(156, 167)(159, 170)(160, 169)(162, 172)(163, 171)(166, 168)(173, 176)(174, 175) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.548 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.546 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 11, 22}) Quotient :: edge^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y3^3 * Y1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 ] Map:: R = (1, 45, 4, 48, 12, 56, 9, 53, 18, 62, 25, 69, 23, 67, 30, 74, 37, 81, 35, 79, 42, 86, 44, 88, 39, 83, 32, 76, 34, 78, 27, 71, 20, 64, 22, 66, 15, 59, 6, 50, 13, 57, 5, 49)(2, 46, 7, 51, 16, 60, 14, 58, 21, 65, 28, 72, 26, 70, 33, 77, 40, 84, 38, 82, 41, 85, 43, 87, 36, 80, 29, 73, 31, 75, 24, 68, 17, 61, 19, 63, 11, 55, 3, 47, 10, 54, 8, 52)(89, 90)(91, 97)(92, 96)(93, 95)(94, 102)(98, 100)(99, 106)(101, 104)(103, 109)(105, 111)(107, 113)(108, 114)(110, 116)(112, 118)(115, 121)(117, 123)(119, 125)(120, 126)(122, 128)(124, 130)(127, 129)(131, 132)(133, 135)(134, 138)(136, 143)(137, 142)(139, 147)(140, 145)(141, 149)(144, 151)(146, 152)(148, 154)(150, 156)(153, 159)(155, 161)(157, 163)(158, 164)(160, 166)(162, 168)(165, 171)(167, 173)(169, 175)(170, 174)(172, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.549 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.547 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y3^11, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 11, 55, 99, 143, 19, 63, 107, 151, 27, 71, 115, 159, 35, 79, 123, 167, 36, 80, 124, 168, 28, 72, 116, 160, 20, 64, 108, 152, 12, 56, 100, 144, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 15, 59, 103, 147, 23, 67, 111, 155, 31, 75, 119, 163, 39, 83, 127, 171, 40, 84, 128, 172, 32, 76, 120, 164, 24, 68, 112, 156, 16, 60, 104, 148, 8, 52, 96, 140)(3, 47, 91, 135, 9, 53, 97, 141, 17, 61, 105, 149, 25, 69, 113, 157, 33, 77, 121, 165, 41, 85, 129, 173, 42, 86, 130, 174, 34, 78, 122, 166, 26, 70, 114, 158, 18, 62, 106, 150, 10, 54, 98, 142)(6, 50, 94, 138, 13, 57, 101, 145, 21, 65, 109, 153, 29, 73, 117, 161, 37, 81, 125, 169, 43, 87, 131, 175, 44, 88, 132, 176, 38, 82, 126, 170, 30, 74, 118, 162, 22, 66, 110, 154, 14, 58, 102, 146) L = (1, 46)(2, 45)(3, 50)(4, 52)(5, 51)(6, 47)(7, 49)(8, 48)(9, 58)(10, 57)(11, 60)(12, 59)(13, 54)(14, 53)(15, 56)(16, 55)(17, 66)(18, 65)(19, 68)(20, 67)(21, 62)(22, 61)(23, 64)(24, 63)(25, 74)(26, 73)(27, 76)(28, 75)(29, 70)(30, 69)(31, 72)(32, 71)(33, 82)(34, 81)(35, 84)(36, 83)(37, 78)(38, 77)(39, 80)(40, 79)(41, 88)(42, 87)(43, 86)(44, 85)(89, 135)(90, 138)(91, 133)(92, 142)(93, 141)(94, 134)(95, 146)(96, 145)(97, 137)(98, 136)(99, 150)(100, 149)(101, 140)(102, 139)(103, 154)(104, 153)(105, 144)(106, 143)(107, 158)(108, 157)(109, 148)(110, 147)(111, 162)(112, 161)(113, 152)(114, 151)(115, 166)(116, 165)(117, 156)(118, 155)(119, 170)(120, 169)(121, 160)(122, 159)(123, 174)(124, 173)(125, 164)(126, 163)(127, 176)(128, 175)(129, 168)(130, 167)(131, 172)(132, 171) 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 ) } Outer automorphisms :: reflexible Dual of E20.542 Transitivity :: VT+ Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.548 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-2, Y3^11, (Y3^-4 * Y2 * Y1)^2, (Y3 * Y1 * Y2)^22 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 32, 76, 120, 164, 40, 84, 128, 172, 41, 85, 129, 173, 33, 77, 121, 165, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 19, 63, 107, 151, 29, 73, 117, 161, 37, 81, 125, 169, 44, 88, 132, 176, 36, 80, 124, 168, 28, 72, 116, 160, 18, 62, 106, 150, 8, 52, 96, 140)(3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 31, 75, 119, 163, 39, 83, 127, 171, 42, 86, 130, 174, 34, 78, 122, 166, 26, 70, 114, 158, 14, 58, 102, 146, 23, 67, 111, 155, 11, 55, 99, 143)(6, 50, 94, 138, 15, 59, 103, 147, 27, 71, 115, 159, 35, 79, 123, 167, 43, 87, 131, 175, 38, 82, 126, 170, 30, 74, 118, 162, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 16, 60, 104, 148) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 70)(16, 67)(17, 57)(18, 56)(19, 69)(20, 55)(21, 54)(22, 74)(23, 60)(24, 72)(25, 63)(26, 59)(27, 78)(28, 68)(29, 77)(30, 66)(31, 82)(32, 80)(33, 73)(34, 71)(35, 86)(36, 76)(37, 85)(38, 75)(39, 87)(40, 88)(41, 81)(42, 79)(43, 83)(44, 84)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 156)(103, 140)(104, 139)(105, 152)(106, 159)(107, 141)(108, 149)(109, 161)(110, 145)(111, 144)(112, 146)(113, 163)(114, 164)(115, 150)(116, 167)(117, 153)(118, 169)(119, 157)(120, 158)(121, 171)(122, 172)(123, 160)(124, 175)(125, 162)(126, 176)(127, 165)(128, 166)(129, 174)(130, 173)(131, 168)(132, 170) 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 ) } Outer automorphisms :: reflexible Dual of E20.545 Transitivity :: VT+ Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.549 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y3^3 * Y1, Y3^11, Y2 * Y3^-1 * Y1 * Y3^2 * Y2 * Y3^-5 * Y1, (Y3 * Y1 * Y2)^22 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 32, 76, 120, 164, 40, 84, 128, 172, 41, 85, 129, 173, 33, 77, 121, 165, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 28, 72, 116, 160, 36, 80, 124, 168, 44, 88, 132, 176, 37, 81, 125, 169, 29, 73, 117, 161, 19, 63, 107, 151, 18, 62, 106, 150, 8, 52, 96, 140)(3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 14, 58, 102, 146, 26, 70, 114, 158, 34, 78, 122, 166, 42, 86, 130, 174, 39, 83, 127, 171, 31, 75, 119, 163, 23, 67, 111, 155, 11, 55, 99, 143)(6, 50, 94, 138, 15, 59, 103, 147, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 30, 74, 118, 162, 38, 82, 126, 170, 43, 87, 131, 175, 35, 79, 123, 167, 27, 71, 115, 159, 16, 60, 104, 148) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 66)(16, 70)(17, 57)(18, 56)(19, 68)(20, 55)(21, 54)(22, 59)(23, 74)(24, 63)(25, 72)(26, 60)(27, 78)(28, 69)(29, 76)(30, 67)(31, 82)(32, 73)(33, 80)(34, 71)(35, 86)(36, 77)(37, 84)(38, 75)(39, 87)(40, 81)(41, 88)(42, 79)(43, 83)(44, 85)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 157)(103, 140)(104, 139)(105, 159)(106, 153)(107, 141)(108, 161)(109, 150)(110, 145)(111, 144)(112, 163)(113, 146)(114, 165)(115, 149)(116, 167)(117, 152)(118, 169)(119, 156)(120, 171)(121, 158)(122, 173)(123, 160)(124, 175)(125, 162)(126, 176)(127, 164)(128, 174)(129, 166)(130, 172)(131, 168)(132, 170) 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 ) } Outer automorphisms :: reflexible Dual of E20.546 Transitivity :: VT+ Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.550 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-4, Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y3^-4 * Y1, Y3^11 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 40, 84, 128, 172, 33, 77, 121, 165, 26, 70, 114, 158, 41, 85, 129, 173, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 31, 75, 119, 163, 44, 88, 132, 176, 35, 79, 123, 167, 19, 63, 107, 151, 34, 78, 122, 166, 32, 76, 120, 164, 18, 62, 106, 150, 8, 52, 96, 140)(3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 38, 82, 126, 170, 28, 72, 116, 160, 14, 58, 102, 146, 27, 71, 115, 159, 42, 86, 130, 174, 39, 83, 127, 171, 23, 67, 111, 155, 11, 55, 99, 143)(6, 50, 94, 138, 15, 59, 103, 147, 29, 73, 117, 161, 37, 81, 125, 169, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 36, 80, 124, 168, 43, 87, 131, 175, 30, 74, 118, 162, 16, 60, 104, 148) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 72)(16, 71)(17, 57)(18, 56)(19, 77)(20, 55)(21, 54)(22, 81)(23, 80)(24, 76)(25, 75)(26, 79)(27, 60)(28, 59)(29, 82)(30, 86)(31, 69)(32, 68)(33, 63)(34, 84)(35, 70)(36, 67)(37, 66)(38, 73)(39, 87)(40, 78)(41, 88)(42, 74)(43, 83)(44, 85)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 158)(103, 140)(104, 139)(105, 162)(106, 161)(107, 141)(108, 167)(109, 166)(110, 145)(111, 144)(112, 171)(113, 170)(114, 146)(115, 165)(116, 173)(117, 150)(118, 149)(119, 175)(120, 169)(121, 159)(122, 153)(123, 152)(124, 176)(125, 164)(126, 157)(127, 156)(128, 174)(129, 160)(130, 172)(131, 163)(132, 168) 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 ) } Outer automorphisms :: reflexible Dual of E20.543 Transitivity :: VT+ Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.551 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3)^2, (R * Y3)^2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^2 * Y2 * Y1 * Y3 * Y2 * Y3^-1, Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^2 * Y1 * Y2 * Y3^4 * Y1, Y3^11 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 40, 84, 128, 172, 26, 70, 114, 158, 33, 77, 121, 165, 41, 85, 129, 173, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 31, 75, 119, 163, 35, 79, 123, 167, 19, 63, 107, 151, 34, 78, 122, 166, 44, 88, 132, 176, 32, 76, 120, 164, 18, 62, 106, 150, 8, 52, 96, 140)(3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 38, 82, 126, 170, 42, 86, 130, 174, 28, 72, 116, 160, 14, 58, 102, 146, 27, 71, 115, 159, 39, 83, 127, 171, 23, 67, 111, 155, 11, 55, 99, 143)(6, 50, 94, 138, 15, 59, 103, 147, 29, 73, 117, 161, 43, 87, 131, 175, 37, 81, 125, 169, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 36, 80, 124, 168, 30, 74, 118, 162, 16, 60, 104, 148) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 72)(16, 71)(17, 57)(18, 56)(19, 77)(20, 55)(21, 54)(22, 81)(23, 80)(24, 76)(25, 75)(26, 78)(27, 60)(28, 59)(29, 86)(30, 83)(31, 69)(32, 68)(33, 63)(34, 70)(35, 85)(36, 67)(37, 66)(38, 87)(39, 74)(40, 88)(41, 79)(42, 73)(43, 82)(44, 84)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 158)(103, 140)(104, 139)(105, 162)(106, 161)(107, 141)(108, 167)(109, 166)(110, 145)(111, 144)(112, 171)(113, 170)(114, 146)(115, 172)(116, 165)(117, 150)(118, 149)(119, 168)(120, 175)(121, 160)(122, 153)(123, 152)(124, 163)(125, 176)(126, 157)(127, 156)(128, 159)(129, 174)(130, 173)(131, 164)(132, 169) 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 ) } Outer automorphisms :: reflexible Dual of E20.544 Transitivity :: VT+ Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.552 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, (Y3 * Y1)^2, Y3^-5 * Y1 * Y2 * Y3^-6, 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 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 11, 55, 99, 143, 19, 63, 107, 151, 27, 71, 115, 159, 35, 79, 123, 167, 43, 87, 131, 175, 38, 82, 126, 170, 30, 74, 118, 162, 22, 66, 110, 154, 14, 58, 102, 146, 6, 50, 94, 138, 13, 57, 101, 145, 21, 65, 109, 153, 29, 73, 117, 161, 37, 81, 125, 169, 44, 88, 132, 176, 36, 80, 124, 168, 28, 72, 116, 160, 20, 64, 108, 152, 12, 56, 100, 144, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 15, 59, 103, 147, 23, 67, 111, 155, 31, 75, 119, 163, 39, 83, 127, 171, 42, 86, 130, 174, 34, 78, 122, 166, 26, 70, 114, 158, 18, 62, 106, 150, 10, 54, 98, 142, 3, 47, 91, 135, 9, 53, 97, 141, 17, 61, 105, 149, 25, 69, 113, 157, 33, 77, 121, 165, 41, 85, 129, 173, 40, 84, 128, 172, 32, 76, 120, 164, 24, 68, 112, 156, 16, 60, 104, 148, 8, 52, 96, 140) L = (1, 46)(2, 45)(3, 50)(4, 52)(5, 51)(6, 47)(7, 49)(8, 48)(9, 58)(10, 57)(11, 60)(12, 59)(13, 54)(14, 53)(15, 56)(16, 55)(17, 66)(18, 65)(19, 68)(20, 67)(21, 62)(22, 61)(23, 64)(24, 63)(25, 74)(26, 73)(27, 76)(28, 75)(29, 70)(30, 69)(31, 72)(32, 71)(33, 82)(34, 81)(35, 84)(36, 83)(37, 78)(38, 77)(39, 80)(40, 79)(41, 87)(42, 88)(43, 85)(44, 86)(89, 135)(90, 138)(91, 133)(92, 142)(93, 141)(94, 134)(95, 146)(96, 145)(97, 137)(98, 136)(99, 150)(100, 149)(101, 140)(102, 139)(103, 154)(104, 153)(105, 144)(106, 143)(107, 158)(108, 157)(109, 148)(110, 147)(111, 162)(112, 161)(113, 152)(114, 151)(115, 166)(116, 165)(117, 156)(118, 155)(119, 170)(120, 169)(121, 160)(122, 159)(123, 174)(124, 173)(125, 164)(126, 163)(127, 175)(128, 176)(129, 168)(130, 167)(131, 171)(132, 172) 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 ) } Outer automorphisms :: reflexible Dual of E20.537 Transitivity :: VT+ Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.553 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, Y3^2 * Y2 * Y3^-2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3^22, Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 26, 70, 114, 158, 38, 82, 126, 170, 44, 88, 132, 176, 35, 79, 123, 167, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 30, 74, 118, 162, 16, 60, 104, 148, 6, 50, 94, 138, 15, 59, 103, 147, 29, 73, 117, 161, 40, 84, 128, 172, 42, 86, 130, 174, 33, 77, 121, 165, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 31, 75, 119, 163, 19, 63, 107, 151, 34, 78, 122, 166, 43, 87, 131, 175, 39, 83, 127, 171, 28, 72, 116, 160, 14, 58, 102, 146, 27, 71, 115, 159, 23, 67, 111, 155, 11, 55, 99, 143, 3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 36, 80, 124, 168, 41, 85, 129, 173, 37, 81, 125, 169, 32, 76, 120, 164, 18, 62, 106, 150, 8, 52, 96, 140) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 72)(16, 71)(17, 57)(18, 56)(19, 77)(20, 55)(21, 54)(22, 79)(23, 74)(24, 76)(25, 75)(26, 81)(27, 60)(28, 59)(29, 83)(30, 67)(31, 69)(32, 68)(33, 63)(34, 86)(35, 66)(36, 88)(37, 70)(38, 85)(39, 73)(40, 87)(41, 82)(42, 78)(43, 84)(44, 80)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 158)(103, 140)(104, 139)(105, 162)(106, 161)(107, 141)(108, 163)(109, 166)(110, 145)(111, 144)(112, 159)(113, 168)(114, 146)(115, 156)(116, 170)(117, 150)(118, 149)(119, 152)(120, 172)(121, 173)(122, 153)(123, 175)(124, 157)(125, 174)(126, 160)(127, 176)(128, 164)(129, 165)(130, 169)(131, 167)(132, 171) 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 ) } Outer automorphisms :: reflexible Dual of E20.540 Transitivity :: VT+ Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.554 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^7 * Y1, (Y3 * Y1 * Y2)^11 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 36, 80, 124, 168, 33, 77, 121, 165, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 32, 76, 120, 164, 42, 86, 130, 174, 44, 88, 132, 176, 39, 83, 127, 171, 28, 72, 116, 160, 16, 60, 104, 148, 6, 50, 94, 138, 15, 59, 103, 147, 27, 71, 115, 159, 37, 81, 125, 169, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 29, 73, 117, 161, 40, 84, 128, 172, 38, 82, 126, 170, 26, 70, 114, 158, 14, 58, 102, 146, 19, 63, 107, 151, 31, 75, 119, 163, 41, 85, 129, 173, 43, 87, 131, 175, 35, 79, 123, 167, 23, 67, 111, 155, 11, 55, 99, 143, 3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 34, 78, 122, 166, 30, 74, 118, 162, 18, 62, 106, 150, 8, 52, 96, 140) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 70)(16, 63)(17, 57)(18, 56)(19, 60)(20, 55)(21, 54)(22, 77)(23, 76)(24, 74)(25, 73)(26, 59)(27, 82)(28, 75)(29, 69)(30, 68)(31, 72)(32, 67)(33, 66)(34, 80)(35, 86)(36, 78)(37, 84)(38, 71)(39, 85)(40, 81)(41, 83)(42, 79)(43, 88)(44, 87)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 152)(103, 140)(104, 139)(105, 160)(106, 159)(107, 141)(108, 146)(109, 163)(110, 145)(111, 144)(112, 167)(113, 166)(114, 164)(115, 150)(116, 149)(117, 171)(118, 169)(119, 153)(120, 158)(121, 173)(122, 157)(123, 156)(124, 175)(125, 162)(126, 174)(127, 161)(128, 176)(129, 165)(130, 170)(131, 168)(132, 172) 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 ) } Outer automorphisms :: reflexible Dual of E20.541 Transitivity :: VT+ Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.555 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y2 * Y3^5 * Y1, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y2 * Y1 * Y3^3 * Y2 * Y1 * Y3^3 * Y2 * Y1 * Y3 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 24, 68, 112, 156, 21, 65, 109, 153, 9, 53, 97, 141, 20, 64, 108, 152, 34, 78, 122, 166, 42, 86, 130, 174, 41, 85, 129, 173, 31, 75, 119, 163, 38, 82, 126, 170, 26, 70, 114, 158, 37, 81, 125, 169, 40, 84, 128, 172, 29, 73, 117, 161, 16, 60, 104, 148, 6, 50, 94, 138, 15, 59, 103, 147, 25, 69, 113, 157, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 17, 61, 105, 149, 30, 74, 118, 162, 28, 72, 116, 160, 14, 58, 102, 146, 27, 71, 115, 159, 39, 83, 127, 171, 44, 88, 132, 176, 43, 87, 131, 175, 36, 80, 124, 168, 33, 77, 121, 165, 19, 63, 107, 151, 32, 76, 120, 164, 35, 79, 123, 167, 23, 67, 111, 155, 11, 55, 99, 143, 3, 47, 91, 135, 10, 54, 98, 142, 22, 66, 110, 154, 18, 62, 106, 150, 8, 52, 96, 140) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 65)(11, 64)(12, 62)(13, 61)(14, 50)(15, 72)(16, 71)(17, 57)(18, 56)(19, 75)(20, 55)(21, 54)(22, 68)(23, 78)(24, 66)(25, 74)(26, 80)(27, 60)(28, 59)(29, 83)(30, 69)(31, 63)(32, 85)(33, 82)(34, 67)(35, 86)(36, 70)(37, 87)(38, 77)(39, 73)(40, 88)(41, 76)(42, 79)(43, 81)(44, 84)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 148)(96, 147)(97, 151)(98, 137)(99, 136)(100, 155)(101, 154)(102, 158)(103, 140)(104, 139)(105, 161)(106, 157)(107, 141)(108, 165)(109, 164)(110, 145)(111, 144)(112, 167)(113, 150)(114, 146)(115, 170)(116, 169)(117, 149)(118, 172)(119, 171)(120, 153)(121, 152)(122, 168)(123, 156)(124, 166)(125, 160)(126, 159)(127, 163)(128, 162)(129, 176)(130, 175)(131, 174)(132, 173) 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 ) } Outer automorphisms :: reflexible Dual of E20.538 Transitivity :: VT+ Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.556 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 11, 22}) Quotient :: loop^2 Aut^+ = D44 (small group id <44, 3>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y3^3 * Y1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 ] Map:: R = (1, 45, 89, 133, 4, 48, 92, 136, 12, 56, 100, 144, 9, 53, 97, 141, 18, 62, 106, 150, 25, 69, 113, 157, 23, 67, 111, 155, 30, 74, 118, 162, 37, 81, 125, 169, 35, 79, 123, 167, 42, 86, 130, 174, 44, 88, 132, 176, 39, 83, 127, 171, 32, 76, 120, 164, 34, 78, 122, 166, 27, 71, 115, 159, 20, 64, 108, 152, 22, 66, 110, 154, 15, 59, 103, 147, 6, 50, 94, 138, 13, 57, 101, 145, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 16, 60, 104, 148, 14, 58, 102, 146, 21, 65, 109, 153, 28, 72, 116, 160, 26, 70, 114, 158, 33, 77, 121, 165, 40, 84, 128, 172, 38, 82, 126, 170, 41, 85, 129, 173, 43, 87, 131, 175, 36, 80, 124, 168, 29, 73, 117, 161, 31, 75, 119, 163, 24, 68, 112, 156, 17, 61, 105, 149, 19, 63, 107, 151, 11, 55, 99, 143, 3, 47, 91, 135, 10, 54, 98, 142, 8, 52, 96, 140) L = (1, 46)(2, 45)(3, 53)(4, 52)(5, 51)(6, 58)(7, 49)(8, 48)(9, 47)(10, 56)(11, 62)(12, 54)(13, 60)(14, 50)(15, 65)(16, 57)(17, 67)(18, 55)(19, 69)(20, 70)(21, 59)(22, 72)(23, 61)(24, 74)(25, 63)(26, 64)(27, 77)(28, 66)(29, 79)(30, 68)(31, 81)(32, 82)(33, 71)(34, 84)(35, 73)(36, 86)(37, 75)(38, 76)(39, 85)(40, 78)(41, 83)(42, 80)(43, 88)(44, 87)(89, 135)(90, 138)(91, 133)(92, 143)(93, 142)(94, 134)(95, 147)(96, 145)(97, 149)(98, 137)(99, 136)(100, 151)(101, 140)(102, 152)(103, 139)(104, 154)(105, 141)(106, 156)(107, 144)(108, 146)(109, 159)(110, 148)(111, 161)(112, 150)(113, 163)(114, 164)(115, 153)(116, 166)(117, 155)(118, 168)(119, 157)(120, 158)(121, 171)(122, 160)(123, 173)(124, 162)(125, 175)(126, 174)(127, 165)(128, 176)(129, 167)(130, 170)(131, 169)(132, 172) 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 ) } Outer automorphisms :: reflexible Dual of E20.539 Transitivity :: VT+ Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.557 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, (R * Y1)^2, Y2^11 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 6, 50)(4, 48, 7, 51)(5, 49, 8, 52)(9, 53, 13, 57)(10, 54, 14, 58)(11, 55, 15, 59)(12, 56, 16, 60)(17, 61, 21, 65)(18, 62, 22, 66)(19, 63, 23, 67)(20, 64, 24, 68)(25, 69, 29, 73)(26, 70, 30, 74)(27, 71, 31, 75)(28, 72, 32, 76)(33, 77, 37, 81)(34, 78, 38, 82)(35, 79, 39, 83)(36, 80, 40, 84)(41, 85, 43, 87)(42, 86, 44, 88)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137)(90, 134, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 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)(95, 139, 102, 146, 110, 154, 118, 162, 126, 170, 131, 175, 132, 176, 127, 171, 119, 163, 111, 155, 103, 147) L = (1, 92)(2, 95)(3, 98)(4, 89)(5, 99)(6, 102)(7, 90)(8, 103)(9, 106)(10, 91)(11, 93)(12, 107)(13, 110)(14, 94)(15, 96)(16, 111)(17, 114)(18, 97)(19, 100)(20, 115)(21, 118)(22, 101)(23, 104)(24, 119)(25, 122)(26, 105)(27, 108)(28, 123)(29, 126)(30, 109)(31, 112)(32, 127)(33, 129)(34, 113)(35, 116)(36, 130)(37, 131)(38, 117)(39, 120)(40, 132)(41, 121)(42, 124)(43, 125)(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) :: { ( 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 E20.568 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.558 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, Y2^11 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 8, 52)(4, 48, 7, 51)(5, 49, 6, 50)(9, 53, 16, 60)(10, 54, 15, 59)(11, 55, 14, 58)(12, 56, 13, 57)(17, 61, 24, 68)(18, 62, 23, 67)(19, 63, 22, 66)(20, 64, 21, 65)(25, 69, 32, 76)(26, 70, 31, 75)(27, 71, 30, 74)(28, 72, 29, 73)(33, 77, 40, 84)(34, 78, 39, 83)(35, 79, 38, 82)(36, 80, 37, 81)(41, 85, 44, 88)(42, 86, 43, 87)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137)(90, 134, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 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)(95, 139, 102, 146, 110, 154, 118, 162, 126, 170, 131, 175, 132, 176, 127, 171, 119, 163, 111, 155, 103, 147) L = (1, 92)(2, 95)(3, 98)(4, 89)(5, 99)(6, 102)(7, 90)(8, 103)(9, 106)(10, 91)(11, 93)(12, 107)(13, 110)(14, 94)(15, 96)(16, 111)(17, 114)(18, 97)(19, 100)(20, 115)(21, 118)(22, 101)(23, 104)(24, 119)(25, 122)(26, 105)(27, 108)(28, 123)(29, 126)(30, 109)(31, 112)(32, 127)(33, 129)(34, 113)(35, 116)(36, 130)(37, 131)(38, 117)(39, 120)(40, 132)(41, 121)(42, 124)(43, 125)(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) :: { ( 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 E20.569 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.559 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1 * Y2^-1)^2, Y2^-2 * Y3^-2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y1)^2, Y3^-2 * Y2^9, Y3^-2 * Y2^3 * Y3^-6, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 19, 63)(12, 56, 17, 61)(13, 57, 20, 64)(14, 58, 16, 60)(15, 59, 18, 62)(21, 65, 28, 72)(22, 66, 27, 71)(23, 67, 26, 70)(24, 68, 25, 69)(29, 73, 35, 79)(30, 74, 36, 80)(31, 75, 33, 77)(32, 76, 34, 78)(37, 81, 44, 88)(38, 82, 43, 87)(39, 83, 42, 86)(40, 84, 41, 85)(89, 133, 91, 135, 99, 143, 109, 153, 117, 161, 125, 169, 128, 172, 119, 163, 112, 156, 102, 146, 93, 137)(90, 134, 95, 139, 104, 148, 113, 157, 121, 165, 129, 173, 132, 176, 123, 167, 116, 160, 107, 151, 97, 141)(92, 136, 100, 144, 94, 138, 101, 145, 110, 154, 118, 162, 126, 170, 127, 171, 120, 164, 111, 155, 103, 147)(96, 140, 105, 149, 98, 142, 106, 150, 114, 158, 122, 166, 130, 174, 131, 175, 124, 168, 115, 159, 108, 152) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 105)(8, 107)(9, 108)(10, 90)(11, 94)(12, 93)(13, 91)(14, 111)(15, 112)(16, 98)(17, 97)(18, 95)(19, 115)(20, 116)(21, 101)(22, 99)(23, 119)(24, 120)(25, 106)(26, 104)(27, 123)(28, 124)(29, 110)(30, 109)(31, 127)(32, 128)(33, 114)(34, 113)(35, 131)(36, 132)(37, 118)(38, 117)(39, 125)(40, 126)(41, 122)(42, 121)(43, 129)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.577 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.560 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y2)^2, Y3^-4 * Y2, Y2 * Y3 * Y2^2 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 24, 68)(12, 56, 25, 69)(13, 57, 23, 67)(14, 58, 26, 70)(15, 59, 21, 65)(16, 60, 19, 63)(17, 61, 20, 64)(18, 62, 22, 66)(27, 71, 40, 84)(28, 72, 41, 85)(29, 73, 39, 83)(30, 74, 42, 86)(31, 75, 37, 81)(32, 76, 35, 79)(33, 77, 36, 80)(34, 78, 38, 82)(43, 87, 44, 88)(89, 133, 91, 135, 99, 143, 115, 159, 122, 166, 106, 150, 102, 146, 118, 162, 120, 164, 104, 148, 93, 137)(90, 134, 95, 139, 107, 151, 123, 167, 130, 174, 114, 158, 110, 154, 126, 170, 128, 172, 112, 156, 97, 141)(92, 136, 100, 144, 116, 160, 121, 165, 105, 149, 94, 138, 101, 145, 117, 161, 131, 175, 119, 163, 103, 147)(96, 140, 108, 152, 124, 168, 129, 173, 113, 157, 98, 142, 109, 153, 125, 169, 132, 176, 127, 171, 111, 155) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 108)(8, 110)(9, 111)(10, 90)(11, 116)(12, 118)(13, 91)(14, 101)(15, 106)(16, 119)(17, 93)(18, 94)(19, 124)(20, 126)(21, 95)(22, 109)(23, 114)(24, 127)(25, 97)(26, 98)(27, 121)(28, 120)(29, 99)(30, 117)(31, 122)(32, 131)(33, 104)(34, 105)(35, 129)(36, 128)(37, 107)(38, 125)(39, 130)(40, 132)(41, 112)(42, 113)(43, 115)(44, 123)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 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 E20.571 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.561 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2 * Y3^4, Y3^-1 * Y2^4 * Y3^-1 * Y2, Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 24, 68)(12, 56, 25, 69)(13, 57, 23, 67)(14, 58, 26, 70)(15, 59, 21, 65)(16, 60, 19, 63)(17, 61, 20, 64)(18, 62, 22, 66)(27, 71, 41, 85)(28, 72, 42, 86)(29, 73, 40, 84)(30, 74, 39, 83)(31, 75, 38, 82)(32, 76, 37, 81)(33, 77, 35, 79)(34, 78, 36, 80)(43, 87, 44, 88)(89, 133, 91, 135, 99, 143, 115, 159, 119, 163, 102, 146, 106, 150, 118, 162, 121, 165, 104, 148, 93, 137)(90, 134, 95, 139, 107, 151, 123, 167, 127, 171, 110, 154, 114, 158, 126, 170, 129, 173, 112, 156, 97, 141)(92, 136, 100, 144, 116, 160, 131, 175, 122, 166, 105, 149, 94, 138, 101, 145, 117, 161, 120, 164, 103, 147)(96, 140, 108, 152, 124, 168, 132, 176, 130, 174, 113, 157, 98, 142, 109, 153, 125, 169, 128, 172, 111, 155) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 108)(8, 110)(9, 111)(10, 90)(11, 116)(12, 106)(13, 91)(14, 105)(15, 119)(16, 120)(17, 93)(18, 94)(19, 124)(20, 114)(21, 95)(22, 113)(23, 127)(24, 128)(25, 97)(26, 98)(27, 131)(28, 118)(29, 99)(30, 101)(31, 122)(32, 115)(33, 117)(34, 104)(35, 132)(36, 126)(37, 107)(38, 109)(39, 130)(40, 123)(41, 125)(42, 112)(43, 121)(44, 129)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.574 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.562 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2^11, (Y3 * Y2^-1)^22 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 18, 62)(12, 56, 17, 61)(13, 57, 16, 60)(14, 58, 15, 59)(19, 63, 26, 70)(20, 64, 25, 69)(21, 65, 24, 68)(22, 66, 23, 67)(27, 71, 34, 78)(28, 72, 33, 77)(29, 73, 32, 76)(30, 74, 31, 75)(35, 79, 42, 86)(36, 80, 41, 85)(37, 81, 40, 84)(38, 82, 39, 83)(43, 87, 44, 88)(89, 133, 91, 135, 99, 143, 107, 151, 115, 159, 123, 167, 126, 170, 118, 162, 110, 154, 102, 146, 93, 137)(90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 130, 174, 122, 166, 114, 158, 106, 150, 97, 141)(92, 136, 94, 138, 100, 144, 108, 152, 116, 160, 124, 168, 131, 175, 125, 169, 117, 161, 109, 153, 101, 145)(96, 140, 98, 142, 104, 148, 112, 156, 120, 164, 128, 172, 132, 176, 129, 173, 121, 165, 113, 157, 105, 149) L = (1, 92)(2, 96)(3, 94)(4, 93)(5, 101)(6, 89)(7, 98)(8, 97)(9, 105)(10, 90)(11, 100)(12, 91)(13, 102)(14, 109)(15, 104)(16, 95)(17, 106)(18, 113)(19, 108)(20, 99)(21, 110)(22, 117)(23, 112)(24, 103)(25, 114)(26, 121)(27, 116)(28, 107)(29, 118)(30, 125)(31, 120)(32, 111)(33, 122)(34, 129)(35, 124)(36, 115)(37, 126)(38, 131)(39, 128)(40, 119)(41, 130)(42, 132)(43, 123)(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) :: { ( 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 E20.572 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.563 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y2^11 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 17, 61)(12, 56, 18, 62)(13, 57, 15, 59)(14, 58, 16, 60)(19, 63, 25, 69)(20, 64, 26, 70)(21, 65, 23, 67)(22, 66, 24, 68)(27, 71, 33, 77)(28, 72, 34, 78)(29, 73, 31, 75)(30, 74, 32, 76)(35, 79, 41, 85)(36, 80, 42, 86)(37, 81, 39, 83)(38, 82, 40, 84)(43, 87, 44, 88)(89, 133, 91, 135, 99, 143, 107, 151, 115, 159, 123, 167, 125, 169, 117, 161, 109, 153, 101, 145, 93, 137)(90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 129, 173, 121, 165, 113, 157, 105, 149, 97, 141)(92, 136, 100, 144, 108, 152, 116, 160, 124, 168, 131, 175, 126, 170, 118, 162, 110, 154, 102, 146, 94, 138)(96, 140, 104, 148, 112, 156, 120, 164, 128, 172, 132, 176, 130, 174, 122, 166, 114, 158, 106, 150, 98, 142) L = (1, 92)(2, 96)(3, 100)(4, 91)(5, 94)(6, 89)(7, 104)(8, 95)(9, 98)(10, 90)(11, 108)(12, 99)(13, 102)(14, 93)(15, 112)(16, 103)(17, 106)(18, 97)(19, 116)(20, 107)(21, 110)(22, 101)(23, 120)(24, 111)(25, 114)(26, 105)(27, 124)(28, 115)(29, 118)(30, 109)(31, 128)(32, 119)(33, 122)(34, 113)(35, 131)(36, 123)(37, 126)(38, 117)(39, 132)(40, 127)(41, 130)(42, 121)(43, 125)(44, 129)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.570 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.564 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y3^-1 * Y2^3 * Y3^-1, Y2^2 * Y3^6, Y3^-2 * Y2^-1 * Y3^-4 * Y2^-1 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 24, 68)(12, 56, 25, 69)(13, 57, 23, 67)(14, 58, 26, 70)(15, 59, 21, 65)(16, 60, 19, 63)(17, 61, 20, 64)(18, 62, 22, 66)(27, 71, 36, 80)(28, 72, 37, 81)(29, 73, 38, 82)(30, 74, 33, 77)(31, 75, 34, 78)(32, 76, 35, 79)(39, 83, 44, 88)(40, 84, 43, 87)(41, 85, 42, 86)(89, 133, 91, 135, 99, 143, 102, 146, 116, 160, 127, 171, 129, 173, 119, 163, 106, 150, 104, 148, 93, 137)(90, 134, 95, 139, 107, 151, 110, 154, 122, 166, 130, 174, 132, 176, 125, 169, 114, 158, 112, 156, 97, 141)(92, 136, 100, 144, 115, 159, 117, 161, 128, 172, 120, 164, 118, 162, 105, 149, 94, 138, 101, 145, 103, 147)(96, 140, 108, 152, 121, 165, 123, 167, 131, 175, 126, 170, 124, 168, 113, 157, 98, 142, 109, 153, 111, 155) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 108)(8, 110)(9, 111)(10, 90)(11, 115)(12, 116)(13, 91)(14, 117)(15, 99)(16, 101)(17, 93)(18, 94)(19, 121)(20, 122)(21, 95)(22, 123)(23, 107)(24, 109)(25, 97)(26, 98)(27, 127)(28, 128)(29, 129)(30, 104)(31, 105)(32, 106)(33, 130)(34, 131)(35, 132)(36, 112)(37, 113)(38, 114)(39, 120)(40, 119)(41, 118)(42, 126)(43, 125)(44, 124)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.575 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.565 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^2, Y2 * Y3^-1 * Y2 * Y3^-5, Y3^-2 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 24, 68)(12, 56, 25, 69)(13, 57, 23, 67)(14, 58, 26, 70)(15, 59, 21, 65)(16, 60, 19, 63)(17, 61, 20, 64)(18, 62, 22, 66)(27, 71, 37, 81)(28, 72, 36, 80)(29, 73, 38, 82)(30, 74, 34, 78)(31, 75, 33, 77)(32, 76, 35, 79)(39, 83, 44, 88)(40, 84, 43, 87)(41, 85, 42, 86)(89, 133, 91, 135, 99, 143, 106, 150, 116, 160, 127, 171, 129, 173, 118, 162, 102, 146, 104, 148, 93, 137)(90, 134, 95, 139, 107, 151, 114, 158, 122, 166, 130, 174, 132, 176, 124, 168, 110, 154, 112, 156, 97, 141)(92, 136, 100, 144, 105, 149, 94, 138, 101, 145, 115, 159, 120, 164, 128, 172, 117, 161, 119, 163, 103, 147)(96, 140, 108, 152, 113, 157, 98, 142, 109, 153, 121, 165, 126, 170, 131, 175, 123, 167, 125, 169, 111, 155) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 108)(8, 110)(9, 111)(10, 90)(11, 105)(12, 104)(13, 91)(14, 117)(15, 118)(16, 119)(17, 93)(18, 94)(19, 113)(20, 112)(21, 95)(22, 123)(23, 124)(24, 125)(25, 97)(26, 98)(27, 99)(28, 101)(29, 127)(30, 128)(31, 129)(32, 106)(33, 107)(34, 109)(35, 130)(36, 131)(37, 132)(38, 114)(39, 115)(40, 116)(41, 120)(42, 121)(43, 122)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.578 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.566 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^2, Y2^-4 * Y3^-2, Y3^-1 * Y2^2 * Y3^-3 * Y2 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 24, 68)(12, 56, 25, 69)(13, 57, 23, 67)(14, 58, 26, 70)(15, 59, 21, 65)(16, 60, 19, 63)(17, 61, 20, 64)(18, 62, 22, 66)(27, 71, 39, 83)(28, 72, 37, 81)(29, 73, 43, 87)(30, 74, 36, 80)(31, 75, 42, 86)(32, 76, 44, 88)(33, 77, 40, 84)(34, 78, 38, 82)(35, 79, 41, 85)(89, 133, 91, 135, 99, 143, 115, 159, 106, 150, 119, 163, 121, 165, 102, 146, 118, 162, 104, 148, 93, 137)(90, 134, 95, 139, 107, 151, 124, 168, 114, 158, 128, 172, 130, 174, 110, 154, 127, 171, 112, 156, 97, 141)(92, 136, 100, 144, 116, 160, 105, 149, 94, 138, 101, 145, 117, 161, 120, 164, 123, 167, 122, 166, 103, 147)(96, 140, 108, 152, 125, 169, 113, 157, 98, 142, 109, 153, 126, 170, 129, 173, 132, 176, 131, 175, 111, 155) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 108)(8, 110)(9, 111)(10, 90)(11, 116)(12, 118)(13, 91)(14, 120)(15, 121)(16, 122)(17, 93)(18, 94)(19, 125)(20, 127)(21, 95)(22, 129)(23, 130)(24, 131)(25, 97)(26, 98)(27, 105)(28, 104)(29, 99)(30, 123)(31, 101)(32, 115)(33, 117)(34, 119)(35, 106)(36, 113)(37, 112)(38, 107)(39, 132)(40, 109)(41, 124)(42, 126)(43, 128)(44, 114)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.576 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.567 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y2)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^-4 * Y3^2, Y2^3 * Y3^4 ] Map:: non-degenerate R = (1, 45, 2, 46)(3, 47, 9, 53)(4, 48, 10, 54)(5, 49, 7, 51)(6, 50, 8, 52)(11, 55, 24, 68)(12, 56, 25, 69)(13, 57, 23, 67)(14, 58, 26, 70)(15, 59, 21, 65)(16, 60, 19, 63)(17, 61, 20, 64)(18, 62, 22, 66)(27, 71, 40, 84)(28, 72, 42, 86)(29, 73, 38, 82)(30, 74, 43, 87)(31, 75, 36, 80)(32, 76, 44, 88)(33, 77, 37, 81)(34, 78, 39, 83)(35, 79, 41, 85)(89, 133, 91, 135, 99, 143, 115, 159, 102, 146, 118, 162, 122, 166, 106, 150, 119, 163, 104, 148, 93, 137)(90, 134, 95, 139, 107, 151, 124, 168, 110, 154, 127, 171, 131, 175, 114, 158, 128, 172, 112, 156, 97, 141)(92, 136, 100, 144, 116, 160, 123, 167, 120, 164, 121, 165, 105, 149, 94, 138, 101, 145, 117, 161, 103, 147)(96, 140, 108, 152, 125, 169, 132, 176, 129, 173, 130, 174, 113, 157, 98, 142, 109, 153, 126, 170, 111, 155) L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 108)(8, 110)(9, 111)(10, 90)(11, 116)(12, 118)(13, 91)(14, 120)(15, 115)(16, 117)(17, 93)(18, 94)(19, 125)(20, 127)(21, 95)(22, 129)(23, 124)(24, 126)(25, 97)(26, 98)(27, 123)(28, 122)(29, 99)(30, 121)(31, 101)(32, 119)(33, 104)(34, 105)(35, 106)(36, 132)(37, 131)(38, 107)(39, 130)(40, 109)(41, 128)(42, 112)(43, 113)(44, 114)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.573 Graph:: simple bipartite v = 26 e = 88 f = 24 degree seq :: [ 4^22, 22^4 ] E20.568 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1 * Y3, Y1^-11 * Y3 ] Map:: non-degenerate R = (1, 45, 2, 46, 6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 35, 79, 27, 71, 19, 63, 11, 55, 4, 48, 8, 52, 15, 59, 23, 67, 31, 75, 39, 83, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49)(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, 34, 78, 26, 70, 18, 62, 10, 54)(89, 133, 91, 135)(90, 134, 95, 139)(92, 136, 97, 141)(93, 137, 98, 142)(94, 138, 102, 146)(96, 140, 104, 148)(99, 143, 105, 149)(100, 144, 106, 150)(101, 145, 110, 154)(103, 147, 112, 156)(107, 151, 113, 157)(108, 152, 114, 158)(109, 153, 118, 162)(111, 155, 120, 164)(115, 159, 121, 165)(116, 160, 122, 166)(117, 161, 126, 170)(119, 163, 128, 172)(123, 167, 129, 173)(124, 168, 130, 174)(125, 169, 131, 175)(127, 171, 132, 176) L = (1, 92)(2, 96)(3, 97)(4, 89)(5, 99)(6, 103)(7, 104)(8, 90)(9, 91)(10, 105)(11, 93)(12, 107)(13, 111)(14, 112)(15, 94)(16, 95)(17, 98)(18, 113)(19, 100)(20, 115)(21, 119)(22, 120)(23, 101)(24, 102)(25, 106)(26, 121)(27, 108)(28, 123)(29, 127)(30, 128)(31, 109)(32, 110)(33, 114)(34, 129)(35, 116)(36, 125)(37, 124)(38, 132)(39, 117)(40, 118)(41, 122)(42, 131)(43, 130)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.557 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.569 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, Y3 * Y1^-11 ] Map:: non-degenerate R = (1, 45, 2, 46, 6, 50, 13, 57, 21, 65, 29, 73, 37, 81, 35, 79, 27, 71, 19, 63, 11, 55, 4, 48, 8, 52, 15, 59, 23, 67, 31, 75, 39, 83, 36, 80, 28, 72, 20, 64, 12, 56, 5, 49)(3, 47, 9, 53, 17, 61, 25, 69, 33, 77, 41, 85, 44, 88, 40, 84, 32, 76, 24, 68, 16, 60, 10, 54, 18, 62, 26, 70, 34, 78, 42, 86, 43, 87, 38, 82, 30, 74, 22, 66, 14, 58, 7, 51)(89, 133, 91, 135)(90, 134, 95, 139)(92, 136, 98, 142)(93, 137, 97, 141)(94, 138, 102, 146)(96, 140, 104, 148)(99, 143, 106, 150)(100, 144, 105, 149)(101, 145, 110, 154)(103, 147, 112, 156)(107, 151, 114, 158)(108, 152, 113, 157)(109, 153, 118, 162)(111, 155, 120, 164)(115, 159, 122, 166)(116, 160, 121, 165)(117, 161, 126, 170)(119, 163, 128, 172)(123, 167, 130, 174)(124, 168, 129, 173)(125, 169, 131, 175)(127, 171, 132, 176) L = (1, 92)(2, 96)(3, 98)(4, 89)(5, 99)(6, 103)(7, 104)(8, 90)(9, 106)(10, 91)(11, 93)(12, 107)(13, 111)(14, 112)(15, 94)(16, 95)(17, 114)(18, 97)(19, 100)(20, 115)(21, 119)(22, 120)(23, 101)(24, 102)(25, 122)(26, 105)(27, 108)(28, 123)(29, 127)(30, 128)(31, 109)(32, 110)(33, 130)(34, 113)(35, 116)(36, 125)(37, 124)(38, 132)(39, 117)(40, 118)(41, 131)(42, 121)(43, 129)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.558 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.570 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^11, Y1^22 ] Map:: non-degenerate R = (1, 45, 2, 46, 5, 49, 9, 53, 13, 57, 17, 61, 21, 65, 25, 69, 29, 73, 33, 77, 37, 81, 41, 85, 40, 84, 36, 80, 32, 76, 28, 72, 24, 68, 20, 64, 16, 60, 12, 56, 8, 52, 4, 48)(3, 47, 7, 51, 11, 55, 15, 59, 19, 63, 23, 67, 27, 71, 31, 75, 35, 79, 39, 83, 43, 87, 44, 88, 42, 86, 38, 82, 34, 78, 30, 74, 26, 70, 22, 66, 18, 62, 14, 58, 10, 54, 6, 50)(89, 133, 91, 135)(90, 134, 94, 138)(92, 136, 95, 139)(93, 137, 98, 142)(96, 140, 99, 143)(97, 141, 102, 146)(100, 144, 103, 147)(101, 145, 106, 150)(104, 148, 107, 151)(105, 149, 110, 154)(108, 152, 111, 155)(109, 153, 114, 158)(112, 156, 115, 159)(113, 157, 118, 162)(116, 160, 119, 163)(117, 161, 122, 166)(120, 164, 123, 167)(121, 165, 126, 170)(124, 168, 127, 171)(125, 169, 130, 174)(128, 172, 131, 175)(129, 173, 132, 176) L = (1, 90)(2, 93)(3, 95)(4, 89)(5, 97)(6, 91)(7, 99)(8, 92)(9, 101)(10, 94)(11, 103)(12, 96)(13, 105)(14, 98)(15, 107)(16, 100)(17, 109)(18, 102)(19, 111)(20, 104)(21, 113)(22, 106)(23, 115)(24, 108)(25, 117)(26, 110)(27, 119)(28, 112)(29, 121)(30, 114)(31, 123)(32, 116)(33, 125)(34, 118)(35, 127)(36, 120)(37, 129)(38, 122)(39, 131)(40, 124)(41, 128)(42, 126)(43, 132)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.563 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.571 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y1^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1 * Y3 * Y2 * Y1^2 * Y3, Y1^-4 * Y3^-1 * Y1^-3, (Y3^-1 * Y1^-1)^11 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 17, 61, 29, 73, 28, 72, 16, 60, 6, 50, 10, 54, 20, 64, 32, 76, 40, 84, 38, 82, 26, 70, 14, 58, 4, 48, 9, 53, 19, 63, 31, 75, 27, 71, 15, 59, 5, 49)(3, 47, 11, 55, 23, 67, 35, 79, 42, 86, 34, 78, 22, 66, 13, 57, 25, 69, 37, 81, 43, 87, 44, 88, 41, 85, 33, 77, 21, 65, 12, 56, 24, 68, 36, 80, 39, 83, 30, 74, 18, 62, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 106, 150)(97, 141, 110, 154)(98, 142, 109, 153)(102, 146, 113, 157)(103, 147, 111, 155)(104, 148, 112, 156)(105, 149, 118, 162)(107, 151, 122, 166)(108, 152, 121, 165)(114, 158, 125, 169)(115, 159, 123, 167)(116, 160, 124, 168)(117, 161, 127, 171)(119, 163, 130, 174)(120, 164, 129, 173)(126, 170, 131, 175)(128, 172, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 98)(5, 102)(6, 89)(7, 107)(8, 109)(9, 108)(10, 90)(11, 112)(12, 113)(13, 91)(14, 94)(15, 114)(16, 93)(17, 119)(18, 121)(19, 120)(20, 95)(21, 101)(22, 96)(23, 124)(24, 125)(25, 99)(26, 104)(27, 126)(28, 103)(29, 115)(30, 129)(31, 128)(32, 105)(33, 110)(34, 106)(35, 127)(36, 131)(37, 111)(38, 116)(39, 132)(40, 117)(41, 122)(42, 118)(43, 123)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.560 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.572 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y1^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (Y3^-1 * Y1 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^-7 * Y3 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 17, 61, 29, 73, 27, 71, 15, 59, 4, 48, 9, 53, 19, 63, 31, 75, 40, 84, 38, 82, 26, 70, 14, 58, 6, 50, 10, 54, 20, 64, 32, 76, 28, 72, 16, 60, 5, 49)(3, 47, 11, 55, 23, 67, 35, 79, 41, 85, 33, 77, 21, 65, 12, 56, 24, 68, 36, 80, 43, 87, 44, 88, 42, 86, 34, 78, 22, 66, 13, 57, 25, 69, 37, 81, 39, 83, 30, 74, 18, 62, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 106, 150)(97, 141, 110, 154)(98, 142, 109, 153)(102, 146, 112, 156)(103, 147, 113, 157)(104, 148, 111, 155)(105, 149, 118, 162)(107, 151, 122, 166)(108, 152, 121, 165)(114, 158, 124, 168)(115, 159, 125, 169)(116, 160, 123, 167)(117, 161, 127, 171)(119, 163, 130, 174)(120, 164, 129, 173)(126, 170, 131, 175)(128, 172, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 103)(6, 89)(7, 107)(8, 109)(9, 94)(10, 90)(11, 112)(12, 110)(13, 91)(14, 93)(15, 114)(16, 115)(17, 119)(18, 121)(19, 98)(20, 95)(21, 122)(22, 96)(23, 124)(24, 101)(25, 99)(26, 104)(27, 126)(28, 117)(29, 128)(30, 129)(31, 108)(32, 105)(33, 130)(34, 106)(35, 131)(36, 113)(37, 111)(38, 116)(39, 123)(40, 120)(41, 132)(42, 118)(43, 125)(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) :: { ( 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 E20.562 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.573 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3, Y1), (Y3 * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^-1 * Y3^-2 * Y1 * Y3^2, Y3^-2 * Y1^-4, Y3^4 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 19, 63, 18, 62, 26, 70, 38, 82, 33, 77, 15, 59, 4, 48, 9, 53, 21, 65, 17, 61, 6, 50, 10, 54, 22, 66, 35, 79, 32, 76, 14, 58, 25, 69, 16, 60, 5, 49)(3, 47, 11, 55, 27, 71, 40, 84, 31, 75, 42, 86, 43, 87, 36, 80, 23, 67, 12, 56, 28, 72, 37, 81, 24, 68, 13, 57, 29, 73, 41, 85, 44, 88, 39, 83, 30, 74, 34, 78, 20, 64, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 108, 152)(97, 141, 112, 156)(98, 142, 111, 155)(102, 146, 119, 163)(103, 147, 117, 161)(104, 148, 115, 159)(105, 149, 116, 160)(106, 150, 118, 162)(107, 151, 122, 166)(109, 153, 125, 169)(110, 154, 124, 168)(113, 157, 128, 172)(114, 158, 127, 171)(120, 164, 130, 174)(121, 165, 129, 173)(123, 167, 131, 175)(126, 170, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 103)(6, 89)(7, 109)(8, 111)(9, 113)(10, 90)(11, 116)(12, 118)(13, 91)(14, 114)(15, 120)(16, 121)(17, 93)(18, 94)(19, 105)(20, 124)(21, 104)(22, 95)(23, 127)(24, 96)(25, 126)(26, 98)(27, 125)(28, 122)(29, 99)(30, 130)(31, 101)(32, 106)(33, 123)(34, 131)(35, 107)(36, 132)(37, 108)(38, 110)(39, 119)(40, 112)(41, 115)(42, 117)(43, 129)(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) :: { ( 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 E20.567 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.574 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |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^-1 * Y3^-5, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^2, Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^2 * Y1^-1 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 19, 63, 14, 58, 25, 69, 38, 82, 33, 77, 17, 61, 6, 50, 10, 54, 22, 66, 15, 59, 4, 48, 9, 53, 21, 65, 35, 79, 32, 76, 18, 62, 26, 70, 16, 60, 5, 49)(3, 47, 11, 55, 27, 71, 39, 83, 30, 74, 42, 86, 43, 87, 37, 81, 24, 68, 13, 57, 29, 73, 36, 80, 23, 67, 12, 56, 28, 72, 41, 85, 44, 88, 40, 84, 31, 75, 34, 78, 20, 64, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 108, 152)(97, 141, 112, 156)(98, 142, 111, 155)(102, 146, 119, 163)(103, 147, 117, 161)(104, 148, 115, 159)(105, 149, 116, 160)(106, 150, 118, 162)(107, 151, 122, 166)(109, 153, 125, 169)(110, 154, 124, 168)(113, 157, 128, 172)(114, 158, 127, 171)(120, 164, 130, 174)(121, 165, 129, 173)(123, 167, 131, 175)(126, 170, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 103)(6, 89)(7, 109)(8, 111)(9, 113)(10, 90)(11, 116)(12, 118)(13, 91)(14, 120)(15, 107)(16, 110)(17, 93)(18, 94)(19, 123)(20, 124)(21, 126)(22, 95)(23, 127)(24, 96)(25, 106)(26, 98)(27, 129)(28, 130)(29, 99)(30, 128)(31, 101)(32, 105)(33, 104)(34, 117)(35, 121)(36, 115)(37, 108)(38, 114)(39, 132)(40, 112)(41, 131)(42, 119)(43, 122)(44, 125)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 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 E20.561 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.575 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-3, (Y3 * Y2)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-6 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 6, 50, 10, 54, 18, 62, 16, 60, 22, 66, 30, 74, 28, 72, 34, 78, 40, 84, 38, 82, 26, 70, 33, 77, 27, 71, 14, 58, 21, 65, 15, 59, 4, 48, 9, 53, 5, 49)(3, 47, 11, 55, 20, 64, 13, 57, 23, 67, 32, 76, 25, 69, 35, 79, 42, 86, 37, 81, 43, 87, 44, 88, 41, 85, 36, 80, 39, 83, 31, 75, 24, 68, 29, 73, 19, 63, 12, 56, 17, 61, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 105, 149)(97, 141, 108, 152)(98, 142, 107, 151)(102, 146, 113, 157)(103, 147, 111, 155)(104, 148, 112, 156)(106, 150, 117, 161)(109, 153, 120, 164)(110, 154, 119, 163)(114, 158, 125, 169)(115, 159, 123, 167)(116, 160, 124, 168)(118, 162, 127, 171)(121, 165, 130, 174)(122, 166, 129, 173)(126, 170, 131, 175)(128, 172, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 103)(6, 89)(7, 93)(8, 107)(9, 109)(10, 90)(11, 105)(12, 112)(13, 91)(14, 114)(15, 115)(16, 94)(17, 117)(18, 95)(19, 119)(20, 96)(21, 121)(22, 98)(23, 99)(24, 124)(25, 101)(26, 122)(27, 126)(28, 104)(29, 127)(30, 106)(31, 129)(32, 108)(33, 128)(34, 110)(35, 111)(36, 131)(37, 113)(38, 116)(39, 132)(40, 118)(41, 125)(42, 120)(43, 123)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.564 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.576 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^6, (Y1^-1 * Y3^-1)^11 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 4, 48, 9, 53, 18, 62, 14, 58, 21, 65, 30, 74, 26, 70, 33, 77, 40, 84, 38, 82, 28, 72, 34, 78, 27, 71, 16, 60, 22, 66, 15, 59, 6, 50, 10, 54, 5, 49)(3, 47, 11, 55, 19, 63, 12, 56, 23, 67, 31, 75, 24, 68, 35, 79, 41, 85, 36, 80, 43, 87, 44, 88, 42, 86, 37, 81, 39, 83, 32, 76, 25, 69, 29, 73, 20, 64, 13, 57, 17, 61, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 105, 149)(97, 141, 108, 152)(98, 142, 107, 151)(102, 146, 113, 157)(103, 147, 111, 155)(104, 148, 112, 156)(106, 150, 117, 161)(109, 153, 120, 164)(110, 154, 119, 163)(114, 158, 125, 169)(115, 159, 123, 167)(116, 160, 124, 168)(118, 162, 127, 171)(121, 165, 130, 174)(122, 166, 129, 173)(126, 170, 131, 175)(128, 172, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 95)(6, 89)(7, 106)(8, 107)(9, 109)(10, 90)(11, 111)(12, 112)(13, 91)(14, 114)(15, 93)(16, 94)(17, 99)(18, 118)(19, 119)(20, 96)(21, 121)(22, 98)(23, 123)(24, 124)(25, 101)(26, 126)(27, 103)(28, 104)(29, 105)(30, 128)(31, 129)(32, 108)(33, 116)(34, 110)(35, 131)(36, 130)(37, 113)(38, 115)(39, 117)(40, 122)(41, 132)(42, 120)(43, 125)(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) :: { ( 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 E20.566 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.577 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), (Y3 * Y2)^2, (R * Y3)^2, (Y1, Y3^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-3 * Y1^-1 * Y3^-1, Y1^-1 * Y3 * Y1^-4, (Y2 * Y3^-1 * Y1)^2 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 19, 63, 15, 59, 4, 48, 9, 53, 21, 65, 35, 79, 33, 77, 14, 58, 25, 69, 18, 62, 26, 70, 38, 82, 32, 76, 17, 61, 6, 50, 10, 54, 22, 66, 16, 60, 5, 49)(3, 47, 11, 55, 27, 71, 36, 80, 23, 67, 12, 56, 28, 72, 41, 85, 44, 88, 39, 83, 30, 74, 40, 84, 31, 75, 42, 86, 43, 87, 37, 81, 24, 68, 13, 57, 29, 73, 34, 78, 20, 64, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 108, 152)(97, 141, 112, 156)(98, 142, 111, 155)(102, 146, 119, 163)(103, 147, 117, 161)(104, 148, 115, 159)(105, 149, 116, 160)(106, 150, 118, 162)(107, 151, 122, 166)(109, 153, 125, 169)(110, 154, 124, 168)(113, 157, 128, 172)(114, 158, 127, 171)(120, 164, 129, 173)(121, 165, 130, 174)(123, 167, 131, 175)(126, 170, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 103)(6, 89)(7, 109)(8, 111)(9, 113)(10, 90)(11, 116)(12, 118)(13, 91)(14, 120)(15, 121)(16, 107)(17, 93)(18, 94)(19, 123)(20, 124)(21, 106)(22, 95)(23, 127)(24, 96)(25, 105)(26, 98)(27, 129)(28, 128)(29, 99)(30, 125)(31, 101)(32, 104)(33, 126)(34, 115)(35, 114)(36, 132)(37, 108)(38, 110)(39, 131)(40, 112)(41, 119)(42, 117)(43, 122)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4, 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 E20.559 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.578 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 11, 22}) Quotient :: dipole Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^4 * Y1^-1, Y1^-2 * Y3^-1 * Y1^-3, (Y2 * Y3 * Y1)^2, Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-2 ] Map:: non-degenerate R = (1, 45, 2, 46, 7, 51, 19, 63, 17, 61, 6, 50, 10, 54, 22, 66, 35, 79, 33, 77, 18, 62, 26, 70, 14, 58, 25, 69, 38, 82, 32, 76, 15, 59, 4, 48, 9, 53, 21, 65, 16, 60, 5, 49)(3, 47, 11, 55, 27, 71, 37, 81, 24, 68, 13, 57, 29, 73, 41, 85, 44, 88, 40, 84, 31, 75, 39, 83, 30, 74, 42, 86, 43, 87, 36, 80, 23, 67, 12, 56, 28, 72, 34, 78, 20, 64, 8, 52)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 101, 145)(93, 137, 99, 143)(94, 138, 100, 144)(95, 139, 108, 152)(97, 141, 112, 156)(98, 142, 111, 155)(102, 146, 119, 163)(103, 147, 117, 161)(104, 148, 115, 159)(105, 149, 116, 160)(106, 150, 118, 162)(107, 151, 122, 166)(109, 153, 125, 169)(110, 154, 124, 168)(113, 157, 128, 172)(114, 158, 127, 171)(120, 164, 129, 173)(121, 165, 130, 174)(123, 167, 131, 175)(126, 170, 132, 176) L = (1, 92)(2, 97)(3, 100)(4, 102)(5, 103)(6, 89)(7, 109)(8, 111)(9, 113)(10, 90)(11, 116)(12, 118)(13, 91)(14, 110)(15, 114)(16, 120)(17, 93)(18, 94)(19, 104)(20, 124)(21, 126)(22, 95)(23, 127)(24, 96)(25, 123)(26, 98)(27, 122)(28, 130)(29, 99)(30, 129)(31, 101)(32, 106)(33, 105)(34, 131)(35, 107)(36, 119)(37, 108)(38, 121)(39, 117)(40, 112)(41, 115)(42, 132)(43, 128)(44, 125)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 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 E20.565 Graph:: bipartite v = 24 e = 88 f = 26 degree seq :: [ 4^22, 44^2 ] E20.579 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {22, 22, 22}) Quotient :: edge Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^-5 * T2, T1^2 * T2 * T1 * T2^5 * T1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 42, 30, 16, 6, 15, 29, 41, 36, 23, 11, 21, 26, 39, 38, 25, 13, 5)(2, 7, 17, 31, 43, 35, 22, 28, 14, 27, 40, 37, 24, 12, 4, 10, 20, 34, 44, 32, 18, 8)(45, 46, 50, 58, 70, 64, 53, 61, 73, 84, 82, 88, 77, 87, 80, 68, 57, 62, 74, 66, 55, 48)(47, 51, 59, 71, 83, 78, 63, 75, 85, 81, 69, 76, 86, 79, 67, 56, 49, 52, 60, 72, 65, 54) 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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.586 Transitivity :: ET+ Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.580 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {22, 22, 22}) Quotient :: edge Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-4, T1^3 * T2^-1 * T1 * T2^-5, T2^-2 * T1^2 * T2^3 * T1^-2 * T2^-1, T1^38 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 39, 26, 23, 11, 21, 35, 42, 30, 16, 6, 15, 29, 41, 38, 25, 13, 5)(2, 7, 17, 31, 43, 37, 24, 12, 4, 10, 20, 34, 40, 28, 14, 27, 22, 36, 44, 32, 18, 8)(45, 46, 50, 58, 70, 68, 57, 62, 74, 84, 77, 87, 82, 88, 79, 64, 53, 61, 73, 66, 55, 48)(47, 51, 59, 71, 67, 56, 49, 52, 60, 72, 83, 81, 69, 76, 86, 78, 63, 75, 85, 80, 65, 54) 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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.584 Transitivity :: ET+ Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.581 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {22, 22, 22}) Quotient :: edge Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^4 * T1^2, T2^2 * T1^-10, T2^2 * T1^-10 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 35, 30, 37, 39, 44, 42, 33, 23, 32, 26, 16, 6, 15, 13, 5)(2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 36, 43, 38, 41, 31, 40, 34, 25, 14, 24, 18, 8)(45, 46, 50, 58, 67, 75, 83, 80, 72, 64, 53, 61, 57, 62, 70, 78, 86, 82, 74, 66, 55, 48)(47, 51, 59, 68, 76, 84, 88, 87, 79, 71, 63, 56, 49, 52, 60, 69, 77, 85, 81, 73, 65, 54) 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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.583 Transitivity :: ET+ Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.582 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {22, 22, 22}) Quotient :: edge Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-2 * T1 * T2^-1 * T1 * T2^-1, T1 * T2 * T1^9 * T2, (T1^-1 * T2^-1)^22 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 33, 23, 32, 42, 44, 39, 37, 28, 35, 30, 21, 11, 19, 13, 5)(2, 7, 17, 25, 14, 24, 34, 41, 31, 40, 36, 43, 38, 29, 20, 27, 22, 12, 4, 10, 18, 8)(45, 46, 50, 58, 67, 75, 83, 82, 74, 66, 57, 62, 53, 61, 70, 78, 86, 80, 72, 64, 55, 48)(47, 51, 59, 68, 76, 84, 81, 73, 65, 56, 49, 52, 60, 69, 77, 85, 88, 87, 79, 71, 63, 54) 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) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.585 Transitivity :: ET+ Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.583 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {22, 22, 22}) Quotient :: loop Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, T2^2 * T1^-2, (F * T2)^2, (F * T1)^2, T1^22, (T2^-1 * T1^-1)^22 ] Map:: non-degenerate R = (1, 45, 3, 47, 6, 50, 12, 56, 15, 59, 20, 64, 23, 67, 28, 72, 31, 75, 36, 80, 39, 83, 44, 88, 41, 85, 38, 82, 33, 77, 30, 74, 25, 69, 22, 66, 17, 61, 14, 58, 9, 53, 5, 49)(2, 46, 7, 51, 11, 55, 16, 60, 19, 63, 24, 68, 27, 71, 32, 76, 35, 79, 40, 84, 43, 87, 42, 86, 37, 81, 34, 78, 29, 73, 26, 70, 21, 65, 18, 62, 13, 57, 10, 54, 4, 48, 8, 52) 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, 67)(20, 68)(21, 61)(22, 62)(23, 71)(24, 72)(25, 65)(26, 66)(27, 75)(28, 76)(29, 69)(30, 70)(31, 79)(32, 80)(33, 73)(34, 74)(35, 83)(36, 84)(37, 77)(38, 78)(39, 87)(40, 88)(41, 81)(42, 82)(43, 85)(44, 86) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.581 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.584 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {22, 22, 22}) Quotient :: loop Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^-5 * T2, T1^2 * T2 * T1 * T2^5 * T1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 42, 86, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 41, 85, 36, 80, 23, 67, 11, 55, 21, 65, 26, 70, 39, 83, 38, 82, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 43, 87, 35, 79, 22, 66, 28, 72, 14, 58, 27, 71, 40, 84, 37, 81, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 34, 78, 44, 88, 32, 76, 18, 62, 8, 52) 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, 64)(27, 83)(28, 65)(29, 84)(30, 66)(31, 85)(32, 86)(33, 87)(34, 63)(35, 67)(36, 68)(37, 69)(38, 88)(39, 78)(40, 82)(41, 81)(42, 79)(43, 80)(44, 77) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.580 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.585 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {22, 22, 22}) Quotient :: loop Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-4, T1^3 * T2^-1 * T1 * T2^-5, T2^-2 * T1^2 * T2^3 * T1^-2 * T2^-1, T1^38 * T2^-2 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 39, 83, 26, 70, 23, 67, 11, 55, 21, 65, 35, 79, 42, 86, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 41, 85, 38, 82, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 43, 87, 37, 81, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 34, 78, 40, 84, 28, 72, 14, 58, 27, 71, 22, 66, 36, 80, 44, 88, 32, 76, 18, 62, 8, 52) 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, 68)(27, 67)(28, 83)(29, 66)(30, 84)(31, 85)(32, 86)(33, 87)(34, 63)(35, 64)(36, 65)(37, 69)(38, 88)(39, 81)(40, 77)(41, 80)(42, 78)(43, 82)(44, 79) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.582 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.586 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {22, 22, 22}) Quotient :: loop Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-2 * T1 * T2^-1 * T1 * T2^-1, T1 * T2 * T1^9 * T2, (T1^-1 * T2^-1)^22 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 16, 60, 6, 50, 15, 59, 26, 70, 33, 77, 23, 67, 32, 76, 42, 86, 44, 88, 39, 83, 37, 81, 28, 72, 35, 79, 30, 74, 21, 65, 11, 55, 19, 63, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 25, 69, 14, 58, 24, 68, 34, 78, 41, 85, 31, 75, 40, 84, 36, 80, 43, 87, 38, 82, 29, 73, 20, 64, 27, 71, 22, 66, 12, 56, 4, 48, 10, 54, 18, 62, 8, 52) 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, 67)(15, 68)(16, 69)(17, 70)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 75)(24, 76)(25, 77)(26, 78)(27, 63)(28, 64)(29, 65)(30, 66)(31, 83)(32, 84)(33, 85)(34, 86)(35, 71)(36, 72)(37, 73)(38, 74)(39, 82)(40, 81)(41, 88)(42, 80)(43, 79)(44, 87) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.579 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.587 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y2, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^2 * Y3^-1 * Y2^-2, Y2^-1 * Y3 * Y2^-5 * Y1^-1, Y2^3 * Y3 * Y2 * Y3^5, Y2^-2 * Y3^-3 * Y2^2 * Y1^-3, Y3^-5 * Y1^17, Y2^-1 * Y3 * Y1^-1 * Y2^2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 39, 83, 33, 77, 24, 68, 13, 57, 18, 62, 30, 74, 43, 87, 35, 79, 20, 64, 9, 53, 17, 61, 29, 73, 42, 86, 37, 81, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 40, 84, 38, 82, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 41, 85, 34, 78, 19, 63, 31, 75, 25, 69, 32, 76, 44, 88, 36, 80, 21, 65, 10, 54)(89, 133, 91, 135, 97, 141, 107, 151, 121, 165, 111, 155, 99, 143, 109, 153, 123, 167, 129, 173, 114, 158, 128, 172, 125, 169, 132, 176, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 113, 157, 101, 145, 93, 137)(90, 134, 95, 139, 105, 149, 119, 163, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 122, 166, 127, 171, 126, 170, 110, 154, 124, 168, 131, 175, 116, 160, 102, 146, 115, 159, 130, 174, 120, 164, 106, 150, 96, 140) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 122)(20, 123)(21, 124)(22, 125)(23, 126)(24, 121)(25, 119)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 113)(33, 127)(34, 129)(35, 131)(36, 132)(37, 130)(38, 128)(39, 114)(40, 115)(41, 116)(42, 117)(43, 118)(44, 120)(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, 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 E20.594 Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.588 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2, Y3^-1), (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1), (Y3^-1, Y2), Y3^2 * Y2 * Y3^-2 * Y2^-1, Y2^-2 * Y1 * Y2^-4 * Y3^-1, Y3 * Y2 * Y3^2 * Y2 * Y1^-5, Y2^3 * Y3^-1 * Y2 * Y3^-5, Y2 * Y3^2 * Y2 * Y1^16, (Y2^-1 * Y3)^22 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 39, 83, 33, 77, 20, 64, 9, 53, 17, 61, 29, 73, 42, 86, 37, 81, 24, 68, 13, 57, 18, 62, 30, 74, 43, 87, 35, 79, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 40, 84, 38, 82, 25, 69, 32, 76, 19, 63, 31, 75, 44, 88, 36, 80, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 41, 85, 34, 78, 21, 65, 10, 54)(89, 133, 91, 135, 97, 141, 107, 151, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 132, 176, 123, 167, 129, 173, 114, 158, 128, 172, 125, 169, 111, 155, 99, 143, 109, 153, 121, 165, 113, 157, 101, 145, 93, 137)(90, 134, 95, 139, 105, 149, 119, 163, 131, 175, 116, 160, 102, 146, 115, 159, 130, 174, 124, 168, 110, 154, 122, 166, 127, 171, 126, 170, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 120, 164, 106, 150, 96, 140) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 120)(20, 121)(21, 122)(22, 123)(23, 124)(24, 125)(25, 126)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 113)(33, 127)(34, 129)(35, 131)(36, 132)(37, 130)(38, 128)(39, 114)(40, 115)(41, 116)(42, 117)(43, 118)(44, 119)(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, 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 E20.592 Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.589 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-3, Y3^3 * Y2^2 * Y1^-1, Y3 * Y2^-1 * Y1^-1 * Y2^-9, Y2 * Y1^-1 * Y2 * Y1^19, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 9, 53, 17, 61, 24, 68, 31, 75, 27, 71, 33, 77, 40, 84, 44, 88, 43, 87, 37, 81, 30, 74, 34, 78, 28, 72, 21, 65, 13, 57, 18, 62, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 23, 67, 19, 63, 25, 69, 32, 76, 39, 83, 35, 79, 41, 85, 38, 82, 42, 86, 36, 80, 29, 73, 22, 66, 26, 70, 20, 64, 12, 56, 5, 49, 8, 52, 16, 60, 10, 54)(89, 133, 91, 135, 97, 141, 107, 151, 115, 159, 123, 167, 131, 175, 124, 168, 116, 160, 108, 152, 99, 143, 104, 148, 94, 138, 103, 147, 112, 156, 120, 164, 128, 172, 126, 170, 118, 162, 110, 154, 101, 145, 93, 137)(90, 134, 95, 139, 105, 149, 113, 157, 121, 165, 129, 173, 125, 169, 117, 161, 109, 153, 100, 144, 92, 136, 98, 142, 102, 146, 111, 155, 119, 163, 127, 171, 132, 176, 130, 174, 122, 166, 114, 158, 106, 150, 96, 140) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 102)(10, 104)(11, 106)(12, 108)(13, 109)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 111)(20, 114)(21, 116)(22, 117)(23, 103)(24, 105)(25, 107)(26, 110)(27, 119)(28, 122)(29, 124)(30, 125)(31, 112)(32, 113)(33, 115)(34, 118)(35, 127)(36, 130)(37, 131)(38, 129)(39, 120)(40, 121)(41, 123)(42, 126)(43, 132)(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, 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 E20.593 Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.590 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), (R * Y2)^2, Y3 * Y2^-2 * Y1^-3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^8 * Y1^-1 * Y2 * Y1^-1 * Y2, Y2^-2 * Y1^18, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^-2 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 13, 57, 18, 62, 24, 68, 31, 75, 30, 74, 34, 78, 40, 84, 44, 88, 43, 87, 36, 80, 27, 71, 33, 77, 29, 73, 20, 64, 9, 53, 17, 61, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 12, 56, 5, 49, 8, 52, 16, 60, 23, 67, 22, 66, 26, 70, 32, 76, 39, 83, 38, 82, 42, 86, 35, 79, 41, 85, 37, 81, 28, 72, 19, 63, 25, 69, 21, 65, 10, 54)(89, 133, 91, 135, 97, 141, 107, 151, 115, 159, 123, 167, 128, 172, 120, 164, 112, 156, 104, 148, 94, 138, 103, 147, 99, 143, 109, 153, 117, 161, 125, 169, 131, 175, 126, 170, 118, 162, 110, 154, 101, 145, 93, 137)(90, 134, 95, 139, 105, 149, 113, 157, 121, 165, 129, 173, 132, 176, 127, 171, 119, 163, 111, 155, 102, 146, 100, 144, 92, 136, 98, 142, 108, 152, 116, 160, 124, 168, 130, 174, 122, 166, 114, 158, 106, 150, 96, 140) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 105)(12, 103)(13, 102)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 116)(20, 117)(21, 113)(22, 111)(23, 104)(24, 106)(25, 107)(26, 110)(27, 124)(28, 125)(29, 121)(30, 119)(31, 112)(32, 114)(33, 115)(34, 118)(35, 130)(36, 131)(37, 129)(38, 127)(39, 120)(40, 122)(41, 123)(42, 126)(43, 132)(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, 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 E20.591 Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.591 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y2^-2, Y3^-2 * Y2^20, (Y3^-1 * Y1^-1)^22, (Y3 * Y2^-1)^22 ] 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, 99, 143, 103, 147, 107, 151, 111, 155, 115, 159, 119, 163, 123, 167, 127, 171, 131, 175, 129, 173, 126, 170, 121, 165, 118, 162, 113, 157, 110, 154, 105, 149, 102, 146, 97, 141, 92, 136)(91, 135, 95, 139, 93, 137, 96, 140, 100, 144, 104, 148, 108, 152, 112, 156, 116, 160, 120, 164, 124, 168, 128, 172, 132, 176, 130, 174, 125, 169, 122, 166, 117, 161, 114, 158, 109, 153, 106, 150, 101, 145, 98, 142) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 93)(7, 92)(8, 90)(9, 101)(10, 102)(11, 96)(12, 94)(13, 105)(14, 106)(15, 100)(16, 99)(17, 109)(18, 110)(19, 104)(20, 103)(21, 113)(22, 114)(23, 108)(24, 107)(25, 117)(26, 118)(27, 112)(28, 111)(29, 121)(30, 122)(31, 116)(32, 115)(33, 125)(34, 126)(35, 120)(36, 119)(37, 129)(38, 130)(39, 124)(40, 123)(41, 132)(42, 131)(43, 128)(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) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.590 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.592 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^2 * Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3 * Y2^-1 * Y3 * Y2^-5, Y2^3 * Y3 * Y2 * Y3^5, Y2^32 * Y3^4, (Y3^-1 * Y1^-1)^22 ] 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, 102, 146, 114, 158, 108, 152, 97, 141, 105, 149, 117, 161, 128, 172, 126, 170, 132, 176, 121, 165, 131, 175, 124, 168, 112, 156, 101, 145, 106, 150, 118, 162, 110, 154, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 115, 159, 127, 171, 122, 166, 107, 151, 119, 163, 129, 173, 125, 169, 113, 157, 120, 164, 130, 174, 123, 167, 111, 155, 100, 144, 93, 137, 96, 140, 104, 148, 116, 160, 109, 153, 98, 142) 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, 114)(22, 116)(23, 99)(24, 100)(25, 101)(26, 127)(27, 128)(28, 102)(29, 129)(30, 104)(31, 131)(32, 106)(33, 130)(34, 132)(35, 110)(36, 111)(37, 112)(38, 113)(39, 126)(40, 125)(41, 124)(42, 118)(43, 123)(44, 120)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.588 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.593 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3^-2 * Y2^-5, Y2^2 * Y3^-1 * Y2 * Y3^-5 * Y2, Y3^-3 * Y2^2 * Y3^3 * Y2^-2, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^22 ] 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, 102, 146, 114, 158, 112, 156, 101, 145, 106, 150, 118, 162, 128, 172, 121, 165, 131, 175, 126, 170, 132, 176, 123, 167, 108, 152, 97, 141, 105, 149, 117, 161, 110, 154, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 115, 159, 111, 155, 100, 144, 93, 137, 96, 140, 104, 148, 116, 160, 127, 171, 125, 169, 113, 157, 120, 164, 130, 174, 122, 166, 107, 151, 119, 163, 129, 173, 124, 168, 109, 153, 98, 142) 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, 111)(27, 110)(28, 102)(29, 129)(30, 104)(31, 131)(32, 106)(33, 127)(34, 128)(35, 130)(36, 132)(37, 112)(38, 113)(39, 114)(40, 116)(41, 126)(42, 118)(43, 125)(44, 120)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.589 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.594 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {22, 22, 22}) Quotient :: dipole Aut^+ = C22 x C2 (small group id <44, 4>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^-1 * Y3^-1 * Y2^-1 * Y3^-3, Y3 * Y2^-1 * Y3 * Y2^-9, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^4, (Y3^-1 * Y1^-1)^22 ] 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, 102, 146, 111, 155, 119, 163, 127, 171, 124, 168, 116, 160, 108, 152, 97, 141, 105, 149, 101, 145, 106, 150, 114, 158, 122, 166, 130, 174, 126, 170, 118, 162, 110, 154, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 112, 156, 120, 164, 128, 172, 132, 176, 131, 175, 123, 167, 115, 159, 107, 151, 100, 144, 93, 137, 96, 140, 104, 148, 113, 157, 121, 165, 129, 173, 125, 169, 117, 161, 109, 153, 98, 142) 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, 112)(15, 101)(16, 94)(17, 100)(18, 96)(19, 99)(20, 115)(21, 116)(22, 117)(23, 120)(24, 106)(25, 102)(26, 104)(27, 110)(28, 123)(29, 124)(30, 125)(31, 128)(32, 114)(33, 111)(34, 113)(35, 118)(36, 131)(37, 127)(38, 129)(39, 132)(40, 122)(41, 119)(42, 121)(43, 126)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.587 Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.595 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-4 * T2^4, T2^2 * T1^2 * T2^-2 * T1^-2, T2^8 * T1^3, T1^11, T2^44, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 3, 9, 19, 26, 38, 43, 34, 22, 32, 18, 8, 2, 7, 17, 31, 37, 44, 35, 23, 11, 21, 30, 16, 6, 15, 29, 40, 41, 36, 24, 12, 4, 10, 20, 28, 14, 27, 39, 42, 33, 25, 13, 5)(45, 46, 50, 58, 70, 81, 85, 77, 66, 55, 48)(47, 51, 59, 71, 82, 88, 80, 69, 76, 65, 54)(49, 52, 60, 72, 63, 75, 84, 86, 78, 67, 56)(53, 61, 73, 83, 87, 79, 68, 57, 62, 74, 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.615 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.596 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, T1^11, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 33, 32, 22, 31, 40, 39, 30, 38, 44, 42, 35, 41, 43, 36, 27, 34, 37, 28, 19, 26, 29, 20, 11, 18, 21, 12, 4, 10, 13, 5)(45, 46, 50, 58, 66, 74, 79, 71, 63, 55, 48)(47, 51, 59, 67, 75, 82, 85, 78, 70, 62, 54)(49, 52, 60, 68, 76, 83, 86, 80, 72, 64, 56)(53, 61, 69, 77, 84, 88, 87, 81, 73, 65, 57) 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.613 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.597 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, (T2, T1), T2^4 * T1, T1^11, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 12, 4, 10, 18, 21, 11, 19, 26, 29, 20, 27, 34, 37, 28, 35, 41, 43, 36, 42, 44, 39, 30, 38, 40, 32, 22, 31, 33, 24, 14, 23, 25, 16, 6, 15, 17, 8, 2, 7, 13, 5)(45, 46, 50, 58, 66, 74, 80, 72, 64, 55, 48)(47, 51, 59, 67, 75, 82, 86, 79, 71, 63, 54)(49, 52, 60, 68, 76, 83, 87, 81, 73, 65, 56)(53, 57, 61, 69, 77, 84, 88, 85, 78, 70, 62) 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.616 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.598 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, (T1, T2^-1), (F * T1)^2, T1^-2 * T2^-4, T1^-11, T1^3 * T2^-1 * T1 * T2^-1 * T1^4 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 35, 30, 37, 43, 40, 31, 39, 34, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 36, 42, 38, 44, 41, 33, 23, 32, 26, 16, 6, 15, 13, 5)(45, 46, 50, 58, 67, 75, 82, 74, 66, 55, 48)(47, 51, 59, 68, 76, 83, 88, 81, 73, 65, 54)(49, 52, 60, 69, 77, 84, 86, 79, 71, 63, 56)(53, 61, 57, 62, 70, 78, 85, 87, 80, 72, 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.611 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.599 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T2^-4 * T1^2, T1^11, T1^11, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 33, 23, 32, 41, 43, 36, 42, 38, 29, 20, 27, 22, 12, 4, 10, 18, 8, 2, 7, 17, 25, 14, 24, 34, 40, 31, 39, 44, 37, 28, 35, 30, 21, 11, 19, 13, 5)(45, 46, 50, 58, 67, 75, 80, 72, 64, 55, 48)(47, 51, 59, 68, 76, 83, 86, 79, 71, 63, 54)(49, 52, 60, 69, 77, 84, 87, 81, 73, 65, 56)(53, 61, 70, 78, 85, 88, 82, 74, 66, 57, 62) 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.614 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.600 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2^3 * T1^4, T2^-8 * T1, T1^-1 * T2 * T1^-2 * T2^3 * T1^-3, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 32, 18, 8, 2, 7, 17, 31, 37, 44, 30, 16, 6, 15, 29, 38, 22, 36, 43, 28, 14, 27, 39, 23, 11, 21, 35, 42, 26, 40, 24, 12, 4, 10, 20, 34, 41, 25, 13, 5)(45, 46, 50, 58, 70, 85, 77, 81, 66, 55, 48)(47, 51, 59, 71, 84, 69, 76, 88, 80, 65, 54)(49, 52, 60, 72, 86, 78, 63, 75, 82, 67, 56)(53, 61, 73, 83, 68, 57, 62, 74, 87, 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.609 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.601 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, (T2^-1, T1), (F * T1)^2, T2^8 * T1, T2^-1 * T1 * T2^-2 * T1^4 * T2^-1, T1^11, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 40, 24, 12, 4, 10, 20, 34, 26, 42, 39, 23, 11, 21, 35, 28, 14, 27, 43, 38, 22, 36, 30, 16, 6, 15, 29, 44, 37, 32, 18, 8, 2, 7, 17, 31, 41, 25, 13, 5)(45, 46, 50, 58, 70, 77, 85, 81, 66, 55, 48)(47, 51, 59, 71, 86, 84, 69, 76, 80, 65, 54)(49, 52, 60, 72, 78, 63, 75, 88, 82, 67, 56)(53, 61, 73, 87, 83, 68, 57, 62, 74, 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.612 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.602 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, T2^-1), T1^-3 * T2^4, T1^11, T1^11, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 36, 44, 38, 41, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 35, 43, 39, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 37, 34, 42, 40, 31, 22, 25, 13, 5)(45, 46, 50, 58, 70, 78, 82, 74, 66, 55, 48)(47, 51, 59, 71, 79, 86, 85, 77, 69, 65, 54)(49, 52, 60, 63, 73, 81, 88, 83, 75, 67, 56)(53, 61, 72, 80, 87, 84, 76, 68, 57, 62, 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.608 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.603 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, T2^-1), T1^3 * T2^4, T1^-11, T1^11, T1^-1 * T2 * T1^-3 * T2^3 * T1^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 32, 39, 42, 34, 37, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 33, 40, 43, 35, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 38, 41, 44, 36, 27, 14, 25, 13, 5)(45, 46, 50, 58, 70, 78, 85, 77, 66, 55, 48)(47, 51, 59, 69, 73, 81, 88, 84, 76, 65, 54)(49, 52, 60, 71, 79, 86, 82, 74, 63, 67, 56)(53, 61, 68, 57, 62, 72, 80, 87, 83, 75, 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) :: { ( 88^11 ), ( 88^44 ) } Outer automorphisms :: reflexible Dual of E20.610 Transitivity :: ET+ Graph:: bipartite v = 5 e = 44 f = 1 degree seq :: [ 11^4, 44 ] E20.604 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^14, (T2^-1 * T1^-1)^11 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 44, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 43, 40, 34, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 36, 42, 41, 35, 29, 23, 17, 11, 5)(45, 46, 50, 47, 51, 56, 53, 57, 62, 59, 63, 68, 65, 69, 74, 71, 75, 80, 77, 81, 86, 83, 87, 85, 88, 84, 79, 82, 78, 73, 76, 72, 67, 70, 66, 61, 64, 60, 55, 58, 54, 49, 52, 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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.620 Transitivity :: ET+ Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.605 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, T2^-1), T2^-1 * T1^-5, T2^-7 * T1^-1 * T2^-2, T2^-4 * T1 * T2^-1 * T1^3 * T2^-3, T2^3 * T1^-1 * T2 * T1^-1 * T2^4 * T1^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 39, 32, 22, 12, 4, 10, 20, 30, 40, 42, 34, 24, 14, 11, 21, 31, 41, 44, 36, 26, 16, 6, 15, 25, 35, 43, 38, 28, 18, 8, 2, 7, 17, 27, 37, 33, 23, 13, 5)(45, 46, 50, 58, 56, 49, 52, 60, 68, 66, 57, 62, 70, 78, 76, 67, 72, 80, 86, 83, 77, 82, 88, 84, 73, 81, 87, 85, 74, 63, 71, 79, 75, 64, 53, 61, 69, 65, 54, 47, 51, 59, 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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.619 Transitivity :: ET+ Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.606 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 44}) Quotient :: edge Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1^-2 * T2 * T1^-5, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-1, T2^3 * T1^-1 * T2 * T1^-1 * T2^2 * T1^4, (T1^-1 * T2^-1)^11 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 23, 11, 21, 35, 42, 44, 39, 28, 14, 27, 38, 32, 18, 8, 2, 7, 17, 31, 24, 12, 4, 10, 20, 34, 41, 36, 22, 26, 37, 43, 40, 30, 16, 6, 15, 29, 25, 13, 5)(45, 46, 50, 58, 70, 65, 54, 47, 51, 59, 71, 81, 79, 64, 53, 61, 73, 82, 87, 86, 78, 63, 75, 69, 76, 84, 88, 85, 77, 68, 57, 62, 74, 83, 80, 67, 56, 49, 52, 60, 72, 66, 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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.618 Transitivity :: ET+ Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.607 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {11, 44, 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, T2^-1), T2^2 * T1^-1 * T2 * T1^-4, T1^-1 * T2^-2 * T1^-2 * T2^-5, T1^-1 * T2^3 * T1^-1 * T2^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 43, 34, 22, 30, 16, 6, 15, 29, 40, 36, 24, 12, 4, 10, 20, 26, 38, 44, 42, 32, 18, 8, 2, 7, 17, 31, 41, 35, 23, 11, 21, 28, 14, 27, 39, 37, 25, 13, 5)(45, 46, 50, 58, 70, 63, 75, 84, 81, 86, 78, 67, 56, 49, 52, 60, 72, 64, 53, 61, 73, 83, 88, 87, 79, 68, 57, 62, 74, 65, 54, 47, 51, 59, 71, 82, 77, 85, 80, 69, 76, 66, 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) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.617 Transitivity :: ET+ Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.608 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-4 * T2^4, T2^2 * T1^2 * T2^-2 * T1^-2, T2^8 * T1^3, T1^11, T2^44, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 26, 70, 38, 82, 43, 87, 34, 78, 22, 66, 32, 76, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 31, 75, 37, 81, 44, 88, 35, 79, 23, 67, 11, 55, 21, 65, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 40, 84, 41, 85, 36, 80, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 28, 72, 14, 58, 27, 71, 39, 83, 42, 86, 33, 77, 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, 82)(28, 63)(29, 83)(30, 64)(31, 84)(32, 65)(33, 66)(34, 67)(35, 68)(36, 69)(37, 85)(38, 88)(39, 87)(40, 86)(41, 77)(42, 78)(43, 79)(44, 80) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.602 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.609 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, T1^11, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 8, 52, 2, 46, 7, 51, 17, 61, 16, 60, 6, 50, 15, 59, 25, 69, 24, 68, 14, 58, 23, 67, 33, 77, 32, 76, 22, 66, 31, 75, 40, 84, 39, 83, 30, 74, 38, 82, 44, 88, 42, 86, 35, 79, 41, 85, 43, 87, 36, 80, 27, 71, 34, 78, 37, 81, 28, 72, 19, 63, 26, 70, 29, 73, 20, 64, 11, 55, 18, 62, 21, 65, 12, 56, 4, 48, 10, 54, 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, 53)(14, 66)(15, 67)(16, 68)(17, 69)(18, 54)(19, 55)(20, 56)(21, 57)(22, 74)(23, 75)(24, 76)(25, 77)(26, 62)(27, 63)(28, 64)(29, 65)(30, 79)(31, 82)(32, 83)(33, 84)(34, 70)(35, 71)(36, 72)(37, 73)(38, 85)(39, 86)(40, 88)(41, 78)(42, 80)(43, 81)(44, 87) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.600 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.610 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, (T2, T1), T2^4 * T1, T1^11, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 12, 56, 4, 48, 10, 54, 18, 62, 21, 65, 11, 55, 19, 63, 26, 70, 29, 73, 20, 64, 27, 71, 34, 78, 37, 81, 28, 72, 35, 79, 41, 85, 43, 87, 36, 80, 42, 86, 44, 88, 39, 83, 30, 74, 38, 82, 40, 84, 32, 76, 22, 66, 31, 75, 33, 77, 24, 68, 14, 58, 23, 67, 25, 69, 16, 60, 6, 50, 15, 59, 17, 61, 8, 52, 2, 46, 7, 51, 13, 57, 5, 49) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 58)(7, 59)(8, 60)(9, 57)(10, 47)(11, 48)(12, 49)(13, 61)(14, 66)(15, 67)(16, 68)(17, 69)(18, 53)(19, 54)(20, 55)(21, 56)(22, 74)(23, 75)(24, 76)(25, 77)(26, 62)(27, 63)(28, 64)(29, 65)(30, 80)(31, 82)(32, 83)(33, 84)(34, 70)(35, 71)(36, 72)(37, 73)(38, 86)(39, 87)(40, 88)(41, 78)(42, 79)(43, 81)(44, 85) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.603 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.611 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, (T1, T2^-1), (F * T1)^2, T1^-2 * T2^-4, T1^-11, T1^3 * T2^-1 * T1 * T2^-1 * T1^4 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 11, 55, 21, 65, 28, 72, 35, 79, 30, 74, 37, 81, 43, 87, 40, 84, 31, 75, 39, 83, 34, 78, 25, 69, 14, 58, 24, 68, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 12, 56, 4, 48, 10, 54, 20, 64, 27, 71, 22, 66, 29, 73, 36, 80, 42, 86, 38, 82, 44, 88, 41, 85, 33, 77, 23, 67, 32, 76, 26, 70, 16, 60, 6, 50, 15, 59, 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, 67)(15, 68)(16, 69)(17, 57)(18, 70)(19, 56)(20, 53)(21, 54)(22, 55)(23, 75)(24, 76)(25, 77)(26, 78)(27, 63)(28, 64)(29, 65)(30, 66)(31, 82)(32, 83)(33, 84)(34, 85)(35, 71)(36, 72)(37, 73)(38, 74)(39, 88)(40, 86)(41, 87)(42, 79)(43, 80)(44, 81) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.598 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.612 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T2^-4 * T1^2, T1^11, T1^11, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 16, 60, 6, 50, 15, 59, 26, 70, 33, 77, 23, 67, 32, 76, 41, 85, 43, 87, 36, 80, 42, 86, 38, 82, 29, 73, 20, 64, 27, 71, 22, 66, 12, 56, 4, 48, 10, 54, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 25, 69, 14, 58, 24, 68, 34, 78, 40, 84, 31, 75, 39, 83, 44, 88, 37, 81, 28, 72, 35, 79, 30, 74, 21, 65, 11, 55, 19, 63, 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, 67)(15, 68)(16, 69)(17, 70)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 75)(24, 76)(25, 77)(26, 78)(27, 63)(28, 64)(29, 65)(30, 66)(31, 80)(32, 83)(33, 84)(34, 85)(35, 71)(36, 72)(37, 73)(38, 74)(39, 86)(40, 87)(41, 88)(42, 79)(43, 81)(44, 82) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.601 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.613 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2^3 * T1^4, T2^-8 * T1, T1^-1 * T2 * T1^-2 * T2^3 * T1^-3, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 32, 76, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 31, 75, 37, 81, 44, 88, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 38, 82, 22, 66, 36, 80, 43, 87, 28, 72, 14, 58, 27, 71, 39, 83, 23, 67, 11, 55, 21, 65, 35, 79, 42, 86, 26, 70, 40, 84, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 34, 78, 41, 85, 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, 85)(27, 84)(28, 86)(29, 83)(30, 87)(31, 82)(32, 88)(33, 81)(34, 63)(35, 64)(36, 65)(37, 66)(38, 67)(39, 68)(40, 69)(41, 77)(42, 78)(43, 79)(44, 80) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.596 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.614 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, (T2^-1, T1), (F * T1)^2, T2^8 * T1, T2^-1 * T1 * T2^-2 * T1^4 * T2^-1, T1^11, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 40, 84, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 34, 78, 26, 70, 42, 86, 39, 83, 23, 67, 11, 55, 21, 65, 35, 79, 28, 72, 14, 58, 27, 71, 43, 87, 38, 82, 22, 66, 36, 80, 30, 74, 16, 60, 6, 50, 15, 59, 29, 73, 44, 88, 37, 81, 32, 76, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 31, 75, 41, 85, 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, 77)(27, 86)(28, 78)(29, 87)(30, 79)(31, 88)(32, 80)(33, 85)(34, 63)(35, 64)(36, 65)(37, 66)(38, 67)(39, 68)(40, 69)(41, 81)(42, 84)(43, 83)(44, 82) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.599 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.615 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, T2^-1), T1^-3 * T2^4, T1^11, T1^11, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 14, 58, 27, 71, 36, 80, 44, 88, 38, 82, 41, 85, 32, 76, 23, 67, 11, 55, 21, 65, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 29, 73, 26, 70, 35, 79, 43, 87, 39, 83, 30, 74, 33, 77, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 16, 60, 6, 50, 15, 59, 28, 72, 37, 81, 34, 78, 42, 86, 40, 84, 31, 75, 22, 66, 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, 63)(17, 72)(18, 64)(19, 73)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 65)(26, 78)(27, 79)(28, 80)(29, 81)(30, 66)(31, 67)(32, 68)(33, 69)(34, 82)(35, 86)(36, 87)(37, 88)(38, 74)(39, 75)(40, 76)(41, 77)(42, 85)(43, 84)(44, 83) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.595 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.616 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, T2^-1), T1^3 * T2^4, T1^-11, T1^11, T1^-1 * T2 * T1^-3 * T2^3 * T1^-4 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 22, 66, 32, 76, 39, 83, 42, 86, 34, 78, 37, 81, 28, 72, 16, 60, 6, 50, 15, 59, 24, 68, 12, 56, 4, 48, 10, 54, 20, 64, 30, 74, 33, 77, 40, 84, 43, 87, 35, 79, 26, 70, 29, 73, 18, 62, 8, 52, 2, 46, 7, 51, 17, 61, 23, 67, 11, 55, 21, 65, 31, 75, 38, 82, 41, 85, 44, 88, 36, 80, 27, 71, 14, 58, 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, 69)(16, 71)(17, 68)(18, 72)(19, 67)(20, 53)(21, 54)(22, 55)(23, 56)(24, 57)(25, 73)(26, 78)(27, 79)(28, 80)(29, 81)(30, 63)(31, 64)(32, 65)(33, 66)(34, 85)(35, 86)(36, 87)(37, 88)(38, 74)(39, 75)(40, 76)(41, 77)(42, 82)(43, 83)(44, 84) local type(s) :: { ( 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44, 11, 44 ) } Outer automorphisms :: reflexible Dual of E20.597 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 44 f = 5 degree seq :: [ 88 ] E20.617 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^-4 * T1^4, T1^8 * T2^3, T1^4 * T2 * T1 * T2^2 * T1^3, T2^11, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-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 * T2^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 26, 70, 38, 82, 42, 86, 33, 77, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 37, 81, 43, 87, 34, 78, 22, 66, 32, 76, 18, 62, 8, 52)(4, 48, 10, 54, 20, 64, 28, 72, 14, 58, 27, 71, 39, 83, 41, 85, 36, 80, 24, 68, 12, 56)(6, 50, 15, 59, 29, 73, 40, 84, 44, 88, 35, 79, 23, 67, 11, 55, 21, 65, 30, 74, 16, 60) 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, 82)(28, 63)(29, 83)(30, 64)(31, 84)(32, 65)(33, 66)(34, 67)(35, 68)(36, 69)(37, 88)(38, 87)(39, 86)(40, 85)(41, 77)(42, 78)(43, 79)(44, 80) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.607 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.618 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 44}) Quotient :: loop Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-4 * T2^2, T2^11, T2^11, T2 * T1 * T2^3 * T1 * T2^5 * T1^2, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 27, 71, 35, 79, 38, 82, 30, 74, 22, 66, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 25, 69, 33, 77, 41, 85, 42, 86, 34, 78, 26, 70, 18, 62, 8, 52)(4, 48, 10, 54, 14, 58, 23, 67, 31, 75, 39, 83, 44, 88, 37, 81, 29, 73, 21, 65, 12, 56)(6, 50, 15, 59, 24, 68, 32, 76, 40, 84, 43, 87, 36, 80, 28, 72, 20, 64, 11, 55, 16, 60) 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, 53)(15, 67)(16, 54)(17, 68)(18, 55)(19, 69)(20, 56)(21, 57)(22, 70)(23, 63)(24, 75)(25, 76)(26, 64)(27, 77)(28, 65)(29, 66)(30, 78)(31, 71)(32, 83)(33, 84)(34, 72)(35, 85)(36, 73)(37, 74)(38, 86)(39, 79)(40, 88)(41, 87)(42, 80)(43, 81)(44, 82) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.606 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.619 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, T2^-1), T2 * T1 * T2^4 * T1^3, T1^2 * T2^-1 * T1^6, T2^2 * T1^-1 * T2 * T1^-1 * T2^3 * T1^-2, (T1^-1 * T2^-1)^44 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 19, 63, 33, 77, 37, 81, 26, 70, 41, 85, 25, 69, 13, 57, 5, 49)(2, 46, 7, 51, 17, 61, 31, 75, 38, 82, 22, 66, 36, 80, 44, 88, 32, 76, 18, 62, 8, 52)(4, 48, 10, 54, 20, 64, 34, 78, 42, 86, 28, 72, 14, 58, 27, 71, 40, 84, 24, 68, 12, 56)(6, 50, 15, 59, 29, 73, 39, 83, 23, 67, 11, 55, 21, 65, 35, 79, 43, 87, 30, 74, 16, 60) 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, 80)(27, 85)(28, 81)(29, 84)(30, 86)(31, 83)(32, 87)(33, 82)(34, 63)(35, 64)(36, 65)(37, 66)(38, 67)(39, 68)(40, 69)(41, 88)(42, 77)(43, 78)(44, 79) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.605 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.620 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {11, 44, 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, (T2, T1^-1), T2 * T1^4, T2^11, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 9, 53, 17, 61, 25, 69, 33, 77, 37, 81, 29, 73, 21, 65, 13, 57, 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, 43, 87, 36, 80, 28, 72, 20, 64, 12, 56)(6, 50, 11, 55, 19, 63, 27, 71, 35, 79, 42, 86, 44, 88, 38, 82, 30, 74, 22, 66, 14, 58) L = (1, 46)(2, 50)(3, 51)(4, 45)(5, 52)(6, 56)(7, 55)(8, 58)(9, 59)(10, 47)(11, 48)(12, 49)(13, 60)(14, 64)(15, 63)(16, 66)(17, 67)(18, 53)(19, 54)(20, 57)(21, 68)(22, 72)(23, 71)(24, 74)(25, 75)(26, 61)(27, 62)(28, 65)(29, 76)(30, 80)(31, 79)(32, 82)(33, 83)(34, 69)(35, 70)(36, 73)(37, 84)(38, 87)(39, 86)(40, 88)(41, 77)(42, 78)(43, 81)(44, 85) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.604 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.621 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y2 * Y3^2 * Y2^3 * Y1^-1, Y1^4 * Y2 * Y3^-1 * Y2^3 * Y3^-2, Y1^11, Y2^44, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 37, 81, 41, 85, 33, 77, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 38, 82, 44, 88, 36, 80, 25, 69, 32, 76, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 28, 72, 19, 63, 31, 75, 40, 84, 42, 86, 34, 78, 23, 67, 12, 56)(9, 53, 17, 61, 29, 73, 39, 83, 43, 87, 35, 79, 24, 68, 13, 57, 18, 62, 30, 74, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 114, 158, 126, 170, 131, 175, 122, 166, 110, 154, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 125, 169, 132, 176, 123, 167, 111, 155, 99, 143, 109, 153, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 128, 172, 129, 173, 124, 168, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 116, 160, 102, 146, 115, 159, 127, 171, 130, 174, 121, 165, 113, 157, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 116)(20, 118)(21, 120)(22, 121)(23, 122)(24, 123)(25, 124)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 113)(33, 129)(34, 130)(35, 131)(36, 132)(37, 114)(38, 115)(39, 117)(40, 119)(41, 125)(42, 128)(43, 127)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 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, 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, 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, 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 E20.645 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.622 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (Y2, Y1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^-4 * Y1^-2, Y1^-11, Y1^11, Y1^3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-4 * Y2^-2, Y3^22, Y3 * Y1^-3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 23, 67, 31, 75, 38, 82, 30, 74, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 24, 68, 32, 76, 39, 83, 44, 88, 37, 81, 29, 73, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 25, 69, 33, 77, 40, 84, 42, 86, 35, 79, 27, 71, 19, 63, 12, 56)(9, 53, 17, 61, 13, 57, 18, 62, 26, 70, 34, 78, 41, 85, 43, 87, 36, 80, 28, 72, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 99, 143, 109, 153, 116, 160, 123, 167, 118, 162, 125, 169, 131, 175, 128, 172, 119, 163, 127, 171, 122, 166, 113, 157, 102, 146, 112, 156, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 100, 144, 92, 136, 98, 142, 108, 152, 115, 159, 110, 154, 117, 161, 124, 168, 130, 174, 126, 170, 132, 176, 129, 173, 121, 165, 111, 155, 120, 164, 114, 158, 104, 148, 94, 138, 103, 147, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 107)(13, 105)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 115)(20, 116)(21, 117)(22, 118)(23, 102)(24, 103)(25, 104)(26, 106)(27, 123)(28, 124)(29, 125)(30, 126)(31, 111)(32, 112)(33, 113)(34, 114)(35, 130)(36, 131)(37, 132)(38, 119)(39, 120)(40, 121)(41, 122)(42, 128)(43, 129)(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) :: { ( 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, 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, 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, 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 E20.641 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.623 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y2^-4 * Y1^2, Y3^-4 * Y1 * Y3^-6, Y3^-4 * Y1^7, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 14, 58, 23, 67, 31, 75, 36, 80, 28, 72, 20, 64, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 24, 68, 32, 76, 39, 83, 42, 86, 35, 79, 27, 71, 19, 63, 10, 54)(5, 49, 8, 52, 16, 60, 25, 69, 33, 77, 40, 84, 43, 87, 37, 81, 29, 73, 21, 65, 12, 56)(9, 53, 17, 61, 26, 70, 34, 78, 41, 85, 44, 88, 38, 82, 30, 74, 22, 66, 13, 57, 18, 62)(89, 133, 91, 135, 97, 141, 104, 148, 94, 138, 103, 147, 114, 158, 121, 165, 111, 155, 120, 164, 129, 173, 131, 175, 124, 168, 130, 174, 126, 170, 117, 161, 108, 152, 115, 159, 110, 154, 100, 144, 92, 136, 98, 142, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 113, 157, 102, 146, 112, 156, 122, 166, 128, 172, 119, 163, 127, 171, 132, 176, 125, 169, 116, 160, 123, 167, 118, 162, 109, 153, 99, 143, 107, 151, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 106)(10, 107)(11, 108)(12, 109)(13, 110)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 115)(20, 116)(21, 117)(22, 118)(23, 102)(24, 103)(25, 104)(26, 105)(27, 123)(28, 124)(29, 125)(30, 126)(31, 111)(32, 112)(33, 113)(34, 114)(35, 130)(36, 119)(37, 131)(38, 132)(39, 120)(40, 121)(41, 122)(42, 127)(43, 128)(44, 129)(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, 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, 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, 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 E20.644 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.624 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, Y2 * Y1 * Y2^-1 * Y3, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y2^2 * Y1 * Y2 * Y3^-3, Y2^2 * Y1 * Y2^2 * Y3^-4, Y2^-8 * Y1, Y1^3 * Y2 * Y1 * Y2^3 * Y3^-1, Y3 * Y2 * Y3^2 * Y2^3 * Y1^-3, 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 14, 58, 26, 70, 41, 85, 33, 77, 37, 81, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 40, 84, 25, 69, 32, 76, 44, 88, 36, 80, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 28, 72, 42, 86, 34, 78, 19, 63, 31, 75, 38, 82, 23, 67, 12, 56)(9, 53, 17, 61, 29, 73, 39, 83, 24, 68, 13, 57, 18, 62, 30, 74, 43, 87, 35, 79, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 121, 165, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 125, 169, 132, 176, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 126, 170, 110, 154, 124, 168, 131, 175, 116, 160, 102, 146, 115, 159, 127, 171, 111, 155, 99, 143, 109, 153, 123, 167, 130, 174, 114, 158, 128, 172, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 122, 166, 129, 173, 113, 157, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 122)(20, 123)(21, 124)(22, 125)(23, 126)(24, 127)(25, 128)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 113)(33, 129)(34, 130)(35, 131)(36, 132)(37, 121)(38, 119)(39, 117)(40, 115)(41, 114)(42, 116)(43, 118)(44, 120)(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, 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, 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, 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 E20.639 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.625 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y2, Y1^-1), (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-2 * Y1^-1 * Y2^2, Y2^8 * Y1, Y2^-1 * Y3^-1 * Y1^2 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 33, 77, 41, 85, 37, 81, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 42, 86, 40, 84, 25, 69, 32, 76, 36, 80, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 28, 72, 34, 78, 19, 63, 31, 75, 44, 88, 38, 82, 23, 67, 12, 56)(9, 53, 17, 61, 29, 73, 43, 87, 39, 83, 24, 68, 13, 57, 18, 62, 30, 74, 35, 79, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 121, 165, 128, 172, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 122, 166, 114, 158, 130, 174, 127, 171, 111, 155, 99, 143, 109, 153, 123, 167, 116, 160, 102, 146, 115, 159, 131, 175, 126, 170, 110, 154, 124, 168, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 132, 176, 125, 169, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 129, 173, 113, 157, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 122)(20, 123)(21, 124)(22, 125)(23, 126)(24, 127)(25, 128)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 113)(33, 114)(34, 116)(35, 118)(36, 120)(37, 129)(38, 132)(39, 131)(40, 130)(41, 121)(42, 115)(43, 117)(44, 119)(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, 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, 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, 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 E20.642 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.626 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2, Y3^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2)^2, Y2^2 * Y3^-1 * Y2^2, Y1^11, Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2^2 * Y3 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 22, 66, 30, 74, 36, 80, 28, 72, 20, 64, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 23, 67, 31, 75, 38, 82, 42, 86, 35, 79, 27, 71, 19, 63, 10, 54)(5, 49, 8, 52, 16, 60, 24, 68, 32, 76, 39, 83, 43, 87, 37, 81, 29, 73, 21, 65, 12, 56)(9, 53, 13, 57, 17, 61, 25, 69, 33, 77, 40, 84, 44, 88, 41, 85, 34, 78, 26, 70, 18, 62)(89, 133, 91, 135, 97, 141, 100, 144, 92, 136, 98, 142, 106, 150, 109, 153, 99, 143, 107, 151, 114, 158, 117, 161, 108, 152, 115, 159, 122, 166, 125, 169, 116, 160, 123, 167, 129, 173, 131, 175, 124, 168, 130, 174, 132, 176, 127, 171, 118, 162, 126, 170, 128, 172, 120, 164, 110, 154, 119, 163, 121, 165, 112, 156, 102, 146, 111, 155, 113, 157, 104, 148, 94, 138, 103, 147, 105, 149, 96, 140, 90, 134, 95, 139, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 106)(10, 107)(11, 108)(12, 109)(13, 97)(14, 94)(15, 95)(16, 96)(17, 101)(18, 114)(19, 115)(20, 116)(21, 117)(22, 102)(23, 103)(24, 104)(25, 105)(26, 122)(27, 123)(28, 124)(29, 125)(30, 110)(31, 111)(32, 112)(33, 113)(34, 129)(35, 130)(36, 118)(37, 131)(38, 119)(39, 120)(40, 121)(41, 132)(42, 126)(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, 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, 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, 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 E20.646 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.627 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), Y2^-4 * Y1, 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 14, 58, 22, 66, 30, 74, 35, 79, 27, 71, 19, 63, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 23, 67, 31, 75, 38, 82, 41, 85, 34, 78, 26, 70, 18, 62, 10, 54)(5, 49, 8, 52, 16, 60, 24, 68, 32, 76, 39, 83, 42, 86, 36, 80, 28, 72, 20, 64, 12, 56)(9, 53, 17, 61, 25, 69, 33, 77, 40, 84, 44, 88, 43, 87, 37, 81, 29, 73, 21, 65, 13, 57)(89, 133, 91, 135, 97, 141, 96, 140, 90, 134, 95, 139, 105, 149, 104, 148, 94, 138, 103, 147, 113, 157, 112, 156, 102, 146, 111, 155, 121, 165, 120, 164, 110, 154, 119, 163, 128, 172, 127, 171, 118, 162, 126, 170, 132, 176, 130, 174, 123, 167, 129, 173, 131, 175, 124, 168, 115, 159, 122, 166, 125, 169, 116, 160, 107, 151, 114, 158, 117, 161, 108, 152, 99, 143, 106, 150, 109, 153, 100, 144, 92, 136, 98, 142, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 101)(10, 106)(11, 107)(12, 108)(13, 109)(14, 94)(15, 95)(16, 96)(17, 97)(18, 114)(19, 115)(20, 116)(21, 117)(22, 102)(23, 103)(24, 104)(25, 105)(26, 122)(27, 123)(28, 124)(29, 125)(30, 110)(31, 111)(32, 112)(33, 113)(34, 129)(35, 118)(36, 130)(37, 131)(38, 119)(39, 120)(40, 121)(41, 126)(42, 127)(43, 132)(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, 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, 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, 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 E20.643 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.628 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y2^2 * Y1^2 * Y2 * Y3^-1 * Y2, Y2^2 * Y1 * Y2^2 * Y1 * Y3^-1, Y1^11, Y2 * Y3 * Y2 * Y3^2 * Y2^2 * Y1^-5, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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, 45, 2, 46, 6, 50, 14, 58, 26, 70, 34, 78, 41, 85, 33, 77, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 25, 69, 29, 73, 37, 81, 44, 88, 40, 84, 32, 76, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 27, 71, 35, 79, 42, 86, 38, 82, 30, 74, 19, 63, 23, 67, 12, 56)(9, 53, 17, 61, 24, 68, 13, 57, 18, 62, 28, 72, 36, 80, 43, 87, 39, 83, 31, 75, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 110, 154, 120, 164, 127, 171, 130, 174, 122, 166, 125, 169, 116, 160, 104, 148, 94, 138, 103, 147, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 118, 162, 121, 165, 128, 172, 131, 175, 123, 167, 114, 158, 117, 161, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 111, 155, 99, 143, 109, 153, 119, 163, 126, 170, 129, 173, 132, 176, 124, 168, 115, 159, 102, 146, 113, 157, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 118)(20, 119)(21, 120)(22, 121)(23, 107)(24, 105)(25, 103)(26, 102)(27, 104)(28, 106)(29, 113)(30, 126)(31, 127)(32, 128)(33, 129)(34, 114)(35, 115)(36, 116)(37, 117)(38, 130)(39, 131)(40, 132)(41, 122)(42, 123)(43, 124)(44, 125)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 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, 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, 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, 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 E20.640 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.629 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y3 * Y1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1, Y3^11, Y3^4 * Y1^-7, Y2^-44 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 34, 78, 38, 82, 30, 74, 22, 66, 11, 55, 4, 48)(3, 47, 7, 51, 15, 59, 27, 71, 35, 79, 42, 86, 41, 85, 33, 77, 25, 69, 21, 65, 10, 54)(5, 49, 8, 52, 16, 60, 19, 63, 29, 73, 37, 81, 44, 88, 39, 83, 31, 75, 23, 67, 12, 56)(9, 53, 17, 61, 28, 72, 36, 80, 43, 87, 40, 84, 32, 76, 24, 68, 13, 57, 18, 62, 20, 64)(89, 133, 91, 135, 97, 141, 107, 151, 102, 146, 115, 159, 124, 168, 132, 176, 126, 170, 129, 173, 120, 164, 111, 155, 99, 143, 109, 153, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 117, 161, 114, 158, 123, 167, 131, 175, 127, 171, 118, 162, 121, 165, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 104, 148, 94, 138, 103, 147, 116, 160, 125, 169, 122, 166, 130, 174, 128, 172, 119, 163, 110, 154, 113, 157, 101, 145, 93, 137) L = (1, 92)(2, 89)(3, 98)(4, 99)(5, 100)(6, 90)(7, 91)(8, 93)(9, 108)(10, 109)(11, 110)(12, 111)(13, 112)(14, 94)(15, 95)(16, 96)(17, 97)(18, 101)(19, 104)(20, 106)(21, 113)(22, 118)(23, 119)(24, 120)(25, 121)(26, 102)(27, 103)(28, 105)(29, 107)(30, 126)(31, 127)(32, 128)(33, 129)(34, 114)(35, 115)(36, 116)(37, 117)(38, 122)(39, 132)(40, 131)(41, 130)(42, 123)(43, 124)(44, 125)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 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, 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, 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, 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 E20.638 Graph:: bipartite v = 5 e = 88 f = 45 degree seq :: [ 22^4, 88 ] E20.630 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1^14, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 12, 56, 18, 62, 24, 68, 30, 74, 36, 80, 42, 86, 39, 83, 33, 77, 27, 71, 21, 65, 15, 59, 9, 53, 3, 47, 7, 51, 13, 57, 19, 63, 25, 69, 31, 75, 37, 81, 43, 87, 41, 85, 35, 79, 29, 73, 23, 67, 17, 61, 11, 55, 5, 49, 8, 52, 14, 58, 20, 64, 26, 70, 32, 76, 38, 82, 44, 88, 40, 84, 34, 78, 28, 72, 22, 66, 16, 60, 10, 54, 4, 48)(89, 133, 91, 135, 96, 140, 90, 134, 95, 139, 102, 146, 94, 138, 101, 145, 108, 152, 100, 144, 107, 151, 114, 158, 106, 150, 113, 157, 120, 164, 112, 156, 119, 163, 126, 170, 118, 162, 125, 169, 132, 176, 124, 168, 131, 175, 128, 172, 130, 174, 129, 173, 122, 166, 127, 171, 123, 167, 116, 160, 121, 165, 117, 161, 110, 154, 115, 159, 111, 155, 104, 148, 109, 153, 105, 149, 98, 142, 103, 147, 99, 143, 92, 136, 97, 141, 93, 137) L = (1, 91)(2, 95)(3, 96)(4, 97)(5, 89)(6, 101)(7, 102)(8, 90)(9, 93)(10, 103)(11, 92)(12, 107)(13, 108)(14, 94)(15, 99)(16, 109)(17, 98)(18, 113)(19, 114)(20, 100)(21, 105)(22, 115)(23, 104)(24, 119)(25, 120)(26, 106)(27, 111)(28, 121)(29, 110)(30, 125)(31, 126)(32, 112)(33, 117)(34, 127)(35, 116)(36, 131)(37, 132)(38, 118)(39, 123)(40, 130)(41, 122)(42, 129)(43, 128)(44, 124)(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 ) } Outer automorphisms :: reflexible Dual of E20.635 Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.631 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, (Y1, Y2^-1), Y1^-1 * Y2^-2 * Y1 * Y2^2, Y2^-4 * Y1^-1 * Y2^-1, Y2^-3 * Y1^-1 * Y2^-2, Y1^-8 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 24, 68, 34, 78, 33, 77, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 26, 70, 36, 80, 42, 86, 39, 83, 29, 73, 19, 63, 13, 57, 18, 62, 28, 72, 38, 82, 44, 88, 40, 84, 30, 74, 20, 64, 9, 53, 17, 61, 27, 71, 37, 81, 43, 87, 41, 85, 31, 75, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 25, 69, 35, 79, 32, 76, 22, 66, 11, 55, 4, 48)(89, 133, 91, 135, 97, 141, 107, 151, 100, 144, 92, 136, 98, 142, 108, 152, 117, 161, 111, 155, 99, 143, 109, 153, 118, 162, 127, 171, 121, 165, 110, 154, 119, 163, 128, 172, 130, 174, 122, 166, 120, 164, 129, 173, 132, 176, 124, 168, 112, 156, 123, 167, 131, 175, 126, 170, 114, 158, 102, 146, 113, 157, 125, 169, 116, 160, 104, 148, 94, 138, 103, 147, 115, 159, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 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, 113)(15, 115)(16, 94)(17, 101)(18, 96)(19, 100)(20, 117)(21, 118)(22, 119)(23, 99)(24, 123)(25, 125)(26, 102)(27, 106)(28, 104)(29, 111)(30, 127)(31, 128)(32, 129)(33, 110)(34, 120)(35, 131)(36, 112)(37, 116)(38, 114)(39, 121)(40, 130)(41, 132)(42, 122)(43, 126)(44, 124)(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 ) } Outer automorphisms :: reflexible Dual of E20.636 Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.632 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, Y1), Y2^-1 * Y1^-1 * Y2^-1 * Y1^-5, Y2^6 * Y1^-1 * Y2, Y2^-3 * Y1^-2 * Y2^2 * Y1 * Y2 * Y1, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 24, 68, 13, 57, 18, 62, 30, 74, 38, 82, 43, 87, 41, 85, 33, 77, 19, 63, 31, 75, 39, 83, 35, 79, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 27, 71, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 37, 81, 36, 80, 25, 69, 32, 76, 40, 84, 44, 88, 42, 86, 34, 78, 20, 64, 9, 53, 17, 61, 29, 73, 22, 66, 11, 55, 4, 48)(89, 133, 91, 135, 97, 141, 107, 151, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 128, 172, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 127, 171, 132, 176, 126, 170, 116, 160, 102, 146, 115, 159, 110, 154, 123, 167, 130, 174, 131, 175, 125, 169, 114, 158, 111, 155, 99, 143, 109, 153, 122, 166, 129, 173, 124, 168, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 121, 165, 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, 120)(20, 121)(21, 122)(22, 123)(23, 99)(24, 100)(25, 101)(26, 111)(27, 110)(28, 102)(29, 127)(30, 104)(31, 128)(32, 106)(33, 113)(34, 129)(35, 130)(36, 112)(37, 114)(38, 116)(39, 132)(40, 118)(41, 124)(42, 131)(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, 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 E20.637 Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.633 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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), Y1^2 * Y2^-1 * Y1 * Y2^-4, Y2^-2 * Y1^-1 * Y2^-1 * Y1^-6, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 38, 82, 37, 81, 25, 69, 32, 76, 20, 64, 9, 53, 17, 61, 29, 73, 41, 85, 35, 79, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 40, 84, 44, 88, 43, 87, 33, 77, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 27, 71, 39, 83, 36, 80, 24, 68, 13, 57, 18, 62, 30, 74, 19, 63, 31, 75, 42, 86, 34, 78, 22, 66, 11, 55, 4, 48)(89, 133, 91, 135, 97, 141, 107, 151, 116, 160, 102, 146, 115, 159, 129, 173, 122, 166, 131, 175, 125, 169, 112, 156, 100, 144, 92, 136, 98, 142, 108, 152, 118, 162, 104, 148, 94, 138, 103, 147, 117, 161, 130, 174, 132, 176, 126, 170, 124, 168, 111, 155, 99, 143, 109, 153, 120, 164, 106, 150, 96, 140, 90, 134, 95, 139, 105, 149, 119, 163, 128, 172, 114, 158, 127, 171, 123, 167, 110, 154, 121, 165, 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, 116)(20, 118)(21, 120)(22, 121)(23, 99)(24, 100)(25, 101)(26, 127)(27, 129)(28, 102)(29, 130)(30, 104)(31, 128)(32, 106)(33, 113)(34, 131)(35, 110)(36, 111)(37, 112)(38, 124)(39, 123)(40, 114)(41, 122)(42, 132)(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, 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 E20.634 Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.634 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3), (R * Y2)^2, Y2^-4 * Y3^-4, Y3^-8 * Y2^3, Y2^4 * Y3^-1 * Y2^3 * Y3^-3, Y2^11, (Y2^-1 * Y3)^44, (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, 102, 146, 114, 158, 125, 169, 130, 174, 121, 165, 110, 154, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 115, 159, 113, 157, 120, 164, 128, 172, 129, 173, 124, 168, 109, 153, 98, 142)(93, 137, 96, 140, 104, 148, 116, 160, 126, 170, 131, 175, 122, 166, 107, 151, 119, 163, 111, 155, 100, 144)(97, 141, 105, 149, 117, 161, 112, 156, 101, 145, 106, 150, 118, 162, 127, 171, 132, 176, 123, 167, 108, 152) 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) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.633 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.635 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, (Y3, Y2), Y3^-4 * Y2, Y2^11, Y2^-3 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-3 * Y3, (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, 102, 146, 110, 154, 118, 162, 123, 167, 115, 159, 107, 151, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 111, 155, 119, 163, 126, 170, 129, 173, 122, 166, 114, 158, 106, 150, 98, 142)(93, 137, 96, 140, 104, 148, 112, 156, 120, 164, 127, 171, 130, 174, 124, 168, 116, 160, 108, 152, 100, 144)(97, 141, 105, 149, 113, 157, 121, 165, 128, 172, 132, 176, 131, 175, 125, 169, 117, 161, 109, 153, 101, 145) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 103)(7, 105)(8, 90)(9, 96)(10, 101)(11, 106)(12, 92)(13, 93)(14, 111)(15, 113)(16, 94)(17, 104)(18, 109)(19, 114)(20, 99)(21, 100)(22, 119)(23, 121)(24, 102)(25, 112)(26, 117)(27, 122)(28, 107)(29, 108)(30, 126)(31, 128)(32, 110)(33, 120)(34, 125)(35, 129)(36, 115)(37, 116)(38, 132)(39, 118)(40, 127)(41, 131)(42, 123)(43, 124)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.630 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.636 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, (Y3, Y2^-1), Y3^4 * Y2, Y2^11, (Y2^-1 * Y3)^44, (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, 102, 146, 110, 154, 118, 162, 124, 168, 116, 160, 108, 152, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 111, 155, 119, 163, 126, 170, 130, 174, 123, 167, 115, 159, 107, 151, 98, 142)(93, 137, 96, 140, 104, 148, 112, 156, 120, 164, 127, 171, 131, 175, 125, 169, 117, 161, 109, 153, 100, 144)(97, 141, 101, 145, 105, 149, 113, 157, 121, 165, 128, 172, 132, 176, 129, 173, 122, 166, 114, 158, 106, 150) L = (1, 91)(2, 95)(3, 97)(4, 98)(5, 89)(6, 103)(7, 101)(8, 90)(9, 100)(10, 106)(11, 107)(12, 92)(13, 93)(14, 111)(15, 105)(16, 94)(17, 96)(18, 109)(19, 114)(20, 115)(21, 99)(22, 119)(23, 113)(24, 102)(25, 104)(26, 117)(27, 122)(28, 123)(29, 108)(30, 126)(31, 121)(32, 110)(33, 112)(34, 125)(35, 129)(36, 130)(37, 116)(38, 128)(39, 118)(40, 120)(41, 131)(42, 132)(43, 124)(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) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.631 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.637 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, Y3^-1), Y2^-2 * Y3^-4, Y2^-11, Y2^11, Y2^3 * Y3^-1 * Y2 * Y3^-1 * Y2^4 * Y3^-2 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-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, 102, 146, 111, 155, 119, 163, 126, 170, 118, 162, 110, 154, 99, 143, 92, 136)(91, 135, 95, 139, 103, 147, 112, 156, 120, 164, 127, 171, 132, 176, 125, 169, 117, 161, 109, 153, 98, 142)(93, 137, 96, 140, 104, 148, 113, 157, 121, 165, 128, 172, 130, 174, 123, 167, 115, 159, 107, 151, 100, 144)(97, 141, 105, 149, 101, 145, 106, 150, 114, 158, 122, 166, 129, 173, 131, 175, 124, 168, 116, 160, 108, 152) 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, 112)(15, 101)(16, 94)(17, 100)(18, 96)(19, 99)(20, 115)(21, 116)(22, 117)(23, 120)(24, 106)(25, 102)(26, 104)(27, 110)(28, 123)(29, 124)(30, 125)(31, 127)(32, 114)(33, 111)(34, 113)(35, 118)(36, 130)(37, 131)(38, 132)(39, 122)(40, 119)(41, 121)(42, 126)(43, 128)(44, 129)(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) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.632 Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.638 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^3 * Y1^-3 * Y3, Y1^4 * Y3 * Y1 * Y3^2 * Y1^3, (Y3 * Y2^-1)^11, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^4 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 37, 81, 44, 88, 36, 80, 25, 69, 32, 76, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 27, 71, 38, 82, 43, 87, 35, 79, 24, 68, 13, 57, 18, 62, 30, 74, 20, 64, 9, 53, 17, 61, 29, 73, 39, 83, 42, 86, 34, 78, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 19, 63, 31, 75, 40, 84, 41, 85, 33, 77, 22, 66, 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, 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, 114)(20, 116)(21, 118)(22, 120)(23, 99)(24, 100)(25, 101)(26, 126)(27, 127)(28, 102)(29, 128)(30, 104)(31, 125)(32, 106)(33, 113)(34, 110)(35, 111)(36, 112)(37, 131)(38, 130)(39, 129)(40, 132)(41, 124)(42, 121)(43, 122)(44, 123)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.629 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.639 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, (Y1, Y3^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^11, (Y3 * Y2^-1)^11, (Y1^-1 * Y3^-1)^44 ] Map:: R = (1, 45, 2, 46, 6, 50, 10, 54, 3, 47, 7, 51, 14, 58, 18, 62, 9, 53, 15, 59, 22, 66, 26, 70, 17, 61, 23, 67, 30, 74, 34, 78, 25, 69, 31, 75, 38, 82, 41, 85, 33, 77, 39, 83, 44, 88, 43, 87, 37, 81, 40, 84, 42, 86, 36, 80, 29, 73, 32, 76, 35, 79, 28, 72, 21, 65, 24, 68, 27, 71, 20, 64, 13, 57, 16, 60, 19, 63, 12, 56, 5, 49, 8, 52, 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, 103)(8, 90)(9, 105)(10, 106)(11, 94)(12, 92)(13, 93)(14, 110)(15, 111)(16, 96)(17, 113)(18, 114)(19, 99)(20, 100)(21, 101)(22, 118)(23, 119)(24, 104)(25, 121)(26, 122)(27, 107)(28, 108)(29, 109)(30, 126)(31, 127)(32, 112)(33, 125)(34, 129)(35, 115)(36, 116)(37, 117)(38, 132)(39, 128)(40, 120)(41, 131)(42, 123)(43, 124)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.624 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.640 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^11, (Y3 * Y2^-1)^11, Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1^2 * Y3^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 12, 56, 5, 49, 8, 52, 14, 58, 20, 64, 13, 57, 16, 60, 22, 66, 28, 72, 21, 65, 24, 68, 30, 74, 36, 80, 29, 73, 32, 76, 38, 82, 43, 87, 37, 81, 40, 84, 44, 88, 41, 85, 33, 77, 39, 83, 42, 86, 34, 78, 25, 69, 31, 75, 35, 79, 26, 70, 17, 61, 23, 67, 27, 71, 18, 62, 9, 53, 15, 59, 19, 63, 10, 54, 3, 47, 7, 51, 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, 99)(7, 103)(8, 90)(9, 105)(10, 106)(11, 107)(12, 92)(13, 93)(14, 94)(15, 111)(16, 96)(17, 113)(18, 114)(19, 115)(20, 100)(21, 101)(22, 102)(23, 119)(24, 104)(25, 121)(26, 122)(27, 123)(28, 108)(29, 109)(30, 110)(31, 127)(32, 112)(33, 125)(34, 129)(35, 130)(36, 116)(37, 117)(38, 118)(39, 128)(40, 120)(41, 131)(42, 132)(43, 124)(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, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.628 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.641 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^-11, (Y3 * Y2^-1)^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 13, 57, 18, 62, 24, 68, 31, 75, 30, 74, 34, 78, 40, 84, 43, 87, 35, 79, 41, 85, 37, 81, 28, 72, 19, 63, 25, 69, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 12, 56, 5, 49, 8, 52, 16, 60, 23, 67, 22, 66, 26, 70, 32, 76, 39, 83, 38, 82, 42, 86, 44, 88, 36, 80, 27, 71, 33, 77, 29, 73, 20, 64, 9, 53, 17, 61, 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, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 100)(15, 99)(16, 94)(17, 113)(18, 96)(19, 115)(20, 116)(21, 117)(22, 101)(23, 102)(24, 104)(25, 121)(26, 106)(27, 123)(28, 124)(29, 125)(30, 110)(31, 111)(32, 112)(33, 129)(34, 114)(35, 126)(36, 131)(37, 132)(38, 118)(39, 119)(40, 120)(41, 130)(42, 122)(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) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.622 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.642 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, (Y3^-1, Y1^-1), (R * Y1)^2, Y3^2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^11, Y3^11, (Y3 * Y2^-1)^11, Y3^22, (Y1^-1 * Y3^-1)^44 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 9, 53, 17, 61, 24, 68, 31, 75, 27, 71, 33, 77, 40, 84, 44, 88, 38, 82, 42, 86, 36, 80, 29, 73, 22, 66, 26, 70, 20, 64, 12, 56, 5, 49, 8, 52, 16, 60, 10, 54, 3, 47, 7, 51, 15, 59, 23, 67, 19, 63, 25, 69, 32, 76, 39, 83, 35, 79, 41, 85, 43, 87, 37, 81, 30, 74, 34, 78, 28, 72, 21, 65, 13, 57, 18, 62, 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, 103)(7, 105)(8, 90)(9, 107)(10, 102)(11, 104)(12, 92)(13, 93)(14, 111)(15, 112)(16, 94)(17, 113)(18, 96)(19, 115)(20, 99)(21, 100)(22, 101)(23, 119)(24, 120)(25, 121)(26, 106)(27, 123)(28, 108)(29, 109)(30, 110)(31, 127)(32, 128)(33, 129)(34, 114)(35, 126)(36, 116)(37, 117)(38, 118)(39, 132)(40, 131)(41, 130)(42, 122)(43, 124)(44, 125)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.625 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.643 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^2 * Y3^-1 * Y1^6, Y3 * Y1 * Y3^4 * Y1^3, Y3^3 * Y1^-1 * Y3^3 * Y1^-3, (Y3 * Y2^-1)^11, (Y1^-1 * Y3^-1)^44 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 36, 80, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 27, 71, 41, 85, 44, 88, 35, 79, 20, 64, 9, 53, 17, 61, 29, 73, 40, 84, 25, 69, 32, 76, 43, 87, 34, 78, 19, 63, 31, 75, 39, 83, 24, 68, 13, 57, 18, 62, 30, 74, 42, 86, 33, 77, 38, 82, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 37, 81, 22, 66, 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, 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, 129)(27, 128)(28, 102)(29, 127)(30, 104)(31, 126)(32, 106)(33, 125)(34, 130)(35, 131)(36, 132)(37, 114)(38, 110)(39, 111)(40, 112)(41, 113)(42, 116)(43, 118)(44, 120)(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, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.627 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.644 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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, (Y1^-1, Y3), (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^2 * Y3^-3, Y1^4 * Y3 * Y1^4, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-4 * Y1^-1, (Y3 * Y2^-1)^11, Y1^-2 * Y3^4 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 * Y1 * Y3^3 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 26, 70, 38, 82, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 28, 72, 33, 77, 44, 88, 39, 83, 24, 68, 13, 57, 18, 62, 30, 74, 34, 78, 19, 63, 31, 75, 43, 87, 40, 84, 25, 69, 32, 76, 35, 79, 20, 64, 9, 53, 17, 61, 29, 73, 42, 86, 41, 85, 36, 80, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 27, 71, 37, 81, 22, 66, 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, 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, 125)(27, 130)(28, 102)(29, 131)(30, 104)(31, 132)(32, 106)(33, 114)(34, 116)(35, 118)(36, 120)(37, 129)(38, 110)(39, 111)(40, 112)(41, 113)(42, 128)(43, 127)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.623 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.645 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 44}) Quotient :: dipole Aut^+ = C44 (small group id <44, 2>) Aut = D88 (small group id <88, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-4 * Y3^3, Y3^-11, Y3^11, (Y3 * Y2^-1)^11, Y3^33, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 19, 63, 28, 72, 35, 79, 42, 86, 41, 85, 38, 82, 31, 75, 24, 68, 13, 57, 18, 62, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 26, 70, 29, 73, 36, 80, 43, 87, 40, 84, 33, 77, 30, 74, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 20, 64, 9, 53, 17, 61, 27, 71, 34, 78, 37, 81, 44, 88, 39, 83, 32, 76, 25, 69, 22, 66, 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, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 114)(15, 115)(16, 94)(17, 116)(18, 96)(19, 117)(20, 102)(21, 104)(22, 106)(23, 99)(24, 100)(25, 101)(26, 122)(27, 123)(28, 124)(29, 125)(30, 110)(31, 111)(32, 112)(33, 113)(34, 130)(35, 131)(36, 132)(37, 129)(38, 118)(39, 119)(40, 120)(41, 121)(42, 128)(43, 127)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 22, 88 ), ( 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.621 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.646 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {11, 44, 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^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^3 * Y1^4, Y3^-11, Y3^11, Y3^3 * Y1^-1 * Y3 * Y1^-1 * Y3^4 * Y1^-2, (Y3 * Y2^-1)^11 ] Map:: R = (1, 45, 2, 46, 6, 50, 14, 58, 25, 69, 28, 72, 35, 79, 42, 86, 37, 81, 40, 84, 31, 75, 20, 64, 9, 53, 17, 61, 23, 67, 12, 56, 5, 49, 8, 52, 16, 60, 26, 70, 33, 77, 36, 80, 43, 87, 38, 82, 29, 73, 32, 76, 21, 65, 10, 54, 3, 47, 7, 51, 15, 59, 24, 68, 13, 57, 18, 62, 27, 71, 34, 78, 41, 85, 44, 88, 39, 83, 30, 74, 19, 63, 22, 66, 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, 103)(7, 105)(8, 90)(9, 107)(10, 108)(11, 109)(12, 92)(13, 93)(14, 112)(15, 111)(16, 94)(17, 110)(18, 96)(19, 117)(20, 118)(21, 119)(22, 120)(23, 99)(24, 100)(25, 101)(26, 102)(27, 104)(28, 106)(29, 125)(30, 126)(31, 127)(32, 128)(33, 113)(34, 114)(35, 115)(36, 116)(37, 129)(38, 130)(39, 131)(40, 132)(41, 121)(42, 122)(43, 123)(44, 124)(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, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88, 22, 88 ) } Outer automorphisms :: reflexible Dual of E20.626 Graph:: bipartite v = 45 e = 88 f = 5 degree seq :: [ 2^44, 88 ] E20.647 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^4 * T2^5, T1^9, T1^-1 * T2 * T1^-2 * T2^2 * T1^-1 * T2 * T1^-1 * T2, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 37, 45, 32, 18, 8, 2, 7, 17, 31, 38, 22, 36, 44, 30, 16, 6, 15, 29, 39, 23, 11, 21, 35, 43, 28, 14, 27, 40, 24, 12, 4, 10, 20, 34, 42, 26, 41, 25, 13, 5)(46, 47, 51, 59, 71, 82, 67, 56, 49)(48, 52, 60, 72, 86, 90, 81, 66, 55)(50, 53, 61, 73, 87, 78, 83, 68, 57)(54, 62, 74, 85, 70, 77, 89, 80, 65)(58, 63, 75, 88, 79, 64, 76, 84, 69) 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) :: { ( 90^9 ), ( 90^45 ) } Outer automorphisms :: reflexible Dual of E20.652 Transitivity :: ET+ Graph:: bipartite v = 6 e = 45 f = 1 degree seq :: [ 9^5, 45 ] E20.648 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-5, T1^9, T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 12, 4, 10, 20, 29, 23, 11, 21, 30, 38, 33, 22, 31, 39, 44, 41, 32, 40, 45, 43, 35, 24, 34, 42, 37, 26, 14, 25, 36, 28, 16, 6, 15, 27, 18, 8, 2, 7, 17, 13, 5)(46, 47, 51, 59, 69, 77, 67, 56, 49)(48, 52, 60, 70, 79, 85, 76, 66, 55)(50, 53, 61, 71, 80, 86, 78, 68, 57)(54, 62, 72, 81, 87, 90, 84, 75, 65)(58, 63, 73, 82, 88, 89, 83, 74, 64) 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) :: { ( 90^9 ), ( 90^45 ) } Outer automorphisms :: reflexible Dual of E20.651 Transitivity :: ET+ Graph:: bipartite v = 6 e = 45 f = 1 degree seq :: [ 9^5, 45 ] E20.649 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^5, T1^-9, T1^9, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 29, 39, 37, 26, 36, 44, 42, 33, 22, 31, 35, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 30, 28, 14, 27, 38, 45, 41, 32, 40, 43, 34, 23, 11, 21, 25, 13, 5)(46, 47, 51, 59, 71, 77, 67, 56, 49)(48, 52, 60, 72, 81, 85, 76, 66, 55)(50, 53, 61, 73, 82, 86, 78, 68, 57)(54, 62, 74, 83, 89, 88, 80, 70, 65)(58, 63, 64, 75, 84, 90, 87, 79, 69) 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) :: { ( 90^9 ), ( 90^45 ) } Outer automorphisms :: reflexible Dual of E20.653 Transitivity :: ET+ Graph:: bipartite v = 6 e = 45 f = 1 degree seq :: [ 9^5, 45 ] E20.650 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 45, 45}) Quotient :: edge Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-3, T2 * T1 * T2^10, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 36, 28, 20, 12, 4, 10, 18, 26, 34, 42, 45, 43, 35, 27, 19, 11, 6, 14, 22, 30, 38, 44, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 37, 29, 21, 13, 5)(46, 47, 51, 55, 48, 52, 59, 63, 54, 60, 67, 71, 62, 68, 75, 79, 70, 76, 83, 87, 78, 84, 89, 90, 86, 82, 85, 88, 81, 74, 77, 80, 73, 66, 69, 72, 65, 58, 61, 64, 57, 50, 53, 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) :: { ( 18^45 ) } Outer automorphisms :: reflexible Dual of E20.654 Transitivity :: ET+ Graph:: bipartite v = 2 e = 45 f = 5 degree seq :: [ 45^2 ] E20.651 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^4 * T2^5, T1^9, T1^-1 * T2 * T1^-2 * T2^2 * T1^-1 * T2 * T1^-1 * T2, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 19, 64, 33, 78, 37, 82, 45, 90, 32, 77, 18, 63, 8, 53, 2, 47, 7, 52, 17, 62, 31, 76, 38, 83, 22, 67, 36, 81, 44, 89, 30, 75, 16, 61, 6, 51, 15, 60, 29, 74, 39, 84, 23, 68, 11, 56, 21, 66, 35, 80, 43, 88, 28, 73, 14, 59, 27, 72, 40, 85, 24, 69, 12, 57, 4, 49, 10, 55, 20, 65, 34, 79, 42, 87, 26, 71, 41, 86, 25, 70, 13, 58, 5, 50) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 59)(7, 60)(8, 61)(9, 62)(10, 48)(11, 49)(12, 50)(13, 63)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 77)(26, 82)(27, 86)(28, 87)(29, 85)(30, 88)(31, 84)(32, 89)(33, 83)(34, 64)(35, 65)(36, 66)(37, 67)(38, 68)(39, 69)(40, 70)(41, 90)(42, 78)(43, 79)(44, 80)(45, 81) local type(s) :: { ( 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45 ) } Outer automorphisms :: reflexible Dual of E20.648 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 45 f = 6 degree seq :: [ 90 ] E20.652 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-5, T1^9, T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^2 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 19, 64, 12, 57, 4, 49, 10, 55, 20, 65, 29, 74, 23, 68, 11, 56, 21, 66, 30, 75, 38, 83, 33, 78, 22, 67, 31, 76, 39, 84, 44, 89, 41, 86, 32, 77, 40, 85, 45, 90, 43, 88, 35, 80, 24, 69, 34, 79, 42, 87, 37, 82, 26, 71, 14, 59, 25, 70, 36, 81, 28, 73, 16, 61, 6, 51, 15, 60, 27, 72, 18, 63, 8, 53, 2, 47, 7, 52, 17, 62, 13, 58, 5, 50) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 59)(7, 60)(8, 61)(9, 62)(10, 48)(11, 49)(12, 50)(13, 63)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 58)(20, 54)(21, 55)(22, 56)(23, 57)(24, 77)(25, 79)(26, 80)(27, 81)(28, 82)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 85)(35, 86)(36, 87)(37, 88)(38, 74)(39, 75)(40, 76)(41, 78)(42, 90)(43, 89)(44, 83)(45, 84) local type(s) :: { ( 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45 ) } Outer automorphisms :: reflexible Dual of E20.647 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 45 f = 6 degree seq :: [ 90 ] E20.653 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^5, T1^-9, T1^9, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 19, 64, 16, 61, 6, 51, 15, 60, 29, 74, 39, 84, 37, 82, 26, 71, 36, 81, 44, 89, 42, 87, 33, 78, 22, 67, 31, 76, 35, 80, 24, 69, 12, 57, 4, 49, 10, 55, 20, 65, 18, 63, 8, 53, 2, 47, 7, 52, 17, 62, 30, 75, 28, 73, 14, 59, 27, 72, 38, 83, 45, 90, 41, 86, 32, 77, 40, 85, 43, 88, 34, 79, 23, 68, 11, 56, 21, 66, 25, 70, 13, 58, 5, 50) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 59)(7, 60)(8, 61)(9, 62)(10, 48)(11, 49)(12, 50)(13, 63)(14, 71)(15, 72)(16, 73)(17, 74)(18, 64)(19, 75)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 65)(26, 77)(27, 81)(28, 82)(29, 83)(30, 84)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70)(36, 85)(37, 86)(38, 89)(39, 90)(40, 76)(41, 78)(42, 79)(43, 80)(44, 88)(45, 87) local type(s) :: { ( 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45, 9, 45 ) } Outer automorphisms :: reflexible Dual of E20.649 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 45 f = 6 degree seq :: [ 90 ] E20.654 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 45, 45}) Quotient :: loop Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T2^4 * T1^5, T2^9, T2^2 * T1^-1 * T2 * T1^-1 * T2^2 * T1^-3, (T1^-1 * T2^-1)^45 ] Map:: non-degenerate R = (1, 46, 3, 48, 9, 54, 19, 64, 33, 78, 41, 86, 25, 70, 13, 58, 5, 50)(2, 47, 7, 52, 17, 62, 31, 76, 37, 82, 45, 90, 32, 77, 18, 63, 8, 53)(4, 49, 10, 55, 20, 65, 34, 79, 42, 87, 26, 71, 40, 85, 24, 69, 12, 57)(6, 51, 15, 60, 29, 74, 38, 83, 22, 67, 36, 81, 44, 89, 30, 75, 16, 61)(11, 56, 21, 66, 35, 80, 43, 88, 28, 73, 14, 59, 27, 72, 39, 84, 23, 68) L = (1, 47)(2, 51)(3, 52)(4, 46)(5, 53)(6, 59)(7, 60)(8, 61)(9, 62)(10, 48)(11, 49)(12, 50)(13, 63)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 54)(21, 55)(22, 56)(23, 57)(24, 58)(25, 77)(26, 86)(27, 85)(28, 87)(29, 84)(30, 88)(31, 83)(32, 89)(33, 82)(34, 64)(35, 65)(36, 66)(37, 67)(38, 68)(39, 69)(40, 70)(41, 90)(42, 78)(43, 79)(44, 80)(45, 81) local type(s) :: { ( 45^18 ) } Outer automorphisms :: reflexible Dual of E20.650 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 45 f = 2 degree seq :: [ 18^5 ] E20.655 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3 * Y1, (Y2^-1, Y1), (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-2, Y1^4 * Y2^5, Y2 * Y3^-2 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1, Y1^9, Y2 * Y1^-2 * Y2^4 * Y1^-3, (Y2^-1 * Y1^-1)^45 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 26, 71, 37, 82, 22, 67, 11, 56, 4, 49)(3, 48, 7, 52, 15, 60, 27, 72, 41, 86, 45, 90, 36, 81, 21, 66, 10, 55)(5, 50, 8, 53, 16, 61, 28, 73, 42, 87, 33, 78, 38, 83, 23, 68, 12, 57)(9, 54, 17, 62, 29, 74, 40, 85, 25, 70, 32, 77, 44, 89, 35, 80, 20, 65)(13, 58, 18, 63, 30, 75, 43, 88, 34, 79, 19, 64, 31, 76, 39, 84, 24, 69)(91, 136, 93, 138, 99, 144, 109, 154, 123, 168, 127, 172, 135, 180, 122, 167, 108, 153, 98, 143, 92, 137, 97, 142, 107, 152, 121, 166, 128, 173, 112, 157, 126, 171, 134, 179, 120, 165, 106, 151, 96, 141, 105, 150, 119, 164, 129, 174, 113, 158, 101, 146, 111, 156, 125, 170, 133, 178, 118, 163, 104, 149, 117, 162, 130, 175, 114, 159, 102, 147, 94, 139, 100, 145, 110, 155, 124, 169, 132, 177, 116, 161, 131, 176, 115, 160, 103, 148, 95, 140) L = (1, 94)(2, 91)(3, 100)(4, 101)(5, 102)(6, 92)(7, 93)(8, 95)(9, 110)(10, 111)(11, 112)(12, 113)(13, 114)(14, 96)(15, 97)(16, 98)(17, 99)(18, 103)(19, 124)(20, 125)(21, 126)(22, 127)(23, 128)(24, 129)(25, 130)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 115)(33, 132)(34, 133)(35, 134)(36, 135)(37, 116)(38, 123)(39, 121)(40, 119)(41, 117)(42, 118)(43, 120)(44, 122)(45, 131)(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, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ) } Outer automorphisms :: reflexible Dual of E20.661 Graph:: bipartite v = 6 e = 90 f = 46 degree seq :: [ 18^5, 90 ] E20.656 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2, Y3^-1), (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3 * Y2^4 * Y3, Y3^6 * Y1^-3, Y1^9, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 6, 51, 14, 59, 26, 71, 32, 77, 22, 67, 11, 56, 4, 49)(3, 48, 7, 52, 15, 60, 27, 72, 36, 81, 40, 85, 31, 76, 21, 66, 10, 55)(5, 50, 8, 53, 16, 61, 28, 73, 37, 82, 41, 86, 33, 78, 23, 68, 12, 57)(9, 54, 17, 62, 29, 74, 38, 83, 44, 89, 43, 88, 35, 80, 25, 70, 20, 65)(13, 58, 18, 63, 19, 64, 30, 75, 39, 84, 45, 90, 42, 87, 34, 79, 24, 69)(91, 136, 93, 138, 99, 144, 109, 154, 106, 151, 96, 141, 105, 150, 119, 164, 129, 174, 127, 172, 116, 161, 126, 171, 134, 179, 132, 177, 123, 168, 112, 157, 121, 166, 125, 170, 114, 159, 102, 147, 94, 139, 100, 145, 110, 155, 108, 153, 98, 143, 92, 137, 97, 142, 107, 152, 120, 165, 118, 163, 104, 149, 117, 162, 128, 173, 135, 180, 131, 176, 122, 167, 130, 175, 133, 178, 124, 169, 113, 158, 101, 146, 111, 156, 115, 160, 103, 148, 95, 140) L = (1, 94)(2, 91)(3, 100)(4, 101)(5, 102)(6, 92)(7, 93)(8, 95)(9, 110)(10, 111)(11, 112)(12, 113)(13, 114)(14, 96)(15, 97)(16, 98)(17, 99)(18, 103)(19, 108)(20, 115)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 104)(27, 105)(28, 106)(29, 107)(30, 109)(31, 130)(32, 116)(33, 131)(34, 132)(35, 133)(36, 117)(37, 118)(38, 119)(39, 120)(40, 126)(41, 127)(42, 135)(43, 134)(44, 128)(45, 129)(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, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ) } Outer automorphisms :: reflexible Dual of E20.662 Graph:: bipartite v = 6 e = 90 f = 46 degree seq :: [ 18^5, 90 ] E20.657 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 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, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^3 * Y3^-1 * Y2^2, Y1^9, Y2^-1 * Y3^2 * Y2^2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 24, 69, 32, 77, 22, 67, 11, 56, 4, 49)(3, 48, 7, 52, 15, 60, 25, 70, 34, 79, 40, 85, 31, 76, 21, 66, 10, 55)(5, 50, 8, 53, 16, 61, 26, 71, 35, 80, 41, 86, 33, 78, 23, 68, 12, 57)(9, 54, 17, 62, 27, 72, 36, 81, 42, 87, 45, 90, 39, 84, 30, 75, 20, 65)(13, 58, 18, 63, 28, 73, 37, 82, 43, 88, 44, 89, 38, 83, 29, 74, 19, 64)(91, 136, 93, 138, 99, 144, 109, 154, 102, 147, 94, 139, 100, 145, 110, 155, 119, 164, 113, 158, 101, 146, 111, 156, 120, 165, 128, 173, 123, 168, 112, 157, 121, 166, 129, 174, 134, 179, 131, 176, 122, 167, 130, 175, 135, 180, 133, 178, 125, 170, 114, 159, 124, 169, 132, 177, 127, 172, 116, 161, 104, 149, 115, 160, 126, 171, 118, 163, 106, 151, 96, 141, 105, 150, 117, 162, 108, 153, 98, 143, 92, 137, 97, 142, 107, 152, 103, 148, 95, 140) L = (1, 94)(2, 91)(3, 100)(4, 101)(5, 102)(6, 92)(7, 93)(8, 95)(9, 110)(10, 111)(11, 112)(12, 113)(13, 109)(14, 96)(15, 97)(16, 98)(17, 99)(18, 103)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 128)(30, 129)(31, 130)(32, 114)(33, 131)(34, 115)(35, 116)(36, 117)(37, 118)(38, 134)(39, 135)(40, 124)(41, 125)(42, 126)(43, 127)(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, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90, 2, 90 ) } Outer automorphisms :: reflexible Dual of E20.660 Graph:: bipartite v = 6 e = 90 f = 46 degree seq :: [ 18^5, 90 ] E20.658 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, (Y2, Y1), Y2^-4 * Y1, Y1^11 * Y2, Y1^4 * Y2^-1 * Y1^4 * Y2^-1 * Y1^3 * Y2^-1 * Y1, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 22, 67, 30, 75, 38, 83, 36, 81, 28, 73, 20, 65, 12, 57, 5, 50, 8, 53, 16, 61, 24, 69, 32, 77, 40, 85, 44, 89, 43, 88, 37, 82, 29, 74, 21, 66, 13, 58, 9, 54, 17, 62, 25, 70, 33, 78, 41, 86, 45, 90, 42, 87, 34, 79, 26, 71, 18, 63, 10, 55, 3, 48, 7, 52, 15, 60, 23, 68, 31, 76, 39, 84, 35, 80, 27, 72, 19, 64, 11, 56, 4, 49)(91, 136, 93, 138, 99, 144, 98, 143, 92, 137, 97, 142, 107, 152, 106, 151, 96, 141, 105, 150, 115, 160, 114, 159, 104, 149, 113, 158, 123, 168, 122, 167, 112, 157, 121, 166, 131, 176, 130, 175, 120, 165, 129, 174, 135, 180, 134, 179, 128, 173, 125, 170, 132, 177, 133, 178, 126, 171, 117, 162, 124, 169, 127, 172, 118, 163, 109, 154, 116, 161, 119, 164, 110, 155, 101, 146, 108, 153, 111, 156, 102, 147, 94, 139, 100, 145, 103, 148, 95, 140) L = (1, 93)(2, 97)(3, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 98)(10, 103)(11, 108)(12, 94)(13, 95)(14, 113)(15, 115)(16, 96)(17, 106)(18, 111)(19, 116)(20, 101)(21, 102)(22, 121)(23, 123)(24, 104)(25, 114)(26, 119)(27, 124)(28, 109)(29, 110)(30, 129)(31, 131)(32, 112)(33, 122)(34, 127)(35, 132)(36, 117)(37, 118)(38, 125)(39, 135)(40, 120)(41, 130)(42, 133)(43, 126)(44, 128)(45, 134)(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, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 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 E20.659 Graph:: bipartite v = 2 e = 90 f = 50 degree seq :: [ 90^2 ] E20.659 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y2^4 * Y3^-5, Y2^9, (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, 96, 141, 104, 149, 116, 161, 127, 172, 112, 157, 101, 146, 94, 139)(93, 138, 97, 142, 105, 150, 117, 162, 132, 177, 131, 176, 126, 171, 111, 156, 100, 145)(95, 140, 98, 143, 106, 151, 118, 163, 123, 168, 135, 180, 128, 173, 113, 158, 102, 147)(99, 144, 107, 152, 119, 164, 133, 178, 130, 175, 115, 160, 122, 167, 125, 170, 110, 155)(103, 148, 108, 153, 120, 165, 124, 169, 109, 154, 121, 166, 134, 179, 129, 174, 114, 159) 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, 117)(15, 119)(16, 96)(17, 121)(18, 98)(19, 123)(20, 124)(21, 125)(22, 126)(23, 101)(24, 102)(25, 103)(26, 132)(27, 133)(28, 104)(29, 134)(30, 106)(31, 135)(32, 108)(33, 116)(34, 118)(35, 120)(36, 122)(37, 131)(38, 112)(39, 113)(40, 114)(41, 115)(42, 130)(43, 129)(44, 128)(45, 127)(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 ), ( 90^18 ) } Outer automorphisms :: reflexible Dual of E20.658 Graph:: simple bipartite v = 50 e = 90 f = 2 degree seq :: [ 2^45, 18^5 ] E20.660 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^9, Y3^4 * Y1^5, (Y3 * Y2^-1)^9, Y3^-27, Y3^36, (Y1^-1 * Y3^-1)^45 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 26, 71, 41, 86, 45, 90, 36, 81, 21, 66, 10, 55, 3, 48, 7, 52, 15, 60, 27, 72, 40, 85, 25, 70, 32, 77, 44, 89, 35, 80, 20, 65, 9, 54, 17, 62, 29, 74, 39, 84, 24, 69, 13, 58, 18, 63, 30, 75, 43, 88, 34, 79, 19, 64, 31, 76, 38, 83, 23, 68, 12, 57, 5, 50, 8, 53, 16, 61, 28, 73, 42, 87, 33, 78, 37, 82, 22, 67, 11, 56, 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, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 109)(10, 110)(11, 111)(12, 94)(13, 95)(14, 117)(15, 119)(16, 96)(17, 121)(18, 98)(19, 123)(20, 124)(21, 125)(22, 126)(23, 101)(24, 102)(25, 103)(26, 130)(27, 129)(28, 104)(29, 128)(30, 106)(31, 127)(32, 108)(33, 131)(34, 132)(35, 133)(36, 134)(37, 135)(38, 112)(39, 113)(40, 114)(41, 115)(42, 116)(43, 118)(44, 120)(45, 122)(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) :: { ( 18, 90 ), ( 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90 ) } Outer automorphisms :: reflexible Dual of E20.657 Graph:: bipartite v = 46 e = 90 f = 6 degree seq :: [ 2^45, 90 ] E20.661 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y3^-1 * Y1^-5, (R * Y2 * Y3^-1)^2, Y3^9, (Y3 * Y2^-1)^9, Y1^-2 * Y3^-2 * Y1 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-4 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 12, 57, 5, 50, 8, 53, 16, 61, 24, 69, 22, 67, 13, 58, 18, 63, 26, 71, 34, 79, 32, 77, 23, 68, 28, 73, 36, 81, 42, 87, 41, 86, 33, 78, 38, 83, 44, 89, 45, 90, 39, 84, 29, 74, 37, 82, 43, 88, 40, 85, 30, 75, 19, 64, 27, 72, 35, 80, 31, 76, 20, 65, 9, 54, 17, 62, 25, 70, 21, 66, 10, 55, 3, 48, 7, 52, 15, 60, 11, 56, 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, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 109)(10, 110)(11, 111)(12, 94)(13, 95)(14, 101)(15, 115)(16, 96)(17, 117)(18, 98)(19, 119)(20, 120)(21, 121)(22, 102)(23, 103)(24, 104)(25, 125)(26, 106)(27, 127)(28, 108)(29, 123)(30, 129)(31, 130)(32, 112)(33, 113)(34, 114)(35, 133)(36, 116)(37, 128)(38, 118)(39, 131)(40, 135)(41, 122)(42, 124)(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) :: { ( 18, 90 ), ( 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90 ) } Outer automorphisms :: reflexible Dual of E20.655 Graph:: bipartite v = 46 e = 90 f = 6 degree seq :: [ 2^45, 90 ] E20.662 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 45, 45}) Quotient :: dipole Aut^+ = C45 (small group id <45, 1>) Aut = D90 (small group id <90, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^5, Y3^-9, Y3^9, (Y3 * Y2^-1)^9, (Y1^-1 * Y3^-1)^45 ] Map:: R = (1, 46, 2, 47, 6, 51, 14, 59, 20, 65, 9, 54, 17, 62, 27, 72, 36, 81, 40, 85, 30, 75, 38, 83, 45, 90, 42, 87, 34, 79, 25, 70, 29, 74, 32, 77, 23, 68, 12, 57, 5, 50, 8, 53, 16, 61, 21, 66, 10, 55, 3, 48, 7, 52, 15, 60, 26, 71, 31, 76, 19, 64, 28, 73, 37, 82, 44, 89, 43, 88, 35, 80, 39, 84, 41, 86, 33, 78, 24, 69, 13, 58, 18, 63, 22, 67, 11, 56, 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, 99)(4, 100)(5, 91)(6, 105)(7, 107)(8, 92)(9, 109)(10, 110)(11, 111)(12, 94)(13, 95)(14, 116)(15, 117)(16, 96)(17, 118)(18, 98)(19, 120)(20, 121)(21, 104)(22, 106)(23, 101)(24, 102)(25, 103)(26, 126)(27, 127)(28, 128)(29, 108)(30, 125)(31, 130)(32, 112)(33, 113)(34, 114)(35, 115)(36, 134)(37, 135)(38, 129)(39, 119)(40, 133)(41, 122)(42, 123)(43, 124)(44, 132)(45, 131)(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) :: { ( 18, 90 ), ( 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90, 18, 90 ) } Outer automorphisms :: reflexible Dual of E20.656 Graph:: bipartite v = 46 e = 90 f = 6 degree seq :: [ 2^45, 90 ] E20.663 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^4, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3^-1 * Y2 * Y3 * Y2, (Y2 * Y1)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 13, 61)(5, 53, 7, 55)(6, 54, 17, 65)(8, 56, 20, 68)(10, 58, 24, 72)(11, 59, 25, 73)(12, 60, 27, 75)(14, 62, 29, 77)(15, 63, 22, 70)(16, 64, 32, 80)(18, 66, 33, 81)(19, 67, 35, 83)(21, 69, 37, 85)(23, 71, 40, 88)(26, 74, 39, 87)(28, 76, 38, 86)(30, 78, 36, 84)(31, 79, 34, 82)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 110, 158, 107, 155)(102, 150, 112, 160, 108, 156)(104, 152, 117, 165, 114, 162)(106, 154, 119, 167, 115, 163)(109, 157, 121, 169, 125, 173)(111, 159, 122, 170, 127, 175)(113, 161, 123, 171, 128, 176)(116, 164, 129, 177, 133, 181)(118, 166, 130, 178, 135, 183)(120, 168, 131, 179, 136, 184)(124, 172, 139, 187, 137, 185)(126, 174, 140, 188, 138, 186)(132, 180, 143, 191, 141, 189)(134, 182, 144, 192, 142, 190) L = (1, 100)(2, 104)(3, 107)(4, 111)(5, 110)(6, 97)(7, 114)(8, 118)(9, 117)(10, 98)(11, 122)(12, 99)(13, 124)(14, 127)(15, 102)(16, 101)(17, 126)(18, 130)(19, 103)(20, 132)(21, 135)(22, 106)(23, 105)(24, 134)(25, 137)(26, 108)(27, 138)(28, 113)(29, 139)(30, 109)(31, 112)(32, 140)(33, 141)(34, 115)(35, 142)(36, 120)(37, 143)(38, 116)(39, 119)(40, 144)(41, 123)(42, 121)(43, 128)(44, 125)(45, 131)(46, 129)(47, 136)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E20.668 Graph:: simple bipartite v = 40 e = 96 f = 18 degree seq :: [ 4^24, 6^16 ] E20.664 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2^4, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 7, 55)(4, 52, 13, 61, 8, 56)(6, 54, 16, 64, 9, 57)(11, 59, 18, 66, 23, 71)(12, 60, 19, 67, 24, 72)(14, 62, 20, 68, 28, 76)(15, 63, 21, 69, 29, 77)(17, 65, 22, 70, 32, 80)(25, 73, 38, 86, 33, 81)(26, 74, 39, 87, 34, 82)(27, 75, 40, 88, 35, 83)(30, 78, 43, 91, 36, 84)(31, 79, 44, 92, 37, 85)(41, 89, 45, 93, 47, 95)(42, 90, 46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 102, 150)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 110, 158, 121, 169, 111, 159)(101, 149, 106, 154, 119, 167, 112, 160)(104, 152, 116, 164, 129, 177, 117, 165)(108, 156, 122, 170, 113, 161, 123, 171)(109, 157, 124, 172, 134, 182, 125, 173)(115, 163, 130, 178, 118, 166, 131, 179)(120, 168, 135, 183, 128, 176, 136, 184)(126, 174, 138, 186, 127, 175, 137, 185)(132, 180, 142, 190, 133, 181, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 109)(6, 113)(7, 115)(8, 98)(9, 118)(10, 120)(11, 121)(12, 99)(13, 101)(14, 126)(15, 127)(16, 128)(17, 102)(18, 129)(19, 103)(20, 132)(21, 133)(22, 105)(23, 134)(24, 106)(25, 107)(26, 137)(27, 138)(28, 139)(29, 140)(30, 110)(31, 111)(32, 112)(33, 114)(34, 141)(35, 142)(36, 116)(37, 117)(38, 119)(39, 143)(40, 144)(41, 122)(42, 123)(43, 124)(44, 125)(45, 130)(46, 131)(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, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.666 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 6^16, 8^12 ] E20.665 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3, Y1^3, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2, Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 8, 56)(4, 52, 9, 57, 7, 55)(6, 54, 17, 65, 10, 58)(12, 60, 22, 70, 27, 75)(13, 61, 23, 71, 14, 62)(15, 63, 20, 68, 24, 72)(16, 64, 21, 69, 25, 73)(18, 66, 26, 74, 19, 67)(28, 76, 40, 88, 29, 77)(30, 78, 32, 80, 41, 89)(31, 79, 33, 81, 42, 90)(34, 82, 38, 86, 35, 83)(36, 84, 39, 87, 37, 85)(43, 91, 47, 95, 44, 92)(45, 93, 48, 96, 46, 94)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 111, 159, 124, 172, 112, 160)(101, 149, 107, 155, 123, 171, 113, 161)(103, 151, 116, 164, 125, 173, 117, 165)(105, 153, 120, 168, 136, 184, 121, 169)(109, 157, 126, 174, 114, 162, 127, 175)(110, 158, 128, 176, 115, 163, 129, 177)(119, 167, 137, 185, 122, 170, 138, 186)(130, 178, 141, 189, 132, 180, 139, 187)(131, 179, 144, 192, 133, 181, 143, 191)(134, 182, 142, 190, 135, 183, 140, 188) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 114)(7, 97)(8, 110)(9, 101)(10, 115)(11, 119)(12, 124)(13, 107)(14, 99)(15, 130)(16, 132)(17, 122)(18, 113)(19, 102)(20, 134)(21, 135)(22, 136)(23, 104)(24, 131)(25, 133)(26, 106)(27, 125)(28, 118)(29, 108)(30, 139)(31, 141)(32, 143)(33, 144)(34, 116)(35, 111)(36, 117)(37, 112)(38, 120)(39, 121)(40, 123)(41, 140)(42, 142)(43, 128)(44, 126)(45, 129)(46, 127)(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, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.667 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 6^16, 8^12 ] E20.666 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1^-2, Y1^-1 * Y2 * Y1 * Y2 * Y1^-2, (R * Y2 * Y3)^2, (Y3 * Y2)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 18, 66, 35, 83, 30, 78, 17, 65, 5, 53)(3, 51, 9, 57, 23, 71, 7, 55, 21, 69, 15, 63, 19, 67, 11, 59)(4, 52, 12, 60, 26, 74, 8, 56, 24, 72, 16, 64, 20, 68, 14, 62)(10, 58, 22, 70, 36, 84, 27, 75, 38, 86, 31, 79, 40, 88, 29, 77)(13, 61, 25, 73, 37, 85, 32, 80, 41, 89, 34, 82, 42, 90, 33, 81)(28, 76, 43, 91, 48, 96, 39, 87, 47, 95, 45, 93, 46, 94, 44, 92)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 114, 162)(106, 154, 124, 172)(107, 155, 126, 174)(108, 156, 128, 176)(110, 158, 130, 178)(112, 160, 129, 177)(113, 161, 119, 167)(116, 164, 133, 181)(117, 165, 131, 179)(118, 166, 135, 183)(120, 168, 137, 185)(122, 170, 138, 186)(123, 171, 139, 187)(125, 173, 141, 189)(127, 175, 140, 188)(132, 180, 142, 190)(134, 182, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 123)(10, 99)(11, 127)(12, 114)(13, 124)(14, 126)(15, 125)(16, 101)(17, 122)(18, 108)(19, 132)(20, 102)(21, 134)(22, 103)(23, 136)(24, 131)(25, 135)(26, 113)(27, 105)(28, 109)(29, 111)(30, 110)(31, 107)(32, 139)(33, 141)(34, 140)(35, 120)(36, 115)(37, 142)(38, 117)(39, 121)(40, 119)(41, 143)(42, 144)(43, 128)(44, 130)(45, 129)(46, 133)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E20.664 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.667 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, (Y2 * R)^2, (R * Y3)^2, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^-2 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1, (Y2 * Y1^-2)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 23, 71, 42, 90, 38, 86, 19, 67, 5, 53)(3, 51, 11, 59, 29, 77, 8, 56, 27, 75, 17, 65, 24, 72, 13, 61)(4, 52, 15, 63, 34, 82, 10, 58, 33, 81, 20, 68, 25, 73, 16, 64)(6, 54, 21, 69, 32, 80, 9, 57, 31, 79, 18, 66, 26, 74, 22, 70)(12, 60, 30, 78, 43, 91, 36, 84, 45, 93, 40, 88, 47, 95, 37, 85)(14, 62, 28, 76, 44, 92, 35, 83, 46, 94, 39, 87, 48, 96, 41, 89)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 120, 168)(105, 153, 124, 172)(106, 154, 126, 174)(107, 155, 119, 167)(109, 157, 134, 182)(111, 159, 132, 180)(112, 160, 136, 184)(114, 162, 137, 185)(115, 163, 125, 173)(116, 164, 133, 181)(117, 165, 131, 179)(118, 166, 135, 183)(121, 169, 139, 187)(122, 170, 140, 188)(123, 171, 138, 186)(127, 175, 142, 190)(128, 176, 144, 192)(129, 177, 141, 189)(130, 178, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 114)(6, 97)(7, 121)(8, 124)(9, 126)(10, 98)(11, 131)(12, 102)(13, 135)(14, 99)(15, 119)(16, 134)(17, 137)(18, 133)(19, 130)(20, 101)(21, 132)(22, 136)(23, 117)(24, 139)(25, 140)(26, 103)(27, 141)(28, 106)(29, 143)(30, 104)(31, 138)(32, 115)(33, 142)(34, 144)(35, 111)(36, 107)(37, 113)(38, 118)(39, 112)(40, 109)(41, 116)(42, 129)(43, 122)(44, 120)(45, 127)(46, 123)(47, 128)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E20.665 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.668 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, (Y2 * Y1^-1)^2, Y1^4, Y3^-1 * Y1^-2 * Y3^-1, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1)^3, Y2^-2 * Y1^2 * Y2^-2, Y3^-1 * Y1^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^-2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 23, 71, 11, 59)(4, 52, 17, 65, 7, 55, 19, 67)(6, 54, 20, 68, 24, 72, 9, 57)(10, 58, 28, 76, 12, 60, 30, 78)(14, 62, 32, 80, 22, 70, 25, 73)(15, 63, 35, 83, 16, 64, 36, 84)(18, 66, 38, 86, 21, 69, 37, 85)(26, 74, 41, 89, 27, 75, 42, 90)(29, 77, 44, 92, 31, 79, 43, 91)(33, 81, 45, 93, 34, 82, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 110, 158, 120, 168, 104, 152, 119, 167, 118, 166, 102, 150)(98, 146, 105, 153, 121, 169, 109, 157, 101, 149, 116, 164, 128, 176, 107, 155)(100, 148, 114, 162, 130, 178, 111, 159, 103, 151, 117, 165, 129, 177, 112, 160)(106, 154, 125, 173, 136, 184, 122, 170, 108, 156, 127, 175, 135, 183, 123, 171)(113, 161, 131, 179, 141, 189, 134, 182, 115, 163, 132, 180, 142, 190, 133, 181)(124, 172, 137, 185, 143, 191, 140, 188, 126, 174, 138, 186, 144, 192, 139, 187) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 117)(7, 97)(8, 103)(9, 122)(10, 101)(11, 127)(12, 98)(13, 125)(14, 129)(15, 119)(16, 99)(17, 126)(18, 102)(19, 124)(20, 123)(21, 120)(22, 130)(23, 112)(24, 114)(25, 135)(26, 116)(27, 105)(28, 113)(29, 107)(30, 115)(31, 109)(32, 136)(33, 118)(34, 110)(35, 139)(36, 140)(37, 137)(38, 138)(39, 128)(40, 121)(41, 134)(42, 133)(43, 132)(44, 131)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.663 Graph:: bipartite v = 18 e = 96 f = 40 degree seq :: [ 8^12, 16^6 ] E20.669 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2 * Y2^-1, Y3^4, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1 * Y3^-2 * Y1, (Y3^-1 * Y2)^3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 20, 68)(8, 56, 24, 72)(9, 57, 27, 75)(10, 58, 28, 76)(12, 60, 21, 69)(13, 61, 22, 70)(14, 62, 23, 71)(16, 64, 25, 73)(17, 65, 26, 74)(29, 77, 39, 87)(30, 78, 40, 88)(31, 79, 37, 85)(32, 80, 38, 86)(33, 81, 45, 93)(34, 82, 46, 94)(35, 83, 44, 92)(36, 84, 43, 91)(41, 89, 47, 95)(42, 90, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 117, 165, 105, 153)(100, 148, 112, 160, 102, 150, 113, 161)(104, 152, 121, 169, 106, 154, 122, 170)(107, 155, 125, 173, 114, 162, 127, 175)(109, 157, 129, 177, 110, 158, 130, 178)(111, 159, 131, 179, 115, 163, 132, 180)(116, 164, 133, 181, 123, 171, 135, 183)(118, 166, 137, 185, 119, 167, 138, 186)(120, 168, 139, 187, 124, 172, 140, 188)(126, 174, 141, 189, 128, 176, 142, 190)(134, 182, 143, 191, 136, 184, 144, 192) L = (1, 100)(2, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 118)(8, 117)(9, 119)(10, 98)(11, 126)(12, 102)(13, 101)(14, 99)(15, 125)(16, 129)(17, 130)(18, 128)(19, 127)(20, 134)(21, 106)(22, 105)(23, 103)(24, 133)(25, 137)(26, 138)(27, 136)(28, 135)(29, 115)(30, 114)(31, 111)(32, 107)(33, 113)(34, 112)(35, 141)(36, 142)(37, 124)(38, 123)(39, 120)(40, 116)(41, 122)(42, 121)(43, 143)(44, 144)(45, 132)(46, 131)(47, 140)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E20.672 Graph:: simple bipartite v = 36 e = 96 f = 22 degree seq :: [ 4^24, 8^12 ] E20.670 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-2 * Y3^-2, Y2^-2 * Y3^2, (R * Y1)^2, Y2^4, (R * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y2^-1)^2, (Y3^-1 * Y2)^3, Y3^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 20, 68)(8, 56, 24, 72)(9, 57, 27, 75)(10, 58, 28, 76)(12, 60, 21, 69)(13, 61, 25, 73)(14, 62, 26, 74)(16, 64, 22, 70)(17, 65, 23, 71)(29, 77, 40, 88)(30, 78, 39, 87)(31, 79, 38, 86)(32, 80, 37, 85)(33, 81, 45, 93)(34, 82, 46, 94)(35, 83, 44, 92)(36, 84, 43, 91)(41, 89, 47, 95)(42, 90, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 117, 165, 105, 153)(100, 148, 112, 160, 102, 150, 113, 161)(104, 152, 121, 169, 106, 154, 122, 170)(107, 155, 125, 173, 114, 162, 127, 175)(109, 157, 129, 177, 110, 158, 130, 178)(111, 159, 126, 174, 115, 163, 128, 176)(116, 164, 133, 181, 123, 171, 135, 183)(118, 166, 137, 185, 119, 167, 138, 186)(120, 168, 134, 182, 124, 172, 136, 184)(131, 179, 141, 189, 132, 180, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192) L = (1, 100)(2, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 118)(8, 117)(9, 119)(10, 98)(11, 126)(12, 102)(13, 101)(14, 99)(15, 131)(16, 129)(17, 130)(18, 128)(19, 132)(20, 134)(21, 106)(22, 105)(23, 103)(24, 139)(25, 137)(26, 138)(27, 136)(28, 140)(29, 141)(30, 114)(31, 142)(32, 107)(33, 113)(34, 112)(35, 115)(36, 111)(37, 143)(38, 123)(39, 144)(40, 116)(41, 122)(42, 121)(43, 124)(44, 120)(45, 127)(46, 125)(47, 135)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E20.671 Graph:: simple bipartite v = 36 e = 96 f = 22 degree seq :: [ 4^24, 8^12 ] E20.671 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (Y2^-1, Y1^-1), (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y2^-2 * Y3 * Y2 * Y3 * Y2^-1, (Y3 * Y2^-2)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 7, 55, 12, 60)(4, 52, 13, 61, 8, 56)(6, 54, 9, 57, 16, 64)(10, 58, 19, 67, 27, 75)(11, 59, 28, 76, 20, 68)(14, 62, 31, 79, 21, 69)(15, 63, 32, 80, 22, 70)(17, 65, 34, 82, 23, 71)(18, 66, 24, 72, 35, 83)(25, 73, 36, 84, 42, 90)(26, 74, 43, 91, 37, 85)(29, 77, 44, 92, 38, 86)(30, 78, 45, 93, 39, 87)(33, 81, 40, 88, 46, 94)(41, 89, 47, 95, 48, 96)(97, 145, 99, 147, 106, 154, 121, 169, 137, 185, 129, 177, 114, 162, 102, 150)(98, 146, 103, 151, 115, 163, 132, 180, 143, 191, 136, 184, 120, 168, 105, 153)(100, 148, 110, 158, 126, 174, 107, 155, 125, 173, 113, 161, 122, 170, 111, 159)(101, 149, 108, 156, 123, 171, 138, 186, 144, 192, 142, 190, 131, 179, 112, 160)(104, 152, 117, 165, 135, 183, 116, 164, 134, 182, 119, 167, 133, 181, 118, 166)(109, 157, 127, 175, 141, 189, 124, 172, 140, 188, 130, 178, 139, 187, 128, 176) L = (1, 100)(2, 104)(3, 107)(4, 97)(5, 109)(6, 113)(7, 116)(8, 98)(9, 119)(10, 122)(11, 99)(12, 124)(13, 101)(14, 121)(15, 129)(16, 130)(17, 102)(18, 126)(19, 133)(20, 103)(21, 132)(22, 136)(23, 105)(24, 135)(25, 110)(26, 106)(27, 139)(28, 108)(29, 137)(30, 114)(31, 138)(32, 142)(33, 111)(34, 112)(35, 141)(36, 117)(37, 115)(38, 143)(39, 120)(40, 118)(41, 125)(42, 127)(43, 123)(44, 144)(45, 131)(46, 128)(47, 134)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.670 Graph:: simple bipartite v = 22 e = 96 f = 36 degree seq :: [ 6^16, 16^6 ] E20.672 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, Y2 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-2, Y2^3 * Y3^-1 * Y2^-1 * Y3^-1, (Y3^-1 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 8, 56)(4, 52, 9, 57, 7, 55)(6, 54, 17, 65, 10, 58)(12, 60, 23, 71, 29, 77)(13, 61, 24, 72, 14, 62)(15, 63, 21, 69, 25, 73)(16, 64, 22, 70, 26, 74)(18, 66, 28, 76, 20, 68)(19, 67, 27, 75, 40, 88)(30, 78, 41, 89, 37, 85)(31, 79, 43, 91, 32, 80)(33, 81, 35, 83, 44, 92)(34, 82, 36, 84, 45, 93)(38, 86, 42, 90, 39, 87)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 126, 174, 142, 190, 134, 182, 115, 163, 102, 150)(98, 146, 104, 152, 119, 167, 133, 181, 144, 192, 135, 183, 123, 171, 106, 154)(100, 148, 111, 159, 132, 180, 110, 158, 131, 179, 116, 164, 127, 175, 112, 160)(101, 149, 107, 155, 125, 173, 137, 185, 143, 191, 138, 186, 136, 184, 113, 161)(103, 151, 117, 165, 130, 178, 109, 157, 129, 177, 114, 162, 128, 176, 118, 166)(105, 153, 121, 169, 141, 189, 120, 168, 140, 188, 124, 172, 139, 187, 122, 170) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 114)(7, 97)(8, 110)(9, 101)(10, 116)(11, 120)(12, 127)(13, 107)(14, 99)(15, 126)(16, 134)(17, 124)(18, 113)(19, 132)(20, 102)(21, 137)(22, 138)(23, 139)(24, 104)(25, 133)(26, 135)(27, 141)(28, 106)(29, 128)(30, 117)(31, 119)(32, 108)(33, 142)(34, 115)(35, 144)(36, 123)(37, 111)(38, 118)(39, 112)(40, 130)(41, 121)(42, 122)(43, 125)(44, 143)(45, 136)(46, 131)(47, 129)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E20.669 Graph:: simple bipartite v = 22 e = 96 f = 36 degree seq :: [ 6^16, 16^6 ] E20.673 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (C6 x D8) : C2 (small group id <96, 139>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3^4, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 13, 61)(5, 53, 9, 57)(6, 54, 17, 65)(8, 56, 20, 68)(10, 58, 24, 72)(11, 59, 25, 73)(12, 60, 27, 75)(14, 62, 28, 76)(15, 63, 22, 70)(16, 64, 32, 80)(18, 66, 33, 81)(19, 67, 35, 83)(21, 69, 36, 84)(23, 71, 40, 88)(26, 74, 34, 82)(29, 77, 38, 86)(30, 78, 37, 85)(31, 79, 39, 87)(41, 89, 46, 94)(42, 90, 45, 93)(43, 91, 48, 96)(44, 92, 47, 95)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 110, 158, 107, 155)(102, 150, 112, 160, 108, 156)(104, 152, 117, 165, 114, 162)(106, 154, 119, 167, 115, 163)(109, 157, 124, 172, 121, 169)(111, 159, 122, 170, 127, 175)(113, 161, 128, 176, 123, 171)(116, 164, 132, 180, 129, 177)(118, 166, 130, 178, 135, 183)(120, 168, 136, 184, 131, 179)(125, 173, 137, 185, 139, 187)(126, 174, 138, 186, 140, 188)(133, 181, 141, 189, 143, 191)(134, 182, 142, 190, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 111)(5, 110)(6, 97)(7, 114)(8, 118)(9, 117)(10, 98)(11, 122)(12, 99)(13, 125)(14, 127)(15, 102)(16, 101)(17, 126)(18, 130)(19, 103)(20, 133)(21, 135)(22, 106)(23, 105)(24, 134)(25, 137)(26, 108)(27, 138)(28, 139)(29, 113)(30, 109)(31, 112)(32, 140)(33, 141)(34, 115)(35, 142)(36, 143)(37, 120)(38, 116)(39, 119)(40, 144)(41, 123)(42, 121)(43, 128)(44, 124)(45, 131)(46, 129)(47, 136)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E20.674 Graph:: simple bipartite v = 40 e = 96 f = 18 degree seq :: [ 4^24, 6^16 ] E20.674 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (C6 x D8) : C2 (small group id <96, 139>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2 * Y3, Y3 * Y1^2 * Y3, Y1^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y2^-1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2^4 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1, Y1^-1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y2^2 * Y1^-1 * Y2^-2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 27, 75, 16, 64)(4, 52, 18, 66, 7, 55, 20, 68)(6, 54, 23, 71, 28, 76, 25, 73)(9, 57, 29, 77, 21, 69, 32, 80)(10, 58, 34, 82, 12, 60, 36, 84)(11, 59, 37, 85, 22, 70, 39, 87)(14, 62, 40, 88, 26, 74, 30, 78)(15, 63, 35, 83, 17, 65, 38, 86)(19, 67, 31, 79, 24, 72, 33, 81)(41, 89, 47, 95, 44, 92, 46, 94)(42, 90, 48, 96, 43, 91, 45, 93)(97, 145, 99, 147, 110, 158, 124, 172, 104, 152, 123, 171, 122, 170, 102, 150)(98, 146, 105, 153, 126, 174, 118, 166, 101, 149, 117, 165, 136, 184, 107, 155)(100, 148, 115, 163, 139, 187, 111, 159, 103, 151, 120, 168, 138, 186, 113, 161)(106, 154, 131, 179, 143, 191, 127, 175, 108, 156, 134, 182, 142, 190, 129, 177)(109, 157, 132, 180, 119, 167, 140, 188, 112, 160, 130, 178, 121, 169, 137, 185)(114, 162, 133, 181, 144, 192, 128, 176, 116, 164, 135, 183, 141, 189, 125, 173) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 120)(7, 97)(8, 103)(9, 127)(10, 101)(11, 134)(12, 98)(13, 133)(14, 138)(15, 123)(16, 135)(17, 99)(18, 132)(19, 102)(20, 130)(21, 129)(22, 131)(23, 125)(24, 124)(25, 128)(26, 139)(27, 113)(28, 115)(29, 121)(30, 142)(31, 117)(32, 119)(33, 105)(34, 114)(35, 107)(36, 116)(37, 112)(38, 118)(39, 109)(40, 143)(41, 141)(42, 122)(43, 110)(44, 144)(45, 140)(46, 136)(47, 126)(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, 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 E20.673 Graph:: bipartite v = 18 e = 96 f = 40 degree seq :: [ 8^12, 16^6 ] E20.675 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y3^-4 * Y2, (Y3^-2 * Y1)^2, (Y3^-2 * Y2^-1)^2, Y1 * Y3^-1 * Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 13, 61)(5, 53, 7, 55)(6, 54, 17, 65)(8, 56, 21, 69)(10, 58, 25, 73)(11, 59, 27, 75)(12, 60, 29, 77)(14, 62, 26, 74)(15, 63, 30, 78)(16, 64, 33, 81)(18, 66, 22, 70)(19, 67, 35, 83)(20, 68, 37, 85)(23, 71, 38, 86)(24, 72, 41, 89)(28, 76, 36, 84)(31, 79, 46, 94)(32, 80, 47, 95)(34, 82, 48, 96)(39, 87, 44, 92)(40, 88, 43, 91)(42, 90, 45, 93)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 107, 155, 111, 159)(102, 150, 108, 156, 112, 160)(104, 152, 115, 163, 119, 167)(106, 154, 116, 164, 120, 168)(109, 157, 126, 174, 123, 171)(110, 158, 124, 172, 114, 162)(113, 161, 129, 177, 125, 173)(117, 165, 134, 182, 131, 179)(118, 166, 132, 180, 122, 170)(121, 169, 137, 185, 133, 181)(127, 175, 141, 189, 139, 187)(128, 176, 130, 178, 140, 188)(135, 183, 144, 192, 143, 191)(136, 184, 138, 186, 142, 190) L = (1, 100)(2, 104)(3, 107)(4, 110)(5, 111)(6, 97)(7, 115)(8, 118)(9, 119)(10, 98)(11, 124)(12, 99)(13, 127)(14, 108)(15, 114)(16, 101)(17, 130)(18, 102)(19, 132)(20, 103)(21, 135)(22, 116)(23, 122)(24, 105)(25, 138)(26, 106)(27, 139)(28, 112)(29, 128)(30, 141)(31, 113)(32, 109)(33, 140)(34, 126)(35, 143)(36, 120)(37, 136)(38, 144)(39, 121)(40, 117)(41, 142)(42, 134)(43, 125)(44, 123)(45, 129)(46, 131)(47, 133)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E20.678 Graph:: simple bipartite v = 40 e = 96 f = 18 degree seq :: [ 4^24, 6^16 ] E20.676 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2^4, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 7, 55, 12, 60)(4, 52, 13, 61, 8, 56)(6, 54, 9, 57, 16, 64)(10, 58, 18, 66, 24, 72)(11, 59, 25, 73, 19, 67)(14, 62, 28, 76, 20, 68)(15, 63, 29, 77, 21, 69)(17, 65, 32, 80, 22, 70)(23, 71, 38, 86, 33, 81)(26, 74, 39, 87, 34, 82)(27, 75, 40, 88, 35, 83)(30, 78, 36, 84, 43, 91)(31, 79, 37, 85, 44, 92)(41, 89, 45, 93, 47, 95)(42, 90, 46, 94, 48, 96)(97, 145, 99, 147, 106, 154, 102, 150)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 110, 158, 119, 167, 111, 159)(101, 149, 108, 156, 120, 168, 112, 160)(104, 152, 116, 164, 129, 177, 117, 165)(107, 155, 122, 170, 113, 161, 123, 171)(109, 157, 124, 172, 134, 182, 125, 173)(115, 163, 130, 178, 118, 166, 131, 179)(121, 169, 135, 183, 128, 176, 136, 184)(126, 174, 138, 186, 127, 175, 137, 185)(132, 180, 142, 190, 133, 181, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 104)(3, 107)(4, 97)(5, 109)(6, 113)(7, 115)(8, 98)(9, 118)(10, 119)(11, 99)(12, 121)(13, 101)(14, 126)(15, 127)(16, 128)(17, 102)(18, 129)(19, 103)(20, 132)(21, 133)(22, 105)(23, 106)(24, 134)(25, 108)(26, 137)(27, 138)(28, 139)(29, 140)(30, 110)(31, 111)(32, 112)(33, 114)(34, 141)(35, 142)(36, 116)(37, 117)(38, 120)(39, 143)(40, 144)(41, 122)(42, 123)(43, 124)(44, 125)(45, 130)(46, 131)(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, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.677 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 6^16, 8^12 ] E20.677 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1^-2, (R * Y2 * Y3)^2, (Y3 * Y2)^3, Y1 * Y2 * Y3 * Y1^-1 * Y2 * Y3, (Y2 * Y1^-2)^2, (Y3 * Y1)^4, Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-3, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, Y1^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 18, 66, 37, 85, 35, 83, 17, 65, 5, 53)(3, 51, 9, 57, 27, 75, 44, 92, 48, 96, 40, 88, 19, 67, 11, 59)(4, 52, 12, 60, 26, 74, 8, 56, 24, 72, 16, 64, 20, 68, 14, 62)(7, 55, 21, 69, 15, 63, 36, 84, 47, 95, 30, 78, 38, 86, 23, 71)(10, 58, 25, 73, 39, 87, 29, 77, 42, 90, 33, 81, 45, 93, 31, 79)(13, 61, 22, 70, 41, 89, 28, 76, 43, 91, 32, 80, 46, 94, 34, 82)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 124, 172)(106, 154, 126, 174)(107, 155, 128, 176)(108, 156, 125, 173)(110, 158, 129, 177)(112, 160, 127, 175)(113, 161, 123, 171)(114, 162, 134, 182)(116, 164, 137, 185)(117, 165, 138, 186)(118, 166, 140, 188)(119, 167, 141, 189)(120, 168, 139, 187)(122, 170, 142, 190)(130, 178, 136, 184)(131, 179, 143, 191)(132, 180, 135, 183)(133, 181, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 125)(10, 99)(11, 129)(12, 114)(13, 126)(14, 131)(15, 130)(16, 101)(17, 122)(18, 108)(19, 135)(20, 102)(21, 139)(22, 103)(23, 142)(24, 133)(25, 140)(26, 113)(27, 141)(28, 134)(29, 105)(30, 109)(31, 136)(32, 143)(33, 107)(34, 111)(35, 110)(36, 137)(37, 120)(38, 124)(39, 115)(40, 127)(41, 132)(42, 144)(43, 117)(44, 121)(45, 123)(46, 119)(47, 128)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E20.676 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.678 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y1, (Y3^-1, Y1^-1), (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y1^4, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (Y3^-1 * Y2^-1)^2, (Y1^-1 * Y3^-1)^3, Y2^3 * Y1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 23, 71, 11, 59)(4, 52, 10, 58, 24, 72, 18, 66)(6, 54, 19, 67, 25, 73, 9, 57)(7, 55, 12, 60, 26, 74, 20, 68)(14, 62, 32, 80, 22, 70, 27, 75)(15, 63, 33, 81, 41, 89, 31, 79)(16, 64, 34, 82, 42, 90, 30, 78)(17, 65, 37, 85, 43, 91, 29, 77)(21, 69, 39, 87, 44, 92, 28, 76)(35, 83, 47, 95, 38, 86, 45, 93)(36, 84, 48, 96, 40, 88, 46, 94)(97, 145, 99, 147, 110, 158, 121, 169, 104, 152, 119, 167, 118, 166, 102, 150)(98, 146, 105, 153, 123, 171, 109, 157, 101, 149, 115, 163, 128, 176, 107, 155)(100, 148, 113, 161, 134, 182, 138, 186, 120, 168, 139, 187, 131, 179, 112, 160)(103, 151, 117, 165, 136, 184, 137, 185, 122, 170, 140, 188, 132, 180, 111, 159)(106, 154, 126, 174, 143, 191, 133, 181, 114, 162, 130, 178, 141, 189, 125, 173)(108, 156, 127, 175, 144, 192, 135, 183, 116, 164, 129, 177, 142, 190, 124, 172) L = (1, 100)(2, 106)(3, 111)(4, 108)(5, 114)(6, 117)(7, 97)(8, 120)(9, 124)(10, 122)(11, 127)(12, 98)(13, 129)(14, 131)(15, 130)(16, 99)(17, 102)(18, 103)(19, 135)(20, 101)(21, 133)(22, 134)(23, 137)(24, 116)(25, 140)(26, 104)(27, 141)(28, 113)(29, 105)(30, 107)(31, 112)(32, 143)(33, 138)(34, 109)(35, 144)(36, 110)(37, 115)(38, 142)(39, 139)(40, 118)(41, 126)(42, 119)(43, 121)(44, 125)(45, 132)(46, 123)(47, 136)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E20.675 Graph:: bipartite v = 18 e = 96 f = 40 degree seq :: [ 8^12, 16^6 ] E20.679 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-3 * Y2^-1, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, Y2^4, (R * Y3)^2, (Y3^-1 * Y1 * Y2^-1)^2, Y3 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, (Y3 * Y1 * Y2^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y3 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 20, 68)(8, 56, 24, 72)(9, 57, 27, 75)(10, 58, 28, 76)(12, 60, 21, 69)(13, 61, 25, 73)(14, 62, 26, 74)(16, 64, 22, 70)(17, 65, 23, 71)(29, 77, 39, 87)(30, 78, 40, 88)(31, 79, 37, 85)(32, 80, 38, 86)(33, 81, 45, 93)(34, 82, 46, 94)(35, 83, 44, 92)(36, 84, 43, 91)(41, 89, 47, 95)(42, 90, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 117, 165, 105, 153)(100, 148, 109, 157, 129, 177, 113, 161)(102, 150, 110, 158, 130, 178, 112, 160)(104, 152, 118, 166, 137, 185, 122, 170)(106, 154, 119, 167, 138, 186, 121, 169)(107, 155, 125, 173, 114, 162, 127, 175)(111, 159, 131, 179, 141, 189, 128, 176)(115, 163, 132, 180, 142, 190, 126, 174)(116, 164, 133, 181, 123, 171, 135, 183)(120, 168, 139, 187, 143, 191, 136, 184)(124, 172, 140, 188, 144, 192, 134, 182) L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 113)(6, 97)(7, 118)(8, 121)(9, 122)(10, 98)(11, 126)(12, 129)(13, 102)(14, 99)(15, 125)(16, 101)(17, 130)(18, 132)(19, 128)(20, 134)(21, 137)(22, 106)(23, 103)(24, 133)(25, 105)(26, 138)(27, 140)(28, 136)(29, 115)(30, 141)(31, 142)(32, 107)(33, 110)(34, 108)(35, 114)(36, 111)(37, 124)(38, 143)(39, 144)(40, 116)(41, 119)(42, 117)(43, 123)(44, 120)(45, 127)(46, 131)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E20.680 Graph:: simple bipartite v = 36 e = 96 f = 22 degree seq :: [ 4^24, 8^12 ] E20.680 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y2^-1 * Y3 * Y2^3 * Y3, (Y3 * Y2^-2)^2, (Y3 * Y2)^4, Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 7, 55)(4, 52, 13, 61, 8, 56)(6, 54, 16, 64, 9, 57)(11, 59, 19, 67, 25, 73)(12, 60, 20, 68, 26, 74)(14, 62, 21, 69, 31, 79)(15, 63, 22, 70, 32, 80)(17, 65, 23, 71, 34, 82)(18, 66, 24, 72, 35, 83)(27, 75, 41, 89, 36, 84)(28, 76, 42, 90, 37, 85)(29, 77, 43, 91, 38, 86)(30, 78, 44, 92, 39, 87)(33, 81, 46, 94, 40, 88)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 123, 171, 141, 189, 129, 177, 114, 162, 102, 150)(98, 146, 103, 151, 115, 163, 132, 180, 143, 191, 136, 184, 120, 168, 105, 153)(100, 148, 110, 158, 126, 174, 108, 156, 125, 173, 113, 161, 124, 172, 111, 159)(101, 149, 106, 154, 121, 169, 137, 185, 144, 192, 142, 190, 131, 179, 112, 160)(104, 152, 117, 165, 135, 183, 116, 164, 134, 182, 119, 167, 133, 181, 118, 166)(109, 157, 127, 175, 140, 188, 122, 170, 139, 187, 130, 178, 138, 186, 128, 176) L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 109)(6, 113)(7, 116)(8, 98)(9, 119)(10, 122)(11, 124)(12, 99)(13, 101)(14, 123)(15, 129)(16, 130)(17, 102)(18, 126)(19, 133)(20, 103)(21, 132)(22, 136)(23, 105)(24, 135)(25, 138)(26, 106)(27, 110)(28, 107)(29, 141)(30, 114)(31, 137)(32, 142)(33, 111)(34, 112)(35, 140)(36, 117)(37, 115)(38, 143)(39, 120)(40, 118)(41, 127)(42, 121)(43, 144)(44, 131)(45, 125)(46, 128)(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, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.679 Graph:: simple bipartite v = 22 e = 96 f = 36 degree seq :: [ 6^16, 16^6 ] E20.681 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y1)^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y3^-4 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 21, 69)(12, 60, 15, 63)(13, 61, 22, 70)(14, 62, 20, 68)(16, 64, 18, 66)(17, 65, 23, 71)(19, 67, 24, 72)(25, 73, 33, 81)(26, 74, 27, 75)(28, 76, 37, 85)(29, 77, 31, 79)(30, 78, 36, 84)(32, 80, 34, 82)(35, 83, 38, 86)(39, 87, 45, 93)(40, 88, 41, 89)(42, 90, 43, 91)(44, 92, 46, 94)(47, 95, 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, 108, 156)(106, 154, 112, 160, 120, 168)(107, 155, 121, 169, 119, 167)(110, 158, 126, 174, 127, 175)(113, 161, 117, 165, 129, 177)(116, 164, 132, 180, 125, 173)(122, 170, 133, 181, 137, 185)(123, 171, 124, 172, 136, 184)(128, 176, 141, 189, 131, 179)(130, 178, 135, 183, 134, 182)(138, 186, 142, 190, 143, 191)(139, 187, 140, 188, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 110)(5, 112)(6, 97)(7, 117)(8, 116)(9, 114)(10, 98)(11, 122)(12, 99)(13, 124)(14, 106)(15, 103)(16, 128)(17, 101)(18, 130)(19, 126)(20, 102)(21, 123)(22, 133)(23, 105)(24, 132)(25, 135)(26, 111)(27, 108)(28, 138)(29, 109)(30, 140)(31, 118)(32, 119)(33, 141)(34, 113)(35, 115)(36, 142)(37, 139)(38, 120)(39, 143)(40, 121)(41, 129)(42, 127)(43, 125)(44, 134)(45, 144)(46, 131)(47, 137)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E20.684 Graph:: simple bipartite v = 40 e = 96 f = 18 degree seq :: [ 4^24, 6^16 ] E20.682 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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^-2, Y1^3, Y2^-1 * Y3 * Y1 * Y2^-1, Y2^-2 * Y3^-1 * Y1^-1, (Y3 * Y1)^2, Y3 * Y2^-2 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * R * Y1 * Y3 * R * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3, Y2^-1 * Y3^-1 * Y2 * R * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2^-1 * R * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y2)^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 13, 61)(4, 52, 9, 57, 7, 55)(6, 54, 14, 62, 12, 60)(8, 56, 17, 65, 19, 67)(10, 58, 20, 68, 18, 66)(15, 63, 25, 73, 27, 75)(16, 64, 28, 76, 26, 74)(21, 69, 33, 81, 35, 83)(22, 70, 36, 84, 34, 82)(23, 71, 37, 85, 29, 77)(24, 72, 38, 86, 30, 78)(31, 79, 41, 89, 40, 88)(32, 80, 42, 90, 39, 87)(43, 91, 48, 96, 46, 94)(44, 92, 47, 95, 45, 93)(97, 145, 99, 147, 105, 153, 102, 150)(98, 146, 104, 152, 103, 151, 106, 154)(100, 148, 111, 159, 101, 149, 112, 160)(107, 155, 117, 165, 110, 158, 118, 166)(108, 156, 119, 167, 109, 157, 120, 168)(113, 161, 125, 173, 116, 164, 126, 174)(114, 162, 127, 175, 115, 163, 128, 176)(121, 169, 135, 183, 124, 172, 136, 184)(122, 170, 132, 180, 123, 171, 129, 177)(130, 178, 139, 187, 131, 179, 140, 188)(133, 181, 141, 189, 134, 182, 142, 190)(137, 185, 143, 191, 138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 98)(5, 103)(6, 109)(7, 97)(8, 114)(9, 101)(10, 115)(11, 102)(12, 107)(13, 110)(14, 99)(15, 122)(16, 123)(17, 106)(18, 113)(19, 116)(20, 104)(21, 130)(22, 131)(23, 126)(24, 125)(25, 112)(26, 121)(27, 124)(28, 111)(29, 134)(30, 133)(31, 135)(32, 136)(33, 118)(34, 129)(35, 132)(36, 117)(37, 120)(38, 119)(39, 137)(40, 138)(41, 128)(42, 127)(43, 141)(44, 142)(45, 144)(46, 143)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.683 Graph:: bipartite v = 28 e = 96 f = 30 degree seq :: [ 6^16, 8^12 ] E20.683 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y1 * Y2 * Y3 * Y1 * Y3, Y2 * Y1^4, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 17, 65, 5, 53)(4, 52, 14, 62, 30, 78, 27, 75, 11, 59, 18, 66, 32, 80, 15, 63)(6, 54, 19, 67, 24, 72, 9, 57, 13, 61, 29, 77, 36, 84, 20, 68)(10, 58, 25, 73, 37, 85, 21, 69, 23, 71, 39, 87, 42, 90, 26, 74)(16, 64, 22, 70, 38, 86, 43, 91, 28, 76, 34, 82, 46, 94, 33, 81)(31, 79, 44, 92, 48, 96, 41, 89, 35, 83, 45, 93, 47, 95, 40, 88)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 113, 161)(105, 153, 116, 164)(106, 154, 119, 167)(110, 158, 114, 162)(111, 159, 123, 171)(112, 160, 124, 172)(115, 163, 125, 173)(117, 165, 122, 170)(118, 166, 130, 178)(120, 168, 132, 180)(121, 169, 135, 183)(126, 174, 128, 176)(127, 175, 131, 179)(129, 177, 139, 187)(133, 181, 138, 186)(134, 182, 142, 190)(136, 184, 137, 185)(140, 188, 141, 189)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 109)(5, 112)(6, 97)(7, 117)(8, 116)(9, 119)(10, 98)(11, 102)(12, 124)(13, 99)(14, 108)(15, 127)(16, 110)(17, 122)(18, 101)(19, 111)(20, 106)(21, 130)(22, 103)(23, 104)(24, 136)(25, 120)(26, 118)(27, 131)(28, 114)(29, 123)(30, 139)(31, 125)(32, 129)(33, 140)(34, 113)(35, 115)(36, 137)(37, 143)(38, 133)(39, 132)(40, 135)(41, 121)(42, 144)(43, 141)(44, 126)(45, 128)(46, 138)(47, 142)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E20.682 Graph:: bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.684 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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, Y1^4, Y3 * Y2^-1 * Y1^2, Y2 * Y1^-2 * Y3^-1, Y2^-2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^-1 * Y1^-2 * Y3, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1^-1)^3, Y2^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 4, 52, 16, 64)(6, 54, 17, 65, 7, 55, 18, 66)(9, 57, 19, 67, 10, 58, 22, 70)(11, 59, 23, 71, 12, 60, 24, 72)(14, 62, 27, 75, 15, 63, 28, 76)(20, 68, 33, 81, 21, 69, 34, 82)(25, 73, 37, 85, 26, 74, 38, 86)(29, 77, 40, 88, 30, 78, 39, 87)(31, 79, 41, 89, 32, 80, 42, 90)(35, 83, 44, 92, 36, 84, 43, 91)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 110, 158, 103, 151, 104, 152, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 116, 164, 108, 156, 101, 149, 106, 154, 117, 165, 107, 155)(109, 157, 120, 168, 132, 180, 122, 170, 112, 160, 119, 167, 131, 179, 121, 169)(113, 161, 125, 173, 128, 176, 118, 166, 114, 162, 126, 174, 127, 175, 115, 163)(123, 171, 134, 182, 142, 190, 136, 184, 124, 172, 133, 181, 141, 189, 135, 183)(129, 177, 138, 186, 144, 192, 140, 188, 130, 178, 137, 185, 143, 191, 139, 187) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 105)(6, 104)(7, 97)(8, 99)(9, 117)(10, 116)(11, 101)(12, 98)(13, 119)(14, 102)(15, 103)(16, 120)(17, 126)(18, 125)(19, 114)(20, 107)(21, 108)(22, 113)(23, 132)(24, 131)(25, 112)(26, 109)(27, 133)(28, 134)(29, 127)(30, 128)(31, 118)(32, 115)(33, 137)(34, 138)(35, 122)(36, 121)(37, 142)(38, 141)(39, 124)(40, 123)(41, 144)(42, 143)(43, 130)(44, 129)(45, 136)(46, 135)(47, 140)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.681 Graph:: bipartite v = 18 e = 96 f = 40 degree seq :: [ 8^12, 16^6 ] E20.685 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y3^4 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 18, 66)(16, 64, 17, 65)(19, 67, 21, 69)(20, 68, 24, 72)(22, 70, 23, 71)(25, 73, 28, 76)(26, 74, 27, 75)(29, 77, 30, 78)(31, 79, 34, 82)(32, 80, 33, 81)(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, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 115, 163, 110, 158, 117, 165)(106, 154, 118, 166, 111, 159, 119, 167)(108, 156, 122, 170, 114, 162, 123, 171)(116, 164, 128, 176, 120, 168, 129, 177)(121, 169, 133, 181, 124, 172, 134, 182)(125, 173, 136, 184, 126, 174, 135, 183)(127, 175, 137, 185, 130, 178, 138, 186)(131, 179, 140, 188, 132, 180, 139, 187)(141, 189, 144, 192, 142, 190, 143, 191) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 114)(8, 98)(9, 116)(10, 99)(11, 119)(12, 104)(13, 118)(14, 120)(15, 101)(16, 125)(17, 126)(18, 102)(19, 112)(20, 111)(21, 113)(22, 131)(23, 132)(24, 106)(25, 107)(26, 134)(27, 133)(28, 109)(29, 130)(30, 127)(31, 115)(32, 138)(33, 137)(34, 117)(35, 121)(36, 124)(37, 141)(38, 142)(39, 122)(40, 123)(41, 143)(42, 144)(43, 128)(44, 129)(45, 135)(46, 136)(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) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E20.686 Graph:: bipartite v = 36 e = 96 f = 22 degree seq :: [ 4^24, 8^12 ] E20.686 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1, Y1^3, Y2^-1 * Y1^-1 * Y2^-1 * Y3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, R * Y2^-1 * R * Y1^-1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2^-2 ] 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, 19, 67)(8, 56, 23, 71, 21, 69)(10, 58, 26, 74, 16, 64)(12, 60, 30, 78, 32, 80)(13, 61, 25, 73, 15, 63)(17, 65, 22, 70, 28, 76)(20, 68, 33, 81, 31, 79)(24, 72, 37, 85, 40, 88)(27, 75, 38, 86, 39, 87)(29, 77, 41, 89, 34, 82)(35, 83, 36, 84, 42, 90)(43, 91, 47, 95, 44, 92)(45, 93, 46, 94, 48, 96)(97, 145, 99, 147, 108, 156, 119, 167, 105, 153, 121, 169, 116, 164, 102, 150)(98, 146, 104, 152, 120, 168, 118, 166, 103, 151, 115, 163, 123, 171, 106, 154)(100, 148, 112, 160, 132, 180, 111, 159, 101, 149, 113, 161, 125, 173, 107, 155)(109, 157, 130, 178, 142, 190, 129, 177, 110, 158, 131, 179, 139, 187, 126, 174)(114, 162, 128, 176, 141, 189, 134, 182, 117, 165, 127, 175, 140, 188, 133, 181)(122, 170, 136, 184, 144, 192, 138, 186, 124, 172, 135, 183, 143, 191, 137, 185) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 104)(7, 97)(8, 114)(9, 101)(10, 113)(11, 121)(12, 127)(13, 107)(14, 111)(15, 99)(16, 124)(17, 122)(18, 119)(19, 117)(20, 128)(21, 102)(22, 112)(23, 115)(24, 135)(25, 110)(26, 118)(27, 136)(28, 106)(29, 131)(30, 116)(31, 126)(32, 129)(33, 108)(34, 138)(35, 137)(36, 130)(37, 123)(38, 120)(39, 133)(40, 134)(41, 132)(42, 125)(43, 141)(44, 144)(45, 143)(46, 140)(47, 142)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E20.685 Graph:: bipartite v = 22 e = 96 f = 36 degree seq :: [ 6^16, 16^6 ] E20.687 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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 :: [ Y1^2, R^2, Y2^3, Y3^3, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3, Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y2^-1 * Y3 * Y1 * Y3^-1, (Y3^-1 * Y2)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 13, 61)(5, 53, 7, 55)(6, 54, 18, 66)(8, 56, 23, 71)(10, 58, 28, 76)(11, 59, 30, 78)(12, 60, 25, 73)(14, 62, 34, 82)(15, 63, 22, 70)(16, 64, 33, 81)(17, 65, 39, 87)(19, 67, 42, 90)(20, 68, 21, 69)(24, 72, 32, 80)(26, 74, 40, 88)(27, 75, 38, 86)(29, 77, 31, 79)(35, 83, 46, 94)(36, 84, 41, 89)(37, 85, 44, 92)(43, 91, 45, 93)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 110, 158, 111, 159)(102, 150, 115, 163, 116, 164)(104, 152, 120, 168, 121, 169)(106, 154, 125, 173, 126, 174)(107, 155, 127, 175, 124, 172)(108, 156, 128, 176, 119, 167)(109, 157, 118, 166, 130, 178)(112, 160, 131, 179, 134, 182)(113, 161, 133, 181, 136, 184)(114, 162, 117, 165, 138, 186)(122, 170, 140, 188, 135, 183)(123, 171, 142, 190, 129, 177)(132, 180, 139, 187, 143, 191)(137, 185, 144, 192, 141, 189) L = (1, 100)(2, 104)(3, 107)(4, 102)(5, 112)(6, 97)(7, 117)(8, 106)(9, 122)(10, 98)(11, 108)(12, 99)(13, 129)(14, 127)(15, 132)(16, 113)(17, 101)(18, 137)(19, 124)(20, 119)(21, 118)(22, 103)(23, 136)(24, 138)(25, 141)(26, 123)(27, 105)(28, 139)(29, 114)(30, 109)(31, 131)(32, 134)(33, 126)(34, 135)(35, 110)(36, 133)(37, 111)(38, 143)(39, 144)(40, 116)(41, 125)(42, 140)(43, 115)(44, 120)(45, 142)(46, 121)(47, 128)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E20.693 Graph:: simple bipartite v = 40 e = 96 f = 18 degree seq :: [ 4^24, 6^16 ] E20.688 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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 :: [ Y1^2, R^2, Y2^3, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, R * Y2 * Y3 * R * Y2^-1, Y3^-1 * Y2 * Y3^2 * Y2, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2, Y3^6, Y3^-2 * Y2 * Y1 * Y3^-1 * Y1, (Y2 * Y3 * Y1)^2, (Y2^-1 * Y3^-1)^3, (Y2 * Y3^-1 * Y1)^2, Y3^6, Y2 * Y3^-2 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 13, 61)(5, 53, 7, 55)(6, 54, 19, 67)(8, 56, 25, 73)(10, 58, 31, 79)(11, 59, 33, 81)(12, 60, 28, 76)(14, 62, 34, 82)(15, 63, 30, 78)(16, 64, 24, 72)(17, 65, 43, 91)(18, 66, 27, 75)(20, 68, 37, 85)(21, 69, 23, 71)(22, 70, 26, 74)(29, 77, 39, 87)(32, 80, 35, 83)(36, 84, 38, 86)(40, 88, 47, 95)(41, 89, 46, 94)(42, 90, 44, 92)(45, 93, 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, 122, 170, 124, 172)(106, 154, 128, 176, 129, 177)(107, 155, 131, 179, 127, 175)(108, 156, 118, 166, 121, 169)(109, 157, 120, 168, 130, 178)(111, 159, 113, 161, 137, 185)(114, 162, 132, 180, 135, 183)(115, 163, 119, 167, 133, 181)(123, 171, 125, 173, 134, 182)(126, 174, 142, 190, 139, 187)(136, 184, 138, 186, 141, 189)(140, 188, 143, 191, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 111)(5, 113)(6, 97)(7, 119)(8, 123)(9, 125)(10, 98)(11, 112)(12, 99)(13, 133)(14, 135)(15, 136)(16, 138)(17, 127)(18, 101)(19, 140)(20, 114)(21, 110)(22, 102)(23, 124)(24, 103)(25, 131)(26, 139)(27, 143)(28, 144)(29, 115)(30, 105)(31, 141)(32, 126)(33, 122)(34, 106)(35, 117)(36, 108)(37, 129)(38, 109)(39, 137)(40, 118)(41, 121)(42, 132)(43, 134)(44, 128)(45, 116)(46, 120)(47, 130)(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, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E20.694 Graph:: simple bipartite v = 40 e = 96 f = 18 degree seq :: [ 4^24, 6^16 ] E20.689 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, Y1^3, (Y1^-1 * Y3^-1)^2, (Y1 * Y3)^2, (R * Y1)^2, Y2^4, (R * Y3)^2, (Y2 * R)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 16, 64, 17, 65)(6, 54, 21, 69, 22, 70)(7, 55, 24, 72, 9, 57)(8, 56, 25, 73, 28, 76)(10, 58, 29, 77, 30, 78)(11, 59, 32, 80, 19, 67)(13, 61, 26, 74, 36, 84)(14, 62, 37, 85, 31, 79)(18, 66, 41, 89, 34, 82)(20, 68, 43, 91, 33, 81)(23, 71, 42, 90, 44, 92)(27, 75, 46, 94, 39, 87)(35, 83, 47, 95, 38, 86)(40, 88, 48, 96, 45, 93)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 122, 170, 106, 154)(100, 148, 110, 158, 119, 167, 103, 151)(101, 149, 114, 162, 132, 180, 116, 164)(105, 153, 123, 171, 127, 175, 107, 155)(108, 156, 129, 177, 117, 165, 130, 178)(111, 159, 121, 169, 118, 166, 125, 173)(112, 160, 115, 163, 138, 186, 135, 183)(113, 161, 136, 184, 140, 188, 131, 179)(120, 168, 141, 189, 133, 181, 134, 182)(124, 172, 137, 185, 126, 174, 139, 187)(128, 176, 144, 192, 142, 190, 143, 191) L = (1, 100)(2, 105)(3, 110)(4, 99)(5, 115)(6, 103)(7, 97)(8, 123)(9, 104)(10, 107)(11, 98)(12, 113)(13, 119)(14, 109)(15, 134)(16, 101)(17, 129)(18, 138)(19, 114)(20, 112)(21, 140)(22, 141)(23, 102)(24, 118)(25, 120)(26, 127)(27, 122)(28, 143)(29, 133)(30, 144)(31, 106)(32, 126)(33, 136)(34, 131)(35, 108)(36, 135)(37, 111)(38, 121)(39, 116)(40, 117)(41, 128)(42, 132)(43, 142)(44, 130)(45, 125)(46, 124)(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, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.691 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 6^16, 8^12 ] E20.690 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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 * Y2 * Y3, Y1^3, (Y1^-1 * Y3^-1)^2, (R * Y2)^2, (R * Y3)^2, Y2^4, (Y3 * Y1)^2, (R * Y1)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (Y1 * Y2^-1)^3, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 14, 62)(4, 52, 16, 64, 17, 65)(6, 54, 22, 70, 23, 71)(7, 55, 24, 72, 9, 57)(8, 56, 25, 73, 27, 75)(10, 58, 30, 78, 31, 79)(11, 59, 32, 80, 20, 68)(13, 61, 26, 74, 37, 85)(15, 63, 39, 87, 34, 82)(18, 66, 42, 90, 28, 76)(19, 67, 43, 91, 33, 81)(21, 69, 44, 92, 35, 83)(29, 77, 47, 95, 40, 88)(36, 84, 46, 94, 38, 86)(41, 89, 48, 96, 45, 93)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 122, 170, 106, 154)(100, 148, 103, 151, 111, 159, 114, 162)(101, 149, 115, 163, 133, 181, 117, 165)(105, 153, 107, 155, 124, 172, 125, 173)(108, 156, 129, 177, 118, 166, 131, 179)(110, 158, 126, 174, 119, 167, 121, 169)(112, 160, 136, 184, 135, 183, 116, 164)(113, 161, 137, 185, 130, 178, 132, 180)(120, 168, 141, 189, 138, 186, 134, 182)(123, 171, 140, 188, 127, 175, 139, 187)(128, 176, 144, 192, 143, 191, 142, 190) L = (1, 100)(2, 105)(3, 103)(4, 102)(5, 116)(6, 114)(7, 97)(8, 107)(9, 106)(10, 125)(11, 98)(12, 130)(13, 111)(14, 134)(15, 99)(16, 101)(17, 129)(18, 109)(19, 112)(20, 117)(21, 135)(22, 113)(23, 141)(24, 110)(25, 138)(26, 124)(27, 142)(28, 104)(29, 122)(30, 120)(31, 144)(32, 123)(33, 132)(34, 131)(35, 137)(36, 108)(37, 136)(38, 121)(39, 133)(40, 115)(41, 118)(42, 119)(43, 143)(44, 128)(45, 126)(46, 139)(47, 127)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.692 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 6^16, 8^12 ] E20.691 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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 :: [ Y2^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y2 * Y1^-1)^3, Y1^8, (Y3^-1 * Y1^-1)^4, Y1^-1 * Y2 * Y1^4 * Y2 * Y1^-3, (Y2 * Y1^2 * Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53, 11, 59, 21, 69, 20, 68, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 27, 75, 36, 84, 31, 79, 17, 65, 8, 56)(6, 54, 13, 61, 25, 73, 41, 89, 35, 83, 44, 92, 26, 74, 14, 62)(9, 57, 18, 66, 32, 80, 38, 86, 22, 70, 37, 85, 29, 77, 16, 64)(12, 60, 23, 71, 39, 87, 33, 81, 19, 67, 34, 82, 40, 88, 24, 72)(28, 76, 45, 93, 48, 96, 42, 90, 30, 78, 46, 94, 47, 95, 43, 91)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 108, 156)(103, 151, 112, 160)(104, 152, 109, 157)(106, 154, 115, 163)(107, 155, 118, 166)(110, 158, 119, 167)(111, 159, 124, 172)(113, 161, 126, 174)(114, 162, 129, 177)(116, 164, 131, 179)(117, 165, 132, 180)(120, 168, 133, 181)(121, 169, 138, 186)(122, 170, 139, 187)(123, 171, 140, 188)(125, 173, 141, 189)(127, 175, 134, 182)(128, 176, 142, 190)(130, 178, 137, 185)(135, 183, 143, 191)(136, 184, 144, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 114)(10, 100)(11, 117)(12, 119)(13, 121)(14, 102)(15, 123)(16, 105)(17, 104)(18, 128)(19, 130)(20, 106)(21, 116)(22, 133)(23, 135)(24, 108)(25, 137)(26, 110)(27, 132)(28, 141)(29, 112)(30, 142)(31, 113)(32, 134)(33, 115)(34, 136)(35, 140)(36, 127)(37, 125)(38, 118)(39, 129)(40, 120)(41, 131)(42, 126)(43, 124)(44, 122)(45, 144)(46, 143)(47, 139)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.689 Graph:: bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.692 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^2, Y3^3 * Y1, (Y3^-1, Y1), Y3^-1 * Y1^-3, (R * Y1)^2, (Y1 * Y3^-1)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, R * Y3^-1 * Y2 * Y3 * Y2 * R * Y2 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 6, 54, 10, 58, 4, 52, 9, 57, 5, 53)(3, 51, 11, 59, 25, 73, 14, 62, 24, 72, 12, 60, 27, 75, 13, 61)(8, 56, 19, 67, 35, 83, 22, 70, 15, 63, 20, 68, 36, 84, 21, 69)(16, 64, 29, 77, 38, 86, 26, 74, 17, 65, 30, 78, 39, 87, 28, 76)(18, 66, 31, 79, 41, 89, 34, 82, 23, 71, 32, 80, 42, 90, 33, 81)(37, 85, 45, 93, 48, 96, 43, 91, 40, 88, 46, 94, 47, 95, 44, 92)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 112, 160)(102, 150, 113, 161)(103, 151, 114, 162)(105, 153, 119, 167)(106, 154, 120, 168)(107, 155, 122, 170)(108, 156, 124, 172)(109, 157, 116, 164)(110, 158, 115, 163)(117, 165, 128, 176)(118, 166, 127, 175)(121, 169, 133, 181)(123, 171, 136, 184)(125, 173, 129, 177)(126, 174, 130, 178)(131, 179, 139, 187)(132, 180, 140, 188)(134, 182, 142, 190)(135, 183, 141, 189)(137, 185, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 101)(8, 116)(9, 102)(10, 98)(11, 123)(12, 121)(13, 120)(14, 99)(15, 115)(16, 126)(17, 125)(18, 128)(19, 132)(20, 131)(21, 111)(22, 104)(23, 127)(24, 107)(25, 109)(26, 112)(27, 110)(28, 113)(29, 135)(30, 134)(31, 138)(32, 137)(33, 119)(34, 114)(35, 117)(36, 118)(37, 142)(38, 124)(39, 122)(40, 141)(41, 129)(42, 130)(43, 133)(44, 136)(45, 143)(46, 144)(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) :: { ( 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 E20.690 Graph:: bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.693 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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, Y3^3, Y3^3, Y1^4, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3, (Y3 * Y2^-1 * Y1^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^-1 * Y2^-4 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-1, Y3 * Y1 * Y2^2 * Y3^-1 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 11, 59)(4, 52, 17, 65, 30, 78, 19, 67)(6, 54, 20, 68, 31, 79, 9, 57)(7, 55, 26, 74, 32, 80, 27, 75)(10, 58, 36, 84, 21, 69, 38, 86)(12, 60, 40, 88, 22, 70, 41, 89)(14, 62, 39, 87, 24, 72, 33, 81)(15, 63, 23, 71, 47, 95, 42, 90)(16, 64, 45, 93, 48, 96, 35, 83)(18, 66, 37, 85, 44, 92, 25, 73)(28, 76, 46, 94, 43, 91, 34, 82)(97, 145, 99, 147, 110, 158, 127, 175, 104, 152, 125, 173, 120, 168, 102, 150)(98, 146, 105, 153, 129, 177, 109, 157, 101, 149, 116, 164, 135, 183, 107, 155)(100, 148, 114, 162, 132, 180, 144, 192, 126, 174, 140, 188, 134, 182, 112, 160)(103, 151, 119, 167, 118, 166, 139, 187, 128, 176, 138, 186, 108, 156, 124, 172)(106, 154, 133, 181, 115, 163, 141, 189, 117, 165, 121, 169, 113, 161, 131, 179)(111, 159, 122, 170, 130, 178, 136, 184, 143, 191, 123, 171, 142, 190, 137, 185) L = (1, 100)(2, 106)(3, 111)(4, 103)(5, 117)(6, 119)(7, 97)(8, 126)(9, 130)(10, 108)(11, 124)(12, 98)(13, 139)(14, 115)(15, 112)(16, 99)(17, 136)(18, 107)(19, 137)(20, 142)(21, 118)(22, 101)(23, 121)(24, 113)(25, 102)(26, 129)(27, 135)(28, 114)(29, 143)(30, 128)(31, 138)(32, 104)(33, 134)(34, 131)(35, 105)(36, 123)(37, 127)(38, 122)(39, 132)(40, 120)(41, 110)(42, 133)(43, 140)(44, 109)(45, 116)(46, 141)(47, 144)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E20.687 Graph:: bipartite v = 18 e = 96 f = 40 degree seq :: [ 8^12, 16^6 ] E20.694 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, (Y2 * Y3^-1)^2, (Y2 * Y1^-1)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y1^-1 * Y3^-3 * Y1^-1, Y1 * Y3^-1 * Y2^-2 * Y3, Y3^2 * Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y1^-1 * Y2^-4 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 31, 79, 11, 59)(4, 52, 17, 65, 30, 78, 20, 68)(6, 54, 21, 69, 32, 80, 9, 57)(7, 55, 27, 75, 19, 67, 28, 76)(10, 58, 36, 84, 22, 70, 37, 85)(12, 60, 41, 89, 23, 71, 42, 90)(14, 62, 39, 87, 25, 73, 33, 81)(15, 63, 43, 91, 46, 94, 24, 72)(16, 64, 45, 93, 44, 92, 35, 83)(18, 66, 26, 74, 40, 88, 47, 95)(29, 77, 48, 96, 38, 86, 34, 82)(97, 145, 99, 147, 110, 158, 128, 176, 104, 152, 127, 175, 121, 169, 102, 150)(98, 146, 105, 153, 129, 177, 109, 157, 101, 149, 117, 165, 135, 183, 107, 155)(100, 148, 114, 162, 132, 180, 140, 188, 126, 174, 136, 184, 133, 181, 112, 160)(103, 151, 120, 168, 108, 156, 134, 182, 115, 163, 139, 187, 119, 167, 125, 173)(106, 154, 122, 170, 116, 164, 141, 189, 118, 166, 143, 191, 113, 161, 131, 179)(111, 159, 124, 172, 144, 192, 137, 185, 142, 190, 123, 171, 130, 178, 138, 186) L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 118)(6, 120)(7, 97)(8, 126)(9, 130)(10, 119)(11, 134)(12, 98)(13, 125)(14, 113)(15, 140)(16, 99)(17, 137)(18, 109)(19, 104)(20, 138)(21, 144)(22, 108)(23, 101)(24, 143)(25, 116)(26, 102)(27, 129)(28, 135)(29, 136)(30, 103)(31, 142)(32, 139)(33, 132)(34, 141)(35, 105)(36, 124)(37, 123)(38, 114)(39, 133)(40, 107)(41, 121)(42, 110)(43, 122)(44, 127)(45, 117)(46, 112)(47, 128)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.688 Graph:: bipartite v = 18 e = 96 f = 40 degree seq :: [ 8^12, 16^6 ] E20.695 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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 :: [ Y1^2, R^2, Y3^3, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1 * Y1, Y2 * Y1 * Y3 * Y2^-1 * Y3^-1 * Y1, (Y2^-1 * Y1 * Y3^-1)^2, (Y2^-2 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1 * Y3^-1)^2, (Y2^-1 * Y1 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 21, 69)(7, 55, 24, 72)(8, 56, 14, 62)(9, 57, 28, 76)(10, 58, 17, 65)(12, 60, 25, 73)(13, 61, 32, 80)(16, 64, 43, 91)(19, 67, 31, 79)(20, 68, 44, 92)(22, 70, 29, 77)(23, 71, 26, 74)(27, 75, 37, 85)(30, 78, 36, 84)(33, 81, 45, 93)(34, 82, 46, 94)(35, 83, 39, 87)(38, 86, 42, 90)(40, 88, 47, 95)(41, 89, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 121, 169, 105, 153)(100, 148, 112, 160, 132, 180, 113, 161)(102, 150, 118, 166, 133, 181, 119, 167)(104, 152, 123, 171, 140, 188, 117, 165)(106, 154, 127, 175, 139, 187, 128, 176)(107, 155, 129, 177, 114, 162, 130, 178)(109, 157, 134, 182, 115, 163, 135, 183)(110, 158, 136, 184, 116, 164, 137, 185)(111, 159, 138, 186, 126, 174, 131, 179)(120, 168, 142, 190, 124, 172, 141, 189)(122, 170, 143, 191, 125, 173, 144, 192) L = (1, 100)(2, 104)(3, 109)(4, 102)(5, 115)(6, 97)(7, 122)(8, 106)(9, 125)(10, 98)(11, 123)(12, 132)(13, 110)(14, 99)(15, 103)(16, 137)(17, 136)(18, 117)(19, 116)(20, 101)(21, 138)(22, 141)(23, 142)(24, 112)(25, 140)(26, 111)(27, 131)(28, 113)(29, 126)(30, 105)(31, 130)(32, 129)(33, 144)(34, 143)(35, 107)(36, 133)(37, 108)(38, 118)(39, 119)(40, 124)(41, 120)(42, 114)(43, 121)(44, 139)(45, 134)(46, 135)(47, 127)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E20.698 Graph:: simple bipartite v = 36 e = 96 f = 22 degree seq :: [ 4^24, 8^12 ] E20.696 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 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 :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-3 * Y2^-1, Y1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1, Y1 * Y3 * Y1 * Y3 * Y2, (Y2^-1 * Y3 * Y1)^2, (Y1 * Y2 * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1, Y3^-2 * Y1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 19, 67)(6, 54, 22, 70)(7, 55, 26, 74)(8, 56, 21, 69)(9, 57, 32, 80)(10, 58, 16, 64)(12, 60, 27, 75)(13, 61, 35, 83)(14, 62, 36, 84)(17, 65, 31, 79)(18, 66, 30, 78)(20, 68, 34, 82)(23, 71, 33, 81)(24, 72, 28, 76)(25, 73, 29, 77)(37, 85, 46, 94)(38, 86, 45, 93)(39, 87, 40, 88)(41, 89, 44, 92)(42, 90, 47, 95)(43, 91, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 123, 171, 105, 153)(100, 148, 112, 160, 121, 169, 114, 162)(102, 150, 119, 167, 113, 161, 120, 168)(104, 152, 118, 166, 132, 180, 127, 175)(106, 154, 130, 178, 126, 174, 131, 179)(107, 155, 133, 181, 115, 163, 134, 182)(109, 157, 136, 184, 116, 164, 137, 185)(110, 158, 138, 186, 117, 165, 139, 187)(111, 159, 140, 188, 125, 173, 135, 183)(122, 170, 141, 189, 128, 176, 142, 190)(124, 172, 143, 191, 129, 177, 144, 192) L = (1, 100)(2, 104)(3, 109)(4, 113)(5, 116)(6, 97)(7, 124)(8, 126)(9, 129)(10, 98)(11, 118)(12, 121)(13, 117)(14, 99)(15, 105)(16, 139)(17, 108)(18, 138)(19, 127)(20, 110)(21, 101)(22, 140)(23, 141)(24, 142)(25, 102)(26, 112)(27, 132)(28, 111)(29, 103)(30, 123)(31, 135)(32, 114)(33, 125)(34, 133)(35, 134)(36, 106)(37, 144)(38, 143)(39, 107)(40, 119)(41, 120)(42, 122)(43, 128)(44, 115)(45, 137)(46, 136)(47, 130)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E20.697 Graph:: simple bipartite v = 36 e = 96 f = 22 degree seq :: [ 4^24, 8^12 ] E20.697 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3 * Y2^2 * Y3, Y2^-2 * Y3 * Y2^-1, (Y3^-1, Y2^-1), Y3^3 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y2 * Y3 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 10, 58)(4, 52, 16, 64, 17, 65)(6, 54, 18, 66, 21, 69)(7, 55, 22, 70, 9, 57)(8, 56, 23, 71, 20, 68)(11, 59, 27, 75, 19, 67)(13, 61, 32, 80, 30, 78)(14, 62, 25, 73, 33, 81)(15, 63, 34, 82, 29, 77)(24, 72, 31, 79, 41, 89)(26, 74, 28, 76, 40, 88)(35, 83, 39, 87, 38, 86)(36, 84, 42, 90, 37, 85)(43, 91, 46, 94, 47, 95)(44, 92, 45, 93, 48, 96)(97, 145, 99, 147, 109, 157, 100, 148, 110, 158, 103, 151, 111, 159, 102, 150)(98, 146, 104, 152, 120, 168, 105, 153, 121, 169, 107, 155, 122, 170, 106, 154)(101, 149, 114, 162, 132, 180, 115, 163, 129, 177, 112, 160, 131, 179, 116, 164)(108, 156, 124, 172, 139, 187, 125, 173, 118, 166, 127, 175, 140, 188, 126, 174)(113, 161, 128, 176, 141, 189, 133, 181, 117, 165, 130, 178, 142, 190, 134, 182)(119, 167, 135, 183, 143, 191, 136, 184, 123, 171, 138, 186, 144, 192, 137, 185) L = (1, 100)(2, 105)(3, 110)(4, 111)(5, 115)(6, 109)(7, 97)(8, 121)(9, 122)(10, 120)(11, 98)(12, 125)(13, 103)(14, 102)(15, 99)(16, 101)(17, 133)(18, 129)(19, 131)(20, 132)(21, 134)(22, 126)(23, 136)(24, 107)(25, 106)(26, 104)(27, 137)(28, 118)(29, 140)(30, 139)(31, 108)(32, 117)(33, 116)(34, 113)(35, 114)(36, 112)(37, 142)(38, 141)(39, 123)(40, 144)(41, 143)(42, 119)(43, 127)(44, 124)(45, 130)(46, 128)(47, 138)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.696 Graph:: bipartite v = 22 e = 96 f = 36 degree seq :: [ 6^16, 16^6 ] E20.698 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 4, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y3^2 * Y1^-1 * Y2^-3 * Y1^-1 * Y2^-1, Y2^8, Y3 * Y1^-1 * Y3^2 * Y2^-1 * Y1^-1 * Y2^-2, (Y3 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 7, 55)(4, 52, 10, 58, 12, 60)(6, 54, 14, 62, 13, 61)(9, 57, 19, 67, 18, 66)(11, 59, 22, 70, 24, 72)(15, 63, 29, 77, 28, 76)(16, 64, 17, 65, 32, 80)(20, 68, 37, 85, 36, 84)(21, 69, 39, 87, 25, 73)(23, 71, 42, 90, 30, 78)(26, 74, 27, 75, 43, 91)(31, 79, 47, 95, 40, 88)(33, 81, 41, 89, 44, 92)(34, 82, 35, 83, 45, 93)(38, 86, 46, 94, 48, 96)(97, 145, 99, 147, 105, 153, 116, 164, 134, 182, 119, 167, 107, 155, 100, 148)(98, 146, 102, 150, 111, 159, 126, 174, 142, 190, 127, 175, 112, 160, 103, 151)(101, 149, 106, 154, 117, 165, 136, 184, 144, 192, 133, 181, 122, 170, 109, 157)(104, 152, 113, 161, 129, 177, 120, 168, 138, 186, 125, 173, 130, 178, 114, 162)(108, 156, 118, 166, 137, 185, 139, 187, 132, 180, 115, 163, 131, 179, 121, 169)(110, 158, 123, 171, 140, 188, 128, 176, 143, 191, 135, 183, 141, 189, 124, 172) L = (1, 100)(2, 103)(3, 97)(4, 107)(5, 109)(6, 98)(7, 112)(8, 114)(9, 99)(10, 101)(11, 119)(12, 121)(13, 122)(14, 124)(15, 102)(16, 127)(17, 104)(18, 130)(19, 132)(20, 105)(21, 106)(22, 108)(23, 134)(24, 129)(25, 131)(26, 133)(27, 110)(28, 141)(29, 138)(30, 111)(31, 142)(32, 140)(33, 113)(34, 125)(35, 115)(36, 139)(37, 144)(38, 116)(39, 143)(40, 117)(41, 118)(42, 120)(43, 137)(44, 123)(45, 135)(46, 126)(47, 128)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.695 Graph:: bipartite v = 22 e = 96 f = 36 degree seq :: [ 6^16, 16^6 ] E20.699 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 12}) Quotient :: halfedge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y2)^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, (Y1^3 * Y2)^2, Y3 * Y1^-2 * Y2 * Y3 * Y1^-3 * Y2, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 62, 14, 74, 26, 84, 36, 93, 45, 88, 40, 89, 41, 73, 25, 61, 13, 53, 5, 49)(3, 57, 9, 67, 19, 81, 33, 80, 32, 72, 24, 87, 39, 94, 46, 90, 42, 75, 27, 63, 15, 55, 7, 51)(4, 59, 11, 70, 22, 85, 37, 95, 47, 92, 44, 79, 31, 69, 21, 83, 35, 76, 28, 64, 16, 56, 8, 52)(10, 65, 17, 77, 29, 91, 43, 96, 48, 86, 38, 71, 23, 60, 12, 66, 18, 78, 30, 82, 34, 68, 20, 58) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 42)(28, 34)(29, 44)(32, 41)(36, 46)(37, 48)(39, 45)(43, 47)(49, 52)(50, 56)(51, 58)(53, 59)(54, 64)(55, 65)(57, 68)(60, 72)(61, 70)(62, 76)(63, 77)(66, 80)(67, 82)(69, 84)(71, 87)(73, 85)(74, 83)(75, 91)(78, 81)(79, 93)(86, 94)(88, 92)(89, 95)(90, 96) local type(s) :: { ( 16^24 ) } Outer automorphisms :: reflexible Dual of E20.700 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 48 f = 6 degree seq :: [ 24^4 ] E20.700 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 8, 12}) Quotient :: halfedge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y1^-1 * Y3 * Y2 * Y3)^2, Y1^8, Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-2 * Y3, Y1^-2 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 62, 14, 74, 26, 73, 25, 61, 13, 53, 5, 49)(3, 57, 9, 67, 19, 81, 33, 89, 41, 75, 27, 63, 15, 55, 7, 51)(4, 59, 11, 70, 22, 85, 37, 90, 42, 76, 28, 64, 16, 56, 8, 52)(10, 65, 17, 77, 29, 88, 40, 93, 45, 94, 46, 82, 34, 68, 20, 58)(12, 66, 18, 78, 30, 91, 43, 96, 48, 84, 36, 86, 38, 71, 23, 60)(21, 83, 35, 95, 47, 92, 44, 80, 32, 72, 24, 87, 39, 79, 31, 69) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 41)(28, 43)(29, 39)(32, 45)(34, 47)(36, 37)(42, 48)(44, 46)(49, 52)(50, 56)(51, 58)(53, 59)(54, 64)(55, 65)(57, 68)(60, 72)(61, 70)(62, 76)(63, 77)(66, 80)(67, 82)(69, 84)(71, 87)(73, 85)(74, 90)(75, 88)(78, 92)(79, 86)(81, 94)(83, 96)(89, 93)(91, 95) local type(s) :: { ( 24^16 ) } Outer automorphisms :: reflexible Dual of E20.699 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 48 f = 4 degree seq :: [ 16^6 ] E20.701 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 12}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^8, Y1 * Y2 * Y1 * Y3^3 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^12 ] Map:: R = (1, 49, 4, 52, 12, 60, 24, 72, 40, 88, 25, 73, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 31, 79, 44, 92, 32, 80, 18, 66, 8, 56)(3, 51, 10, 58, 22, 70, 38, 86, 48, 96, 39, 87, 23, 71, 11, 59)(6, 54, 15, 63, 29, 77, 43, 91, 45, 93, 33, 81, 30, 78, 16, 64)(9, 57, 20, 68, 36, 84, 26, 74, 41, 89, 47, 95, 37, 85, 21, 69)(14, 62, 27, 75, 35, 83, 19, 67, 34, 82, 46, 94, 42, 90, 28, 76)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 117)(107, 116)(108, 114)(109, 113)(111, 124)(112, 123)(115, 129)(118, 133)(119, 132)(120, 128)(121, 127)(122, 135)(125, 138)(126, 131)(130, 141)(134, 143)(136, 140)(137, 144)(139, 142)(145, 147)(146, 150)(148, 155)(149, 154)(151, 160)(152, 159)(153, 163)(156, 167)(157, 166)(158, 170)(161, 174)(162, 173)(164, 179)(165, 178)(168, 183)(169, 182)(171, 180)(172, 185)(175, 177)(176, 187)(181, 190)(184, 192)(186, 191)(188, 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) :: { ( 48, 48 ), ( 48^16 ) } Outer automorphisms :: reflexible Dual of E20.704 Graph:: simple bipartite v = 54 e = 96 f = 4 degree seq :: [ 2^48, 16^6 ] E20.702 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 8, 12}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y2 * Y3 * Y2 * Y1 * Y3^-1, Y3^5 * Y1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y1 * Y2)^8 ] Map:: R = (1, 49, 4, 52, 12, 60, 24, 72, 40, 88, 33, 81, 43, 91, 26, 74, 41, 89, 25, 73, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 31, 79, 46, 94, 42, 90, 35, 83, 19, 67, 34, 82, 32, 80, 18, 66, 8, 56)(3, 51, 10, 58, 22, 70, 38, 86, 28, 76, 14, 62, 27, 75, 44, 92, 48, 96, 39, 87, 23, 71, 11, 59)(6, 54, 15, 63, 29, 77, 37, 85, 21, 69, 9, 57, 20, 68, 36, 84, 47, 95, 45, 93, 30, 78, 16, 64)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 117)(107, 116)(108, 114)(109, 113)(111, 124)(112, 123)(115, 129)(118, 133)(119, 132)(120, 128)(121, 127)(122, 138)(125, 134)(126, 140)(130, 136)(131, 139)(135, 143)(137, 142)(141, 144)(145, 147)(146, 150)(148, 155)(149, 154)(151, 160)(152, 159)(153, 163)(156, 167)(157, 166)(158, 170)(161, 174)(162, 173)(164, 179)(165, 178)(168, 183)(169, 182)(171, 187)(172, 185)(175, 189)(176, 181)(177, 188)(180, 186)(184, 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) :: { ( 32, 32 ), ( 32^24 ) } Outer automorphisms :: reflexible Dual of E20.703 Graph:: simple bipartite v = 52 e = 96 f = 6 degree seq :: [ 2^48, 24^4 ] E20.703 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 12}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^8, Y1 * Y2 * Y1 * Y3^3 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^12 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 24, 72, 120, 168, 40, 88, 136, 184, 25, 73, 121, 169, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 17, 65, 113, 161, 31, 79, 127, 175, 44, 92, 140, 188, 32, 80, 128, 176, 18, 66, 114, 162, 8, 56, 104, 152)(3, 51, 99, 147, 10, 58, 106, 154, 22, 70, 118, 166, 38, 86, 134, 182, 48, 96, 144, 192, 39, 87, 135, 183, 23, 71, 119, 167, 11, 59, 107, 155)(6, 54, 102, 150, 15, 63, 111, 159, 29, 77, 125, 173, 43, 91, 139, 187, 45, 93, 141, 189, 33, 81, 129, 177, 30, 78, 126, 174, 16, 64, 112, 160)(9, 57, 105, 153, 20, 68, 116, 164, 36, 84, 132, 180, 26, 74, 122, 170, 41, 89, 137, 185, 47, 95, 143, 191, 37, 85, 133, 181, 21, 69, 117, 165)(14, 62, 110, 158, 27, 75, 123, 171, 35, 83, 131, 179, 19, 67, 115, 163, 34, 82, 130, 178, 46, 94, 142, 190, 42, 90, 138, 186, 28, 76, 124, 172) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 69)(11, 68)(12, 66)(13, 65)(14, 54)(15, 76)(16, 75)(17, 61)(18, 60)(19, 81)(20, 59)(21, 58)(22, 85)(23, 84)(24, 80)(25, 79)(26, 87)(27, 64)(28, 63)(29, 90)(30, 83)(31, 73)(32, 72)(33, 67)(34, 93)(35, 78)(36, 71)(37, 70)(38, 95)(39, 74)(40, 92)(41, 96)(42, 77)(43, 94)(44, 88)(45, 82)(46, 91)(47, 86)(48, 89)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 160)(104, 159)(105, 163)(106, 149)(107, 148)(108, 167)(109, 166)(110, 170)(111, 152)(112, 151)(113, 174)(114, 173)(115, 153)(116, 179)(117, 178)(118, 157)(119, 156)(120, 183)(121, 182)(122, 158)(123, 180)(124, 185)(125, 162)(126, 161)(127, 177)(128, 187)(129, 175)(130, 165)(131, 164)(132, 171)(133, 190)(134, 169)(135, 168)(136, 192)(137, 172)(138, 191)(139, 176)(140, 189)(141, 188)(142, 181)(143, 186)(144, 184) 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 E20.702 Transitivity :: VT+ Graph:: bipartite v = 6 e = 96 f = 52 degree seq :: [ 32^6 ] E20.704 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 8, 12}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y2 * Y3 * Y2 * Y1 * Y3^-1, Y3^5 * Y1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y1 * Y2)^8 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 24, 72, 120, 168, 40, 88, 136, 184, 33, 81, 129, 177, 43, 91, 139, 187, 26, 74, 122, 170, 41, 89, 137, 185, 25, 73, 121, 169, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 17, 65, 113, 161, 31, 79, 127, 175, 46, 94, 142, 190, 42, 90, 138, 186, 35, 83, 131, 179, 19, 67, 115, 163, 34, 82, 130, 178, 32, 80, 128, 176, 18, 66, 114, 162, 8, 56, 104, 152)(3, 51, 99, 147, 10, 58, 106, 154, 22, 70, 118, 166, 38, 86, 134, 182, 28, 76, 124, 172, 14, 62, 110, 158, 27, 75, 123, 171, 44, 92, 140, 188, 48, 96, 144, 192, 39, 87, 135, 183, 23, 71, 119, 167, 11, 59, 107, 155)(6, 54, 102, 150, 15, 63, 111, 159, 29, 77, 125, 173, 37, 85, 133, 181, 21, 69, 117, 165, 9, 57, 105, 153, 20, 68, 116, 164, 36, 84, 132, 180, 47, 95, 143, 191, 45, 93, 141, 189, 30, 78, 126, 174, 16, 64, 112, 160) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 69)(11, 68)(12, 66)(13, 65)(14, 54)(15, 76)(16, 75)(17, 61)(18, 60)(19, 81)(20, 59)(21, 58)(22, 85)(23, 84)(24, 80)(25, 79)(26, 90)(27, 64)(28, 63)(29, 86)(30, 92)(31, 73)(32, 72)(33, 67)(34, 88)(35, 91)(36, 71)(37, 70)(38, 77)(39, 95)(40, 82)(41, 94)(42, 74)(43, 83)(44, 78)(45, 96)(46, 89)(47, 87)(48, 93)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 160)(104, 159)(105, 163)(106, 149)(107, 148)(108, 167)(109, 166)(110, 170)(111, 152)(112, 151)(113, 174)(114, 173)(115, 153)(116, 179)(117, 178)(118, 157)(119, 156)(120, 183)(121, 182)(122, 158)(123, 187)(124, 185)(125, 162)(126, 161)(127, 189)(128, 181)(129, 188)(130, 165)(131, 164)(132, 186)(133, 176)(134, 169)(135, 168)(136, 192)(137, 172)(138, 180)(139, 171)(140, 177)(141, 175)(142, 191)(143, 190)(144, 184) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E20.701 Transitivity :: VT+ Graph:: bipartite v = 4 e = 96 f = 54 degree seq :: [ 48^4 ] E20.705 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (Y1 * Y2)^2, Y2 * Y3^4, (Y3 * Y1 * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1, Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 13, 61)(7, 55, 17, 65)(8, 56, 19, 67)(9, 57, 21, 69)(10, 58, 22, 70)(12, 60, 20, 68)(14, 62, 18, 66)(15, 63, 26, 74)(16, 64, 27, 75)(23, 71, 32, 80)(24, 72, 33, 81)(25, 73, 34, 82)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(35, 83, 44, 92)(40, 88, 47, 95)(41, 89, 48, 96)(42, 90, 45, 93)(43, 91, 46, 94)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 106, 154)(103, 151, 111, 159)(104, 152, 112, 160)(107, 155, 117, 165)(108, 156, 110, 158)(109, 157, 118, 166)(113, 161, 122, 170)(114, 162, 116, 164)(115, 163, 123, 171)(119, 167, 127, 175)(120, 168, 121, 169)(124, 172, 131, 179)(125, 173, 126, 174)(128, 176, 135, 183)(129, 177, 130, 178)(132, 180, 140, 188)(133, 181, 134, 182)(136, 184, 139, 187)(137, 185, 138, 186)(141, 189, 144, 192)(142, 190, 143, 191) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 97)(6, 111)(7, 114)(8, 98)(9, 110)(10, 99)(11, 119)(12, 106)(13, 121)(14, 101)(15, 116)(16, 102)(17, 124)(18, 112)(19, 126)(20, 104)(21, 127)(22, 120)(23, 109)(24, 107)(25, 117)(26, 131)(27, 125)(28, 115)(29, 113)(30, 122)(31, 118)(32, 136)(33, 138)(34, 137)(35, 123)(36, 141)(37, 143)(38, 142)(39, 139)(40, 129)(41, 128)(42, 135)(43, 130)(44, 144)(45, 133)(46, 132)(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) :: { ( 16, 24, 16, 24 ) } Outer automorphisms :: reflexible Dual of E20.718 Graph:: simple bipartite v = 48 e = 96 f = 10 degree seq :: [ 4^48 ] E20.706 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^-3 * Y2^-3, Y2^-3 * Y3^-3, Y3^-6 * Y2^2, Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 24, 72)(12, 60, 25, 73)(13, 61, 23, 71)(14, 62, 26, 74)(15, 63, 21, 69)(16, 64, 19, 67)(17, 65, 20, 68)(18, 66, 22, 70)(27, 75, 40, 88)(28, 76, 38, 86)(29, 77, 42, 90)(30, 78, 36, 84)(31, 79, 41, 89)(32, 80, 35, 83)(33, 81, 39, 87)(34, 82, 37, 85)(43, 91, 46, 94)(44, 92, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147, 107, 155, 123, 171, 139, 187, 128, 176, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 131, 179, 142, 190, 136, 184, 120, 168, 105, 153)(100, 148, 108, 156, 124, 172, 114, 162, 127, 175, 141, 189, 130, 178, 111, 159)(102, 150, 109, 157, 125, 173, 140, 188, 129, 177, 110, 158, 126, 174, 113, 161)(104, 152, 116, 164, 132, 180, 122, 170, 135, 183, 144, 192, 138, 186, 119, 167)(106, 154, 117, 165, 133, 181, 143, 191, 137, 185, 118, 166, 134, 182, 121, 169) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 132)(20, 134)(21, 103)(22, 136)(23, 137)(24, 138)(25, 105)(26, 106)(27, 114)(28, 113)(29, 107)(30, 112)(31, 109)(32, 141)(33, 139)(34, 140)(35, 122)(36, 121)(37, 115)(38, 120)(39, 117)(40, 144)(41, 142)(42, 143)(43, 127)(44, 123)(45, 125)(46, 135)(47, 131)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.713 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.707 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-3, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 21, 69)(12, 60, 22, 70)(13, 61, 20, 68)(14, 62, 19, 67)(15, 63, 17, 65)(16, 64, 18, 66)(23, 71, 33, 81)(24, 72, 34, 82)(25, 73, 32, 80)(26, 74, 31, 79)(27, 75, 29, 77)(28, 76, 30, 78)(35, 83, 40, 88)(36, 84, 44, 92)(37, 85, 43, 91)(38, 86, 42, 90)(39, 87, 41, 89)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 123, 171, 111, 159, 101, 149)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 129, 177, 117, 165, 105, 153)(100, 148, 108, 156, 120, 168, 132, 180, 141, 189, 134, 182, 122, 170, 110, 158)(102, 150, 109, 157, 121, 169, 133, 181, 142, 190, 135, 183, 124, 172, 112, 160)(104, 152, 114, 162, 126, 174, 137, 185, 143, 191, 139, 187, 128, 176, 116, 164)(106, 154, 115, 163, 127, 175, 138, 186, 144, 192, 140, 188, 130, 178, 118, 166) L = (1, 100)(2, 104)(3, 108)(4, 109)(5, 110)(6, 97)(7, 114)(8, 115)(9, 116)(10, 98)(11, 120)(12, 121)(13, 99)(14, 102)(15, 122)(16, 101)(17, 126)(18, 127)(19, 103)(20, 106)(21, 128)(22, 105)(23, 132)(24, 133)(25, 107)(26, 112)(27, 134)(28, 111)(29, 137)(30, 138)(31, 113)(32, 118)(33, 139)(34, 117)(35, 141)(36, 142)(37, 119)(38, 124)(39, 123)(40, 143)(41, 144)(42, 125)(43, 130)(44, 129)(45, 135)(46, 131)(47, 140)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.712 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.708 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2 * Y2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3^-1, Y2^8, Y3^8, (Y3 * Y2^-1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 23, 71)(12, 60, 20, 68)(13, 61, 25, 73)(14, 62, 22, 70)(15, 63, 19, 67)(16, 64, 26, 74)(17, 65, 21, 69)(18, 66, 24, 72)(27, 75, 41, 89)(28, 76, 40, 88)(29, 77, 38, 86)(30, 78, 37, 85)(31, 79, 42, 90)(32, 80, 36, 84)(33, 81, 35, 83)(34, 82, 39, 87)(43, 91, 46, 94)(44, 92, 47, 95)(45, 93, 48, 96)(97, 145, 99, 147, 107, 155, 123, 171, 139, 187, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 115, 163, 131, 179, 142, 190, 137, 185, 119, 167, 105, 153)(100, 148, 110, 158, 102, 150, 114, 162, 124, 172, 141, 189, 128, 176, 112, 160)(104, 152, 118, 166, 106, 154, 122, 170, 132, 180, 144, 192, 136, 184, 120, 168)(108, 156, 125, 173, 109, 157, 127, 175, 140, 188, 130, 178, 113, 161, 126, 174)(116, 164, 133, 181, 117, 165, 135, 183, 143, 191, 138, 186, 121, 169, 134, 182) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 116)(8, 119)(9, 121)(10, 98)(11, 102)(12, 101)(13, 99)(14, 126)(15, 128)(16, 130)(17, 129)(18, 125)(19, 106)(20, 105)(21, 103)(22, 134)(23, 136)(24, 138)(25, 137)(26, 133)(27, 109)(28, 107)(29, 110)(30, 112)(31, 114)(32, 139)(33, 140)(34, 141)(35, 117)(36, 115)(37, 118)(38, 120)(39, 122)(40, 142)(41, 143)(42, 144)(43, 124)(44, 123)(45, 127)(46, 132)(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, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E20.714 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.709 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, R * Y2 * Y3 * R * Y2^-1 * Y3^-1, Y2^-1 * R * Y3^2 * R * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3, Y3^8, Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 23, 71)(12, 60, 20, 68)(13, 61, 25, 73)(14, 62, 22, 70)(15, 63, 19, 67)(16, 64, 26, 74)(17, 65, 21, 69)(18, 66, 24, 72)(27, 75, 42, 90)(28, 76, 41, 89)(29, 77, 38, 86)(30, 78, 37, 85)(31, 79, 40, 88)(32, 80, 39, 87)(33, 81, 36, 84)(34, 82, 35, 83)(43, 91, 46, 94)(44, 92, 47, 95)(45, 93, 48, 96)(97, 145, 99, 147, 107, 155, 123, 171, 139, 187, 130, 178, 111, 159, 101, 149)(98, 146, 103, 151, 115, 163, 131, 179, 142, 190, 138, 186, 119, 167, 105, 153)(100, 148, 110, 158, 102, 150, 114, 162, 124, 172, 141, 189, 129, 177, 112, 160)(104, 152, 118, 166, 106, 154, 122, 170, 132, 180, 144, 192, 137, 185, 120, 168)(108, 156, 125, 173, 109, 157, 127, 175, 140, 188, 128, 176, 113, 161, 126, 174)(116, 164, 133, 181, 117, 165, 135, 183, 143, 191, 136, 184, 121, 169, 134, 182) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 116)(8, 119)(9, 121)(10, 98)(11, 102)(12, 101)(13, 99)(14, 127)(15, 129)(16, 125)(17, 130)(18, 128)(19, 106)(20, 105)(21, 103)(22, 135)(23, 137)(24, 133)(25, 138)(26, 136)(27, 109)(28, 107)(29, 141)(30, 114)(31, 112)(32, 110)(33, 139)(34, 140)(35, 117)(36, 115)(37, 144)(38, 122)(39, 120)(40, 118)(41, 142)(42, 143)(43, 124)(44, 123)(45, 126)(46, 132)(47, 131)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E20.715 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.710 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^-4 * Y1, (R * Y2 * Y3)^2, R * Y2^2 * R * Y2^-2, (Y3 * Y2^-2)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y3 * Y2 * Y1 * Y3 * Y2 ] 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, 22, 70)(20, 68, 26, 74)(21, 69, 25, 73)(23, 71, 27, 75)(24, 72, 28, 76)(29, 77, 35, 83)(30, 78, 34, 82)(31, 79, 36, 84)(32, 80, 33, 81)(37, 85, 43, 91)(38, 86, 39, 87)(40, 88, 44, 92)(41, 89, 42, 90)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 105, 153, 104, 152, 98, 146, 102, 150, 110, 158, 101, 149)(100, 148, 107, 155, 118, 166, 113, 161, 103, 151, 112, 160, 115, 163, 108, 156)(106, 154, 116, 164, 109, 157, 121, 169, 111, 159, 122, 170, 114, 162, 117, 165)(119, 167, 127, 175, 120, 168, 129, 177, 123, 171, 132, 180, 124, 172, 128, 176)(125, 173, 133, 181, 126, 174, 135, 183, 131, 179, 139, 187, 130, 178, 134, 182)(136, 184, 143, 191, 137, 185, 141, 189, 140, 188, 142, 190, 138, 186, 144, 192) 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, 130)(26, 131)(27, 112)(28, 113)(29, 116)(30, 117)(31, 136)(32, 137)(33, 138)(34, 121)(35, 122)(36, 140)(37, 141)(38, 142)(39, 143)(40, 127)(41, 128)(42, 129)(43, 144)(44, 132)(45, 133)(46, 134)(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, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E20.717 Graph:: bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.711 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y2^4 * Y3 * Y1, (R * Y2 * Y3)^2, Y2^-1 * Y3 * Y2^2 * Y1 * Y2^-1, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^-1 * Y3 * Y1 * Y2 * Y1 * Y3, Y2^-1 * Y1 * Y2^2 * Y3 * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 17, 65)(8, 56, 22, 70)(10, 58, 24, 72)(11, 59, 20, 68)(12, 60, 19, 67)(13, 61, 23, 71)(15, 63, 21, 69)(16, 64, 18, 66)(25, 73, 33, 81)(26, 74, 35, 83)(27, 75, 34, 82)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 39, 87)(31, 79, 38, 86)(32, 80, 40, 88)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 106, 154, 117, 165, 103, 151, 116, 164, 112, 160, 101, 149)(98, 146, 102, 150, 114, 162, 109, 157, 100, 148, 108, 156, 120, 168, 104, 152)(105, 153, 121, 169, 110, 158, 124, 172, 107, 155, 123, 171, 111, 159, 122, 170)(113, 161, 125, 173, 118, 166, 128, 176, 115, 163, 127, 175, 119, 167, 126, 174)(129, 177, 137, 185, 131, 179, 140, 188, 130, 178, 139, 187, 132, 180, 138, 186)(133, 181, 141, 189, 135, 183, 144, 192, 134, 182, 143, 191, 136, 184, 142, 190) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 111)(6, 115)(7, 98)(8, 119)(9, 116)(10, 114)(11, 99)(12, 113)(13, 118)(14, 117)(15, 101)(16, 120)(17, 108)(18, 106)(19, 102)(20, 105)(21, 110)(22, 109)(23, 104)(24, 112)(25, 130)(26, 132)(27, 129)(28, 131)(29, 134)(30, 136)(31, 133)(32, 135)(33, 123)(34, 121)(35, 124)(36, 122)(37, 127)(38, 125)(39, 128)(40, 126)(41, 142)(42, 141)(43, 144)(44, 143)(45, 138)(46, 137)(47, 140)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E20.716 Graph:: bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.712 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y3^-2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^12, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 37, 85, 29, 77, 21, 69, 13, 61, 5, 53)(3, 51, 10, 58, 19, 67, 27, 75, 35, 83, 43, 91, 46, 94, 40, 88, 32, 80, 24, 72, 16, 64, 8, 56)(4, 52, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 45, 93, 38, 86, 30, 78, 22, 70, 14, 62, 6, 54)(11, 59, 20, 68, 28, 76, 36, 84, 44, 92, 48, 96, 47, 95, 42, 90, 34, 82, 26, 74, 18, 66, 12, 60)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 106, 154)(102, 150, 107, 155)(103, 151, 112, 160)(105, 153, 114, 162)(109, 157, 115, 163)(110, 158, 116, 164)(111, 159, 120, 168)(113, 161, 122, 170)(117, 165, 123, 171)(118, 166, 124, 172)(119, 167, 128, 176)(121, 169, 130, 178)(125, 173, 131, 179)(126, 174, 132, 180)(127, 175, 136, 184)(129, 177, 138, 186)(133, 181, 139, 187)(134, 182, 140, 188)(135, 183, 142, 190)(137, 185, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 98)(5, 102)(6, 97)(7, 113)(8, 108)(9, 103)(10, 116)(11, 106)(12, 99)(13, 110)(14, 101)(15, 121)(16, 114)(17, 111)(18, 104)(19, 124)(20, 115)(21, 118)(22, 109)(23, 129)(24, 122)(25, 119)(26, 112)(27, 132)(28, 123)(29, 126)(30, 117)(31, 137)(32, 130)(33, 127)(34, 120)(35, 140)(36, 131)(37, 134)(38, 125)(39, 141)(40, 138)(41, 135)(42, 128)(43, 144)(44, 139)(45, 133)(46, 143)(47, 136)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.707 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.713 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, (Y3^-1 * Y1^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 35, 83, 18, 66, 26, 74, 14, 62, 25, 73, 33, 81, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 42, 90, 41, 89, 31, 79, 40, 88, 30, 78, 45, 93, 36, 84, 20, 68, 8, 56)(4, 52, 9, 57, 21, 69, 34, 82, 17, 65, 6, 54, 10, 58, 22, 70, 37, 85, 46, 94, 32, 80, 15, 63)(12, 60, 28, 76, 43, 91, 39, 87, 24, 72, 13, 61, 29, 77, 44, 92, 48, 96, 47, 95, 38, 86, 23, 71)(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, 132, 180)(117, 165, 135, 183)(118, 166, 134, 182)(121, 169, 137, 185)(122, 170, 136, 184)(128, 176, 140, 188)(129, 177, 138, 186)(130, 178, 139, 187)(131, 179, 141, 189)(133, 181, 143, 191)(142, 190, 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, 130)(20, 134)(21, 129)(22, 103)(23, 136)(24, 104)(25, 133)(26, 106)(27, 139)(28, 141)(29, 107)(30, 140)(31, 109)(32, 114)(33, 142)(34, 112)(35, 113)(36, 143)(37, 115)(38, 127)(39, 116)(40, 125)(41, 120)(42, 135)(43, 132)(44, 123)(45, 144)(46, 131)(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, 16, 4, 16 ), ( 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 E20.706 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.714 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y1 * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1^-2 * Y3^-1, Y1^3 * Y3^-2, (R * Y2 * Y3^-1)^2, Y1 * Y3^3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 15, 63, 27, 75, 39, 87, 44, 92, 40, 88, 38, 86, 22, 70, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 33, 81, 45, 93, 46, 94, 48, 96, 47, 95, 43, 91, 37, 85, 23, 71, 8, 56)(4, 52, 14, 62, 10, 58, 28, 76, 19, 67, 9, 57, 26, 74, 17, 65, 21, 69, 6, 54, 20, 68, 16, 64)(12, 60, 32, 80, 31, 79, 42, 90, 25, 73, 30, 78, 41, 89, 24, 72, 36, 84, 13, 61, 35, 83, 34, 82)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 119, 167)(105, 153, 121, 169)(106, 154, 120, 168)(110, 158, 132, 180)(111, 159, 133, 181)(112, 160, 131, 179)(113, 161, 127, 175)(114, 162, 125, 173)(115, 163, 126, 174)(116, 164, 130, 178)(117, 165, 128, 176)(118, 166, 129, 177)(122, 170, 138, 186)(123, 171, 139, 187)(124, 172, 137, 185)(134, 182, 141, 189)(135, 183, 143, 191)(136, 184, 142, 190)(140, 188, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 113)(6, 97)(7, 116)(8, 120)(9, 123)(10, 98)(11, 126)(12, 129)(13, 99)(14, 134)(15, 124)(16, 114)(17, 103)(18, 106)(19, 101)(20, 135)(21, 136)(22, 102)(23, 127)(24, 125)(25, 104)(26, 118)(27, 117)(28, 140)(29, 131)(30, 141)(31, 107)(32, 139)(33, 138)(34, 119)(35, 142)(36, 143)(37, 109)(38, 115)(39, 110)(40, 112)(41, 133)(42, 144)(43, 121)(44, 122)(45, 132)(46, 128)(47, 130)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.708 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.715 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y1 * Y3 * Y1^-2 * Y3, Y3^2 * Y1^3, Y1^-1 * Y3^3 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y1 * Y3^-3 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 28, 76, 38, 86, 44, 92, 40, 88, 39, 87, 15, 63, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 37, 85, 45, 93, 46, 94, 48, 96, 47, 95, 41, 89, 33, 81, 23, 71, 8, 56)(4, 52, 14, 62, 21, 69, 6, 54, 20, 68, 9, 57, 26, 74, 17, 65, 10, 58, 27, 75, 19, 67, 16, 64)(12, 60, 32, 80, 36, 84, 13, 61, 35, 83, 30, 78, 42, 90, 24, 72, 31, 79, 43, 91, 25, 73, 34, 82)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 119, 167)(105, 153, 121, 169)(106, 154, 120, 168)(110, 158, 132, 180)(111, 159, 133, 181)(112, 160, 131, 179)(113, 161, 127, 175)(114, 162, 125, 173)(115, 163, 126, 174)(116, 164, 130, 178)(117, 165, 128, 176)(118, 166, 129, 177)(122, 170, 139, 187)(123, 171, 138, 186)(124, 172, 137, 185)(134, 182, 143, 191)(135, 183, 141, 189)(136, 184, 142, 190)(140, 188, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 113)(6, 97)(7, 115)(8, 120)(9, 114)(10, 98)(11, 126)(12, 129)(13, 99)(14, 103)(15, 123)(16, 124)(17, 135)(18, 117)(19, 101)(20, 134)(21, 136)(22, 102)(23, 132)(24, 137)(25, 104)(26, 118)(27, 140)(28, 106)(29, 121)(30, 119)(31, 107)(32, 125)(33, 139)(34, 141)(35, 142)(36, 143)(37, 109)(38, 110)(39, 116)(40, 112)(41, 131)(42, 133)(43, 144)(44, 122)(45, 127)(46, 128)(47, 130)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.709 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.716 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (Y1^-2 * Y3)^2, Y2 * Y1^6, (Y2 * Y1^2 * Y3)^2, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 24, 72, 10, 58, 3, 51, 7, 55, 16, 64, 29, 77, 14, 62, 5, 53)(4, 52, 11, 59, 25, 73, 41, 89, 31, 79, 22, 70, 9, 57, 21, 69, 37, 85, 32, 80, 17, 65, 12, 60)(8, 56, 19, 67, 13, 61, 28, 76, 45, 93, 34, 82, 18, 66, 33, 81, 23, 71, 40, 88, 30, 78, 20, 68)(26, 74, 42, 90, 27, 75, 44, 92, 47, 95, 46, 94, 38, 86, 35, 83, 39, 87, 36, 84, 48, 96, 43, 91)(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, 141, 189)(128, 176, 137, 185)(131, 179, 138, 186)(132, 180, 140, 188)(139, 187, 142, 190)(143, 191, 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, 142)(29, 141)(30, 111)(31, 112)(32, 143)(33, 138)(34, 140)(35, 115)(36, 116)(37, 120)(38, 117)(39, 118)(40, 139)(41, 144)(42, 129)(43, 136)(44, 130)(45, 125)(46, 124)(47, 128)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 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 E20.711 Graph:: bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.717 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, (Y1^-2 * Y2)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, (Y3 * Y1^-2)^2, Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2, Y1^-3 * Y2 * Y3 * Y1^-3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 28, 76, 10, 58, 21, 69, 38, 86, 34, 82, 16, 64, 5, 53)(3, 51, 9, 57, 25, 73, 40, 88, 19, 67, 13, 61, 4, 52, 12, 60, 31, 79, 39, 87, 18, 66, 11, 59)(7, 55, 20, 68, 14, 62, 32, 80, 37, 85, 24, 72, 8, 56, 23, 71, 15, 63, 33, 81, 36, 84, 22, 70)(26, 74, 42, 90, 29, 77, 44, 92, 47, 95, 46, 94, 27, 75, 41, 89, 30, 78, 43, 91, 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, 132, 180)(115, 163, 134, 182)(116, 164, 137, 185)(118, 166, 139, 187)(119, 167, 138, 186)(120, 168, 140, 188)(127, 175, 131, 179)(128, 176, 142, 190)(129, 177, 141, 189)(130, 178, 133, 181)(135, 183, 143, 191)(136, 184, 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, 133)(18, 134)(19, 102)(20, 138)(21, 103)(22, 140)(23, 137)(24, 139)(25, 131)(26, 108)(27, 105)(28, 110)(29, 109)(30, 107)(31, 112)(32, 141)(33, 142)(34, 132)(35, 121)(36, 130)(37, 113)(38, 114)(39, 144)(40, 143)(41, 119)(42, 116)(43, 120)(44, 118)(45, 128)(46, 129)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 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 E20.710 Graph:: bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.718 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x Q8) : C2 (small group id <48, 17>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y1^2, Y3^2 * Y1^-1 * Y3, Y1^2 * Y3^-1 * Y1, Y3^2 * Y1^-1 * Y3, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (Y3^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (Y3 * Y2^-1)^2, (Y1^-1 * Y2^-1)^2, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^5 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 4, 52, 10, 58, 7, 55, 12, 60, 5, 53)(3, 51, 13, 61, 27, 75, 15, 63, 26, 74, 16, 64, 21, 69, 11, 59)(6, 54, 18, 66, 24, 72, 19, 67, 25, 73, 17, 65, 22, 70, 9, 57)(14, 62, 28, 76, 37, 85, 31, 79, 42, 90, 32, 80, 43, 91, 29, 77)(20, 68, 23, 71, 38, 86, 33, 81, 40, 88, 35, 83, 41, 89, 34, 82)(30, 78, 45, 93, 48, 96, 39, 87, 36, 84, 46, 94, 47, 95, 44, 92)(97, 145, 99, 147, 110, 158, 126, 174, 136, 184, 121, 169, 106, 154, 122, 170, 138, 186, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 128, 176, 111, 159, 103, 151, 115, 163, 131, 179, 140, 188, 124, 172, 107, 155)(100, 148, 113, 161, 129, 177, 141, 189, 125, 173, 109, 157, 101, 149, 114, 162, 130, 178, 142, 190, 127, 175, 112, 160)(104, 152, 117, 165, 133, 181, 143, 191, 137, 185, 120, 168, 108, 156, 123, 171, 139, 187, 144, 192, 134, 182, 118, 166) L = (1, 100)(2, 106)(3, 111)(4, 108)(5, 104)(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, 109)(22, 114)(23, 136)(24, 113)(25, 105)(26, 107)(27, 112)(28, 138)(29, 133)(30, 135)(31, 139)(32, 110)(33, 137)(34, 134)(35, 116)(36, 140)(37, 128)(38, 131)(39, 143)(40, 130)(41, 119)(42, 125)(43, 124)(44, 144)(45, 132)(46, 126)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^16 ), ( 4^24 ) } Outer automorphisms :: reflexible Dual of E20.705 Graph:: bipartite v = 10 e = 96 f = 48 degree seq :: [ 16^6, 24^4 ] E20.719 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2 * Y2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1, Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-1 * Y1)^2, Y2^-3 * Y3^2 * Y2^-3, (Y3 * Y2^-1)^12 ] 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, 21, 69)(9, 57, 28, 76)(12, 60, 26, 74)(13, 61, 25, 73)(14, 62, 27, 75)(15, 63, 23, 71)(16, 64, 22, 70)(17, 65, 24, 72)(19, 67, 30, 78)(20, 68, 29, 77)(31, 79, 42, 90)(32, 80, 40, 88)(33, 81, 41, 89)(34, 82, 38, 86)(35, 83, 39, 87)(36, 84, 37, 85)(43, 91, 46, 94)(44, 92, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147, 108, 156, 127, 175, 139, 187, 131, 179, 112, 160, 101, 149)(98, 146, 103, 151, 118, 166, 133, 181, 142, 190, 137, 185, 122, 170, 105, 153)(100, 148, 111, 159, 102, 150, 116, 164, 128, 176, 141, 189, 130, 178, 113, 161)(104, 152, 121, 169, 106, 154, 126, 174, 134, 182, 144, 192, 136, 184, 123, 171)(107, 155, 119, 167, 114, 162, 120, 168, 135, 183, 143, 191, 138, 186, 125, 173)(109, 157, 124, 172, 110, 158, 129, 177, 140, 188, 132, 180, 115, 163, 117, 165) L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 115)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 123)(12, 102)(13, 101)(14, 99)(15, 117)(16, 130)(17, 132)(18, 121)(19, 131)(20, 124)(21, 113)(22, 106)(23, 105)(24, 103)(25, 107)(26, 136)(27, 138)(28, 111)(29, 137)(30, 114)(31, 110)(32, 108)(33, 116)(34, 139)(35, 140)(36, 141)(37, 120)(38, 118)(39, 126)(40, 142)(41, 143)(42, 144)(43, 128)(44, 127)(45, 129)(46, 134)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E20.721 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.720 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, Y3^-2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, Y3^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * Y3 * Y1)^2, Y2^-2 * Y3^2 * Y2^-4 ] 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, 21, 69)(9, 57, 28, 76)(12, 60, 26, 74)(13, 61, 25, 73)(14, 62, 27, 75)(15, 63, 23, 71)(16, 64, 22, 70)(17, 65, 24, 72)(19, 67, 30, 78)(20, 68, 29, 77)(31, 79, 45, 93)(32, 80, 41, 89)(33, 81, 43, 91)(34, 82, 39, 87)(35, 83, 44, 92)(36, 84, 40, 88)(37, 85, 42, 90)(38, 86, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 108, 156, 128, 176, 142, 190, 133, 181, 112, 160, 101, 149)(98, 146, 103, 151, 118, 166, 135, 183, 144, 192, 140, 188, 122, 170, 105, 153)(100, 148, 111, 159, 102, 150, 116, 164, 129, 177, 141, 189, 132, 180, 113, 161)(104, 152, 121, 169, 106, 154, 126, 174, 136, 184, 143, 191, 139, 187, 123, 171)(107, 155, 127, 175, 114, 162, 125, 173, 138, 186, 119, 167, 137, 185, 120, 168)(109, 157, 130, 178, 110, 158, 117, 165, 134, 182, 124, 172, 115, 163, 131, 179) L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 115)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 123)(12, 102)(13, 101)(14, 99)(15, 117)(16, 132)(17, 130)(18, 121)(19, 133)(20, 124)(21, 113)(22, 106)(23, 105)(24, 103)(25, 107)(26, 139)(27, 137)(28, 111)(29, 140)(30, 114)(31, 135)(32, 110)(33, 108)(34, 141)(35, 116)(36, 142)(37, 134)(38, 128)(39, 120)(40, 118)(41, 143)(42, 126)(43, 144)(44, 127)(45, 131)(46, 129)(47, 138)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.722 Graph:: simple bipartite v = 30 e = 96 f = 28 degree seq :: [ 4^24, 16^6 ] E20.721 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y2 * Y3)^2, (Y3^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1^-1 * Y3 * Y1, Y1 * Y3^-2 * Y1^2, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y1^2 * Y2 * Y1^-2 * Y2, Y1 * Y3^3 * Y1 * Y3, (Y3^-1 * Y2 * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 16, 64, 31, 79, 38, 86, 46, 94, 33, 81, 44, 92, 24, 72, 20, 68, 5, 53)(3, 51, 11, 59, 25, 73, 37, 85, 45, 93, 18, 66, 28, 76, 8, 56, 26, 74, 43, 91, 40, 88, 13, 61)(4, 52, 15, 63, 10, 58, 32, 80, 21, 69, 9, 57, 30, 78, 19, 67, 23, 71, 6, 54, 22, 70, 17, 65)(12, 60, 36, 84, 35, 83, 48, 96, 41, 89, 34, 82, 47, 95, 39, 87, 29, 77, 14, 62, 42, 90, 27, 75)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 114, 162)(102, 150, 108, 156)(103, 151, 121, 169)(105, 153, 125, 173)(106, 154, 123, 171)(107, 155, 129, 177)(109, 157, 134, 182)(111, 159, 137, 185)(112, 160, 139, 187)(113, 161, 131, 179)(115, 163, 138, 186)(116, 164, 136, 184)(117, 165, 132, 180)(118, 166, 135, 183)(119, 167, 130, 178)(120, 168, 133, 181)(122, 170, 140, 188)(124, 172, 142, 190)(126, 174, 144, 192)(127, 175, 141, 189)(128, 176, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 118)(8, 123)(9, 127)(10, 98)(11, 130)(12, 133)(13, 135)(14, 99)(15, 140)(16, 128)(17, 116)(18, 132)(19, 103)(20, 106)(21, 101)(22, 134)(23, 129)(24, 102)(25, 138)(26, 137)(27, 136)(28, 143)(29, 104)(30, 120)(31, 119)(32, 142)(33, 113)(34, 141)(35, 107)(36, 122)(37, 144)(38, 111)(39, 121)(40, 131)(41, 109)(42, 114)(43, 110)(44, 117)(45, 125)(46, 126)(47, 139)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.719 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.722 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 8, 12}) Quotient :: dipole Aut^+ = (C3 x D8) : C2 (small group id <48, 15>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1^-2 * Y3, Y3^2 * Y1^3, (Y2 * Y3 * Y1^-1)^2, Y1 * Y3^-3 * Y1 * Y3^-1, Y3^3 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2 * Y1^-1)^2, Y1^2 * Y2 * Y1^-2 * Y2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1 * Y2)^2, Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 24, 72, 32, 80, 38, 86, 46, 94, 33, 81, 44, 92, 16, 64, 20, 68, 5, 53)(3, 51, 11, 59, 25, 73, 43, 91, 45, 93, 18, 66, 28, 76, 8, 56, 26, 74, 37, 85, 40, 88, 13, 61)(4, 52, 15, 63, 23, 71, 6, 54, 22, 70, 9, 57, 30, 78, 19, 67, 10, 58, 31, 79, 21, 69, 17, 65)(12, 60, 36, 84, 29, 77, 14, 62, 42, 90, 34, 82, 47, 95, 39, 87, 35, 83, 48, 96, 41, 89, 27, 75)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 114, 162)(102, 150, 108, 156)(103, 151, 121, 169)(105, 153, 125, 173)(106, 154, 123, 171)(107, 155, 129, 177)(109, 157, 134, 182)(111, 159, 137, 185)(112, 160, 139, 187)(113, 161, 131, 179)(115, 163, 138, 186)(116, 164, 136, 184)(117, 165, 132, 180)(118, 166, 135, 183)(119, 167, 130, 178)(120, 168, 133, 181)(122, 170, 140, 188)(124, 172, 142, 190)(126, 174, 144, 192)(127, 175, 143, 191)(128, 176, 141, 189) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 117)(8, 123)(9, 116)(10, 98)(11, 130)(12, 133)(13, 135)(14, 99)(15, 103)(16, 127)(17, 128)(18, 132)(19, 140)(20, 119)(21, 101)(22, 134)(23, 129)(24, 102)(25, 137)(26, 138)(27, 141)(28, 143)(29, 104)(30, 120)(31, 142)(32, 106)(33, 113)(34, 136)(35, 107)(36, 121)(37, 144)(38, 111)(39, 122)(40, 125)(41, 109)(42, 114)(43, 110)(44, 118)(45, 131)(46, 126)(47, 139)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.720 Graph:: simple bipartite v = 28 e = 96 f = 30 degree seq :: [ 4^24, 24^4 ] E20.723 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 16, 16}) Quotient :: edge Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T1^2 * T2^-1 * T1^2 * T2, T1^3 * T2^-4, T2^-1 * T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1, T1^12 ] Map:: non-degenerate R = (1, 3, 10, 30, 18, 43, 48, 24, 46, 21, 45, 44, 35, 41, 17, 5)(2, 7, 22, 37, 42, 34, 40, 16, 33, 11, 32, 36, 13, 27, 26, 8)(4, 12, 31, 20, 6, 19, 39, 15, 29, 9, 28, 25, 47, 23, 38, 14)(49, 50, 54, 66, 90, 77, 94, 81, 95, 83, 61, 52)(51, 57, 75, 91, 71, 55, 69, 60, 82, 89, 67, 59)(53, 63, 84, 78, 73, 56, 72, 62, 85, 92, 68, 64)(58, 70, 87, 96, 88, 76, 93, 80, 86, 65, 74, 79) 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) :: { ( 32^12 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E20.727 Transitivity :: ET+ Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 12^4, 16^3 ] E20.724 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 16, 16}) Quotient :: edge Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-1 * T2^-2 * T1, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T1 * T2^3 * T1^-2 * T2, T1^12 ] Map:: non-degenerate R = (1, 3, 10, 30, 35, 44, 48, 24, 46, 21, 45, 43, 18, 41, 17, 5)(2, 7, 22, 36, 13, 27, 40, 16, 33, 11, 32, 37, 42, 34, 26, 8)(4, 12, 31, 25, 47, 23, 39, 15, 29, 9, 28, 20, 6, 19, 38, 14)(49, 50, 54, 66, 90, 77, 94, 81, 95, 83, 61, 52)(51, 57, 75, 89, 71, 55, 69, 60, 82, 92, 67, 59)(53, 63, 84, 91, 73, 56, 72, 62, 85, 78, 68, 64)(58, 70, 86, 65, 74, 76, 93, 80, 87, 96, 88, 79) 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) :: { ( 32^12 ), ( 32^16 ) } Outer automorphisms :: reflexible Dual of E20.726 Transitivity :: ET+ Graph:: bipartite v = 7 e = 48 f = 3 degree seq :: [ 12^4, 16^3 ] E20.725 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 16, 16}) Quotient :: edge Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T2^2 * T1^-1 * T2^-2 * T1, T2 * T1^-2 * T2^-1 * T1^2, T2^-2 * T1^-3 * T2^-2 * T1^-1, T2^4 * T1^-1 * T2^2 * T1^-1, T1^-1 * T2^2 * T1^-5 ] Map:: non-degenerate R = (1, 3, 10, 29, 44, 20, 6, 19, 42, 33, 13, 31, 38, 37, 17, 5)(2, 7, 22, 46, 32, 40, 18, 39, 35, 14, 4, 12, 30, 48, 26, 8)(9, 27, 47, 25, 43, 23, 41, 36, 16, 24, 11, 21, 45, 34, 15, 28)(49, 50, 54, 66, 86, 78, 58, 70, 90, 83, 65, 74, 92, 80, 61, 52)(51, 57, 67, 89, 85, 93, 77, 95, 81, 64, 53, 63, 68, 91, 79, 59)(55, 69, 87, 75, 96, 84, 94, 82, 62, 73, 56, 72, 88, 76, 60, 71) 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) :: { ( 24^16 ) } Outer automorphisms :: reflexible Dual of E20.728 Transitivity :: ET+ Graph:: bipartite v = 6 e = 48 f = 4 degree seq :: [ 16^6 ] E20.726 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 16, 16}) Quotient :: loop Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T1^2 * T2^-1 * T1^2 * T2, T1^3 * T2^-4, T2^-1 * T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1, T1^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 30, 78, 18, 66, 43, 91, 48, 96, 24, 72, 46, 94, 21, 69, 45, 93, 44, 92, 35, 83, 41, 89, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 37, 85, 42, 90, 34, 82, 40, 88, 16, 64, 33, 81, 11, 59, 32, 80, 36, 84, 13, 61, 27, 75, 26, 74, 8, 56)(4, 52, 12, 60, 31, 79, 20, 68, 6, 54, 19, 67, 39, 87, 15, 63, 29, 77, 9, 57, 28, 76, 25, 73, 47, 95, 23, 71, 38, 86, 14, 62) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 75)(10, 70)(11, 51)(12, 82)(13, 52)(14, 85)(15, 84)(16, 53)(17, 74)(18, 90)(19, 59)(20, 64)(21, 60)(22, 87)(23, 55)(24, 62)(25, 56)(26, 79)(27, 91)(28, 93)(29, 94)(30, 73)(31, 58)(32, 86)(33, 95)(34, 89)(35, 61)(36, 78)(37, 92)(38, 65)(39, 96)(40, 76)(41, 67)(42, 77)(43, 71)(44, 68)(45, 80)(46, 81)(47, 83)(48, 88) 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 ) } Outer automorphisms :: reflexible Dual of E20.724 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 48 f = 7 degree seq :: [ 32^3 ] E20.727 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 16, 16}) Quotient :: loop Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-1 * T2^-2 * T1, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T1 * T2^3 * T1^-2 * T2, T1^12 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 30, 78, 35, 83, 44, 92, 48, 96, 24, 72, 46, 94, 21, 69, 45, 93, 43, 91, 18, 66, 41, 89, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 36, 84, 13, 61, 27, 75, 40, 88, 16, 64, 33, 81, 11, 59, 32, 80, 37, 85, 42, 90, 34, 82, 26, 74, 8, 56)(4, 52, 12, 60, 31, 79, 25, 73, 47, 95, 23, 71, 39, 87, 15, 63, 29, 77, 9, 57, 28, 76, 20, 68, 6, 54, 19, 67, 38, 86, 14, 62) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 75)(10, 70)(11, 51)(12, 82)(13, 52)(14, 85)(15, 84)(16, 53)(17, 74)(18, 90)(19, 59)(20, 64)(21, 60)(22, 86)(23, 55)(24, 62)(25, 56)(26, 76)(27, 89)(28, 93)(29, 94)(30, 68)(31, 58)(32, 87)(33, 95)(34, 92)(35, 61)(36, 91)(37, 78)(38, 65)(39, 96)(40, 79)(41, 71)(42, 77)(43, 73)(44, 67)(45, 80)(46, 81)(47, 83)(48, 88) 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 ) } Outer automorphisms :: reflexible Dual of E20.723 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 48 f = 7 degree seq :: [ 32^3 ] E20.728 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 16, 16}) Quotient :: loop Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-1 * T2^2 * T1, T2^-1 * T1^-2 * T2 * T1^2, T1^3 * T2^-3 * T1, T2^12, (T2^-1 * T1^-1)^16 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 29, 77, 45, 93, 23, 71, 44, 92, 25, 73, 46, 94, 41, 89, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 43, 91, 28, 76, 9, 57, 27, 75, 15, 63, 39, 87, 36, 84, 26, 74, 8, 56)(4, 52, 12, 60, 34, 82, 18, 66, 33, 81, 11, 59, 31, 79, 16, 64, 40, 88, 47, 95, 30, 78, 14, 62)(6, 54, 19, 67, 35, 83, 48, 96, 38, 86, 21, 69, 42, 90, 24, 72, 37, 85, 13, 61, 32, 80, 20, 68) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 67)(10, 74)(11, 51)(12, 71)(13, 52)(14, 73)(15, 68)(16, 53)(17, 70)(18, 77)(19, 88)(20, 78)(21, 81)(22, 80)(23, 55)(24, 82)(25, 56)(26, 83)(27, 90)(28, 85)(29, 91)(30, 58)(31, 92)(32, 59)(33, 94)(34, 65)(35, 60)(36, 61)(37, 64)(38, 62)(39, 86)(40, 93)(41, 84)(42, 95)(43, 96)(44, 75)(45, 87)(46, 76)(47, 89)(48, 79) local type(s) :: { ( 16^24 ) } Outer automorphisms :: reflexible Dual of E20.725 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 6 degree seq :: [ 24^4 ] E20.729 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 16, 16}) Quotient :: dipole Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y3 * Y2^2 * Y3 * Y2 * Y3^-1 * Y2, Y1 * Y2^3 * Y3 * Y1^-1 * Y2, Y1^2 * Y2^-3 * Y3 * Y2^-1, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y1^-1 * Y3 * Y1^-3 * Y2, Y1^12, (Y1 * Y2^-1)^16 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 42, 90, 29, 77, 46, 94, 33, 81, 47, 95, 35, 83, 13, 61, 4, 52)(3, 51, 9, 57, 27, 75, 41, 89, 23, 71, 7, 55, 21, 69, 12, 60, 34, 82, 44, 92, 19, 67, 11, 59)(5, 53, 15, 63, 36, 84, 43, 91, 25, 73, 8, 56, 24, 72, 14, 62, 37, 85, 30, 78, 20, 68, 16, 64)(10, 58, 22, 70, 38, 86, 17, 65, 26, 74, 28, 76, 45, 93, 32, 80, 39, 87, 48, 96, 40, 88, 31, 79)(97, 145, 99, 147, 106, 154, 126, 174, 131, 179, 140, 188, 144, 192, 120, 168, 142, 190, 117, 165, 141, 189, 139, 187, 114, 162, 137, 185, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 132, 180, 109, 157, 123, 171, 136, 184, 112, 160, 129, 177, 107, 155, 128, 176, 133, 181, 138, 186, 130, 178, 122, 170, 104, 152)(100, 148, 108, 156, 127, 175, 121, 169, 143, 191, 119, 167, 135, 183, 111, 159, 125, 173, 105, 153, 124, 172, 116, 164, 102, 150, 115, 163, 134, 182, 110, 158) L = (1, 100)(2, 97)(3, 107)(4, 109)(5, 112)(6, 98)(7, 119)(8, 121)(9, 99)(10, 127)(11, 115)(12, 117)(13, 131)(14, 120)(15, 101)(16, 116)(17, 134)(18, 102)(19, 140)(20, 126)(21, 103)(22, 106)(23, 137)(24, 104)(25, 139)(26, 113)(27, 105)(28, 122)(29, 138)(30, 133)(31, 136)(32, 141)(33, 142)(34, 108)(35, 143)(36, 111)(37, 110)(38, 118)(39, 128)(40, 144)(41, 123)(42, 114)(43, 132)(44, 130)(45, 124)(46, 125)(47, 129)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E20.733 Graph:: bipartite v = 7 e = 96 f = 51 degree seq :: [ 24^4, 32^3 ] E20.730 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 16, 16}) Quotient :: dipole Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y2 * Y1^-2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y2^-1 * Y1^-2 * Y2 * Y3 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, Y2 * Y3 * Y2^3 * Y3^-2, Y2^2 * Y1^2 * Y2 * Y1^-1 * Y2, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^12, (Y3 * Y2^-1)^16 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 42, 90, 29, 77, 46, 94, 33, 81, 47, 95, 35, 83, 13, 61, 4, 52)(3, 51, 9, 57, 27, 75, 43, 91, 23, 71, 7, 55, 21, 69, 12, 60, 34, 82, 41, 89, 19, 67, 11, 59)(5, 53, 15, 63, 36, 84, 30, 78, 25, 73, 8, 56, 24, 72, 14, 62, 37, 85, 44, 92, 20, 68, 16, 64)(10, 58, 22, 70, 39, 87, 48, 96, 40, 88, 28, 76, 45, 93, 32, 80, 38, 86, 17, 65, 26, 74, 31, 79)(97, 145, 99, 147, 106, 154, 126, 174, 114, 162, 139, 187, 144, 192, 120, 168, 142, 190, 117, 165, 141, 189, 140, 188, 131, 179, 137, 185, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 133, 181, 138, 186, 130, 178, 136, 184, 112, 160, 129, 177, 107, 155, 128, 176, 132, 180, 109, 157, 123, 171, 122, 170, 104, 152)(100, 148, 108, 156, 127, 175, 116, 164, 102, 150, 115, 163, 135, 183, 111, 159, 125, 173, 105, 153, 124, 172, 121, 169, 143, 191, 119, 167, 134, 182, 110, 158) L = (1, 100)(2, 97)(3, 107)(4, 109)(5, 112)(6, 98)(7, 119)(8, 121)(9, 99)(10, 127)(11, 115)(12, 117)(13, 131)(14, 120)(15, 101)(16, 116)(17, 134)(18, 102)(19, 137)(20, 140)(21, 103)(22, 106)(23, 139)(24, 104)(25, 126)(26, 113)(27, 105)(28, 136)(29, 138)(30, 132)(31, 122)(32, 141)(33, 142)(34, 108)(35, 143)(36, 111)(37, 110)(38, 128)(39, 118)(40, 144)(41, 130)(42, 114)(43, 123)(44, 133)(45, 124)(46, 125)(47, 129)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 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 E20.734 Graph:: bipartite v = 7 e = 96 f = 51 degree seq :: [ 24^4, 32^3 ] E20.731 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 16, 16}) Quotient :: dipole Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^4 * Y1^-1 * Y2^2 * Y1^-1, Y2^-1 * Y1^-3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^16, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 38, 86, 29, 77, 10, 58, 22, 70, 42, 90, 36, 84, 17, 65, 26, 74, 44, 92, 33, 81, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 41, 89, 37, 85, 47, 95, 28, 76, 45, 93, 34, 82, 16, 64, 5, 53, 15, 63, 20, 68, 43, 91, 30, 78, 11, 59)(7, 55, 21, 69, 39, 87, 31, 79, 48, 96, 27, 75, 46, 94, 35, 83, 14, 62, 25, 73, 8, 56, 24, 72, 40, 88, 32, 80, 12, 60, 23, 71)(97, 145, 99, 147, 106, 154, 124, 172, 140, 188, 116, 164, 102, 150, 115, 163, 138, 186, 130, 178, 109, 157, 126, 174, 134, 182, 133, 181, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 142, 190, 129, 177, 136, 184, 114, 162, 135, 183, 132, 180, 110, 158, 100, 148, 108, 156, 125, 173, 144, 192, 122, 170, 104, 152)(105, 153, 120, 168, 141, 189, 117, 165, 139, 187, 131, 179, 137, 185, 128, 176, 112, 160, 127, 175, 107, 155, 121, 169, 143, 191, 119, 167, 111, 159, 123, 171) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 120)(10, 124)(11, 121)(12, 125)(13, 126)(14, 100)(15, 123)(16, 127)(17, 101)(18, 135)(19, 138)(20, 102)(21, 139)(22, 142)(23, 111)(24, 141)(25, 143)(26, 104)(27, 105)(28, 140)(29, 144)(30, 134)(31, 107)(32, 112)(33, 136)(34, 109)(35, 137)(36, 110)(37, 113)(38, 133)(39, 132)(40, 114)(41, 128)(42, 130)(43, 131)(44, 116)(45, 117)(46, 129)(47, 119)(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, 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 E20.732 Graph:: bipartite v = 6 e = 96 f = 52 degree seq :: [ 32^6 ] E20.732 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 16, 16}) Quotient :: dipole Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2^-1, Y3^-2 * Y2^-1 * Y3^2 * Y2, Y2 * Y3^-1 * Y2^-2 * Y3^-3, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^12, (Y3^-1 * Y1^-1)^16 ] 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, 114, 162, 138, 186, 125, 173, 142, 190, 129, 177, 143, 191, 131, 179, 109, 157, 100, 148)(99, 147, 105, 153, 123, 171, 139, 187, 119, 167, 103, 151, 117, 165, 108, 156, 130, 178, 137, 185, 115, 163, 107, 155)(101, 149, 111, 159, 132, 180, 126, 174, 121, 169, 104, 152, 120, 168, 110, 158, 133, 181, 140, 188, 116, 164, 112, 160)(106, 154, 118, 166, 135, 183, 144, 192, 136, 184, 124, 172, 141, 189, 128, 176, 134, 182, 113, 161, 122, 170, 127, 175) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 124)(10, 126)(11, 128)(12, 127)(13, 123)(14, 100)(15, 125)(16, 129)(17, 101)(18, 139)(19, 135)(20, 102)(21, 141)(22, 133)(23, 134)(24, 142)(25, 143)(26, 104)(27, 122)(28, 121)(29, 105)(30, 114)(31, 116)(32, 132)(33, 107)(34, 136)(35, 137)(36, 109)(37, 138)(38, 110)(39, 111)(40, 112)(41, 113)(42, 130)(43, 144)(44, 131)(45, 140)(46, 117)(47, 119)(48, 120)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 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, 32 ), ( 32^24 ) } Outer automorphisms :: reflexible Dual of E20.731 Graph:: simple bipartite v = 52 e = 96 f = 6 degree seq :: [ 2^48, 24^4 ] E20.733 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 16, 16}) Quotient :: dipole Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-2 * Y1^-1 * Y3^-2, Y3^-1 * Y1^-2 * Y3 * Y1^2, Y3^-2 * Y1^2 * Y3^-1 * Y1^2, Y3 * Y1 * Y3^-5 * Y1^-1, (Y3^-1 * Y1 * Y3^-1 * Y1^-1)^2, Y1^16, (Y3 * Y2^-1)^12, (Y3 * Y1^-1)^16 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 29, 77, 43, 91, 48, 96, 31, 79, 44, 92, 27, 75, 42, 90, 47, 95, 41, 89, 36, 84, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 40, 88, 45, 93, 39, 87, 38, 86, 14, 62, 25, 73, 8, 56, 24, 72, 34, 82, 17, 65, 22, 70, 32, 80, 11, 59)(5, 53, 15, 63, 20, 68, 30, 78, 10, 58, 26, 74, 35, 83, 12, 60, 23, 71, 7, 55, 21, 69, 33, 81, 46, 94, 28, 76, 37, 85, 16, 64)(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, 127)(12, 130)(13, 128)(14, 100)(15, 135)(16, 136)(17, 101)(18, 129)(19, 131)(20, 102)(21, 138)(22, 139)(23, 140)(24, 133)(25, 142)(26, 104)(27, 111)(28, 105)(29, 141)(30, 110)(31, 112)(32, 116)(33, 107)(34, 114)(35, 144)(36, 122)(37, 109)(38, 117)(39, 132)(40, 143)(41, 113)(42, 120)(43, 124)(44, 121)(45, 119)(46, 137)(47, 126)(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) :: { ( 24, 32 ), ( 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32 ) } Outer automorphisms :: reflexible Dual of E20.729 Graph:: simple bipartite v = 51 e = 96 f = 7 degree seq :: [ 2^48, 32^3 ] E20.734 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 16, 16}) Quotient :: dipole Aut^+ = C3 : C16 (small group id <48, 1>) Aut = (C3 x D16) : C2 (small group id <96, 33>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3^2 * Y1, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1, Y1 * Y3 * Y1^3 * Y3^-2, Y3 * Y1 * Y3^-5 * Y1^-1, Y1^16, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 41, 89, 46, 94, 48, 96, 31, 79, 43, 91, 27, 75, 42, 90, 47, 95, 29, 77, 36, 84, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 34, 82, 17, 65, 22, 70, 38, 86, 14, 62, 25, 73, 8, 56, 24, 72, 40, 88, 44, 92, 39, 87, 32, 80, 11, 59)(5, 53, 15, 63, 20, 68, 33, 81, 45, 93, 28, 76, 35, 83, 12, 60, 23, 71, 7, 55, 21, 69, 30, 78, 10, 58, 26, 74, 37, 85, 16, 64)(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, 127)(12, 130)(13, 128)(14, 100)(15, 135)(16, 136)(17, 101)(18, 126)(19, 133)(20, 102)(21, 138)(22, 132)(23, 139)(24, 131)(25, 141)(26, 104)(27, 111)(28, 105)(29, 140)(30, 110)(31, 112)(32, 117)(33, 107)(34, 143)(35, 144)(36, 124)(37, 109)(38, 116)(39, 142)(40, 114)(41, 113)(42, 120)(43, 121)(44, 119)(45, 137)(46, 122)(47, 129)(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) :: { ( 24, 32 ), ( 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32, 24, 32 ) } Outer automorphisms :: reflexible Dual of E20.730 Graph:: simple bipartite v = 51 e = 96 f = 7 degree seq :: [ 2^48, 32^3 ] E20.735 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 24}) Quotient :: halfedge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2 * Y1)^2, Y1 * Y2 * Y1^-2 * Y3, (Y3 * Y2)^8, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 60, 12, 63, 15, 68, 20, 73, 25, 75, 27, 80, 32, 85, 37, 87, 39, 92, 44, 96, 48, 94, 46, 89, 41, 84, 36, 82, 34, 77, 29, 72, 24, 70, 22, 65, 17, 58, 10, 61, 13, 53, 5, 49)(3, 57, 9, 64, 16, 66, 18, 71, 23, 76, 28, 78, 30, 83, 35, 88, 40, 90, 42, 95, 47, 93, 45, 91, 43, 86, 38, 81, 33, 79, 31, 74, 26, 69, 21, 67, 19, 62, 14, 56, 8, 52, 4, 59, 11, 55, 7, 51) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 11)(8, 15)(10, 18)(13, 16)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 35)(31, 37)(33, 39)(34, 40)(36, 42)(38, 44)(41, 47)(43, 48)(45, 46)(49, 52)(50, 56)(51, 58)(53, 59)(54, 62)(55, 61)(57, 65)(60, 67)(63, 69)(64, 70)(66, 72)(68, 74)(71, 77)(73, 79)(75, 81)(76, 82)(78, 84)(80, 86)(83, 89)(85, 91)(87, 93)(88, 94)(90, 96)(92, 95) local type(s) :: { ( 12^48 ) } Outer automorphisms :: reflexible Dual of E20.736 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 8 degree seq :: [ 48^2 ] E20.736 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 24}) Quotient :: halfedge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^6, Y2 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1 * Y2 * Y1^-1, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y3, (Y2 * Y1 * Y3)^24 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 62, 14, 61, 13, 53, 5, 49)(3, 57, 9, 67, 19, 73, 25, 63, 15, 55, 7, 51)(4, 59, 11, 70, 22, 74, 26, 64, 16, 56, 8, 52)(10, 65, 17, 75, 27, 85, 37, 79, 31, 68, 20, 58)(12, 66, 18, 76, 28, 86, 38, 82, 34, 71, 23, 60)(21, 80, 32, 91, 43, 96, 48, 87, 39, 77, 29, 69)(24, 83, 35, 94, 46, 93, 45, 88, 40, 78, 30, 72)(33, 89, 41, 95, 47, 84, 36, 90, 42, 92, 44, 81) 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, 32)(22, 34)(24, 36)(26, 38)(27, 39)(30, 42)(31, 43)(33, 45)(35, 47)(37, 48)(40, 44)(41, 46)(49, 52)(50, 56)(51, 58)(53, 59)(54, 64)(55, 65)(57, 68)(60, 72)(61, 70)(62, 74)(63, 75)(66, 78)(67, 79)(69, 81)(71, 83)(73, 85)(76, 88)(77, 89)(80, 92)(82, 94)(84, 96)(86, 93)(87, 95)(90, 91) local type(s) :: { ( 48^12 ) } Outer automorphisms :: reflexible Dual of E20.735 Transitivity :: VT+ AT Graph:: bipartite v = 8 e = 48 f = 2 degree seq :: [ 12^8 ] E20.737 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^6, Y1 * Y2 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 ] Map:: R = (1, 49, 4, 52, 12, 60, 24, 72, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 30, 78, 18, 66, 8, 56)(3, 51, 10, 58, 22, 70, 36, 84, 23, 71, 11, 59)(6, 54, 15, 63, 28, 76, 42, 90, 29, 77, 16, 64)(9, 57, 20, 68, 34, 82, 48, 96, 35, 83, 21, 69)(14, 62, 26, 74, 40, 88, 43, 91, 41, 89, 27, 75)(19, 67, 32, 80, 46, 94, 37, 85, 47, 95, 33, 81)(25, 73, 38, 86, 45, 93, 31, 79, 44, 92, 39, 87)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 117)(107, 116)(108, 114)(109, 113)(111, 123)(112, 122)(115, 127)(118, 131)(119, 130)(120, 126)(121, 133)(124, 137)(125, 136)(128, 141)(129, 140)(132, 144)(134, 142)(135, 143)(138, 139)(145, 147)(146, 150)(148, 155)(149, 154)(151, 160)(152, 159)(153, 163)(156, 167)(157, 166)(158, 169)(161, 173)(162, 172)(164, 177)(165, 176)(168, 180)(170, 183)(171, 182)(174, 186)(175, 187)(178, 191)(179, 190)(181, 192)(184, 188)(185, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^12 ) } Outer automorphisms :: reflexible Dual of E20.740 Graph:: simple bipartite v = 56 e = 96 f = 2 degree seq :: [ 2^48, 12^8 ] E20.738 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-3 * Y1, (Y1 * Y2)^8, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 49, 4, 52, 12, 60, 6, 54, 15, 63, 22, 70, 20, 68, 27, 75, 34, 82, 32, 80, 39, 87, 46, 94, 44, 92, 48, 96, 42, 90, 35, 83, 37, 85, 30, 78, 23, 71, 25, 73, 18, 66, 9, 57, 13, 61, 5, 53)(2, 50, 7, 55, 11, 59, 3, 51, 10, 58, 19, 67, 17, 65, 24, 72, 31, 79, 29, 77, 36, 84, 43, 91, 41, 89, 47, 95, 45, 93, 38, 86, 40, 88, 33, 81, 26, 74, 28, 76, 21, 69, 14, 62, 16, 64, 8, 56)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 114)(107, 109)(108, 112)(111, 117)(113, 119)(115, 121)(116, 122)(118, 124)(120, 126)(123, 129)(125, 131)(127, 133)(128, 134)(130, 136)(132, 138)(135, 141)(137, 140)(139, 144)(142, 143)(145, 147)(146, 150)(148, 155)(149, 154)(151, 156)(152, 159)(153, 161)(157, 163)(158, 164)(160, 166)(162, 168)(165, 171)(167, 173)(169, 175)(170, 176)(172, 178)(174, 180)(177, 183)(179, 185)(181, 187)(182, 188)(184, 190)(186, 191)(189, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 24, 24 ), ( 24^48 ) } Outer automorphisms :: reflexible Dual of E20.739 Graph:: simple bipartite v = 50 e = 96 f = 8 degree seq :: [ 2^48, 48^2 ] E20.739 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^6, Y1 * Y2 * Y1 * Y2 * Y3^3 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 24, 72, 120, 168, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 17, 65, 113, 161, 30, 78, 126, 174, 18, 66, 114, 162, 8, 56, 104, 152)(3, 51, 99, 147, 10, 58, 106, 154, 22, 70, 118, 166, 36, 84, 132, 180, 23, 71, 119, 167, 11, 59, 107, 155)(6, 54, 102, 150, 15, 63, 111, 159, 28, 76, 124, 172, 42, 90, 138, 186, 29, 77, 125, 173, 16, 64, 112, 160)(9, 57, 105, 153, 20, 68, 116, 164, 34, 82, 130, 178, 48, 96, 144, 192, 35, 83, 131, 179, 21, 69, 117, 165)(14, 62, 110, 158, 26, 74, 122, 170, 40, 88, 136, 184, 43, 91, 139, 187, 41, 89, 137, 185, 27, 75, 123, 171)(19, 67, 115, 163, 32, 80, 128, 176, 46, 94, 142, 190, 37, 85, 133, 181, 47, 95, 143, 191, 33, 81, 129, 177)(25, 73, 121, 169, 38, 86, 134, 182, 45, 93, 141, 189, 31, 79, 127, 175, 44, 92, 140, 188, 39, 87, 135, 183) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 69)(11, 68)(12, 66)(13, 65)(14, 54)(15, 75)(16, 74)(17, 61)(18, 60)(19, 79)(20, 59)(21, 58)(22, 83)(23, 82)(24, 78)(25, 85)(26, 64)(27, 63)(28, 89)(29, 88)(30, 72)(31, 67)(32, 93)(33, 92)(34, 71)(35, 70)(36, 96)(37, 73)(38, 94)(39, 95)(40, 77)(41, 76)(42, 91)(43, 90)(44, 81)(45, 80)(46, 86)(47, 87)(48, 84)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 160)(104, 159)(105, 163)(106, 149)(107, 148)(108, 167)(109, 166)(110, 169)(111, 152)(112, 151)(113, 173)(114, 172)(115, 153)(116, 177)(117, 176)(118, 157)(119, 156)(120, 180)(121, 158)(122, 183)(123, 182)(124, 162)(125, 161)(126, 186)(127, 187)(128, 165)(129, 164)(130, 191)(131, 190)(132, 168)(133, 192)(134, 171)(135, 170)(136, 188)(137, 189)(138, 174)(139, 175)(140, 184)(141, 185)(142, 179)(143, 178)(144, 181) 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 E20.738 Transitivity :: VT+ Graph:: bipartite v = 8 e = 96 f = 50 degree seq :: [ 24^8 ] E20.740 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-3 * Y1, (Y1 * Y2)^8, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 6, 54, 102, 150, 15, 63, 111, 159, 22, 70, 118, 166, 20, 68, 116, 164, 27, 75, 123, 171, 34, 82, 130, 178, 32, 80, 128, 176, 39, 87, 135, 183, 46, 94, 142, 190, 44, 92, 140, 188, 48, 96, 144, 192, 42, 90, 138, 186, 35, 83, 131, 179, 37, 85, 133, 181, 30, 78, 126, 174, 23, 71, 119, 167, 25, 73, 121, 169, 18, 66, 114, 162, 9, 57, 105, 153, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 19, 67, 115, 163, 17, 65, 113, 161, 24, 72, 120, 168, 31, 79, 127, 175, 29, 77, 125, 173, 36, 84, 132, 180, 43, 91, 139, 187, 41, 89, 137, 185, 47, 95, 143, 191, 45, 93, 141, 189, 38, 86, 134, 182, 40, 88, 136, 184, 33, 81, 129, 177, 26, 74, 122, 170, 28, 76, 124, 172, 21, 69, 117, 165, 14, 62, 110, 158, 16, 64, 112, 160, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 66)(11, 61)(12, 64)(13, 59)(14, 54)(15, 69)(16, 60)(17, 71)(18, 58)(19, 73)(20, 74)(21, 63)(22, 76)(23, 65)(24, 78)(25, 67)(26, 68)(27, 81)(28, 70)(29, 83)(30, 72)(31, 85)(32, 86)(33, 75)(34, 88)(35, 77)(36, 90)(37, 79)(38, 80)(39, 93)(40, 82)(41, 92)(42, 84)(43, 96)(44, 89)(45, 87)(46, 95)(47, 94)(48, 91)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 156)(104, 159)(105, 161)(106, 149)(107, 148)(108, 151)(109, 163)(110, 164)(111, 152)(112, 166)(113, 153)(114, 168)(115, 157)(116, 158)(117, 171)(118, 160)(119, 173)(120, 162)(121, 175)(122, 176)(123, 165)(124, 178)(125, 167)(126, 180)(127, 169)(128, 170)(129, 183)(130, 172)(131, 185)(132, 174)(133, 187)(134, 188)(135, 177)(136, 190)(137, 179)(138, 191)(139, 181)(140, 182)(141, 192)(142, 184)(143, 186)(144, 189) 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 ) } Outer automorphisms :: reflexible Dual of E20.737 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 56 degree seq :: [ 96^2 ] E20.741 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y1 * Y3^2 * Y1 * Y3^-2, Y3^6, Y3^-1 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1, (Y3^-2 * Y1 * Y3^-1 * Y2)^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 13, 61)(7, 55, 17, 65)(8, 56, 19, 67)(9, 57, 21, 69)(10, 58, 23, 71)(12, 60, 18, 66)(14, 62, 20, 68)(15, 63, 29, 77)(16, 64, 31, 79)(22, 70, 30, 78)(24, 72, 32, 80)(25, 73, 41, 89)(26, 74, 43, 91)(27, 75, 42, 90)(28, 76, 44, 92)(33, 81, 37, 85)(34, 82, 38, 86)(35, 83, 46, 94)(36, 84, 40, 88)(39, 87, 47, 95)(45, 93, 48, 96)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 106, 154)(103, 151, 111, 159)(104, 152, 112, 160)(107, 155, 117, 165)(108, 156, 118, 166)(109, 157, 119, 167)(110, 158, 120, 168)(113, 161, 125, 173)(114, 162, 126, 174)(115, 163, 127, 175)(116, 164, 128, 176)(121, 169, 133, 181)(122, 170, 134, 182)(123, 171, 135, 183)(124, 172, 136, 184)(129, 177, 137, 185)(130, 178, 139, 187)(131, 179, 141, 189)(132, 180, 140, 188)(138, 186, 143, 191)(142, 190, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 97)(6, 111)(7, 114)(8, 98)(9, 118)(10, 99)(11, 121)(12, 123)(13, 122)(14, 101)(15, 126)(16, 102)(17, 129)(18, 131)(19, 130)(20, 104)(21, 133)(22, 135)(23, 134)(24, 106)(25, 138)(26, 107)(27, 110)(28, 109)(29, 137)(30, 141)(31, 139)(32, 112)(33, 142)(34, 113)(35, 116)(36, 115)(37, 143)(38, 117)(39, 120)(40, 119)(41, 144)(42, 124)(43, 125)(44, 127)(45, 128)(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) :: { ( 12, 48, 12, 48 ) } Outer automorphisms :: reflexible Dual of E20.752 Graph:: simple bipartite v = 48 e = 96 f = 10 degree seq :: [ 4^48 ] E20.742 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y2^6, Y3^4 * Y2^3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 24, 72)(12, 60, 25, 73)(13, 61, 23, 71)(14, 62, 26, 74)(15, 63, 21, 69)(16, 64, 19, 67)(17, 65, 20, 68)(18, 66, 22, 70)(27, 75, 38, 86)(28, 76, 46, 94)(29, 77, 45, 93)(30, 78, 47, 95)(31, 79, 44, 92)(32, 80, 48, 96)(33, 81, 42, 90)(34, 82, 40, 88)(35, 83, 39, 87)(36, 84, 41, 89)(37, 85, 43, 91)(97, 145, 99, 147, 107, 155, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 134, 182, 120, 168, 105, 153)(100, 148, 108, 156, 124, 172, 133, 181, 130, 178, 111, 159)(102, 150, 109, 157, 125, 173, 128, 176, 131, 179, 113, 161)(104, 152, 116, 164, 135, 183, 144, 192, 141, 189, 119, 167)(106, 154, 117, 165, 136, 184, 139, 187, 142, 190, 121, 169)(110, 158, 126, 174, 132, 180, 114, 162, 127, 175, 129, 177)(118, 166, 137, 185, 143, 191, 122, 170, 138, 186, 140, 188) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 135)(20, 137)(21, 103)(22, 139)(23, 140)(24, 141)(25, 105)(26, 106)(27, 133)(28, 132)(29, 107)(30, 131)(31, 109)(32, 123)(33, 125)(34, 127)(35, 112)(36, 113)(37, 114)(38, 144)(39, 143)(40, 115)(41, 142)(42, 117)(43, 134)(44, 136)(45, 138)(46, 120)(47, 121)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E20.747 Graph:: simple bipartite v = 32 e = 96 f = 26 degree seq :: [ 4^24, 12^8 ] E20.743 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2 * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^4, 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 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 24, 72)(12, 60, 25, 73)(13, 61, 23, 71)(14, 62, 26, 74)(15, 63, 21, 69)(16, 64, 19, 67)(17, 65, 20, 68)(18, 66, 22, 70)(27, 75, 34, 82)(28, 76, 40, 88)(29, 77, 39, 87)(30, 78, 38, 86)(31, 79, 37, 85)(32, 80, 36, 84)(33, 81, 35, 83)(41, 89, 46, 94)(42, 90, 45, 93)(43, 91, 48, 96)(44, 92, 47, 95)(97, 145, 99, 147, 107, 155, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 130, 178, 120, 168, 105, 153)(100, 148, 108, 156, 124, 172, 137, 185, 128, 176, 111, 159)(102, 150, 109, 157, 125, 173, 138, 186, 129, 177, 113, 161)(104, 152, 116, 164, 131, 179, 141, 189, 135, 183, 119, 167)(106, 154, 117, 165, 132, 180, 142, 190, 136, 184, 121, 169)(110, 158, 114, 162, 126, 174, 139, 187, 140, 188, 127, 175)(118, 166, 122, 170, 133, 181, 143, 191, 144, 192, 134, 182) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 124)(12, 114)(13, 99)(14, 113)(15, 127)(16, 128)(17, 101)(18, 102)(19, 131)(20, 122)(21, 103)(22, 121)(23, 134)(24, 135)(25, 105)(26, 106)(27, 137)(28, 126)(29, 107)(30, 109)(31, 129)(32, 140)(33, 112)(34, 141)(35, 133)(36, 115)(37, 117)(38, 136)(39, 144)(40, 120)(41, 139)(42, 123)(43, 125)(44, 138)(45, 143)(46, 130)(47, 132)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E20.748 Graph:: simple bipartite v = 32 e = 96 f = 26 degree seq :: [ 4^24, 12^8 ] E20.744 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^6, Y3^4 * Y2^3 ] Map:: 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, 19, 67)(12, 60, 21, 69)(13, 61, 20, 68)(14, 62, 26, 74)(15, 63, 25, 73)(16, 64, 24, 72)(17, 65, 23, 71)(18, 66, 22, 70)(27, 75, 38, 86)(28, 76, 40, 88)(29, 77, 39, 87)(30, 78, 42, 90)(31, 79, 41, 89)(32, 80, 48, 96)(33, 81, 47, 95)(34, 82, 46, 94)(35, 83, 45, 93)(36, 84, 44, 92)(37, 85, 43, 91)(97, 145, 99, 147, 107, 155, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 134, 182, 120, 168, 105, 153)(100, 148, 108, 156, 124, 172, 133, 181, 130, 178, 111, 159)(102, 150, 109, 157, 125, 173, 128, 176, 131, 179, 113, 161)(104, 152, 116, 164, 135, 183, 144, 192, 141, 189, 119, 167)(106, 154, 117, 165, 136, 184, 139, 187, 142, 190, 121, 169)(110, 158, 126, 174, 132, 180, 114, 162, 127, 175, 129, 177)(118, 166, 137, 185, 143, 191, 122, 170, 138, 186, 140, 188) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 135)(20, 137)(21, 103)(22, 139)(23, 140)(24, 141)(25, 105)(26, 106)(27, 133)(28, 132)(29, 107)(30, 131)(31, 109)(32, 123)(33, 125)(34, 127)(35, 112)(36, 113)(37, 114)(38, 144)(39, 143)(40, 115)(41, 142)(42, 117)(43, 134)(44, 136)(45, 138)(46, 120)(47, 121)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E20.751 Graph:: simple bipartite v = 32 e = 96 f = 26 degree seq :: [ 4^24, 12^8 ] E20.745 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y2 * Y3)^2, Y2 * Y3 * Y2^-2 * Y3 * Y2, Y2^6, (Y2^-1 * R * Y2^-1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2, (Y3 * Y2^-2 * Y1 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 8, 56)(9, 57, 15, 63)(10, 58, 16, 64)(11, 59, 17, 65)(12, 60, 18, 66)(13, 61, 19, 67)(14, 62, 20, 68)(21, 69, 29, 77)(22, 70, 30, 78)(23, 71, 31, 79)(24, 72, 32, 80)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(37, 85, 45, 93)(38, 86, 46, 94)(39, 87, 41, 89)(40, 88, 42, 90)(43, 91, 44, 92)(47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 117, 165, 110, 158, 101, 149)(98, 146, 102, 150, 111, 159, 125, 173, 116, 164, 104, 152)(100, 148, 107, 155, 118, 166, 134, 182, 123, 171, 108, 156)(103, 151, 113, 161, 126, 174, 142, 190, 131, 179, 114, 162)(106, 154, 119, 167, 133, 181, 124, 172, 109, 157, 120, 168)(112, 160, 127, 175, 141, 189, 132, 180, 115, 163, 128, 176)(121, 169, 137, 185, 143, 191, 139, 187, 122, 170, 138, 186)(129, 177, 135, 183, 144, 192, 140, 188, 130, 178, 136, 184) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 112)(7, 98)(8, 115)(9, 118)(10, 99)(11, 121)(12, 122)(13, 101)(14, 123)(15, 126)(16, 102)(17, 129)(18, 130)(19, 104)(20, 131)(21, 133)(22, 105)(23, 135)(24, 136)(25, 107)(26, 108)(27, 110)(28, 140)(29, 141)(30, 111)(31, 137)(32, 138)(33, 113)(34, 114)(35, 116)(36, 139)(37, 117)(38, 143)(39, 119)(40, 120)(41, 127)(42, 128)(43, 132)(44, 124)(45, 125)(46, 144)(47, 134)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E20.750 Graph:: simple bipartite v = 32 e = 96 f = 26 degree seq :: [ 4^24, 12^8 ] E20.746 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3 * Y2 * Y3, (R * Y2 * Y3)^2, Y2^6, Y2^2 * Y1 * Y2^-2 * Y1, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y1, Y1 * Y2^-2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 14, 62)(6, 54, 17, 65)(8, 56, 22, 70)(10, 58, 18, 66)(11, 59, 20, 68)(12, 60, 19, 67)(13, 61, 23, 71)(15, 63, 21, 69)(16, 64, 24, 72)(25, 73, 38, 86)(26, 74, 39, 87)(27, 75, 43, 91)(28, 76, 37, 85)(29, 77, 34, 82)(30, 78, 35, 83)(31, 79, 40, 88)(32, 80, 42, 90)(33, 81, 41, 89)(36, 84, 46, 94)(44, 92, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147, 106, 154, 123, 171, 112, 160, 101, 149)(98, 146, 102, 150, 114, 162, 132, 180, 120, 168, 104, 152)(100, 148, 108, 156, 124, 172, 141, 189, 127, 175, 109, 157)(103, 151, 116, 164, 133, 181, 144, 192, 136, 184, 117, 165)(105, 153, 121, 169, 139, 187, 128, 176, 110, 158, 122, 170)(107, 155, 125, 173, 140, 188, 129, 177, 111, 159, 126, 174)(113, 161, 130, 178, 142, 190, 137, 185, 118, 166, 131, 179)(115, 163, 134, 182, 143, 191, 138, 186, 119, 167, 135, 183) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 111)(6, 115)(7, 98)(8, 119)(9, 116)(10, 124)(11, 99)(12, 113)(13, 118)(14, 117)(15, 101)(16, 127)(17, 108)(18, 133)(19, 102)(20, 105)(21, 110)(22, 109)(23, 104)(24, 136)(25, 130)(26, 131)(27, 140)(28, 106)(29, 134)(30, 135)(31, 112)(32, 137)(33, 138)(34, 121)(35, 122)(36, 143)(37, 114)(38, 125)(39, 126)(40, 120)(41, 128)(42, 129)(43, 144)(44, 123)(45, 142)(46, 141)(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, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E20.749 Graph:: simple bipartite v = 32 e = 96 f = 26 degree seq :: [ 4^24, 12^8 ] E20.747 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^8, (Y1^-1 * Y3^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 4, 52, 9, 57, 18, 66, 14, 62, 21, 69, 30, 78, 26, 74, 33, 81, 41, 89, 38, 86, 44, 92, 39, 87, 28, 76, 34, 82, 27, 75, 16, 64, 22, 70, 15, 63, 6, 54, 10, 58, 5, 53)(3, 51, 11, 59, 19, 67, 12, 60, 23, 71, 31, 79, 24, 72, 35, 83, 42, 90, 36, 84, 45, 93, 48, 96, 46, 94, 47, 95, 43, 91, 37, 85, 40, 88, 32, 80, 25, 73, 29, 77, 20, 68, 13, 61, 17, 65, 8, 56)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 109, 157)(101, 149, 107, 155)(102, 150, 108, 156)(103, 151, 113, 161)(105, 153, 116, 164)(106, 154, 115, 163)(110, 158, 121, 169)(111, 159, 119, 167)(112, 160, 120, 168)(114, 162, 125, 173)(117, 165, 128, 176)(118, 166, 127, 175)(122, 170, 133, 181)(123, 171, 131, 179)(124, 172, 132, 180)(126, 174, 136, 184)(129, 177, 139, 187)(130, 178, 138, 186)(134, 182, 142, 190)(135, 183, 141, 189)(137, 185, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 103)(6, 97)(7, 114)(8, 115)(9, 117)(10, 98)(11, 119)(12, 120)(13, 99)(14, 122)(15, 101)(16, 102)(17, 107)(18, 126)(19, 127)(20, 104)(21, 129)(22, 106)(23, 131)(24, 132)(25, 109)(26, 134)(27, 111)(28, 112)(29, 113)(30, 137)(31, 138)(32, 116)(33, 140)(34, 118)(35, 141)(36, 142)(37, 121)(38, 124)(39, 123)(40, 125)(41, 135)(42, 144)(43, 128)(44, 130)(45, 143)(46, 133)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E20.742 Graph:: bipartite v = 26 e = 96 f = 32 degree seq :: [ 4^24, 48^2 ] E20.748 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (Y1, Y3^-1), (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3 * Y1^3, Y3 * Y1^5, (Y2 * Y3 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-5, Y3^-1 * Y1^-1 * Y3^-4, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 17, 65, 6, 54, 10, 58, 22, 70, 36, 84, 32, 80, 18, 66, 26, 74, 40, 88, 33, 81, 14, 62, 25, 73, 39, 87, 34, 82, 15, 63, 4, 52, 9, 57, 21, 69, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 38, 86, 24, 72, 13, 61, 29, 77, 43, 91, 48, 96, 42, 90, 31, 79, 45, 93, 47, 95, 41, 89, 30, 78, 44, 92, 46, 94, 37, 85, 23, 71, 12, 60, 28, 76, 35, 83, 20, 68, 8, 56)(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, 134, 182)(118, 166, 133, 181)(121, 169, 138, 186)(122, 170, 137, 185)(128, 176, 140, 188)(129, 177, 141, 189)(130, 178, 139, 187)(132, 180, 142, 190)(135, 183, 144, 192)(136, 184, 143, 191) 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, 128)(15, 129)(16, 130)(17, 101)(18, 102)(19, 112)(20, 133)(21, 135)(22, 103)(23, 137)(24, 104)(25, 114)(26, 106)(27, 131)(28, 140)(29, 107)(30, 138)(31, 109)(32, 113)(33, 132)(34, 136)(35, 142)(36, 115)(37, 143)(38, 116)(39, 122)(40, 118)(41, 144)(42, 120)(43, 123)(44, 127)(45, 125)(46, 141)(47, 139)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E20.743 Graph:: bipartite v = 26 e = 96 f = 32 degree seq :: [ 4^24, 48^2 ] E20.749 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y1^-2 * Y3 * Y2 * Y1, (Y1^-1 * Y3 * Y1^-2)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^24 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 15, 63, 33, 81, 42, 90, 46, 94, 26, 74, 39, 87, 44, 92, 24, 72, 10, 58, 3, 51, 7, 55, 16, 64, 34, 82, 47, 95, 27, 75, 40, 88, 41, 89, 48, 96, 32, 80, 14, 62, 5, 53)(4, 52, 11, 59, 25, 73, 45, 93, 43, 91, 23, 71, 20, 68, 8, 56, 19, 67, 38, 86, 31, 79, 22, 70, 9, 57, 21, 69, 17, 65, 36, 84, 30, 78, 13, 61, 29, 77, 18, 66, 37, 85, 35, 83, 28, 76, 12, 60)(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, 130, 178)(113, 161, 121, 169)(115, 163, 133, 181)(116, 164, 125, 173)(122, 170, 137, 185)(123, 171, 138, 186)(124, 172, 127, 175)(126, 174, 139, 187)(128, 176, 140, 188)(129, 177, 143, 191)(131, 179, 134, 182)(132, 180, 141, 189)(135, 183, 144, 192)(136, 184, 142, 190) 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, 127)(15, 131)(16, 121)(17, 102)(18, 103)(19, 135)(20, 136)(21, 137)(22, 138)(23, 106)(24, 124)(25, 112)(26, 107)(27, 108)(28, 120)(29, 142)(30, 143)(31, 110)(32, 141)(33, 139)(34, 134)(35, 111)(36, 140)(37, 144)(38, 130)(39, 115)(40, 116)(41, 117)(42, 118)(43, 129)(44, 132)(45, 128)(46, 125)(47, 126)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E20.746 Graph:: bipartite v = 26 e = 96 f = 32 degree seq :: [ 4^24, 48^2 ] E20.750 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y2 * Y1^2 * Y3 * Y1^-2, Y1^-1 * Y3 * Y1^2 * Y2 * Y1^-1, (Y2 * Y1^-3)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1 * Y2, Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 17, 65, 35, 83, 29, 77, 44, 92, 25, 73, 41, 89, 48, 96, 45, 93, 27, 75, 10, 58, 21, 69, 39, 87, 47, 95, 46, 94, 28, 76, 43, 91, 26, 74, 42, 90, 34, 82, 16, 64, 5, 53)(3, 51, 9, 57, 19, 67, 40, 88, 33, 81, 15, 63, 22, 70, 7, 55, 20, 68, 37, 85, 31, 79, 13, 61, 4, 52, 12, 60, 18, 66, 38, 86, 32, 80, 14, 62, 24, 72, 8, 56, 23, 71, 36, 84, 30, 78, 11, 59)(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, 122, 170)(109, 157, 125, 173)(111, 159, 123, 171)(112, 160, 127, 175)(113, 161, 132, 180)(115, 163, 135, 183)(116, 164, 137, 185)(118, 166, 139, 187)(119, 167, 138, 186)(120, 168, 140, 188)(126, 174, 141, 189)(128, 176, 142, 190)(129, 177, 131, 179)(130, 178, 136, 184)(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, 122)(10, 99)(11, 125)(12, 121)(13, 124)(14, 123)(15, 101)(16, 126)(17, 133)(18, 135)(19, 102)(20, 138)(21, 103)(22, 140)(23, 137)(24, 139)(25, 108)(26, 105)(27, 110)(28, 109)(29, 107)(30, 112)(31, 141)(32, 131)(33, 142)(34, 134)(35, 128)(36, 143)(37, 113)(38, 130)(39, 114)(40, 144)(41, 119)(42, 116)(43, 120)(44, 118)(45, 127)(46, 129)(47, 132)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.745 Graph:: bipartite v = 26 e = 96 f = 32 degree seq :: [ 4^24, 48^2 ] E20.751 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-3, (Y1^-1, Y3^-1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3^-2 * Y2 * Y1, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^8, Y2 * Y1^-1 * Y2 * Y1 * Y3^-3 * Y1 * Y3^-3 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 4, 52, 9, 57, 20, 68, 15, 63, 25, 73, 38, 86, 32, 80, 41, 89, 47, 95, 45, 93, 48, 96, 43, 91, 34, 82, 42, 90, 29, 77, 18, 66, 26, 74, 17, 65, 6, 54, 10, 58, 5, 53)(3, 51, 11, 59, 27, 75, 12, 60, 24, 72, 40, 88, 23, 71, 8, 56, 21, 69, 39, 87, 22, 70, 37, 85, 46, 94, 36, 84, 19, 67, 35, 83, 33, 81, 16, 64, 31, 79, 44, 92, 30, 78, 14, 62, 28, 76, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 112, 160)(102, 150, 108, 156)(103, 151, 115, 163)(105, 153, 120, 168)(106, 154, 118, 166)(107, 155, 121, 169)(109, 157, 125, 173)(111, 159, 127, 175)(113, 161, 126, 174)(114, 162, 119, 167)(116, 164, 133, 181)(117, 165, 134, 182)(122, 170, 132, 180)(123, 171, 139, 187)(124, 172, 137, 185)(128, 176, 131, 179)(129, 177, 138, 186)(130, 178, 135, 183)(136, 184, 143, 191)(140, 188, 144, 192)(141, 189, 142, 190) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 103)(6, 97)(7, 116)(8, 118)(9, 121)(10, 98)(11, 120)(12, 119)(13, 123)(14, 99)(15, 128)(16, 126)(17, 101)(18, 102)(19, 112)(20, 134)(21, 133)(22, 132)(23, 135)(24, 104)(25, 137)(26, 106)(27, 136)(28, 107)(29, 113)(30, 109)(31, 110)(32, 141)(33, 140)(34, 114)(35, 127)(36, 129)(37, 115)(38, 143)(39, 142)(40, 117)(41, 144)(42, 122)(43, 125)(44, 124)(45, 130)(46, 131)(47, 139)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E20.744 Graph:: bipartite v = 26 e = 96 f = 32 degree seq :: [ 4^24, 48^2 ] E20.752 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3, Y1^-1), (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-2 * Y2 * Y1^-1, Y1 * Y2^3 * Y3^-1 * Y2^-1, Y2 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1, Y1^6, Y3^-1 * Y2^2 * Y1^-1 * Y2^-2, Y2 * Y3 * Y1^-2 * Y2 * Y3, (Y3 * Y2^2)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 27, 75, 19, 67, 5, 53)(3, 51, 13, 61, 28, 76, 11, 59, 36, 84, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60, 30, 78, 20, 68)(6, 54, 22, 70, 29, 77, 21, 69, 33, 81, 9, 57)(14, 62, 42, 90, 45, 93, 41, 89, 48, 96, 38, 86)(15, 63, 35, 83, 17, 65, 37, 85, 26, 74, 39, 87)(18, 66, 32, 80, 23, 71, 34, 82, 25, 73, 40, 88)(24, 72, 43, 91, 46, 94, 31, 79, 47, 95, 44, 92)(97, 145, 99, 147, 110, 158, 136, 184, 108, 156, 133, 181, 143, 191, 129, 177, 115, 163, 132, 180, 144, 192, 130, 178, 106, 154, 131, 179, 142, 190, 125, 173, 104, 152, 124, 172, 141, 189, 128, 176, 116, 164, 135, 183, 120, 168, 102, 150)(98, 146, 105, 153, 127, 175, 111, 159, 126, 174, 121, 169, 137, 185, 109, 157, 101, 149, 117, 165, 139, 187, 122, 170, 103, 151, 119, 167, 138, 186, 112, 160, 123, 171, 118, 166, 140, 188, 113, 161, 100, 148, 114, 162, 134, 182, 107, 155) L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 116)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 133)(12, 98)(13, 131)(14, 139)(15, 132)(16, 135)(17, 99)(18, 125)(19, 126)(20, 123)(21, 136)(22, 130)(23, 129)(24, 137)(25, 102)(26, 124)(27, 108)(28, 113)(29, 121)(30, 104)(31, 110)(32, 117)(33, 114)(34, 105)(35, 112)(36, 122)(37, 109)(38, 120)(39, 107)(40, 118)(41, 143)(42, 142)(43, 144)(44, 141)(45, 127)(46, 134)(47, 138)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^12 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E20.741 Graph:: bipartite v = 10 e = 96 f = 48 degree seq :: [ 12^8, 48^2 ] E20.753 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {12, 12, 24}) Quotient :: edge Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2, T1 * T2^-3 * T1 * T2, T2^3 * T1^2 * T2, (T2 * T1^-1)^4, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-3 ] Map:: non-degenerate R = (1, 3, 10, 21, 13, 32, 43, 23, 42, 48, 40, 34, 44, 24, 41, 47, 36, 25, 39, 20, 6, 19, 17, 5)(2, 7, 22, 14, 4, 12, 28, 9, 27, 45, 33, 11, 31, 38, 29, 46, 35, 15, 30, 37, 18, 16, 26, 8)(49, 50, 54, 66, 84, 83, 92, 79, 90, 75, 61, 52)(51, 57, 67, 62, 73, 56, 72, 85, 96, 94, 80, 59)(53, 63, 68, 86, 95, 93, 82, 60, 71, 55, 69, 64)(58, 77, 65, 81, 87, 76, 89, 70, 88, 74, 91, 78) 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) :: { ( 24^12 ), ( 24^24 ) } Outer automorphisms :: reflexible Dual of E20.754 Transitivity :: ET+ Graph:: bipartite v = 6 e = 48 f = 4 degree seq :: [ 12^4, 24^2 ] E20.754 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {12, 12, 24}) Quotient :: loop Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ F^2, T1^2 * T2^-2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1, T2^2 * T1^10, (T1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 49, 3, 51, 6, 54, 15, 63, 26, 74, 39, 87, 46, 94, 45, 93, 35, 83, 23, 71, 11, 59, 5, 53)(2, 50, 7, 55, 14, 62, 27, 75, 38, 86, 47, 95, 44, 92, 36, 84, 22, 70, 12, 60, 4, 52, 8, 56)(9, 57, 19, 67, 28, 76, 41, 89, 48, 96, 42, 90, 37, 85, 25, 73, 13, 61, 21, 69, 10, 58, 20, 68)(16, 64, 29, 77, 40, 88, 34, 82, 43, 91, 33, 81, 24, 72, 32, 80, 18, 66, 31, 79, 17, 65, 30, 78) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 58)(6, 62)(7, 64)(8, 65)(9, 63)(10, 51)(11, 52)(12, 66)(13, 53)(14, 74)(15, 76)(16, 75)(17, 55)(18, 56)(19, 80)(20, 81)(21, 82)(22, 59)(23, 61)(24, 60)(25, 77)(26, 86)(27, 88)(28, 87)(29, 69)(30, 73)(31, 90)(32, 89)(33, 67)(34, 68)(35, 70)(36, 72)(37, 71)(38, 94)(39, 96)(40, 95)(41, 79)(42, 78)(43, 84)(44, 83)(45, 85)(46, 92)(47, 91)(48, 93) 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 ) } Outer automorphisms :: reflexible Dual of E20.753 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 48 f = 6 degree seq :: [ 24^4 ] E20.755 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2^-3 * Y1, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2^2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-2, (Y2 * Y1^-1)^4, (Y2 * Y1 * Y2)^4, (Y3^-1 * Y1^-1)^12 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 35, 83, 44, 92, 31, 79, 42, 90, 27, 75, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 14, 62, 25, 73, 8, 56, 24, 72, 37, 85, 48, 96, 46, 94, 32, 80, 11, 59)(5, 53, 15, 63, 20, 68, 38, 86, 47, 95, 45, 93, 34, 82, 12, 60, 23, 71, 7, 55, 21, 69, 16, 64)(10, 58, 29, 77, 17, 65, 33, 81, 39, 87, 28, 76, 41, 89, 22, 70, 40, 88, 26, 74, 43, 91, 30, 78)(97, 145, 99, 147, 106, 154, 117, 165, 109, 157, 128, 176, 139, 187, 119, 167, 138, 186, 144, 192, 136, 184, 130, 178, 140, 188, 120, 168, 137, 185, 143, 191, 132, 180, 121, 169, 135, 183, 116, 164, 102, 150, 115, 163, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 110, 158, 100, 148, 108, 156, 124, 172, 105, 153, 123, 171, 141, 189, 129, 177, 107, 155, 127, 175, 134, 182, 125, 173, 142, 190, 131, 179, 111, 159, 126, 174, 133, 181, 114, 162, 112, 160, 122, 170, 104, 152) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 117)(11, 127)(12, 124)(13, 128)(14, 100)(15, 126)(16, 122)(17, 101)(18, 112)(19, 113)(20, 102)(21, 109)(22, 110)(23, 138)(24, 137)(25, 135)(26, 104)(27, 141)(28, 105)(29, 142)(30, 133)(31, 134)(32, 139)(33, 107)(34, 140)(35, 111)(36, 121)(37, 114)(38, 125)(39, 116)(40, 130)(41, 143)(42, 144)(43, 119)(44, 120)(45, 129)(46, 131)(47, 132)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E20.756 Graph:: bipartite v = 6 e = 96 f = 52 degree seq :: [ 24^4, 48^2 ] E20.756 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {12, 12, 24}) Quotient :: dipole Aut^+ = C3 x Q16 (small group id <48, 27>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^4 * Y2^-2, Y3 * Y2 * Y3^-1 * Y2 * Y3^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2^-2)^2, Y3^-1 * Y2^-1 * Y3^2 * Y2^2 * Y3 * Y2, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-1 * Y3^-2, (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, 114, 162, 132, 180, 123, 171, 136, 184, 131, 179, 140, 188, 127, 175, 109, 157, 100, 148)(99, 147, 105, 153, 115, 163, 134, 182, 143, 191, 142, 190, 129, 177, 110, 158, 121, 169, 104, 152, 120, 168, 107, 155)(101, 149, 111, 159, 116, 164, 108, 156, 119, 167, 103, 151, 117, 165, 133, 181, 144, 192, 141, 189, 128, 176, 112, 160)(106, 154, 125, 173, 135, 183, 130, 178, 137, 185, 122, 170, 139, 187, 118, 166, 138, 186, 124, 172, 113, 161, 126, 174) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 123)(10, 116)(11, 114)(12, 122)(13, 120)(14, 100)(15, 130)(16, 125)(17, 101)(18, 133)(19, 135)(20, 102)(21, 136)(22, 107)(23, 132)(24, 113)(25, 138)(26, 104)(27, 141)(28, 105)(29, 142)(30, 134)(31, 111)(32, 109)(33, 139)(34, 110)(35, 112)(36, 143)(37, 124)(38, 131)(39, 119)(40, 129)(41, 117)(42, 128)(43, 144)(44, 121)(45, 126)(46, 127)(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) :: { ( 24, 48 ), ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E20.755 Graph:: simple bipartite v = 52 e = 96 f = 6 degree seq :: [ 2^48, 24^4 ] E20.757 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^6, T1 * T2^8, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 35, 23, 12, 4, 10, 20, 32, 42, 44, 34, 22, 11, 21, 33, 43, 48, 46, 38, 26, 14, 25, 37, 45, 47, 40, 28, 16, 6, 15, 27, 39, 41, 30, 18, 8, 2, 7, 17, 29, 36, 24, 13, 5)(49, 50, 54, 62, 59, 52)(51, 55, 63, 73, 69, 58)(53, 56, 64, 74, 70, 60)(57, 65, 75, 85, 81, 68)(61, 66, 76, 86, 82, 71)(67, 77, 87, 93, 91, 80)(72, 78, 88, 94, 92, 83)(79, 84, 89, 95, 96, 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) :: { ( 96^6 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E20.758 Transitivity :: ET+ Graph:: bipartite v = 9 e = 48 f = 1 degree seq :: [ 6^8, 48 ] E20.758 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^6, T1 * T2^8, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 19, 67, 31, 79, 35, 83, 23, 71, 12, 60, 4, 52, 10, 58, 20, 68, 32, 80, 42, 90, 44, 92, 34, 82, 22, 70, 11, 59, 21, 69, 33, 81, 43, 91, 48, 96, 46, 94, 38, 86, 26, 74, 14, 62, 25, 73, 37, 85, 45, 93, 47, 95, 40, 88, 28, 76, 16, 64, 6, 54, 15, 63, 27, 75, 39, 87, 41, 89, 30, 78, 18, 66, 8, 56, 2, 50, 7, 55, 17, 65, 29, 77, 36, 84, 24, 72, 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, 59)(15, 73)(16, 74)(17, 75)(18, 76)(19, 77)(20, 57)(21, 58)(22, 60)(23, 61)(24, 78)(25, 69)(26, 70)(27, 85)(28, 86)(29, 87)(30, 88)(31, 84)(32, 67)(33, 68)(34, 71)(35, 72)(36, 89)(37, 81)(38, 82)(39, 93)(40, 94)(41, 95)(42, 79)(43, 80)(44, 83)(45, 91)(46, 92)(47, 96)(48, 90) local type(s) :: { ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) } Outer automorphisms :: reflexible Dual of E20.757 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 9 degree seq :: [ 96 ] E20.759 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3^6, Y1^6, Y3^-1 * Y2^8, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 11, 59, 4, 52)(3, 51, 7, 55, 15, 63, 25, 73, 21, 69, 10, 58)(5, 53, 8, 56, 16, 64, 26, 74, 22, 70, 12, 60)(9, 57, 17, 65, 27, 75, 37, 85, 33, 81, 20, 68)(13, 61, 18, 66, 28, 76, 38, 86, 34, 82, 23, 71)(19, 67, 29, 77, 39, 87, 45, 93, 43, 91, 32, 80)(24, 72, 30, 78, 40, 88, 46, 94, 44, 92, 35, 83)(31, 79, 36, 84, 41, 89, 47, 95, 48, 96, 42, 90)(97, 145, 99, 147, 105, 153, 115, 163, 127, 175, 131, 179, 119, 167, 108, 156, 100, 148, 106, 154, 116, 164, 128, 176, 138, 186, 140, 188, 130, 178, 118, 166, 107, 155, 117, 165, 129, 177, 139, 187, 144, 192, 142, 190, 134, 182, 122, 170, 110, 158, 121, 169, 133, 181, 141, 189, 143, 191, 136, 184, 124, 172, 112, 160, 102, 150, 111, 159, 123, 171, 135, 183, 137, 185, 126, 174, 114, 162, 104, 152, 98, 146, 103, 151, 113, 161, 125, 173, 132, 180, 120, 168, 109, 157, 101, 149) L = (1, 100)(2, 97)(3, 106)(4, 107)(5, 108)(6, 98)(7, 99)(8, 101)(9, 116)(10, 117)(11, 110)(12, 118)(13, 119)(14, 102)(15, 103)(16, 104)(17, 105)(18, 109)(19, 128)(20, 129)(21, 121)(22, 122)(23, 130)(24, 131)(25, 111)(26, 112)(27, 113)(28, 114)(29, 115)(30, 120)(31, 138)(32, 139)(33, 133)(34, 134)(35, 140)(36, 127)(37, 123)(38, 124)(39, 125)(40, 126)(41, 132)(42, 144)(43, 141)(44, 142)(45, 135)(46, 136)(47, 137)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 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 E20.760 Graph:: bipartite v = 9 e = 96 f = 49 degree seq :: [ 12^8, 96 ] E20.760 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^6, Y1^8 * Y3, Y1^2 * Y3^-2 * Y1^-3 * Y3^2 * Y1, (Y3 * Y2^-1)^6, (Y1^-1 * Y3^-1)^48 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 25, 73, 35, 83, 23, 71, 12, 60, 5, 53, 8, 56, 16, 64, 27, 75, 37, 85, 44, 92, 36, 84, 24, 72, 13, 61, 18, 66, 29, 77, 39, 87, 45, 93, 47, 95, 41, 89, 31, 79, 19, 67, 30, 78, 40, 88, 46, 94, 48, 96, 42, 90, 32, 80, 20, 68, 9, 57, 17, 65, 28, 76, 38, 86, 43, 91, 33, 81, 21, 69, 10, 58, 3, 51, 7, 55, 15, 63, 26, 74, 34, 82, 22, 70, 11, 59, 4, 52)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 105)(4, 106)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 116)(11, 117)(12, 100)(13, 101)(14, 122)(15, 124)(16, 102)(17, 126)(18, 104)(19, 109)(20, 127)(21, 128)(22, 129)(23, 107)(24, 108)(25, 130)(26, 134)(27, 110)(28, 136)(29, 112)(30, 114)(31, 120)(32, 137)(33, 138)(34, 139)(35, 118)(36, 119)(37, 121)(38, 142)(39, 123)(40, 125)(41, 132)(42, 143)(43, 144)(44, 131)(45, 133)(46, 135)(47, 140)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 96 ), ( 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96, 12, 96 ) } Outer automorphisms :: reflexible Dual of E20.759 Graph:: bipartite v = 49 e = 96 f = 9 degree seq :: [ 2^48, 96 ] E20.761 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 25}) Quotient :: halfedge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^2, Y3 * Y1 * Y2 * Y1^-3, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 52, 2, 56, 6, 64, 14, 62, 12, 68, 18, 74, 24, 81, 31, 80, 30, 84, 34, 90, 40, 97, 47, 96, 46, 95, 45, 99, 49, 93, 43, 86, 36, 79, 29, 83, 33, 77, 27, 70, 20, 60, 10, 67, 17, 63, 13, 55, 5, 51)(3, 59, 9, 69, 19, 75, 25, 71, 21, 78, 28, 85, 35, 91, 41, 87, 37, 94, 44, 100, 50, 98, 48, 92, 42, 88, 38, 89, 39, 82, 32, 76, 26, 72, 22, 73, 23, 66, 16, 58, 8, 54, 4, 61, 11, 65, 15, 57, 7, 53) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 14)(13, 19)(16, 24)(17, 25)(20, 28)(22, 30)(23, 31)(26, 34)(27, 35)(29, 37)(32, 40)(33, 41)(36, 44)(38, 46)(39, 47)(42, 45)(43, 50)(48, 49)(51, 54)(52, 58)(53, 60)(55, 61)(56, 66)(57, 67)(59, 70)(62, 72)(63, 65)(64, 73)(68, 76)(69, 77)(71, 79)(74, 82)(75, 83)(78, 86)(80, 88)(81, 89)(84, 92)(85, 93)(87, 95)(90, 98)(91, 99)(94, 96)(97, 100) local type(s) :: { ( 10^50 ) } Outer automorphisms :: reflexible Dual of E20.763 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 50 f = 10 degree seq :: [ 50^2 ] E20.762 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 25}) Quotient :: halfedge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y2)^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y1^2 * Y2, Y1^3 * Y2 * Y1^-6 * Y3, Y1^3 * Y3 * Y2 * Y1^2 * Y3 * Y1^-1 * Y2 * Y1, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3, Y1 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 ] Map:: non-degenerate R = (1, 52, 2, 56, 6, 64, 14, 76, 26, 89, 39, 98, 48, 86, 36, 73, 23, 62, 12, 68, 18, 80, 30, 93, 43, 96, 46, 84, 34, 70, 20, 60, 10, 67, 17, 79, 29, 92, 42, 100, 50, 88, 38, 75, 25, 63, 13, 55, 5, 51)(3, 59, 9, 69, 19, 83, 33, 95, 45, 94, 44, 82, 32, 74, 24, 81, 31, 71, 21, 85, 35, 97, 47, 91, 41, 78, 28, 66, 16, 58, 8, 54, 4, 61, 11, 72, 22, 87, 37, 99, 49, 90, 40, 77, 27, 65, 15, 57, 7, 53) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 36)(24, 29)(25, 33)(26, 40)(28, 43)(32, 42)(34, 47)(37, 48)(38, 45)(39, 49)(41, 46)(44, 50)(51, 54)(52, 58)(53, 60)(55, 61)(56, 66)(57, 67)(59, 70)(62, 74)(63, 72)(64, 78)(65, 79)(68, 82)(69, 84)(71, 86)(73, 81)(75, 87)(76, 91)(77, 92)(80, 94)(83, 96)(85, 98)(88, 99)(89, 97)(90, 100)(93, 95) local type(s) :: { ( 10^50 ) } Outer automorphisms :: reflexible Dual of E20.764 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 50 f = 10 degree seq :: [ 50^2 ] E20.763 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 25}) Quotient :: halfedge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^5, Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, (Y2 * Y1 * Y3)^25 ] Map:: non-degenerate R = (1, 52, 2, 56, 6, 63, 13, 55, 5, 51)(3, 59, 9, 68, 18, 64, 14, 57, 7, 53)(4, 61, 11, 71, 21, 65, 15, 58, 8, 54)(10, 66, 16, 74, 24, 78, 28, 69, 19, 60)(12, 67, 17, 75, 25, 81, 31, 72, 22, 62)(20, 79, 29, 88, 38, 84, 34, 76, 26, 70)(23, 82, 32, 91, 41, 85, 35, 77, 27, 73)(30, 86, 36, 94, 44, 97, 47, 89, 39, 80)(33, 87, 37, 95, 45, 98, 48, 92, 42, 83)(40, 93, 43, 99, 49, 100, 50, 96, 46, 90) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 17)(10, 20)(11, 22)(13, 18)(15, 25)(16, 26)(19, 29)(21, 31)(23, 33)(24, 34)(27, 37)(28, 38)(30, 40)(32, 42)(35, 45)(36, 46)(39, 43)(41, 48)(44, 50)(47, 49)(51, 54)(52, 58)(53, 60)(55, 61)(56, 65)(57, 66)(59, 69)(62, 73)(63, 71)(64, 74)(67, 77)(68, 78)(70, 80)(72, 82)(75, 85)(76, 86)(79, 89)(81, 91)(83, 93)(84, 94)(87, 90)(88, 97)(92, 99)(95, 96)(98, 100) local type(s) :: { ( 50^10 ) } Outer automorphisms :: reflexible Dual of E20.761 Transitivity :: VT+ AT Graph:: bipartite v = 10 e = 50 f = 2 degree seq :: [ 10^10 ] E20.764 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 25}) Quotient :: halfedge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^5, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, (Y2 * Y1 * Y3)^25 ] Map:: non-degenerate R = (1, 52, 2, 56, 6, 63, 13, 55, 5, 51)(3, 59, 9, 68, 18, 64, 14, 57, 7, 53)(4, 61, 11, 71, 21, 65, 15, 58, 8, 54)(10, 66, 16, 74, 24, 78, 28, 69, 19, 60)(12, 67, 17, 75, 25, 81, 31, 72, 22, 62)(20, 79, 29, 88, 38, 84, 34, 76, 26, 70)(23, 82, 32, 91, 41, 85, 35, 77, 27, 73)(30, 86, 36, 94, 44, 98, 48, 89, 39, 80)(33, 87, 37, 95, 45, 99, 49, 92, 42, 83)(40, 97, 47, 93, 43, 100, 50, 96, 46, 90) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 17)(10, 20)(11, 22)(13, 18)(15, 25)(16, 26)(19, 29)(21, 31)(23, 33)(24, 34)(27, 37)(28, 38)(30, 40)(32, 42)(35, 45)(36, 46)(39, 47)(41, 49)(43, 48)(44, 50)(51, 54)(52, 58)(53, 60)(55, 61)(56, 65)(57, 66)(59, 69)(62, 73)(63, 71)(64, 74)(67, 77)(68, 78)(70, 80)(72, 82)(75, 85)(76, 86)(79, 89)(81, 91)(83, 93)(84, 94)(87, 97)(88, 98)(90, 95)(92, 100)(96, 99) local type(s) :: { ( 50^10 ) } Outer automorphisms :: reflexible Dual of E20.762 Transitivity :: VT+ AT Graph:: bipartite v = 10 e = 50 f = 2 degree seq :: [ 10^10 ] E20.765 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 25}) Quotient :: edge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 51, 4, 54, 12, 62, 13, 63, 5, 55)(2, 52, 7, 57, 17, 67, 18, 68, 8, 58)(3, 53, 10, 60, 22, 72, 23, 73, 11, 61)(6, 56, 15, 65, 27, 77, 28, 78, 16, 66)(9, 59, 20, 70, 32, 82, 33, 83, 21, 71)(14, 64, 25, 75, 37, 87, 38, 88, 26, 76)(19, 69, 30, 80, 42, 92, 43, 93, 31, 81)(24, 74, 35, 85, 45, 95, 46, 96, 36, 86)(29, 79, 40, 90, 48, 98, 49, 99, 41, 91)(34, 84, 39, 89, 47, 97, 50, 100, 44, 94)(101, 102)(103, 109)(104, 108)(105, 107)(106, 114)(110, 121)(111, 120)(112, 118)(113, 117)(115, 126)(116, 125)(119, 129)(122, 133)(123, 132)(124, 134)(127, 138)(128, 137)(130, 141)(131, 140)(135, 144)(136, 139)(142, 149)(143, 148)(145, 150)(146, 147)(151, 153)(152, 156)(154, 161)(155, 160)(157, 166)(158, 165)(159, 169)(162, 173)(163, 172)(164, 174)(167, 178)(168, 177)(170, 181)(171, 180)(175, 186)(176, 185)(179, 189)(182, 193)(183, 192)(184, 190)(187, 196)(188, 195)(191, 197)(194, 198)(199, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 100, 100 ), ( 100^10 ) } Outer automorphisms :: reflexible Dual of E20.771 Graph:: simple bipartite v = 60 e = 100 f = 2 degree seq :: [ 2^50, 10^10 ] E20.766 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 25}) Quotient :: edge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 51, 4, 54, 12, 62, 13, 63, 5, 55)(2, 52, 7, 57, 17, 67, 18, 68, 8, 58)(3, 53, 10, 60, 22, 72, 23, 73, 11, 61)(6, 56, 15, 65, 27, 77, 28, 78, 16, 66)(9, 59, 20, 70, 32, 82, 33, 83, 21, 71)(14, 64, 25, 75, 37, 87, 38, 88, 26, 76)(19, 69, 30, 80, 42, 92, 43, 93, 31, 81)(24, 74, 35, 85, 47, 97, 48, 98, 36, 86)(29, 79, 40, 90, 44, 94, 50, 100, 41, 91)(34, 84, 45, 95, 39, 89, 49, 99, 46, 96)(101, 102)(103, 109)(104, 108)(105, 107)(106, 114)(110, 121)(111, 120)(112, 118)(113, 117)(115, 126)(116, 125)(119, 129)(122, 133)(123, 132)(124, 134)(127, 138)(128, 137)(130, 141)(131, 140)(135, 146)(136, 145)(139, 148)(142, 150)(143, 144)(147, 149)(151, 153)(152, 156)(154, 161)(155, 160)(157, 166)(158, 165)(159, 169)(162, 173)(163, 172)(164, 174)(167, 178)(168, 177)(170, 181)(171, 180)(175, 186)(176, 185)(179, 189)(182, 193)(183, 192)(184, 194)(187, 198)(188, 197)(190, 195)(191, 199)(196, 200) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 100, 100 ), ( 100^10 ) } Outer automorphisms :: reflexible Dual of E20.772 Graph:: simple bipartite v = 60 e = 100 f = 2 degree seq :: [ 2^50, 10^10 ] E20.767 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 25}) Quotient :: edge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y2 * Y3^-3 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^5 ] Map:: R = (1, 51, 4, 54, 12, 62, 16, 66, 6, 56, 15, 65, 26, 76, 33, 83, 23, 73, 32, 82, 42, 92, 47, 97, 39, 89, 43, 93, 49, 99, 46, 96, 37, 87, 27, 77, 36, 86, 30, 80, 21, 71, 9, 59, 20, 70, 13, 63, 5, 55)(2, 52, 7, 57, 17, 67, 11, 61, 3, 53, 10, 60, 22, 72, 29, 79, 19, 69, 28, 78, 38, 88, 45, 95, 35, 85, 44, 94, 50, 100, 48, 98, 41, 91, 31, 81, 40, 90, 34, 84, 25, 75, 14, 64, 24, 74, 18, 68, 8, 58)(101, 102)(103, 109)(104, 108)(105, 107)(106, 114)(110, 121)(111, 120)(112, 118)(113, 117)(115, 125)(116, 124)(119, 127)(122, 130)(123, 131)(126, 134)(128, 137)(129, 136)(132, 141)(133, 140)(135, 143)(138, 146)(139, 144)(142, 148)(145, 149)(147, 150)(151, 153)(152, 156)(154, 161)(155, 160)(157, 166)(158, 165)(159, 169)(162, 167)(163, 172)(164, 173)(168, 176)(170, 179)(171, 178)(174, 183)(175, 182)(177, 185)(180, 188)(181, 189)(184, 192)(186, 195)(187, 194)(190, 197)(191, 193)(196, 200)(198, 199) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^50 ) } Outer automorphisms :: reflexible Dual of E20.769 Graph:: simple bipartite v = 52 e = 100 f = 10 degree seq :: [ 2^50, 50^2 ] E20.768 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 25}) Quotient :: edge^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y3^2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3^-5, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^4 ] Map:: R = (1, 51, 4, 54, 12, 62, 24, 74, 37, 87, 49, 99, 42, 92, 30, 80, 16, 66, 6, 56, 15, 65, 29, 79, 41, 91, 46, 96, 34, 84, 21, 71, 9, 59, 20, 70, 26, 76, 39, 89, 50, 100, 38, 88, 25, 75, 13, 63, 5, 55)(2, 52, 7, 57, 17, 67, 31, 81, 43, 93, 48, 98, 36, 86, 23, 73, 11, 61, 3, 53, 10, 60, 22, 72, 35, 85, 47, 97, 40, 90, 28, 78, 14, 64, 27, 77, 19, 69, 33, 83, 45, 95, 44, 94, 32, 82, 18, 68, 8, 58)(101, 102)(103, 109)(104, 108)(105, 107)(106, 114)(110, 121)(111, 120)(112, 118)(113, 117)(115, 128)(116, 127)(119, 130)(122, 134)(123, 126)(124, 132)(125, 131)(129, 140)(133, 142)(135, 146)(136, 139)(137, 144)(138, 143)(141, 147)(145, 149)(148, 150)(151, 153)(152, 156)(154, 161)(155, 160)(157, 166)(158, 165)(159, 169)(162, 173)(163, 172)(164, 176)(167, 180)(168, 179)(170, 177)(171, 183)(174, 186)(175, 185)(178, 189)(181, 192)(182, 191)(184, 195)(187, 198)(188, 197)(190, 200)(193, 199)(194, 196) L = (1, 101)(2, 102)(3, 103)(4, 104)(5, 105)(6, 106)(7, 107)(8, 108)(9, 109)(10, 110)(11, 111)(12, 112)(13, 113)(14, 114)(15, 115)(16, 116)(17, 117)(18, 118)(19, 119)(20, 120)(21, 121)(22, 122)(23, 123)(24, 124)(25, 125)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 132)(33, 133)(34, 134)(35, 135)(36, 136)(37, 137)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 20, 20 ), ( 20^50 ) } Outer automorphisms :: reflexible Dual of E20.770 Graph:: simple bipartite v = 52 e = 100 f = 10 degree seq :: [ 2^50, 50^2 ] E20.769 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 25}) Quotient :: loop^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 51, 101, 151, 4, 54, 104, 154, 12, 62, 112, 162, 13, 63, 113, 163, 5, 55, 105, 155)(2, 52, 102, 152, 7, 57, 107, 157, 17, 67, 117, 167, 18, 68, 118, 168, 8, 58, 108, 158)(3, 53, 103, 153, 10, 60, 110, 160, 22, 72, 122, 172, 23, 73, 123, 173, 11, 61, 111, 161)(6, 56, 106, 156, 15, 65, 115, 165, 27, 77, 127, 177, 28, 78, 128, 178, 16, 66, 116, 166)(9, 59, 109, 159, 20, 70, 120, 170, 32, 82, 132, 182, 33, 83, 133, 183, 21, 71, 121, 171)(14, 64, 114, 164, 25, 75, 125, 175, 37, 87, 137, 187, 38, 88, 138, 188, 26, 76, 126, 176)(19, 69, 119, 169, 30, 80, 130, 180, 42, 92, 142, 192, 43, 93, 143, 193, 31, 81, 131, 181)(24, 74, 124, 174, 35, 85, 135, 185, 45, 95, 145, 195, 46, 96, 146, 196, 36, 86, 136, 186)(29, 79, 129, 179, 40, 90, 140, 190, 48, 98, 148, 198, 49, 99, 149, 199, 41, 91, 141, 191)(34, 84, 134, 184, 39, 89, 139, 189, 47, 97, 147, 197, 50, 100, 150, 200, 44, 94, 144, 194) L = (1, 52)(2, 51)(3, 59)(4, 58)(5, 57)(6, 64)(7, 55)(8, 54)(9, 53)(10, 71)(11, 70)(12, 68)(13, 67)(14, 56)(15, 76)(16, 75)(17, 63)(18, 62)(19, 79)(20, 61)(21, 60)(22, 83)(23, 82)(24, 84)(25, 66)(26, 65)(27, 88)(28, 87)(29, 69)(30, 91)(31, 90)(32, 73)(33, 72)(34, 74)(35, 94)(36, 89)(37, 78)(38, 77)(39, 86)(40, 81)(41, 80)(42, 99)(43, 98)(44, 85)(45, 100)(46, 97)(47, 96)(48, 93)(49, 92)(50, 95)(101, 153)(102, 156)(103, 151)(104, 161)(105, 160)(106, 152)(107, 166)(108, 165)(109, 169)(110, 155)(111, 154)(112, 173)(113, 172)(114, 174)(115, 158)(116, 157)(117, 178)(118, 177)(119, 159)(120, 181)(121, 180)(122, 163)(123, 162)(124, 164)(125, 186)(126, 185)(127, 168)(128, 167)(129, 189)(130, 171)(131, 170)(132, 193)(133, 192)(134, 190)(135, 176)(136, 175)(137, 196)(138, 195)(139, 179)(140, 184)(141, 197)(142, 183)(143, 182)(144, 198)(145, 188)(146, 187)(147, 191)(148, 194)(149, 200)(150, 199) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E20.767 Transitivity :: VT+ Graph:: bipartite v = 10 e = 100 f = 52 degree seq :: [ 20^10 ] E20.770 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 25}) Quotient :: loop^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 51, 101, 151, 4, 54, 104, 154, 12, 62, 112, 162, 13, 63, 113, 163, 5, 55, 105, 155)(2, 52, 102, 152, 7, 57, 107, 157, 17, 67, 117, 167, 18, 68, 118, 168, 8, 58, 108, 158)(3, 53, 103, 153, 10, 60, 110, 160, 22, 72, 122, 172, 23, 73, 123, 173, 11, 61, 111, 161)(6, 56, 106, 156, 15, 65, 115, 165, 27, 77, 127, 177, 28, 78, 128, 178, 16, 66, 116, 166)(9, 59, 109, 159, 20, 70, 120, 170, 32, 82, 132, 182, 33, 83, 133, 183, 21, 71, 121, 171)(14, 64, 114, 164, 25, 75, 125, 175, 37, 87, 137, 187, 38, 88, 138, 188, 26, 76, 126, 176)(19, 69, 119, 169, 30, 80, 130, 180, 42, 92, 142, 192, 43, 93, 143, 193, 31, 81, 131, 181)(24, 74, 124, 174, 35, 85, 135, 185, 47, 97, 147, 197, 48, 98, 148, 198, 36, 86, 136, 186)(29, 79, 129, 179, 40, 90, 140, 190, 44, 94, 144, 194, 50, 100, 150, 200, 41, 91, 141, 191)(34, 84, 134, 184, 45, 95, 145, 195, 39, 89, 139, 189, 49, 99, 149, 199, 46, 96, 146, 196) L = (1, 52)(2, 51)(3, 59)(4, 58)(5, 57)(6, 64)(7, 55)(8, 54)(9, 53)(10, 71)(11, 70)(12, 68)(13, 67)(14, 56)(15, 76)(16, 75)(17, 63)(18, 62)(19, 79)(20, 61)(21, 60)(22, 83)(23, 82)(24, 84)(25, 66)(26, 65)(27, 88)(28, 87)(29, 69)(30, 91)(31, 90)(32, 73)(33, 72)(34, 74)(35, 96)(36, 95)(37, 78)(38, 77)(39, 98)(40, 81)(41, 80)(42, 100)(43, 94)(44, 93)(45, 86)(46, 85)(47, 99)(48, 89)(49, 97)(50, 92)(101, 153)(102, 156)(103, 151)(104, 161)(105, 160)(106, 152)(107, 166)(108, 165)(109, 169)(110, 155)(111, 154)(112, 173)(113, 172)(114, 174)(115, 158)(116, 157)(117, 178)(118, 177)(119, 159)(120, 181)(121, 180)(122, 163)(123, 162)(124, 164)(125, 186)(126, 185)(127, 168)(128, 167)(129, 189)(130, 171)(131, 170)(132, 193)(133, 192)(134, 194)(135, 176)(136, 175)(137, 198)(138, 197)(139, 179)(140, 195)(141, 199)(142, 183)(143, 182)(144, 184)(145, 190)(146, 200)(147, 188)(148, 187)(149, 191)(150, 196) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E20.768 Transitivity :: VT+ Graph:: bipartite v = 10 e = 100 f = 52 degree seq :: [ 20^10 ] E20.771 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 25}) Quotient :: loop^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y2 * Y3^-3 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^5 ] Map:: R = (1, 51, 101, 151, 4, 54, 104, 154, 12, 62, 112, 162, 16, 66, 116, 166, 6, 56, 106, 156, 15, 65, 115, 165, 26, 76, 126, 176, 33, 83, 133, 183, 23, 73, 123, 173, 32, 82, 132, 182, 42, 92, 142, 192, 47, 97, 147, 197, 39, 89, 139, 189, 43, 93, 143, 193, 49, 99, 149, 199, 46, 96, 146, 196, 37, 87, 137, 187, 27, 77, 127, 177, 36, 86, 136, 186, 30, 80, 130, 180, 21, 71, 121, 171, 9, 59, 109, 159, 20, 70, 120, 170, 13, 63, 113, 163, 5, 55, 105, 155)(2, 52, 102, 152, 7, 57, 107, 157, 17, 67, 117, 167, 11, 61, 111, 161, 3, 53, 103, 153, 10, 60, 110, 160, 22, 72, 122, 172, 29, 79, 129, 179, 19, 69, 119, 169, 28, 78, 128, 178, 38, 88, 138, 188, 45, 95, 145, 195, 35, 85, 135, 185, 44, 94, 144, 194, 50, 100, 150, 200, 48, 98, 148, 198, 41, 91, 141, 191, 31, 81, 131, 181, 40, 90, 140, 190, 34, 84, 134, 184, 25, 75, 125, 175, 14, 64, 114, 164, 24, 74, 124, 174, 18, 68, 118, 168, 8, 58, 108, 158) L = (1, 52)(2, 51)(3, 59)(4, 58)(5, 57)(6, 64)(7, 55)(8, 54)(9, 53)(10, 71)(11, 70)(12, 68)(13, 67)(14, 56)(15, 75)(16, 74)(17, 63)(18, 62)(19, 77)(20, 61)(21, 60)(22, 80)(23, 81)(24, 66)(25, 65)(26, 84)(27, 69)(28, 87)(29, 86)(30, 72)(31, 73)(32, 91)(33, 90)(34, 76)(35, 93)(36, 79)(37, 78)(38, 96)(39, 94)(40, 83)(41, 82)(42, 98)(43, 85)(44, 89)(45, 99)(46, 88)(47, 100)(48, 92)(49, 95)(50, 97)(101, 153)(102, 156)(103, 151)(104, 161)(105, 160)(106, 152)(107, 166)(108, 165)(109, 169)(110, 155)(111, 154)(112, 167)(113, 172)(114, 173)(115, 158)(116, 157)(117, 162)(118, 176)(119, 159)(120, 179)(121, 178)(122, 163)(123, 164)(124, 183)(125, 182)(126, 168)(127, 185)(128, 171)(129, 170)(130, 188)(131, 189)(132, 175)(133, 174)(134, 192)(135, 177)(136, 195)(137, 194)(138, 180)(139, 181)(140, 197)(141, 193)(142, 184)(143, 191)(144, 187)(145, 186)(146, 200)(147, 190)(148, 199)(149, 198)(150, 196) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E20.765 Transitivity :: VT+ Graph:: bipartite v = 2 e = 100 f = 60 degree seq :: [ 100^2 ] E20.772 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 25}) Quotient :: loop^2 Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y3^2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3^-5, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^4 ] Map:: R = (1, 51, 101, 151, 4, 54, 104, 154, 12, 62, 112, 162, 24, 74, 124, 174, 37, 87, 137, 187, 49, 99, 149, 199, 42, 92, 142, 192, 30, 80, 130, 180, 16, 66, 116, 166, 6, 56, 106, 156, 15, 65, 115, 165, 29, 79, 129, 179, 41, 91, 141, 191, 46, 96, 146, 196, 34, 84, 134, 184, 21, 71, 121, 171, 9, 59, 109, 159, 20, 70, 120, 170, 26, 76, 126, 176, 39, 89, 139, 189, 50, 100, 150, 200, 38, 88, 138, 188, 25, 75, 125, 175, 13, 63, 113, 163, 5, 55, 105, 155)(2, 52, 102, 152, 7, 57, 107, 157, 17, 67, 117, 167, 31, 81, 131, 181, 43, 93, 143, 193, 48, 98, 148, 198, 36, 86, 136, 186, 23, 73, 123, 173, 11, 61, 111, 161, 3, 53, 103, 153, 10, 60, 110, 160, 22, 72, 122, 172, 35, 85, 135, 185, 47, 97, 147, 197, 40, 90, 140, 190, 28, 78, 128, 178, 14, 64, 114, 164, 27, 77, 127, 177, 19, 69, 119, 169, 33, 83, 133, 183, 45, 95, 145, 195, 44, 94, 144, 194, 32, 82, 132, 182, 18, 68, 118, 168, 8, 58, 108, 158) L = (1, 52)(2, 51)(3, 59)(4, 58)(5, 57)(6, 64)(7, 55)(8, 54)(9, 53)(10, 71)(11, 70)(12, 68)(13, 67)(14, 56)(15, 78)(16, 77)(17, 63)(18, 62)(19, 80)(20, 61)(21, 60)(22, 84)(23, 76)(24, 82)(25, 81)(26, 73)(27, 66)(28, 65)(29, 90)(30, 69)(31, 75)(32, 74)(33, 92)(34, 72)(35, 96)(36, 89)(37, 94)(38, 93)(39, 86)(40, 79)(41, 97)(42, 83)(43, 88)(44, 87)(45, 99)(46, 85)(47, 91)(48, 100)(49, 95)(50, 98)(101, 153)(102, 156)(103, 151)(104, 161)(105, 160)(106, 152)(107, 166)(108, 165)(109, 169)(110, 155)(111, 154)(112, 173)(113, 172)(114, 176)(115, 158)(116, 157)(117, 180)(118, 179)(119, 159)(120, 177)(121, 183)(122, 163)(123, 162)(124, 186)(125, 185)(126, 164)(127, 170)(128, 189)(129, 168)(130, 167)(131, 192)(132, 191)(133, 171)(134, 195)(135, 175)(136, 174)(137, 198)(138, 197)(139, 178)(140, 200)(141, 182)(142, 181)(143, 199)(144, 196)(145, 184)(146, 194)(147, 188)(148, 187)(149, 193)(150, 190) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E20.766 Transitivity :: VT+ Graph:: bipartite v = 2 e = 100 f = 60 degree seq :: [ 100^2 ] E20.773 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, Y2^5, Y2^-1 * Y3^5, Y3^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 51, 2, 52)(3, 53, 9, 59)(4, 54, 10, 60)(5, 55, 7, 57)(6, 56, 8, 58)(11, 61, 24, 74)(12, 62, 25, 75)(13, 63, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 19, 69)(17, 67, 20, 70)(18, 68, 22, 72)(27, 77, 41, 91)(28, 78, 40, 90)(29, 79, 42, 92)(30, 80, 39, 89)(31, 81, 38, 88)(32, 82, 36, 86)(33, 83, 35, 85)(34, 84, 37, 87)(43, 93, 50, 100)(44, 94, 49, 99)(45, 95, 48, 98)(46, 96, 47, 97)(101, 151, 103, 153, 111, 161, 116, 166, 105, 155)(102, 152, 107, 157, 119, 169, 124, 174, 109, 159)(104, 154, 112, 162, 127, 177, 132, 182, 115, 165)(106, 156, 113, 163, 128, 178, 133, 183, 117, 167)(108, 158, 120, 170, 135, 185, 140, 190, 123, 173)(110, 160, 121, 171, 136, 186, 141, 191, 125, 175)(114, 164, 129, 179, 143, 193, 145, 195, 131, 181)(118, 168, 130, 180, 144, 194, 146, 196, 134, 184)(122, 172, 137, 187, 147, 197, 149, 199, 139, 189)(126, 176, 138, 188, 148, 198, 150, 200, 142, 192) L = (1, 104)(2, 108)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 122)(9, 123)(10, 102)(11, 127)(12, 129)(13, 103)(14, 130)(15, 131)(16, 132)(17, 105)(18, 106)(19, 135)(20, 137)(21, 107)(22, 138)(23, 139)(24, 140)(25, 109)(26, 110)(27, 143)(28, 111)(29, 144)(30, 113)(31, 118)(32, 145)(33, 116)(34, 117)(35, 147)(36, 119)(37, 148)(38, 121)(39, 126)(40, 149)(41, 124)(42, 125)(43, 146)(44, 128)(45, 134)(46, 133)(47, 150)(48, 136)(49, 142)(50, 141)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 50, 4, 50 ), ( 4, 50, 4, 50, 4, 50, 4, 50, 4, 50 ) } Outer automorphisms :: reflexible Dual of E20.777 Graph:: simple bipartite v = 35 e = 100 f = 27 degree seq :: [ 4^25, 10^10 ] E20.774 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^5, Y2^-1 * Y3^-5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 51, 2, 52)(3, 53, 9, 59)(4, 54, 10, 60)(5, 55, 7, 57)(6, 56, 8, 58)(11, 61, 24, 74)(12, 62, 25, 75)(13, 63, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 19, 69)(17, 67, 20, 70)(18, 68, 22, 72)(27, 77, 42, 92)(28, 78, 41, 91)(29, 79, 39, 89)(30, 80, 40, 90)(31, 81, 37, 87)(32, 82, 38, 88)(33, 83, 36, 86)(34, 84, 35, 85)(43, 93, 49, 99)(44, 94, 50, 100)(45, 95, 47, 97)(46, 96, 48, 98)(101, 151, 103, 153, 111, 161, 116, 166, 105, 155)(102, 152, 107, 157, 119, 169, 124, 174, 109, 159)(104, 154, 112, 162, 127, 177, 133, 183, 115, 165)(106, 156, 113, 163, 128, 178, 134, 184, 117, 167)(108, 158, 120, 170, 135, 185, 141, 191, 123, 173)(110, 160, 121, 171, 136, 186, 142, 192, 125, 175)(114, 164, 129, 179, 143, 193, 146, 196, 132, 182)(118, 168, 130, 180, 144, 194, 145, 195, 131, 181)(122, 172, 137, 187, 147, 197, 150, 200, 140, 190)(126, 176, 138, 188, 148, 198, 149, 199, 139, 189) L = (1, 104)(2, 108)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 122)(9, 123)(10, 102)(11, 127)(12, 129)(13, 103)(14, 131)(15, 132)(16, 133)(17, 105)(18, 106)(19, 135)(20, 137)(21, 107)(22, 139)(23, 140)(24, 141)(25, 109)(26, 110)(27, 143)(28, 111)(29, 118)(30, 113)(31, 117)(32, 145)(33, 146)(34, 116)(35, 147)(36, 119)(37, 126)(38, 121)(39, 125)(40, 149)(41, 150)(42, 124)(43, 130)(44, 128)(45, 134)(46, 144)(47, 138)(48, 136)(49, 142)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 50, 4, 50 ), ( 4, 50, 4, 50, 4, 50, 4, 50, 4, 50 ) } Outer automorphisms :: reflexible Dual of E20.778 Graph:: simple bipartite v = 35 e = 100 f = 27 degree seq :: [ 4^25, 10^10 ] E20.775 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^-5, Y2^5, Y2^-2 * Y3^5 ] Map:: non-degenerate R = (1, 51, 2, 52)(3, 53, 9, 59)(4, 54, 10, 60)(5, 55, 7, 57)(6, 56, 8, 58)(11, 61, 24, 74)(12, 62, 25, 75)(13, 63, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 19, 69)(17, 67, 20, 70)(18, 68, 22, 72)(27, 77, 44, 94)(28, 78, 43, 93)(29, 79, 45, 95)(30, 80, 42, 92)(31, 81, 46, 96)(32, 82, 40, 90)(33, 83, 38, 88)(34, 84, 37, 87)(35, 85, 39, 89)(36, 86, 41, 91)(47, 97, 50, 100)(48, 98, 49, 99)(101, 151, 103, 153, 111, 161, 116, 166, 105, 155)(102, 152, 107, 157, 119, 169, 124, 174, 109, 159)(104, 154, 112, 162, 127, 177, 133, 183, 115, 165)(106, 156, 113, 163, 128, 178, 134, 184, 117, 167)(108, 158, 120, 170, 137, 187, 143, 193, 123, 173)(110, 160, 121, 171, 138, 188, 144, 194, 125, 175)(114, 164, 129, 179, 147, 197, 136, 186, 132, 182)(118, 168, 130, 180, 131, 181, 148, 198, 135, 185)(122, 172, 139, 189, 149, 199, 146, 196, 142, 192)(126, 176, 140, 190, 141, 191, 150, 200, 145, 195) L = (1, 104)(2, 108)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 122)(9, 123)(10, 102)(11, 127)(12, 129)(13, 103)(14, 131)(15, 132)(16, 133)(17, 105)(18, 106)(19, 137)(20, 139)(21, 107)(22, 141)(23, 142)(24, 143)(25, 109)(26, 110)(27, 147)(28, 111)(29, 148)(30, 113)(31, 128)(32, 130)(33, 136)(34, 116)(35, 117)(36, 118)(37, 149)(38, 119)(39, 150)(40, 121)(41, 138)(42, 140)(43, 146)(44, 124)(45, 125)(46, 126)(47, 135)(48, 134)(49, 145)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 50, 4, 50 ), ( 4, 50, 4, 50, 4, 50, 4, 50, 4, 50 ) } Outer automorphisms :: reflexible Dual of E20.780 Graph:: simple bipartite v = 35 e = 100 f = 27 degree seq :: [ 4^25, 10^10 ] E20.776 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^5, Y2^5, Y2^2 * Y3^5, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^3 * Y2^-1, Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2 * Y3^-2 * Y2 * Y3 ] Map:: non-degenerate R = (1, 51, 2, 52)(3, 53, 9, 59)(4, 54, 10, 60)(5, 55, 7, 57)(6, 56, 8, 58)(11, 61, 24, 74)(12, 62, 25, 75)(13, 63, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 19, 69)(17, 67, 20, 70)(18, 68, 22, 72)(27, 77, 44, 94)(28, 78, 43, 93)(29, 79, 45, 95)(30, 80, 42, 92)(31, 81, 46, 96)(32, 82, 40, 90)(33, 83, 38, 88)(34, 84, 37, 87)(35, 85, 39, 89)(36, 86, 41, 91)(47, 97, 50, 100)(48, 98, 49, 99)(101, 151, 103, 153, 111, 161, 116, 166, 105, 155)(102, 152, 107, 157, 119, 169, 124, 174, 109, 159)(104, 154, 112, 162, 127, 177, 133, 183, 115, 165)(106, 156, 113, 163, 128, 178, 134, 184, 117, 167)(108, 158, 120, 170, 137, 187, 143, 193, 123, 173)(110, 160, 121, 171, 138, 188, 144, 194, 125, 175)(114, 164, 129, 179, 136, 186, 148, 198, 132, 182)(118, 168, 130, 180, 147, 197, 131, 181, 135, 185)(122, 172, 139, 189, 146, 196, 150, 200, 142, 192)(126, 176, 140, 190, 149, 199, 141, 191, 145, 195) L = (1, 104)(2, 108)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 122)(9, 123)(10, 102)(11, 127)(12, 129)(13, 103)(14, 131)(15, 132)(16, 133)(17, 105)(18, 106)(19, 137)(20, 139)(21, 107)(22, 141)(23, 142)(24, 143)(25, 109)(26, 110)(27, 136)(28, 111)(29, 135)(30, 113)(31, 134)(32, 147)(33, 148)(34, 116)(35, 117)(36, 118)(37, 146)(38, 119)(39, 145)(40, 121)(41, 144)(42, 149)(43, 150)(44, 124)(45, 125)(46, 126)(47, 128)(48, 130)(49, 138)(50, 140)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 50, 4, 50 ), ( 4, 50, 4, 50, 4, 50, 4, 50, 4, 50 ) } Outer automorphisms :: reflexible Dual of E20.779 Graph:: simple bipartite v = 35 e = 100 f = 27 degree seq :: [ 4^25, 10^10 ] E20.777 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |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^-4 * Y1, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^3, (Y1^-1 * Y3^-1)^5 ] Map:: non-degenerate R = (1, 51, 2, 52, 7, 57, 19, 69, 33, 83, 17, 67, 6, 56, 10, 60, 22, 72, 36, 86, 46, 96, 34, 84, 18, 68, 14, 64, 25, 75, 39, 89, 45, 95, 31, 81, 15, 65, 4, 54, 9, 59, 21, 71, 32, 82, 16, 66, 5, 55)(3, 53, 11, 61, 26, 76, 41, 91, 38, 88, 24, 74, 13, 63, 28, 78, 43, 93, 49, 99, 48, 98, 40, 90, 30, 80, 29, 79, 44, 94, 50, 100, 47, 97, 37, 87, 23, 73, 12, 62, 27, 77, 42, 92, 35, 85, 20, 70, 8, 58)(101, 151, 103, 153)(102, 152, 108, 158)(104, 154, 113, 163)(105, 155, 111, 161)(106, 156, 112, 162)(107, 157, 120, 170)(109, 159, 124, 174)(110, 160, 123, 173)(114, 164, 130, 180)(115, 165, 128, 178)(116, 166, 126, 176)(117, 167, 127, 177)(118, 168, 129, 179)(119, 169, 135, 185)(121, 171, 138, 188)(122, 172, 137, 187)(125, 175, 140, 190)(131, 181, 143, 193)(132, 182, 141, 191)(133, 183, 142, 192)(134, 184, 144, 194)(136, 186, 147, 197)(139, 189, 148, 198)(145, 195, 149, 199)(146, 196, 150, 200) L = (1, 104)(2, 109)(3, 112)(4, 114)(5, 115)(6, 101)(7, 121)(8, 123)(9, 125)(10, 102)(11, 127)(12, 129)(13, 103)(14, 110)(15, 118)(16, 131)(17, 105)(18, 106)(19, 132)(20, 137)(21, 139)(22, 107)(23, 130)(24, 108)(25, 122)(26, 142)(27, 144)(28, 111)(29, 128)(30, 113)(31, 134)(32, 145)(33, 116)(34, 117)(35, 147)(36, 119)(37, 140)(38, 120)(39, 136)(40, 124)(41, 135)(42, 150)(43, 126)(44, 143)(45, 146)(46, 133)(47, 148)(48, 138)(49, 141)(50, 149)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 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 E20.773 Graph:: bipartite v = 27 e = 100 f = 35 degree seq :: [ 4^25, 50^2 ] E20.778 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, (Y1 * Y2)^2, Y1^3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^6 * Y1, Y1^-1 * Y3^3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 51, 2, 52, 7, 57, 15, 65, 4, 54, 9, 59, 20, 70, 31, 81, 14, 64, 23, 73, 36, 86, 45, 95, 30, 80, 34, 84, 39, 89, 46, 96, 33, 83, 18, 68, 24, 74, 32, 82, 17, 67, 6, 56, 10, 60, 16, 66, 5, 55)(3, 53, 11, 61, 25, 75, 21, 71, 12, 62, 26, 76, 40, 90, 37, 87, 28, 78, 41, 91, 49, 99, 48, 98, 43, 93, 44, 94, 50, 100, 47, 97, 38, 88, 29, 79, 42, 92, 35, 85, 22, 72, 13, 63, 27, 77, 19, 69, 8, 58)(101, 151, 103, 153)(102, 152, 108, 158)(104, 154, 113, 163)(105, 155, 111, 161)(106, 156, 112, 162)(107, 157, 119, 169)(109, 159, 122, 172)(110, 160, 121, 171)(114, 164, 129, 179)(115, 165, 127, 177)(116, 166, 125, 175)(117, 167, 126, 176)(118, 168, 128, 178)(120, 170, 135, 185)(123, 173, 138, 188)(124, 174, 137, 187)(130, 180, 144, 194)(131, 181, 142, 192)(132, 182, 140, 190)(133, 183, 141, 191)(134, 184, 143, 193)(136, 186, 147, 197)(139, 189, 148, 198)(145, 195, 150, 200)(146, 196, 149, 199) L = (1, 104)(2, 109)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 121)(9, 123)(10, 102)(11, 126)(12, 128)(13, 103)(14, 130)(15, 131)(16, 107)(17, 105)(18, 106)(19, 125)(20, 136)(21, 137)(22, 108)(23, 134)(24, 110)(25, 140)(26, 141)(27, 111)(28, 143)(29, 113)(30, 133)(31, 145)(32, 116)(33, 117)(34, 118)(35, 119)(36, 139)(37, 148)(38, 122)(39, 124)(40, 149)(41, 144)(42, 127)(43, 138)(44, 129)(45, 146)(46, 132)(47, 135)(48, 147)(49, 150)(50, 142)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 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 E20.774 Graph:: bipartite v = 27 e = 100 f = 35 degree seq :: [ 4^25, 50^2 ] E20.779 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3^-1, Y1^-1), Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^5, Y3 * Y1 * Y3^15 ] Map:: non-degenerate R = (1, 51, 2, 52, 7, 57, 14, 64, 23, 73, 34, 84, 41, 91, 43, 93, 32, 82, 30, 80, 17, 67, 6, 56, 10, 60, 15, 65, 4, 54, 9, 59, 20, 70, 29, 79, 36, 86, 44, 94, 42, 92, 31, 81, 18, 68, 16, 66, 5, 55)(3, 53, 11, 61, 24, 74, 27, 77, 38, 88, 47, 97, 49, 99, 46, 96, 40, 90, 33, 83, 22, 72, 13, 63, 26, 76, 21, 71, 12, 62, 25, 75, 37, 87, 39, 89, 48, 98, 50, 100, 45, 95, 35, 85, 28, 78, 19, 69, 8, 58)(101, 151, 103, 153)(102, 152, 108, 158)(104, 154, 113, 163)(105, 155, 111, 161)(106, 156, 112, 162)(107, 157, 119, 169)(109, 159, 122, 172)(110, 160, 121, 171)(114, 164, 128, 178)(115, 165, 126, 176)(116, 166, 124, 174)(117, 167, 125, 175)(118, 168, 127, 177)(120, 170, 133, 183)(123, 173, 135, 185)(129, 179, 140, 190)(130, 180, 137, 187)(131, 181, 138, 188)(132, 182, 139, 189)(134, 184, 145, 195)(136, 186, 146, 196)(141, 191, 150, 200)(142, 192, 147, 197)(143, 193, 148, 198)(144, 194, 149, 199) L = (1, 104)(2, 109)(3, 112)(4, 114)(5, 115)(6, 101)(7, 120)(8, 121)(9, 123)(10, 102)(11, 125)(12, 127)(13, 103)(14, 129)(15, 107)(16, 110)(17, 105)(18, 106)(19, 126)(20, 134)(21, 124)(22, 108)(23, 136)(24, 137)(25, 138)(26, 111)(27, 139)(28, 113)(29, 141)(30, 116)(31, 117)(32, 118)(33, 119)(34, 144)(35, 122)(36, 143)(37, 147)(38, 148)(39, 149)(40, 128)(41, 142)(42, 130)(43, 131)(44, 132)(45, 133)(46, 135)(47, 150)(48, 146)(49, 145)(50, 140)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 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 E20.776 Graph:: bipartite v = 27 e = 100 f = 35 degree seq :: [ 4^25, 50^2 ] E20.780 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 25}) Quotient :: dipole Aut^+ = D50 (small group id <50, 1>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3, Y1^-1), (Y1^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-2 * Y1^4 * Y3^-1 * Y1^-1, Y1^3 * Y3 * Y1 * Y3 * Y1^3 ] Map:: non-degenerate R = (1, 51, 2, 52, 7, 57, 19, 69, 33, 83, 44, 94, 32, 82, 18, 68, 15, 65, 4, 54, 9, 59, 21, 71, 35, 85, 43, 93, 31, 81, 17, 67, 6, 56, 10, 60, 14, 64, 24, 74, 37, 87, 42, 92, 30, 80, 16, 66, 5, 55)(3, 53, 11, 61, 25, 75, 39, 89, 48, 98, 47, 97, 38, 88, 29, 79, 22, 72, 12, 62, 26, 76, 40, 90, 49, 99, 46, 96, 36, 86, 23, 73, 13, 63, 27, 77, 28, 78, 41, 91, 50, 100, 45, 95, 34, 84, 20, 70, 8, 58)(101, 151, 103, 153)(102, 152, 108, 158)(104, 154, 113, 163)(105, 155, 111, 161)(106, 156, 112, 162)(107, 157, 120, 170)(109, 159, 123, 173)(110, 160, 122, 172)(114, 164, 129, 179)(115, 165, 127, 177)(116, 166, 125, 175)(117, 167, 126, 176)(118, 168, 128, 178)(119, 169, 134, 184)(121, 171, 136, 186)(124, 174, 138, 188)(130, 180, 139, 189)(131, 181, 140, 190)(132, 182, 141, 191)(133, 183, 145, 195)(135, 185, 146, 196)(137, 187, 147, 197)(142, 192, 148, 198)(143, 193, 149, 199)(144, 194, 150, 200) L = (1, 104)(2, 109)(3, 112)(4, 114)(5, 115)(6, 101)(7, 121)(8, 122)(9, 124)(10, 102)(11, 126)(12, 128)(13, 103)(14, 107)(15, 110)(16, 118)(17, 105)(18, 106)(19, 135)(20, 129)(21, 137)(22, 127)(23, 108)(24, 119)(25, 140)(26, 141)(27, 111)(28, 125)(29, 113)(30, 132)(31, 116)(32, 117)(33, 143)(34, 138)(35, 142)(36, 120)(37, 133)(38, 123)(39, 149)(40, 150)(41, 139)(42, 144)(43, 130)(44, 131)(45, 147)(46, 134)(47, 136)(48, 146)(49, 145)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 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 E20.775 Graph:: bipartite v = 27 e = 100 f = 35 degree seq :: [ 4^25, 50^2 ] E20.781 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 50, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-5, T1^5, T2^10 * T1^-2, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 45, 35, 25, 15, 6, 14, 24, 34, 44, 50, 42, 32, 22, 12, 4, 10, 19, 29, 39, 47, 37, 27, 17, 8, 2, 7, 16, 26, 36, 46, 49, 41, 31, 21, 11, 20, 30, 40, 48, 43, 33, 23, 13, 5)(51, 52, 56, 61, 54)(53, 57, 64, 70, 60)(55, 58, 65, 71, 62)(59, 66, 74, 80, 69)(63, 67, 75, 81, 72)(68, 76, 84, 90, 79)(73, 77, 85, 91, 82)(78, 86, 94, 98, 89)(83, 87, 95, 99, 92)(88, 96, 100, 93, 97) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 100^5 ), ( 100^50 ) } Outer automorphisms :: reflexible Dual of E20.788 Transitivity :: ET+ Graph:: bipartite v = 11 e = 50 f = 1 degree seq :: [ 5^10, 50 ] E20.782 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 50, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-5, T1^5, T1^-2 * T2^-10, T2^-1 * T1 * T2^-4 * T1 * T2^-5 * T1, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 48, 41, 31, 21, 11, 20, 30, 40, 50, 47, 37, 27, 17, 8, 2, 7, 16, 26, 36, 46, 42, 32, 22, 12, 4, 10, 19, 29, 39, 49, 45, 35, 25, 15, 6, 14, 24, 34, 44, 43, 33, 23, 13, 5)(51, 52, 56, 61, 54)(53, 57, 64, 70, 60)(55, 58, 65, 71, 62)(59, 66, 74, 80, 69)(63, 67, 75, 81, 72)(68, 76, 84, 90, 79)(73, 77, 85, 91, 82)(78, 86, 94, 100, 89)(83, 87, 95, 98, 92)(88, 96, 93, 97, 99) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 100^5 ), ( 100^50 ) } Outer automorphisms :: reflexible Dual of E20.787 Transitivity :: ET+ Graph:: bipartite v = 11 e = 50 f = 1 degree seq :: [ 5^10, 50 ] E20.783 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 50, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^5, T2^-10 * T1, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 37, 27, 17, 8, 2, 7, 16, 26, 36, 46, 45, 35, 25, 15, 6, 14, 24, 34, 44, 50, 48, 41, 31, 21, 11, 20, 30, 40, 47, 49, 42, 32, 22, 12, 4, 10, 19, 29, 39, 43, 33, 23, 13, 5)(51, 52, 56, 61, 54)(53, 57, 64, 70, 60)(55, 58, 65, 71, 62)(59, 66, 74, 80, 69)(63, 67, 75, 81, 72)(68, 76, 84, 90, 79)(73, 77, 85, 91, 82)(78, 86, 94, 97, 89)(83, 87, 95, 98, 92)(88, 96, 100, 99, 93) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 100^5 ), ( 100^50 ) } Outer automorphisms :: reflexible Dual of E20.790 Transitivity :: ET+ Graph:: bipartite v = 11 e = 50 f = 1 degree seq :: [ 5^10, 50 ] E20.784 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 50, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^5, T1 * T2^10, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 42, 32, 22, 12, 4, 10, 19, 29, 39, 47, 49, 41, 31, 21, 11, 20, 30, 40, 48, 50, 45, 35, 25, 15, 6, 14, 24, 34, 44, 46, 37, 27, 17, 8, 2, 7, 16, 26, 36, 43, 33, 23, 13, 5)(51, 52, 56, 61, 54)(53, 57, 64, 70, 60)(55, 58, 65, 71, 62)(59, 66, 74, 80, 69)(63, 67, 75, 81, 72)(68, 76, 84, 90, 79)(73, 77, 85, 91, 82)(78, 86, 94, 98, 89)(83, 87, 95, 99, 92)(88, 93, 96, 100, 97) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 100^5 ), ( 100^50 ) } Outer automorphisms :: reflexible Dual of E20.789 Transitivity :: ET+ Graph:: bipartite v = 11 e = 50 f = 1 degree seq :: [ 5^10, 50 ] E20.785 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 50, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T2)^2, (F * T1)^2, T1^-4 * T2^6, T1^5 * T2^5, T1^-9 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 44, 26, 43, 40, 24, 12, 4, 10, 20, 34, 46, 28, 14, 27, 45, 39, 23, 11, 21, 35, 48, 30, 16, 6, 15, 29, 47, 38, 22, 36, 50, 32, 18, 8, 2, 7, 17, 31, 49, 37, 42, 41, 25, 13, 5)(51, 52, 56, 64, 76, 92, 86, 71, 60, 53, 57, 65, 77, 93, 91, 100, 85, 70, 59, 67, 79, 95, 90, 75, 82, 98, 84, 69, 81, 97, 89, 74, 63, 68, 80, 96, 83, 99, 88, 73, 62, 55, 58, 66, 78, 94, 87, 72, 61, 54) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^50 ) } Outer automorphisms :: reflexible Dual of E20.792 Transitivity :: ET+ Graph:: bipartite v = 2 e = 50 f = 10 degree seq :: [ 50^2 ] E20.786 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 50, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2^2 * T1^2 * T2^-2 * T1^-1, T1^3 * T2 * T1 * T2^4 * T1, T2^5 * T1^-2 * T2^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 48, 30, 16, 6, 15, 29, 47, 38, 22, 36, 44, 26, 43, 40, 24, 12, 4, 10, 20, 34, 50, 32, 18, 8, 2, 7, 17, 31, 49, 37, 46, 28, 14, 27, 45, 39, 23, 11, 21, 35, 42, 41, 25, 13, 5)(51, 52, 56, 64, 76, 92, 84, 69, 81, 97, 89, 74, 63, 68, 80, 96, 86, 71, 60, 53, 57, 65, 77, 93, 91, 100, 83, 99, 88, 73, 62, 55, 58, 66, 78, 94, 85, 70, 59, 67, 79, 95, 90, 75, 82, 98, 87, 72, 61, 54) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 10^50 ) } Outer automorphisms :: reflexible Dual of E20.791 Transitivity :: ET+ Graph:: bipartite v = 2 e = 50 f = 10 degree seq :: [ 50^2 ] E20.787 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 50, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-5, T1^5, T2^10 * T1^-2, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 18, 68, 28, 78, 38, 88, 45, 95, 35, 85, 25, 75, 15, 65, 6, 56, 14, 64, 24, 74, 34, 84, 44, 94, 50, 100, 42, 92, 32, 82, 22, 72, 12, 62, 4, 54, 10, 60, 19, 69, 29, 79, 39, 89, 47, 97, 37, 87, 27, 77, 17, 67, 8, 58, 2, 52, 7, 57, 16, 66, 26, 76, 36, 86, 46, 96, 49, 99, 41, 91, 31, 81, 21, 71, 11, 61, 20, 70, 30, 80, 40, 90, 48, 98, 43, 93, 33, 83, 23, 73, 13, 63, 5, 55) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 74)(17, 75)(18, 76)(19, 59)(20, 60)(21, 62)(22, 63)(23, 77)(24, 80)(25, 81)(26, 84)(27, 85)(28, 86)(29, 68)(30, 69)(31, 72)(32, 73)(33, 87)(34, 90)(35, 91)(36, 94)(37, 95)(38, 96)(39, 78)(40, 79)(41, 82)(42, 83)(43, 97)(44, 98)(45, 99)(46, 100)(47, 88)(48, 89)(49, 92)(50, 93) local type(s) :: { ( 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50 ) } Outer automorphisms :: reflexible Dual of E20.782 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 50 f = 11 degree seq :: [ 100 ] E20.788 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 50, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-5, T1^5, T1^-2 * T2^-10, T2^-1 * T1 * T2^-4 * T1 * T2^-5 * T1, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 18, 68, 28, 78, 38, 88, 48, 98, 41, 91, 31, 81, 21, 71, 11, 61, 20, 70, 30, 80, 40, 90, 50, 100, 47, 97, 37, 87, 27, 77, 17, 67, 8, 58, 2, 52, 7, 57, 16, 66, 26, 76, 36, 86, 46, 96, 42, 92, 32, 82, 22, 72, 12, 62, 4, 54, 10, 60, 19, 69, 29, 79, 39, 89, 49, 99, 45, 95, 35, 85, 25, 75, 15, 65, 6, 56, 14, 64, 24, 74, 34, 84, 44, 94, 43, 93, 33, 83, 23, 73, 13, 63, 5, 55) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 74)(17, 75)(18, 76)(19, 59)(20, 60)(21, 62)(22, 63)(23, 77)(24, 80)(25, 81)(26, 84)(27, 85)(28, 86)(29, 68)(30, 69)(31, 72)(32, 73)(33, 87)(34, 90)(35, 91)(36, 94)(37, 95)(38, 96)(39, 78)(40, 79)(41, 82)(42, 83)(43, 97)(44, 100)(45, 98)(46, 93)(47, 99)(48, 92)(49, 88)(50, 89) local type(s) :: { ( 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50 ) } Outer automorphisms :: reflexible Dual of E20.781 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 50 f = 11 degree seq :: [ 100 ] E20.789 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 50, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^5, T2^-10 * T1, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 18, 68, 28, 78, 38, 88, 37, 87, 27, 77, 17, 67, 8, 58, 2, 52, 7, 57, 16, 66, 26, 76, 36, 86, 46, 96, 45, 95, 35, 85, 25, 75, 15, 65, 6, 56, 14, 64, 24, 74, 34, 84, 44, 94, 50, 100, 48, 98, 41, 91, 31, 81, 21, 71, 11, 61, 20, 70, 30, 80, 40, 90, 47, 97, 49, 99, 42, 92, 32, 82, 22, 72, 12, 62, 4, 54, 10, 60, 19, 69, 29, 79, 39, 89, 43, 93, 33, 83, 23, 73, 13, 63, 5, 55) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 74)(17, 75)(18, 76)(19, 59)(20, 60)(21, 62)(22, 63)(23, 77)(24, 80)(25, 81)(26, 84)(27, 85)(28, 86)(29, 68)(30, 69)(31, 72)(32, 73)(33, 87)(34, 90)(35, 91)(36, 94)(37, 95)(38, 96)(39, 78)(40, 79)(41, 82)(42, 83)(43, 88)(44, 97)(45, 98)(46, 100)(47, 89)(48, 92)(49, 93)(50, 99) local type(s) :: { ( 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50 ) } Outer automorphisms :: reflexible Dual of E20.784 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 50 f = 11 degree seq :: [ 100 ] E20.790 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 50, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^5, T1 * T2^10, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 18, 68, 28, 78, 38, 88, 42, 92, 32, 82, 22, 72, 12, 62, 4, 54, 10, 60, 19, 69, 29, 79, 39, 89, 47, 97, 49, 99, 41, 91, 31, 81, 21, 71, 11, 61, 20, 70, 30, 80, 40, 90, 48, 98, 50, 100, 45, 95, 35, 85, 25, 75, 15, 65, 6, 56, 14, 64, 24, 74, 34, 84, 44, 94, 46, 96, 37, 87, 27, 77, 17, 67, 8, 58, 2, 52, 7, 57, 16, 66, 26, 76, 36, 86, 43, 93, 33, 83, 23, 73, 13, 63, 5, 55) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 64)(8, 65)(9, 66)(10, 53)(11, 54)(12, 55)(13, 67)(14, 70)(15, 71)(16, 74)(17, 75)(18, 76)(19, 59)(20, 60)(21, 62)(22, 63)(23, 77)(24, 80)(25, 81)(26, 84)(27, 85)(28, 86)(29, 68)(30, 69)(31, 72)(32, 73)(33, 87)(34, 90)(35, 91)(36, 94)(37, 95)(38, 93)(39, 78)(40, 79)(41, 82)(42, 83)(43, 96)(44, 98)(45, 99)(46, 100)(47, 88)(48, 89)(49, 92)(50, 97) local type(s) :: { ( 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50, 5, 50 ) } Outer automorphisms :: reflexible Dual of E20.783 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 50 f = 11 degree seq :: [ 100 ] E20.791 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 50, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T2^5, T2^5, T2^2 * T1^-10, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 13, 63, 5, 55)(2, 52, 7, 57, 17, 67, 18, 68, 8, 58)(4, 54, 10, 60, 19, 69, 23, 73, 12, 62)(6, 56, 15, 65, 27, 77, 28, 78, 16, 66)(11, 61, 20, 70, 29, 79, 33, 83, 22, 72)(14, 64, 25, 75, 37, 87, 38, 88, 26, 76)(21, 71, 30, 80, 39, 89, 43, 93, 32, 82)(24, 74, 35, 85, 47, 97, 48, 98, 36, 86)(31, 81, 40, 90, 44, 94, 50, 100, 42, 92)(34, 84, 45, 95, 49, 99, 41, 91, 46, 96) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 64)(7, 65)(8, 66)(9, 67)(10, 53)(11, 54)(12, 55)(13, 68)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 79)(40, 80)(41, 81)(42, 82)(43, 83)(44, 89)(45, 100)(46, 90)(47, 99)(48, 91)(49, 92)(50, 93) local type(s) :: { ( 50^10 ) } Outer automorphisms :: reflexible Dual of E20.786 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 50 f = 2 degree seq :: [ 10^10 ] E20.792 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 50, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^5, T1^10 * T2, (T1^-1 * T2^-1)^50 ] Map:: non-degenerate R = (1, 51, 3, 53, 9, 59, 13, 63, 5, 55)(2, 52, 7, 57, 17, 67, 18, 68, 8, 58)(4, 54, 10, 60, 19, 69, 23, 73, 12, 62)(6, 56, 15, 65, 27, 77, 28, 78, 16, 66)(11, 61, 20, 70, 29, 79, 33, 83, 22, 72)(14, 64, 25, 75, 37, 87, 38, 88, 26, 76)(21, 71, 30, 80, 39, 89, 43, 93, 32, 82)(24, 74, 35, 85, 45, 95, 46, 96, 36, 86)(31, 81, 40, 90, 47, 97, 49, 99, 42, 92)(34, 84, 41, 91, 48, 98, 50, 100, 44, 94) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 64)(7, 65)(8, 66)(9, 67)(10, 53)(11, 54)(12, 55)(13, 68)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 92)(35, 91)(36, 94)(37, 95)(38, 96)(39, 79)(40, 80)(41, 81)(42, 82)(43, 83)(44, 99)(45, 98)(46, 100)(47, 89)(48, 90)(49, 93)(50, 97) local type(s) :: { ( 50^10 ) } Outer automorphisms :: reflexible Dual of E20.785 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 50 f = 2 degree seq :: [ 10^10 ] E20.793 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3 * Y2 * Y1 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^5, Y2^-3 * Y1 * Y2^3 * Y3, Y3^10, Y1^-1 * Y2^-10 * Y1^-1, Y2 * Y3^-2 * Y2^-4 * Y3^-1 * Y1^2 * Y2^3, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2 ] Map:: R = (1, 51, 2, 52, 6, 56, 11, 61, 4, 54)(3, 53, 7, 57, 14, 64, 20, 70, 10, 60)(5, 55, 8, 58, 15, 65, 21, 71, 12, 62)(9, 59, 16, 66, 24, 74, 30, 80, 19, 69)(13, 63, 17, 67, 25, 75, 31, 81, 22, 72)(18, 68, 26, 76, 34, 84, 40, 90, 29, 79)(23, 73, 27, 77, 35, 85, 41, 91, 32, 82)(28, 78, 36, 86, 44, 94, 50, 100, 39, 89)(33, 83, 37, 87, 45, 95, 48, 98, 42, 92)(38, 88, 46, 96, 43, 93, 47, 97, 49, 99)(101, 151, 103, 153, 109, 159, 118, 168, 128, 178, 138, 188, 148, 198, 141, 191, 131, 181, 121, 171, 111, 161, 120, 170, 130, 180, 140, 190, 150, 200, 147, 197, 137, 187, 127, 177, 117, 167, 108, 158, 102, 152, 107, 157, 116, 166, 126, 176, 136, 186, 146, 196, 142, 192, 132, 182, 122, 172, 112, 162, 104, 154, 110, 160, 119, 169, 129, 179, 139, 189, 149, 199, 145, 195, 135, 185, 125, 175, 115, 165, 106, 156, 114, 164, 124, 174, 134, 184, 144, 194, 143, 193, 133, 183, 123, 173, 113, 163, 105, 155) L = (1, 104)(2, 101)(3, 110)(4, 111)(5, 112)(6, 102)(7, 103)(8, 105)(9, 119)(10, 120)(11, 106)(12, 121)(13, 122)(14, 107)(15, 108)(16, 109)(17, 113)(18, 129)(19, 130)(20, 114)(21, 115)(22, 131)(23, 132)(24, 116)(25, 117)(26, 118)(27, 123)(28, 139)(29, 140)(30, 124)(31, 125)(32, 141)(33, 142)(34, 126)(35, 127)(36, 128)(37, 133)(38, 149)(39, 150)(40, 134)(41, 135)(42, 148)(43, 146)(44, 136)(45, 137)(46, 138)(47, 143)(48, 145)(49, 147)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ), ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ) } Outer automorphisms :: reflexible Dual of E20.801 Graph:: bipartite v = 11 e = 100 f = 51 degree seq :: [ 10^10, 100 ] E20.794 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2)^2, Y1^5, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y2^3 * Y3 * Y2^7 * Y1^-1, (Y1^-2 * Y3)^5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 51, 2, 52, 6, 56, 11, 61, 4, 54)(3, 53, 7, 57, 14, 64, 20, 70, 10, 60)(5, 55, 8, 58, 15, 65, 21, 71, 12, 62)(9, 59, 16, 66, 24, 74, 30, 80, 19, 69)(13, 63, 17, 67, 25, 75, 31, 81, 22, 72)(18, 68, 26, 76, 34, 84, 40, 90, 29, 79)(23, 73, 27, 77, 35, 85, 41, 91, 32, 82)(28, 78, 36, 86, 44, 94, 48, 98, 39, 89)(33, 83, 37, 87, 45, 95, 49, 99, 42, 92)(38, 88, 46, 96, 50, 100, 43, 93, 47, 97)(101, 151, 103, 153, 109, 159, 118, 168, 128, 178, 138, 188, 145, 195, 135, 185, 125, 175, 115, 165, 106, 156, 114, 164, 124, 174, 134, 184, 144, 194, 150, 200, 142, 192, 132, 182, 122, 172, 112, 162, 104, 154, 110, 160, 119, 169, 129, 179, 139, 189, 147, 197, 137, 187, 127, 177, 117, 167, 108, 158, 102, 152, 107, 157, 116, 166, 126, 176, 136, 186, 146, 196, 149, 199, 141, 191, 131, 181, 121, 171, 111, 161, 120, 170, 130, 180, 140, 190, 148, 198, 143, 193, 133, 183, 123, 173, 113, 163, 105, 155) L = (1, 104)(2, 101)(3, 110)(4, 111)(5, 112)(6, 102)(7, 103)(8, 105)(9, 119)(10, 120)(11, 106)(12, 121)(13, 122)(14, 107)(15, 108)(16, 109)(17, 113)(18, 129)(19, 130)(20, 114)(21, 115)(22, 131)(23, 132)(24, 116)(25, 117)(26, 118)(27, 123)(28, 139)(29, 140)(30, 124)(31, 125)(32, 141)(33, 142)(34, 126)(35, 127)(36, 128)(37, 133)(38, 147)(39, 148)(40, 134)(41, 135)(42, 149)(43, 150)(44, 136)(45, 137)(46, 138)(47, 143)(48, 144)(49, 145)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ), ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ) } Outer automorphisms :: reflexible Dual of E20.802 Graph:: bipartite v = 11 e = 100 f = 51 degree seq :: [ 10^10, 100 ] E20.795 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y1^5, Y3^5, 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 51, 2, 52, 6, 56, 11, 61, 4, 54)(3, 53, 7, 57, 14, 64, 20, 70, 10, 60)(5, 55, 8, 58, 15, 65, 21, 71, 12, 62)(9, 59, 16, 66, 24, 74, 30, 80, 19, 69)(13, 63, 17, 67, 25, 75, 31, 81, 22, 72)(18, 68, 26, 76, 34, 84, 40, 90, 29, 79)(23, 73, 27, 77, 35, 85, 41, 91, 32, 82)(28, 78, 36, 86, 44, 94, 47, 97, 39, 89)(33, 83, 37, 87, 45, 95, 48, 98, 42, 92)(38, 88, 46, 96, 50, 100, 49, 99, 43, 93)(101, 151, 103, 153, 109, 159, 118, 168, 128, 178, 138, 188, 137, 187, 127, 177, 117, 167, 108, 158, 102, 152, 107, 157, 116, 166, 126, 176, 136, 186, 146, 196, 145, 195, 135, 185, 125, 175, 115, 165, 106, 156, 114, 164, 124, 174, 134, 184, 144, 194, 150, 200, 148, 198, 141, 191, 131, 181, 121, 171, 111, 161, 120, 170, 130, 180, 140, 190, 147, 197, 149, 199, 142, 192, 132, 182, 122, 172, 112, 162, 104, 154, 110, 160, 119, 169, 129, 179, 139, 189, 143, 193, 133, 183, 123, 173, 113, 163, 105, 155) L = (1, 104)(2, 101)(3, 110)(4, 111)(5, 112)(6, 102)(7, 103)(8, 105)(9, 119)(10, 120)(11, 106)(12, 121)(13, 122)(14, 107)(15, 108)(16, 109)(17, 113)(18, 129)(19, 130)(20, 114)(21, 115)(22, 131)(23, 132)(24, 116)(25, 117)(26, 118)(27, 123)(28, 139)(29, 140)(30, 124)(31, 125)(32, 141)(33, 142)(34, 126)(35, 127)(36, 128)(37, 133)(38, 143)(39, 147)(40, 134)(41, 135)(42, 148)(43, 149)(44, 136)(45, 137)(46, 138)(47, 144)(48, 145)(49, 150)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ), ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ) } Outer automorphisms :: reflexible Dual of E20.804 Graph:: bipartite v = 11 e = 100 f = 51 degree seq :: [ 10^10, 100 ] E20.796 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^5, Y2^10 * Y1, Y2^4 * Y3 * Y1^-1 * Y2^-4 * Y3^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 51, 2, 52, 6, 56, 11, 61, 4, 54)(3, 53, 7, 57, 14, 64, 20, 70, 10, 60)(5, 55, 8, 58, 15, 65, 21, 71, 12, 62)(9, 59, 16, 66, 24, 74, 30, 80, 19, 69)(13, 63, 17, 67, 25, 75, 31, 81, 22, 72)(18, 68, 26, 76, 34, 84, 40, 90, 29, 79)(23, 73, 27, 77, 35, 85, 41, 91, 32, 82)(28, 78, 36, 86, 44, 94, 48, 98, 39, 89)(33, 83, 37, 87, 45, 95, 49, 99, 42, 92)(38, 88, 43, 93, 46, 96, 50, 100, 47, 97)(101, 151, 103, 153, 109, 159, 118, 168, 128, 178, 138, 188, 142, 192, 132, 182, 122, 172, 112, 162, 104, 154, 110, 160, 119, 169, 129, 179, 139, 189, 147, 197, 149, 199, 141, 191, 131, 181, 121, 171, 111, 161, 120, 170, 130, 180, 140, 190, 148, 198, 150, 200, 145, 195, 135, 185, 125, 175, 115, 165, 106, 156, 114, 164, 124, 174, 134, 184, 144, 194, 146, 196, 137, 187, 127, 177, 117, 167, 108, 158, 102, 152, 107, 157, 116, 166, 126, 176, 136, 186, 143, 193, 133, 183, 123, 173, 113, 163, 105, 155) L = (1, 104)(2, 101)(3, 110)(4, 111)(5, 112)(6, 102)(7, 103)(8, 105)(9, 119)(10, 120)(11, 106)(12, 121)(13, 122)(14, 107)(15, 108)(16, 109)(17, 113)(18, 129)(19, 130)(20, 114)(21, 115)(22, 131)(23, 132)(24, 116)(25, 117)(26, 118)(27, 123)(28, 139)(29, 140)(30, 124)(31, 125)(32, 141)(33, 142)(34, 126)(35, 127)(36, 128)(37, 133)(38, 147)(39, 148)(40, 134)(41, 135)(42, 149)(43, 138)(44, 136)(45, 137)(46, 143)(47, 150)(48, 144)(49, 145)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ), ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ) } Outer automorphisms :: reflexible Dual of E20.803 Graph:: bipartite v = 11 e = 100 f = 51 degree seq :: [ 10^10, 100 ] E20.797 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^4 * Y1 * Y2 * Y1^4, Y2^7 * Y1^-1 * Y2^2, Y2 * Y1^-2 * Y2^2 * Y1^-4 * Y2, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 26, 76, 42, 92, 33, 83, 49, 99, 38, 88, 23, 73, 12, 62, 5, 55, 8, 58, 16, 66, 28, 78, 44, 94, 34, 84, 19, 69, 31, 81, 47, 97, 39, 89, 24, 74, 13, 63, 18, 68, 30, 80, 46, 96, 35, 85, 20, 70, 9, 59, 17, 67, 29, 79, 45, 95, 40, 90, 25, 75, 32, 82, 48, 98, 36, 86, 21, 71, 10, 60, 3, 53, 7, 57, 15, 65, 27, 77, 43, 93, 41, 91, 50, 100, 37, 87, 22, 72, 11, 61, 4, 54)(101, 151, 103, 153, 109, 159, 119, 169, 133, 183, 150, 200, 132, 182, 118, 168, 108, 158, 102, 152, 107, 157, 117, 167, 131, 181, 149, 199, 137, 187, 148, 198, 130, 180, 116, 166, 106, 156, 115, 165, 129, 179, 147, 197, 138, 188, 122, 172, 136, 186, 146, 196, 128, 178, 114, 164, 127, 177, 145, 195, 139, 189, 123, 173, 111, 161, 121, 171, 135, 185, 144, 194, 126, 176, 143, 193, 140, 190, 124, 174, 112, 162, 104, 154, 110, 160, 120, 170, 134, 184, 142, 192, 141, 191, 125, 175, 113, 163, 105, 155) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 119)(10, 120)(11, 121)(12, 104)(13, 105)(14, 127)(15, 129)(16, 106)(17, 131)(18, 108)(19, 133)(20, 134)(21, 135)(22, 136)(23, 111)(24, 112)(25, 113)(26, 143)(27, 145)(28, 114)(29, 147)(30, 116)(31, 149)(32, 118)(33, 150)(34, 142)(35, 144)(36, 146)(37, 148)(38, 122)(39, 123)(40, 124)(41, 125)(42, 141)(43, 140)(44, 126)(45, 139)(46, 128)(47, 138)(48, 130)(49, 137)(50, 132)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E20.800 Graph:: bipartite v = 2 e = 100 f = 60 degree seq :: [ 100^2 ] E20.798 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-7 * Y2, Y2^4 * Y1 * Y2 * Y1^4, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 26, 76, 42, 92, 35, 85, 20, 70, 9, 59, 17, 67, 29, 79, 45, 95, 40, 90, 25, 75, 32, 82, 48, 98, 33, 83, 49, 99, 38, 88, 23, 73, 12, 62, 5, 55, 8, 58, 16, 66, 28, 78, 44, 94, 36, 86, 21, 71, 10, 60, 3, 53, 7, 57, 15, 65, 27, 77, 43, 93, 41, 91, 50, 100, 34, 84, 19, 69, 31, 81, 47, 97, 39, 89, 24, 74, 13, 63, 18, 68, 30, 80, 46, 96, 37, 87, 22, 72, 11, 61, 4, 54)(101, 151, 103, 153, 109, 159, 119, 169, 133, 183, 146, 196, 128, 178, 114, 164, 127, 177, 145, 195, 139, 189, 123, 173, 111, 161, 121, 171, 135, 185, 150, 200, 132, 182, 118, 168, 108, 158, 102, 152, 107, 157, 117, 167, 131, 181, 149, 199, 137, 187, 144, 194, 126, 176, 143, 193, 140, 190, 124, 174, 112, 162, 104, 154, 110, 160, 120, 170, 134, 184, 148, 198, 130, 180, 116, 166, 106, 156, 115, 165, 129, 179, 147, 197, 138, 188, 122, 172, 136, 186, 142, 192, 141, 191, 125, 175, 113, 163, 105, 155) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 119)(10, 120)(11, 121)(12, 104)(13, 105)(14, 127)(15, 129)(16, 106)(17, 131)(18, 108)(19, 133)(20, 134)(21, 135)(22, 136)(23, 111)(24, 112)(25, 113)(26, 143)(27, 145)(28, 114)(29, 147)(30, 116)(31, 149)(32, 118)(33, 146)(34, 148)(35, 150)(36, 142)(37, 144)(38, 122)(39, 123)(40, 124)(41, 125)(42, 141)(43, 140)(44, 126)(45, 139)(46, 128)(47, 138)(48, 130)(49, 137)(50, 132)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E20.799 Graph:: bipartite v = 2 e = 100 f = 60 degree seq :: [ 100^2 ] E20.799 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2), Y2^-5, Y2^5, Y3^10 * Y2^-2, (Y2^-1 * Y3)^50, (Y3^-1 * Y1^-1)^50 ] Map:: R = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)(101, 151, 102, 152, 106, 156, 111, 161, 104, 154)(103, 153, 107, 157, 114, 164, 120, 170, 110, 160)(105, 155, 108, 158, 115, 165, 121, 171, 112, 162)(109, 159, 116, 166, 124, 174, 130, 180, 119, 169)(113, 163, 117, 167, 125, 175, 131, 181, 122, 172)(118, 168, 126, 176, 134, 184, 140, 190, 129, 179)(123, 173, 127, 177, 135, 185, 141, 191, 132, 182)(128, 178, 136, 186, 144, 194, 148, 198, 139, 189)(133, 183, 137, 187, 145, 195, 149, 199, 142, 192)(138, 188, 146, 196, 150, 200, 143, 193, 147, 197) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 114)(7, 116)(8, 102)(9, 118)(10, 119)(11, 120)(12, 104)(13, 105)(14, 124)(15, 106)(16, 126)(17, 108)(18, 128)(19, 129)(20, 130)(21, 111)(22, 112)(23, 113)(24, 134)(25, 115)(26, 136)(27, 117)(28, 138)(29, 139)(30, 140)(31, 121)(32, 122)(33, 123)(34, 144)(35, 125)(36, 146)(37, 127)(38, 145)(39, 147)(40, 148)(41, 131)(42, 132)(43, 133)(44, 150)(45, 135)(46, 149)(47, 137)(48, 143)(49, 141)(50, 142)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 100, 100 ), ( 100^10 ) } Outer automorphisms :: reflexible Dual of E20.798 Graph:: simple bipartite v = 60 e = 100 f = 2 degree seq :: [ 2^50, 10^10 ] E20.800 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^5, Y2^-1 * Y3^10, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^50 ] Map:: R = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)(101, 151, 102, 152, 106, 156, 111, 161, 104, 154)(103, 153, 107, 157, 114, 164, 120, 170, 110, 160)(105, 155, 108, 158, 115, 165, 121, 171, 112, 162)(109, 159, 116, 166, 124, 174, 130, 180, 119, 169)(113, 163, 117, 167, 125, 175, 131, 181, 122, 172)(118, 168, 126, 176, 134, 184, 140, 190, 129, 179)(123, 173, 127, 177, 135, 185, 141, 191, 132, 182)(128, 178, 136, 186, 144, 194, 147, 197, 139, 189)(133, 183, 137, 187, 145, 195, 148, 198, 142, 192)(138, 188, 146, 196, 150, 200, 149, 199, 143, 193) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 114)(7, 116)(8, 102)(9, 118)(10, 119)(11, 120)(12, 104)(13, 105)(14, 124)(15, 106)(16, 126)(17, 108)(18, 128)(19, 129)(20, 130)(21, 111)(22, 112)(23, 113)(24, 134)(25, 115)(26, 136)(27, 117)(28, 138)(29, 139)(30, 140)(31, 121)(32, 122)(33, 123)(34, 144)(35, 125)(36, 146)(37, 127)(38, 137)(39, 143)(40, 147)(41, 131)(42, 132)(43, 133)(44, 150)(45, 135)(46, 145)(47, 149)(48, 141)(49, 142)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 100, 100 ), ( 100^10 ) } Outer automorphisms :: reflexible Dual of E20.797 Graph:: simple bipartite v = 60 e = 100 f = 2 degree seq :: [ 2^50, 10^10 ] E20.801 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^5, Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, Y3^2 * Y1^-10, (Y1^-1 * Y3^-1)^50 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 24, 74, 34, 84, 44, 94, 39, 89, 29, 79, 19, 69, 9, 59, 17, 67, 27, 77, 37, 87, 47, 97, 49, 99, 42, 92, 32, 82, 22, 72, 12, 62, 5, 55, 8, 58, 16, 66, 26, 76, 36, 86, 46, 96, 40, 90, 30, 80, 20, 70, 10, 60, 3, 53, 7, 57, 15, 65, 25, 75, 35, 85, 45, 95, 50, 100, 43, 93, 33, 83, 23, 73, 13, 63, 18, 68, 28, 78, 38, 88, 48, 98, 41, 91, 31, 81, 21, 71, 11, 61, 4, 54)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 113)(10, 119)(11, 120)(12, 104)(13, 105)(14, 125)(15, 127)(16, 106)(17, 118)(18, 108)(19, 123)(20, 129)(21, 130)(22, 111)(23, 112)(24, 135)(25, 137)(26, 114)(27, 128)(28, 116)(29, 133)(30, 139)(31, 140)(32, 121)(33, 122)(34, 145)(35, 147)(36, 124)(37, 138)(38, 126)(39, 143)(40, 144)(41, 146)(42, 131)(43, 132)(44, 150)(45, 149)(46, 134)(47, 148)(48, 136)(49, 141)(50, 142)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 100 ), ( 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100 ) } Outer automorphisms :: reflexible Dual of E20.793 Graph:: bipartite v = 51 e = 100 f = 11 degree seq :: [ 2^50, 100 ] E20.802 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, Y3^-2 * Y1^-10 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 24, 74, 34, 84, 44, 94, 43, 93, 33, 83, 23, 73, 13, 63, 18, 68, 28, 78, 38, 88, 48, 98, 50, 100, 40, 90, 30, 80, 20, 70, 10, 60, 3, 53, 7, 57, 15, 65, 25, 75, 35, 85, 45, 95, 42, 92, 32, 82, 22, 72, 12, 62, 5, 55, 8, 58, 16, 66, 26, 76, 36, 86, 46, 96, 49, 99, 39, 89, 29, 79, 19, 69, 9, 59, 17, 67, 27, 77, 37, 87, 47, 97, 41, 91, 31, 81, 21, 71, 11, 61, 4, 54)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 113)(10, 119)(11, 120)(12, 104)(13, 105)(14, 125)(15, 127)(16, 106)(17, 118)(18, 108)(19, 123)(20, 129)(21, 130)(22, 111)(23, 112)(24, 135)(25, 137)(26, 114)(27, 128)(28, 116)(29, 133)(30, 139)(31, 140)(32, 121)(33, 122)(34, 145)(35, 147)(36, 124)(37, 138)(38, 126)(39, 143)(40, 149)(41, 150)(42, 131)(43, 132)(44, 142)(45, 141)(46, 134)(47, 148)(48, 136)(49, 144)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 100 ), ( 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100 ) } Outer automorphisms :: reflexible Dual of E20.794 Graph:: bipartite v = 51 e = 100 f = 11 degree seq :: [ 2^50, 100 ] E20.803 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, Y1^10 * Y3^-1, (Y1^-1 * Y3^-1)^50 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 24, 74, 34, 84, 40, 90, 30, 80, 20, 70, 10, 60, 3, 53, 7, 57, 15, 65, 25, 75, 35, 85, 44, 94, 47, 97, 39, 89, 29, 79, 19, 69, 9, 59, 17, 67, 27, 77, 37, 87, 45, 95, 50, 100, 49, 99, 43, 93, 33, 83, 23, 73, 13, 63, 18, 68, 28, 78, 38, 88, 46, 96, 48, 98, 42, 92, 32, 82, 22, 72, 12, 62, 5, 55, 8, 58, 16, 66, 26, 76, 36, 86, 41, 91, 31, 81, 21, 71, 11, 61, 4, 54)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 113)(10, 119)(11, 120)(12, 104)(13, 105)(14, 125)(15, 127)(16, 106)(17, 118)(18, 108)(19, 123)(20, 129)(21, 130)(22, 111)(23, 112)(24, 135)(25, 137)(26, 114)(27, 128)(28, 116)(29, 133)(30, 139)(31, 140)(32, 121)(33, 122)(34, 144)(35, 145)(36, 124)(37, 138)(38, 126)(39, 143)(40, 147)(41, 134)(42, 131)(43, 132)(44, 150)(45, 146)(46, 136)(47, 149)(48, 141)(49, 142)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 100 ), ( 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100 ) } Outer automorphisms :: reflexible Dual of E20.796 Graph:: bipartite v = 51 e = 100 f = 11 degree seq :: [ 2^50, 100 ] E20.804 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 50, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, Y1^10 * Y3, (Y1^-1 * Y3^-1)^50 ] Map:: R = (1, 51, 2, 52, 6, 56, 14, 64, 24, 74, 34, 84, 42, 92, 32, 82, 22, 72, 12, 62, 5, 55, 8, 58, 16, 66, 26, 76, 36, 86, 44, 94, 49, 99, 43, 93, 33, 83, 23, 73, 13, 63, 18, 68, 28, 78, 38, 88, 46, 96, 50, 100, 47, 97, 39, 89, 29, 79, 19, 69, 9, 59, 17, 67, 27, 77, 37, 87, 45, 95, 48, 98, 40, 90, 30, 80, 20, 70, 10, 60, 3, 53, 7, 57, 15, 65, 25, 75, 35, 85, 41, 91, 31, 81, 21, 71, 11, 61, 4, 54)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 115)(7, 117)(8, 102)(9, 113)(10, 119)(11, 120)(12, 104)(13, 105)(14, 125)(15, 127)(16, 106)(17, 118)(18, 108)(19, 123)(20, 129)(21, 130)(22, 111)(23, 112)(24, 135)(25, 137)(26, 114)(27, 128)(28, 116)(29, 133)(30, 139)(31, 140)(32, 121)(33, 122)(34, 141)(35, 145)(36, 124)(37, 138)(38, 126)(39, 143)(40, 147)(41, 148)(42, 131)(43, 132)(44, 134)(45, 146)(46, 136)(47, 149)(48, 150)(49, 142)(50, 144)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 10, 100 ), ( 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100, 10, 100 ) } Outer automorphisms :: reflexible Dual of E20.795 Graph:: bipartite v = 51 e = 100 f = 11 degree seq :: [ 2^50, 100 ] E20.805 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 11, 55}) Quotient :: edge Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^5, T2^11 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 38, 43, 33, 23, 13, 5)(2, 7, 16, 26, 36, 46, 47, 37, 27, 17, 8)(4, 10, 19, 29, 39, 48, 51, 42, 32, 22, 12)(6, 14, 24, 34, 44, 52, 53, 45, 35, 25, 15)(11, 20, 30, 40, 49, 54, 55, 50, 41, 31, 21)(56, 57, 61, 66, 59)(58, 62, 69, 75, 65)(60, 63, 70, 76, 67)(64, 71, 79, 85, 74)(68, 72, 80, 86, 77)(73, 81, 89, 95, 84)(78, 82, 90, 96, 87)(83, 91, 99, 104, 94)(88, 92, 100, 105, 97)(93, 101, 107, 109, 103)(98, 102, 108, 110, 106) L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110) local type(s) :: { ( 110^5 ), ( 110^11 ) } Outer automorphisms :: reflexible Dual of E20.809 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 55 f = 1 degree seq :: [ 5^11, 11^5 ] E20.806 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 11, 55}) Quotient :: edge Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-5 * T2^-5, T1^-1 * T2^10, T2^-2 * T1^2 * T2^-1 * T1^3 * T2^-2 * T1, T1^11 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 51, 50, 32, 18, 8, 2, 7, 17, 31, 49, 37, 55, 48, 30, 16, 6, 15, 29, 47, 38, 22, 36, 54, 46, 28, 14, 27, 45, 39, 23, 11, 21, 35, 53, 44, 26, 43, 40, 24, 12, 4, 10, 20, 34, 52, 42, 41, 25, 13, 5)(56, 57, 61, 69, 81, 97, 106, 92, 77, 66, 59)(58, 62, 70, 82, 98, 96, 105, 110, 91, 76, 65)(60, 63, 71, 83, 99, 107, 88, 104, 93, 78, 67)(64, 72, 84, 100, 95, 80, 87, 103, 109, 90, 75)(68, 73, 85, 101, 108, 89, 74, 86, 102, 94, 79) 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) :: { ( 10^11 ), ( 10^55 ) } Outer automorphisms :: reflexible Dual of E20.810 Transitivity :: ET+ Graph:: bipartite v = 6 e = 55 f = 11 degree seq :: [ 11^5, 55 ] E20.807 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 11, 55}) Quotient :: edge Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^5, T1^-11 * T2^-1, T2^-1 * T1^4 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1, (T1^-1 * T2^-1)^11 ] Map:: non-degenerate R = (1, 3, 9, 13, 5)(2, 7, 17, 18, 8)(4, 10, 19, 23, 12)(6, 15, 27, 28, 16)(11, 20, 29, 33, 22)(14, 25, 37, 38, 26)(21, 30, 39, 43, 32)(24, 35, 47, 48, 36)(31, 40, 49, 51, 42)(34, 45, 53, 54, 46)(41, 50, 55, 52, 44)(56, 57, 61, 69, 79, 89, 99, 97, 87, 77, 67, 60, 63, 71, 81, 91, 101, 107, 106, 98, 88, 78, 68, 73, 83, 93, 103, 109, 110, 104, 94, 84, 74, 64, 72, 82, 92, 102, 108, 105, 95, 85, 75, 65, 58, 62, 70, 80, 90, 100, 96, 86, 76, 66, 59) L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110) local type(s) :: { ( 22^5 ), ( 22^55 ) } Outer automorphisms :: reflexible Dual of E20.808 Transitivity :: ET+ Graph:: bipartite v = 12 e = 55 f = 5 degree seq :: [ 5^11, 55 ] E20.808 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 11, 55}) Quotient :: loop Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^5, T2^11 ] Map:: non-degenerate R = (1, 56, 3, 58, 9, 64, 18, 73, 28, 83, 38, 93, 43, 98, 33, 88, 23, 78, 13, 68, 5, 60)(2, 57, 7, 62, 16, 71, 26, 81, 36, 91, 46, 101, 47, 102, 37, 92, 27, 82, 17, 72, 8, 63)(4, 59, 10, 65, 19, 74, 29, 84, 39, 94, 48, 103, 51, 106, 42, 97, 32, 87, 22, 77, 12, 67)(6, 61, 14, 69, 24, 79, 34, 89, 44, 99, 52, 107, 53, 108, 45, 100, 35, 90, 25, 80, 15, 70)(11, 66, 20, 75, 30, 85, 40, 95, 49, 104, 54, 109, 55, 110, 50, 105, 41, 96, 31, 86, 21, 76) L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 66)(7, 69)(8, 70)(9, 71)(10, 58)(11, 59)(12, 60)(13, 72)(14, 75)(15, 76)(16, 79)(17, 80)(18, 81)(19, 64)(20, 65)(21, 67)(22, 68)(23, 82)(24, 85)(25, 86)(26, 89)(27, 90)(28, 91)(29, 73)(30, 74)(31, 77)(32, 78)(33, 92)(34, 95)(35, 96)(36, 99)(37, 100)(38, 101)(39, 83)(40, 84)(41, 87)(42, 88)(43, 102)(44, 104)(45, 105)(46, 107)(47, 108)(48, 93)(49, 94)(50, 97)(51, 98)(52, 109)(53, 110)(54, 103)(55, 106) local type(s) :: { ( 5, 55, 5, 55, 5, 55, 5, 55, 5, 55, 5, 55, 5, 55, 5, 55, 5, 55, 5, 55, 5, 55 ) } Outer automorphisms :: reflexible Dual of E20.807 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 55 f = 12 degree seq :: [ 22^5 ] E20.809 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 11, 55}) Quotient :: loop Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-5 * T2^-5, T1^-1 * T2^10, T2^-2 * T1^2 * T2^-1 * T1^3 * T2^-2 * T1, T1^11 ] Map:: non-degenerate R = (1, 56, 3, 58, 9, 64, 19, 74, 33, 88, 51, 106, 50, 105, 32, 87, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 31, 86, 49, 104, 37, 92, 55, 110, 48, 103, 30, 85, 16, 71, 6, 61, 15, 70, 29, 84, 47, 102, 38, 93, 22, 77, 36, 91, 54, 109, 46, 101, 28, 83, 14, 69, 27, 82, 45, 100, 39, 94, 23, 78, 11, 66, 21, 76, 35, 90, 53, 108, 44, 99, 26, 81, 43, 98, 40, 95, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 34, 89, 52, 107, 42, 97, 41, 96, 25, 80, 13, 68, 5, 60) L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 81)(15, 82)(16, 83)(17, 84)(18, 85)(19, 86)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 87)(26, 97)(27, 98)(28, 99)(29, 100)(30, 101)(31, 102)(32, 103)(33, 104)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(41, 105)(42, 106)(43, 96)(44, 107)(45, 95)(46, 108)(47, 94)(48, 109)(49, 93)(50, 110)(51, 92)(52, 88)(53, 89)(54, 90)(55, 91) local type(s) :: { ( 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11, 5, 11 ) } Outer automorphisms :: reflexible Dual of E20.805 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 55 f = 16 degree seq :: [ 110 ] E20.810 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 11, 55}) Quotient :: loop Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^5, T1^-11 * T2^-1, T2^-1 * T1^4 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1, (T1^-1 * T2^-1)^11 ] Map:: non-degenerate R = (1, 56, 3, 58, 9, 64, 13, 68, 5, 60)(2, 57, 7, 62, 17, 72, 18, 73, 8, 63)(4, 59, 10, 65, 19, 74, 23, 78, 12, 67)(6, 61, 15, 70, 27, 82, 28, 83, 16, 71)(11, 66, 20, 75, 29, 84, 33, 88, 22, 77)(14, 69, 25, 80, 37, 92, 38, 93, 26, 81)(21, 76, 30, 85, 39, 94, 43, 98, 32, 87)(24, 79, 35, 90, 47, 102, 48, 103, 36, 91)(31, 86, 40, 95, 49, 104, 51, 106, 42, 97)(34, 89, 45, 100, 53, 108, 54, 109, 46, 101)(41, 96, 50, 105, 55, 110, 52, 107, 44, 99) L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 79)(15, 80)(16, 81)(17, 82)(18, 83)(19, 64)(20, 65)(21, 66)(22, 67)(23, 68)(24, 89)(25, 90)(26, 91)(27, 92)(28, 93)(29, 74)(30, 75)(31, 76)(32, 77)(33, 78)(34, 99)(35, 100)(36, 101)(37, 102)(38, 103)(39, 84)(40, 85)(41, 86)(42, 87)(43, 88)(44, 97)(45, 96)(46, 107)(47, 108)(48, 109)(49, 94)(50, 95)(51, 98)(52, 106)(53, 105)(54, 110)(55, 104) local type(s) :: { ( 11, 55, 11, 55, 11, 55, 11, 55, 11, 55 ) } Outer automorphisms :: reflexible Dual of E20.806 Transitivity :: ET+ VT+ AT Graph:: v = 11 e = 55 f = 6 degree seq :: [ 10^11 ] E20.811 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 11, 55}) Quotient :: dipole Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^5, Y2^11, Y3^55 ] Map:: R = (1, 56, 2, 57, 6, 61, 11, 66, 4, 59)(3, 58, 7, 62, 14, 69, 20, 75, 10, 65)(5, 60, 8, 63, 15, 70, 21, 76, 12, 67)(9, 64, 16, 71, 24, 79, 30, 85, 19, 74)(13, 68, 17, 72, 25, 80, 31, 86, 22, 77)(18, 73, 26, 81, 34, 89, 40, 95, 29, 84)(23, 78, 27, 82, 35, 90, 41, 96, 32, 87)(28, 83, 36, 91, 44, 99, 49, 104, 39, 94)(33, 88, 37, 92, 45, 100, 50, 105, 42, 97)(38, 93, 46, 101, 52, 107, 54, 109, 48, 103)(43, 98, 47, 102, 53, 108, 55, 110, 51, 106)(111, 166, 113, 168, 119, 174, 128, 183, 138, 193, 148, 203, 153, 208, 143, 198, 133, 188, 123, 178, 115, 170)(112, 167, 117, 172, 126, 181, 136, 191, 146, 201, 156, 211, 157, 212, 147, 202, 137, 192, 127, 182, 118, 173)(114, 169, 120, 175, 129, 184, 139, 194, 149, 204, 158, 213, 161, 216, 152, 207, 142, 197, 132, 187, 122, 177)(116, 171, 124, 179, 134, 189, 144, 199, 154, 209, 162, 217, 163, 218, 155, 210, 145, 200, 135, 190, 125, 180)(121, 176, 130, 185, 140, 195, 150, 205, 159, 214, 164, 219, 165, 220, 160, 215, 151, 206, 141, 196, 131, 186) L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 129)(10, 130)(11, 116)(12, 131)(13, 132)(14, 117)(15, 118)(16, 119)(17, 123)(18, 139)(19, 140)(20, 124)(21, 125)(22, 141)(23, 142)(24, 126)(25, 127)(26, 128)(27, 133)(28, 149)(29, 150)(30, 134)(31, 135)(32, 151)(33, 152)(34, 136)(35, 137)(36, 138)(37, 143)(38, 158)(39, 159)(40, 144)(41, 145)(42, 160)(43, 161)(44, 146)(45, 147)(46, 148)(47, 153)(48, 164)(49, 154)(50, 155)(51, 165)(52, 156)(53, 157)(54, 162)(55, 163)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ), ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) } Outer automorphisms :: reflexible Dual of E20.814 Graph:: bipartite v = 16 e = 110 f = 56 degree seq :: [ 10^11, 22^5 ] E20.812 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 11, 55}) Quotient :: dipole Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y1^-5 * Y2^-5, (Y3^-1 * Y1^-1)^5, Y1^-1 * Y2^10, Y1^11 ] Map:: R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 42, 97, 51, 106, 37, 92, 22, 77, 11, 66, 4, 59)(3, 58, 7, 62, 15, 70, 27, 82, 43, 98, 41, 96, 50, 105, 55, 110, 36, 91, 21, 76, 10, 65)(5, 60, 8, 63, 16, 71, 28, 83, 44, 99, 52, 107, 33, 88, 49, 104, 38, 93, 23, 78, 12, 67)(9, 64, 17, 72, 29, 84, 45, 100, 40, 95, 25, 80, 32, 87, 48, 103, 54, 109, 35, 90, 20, 75)(13, 68, 18, 73, 30, 85, 46, 101, 53, 108, 34, 89, 19, 74, 31, 86, 47, 102, 39, 94, 24, 79)(111, 166, 113, 168, 119, 174, 129, 184, 143, 198, 161, 216, 160, 215, 142, 197, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 141, 196, 159, 214, 147, 202, 165, 220, 158, 213, 140, 195, 126, 181, 116, 171, 125, 180, 139, 194, 157, 212, 148, 203, 132, 187, 146, 201, 164, 219, 156, 211, 138, 193, 124, 179, 137, 192, 155, 210, 149, 204, 133, 188, 121, 176, 131, 186, 145, 200, 163, 218, 154, 209, 136, 191, 153, 208, 150, 205, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 144, 199, 162, 217, 152, 207, 151, 206, 135, 190, 123, 178, 115, 170) L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 153)(27, 155)(28, 124)(29, 157)(30, 126)(31, 159)(32, 128)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 132)(39, 133)(40, 134)(41, 135)(42, 151)(43, 150)(44, 136)(45, 149)(46, 138)(47, 148)(48, 140)(49, 147)(50, 142)(51, 160)(52, 152)(53, 154)(54, 156)(55, 158)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E20.813 Graph:: bipartite v = 6 e = 110 f = 66 degree seq :: [ 22^5, 110 ] E20.813 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 11, 55}) Quotient :: dipole Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^5, Y2^-1 * Y3^11, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^55 ] Map:: R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 121, 176, 114, 169)(113, 168, 117, 172, 124, 179, 130, 185, 120, 175)(115, 170, 118, 173, 125, 180, 131, 186, 122, 177)(119, 174, 126, 181, 134, 189, 140, 195, 129, 184)(123, 178, 127, 182, 135, 190, 141, 196, 132, 187)(128, 183, 136, 191, 144, 199, 150, 205, 139, 194)(133, 188, 137, 192, 145, 200, 151, 206, 142, 197)(138, 193, 146, 201, 154, 209, 159, 214, 149, 204)(143, 198, 147, 202, 155, 210, 160, 215, 152, 207)(148, 203, 156, 211, 162, 217, 164, 219, 158, 213)(153, 208, 157, 212, 163, 218, 165, 220, 161, 216) L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 124)(7, 126)(8, 112)(9, 128)(10, 129)(11, 130)(12, 114)(13, 115)(14, 134)(15, 116)(16, 136)(17, 118)(18, 138)(19, 139)(20, 140)(21, 121)(22, 122)(23, 123)(24, 144)(25, 125)(26, 146)(27, 127)(28, 148)(29, 149)(30, 150)(31, 131)(32, 132)(33, 133)(34, 154)(35, 135)(36, 156)(37, 137)(38, 157)(39, 158)(40, 159)(41, 141)(42, 142)(43, 143)(44, 162)(45, 145)(46, 163)(47, 147)(48, 153)(49, 164)(50, 151)(51, 152)(52, 165)(53, 155)(54, 161)(55, 160)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 22, 110 ), ( 22, 110, 22, 110, 22, 110, 22, 110, 22, 110 ) } Outer automorphisms :: reflexible Dual of E20.812 Graph:: simple bipartite v = 66 e = 110 f = 6 degree seq :: [ 2^55, 10^11 ] E20.814 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 11, 55}) Quotient :: dipole Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, Y1^-3 * Y3^-1 * Y1^-8, Y3^-1 * Y1^4 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1, (Y1^-1 * Y3^-1)^11 ] Map:: R = (1, 56, 2, 57, 6, 61, 14, 69, 24, 79, 34, 89, 44, 99, 42, 97, 32, 87, 22, 77, 12, 67, 5, 60, 8, 63, 16, 71, 26, 81, 36, 91, 46, 101, 52, 107, 51, 106, 43, 98, 33, 88, 23, 78, 13, 68, 18, 73, 28, 83, 38, 93, 48, 103, 54, 109, 55, 110, 49, 104, 39, 94, 29, 84, 19, 74, 9, 64, 17, 72, 27, 82, 37, 92, 47, 102, 53, 108, 50, 105, 40, 95, 30, 85, 20, 75, 10, 65, 3, 58, 7, 62, 15, 70, 25, 80, 35, 90, 45, 100, 41, 96, 31, 86, 21, 76, 11, 66, 4, 59)(111, 166)(112, 167)(113, 168)(114, 169)(115, 170)(116, 171)(117, 172)(118, 173)(119, 174)(120, 175)(121, 176)(122, 177)(123, 178)(124, 179)(125, 180)(126, 181)(127, 182)(128, 183)(129, 184)(130, 185)(131, 186)(132, 187)(133, 188)(134, 189)(135, 190)(136, 191)(137, 192)(138, 193)(139, 194)(140, 195)(141, 196)(142, 197)(143, 198)(144, 199)(145, 200)(146, 201)(147, 202)(148, 203)(149, 204)(150, 205)(151, 206)(152, 207)(153, 208)(154, 209)(155, 210)(156, 211)(157, 212)(158, 213)(159, 214)(160, 215)(161, 216)(162, 217)(163, 218)(164, 219)(165, 220) L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 123)(10, 129)(11, 130)(12, 114)(13, 115)(14, 135)(15, 137)(16, 116)(17, 128)(18, 118)(19, 133)(20, 139)(21, 140)(22, 121)(23, 122)(24, 145)(25, 147)(26, 124)(27, 138)(28, 126)(29, 143)(30, 149)(31, 150)(32, 131)(33, 132)(34, 155)(35, 157)(36, 134)(37, 148)(38, 136)(39, 153)(40, 159)(41, 160)(42, 141)(43, 142)(44, 151)(45, 163)(46, 144)(47, 158)(48, 146)(49, 161)(50, 165)(51, 152)(52, 154)(53, 164)(54, 156)(55, 162)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 10, 22 ), ( 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22, 10, 22 ) } Outer automorphisms :: reflexible Dual of E20.811 Graph:: bipartite v = 56 e = 110 f = 16 degree seq :: [ 2^55, 110 ] E20.815 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 11, 55}) Quotient :: dipole Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3^5, Y1^5, Y3 * Y2^-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 ] Map:: R = (1, 56, 2, 57, 6, 61, 11, 66, 4, 59)(3, 58, 7, 62, 14, 69, 20, 75, 10, 65)(5, 60, 8, 63, 15, 70, 21, 76, 12, 67)(9, 64, 16, 71, 24, 79, 30, 85, 19, 74)(13, 68, 17, 72, 25, 80, 31, 86, 22, 77)(18, 73, 26, 81, 34, 89, 40, 95, 29, 84)(23, 78, 27, 82, 35, 90, 41, 96, 32, 87)(28, 83, 36, 91, 44, 99, 50, 105, 39, 94)(33, 88, 37, 92, 45, 100, 51, 106, 42, 97)(38, 93, 46, 101, 52, 107, 55, 110, 49, 104)(43, 98, 47, 102, 53, 108, 54, 109, 48, 103)(111, 166, 113, 168, 119, 174, 128, 183, 138, 193, 148, 203, 158, 213, 152, 207, 142, 197, 132, 187, 122, 177, 114, 169, 120, 175, 129, 184, 139, 194, 149, 204, 159, 214, 164, 219, 161, 216, 151, 206, 141, 196, 131, 186, 121, 176, 130, 185, 140, 195, 150, 205, 160, 215, 165, 220, 163, 218, 155, 210, 145, 200, 135, 190, 125, 180, 116, 171, 124, 179, 134, 189, 144, 199, 154, 209, 162, 217, 157, 212, 147, 202, 137, 192, 127, 182, 118, 173, 112, 167, 117, 172, 126, 181, 136, 191, 146, 201, 156, 211, 153, 208, 143, 198, 133, 188, 123, 178, 115, 170) L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 129)(10, 130)(11, 116)(12, 131)(13, 132)(14, 117)(15, 118)(16, 119)(17, 123)(18, 139)(19, 140)(20, 124)(21, 125)(22, 141)(23, 142)(24, 126)(25, 127)(26, 128)(27, 133)(28, 149)(29, 150)(30, 134)(31, 135)(32, 151)(33, 152)(34, 136)(35, 137)(36, 138)(37, 143)(38, 159)(39, 160)(40, 144)(41, 145)(42, 161)(43, 158)(44, 146)(45, 147)(46, 148)(47, 153)(48, 164)(49, 165)(50, 154)(51, 155)(52, 156)(53, 157)(54, 163)(55, 162)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 2, 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, 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 E20.816 Graph:: bipartite v = 12 e = 110 f = 60 degree seq :: [ 10^11, 110 ] E20.816 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 11, 55}) Quotient :: dipole Aut^+ = C55 (small group id <55, 2>) Aut = D110 (small group id <110, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^-5 * Y3^-5, Y1^-1 * Y3^10, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1^2 * Y3^-3 * Y1, Y1^11, (Y3 * Y2^-1)^55 ] Map:: R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 42, 97, 51, 106, 37, 92, 22, 77, 11, 66, 4, 59)(3, 58, 7, 62, 15, 70, 27, 82, 43, 98, 41, 96, 50, 105, 55, 110, 36, 91, 21, 76, 10, 65)(5, 60, 8, 63, 16, 71, 28, 83, 44, 99, 52, 107, 33, 88, 49, 104, 38, 93, 23, 78, 12, 67)(9, 64, 17, 72, 29, 84, 45, 100, 40, 95, 25, 80, 32, 87, 48, 103, 54, 109, 35, 90, 20, 75)(13, 68, 18, 73, 30, 85, 46, 101, 53, 108, 34, 89, 19, 74, 31, 86, 47, 102, 39, 94, 24, 79)(111, 166)(112, 167)(113, 168)(114, 169)(115, 170)(116, 171)(117, 172)(118, 173)(119, 174)(120, 175)(121, 176)(122, 177)(123, 178)(124, 179)(125, 180)(126, 181)(127, 182)(128, 183)(129, 184)(130, 185)(131, 186)(132, 187)(133, 188)(134, 189)(135, 190)(136, 191)(137, 192)(138, 193)(139, 194)(140, 195)(141, 196)(142, 197)(143, 198)(144, 199)(145, 200)(146, 201)(147, 202)(148, 203)(149, 204)(150, 205)(151, 206)(152, 207)(153, 208)(154, 209)(155, 210)(156, 211)(157, 212)(158, 213)(159, 214)(160, 215)(161, 216)(162, 217)(163, 218)(164, 219)(165, 220) L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 153)(27, 155)(28, 124)(29, 157)(30, 126)(31, 159)(32, 128)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 132)(39, 133)(40, 134)(41, 135)(42, 151)(43, 150)(44, 136)(45, 149)(46, 138)(47, 148)(48, 140)(49, 147)(50, 142)(51, 160)(52, 152)(53, 154)(54, 156)(55, 158)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220) local type(s) :: { ( 10, 110 ), ( 10, 110, 10, 110, 10, 110, 10, 110, 10, 110, 10, 110, 10, 110, 10, 110, 10, 110, 10, 110, 10, 110 ) } Outer automorphisms :: reflexible Dual of E20.815 Graph:: simple bipartite v = 60 e = 110 f = 12 degree seq :: [ 2^55, 22^5 ] E20.817 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^14 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 6, 62)(4, 60, 9, 65)(5, 61, 10, 66)(7, 63, 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)(114, 170, 118, 174)(116, 172, 117, 173)(119, 175, 120, 176)(121, 177, 122, 178)(123, 179, 124, 180)(125, 181, 126, 182)(127, 183, 128, 184)(129, 185, 130, 186)(131, 187, 132, 188)(133, 189, 134, 190)(135, 191, 136, 192)(137, 193, 138, 194)(139, 195, 140, 196)(141, 197, 142, 198)(143, 199, 144, 200)(145, 201, 146, 202)(147, 203, 148, 204)(149, 205, 150, 206)(151, 207, 152, 208)(153, 209, 154, 210)(155, 211, 156, 212)(157, 213, 158, 214)(159, 215, 160, 216)(161, 217, 162, 218)(163, 219, 164, 220)(165, 221, 166, 222)(167, 223, 168, 224) L = (1, 116)(2, 119)(3, 117)(4, 115)(5, 113)(6, 120)(7, 118)(8, 114)(9, 125)(10, 126)(11, 127)(12, 128)(13, 122)(14, 121)(15, 124)(16, 123)(17, 133)(18, 134)(19, 135)(20, 136)(21, 130)(22, 129)(23, 132)(24, 131)(25, 141)(26, 142)(27, 143)(28, 144)(29, 138)(30, 137)(31, 140)(32, 139)(33, 149)(34, 150)(35, 151)(36, 152)(37, 146)(38, 145)(39, 148)(40, 147)(41, 157)(42, 158)(43, 159)(44, 160)(45, 154)(46, 153)(47, 156)(48, 155)(49, 165)(50, 166)(51, 167)(52, 168)(53, 162)(54, 161)(55, 164)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.828 Graph:: simple bipartite v = 56 e = 112 f = 18 degree seq :: [ 4^56 ] E20.818 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2, (Y1 * Y2)^4, Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 11, 67)(6, 62, 13, 69)(8, 64, 16, 72)(10, 66, 19, 75)(12, 68, 21, 77)(14, 70, 24, 80)(15, 71, 20, 76)(17, 73, 26, 82)(18, 74, 27, 83)(22, 78, 30, 86)(23, 79, 31, 87)(25, 81, 33, 89)(28, 84, 36, 92)(29, 85, 37, 93)(32, 88, 40, 96)(34, 90, 42, 98)(35, 91, 43, 99)(38, 94, 46, 102)(39, 95, 47, 103)(41, 97, 49, 105)(44, 100, 52, 108)(45, 101, 53, 109)(48, 104, 56, 112)(50, 106, 55, 111)(51, 107, 54, 110)(113, 169, 115, 171)(114, 170, 117, 173)(116, 172, 122, 178)(118, 174, 126, 182)(119, 175, 127, 183)(120, 176, 129, 185)(121, 177, 128, 184)(123, 179, 132, 188)(124, 180, 134, 190)(125, 181, 133, 189)(130, 186, 140, 196)(131, 187, 138, 194)(135, 191, 144, 200)(136, 192, 142, 198)(137, 193, 146, 202)(139, 195, 145, 201)(141, 197, 150, 206)(143, 199, 149, 205)(147, 203, 156, 212)(148, 204, 154, 210)(151, 207, 160, 216)(152, 208, 158, 214)(153, 209, 162, 218)(155, 211, 161, 217)(157, 213, 166, 222)(159, 215, 165, 221)(163, 219, 168, 224)(164, 220, 167, 223) L = (1, 116)(2, 118)(3, 120)(4, 113)(5, 124)(6, 114)(7, 126)(8, 115)(9, 130)(10, 123)(11, 122)(12, 117)(13, 135)(14, 119)(15, 134)(16, 137)(17, 132)(18, 121)(19, 140)(20, 129)(21, 141)(22, 127)(23, 125)(24, 144)(25, 128)(26, 146)(27, 147)(28, 131)(29, 133)(30, 150)(31, 151)(32, 136)(33, 153)(34, 138)(35, 139)(36, 156)(37, 157)(38, 142)(39, 143)(40, 160)(41, 145)(42, 162)(43, 163)(44, 148)(45, 149)(46, 166)(47, 167)(48, 152)(49, 165)(50, 154)(51, 155)(52, 168)(53, 161)(54, 158)(55, 159)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.827 Graph:: simple bipartite v = 56 e = 112 f = 18 degree seq :: [ 4^56 ] E20.819 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = D56 (small group id <56, 5>) Aut = C2 x D56 (small group id <112, 29>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2^-1 * Y1)^2, Y3^7 * Y2^-1, (Y2^-1 * Y3)^14 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 18, 74)(12, 68, 23, 79)(13, 69, 22, 78)(14, 70, 24, 80)(15, 71, 20, 76)(16, 72, 19, 75)(17, 73, 21, 77)(25, 81, 34, 90)(26, 82, 33, 89)(27, 83, 39, 95)(28, 84, 38, 94)(29, 85, 40, 96)(30, 86, 36, 92)(31, 87, 35, 91)(32, 88, 37, 93)(41, 97, 48, 104)(42, 98, 47, 103)(43, 99, 52, 108)(44, 100, 51, 107)(45, 101, 50, 106)(46, 102, 49, 105)(53, 109, 56, 112)(54, 110, 55, 111)(113, 169, 115, 171, 123, 179, 117, 173)(114, 170, 119, 175, 130, 186, 121, 177)(116, 172, 124, 180, 137, 193, 127, 183)(118, 174, 125, 181, 138, 194, 128, 184)(120, 176, 131, 187, 145, 201, 134, 190)(122, 178, 132, 188, 146, 202, 135, 191)(126, 182, 139, 195, 153, 209, 142, 198)(129, 185, 140, 196, 154, 210, 143, 199)(133, 189, 147, 203, 159, 215, 150, 206)(136, 192, 148, 204, 160, 216, 151, 207)(141, 197, 155, 211, 165, 221, 157, 213)(144, 200, 156, 212, 166, 222, 158, 214)(149, 205, 161, 217, 167, 223, 163, 219)(152, 208, 162, 218, 168, 224, 164, 220) L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 131)(8, 133)(9, 134)(10, 114)(11, 137)(12, 139)(13, 115)(14, 141)(15, 142)(16, 117)(17, 118)(18, 145)(19, 147)(20, 119)(21, 149)(22, 150)(23, 121)(24, 122)(25, 153)(26, 123)(27, 155)(28, 125)(29, 156)(30, 157)(31, 128)(32, 129)(33, 159)(34, 130)(35, 161)(36, 132)(37, 162)(38, 163)(39, 135)(40, 136)(41, 165)(42, 138)(43, 166)(44, 140)(45, 144)(46, 143)(47, 167)(48, 146)(49, 168)(50, 148)(51, 152)(52, 151)(53, 158)(54, 154)(55, 164)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.823 Graph:: simple bipartite v = 42 e = 112 f = 32 degree seq :: [ 4^28, 8^14 ] E20.820 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2 * Y1 * Y2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y3 * Y2^-1)^14 ] Map:: polytopal non-degenerate R = (1, 57, 2, 58)(3, 59, 5, 61)(4, 60, 6, 62)(7, 63, 10, 66)(8, 64, 9, 65)(11, 67, 12, 68)(13, 69, 14, 70)(15, 71, 16, 72)(17, 73, 18, 74)(19, 75, 20, 76)(21, 77, 22, 78)(23, 79, 24, 80)(25, 81, 26, 82)(27, 83, 28, 84)(29, 85, 30, 86)(31, 87, 32, 88)(33, 89, 34, 90)(35, 91, 36, 92)(37, 93, 38, 94)(39, 95, 40, 96)(41, 97, 42, 98)(43, 99, 44, 100)(45, 101, 46, 102)(47, 103, 48, 104)(49, 105, 50, 106)(51, 107, 52, 108)(53, 109, 54, 110)(55, 111, 56, 112)(113, 169, 115, 171, 114, 170, 117, 173)(116, 172, 120, 176, 118, 174, 121, 177)(119, 175, 123, 179, 122, 178, 124, 180)(125, 181, 129, 185, 126, 182, 130, 186)(127, 183, 131, 187, 128, 184, 132, 188)(133, 189, 137, 193, 134, 190, 138, 194)(135, 191, 139, 195, 136, 192, 140, 196)(141, 197, 145, 201, 142, 198, 146, 202)(143, 199, 147, 203, 144, 200, 148, 204)(149, 205, 153, 209, 150, 206, 154, 210)(151, 207, 155, 211, 152, 208, 156, 212)(157, 213, 161, 217, 158, 214, 162, 218)(159, 215, 163, 219, 160, 216, 164, 220)(165, 221, 168, 224, 166, 222, 167, 223) L = (1, 116)(2, 118)(3, 119)(4, 113)(5, 122)(6, 114)(7, 115)(8, 125)(9, 126)(10, 117)(11, 127)(12, 128)(13, 120)(14, 121)(15, 123)(16, 124)(17, 133)(18, 134)(19, 135)(20, 136)(21, 129)(22, 130)(23, 131)(24, 132)(25, 141)(26, 142)(27, 143)(28, 144)(29, 137)(30, 138)(31, 139)(32, 140)(33, 149)(34, 150)(35, 151)(36, 152)(37, 145)(38, 146)(39, 147)(40, 148)(41, 157)(42, 158)(43, 159)(44, 160)(45, 153)(46, 154)(47, 155)(48, 156)(49, 165)(50, 166)(51, 167)(52, 168)(53, 161)(54, 162)(55, 163)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.825 Graph:: bipartite v = 42 e = 112 f = 32 degree seq :: [ 4^28, 8^14 ] E20.821 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^-2 * Y3 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y2^-1 * 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 ] 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, 119, 175, 117, 173)(114, 170, 118, 174, 116, 172, 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, 122)(4, 113)(5, 121)(6, 124)(7, 114)(8, 123)(9, 117)(10, 115)(11, 120)(12, 118)(13, 130)(14, 129)(15, 132)(16, 131)(17, 126)(18, 125)(19, 128)(20, 127)(21, 138)(22, 137)(23, 140)(24, 139)(25, 134)(26, 133)(27, 136)(28, 135)(29, 146)(30, 145)(31, 148)(32, 147)(33, 142)(34, 141)(35, 144)(36, 143)(37, 154)(38, 153)(39, 156)(40, 155)(41, 150)(42, 149)(43, 152)(44, 151)(45, 162)(46, 161)(47, 164)(48, 163)(49, 158)(50, 157)(51, 160)(52, 159)(53, 167)(54, 168)(55, 165)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.824 Graph:: bipartite v = 42 e = 112 f = 32 degree seq :: [ 4^28, 8^14 ] E20.822 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^-2, (R * Y3)^2, Y3^-1 * Y2^2 * Y3^-1, (R * Y1)^2, Y3^4, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, R * Y2 * Y3 * R * Y2^-1 * Y3^-1, Y2^-1 * R * Y3^2 * R * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 16, 72)(12, 68, 17, 73)(13, 69, 18, 74)(14, 70, 19, 75)(15, 71, 20, 76)(21, 77, 26, 82)(22, 78, 25, 81)(23, 79, 28, 84)(24, 80, 27, 83)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 42, 98)(38, 94, 41, 97)(39, 95, 44, 100)(40, 96, 43, 99)(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, 123, 179, 117, 173)(114, 170, 119, 175, 128, 184, 121, 177)(116, 172, 126, 182, 118, 174, 127, 183)(120, 176, 131, 187, 122, 178, 132, 188)(124, 180, 133, 189, 125, 181, 134, 190)(129, 185, 137, 193, 130, 186, 138, 194)(135, 191, 143, 199, 136, 192, 144, 200)(139, 195, 147, 203, 140, 196, 148, 204)(141, 197, 149, 205, 142, 198, 150, 206)(145, 201, 153, 209, 146, 202, 154, 210)(151, 207, 159, 215, 152, 208, 160, 216)(155, 211, 163, 219, 156, 212, 164, 220)(157, 213, 165, 221, 158, 214, 166, 222)(161, 217, 167, 223, 162, 218, 168, 224) L = (1, 116)(2, 120)(3, 124)(4, 123)(5, 125)(6, 113)(7, 129)(8, 128)(9, 130)(10, 114)(11, 118)(12, 117)(13, 115)(14, 135)(15, 136)(16, 122)(17, 121)(18, 119)(19, 139)(20, 140)(21, 141)(22, 142)(23, 127)(24, 126)(25, 145)(26, 146)(27, 132)(28, 131)(29, 134)(30, 133)(31, 151)(32, 152)(33, 138)(34, 137)(35, 155)(36, 156)(37, 157)(38, 158)(39, 144)(40, 143)(41, 161)(42, 162)(43, 148)(44, 147)(45, 150)(46, 149)(47, 166)(48, 165)(49, 154)(50, 153)(51, 168)(52, 167)(53, 159)(54, 160)(55, 163)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.826 Graph:: simple bipartite v = 42 e = 112 f = 32 degree seq :: [ 4^28, 8^14 ] E20.823 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = D56 (small group id <56, 5>) Aut = C2 x D56 (small group id <112, 29>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^5, Y1 * Y3^-6, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 57, 2, 58, 7, 63, 19, 75, 33, 89, 14, 70, 25, 81, 43, 99, 37, 93, 18, 74, 26, 82, 35, 91, 16, 72, 5, 61)(3, 59, 11, 67, 27, 83, 47, 103, 44, 100, 30, 86, 50, 106, 55, 111, 45, 101, 31, 87, 51, 107, 39, 95, 20, 76, 8, 64)(4, 60, 9, 65, 21, 77, 40, 96, 38, 94, 32, 88, 46, 102, 36, 92, 17, 73, 6, 62, 10, 66, 22, 78, 34, 90, 15, 71)(12, 68, 28, 84, 48, 104, 56, 112, 53, 109, 52, 108, 54, 110, 42, 98, 24, 80, 13, 69, 29, 85, 49, 105, 41, 97, 23, 79)(113, 169, 115, 171)(114, 170, 120, 176)(116, 172, 125, 181)(117, 173, 123, 179)(118, 174, 124, 180)(119, 175, 132, 188)(121, 177, 136, 192)(122, 178, 135, 191)(126, 182, 143, 199)(127, 183, 141, 197)(128, 184, 139, 195)(129, 185, 140, 196)(130, 186, 142, 198)(131, 187, 151, 207)(133, 189, 154, 210)(134, 190, 153, 209)(137, 193, 157, 213)(138, 194, 156, 212)(144, 200, 165, 221)(145, 201, 163, 219)(146, 202, 161, 217)(147, 203, 159, 215)(148, 204, 160, 216)(149, 205, 162, 218)(150, 206, 164, 220)(152, 208, 166, 222)(155, 211, 167, 223)(158, 214, 168, 224) L = (1, 116)(2, 121)(3, 124)(4, 126)(5, 127)(6, 113)(7, 133)(8, 135)(9, 137)(10, 114)(11, 140)(12, 142)(13, 115)(14, 144)(15, 145)(16, 146)(17, 117)(18, 118)(19, 152)(20, 153)(21, 155)(22, 119)(23, 156)(24, 120)(25, 158)(26, 122)(27, 160)(28, 162)(29, 123)(30, 164)(31, 125)(32, 138)(33, 150)(34, 131)(35, 134)(36, 128)(37, 129)(38, 130)(39, 161)(40, 149)(41, 159)(42, 132)(43, 148)(44, 165)(45, 136)(46, 147)(47, 168)(48, 167)(49, 139)(50, 166)(51, 141)(52, 163)(53, 143)(54, 151)(55, 154)(56, 157)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.819 Graph:: simple bipartite v = 32 e = 112 f = 42 degree seq :: [ 4^28, 28^4 ] E20.824 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y1 * Y3 * Y1, Y1^14 ] Map:: non-degenerate R = (1, 57, 2, 58, 6, 62, 15, 71, 23, 79, 31, 87, 39, 95, 47, 103, 46, 102, 38, 94, 30, 86, 22, 78, 14, 70, 5, 61)(3, 59, 7, 63, 16, 72, 24, 80, 32, 88, 40, 96, 48, 104, 54, 110, 51, 107, 43, 99, 35, 91, 27, 83, 19, 75, 10, 66)(4, 60, 11, 67, 20, 76, 28, 84, 36, 92, 44, 100, 52, 108, 56, 112, 49, 105, 42, 98, 33, 89, 26, 82, 17, 73, 12, 68)(8, 64, 9, 65, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 53, 109, 55, 111, 50, 106, 41, 97, 34, 90, 25, 81, 18, 74)(113, 169, 115, 171)(114, 170, 119, 175)(116, 172, 121, 177)(117, 173, 122, 178)(118, 174, 128, 184)(120, 176, 124, 180)(123, 179, 125, 181)(126, 182, 131, 187)(127, 183, 136, 192)(129, 185, 130, 186)(132, 188, 133, 189)(134, 190, 139, 195)(135, 191, 144, 200)(137, 193, 138, 194)(140, 196, 141, 197)(142, 198, 147, 203)(143, 199, 152, 208)(145, 201, 146, 202)(148, 204, 149, 205)(150, 206, 155, 211)(151, 207, 160, 216)(153, 209, 154, 210)(156, 212, 157, 213)(158, 214, 163, 219)(159, 215, 166, 222)(161, 217, 162, 218)(164, 220, 165, 221)(167, 223, 168, 224) L = (1, 116)(2, 120)(3, 121)(4, 113)(5, 125)(6, 129)(7, 124)(8, 114)(9, 115)(10, 123)(11, 122)(12, 119)(13, 117)(14, 132)(15, 137)(16, 130)(17, 118)(18, 128)(19, 133)(20, 126)(21, 131)(22, 141)(23, 145)(24, 138)(25, 127)(26, 136)(27, 140)(28, 139)(29, 134)(30, 148)(31, 153)(32, 146)(33, 135)(34, 144)(35, 149)(36, 142)(37, 147)(38, 157)(39, 161)(40, 154)(41, 143)(42, 152)(43, 156)(44, 155)(45, 150)(46, 164)(47, 167)(48, 162)(49, 151)(50, 160)(51, 165)(52, 158)(53, 163)(54, 168)(55, 159)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 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 E20.821 Graph:: simple bipartite v = 32 e = 112 f = 42 degree seq :: [ 4^28, 28^4 ] E20.825 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y3, (R * Y1)^2, Y1^14 ] Map:: polytopal non-degenerate R = (1, 57, 2, 58, 6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 44, 100, 36, 92, 28, 84, 20, 76, 12, 68, 5, 61)(3, 59, 9, 65, 17, 73, 25, 81, 33, 89, 41, 97, 49, 105, 53, 109, 46, 102, 39, 95, 30, 86, 23, 79, 14, 70, 8, 64)(4, 60, 11, 67, 19, 75, 27, 83, 35, 91, 43, 99, 51, 107, 52, 108, 47, 103, 38, 94, 31, 87, 22, 78, 15, 71, 7, 63)(10, 66, 16, 72, 24, 80, 32, 88, 40, 96, 48, 104, 54, 110, 56, 112, 55, 111, 50, 106, 42, 98, 34, 90, 26, 82, 18, 74)(113, 169, 115, 171)(114, 170, 119, 175)(116, 172, 122, 178)(117, 173, 123, 179)(118, 174, 126, 182)(120, 176, 128, 184)(121, 177, 130, 186)(124, 180, 129, 185)(125, 181, 134, 190)(127, 183, 136, 192)(131, 187, 138, 194)(132, 188, 139, 195)(133, 189, 142, 198)(135, 191, 144, 200)(137, 193, 146, 202)(140, 196, 145, 201)(141, 197, 150, 206)(143, 199, 152, 208)(147, 203, 154, 210)(148, 204, 155, 211)(149, 205, 158, 214)(151, 207, 160, 216)(153, 209, 162, 218)(156, 212, 161, 217)(157, 213, 164, 220)(159, 215, 166, 222)(163, 219, 167, 223)(165, 221, 168, 224) L = (1, 116)(2, 120)(3, 122)(4, 113)(5, 121)(6, 127)(7, 128)(8, 114)(9, 117)(10, 115)(11, 130)(12, 131)(13, 135)(14, 136)(15, 118)(16, 119)(17, 138)(18, 123)(19, 124)(20, 137)(21, 143)(22, 144)(23, 125)(24, 126)(25, 132)(26, 129)(27, 146)(28, 147)(29, 151)(30, 152)(31, 133)(32, 134)(33, 154)(34, 139)(35, 140)(36, 153)(37, 159)(38, 160)(39, 141)(40, 142)(41, 148)(42, 145)(43, 162)(44, 163)(45, 165)(46, 166)(47, 149)(48, 150)(49, 167)(50, 155)(51, 156)(52, 168)(53, 157)(54, 158)(55, 161)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 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 E20.820 Graph:: simple bipartite v = 32 e = 112 f = 42 degree seq :: [ 4^28, 28^4 ] E20.826 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y1)^2, (Y1^-1 * Y2)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y1^4 * Y3^-1 * Y1^-3 * Y3^-1 ] Map:: non-degenerate R = (1, 57, 2, 58, 7, 63, 18, 74, 33, 89, 46, 102, 30, 86, 15, 71, 24, 80, 39, 95, 47, 103, 31, 87, 16, 72, 5, 61)(3, 59, 11, 67, 25, 81, 41, 97, 53, 109, 52, 108, 40, 96, 28, 84, 44, 100, 56, 112, 49, 105, 34, 90, 19, 75, 8, 64)(4, 60, 14, 70, 29, 85, 45, 101, 36, 92, 21, 77, 10, 66, 6, 62, 17, 73, 32, 88, 48, 104, 35, 91, 20, 76, 9, 65)(12, 68, 22, 78, 37, 93, 50, 106, 55, 111, 43, 99, 27, 83, 13, 69, 23, 79, 38, 94, 51, 107, 54, 110, 42, 98, 26, 82)(113, 169, 115, 171)(114, 170, 120, 176)(116, 172, 125, 181)(117, 173, 123, 179)(118, 174, 124, 180)(119, 175, 131, 187)(121, 177, 135, 191)(122, 178, 134, 190)(126, 182, 139, 195)(127, 183, 140, 196)(128, 184, 137, 193)(129, 185, 138, 194)(130, 186, 146, 202)(132, 188, 150, 206)(133, 189, 149, 205)(136, 192, 152, 208)(141, 197, 155, 211)(142, 198, 156, 212)(143, 199, 153, 209)(144, 200, 154, 210)(145, 201, 161, 217)(147, 203, 163, 219)(148, 204, 162, 218)(151, 207, 164, 220)(157, 213, 167, 223)(158, 214, 168, 224)(159, 215, 165, 221)(160, 216, 166, 222) L = (1, 116)(2, 121)(3, 124)(4, 127)(5, 126)(6, 113)(7, 132)(8, 134)(9, 136)(10, 114)(11, 138)(12, 140)(13, 115)(14, 142)(15, 118)(16, 141)(17, 117)(18, 147)(19, 149)(20, 151)(21, 119)(22, 152)(23, 120)(24, 122)(25, 154)(26, 156)(27, 123)(28, 125)(29, 158)(30, 129)(31, 157)(32, 128)(33, 160)(34, 162)(35, 159)(36, 130)(37, 164)(38, 131)(39, 133)(40, 135)(41, 166)(42, 168)(43, 137)(44, 139)(45, 145)(46, 144)(47, 148)(48, 143)(49, 167)(50, 165)(51, 146)(52, 150)(53, 163)(54, 161)(55, 153)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 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 E20.822 Graph:: simple bipartite v = 32 e = 112 f = 42 degree seq :: [ 4^28, 28^4 ] E20.827 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^4, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, (R * Y3)^2, Y1^-1 * Y2^2 * Y1 * Y2^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-4 ] Map:: polytopal non-degenerate R = (1, 57, 2, 58, 7, 63, 5, 61)(3, 59, 10, 66, 18, 74, 13, 69)(4, 60, 14, 70, 19, 75, 9, 65)(6, 62, 8, 64, 20, 76, 16, 72)(11, 67, 24, 80, 33, 89, 27, 83)(12, 68, 28, 84, 34, 90, 23, 79)(15, 71, 29, 85, 35, 91, 22, 78)(17, 73, 21, 77, 36, 92, 31, 87)(25, 81, 40, 96, 48, 104, 43, 99)(26, 82, 44, 100, 49, 105, 39, 95)(30, 86, 45, 101, 50, 106, 38, 94)(32, 88, 37, 93, 41, 97, 47, 103)(42, 98, 54, 110, 56, 112, 52, 108)(46, 102, 55, 111, 53, 109, 51, 107)(113, 169, 115, 171, 123, 179, 137, 193, 153, 209, 148, 204, 132, 188, 119, 175, 130, 186, 145, 201, 160, 216, 144, 200, 129, 185, 118, 174)(114, 170, 120, 176, 133, 189, 149, 205, 155, 211, 139, 195, 125, 181, 117, 173, 128, 184, 143, 199, 159, 215, 152, 208, 136, 192, 122, 178)(116, 172, 127, 183, 142, 198, 158, 214, 168, 224, 161, 217, 146, 202, 131, 187, 147, 203, 162, 218, 165, 221, 154, 210, 138, 194, 124, 180)(121, 177, 135, 191, 151, 207, 164, 220, 167, 223, 157, 213, 141, 197, 126, 182, 140, 196, 156, 212, 166, 222, 163, 219, 150, 206, 134, 190) L = (1, 116)(2, 121)(3, 124)(4, 113)(5, 126)(6, 127)(7, 131)(8, 134)(9, 114)(10, 135)(11, 138)(12, 115)(13, 140)(14, 117)(15, 118)(16, 141)(17, 142)(18, 146)(19, 119)(20, 147)(21, 150)(22, 120)(23, 122)(24, 151)(25, 154)(26, 123)(27, 156)(28, 125)(29, 128)(30, 129)(31, 157)(32, 158)(33, 161)(34, 130)(35, 132)(36, 162)(37, 163)(38, 133)(39, 136)(40, 164)(41, 165)(42, 137)(43, 166)(44, 139)(45, 143)(46, 144)(47, 167)(48, 168)(49, 145)(50, 148)(51, 149)(52, 152)(53, 153)(54, 155)(55, 159)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4^8 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E20.818 Graph:: bipartite v = 18 e = 112 f = 56 degree seq :: [ 8^14, 28^4 ] E20.828 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) Quotient :: dipole Aut^+ = (C14 x C2) : C2 (small group id <56, 7>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^4, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^14 ] Map:: non-degenerate R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 9, 65, 13, 69, 8, 64)(5, 61, 11, 67, 14, 70, 7, 63)(10, 66, 16, 72, 21, 77, 17, 73)(12, 68, 15, 71, 22, 78, 19, 75)(18, 74, 25, 81, 29, 85, 24, 80)(20, 76, 27, 83, 30, 86, 23, 79)(26, 82, 32, 88, 37, 93, 33, 89)(28, 84, 31, 87, 38, 94, 35, 91)(34, 90, 41, 97, 45, 101, 40, 96)(36, 92, 43, 99, 46, 102, 39, 95)(42, 98, 48, 104, 52, 108, 49, 105)(44, 100, 47, 103, 53, 109, 51, 107)(50, 106, 55, 111, 56, 112, 54, 110)(113, 169, 115, 171, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 119, 175, 127, 183, 135, 191, 143, 199, 151, 207, 159, 215, 166, 222, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)(116, 172, 123, 179, 131, 187, 139, 195, 147, 203, 155, 211, 163, 219, 167, 223, 161, 217, 153, 209, 145, 201, 137, 193, 129, 185, 121, 177)(118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 164, 220, 168, 224, 165, 221, 158, 214, 150, 206, 142, 198, 134, 190, 126, 182) L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 123)(6, 116)(7, 117)(8, 115)(9, 125)(10, 128)(11, 126)(12, 127)(13, 120)(14, 119)(15, 134)(16, 133)(17, 122)(18, 137)(19, 124)(20, 139)(21, 129)(22, 131)(23, 132)(24, 130)(25, 141)(26, 144)(27, 142)(28, 143)(29, 136)(30, 135)(31, 150)(32, 149)(33, 138)(34, 153)(35, 140)(36, 155)(37, 145)(38, 147)(39, 148)(40, 146)(41, 157)(42, 160)(43, 158)(44, 159)(45, 152)(46, 151)(47, 165)(48, 164)(49, 154)(50, 167)(51, 156)(52, 161)(53, 163)(54, 162)(55, 168)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4^8 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E20.817 Graph:: bipartite v = 18 e = 112 f = 56 degree seq :: [ 8^14, 28^4 ] E20.829 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) 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, Y3^4, Y3^-2 * Y2^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (Y1 * Y3)^2, (R * Y3)^2, Y2^-1 * Y1 * Y3^-2 * Y1 * Y2^-1, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] 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, 18, 74)(9, 65, 24, 80)(12, 68, 19, 75)(13, 69, 22, 78)(14, 70, 23, 79)(15, 71, 20, 76)(16, 72, 21, 77)(25, 81, 33, 89)(26, 82, 36, 92)(27, 83, 34, 90)(28, 84, 35, 91)(29, 85, 37, 93)(30, 86, 40, 96)(31, 87, 38, 94)(32, 88, 39, 95)(41, 97, 49, 105)(42, 98, 52, 108)(43, 99, 50, 106)(44, 100, 51, 107)(45, 101, 53, 109)(46, 102, 56, 112)(47, 103, 54, 110)(48, 104, 55, 111)(113, 169, 115, 171, 124, 180, 117, 173)(114, 170, 119, 175, 131, 187, 121, 177)(116, 172, 127, 183, 118, 174, 128, 184)(120, 176, 134, 190, 122, 178, 135, 191)(123, 179, 137, 193, 129, 185, 138, 194)(125, 181, 139, 195, 126, 182, 140, 196)(130, 186, 141, 197, 136, 192, 142, 198)(132, 188, 143, 199, 133, 189, 144, 200)(145, 201, 153, 209, 148, 204, 154, 210)(146, 202, 155, 211, 147, 203, 156, 212)(149, 205, 157, 213, 152, 208, 158, 214)(150, 206, 159, 215, 151, 207, 160, 216)(161, 217, 166, 222, 164, 220, 167, 223)(162, 218, 168, 224, 163, 219, 165, 221) L = (1, 116)(2, 120)(3, 125)(4, 124)(5, 126)(6, 113)(7, 132)(8, 131)(9, 133)(10, 114)(11, 135)(12, 118)(13, 117)(14, 115)(15, 130)(16, 136)(17, 134)(18, 128)(19, 122)(20, 121)(21, 119)(22, 123)(23, 129)(24, 127)(25, 146)(26, 147)(27, 145)(28, 148)(29, 150)(30, 151)(31, 149)(32, 152)(33, 140)(34, 138)(35, 137)(36, 139)(37, 144)(38, 142)(39, 141)(40, 143)(41, 162)(42, 163)(43, 161)(44, 164)(45, 166)(46, 167)(47, 165)(48, 168)(49, 156)(50, 154)(51, 153)(52, 155)(53, 160)(54, 158)(55, 157)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.830 Graph:: simple bipartite v = 42 e = 112 f = 32 degree seq :: [ 4^28, 8^14 ] E20.830 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 14}) 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 :: [ R^2, Y2^2, (Y3 * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^4, (R * Y2 * Y3^-1)^2, Y1^3 * Y3^-1 * Y1^-4 * Y3^-1, Y1 * Y2 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2 * Y2 * Y1 ] Map:: non-degenerate R = (1, 57, 2, 58, 7, 63, 18, 74, 33, 89, 46, 102, 30, 86, 15, 71, 24, 80, 39, 95, 47, 103, 31, 87, 16, 72, 5, 61)(3, 59, 8, 64, 19, 75, 34, 90, 49, 105, 54, 110, 42, 98, 26, 82, 40, 96, 52, 108, 55, 111, 43, 99, 27, 83, 12, 68)(4, 60, 14, 70, 29, 85, 45, 101, 36, 92, 21, 77, 10, 66, 6, 62, 17, 73, 32, 88, 48, 104, 35, 91, 20, 76, 9, 65)(11, 67, 25, 81, 41, 97, 53, 109, 51, 107, 38, 94, 23, 79, 13, 69, 28, 84, 44, 100, 56, 112, 50, 106, 37, 93, 22, 78)(113, 169, 115, 171)(114, 170, 120, 176)(116, 172, 125, 181)(117, 173, 124, 180)(118, 174, 123, 179)(119, 175, 131, 187)(121, 177, 135, 191)(122, 178, 134, 190)(126, 182, 140, 196)(127, 183, 138, 194)(128, 184, 139, 195)(129, 185, 137, 193)(130, 186, 146, 202)(132, 188, 150, 206)(133, 189, 149, 205)(136, 192, 152, 208)(141, 197, 156, 212)(142, 198, 154, 210)(143, 199, 155, 211)(144, 200, 153, 209)(145, 201, 161, 217)(147, 203, 163, 219)(148, 204, 162, 218)(151, 207, 164, 220)(157, 213, 168, 224)(158, 214, 166, 222)(159, 215, 167, 223)(160, 216, 165, 221) L = (1, 116)(2, 121)(3, 123)(4, 127)(5, 126)(6, 113)(7, 132)(8, 134)(9, 136)(10, 114)(11, 138)(12, 137)(13, 115)(14, 142)(15, 118)(16, 141)(17, 117)(18, 147)(19, 149)(20, 151)(21, 119)(22, 152)(23, 120)(24, 122)(25, 154)(26, 125)(27, 153)(28, 124)(29, 158)(30, 129)(31, 157)(32, 128)(33, 160)(34, 162)(35, 159)(36, 130)(37, 164)(38, 131)(39, 133)(40, 135)(41, 166)(42, 140)(43, 165)(44, 139)(45, 145)(46, 144)(47, 148)(48, 143)(49, 168)(50, 167)(51, 146)(52, 150)(53, 161)(54, 156)(55, 163)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E20.829 Graph:: simple bipartite v = 32 e = 112 f = 42 degree seq :: [ 4^28, 28^4 ] E20.831 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 8, 14}) Quotient :: edge Aut^+ = C7 : C8 (small group id <56, 1>) Aut = (C7 x D8) : C2 (small group id <112, 14>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^8, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-4 * T1, T2^14 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 49, 42, 26, 41, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 52, 36, 24, 39, 55, 48, 32, 18, 8)(4, 11, 22, 37, 53, 44, 28, 14, 27, 43, 50, 34, 20, 10)(6, 15, 29, 45, 54, 38, 23, 12, 21, 35, 51, 46, 30, 16)(57, 58, 62, 70, 82, 80, 68, 60)(59, 64, 71, 84, 97, 92, 77, 66)(61, 63, 72, 83, 98, 95, 79, 67)(65, 74, 85, 100, 112, 108, 91, 76)(69, 73, 86, 99, 105, 111, 94, 78)(75, 88, 101, 109, 96, 103, 107, 90)(81, 87, 102, 106, 89, 104, 110, 93) 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) :: { ( 16^8 ), ( 16^14 ) } Outer automorphisms :: reflexible Dual of E20.832 Transitivity :: ET+ Graph:: bipartite v = 11 e = 56 f = 7 degree seq :: [ 8^7, 14^4 ] E20.832 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 8, 14}) Quotient :: loop Aut^+ = C7 : C8 (small group id <56, 1>) Aut = (C7 x D8) : C2 (small group id <112, 14>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1 * T2^2 * T1, (F * T1)^2, T2^-1 * T1 * T2^-4 * T1 * T2^-1, T1^8, (T1^-1 * T2^2 * T1^-1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 57, 3, 59, 10, 66, 21, 77, 26, 82, 15, 71, 6, 62, 5, 61)(2, 58, 7, 63, 4, 60, 12, 68, 22, 78, 27, 83, 14, 70, 8, 64)(9, 65, 19, 75, 11, 67, 23, 79, 28, 84, 25, 81, 13, 69, 20, 76)(16, 72, 29, 85, 17, 73, 31, 87, 24, 80, 32, 88, 18, 74, 30, 86)(33, 89, 41, 97, 34, 90, 43, 99, 36, 92, 44, 100, 35, 91, 42, 98)(37, 93, 45, 101, 38, 94, 47, 103, 40, 96, 48, 104, 39, 95, 46, 102)(49, 105, 55, 111, 50, 106, 53, 109, 52, 108, 54, 110, 51, 107, 56, 112) L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 69)(6, 70)(7, 72)(8, 74)(9, 61)(10, 60)(11, 59)(12, 73)(13, 71)(14, 82)(15, 84)(16, 64)(17, 63)(18, 83)(19, 89)(20, 91)(21, 67)(22, 66)(23, 90)(24, 68)(25, 92)(26, 78)(27, 80)(28, 77)(29, 93)(30, 95)(31, 94)(32, 96)(33, 76)(34, 75)(35, 81)(36, 79)(37, 86)(38, 85)(39, 88)(40, 87)(41, 105)(42, 107)(43, 106)(44, 108)(45, 109)(46, 111)(47, 110)(48, 112)(49, 98)(50, 97)(51, 100)(52, 99)(53, 102)(54, 101)(55, 104)(56, 103) local type(s) :: { ( 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14 ) } Outer automorphisms :: reflexible Dual of E20.831 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 56 f = 11 degree seq :: [ 16^7 ] E20.833 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 14}) Quotient :: dipole Aut^+ = C7 : C8 (small group id <56, 1>) Aut = (C7 x D8) : C2 (small group id <112, 14>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^8, Y1^3 * Y2^-1 * Y1 * Y2^6, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 24, 80, 12, 68, 4, 60)(3, 59, 8, 64, 15, 71, 28, 84, 41, 97, 36, 92, 21, 77, 10, 66)(5, 61, 7, 63, 16, 72, 27, 83, 42, 98, 39, 95, 23, 79, 11, 67)(9, 65, 18, 74, 29, 85, 44, 100, 56, 112, 52, 108, 35, 91, 20, 76)(13, 69, 17, 73, 30, 86, 43, 99, 49, 105, 55, 111, 38, 94, 22, 78)(19, 75, 32, 88, 45, 101, 53, 109, 40, 96, 47, 103, 51, 107, 34, 90)(25, 81, 31, 87, 46, 102, 50, 106, 33, 89, 48, 104, 54, 110, 37, 93)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 161, 217, 154, 210, 138, 194, 153, 209, 168, 224, 152, 208, 137, 193, 125, 181, 117, 173)(114, 170, 119, 175, 129, 185, 143, 199, 159, 215, 164, 220, 148, 204, 136, 192, 151, 207, 167, 223, 160, 216, 144, 200, 130, 186, 120, 176)(116, 172, 123, 179, 134, 190, 149, 205, 165, 221, 156, 212, 140, 196, 126, 182, 139, 195, 155, 211, 162, 218, 146, 202, 132, 188, 122, 178)(118, 174, 127, 183, 141, 197, 157, 213, 166, 222, 150, 206, 135, 191, 124, 180, 133, 189, 147, 203, 163, 219, 158, 214, 142, 198, 128, 184) L = (1, 115)(2, 119)(3, 121)(4, 123)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 116)(11, 134)(12, 133)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 122)(21, 147)(22, 149)(23, 124)(24, 151)(25, 125)(26, 153)(27, 155)(28, 126)(29, 157)(30, 128)(31, 159)(32, 130)(33, 161)(34, 132)(35, 163)(36, 136)(37, 165)(38, 135)(39, 167)(40, 137)(41, 168)(42, 138)(43, 162)(44, 140)(45, 166)(46, 142)(47, 164)(48, 144)(49, 154)(50, 146)(51, 158)(52, 148)(53, 156)(54, 150)(55, 160)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 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 E20.834 Graph:: bipartite v = 11 e = 112 f = 63 degree seq :: [ 16^7, 28^4 ] E20.834 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 14}) Quotient :: dipole Aut^+ = C7 : C8 (small group id <56, 1>) Aut = (C7 x D8) : C2 (small group id <112, 14>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^8, Y2^2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-4, (Y3^-1 * Y1^-1)^14 ] Map:: R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170, 118, 174, 126, 182, 138, 194, 136, 192, 124, 180, 116, 172)(115, 171, 120, 176, 127, 183, 140, 196, 153, 209, 148, 204, 133, 189, 122, 178)(117, 173, 119, 175, 128, 184, 139, 195, 154, 210, 151, 207, 135, 191, 123, 179)(121, 177, 130, 186, 141, 197, 156, 212, 168, 224, 164, 220, 147, 203, 132, 188)(125, 181, 129, 185, 142, 198, 155, 211, 161, 217, 167, 223, 150, 206, 134, 190)(131, 187, 144, 200, 157, 213, 165, 221, 152, 208, 159, 215, 163, 219, 146, 202)(137, 193, 143, 199, 158, 214, 162, 218, 145, 201, 160, 216, 166, 222, 149, 205) L = (1, 115)(2, 119)(3, 121)(4, 123)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 116)(11, 134)(12, 133)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 122)(21, 147)(22, 149)(23, 124)(24, 151)(25, 125)(26, 153)(27, 155)(28, 126)(29, 157)(30, 128)(31, 159)(32, 130)(33, 161)(34, 132)(35, 163)(36, 136)(37, 165)(38, 135)(39, 167)(40, 137)(41, 168)(42, 138)(43, 162)(44, 140)(45, 166)(46, 142)(47, 164)(48, 144)(49, 154)(50, 146)(51, 158)(52, 148)(53, 156)(54, 150)(55, 160)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 16, 28 ), ( 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28 ) } Outer automorphisms :: reflexible Dual of E20.833 Graph:: simple bipartite v = 63 e = 112 f = 11 degree seq :: [ 2^56, 16^7 ] E20.835 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 28, 28}) Quotient :: edge Aut^+ = C7 x Q8 (small group id <56, 10>) Aut = (C4 x D14) : C2 (small group id <112, 34>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^13 * T1^2 * T2 ] Map:: non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 51, 43, 35, 27, 19, 11, 4, 9, 17, 25, 33, 41, 49, 56, 48, 40, 32, 24, 16, 8)(57, 58, 62, 60)(59, 65, 69, 63)(61, 67, 70, 64)(66, 71, 77, 73)(68, 72, 78, 75)(74, 81, 85, 79)(76, 83, 86, 80)(82, 87, 93, 89)(84, 88, 94, 91)(90, 97, 101, 95)(92, 99, 102, 96)(98, 103, 109, 105)(100, 104, 110, 107)(106, 112, 108, 111) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 56^4 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E20.836 Transitivity :: ET+ Graph:: bipartite v = 16 e = 56 f = 2 degree seq :: [ 4^14, 28^2 ] E20.836 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 28, 28}) Quotient :: loop Aut^+ = C7 x Q8 (small group id <56, 10>) Aut = (C4 x D14) : C2 (small group id <112, 34>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^13 * T1^2 * T2 ] Map:: non-degenerate R = (1, 57, 3, 59, 10, 66, 18, 74, 26, 82, 34, 90, 42, 98, 50, 106, 54, 110, 46, 102, 38, 94, 30, 86, 22, 78, 14, 70, 6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 53, 109, 52, 108, 44, 100, 36, 92, 28, 84, 20, 76, 12, 68, 5, 61)(2, 58, 7, 63, 15, 71, 23, 79, 31, 87, 39, 95, 47, 103, 55, 111, 51, 107, 43, 99, 35, 91, 27, 83, 19, 75, 11, 67, 4, 60, 9, 65, 17, 73, 25, 81, 33, 89, 41, 97, 49, 105, 56, 112, 48, 104, 40, 96, 32, 88, 24, 80, 16, 72, 8, 64) L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 67)(6, 60)(7, 59)(8, 61)(9, 69)(10, 71)(11, 70)(12, 72)(13, 63)(14, 64)(15, 77)(16, 78)(17, 66)(18, 81)(19, 68)(20, 83)(21, 73)(22, 75)(23, 74)(24, 76)(25, 85)(26, 87)(27, 86)(28, 88)(29, 79)(30, 80)(31, 93)(32, 94)(33, 82)(34, 97)(35, 84)(36, 99)(37, 89)(38, 91)(39, 90)(40, 92)(41, 101)(42, 103)(43, 102)(44, 104)(45, 95)(46, 96)(47, 109)(48, 110)(49, 98)(50, 112)(51, 100)(52, 111)(53, 105)(54, 107)(55, 106)(56, 108) local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E20.835 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 56 f = 16 degree seq :: [ 56^2 ] E20.837 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 28, 28}) Quotient :: dipole Aut^+ = C7 x Q8 (small group id <56, 10>) Aut = (C4 x D14) : C2 (small group id <112, 34>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y1^4, Y3 * Y2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^14 * Y1^-1, (Y2^-1 * Y1)^28 ] Map:: R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 9, 65, 13, 69, 7, 63)(5, 61, 11, 67, 14, 70, 8, 64)(10, 66, 15, 71, 21, 77, 17, 73)(12, 68, 16, 72, 22, 78, 19, 75)(18, 74, 25, 81, 29, 85, 23, 79)(20, 76, 27, 83, 30, 86, 24, 80)(26, 82, 31, 87, 37, 93, 33, 89)(28, 84, 32, 88, 38, 94, 35, 91)(34, 90, 41, 97, 45, 101, 39, 95)(36, 92, 43, 99, 46, 102, 40, 96)(42, 98, 47, 103, 53, 109, 49, 105)(44, 100, 48, 104, 54, 110, 51, 107)(50, 106, 56, 112, 52, 108, 55, 111)(113, 169, 115, 171, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 166, 222, 158, 214, 150, 206, 142, 198, 134, 190, 126, 182, 118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 119, 175, 127, 183, 135, 191, 143, 199, 151, 207, 159, 215, 167, 223, 163, 219, 155, 211, 147, 203, 139, 195, 131, 187, 123, 179, 116, 172, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176) L = (1, 116)(2, 113)(3, 119)(4, 118)(5, 120)(6, 114)(7, 125)(8, 126)(9, 115)(10, 129)(11, 117)(12, 131)(13, 121)(14, 123)(15, 122)(16, 124)(17, 133)(18, 135)(19, 134)(20, 136)(21, 127)(22, 128)(23, 141)(24, 142)(25, 130)(26, 145)(27, 132)(28, 147)(29, 137)(30, 139)(31, 138)(32, 140)(33, 149)(34, 151)(35, 150)(36, 152)(37, 143)(38, 144)(39, 157)(40, 158)(41, 146)(42, 161)(43, 148)(44, 163)(45, 153)(46, 155)(47, 154)(48, 156)(49, 165)(50, 167)(51, 166)(52, 168)(53, 159)(54, 160)(55, 164)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) } Outer automorphisms :: reflexible Dual of E20.838 Graph:: bipartite v = 16 e = 112 f = 58 degree seq :: [ 8^14, 56^2 ] E20.838 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 28, 28}) Quotient :: dipole Aut^+ = C7 x Q8 (small group id <56, 10>) Aut = (C4 x D14) : C2 (small group id <112, 34>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3^-1 * Y1^-5 * Y3 * Y1^-8 ] Map:: R = (1, 57, 2, 58, 6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 53, 109, 49, 105, 41, 97, 33, 89, 25, 81, 17, 73, 9, 65, 16, 72, 24, 80, 32, 88, 40, 96, 48, 104, 56, 112, 52, 108, 44, 100, 36, 92, 28, 84, 20, 76, 12, 68, 4, 60)(3, 59, 8, 64, 14, 70, 23, 79, 30, 86, 39, 95, 46, 102, 55, 111, 51, 107, 43, 99, 35, 91, 27, 83, 19, 75, 11, 67, 5, 61, 7, 63, 15, 71, 22, 78, 31, 87, 38, 94, 47, 103, 54, 110, 50, 106, 42, 98, 34, 90, 26, 82, 18, 74, 10, 66)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224) L = (1, 115)(2, 119)(3, 121)(4, 123)(5, 113)(6, 126)(7, 128)(8, 114)(9, 117)(10, 116)(11, 129)(12, 130)(13, 134)(14, 136)(15, 118)(16, 120)(17, 122)(18, 137)(19, 124)(20, 139)(21, 142)(22, 144)(23, 125)(24, 127)(25, 131)(26, 132)(27, 145)(28, 146)(29, 150)(30, 152)(31, 133)(32, 135)(33, 138)(34, 153)(35, 140)(36, 155)(37, 158)(38, 160)(39, 141)(40, 143)(41, 147)(42, 148)(43, 161)(44, 162)(45, 166)(46, 168)(47, 149)(48, 151)(49, 154)(50, 165)(51, 156)(52, 167)(53, 163)(54, 164)(55, 157)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E20.837 Graph:: simple bipartite v = 58 e = 112 f = 16 degree seq :: [ 2^56, 56^2 ] E20.839 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {3, 3, 3, 3}) Quotient :: dipole Aut^+ = C19 : C3 (small group id <57, 1>) Aut = (C19 : C3) : C2 (small group id <114, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^3, R^2 * Y3^-1, Y2^3, Y2 * R^-1 * Y1 * R, (Y2 * Y1^-1)^3, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 58, 2, 59, 4, 61)(3, 60, 8, 65, 9, 66)(5, 62, 12, 69, 13, 70)(6, 63, 14, 71, 15, 72)(7, 64, 16, 73, 17, 74)(10, 67, 21, 78, 22, 79)(11, 68, 23, 80, 24, 81)(18, 75, 33, 90, 34, 91)(19, 76, 26, 83, 35, 92)(20, 77, 36, 93, 37, 94)(25, 82, 42, 99, 43, 100)(27, 84, 44, 101, 45, 102)(28, 85, 46, 103, 47, 104)(29, 86, 31, 88, 48, 105)(30, 87, 49, 106, 50, 107)(32, 89, 51, 108, 52, 109)(38, 95, 53, 110, 56, 113)(39, 96, 40, 97, 55, 112)(41, 98, 54, 111, 57, 114)(115, 172, 117, 174, 119, 176)(116, 173, 120, 177, 121, 178)(118, 175, 124, 181, 125, 182)(122, 179, 132, 189, 133, 190)(123, 180, 130, 187, 134, 191)(126, 183, 139, 196, 136, 193)(127, 184, 140, 197, 141, 198)(128, 185, 142, 199, 143, 200)(129, 186, 137, 194, 144, 201)(131, 188, 145, 202, 146, 203)(135, 192, 152, 209, 153, 210)(138, 195, 154, 211, 155, 212)(147, 204, 161, 218, 163, 220)(148, 205, 150, 207, 167, 224)(149, 206, 164, 221, 168, 225)(151, 208, 165, 222, 169, 226)(156, 213, 160, 217, 170, 227)(157, 214, 158, 215, 162, 219)(159, 216, 171, 228, 166, 223) L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228) local type(s) :: { ( 6^6 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT Graph:: bipartite v = 38 e = 114 f = 38 degree seq :: [ 6^38 ] E20.840 :: Family: { 5P } :: Oriented family(ies): { E5b } Signature :: (0; {3, 3, 3, 3}) Quotient :: dipole Aut^+ = C19 : C3 (small group id <57, 1>) Aut = C2 x (C19 : C3) (small group id <114, 2>) |r| :: 6 Presentation :: [ Y3^3, Y2^3, R^2 * Y3^-1, Y1^3, Y2 * R^-1 * Y1 * R, Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y3 * Y1 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1 * Y2^-1, R^-1 * Y2^-1 * R * Y1 * Y2^-1, Y1 * Y2 * Y3^-1 * Y2^-1 * Y1 * Y2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y2 * Y1^-1)^3, Y1 * Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y2^-1 ] Map:: polyhedral non-degenerate R = (1, 58, 2, 59, 5, 62)(3, 60, 12, 69, 14, 71)(4, 61, 16, 73, 13, 70)(6, 63, 23, 80, 24, 81)(7, 64, 26, 83, 27, 84)(8, 65, 28, 85, 30, 87)(9, 66, 17, 74, 29, 86)(10, 67, 34, 91, 35, 92)(11, 68, 36, 93, 37, 94)(15, 72, 44, 101, 45, 102)(18, 75, 47, 104, 48, 105)(19, 76, 49, 106, 50, 107)(20, 77, 32, 89, 38, 95)(21, 78, 52, 109, 41, 98)(22, 79, 53, 110, 25, 82)(31, 88, 56, 113, 40, 97)(33, 90, 55, 112, 43, 100)(39, 96, 42, 99, 51, 108)(46, 103, 57, 114, 54, 111)(115, 172, 117, 174, 120, 177)(116, 173, 122, 179, 124, 181)(118, 175, 131, 188, 132, 189)(119, 176, 133, 190, 135, 192)(121, 178, 136, 193, 125, 182)(123, 180, 146, 203, 147, 204)(126, 183, 152, 209, 154, 211)(127, 184, 156, 213, 142, 199)(128, 185, 148, 205, 157, 214)(129, 186, 140, 197, 155, 212)(130, 187, 160, 217, 134, 191)(137, 194, 162, 219, 164, 221)(138, 195, 145, 202, 150, 207)(139, 196, 158, 215, 169, 226)(141, 198, 170, 227, 171, 228)(143, 200, 159, 216, 163, 220)(144, 201, 166, 223, 168, 225)(149, 206, 165, 222, 167, 224)(151, 208, 153, 210, 161, 218) L = (1, 118)(2, 123)(3, 127)(4, 121)(5, 134)(6, 130)(7, 115)(8, 143)(9, 125)(10, 131)(11, 116)(12, 153)(13, 129)(14, 132)(15, 117)(16, 139)(17, 141)(18, 140)(19, 152)(20, 136)(21, 146)(22, 119)(23, 168)(24, 142)(25, 120)(26, 128)(27, 124)(28, 158)(29, 145)(30, 147)(31, 122)(32, 151)(33, 150)(34, 162)(35, 163)(36, 144)(37, 135)(38, 165)(39, 155)(40, 156)(41, 126)(42, 159)(43, 161)(44, 138)(45, 154)(46, 167)(47, 166)(48, 171)(49, 170)(50, 160)(51, 133)(52, 157)(53, 164)(54, 169)(55, 137)(56, 149)(57, 148)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228) local type(s) :: { ( 6^6 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT Graph:: simple bipartite v = 38 e = 114 f = 38 degree seq :: [ 6^38 ] E20.841 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 3, 3, 5}) Quotient :: edge^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^2 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2, R * Y1 * R * Y2, Y2 * Y1 * Y2 * Y1 * Y3, (Y1^-1 * Y3^-1 * Y2^-1)^2, (Y2 * Y1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 4, 64, 12, 72, 19, 79, 7, 67)(2, 62, 9, 69, 23, 83, 6, 66, 11, 71)(3, 63, 13, 73, 21, 81, 35, 95, 15, 75)(5, 65, 18, 78, 30, 90, 10, 70, 20, 80)(8, 68, 25, 85, 28, 88, 44, 104, 27, 87)(14, 74, 34, 94, 49, 109, 31, 91, 16, 76)(17, 77, 24, 84, 37, 97, 47, 107, 39, 99)(22, 82, 26, 86, 43, 103, 40, 100, 32, 92)(29, 89, 38, 98, 55, 115, 46, 106, 41, 101)(33, 93, 36, 96, 50, 110, 56, 116, 52, 112)(42, 102, 45, 105, 57, 117, 59, 119, 58, 118)(48, 108, 51, 111, 60, 120, 54, 114, 53, 113)(121, 122, 125)(123, 132, 134)(124, 133, 131)(126, 141, 142)(127, 138, 144)(128, 143, 146)(129, 145, 140)(130, 148, 149)(135, 154, 156)(136, 139, 157)(137, 150, 158)(147, 163, 165)(151, 167, 168)(152, 155, 170)(153, 169, 171)(159, 175, 173)(160, 176, 162)(161, 164, 177)(166, 179, 174)(172, 180, 178)(181, 183, 186)(182, 188, 190)(184, 196, 195)(185, 197, 199)(187, 191, 200)(189, 202, 207)(192, 204, 211)(193, 212, 203)(194, 213, 215)(198, 209, 219)(201, 216, 220)(205, 221, 210)(206, 222, 224)(208, 225, 226)(214, 228, 232)(217, 233, 229)(218, 234, 227)(223, 230, 238)(231, 239, 236)(235, 237, 240) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8^3 ), ( 8^10 ) } Outer automorphisms :: reflexible Dual of E20.844 Graph:: simple bipartite v = 52 e = 120 f = 30 degree seq :: [ 3^40, 10^12 ] E20.842 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 3, 3, 5}) Quotient :: edge^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, Y1^3, Y2^3, (R * Y3)^2, R * Y2 * R * Y1, (Y1^-1 * Y3)^5, (Y1^-1 * Y3 * Y2^-1)^5, (Y3 * Y1 * Y3 * Y1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 3, 63)(2, 62, 5, 65)(4, 64, 8, 68)(6, 66, 11, 71)(7, 67, 12, 72)(9, 69, 15, 75)(10, 70, 16, 76)(13, 73, 21, 81)(14, 74, 22, 82)(17, 77, 27, 87)(18, 78, 28, 88)(19, 79, 29, 89)(20, 80, 23, 83)(24, 84, 33, 93)(25, 85, 34, 94)(26, 86, 30, 90)(31, 91, 39, 99)(32, 92, 40, 100)(35, 95, 45, 105)(36, 96, 37, 97)(38, 98, 46, 106)(41, 101, 51, 111)(42, 102, 43, 103)(44, 104, 52, 112)(47, 107, 56, 116)(48, 108, 49, 109)(50, 110, 53, 113)(54, 114, 58, 118)(55, 115, 59, 119)(57, 117, 60, 120)(121, 122, 124)(123, 126, 127)(125, 129, 130)(128, 133, 134)(131, 137, 138)(132, 139, 140)(135, 143, 144)(136, 145, 146)(141, 150, 151)(142, 152, 147)(148, 155, 156)(149, 157, 158)(153, 161, 162)(154, 163, 164)(159, 167, 168)(160, 169, 170)(165, 173, 174)(166, 175, 171)(172, 177, 176)(178, 180, 179)(181, 182, 184)(183, 186, 187)(185, 189, 190)(188, 193, 194)(191, 197, 198)(192, 199, 200)(195, 203, 204)(196, 205, 206)(201, 210, 211)(202, 212, 207)(208, 215, 216)(209, 217, 218)(213, 221, 222)(214, 223, 224)(219, 227, 228)(220, 229, 230)(225, 233, 234)(226, 235, 231)(232, 237, 236)(238, 240, 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) :: { ( 20^3 ), ( 20^4 ) } Outer automorphisms :: reflexible Dual of E20.843 Graph:: simple bipartite v = 70 e = 120 f = 12 degree seq :: [ 3^40, 4^30 ] E20.843 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 3, 3, 5}) Quotient :: loop^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^2 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2, R * Y1 * R * Y2, Y2 * Y1 * Y2 * Y1 * Y3, (Y1^-1 * Y3^-1 * Y2^-1)^2, (Y2 * Y1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 19, 79, 139, 199, 7, 67, 127, 187)(2, 62, 122, 182, 9, 69, 129, 189, 23, 83, 143, 203, 6, 66, 126, 186, 11, 71, 131, 191)(3, 63, 123, 183, 13, 73, 133, 193, 21, 81, 141, 201, 35, 95, 155, 215, 15, 75, 135, 195)(5, 65, 125, 185, 18, 78, 138, 198, 30, 90, 150, 210, 10, 70, 130, 190, 20, 80, 140, 200)(8, 68, 128, 188, 25, 85, 145, 205, 28, 88, 148, 208, 44, 104, 164, 224, 27, 87, 147, 207)(14, 74, 134, 194, 34, 94, 154, 214, 49, 109, 169, 229, 31, 91, 151, 211, 16, 76, 136, 196)(17, 77, 137, 197, 24, 84, 144, 204, 37, 97, 157, 217, 47, 107, 167, 227, 39, 99, 159, 219)(22, 82, 142, 202, 26, 86, 146, 206, 43, 103, 163, 223, 40, 100, 160, 220, 32, 92, 152, 212)(29, 89, 149, 209, 38, 98, 158, 218, 55, 115, 175, 235, 46, 106, 166, 226, 41, 101, 161, 221)(33, 93, 153, 213, 36, 96, 156, 216, 50, 110, 170, 230, 56, 116, 176, 236, 52, 112, 172, 232)(42, 102, 162, 222, 45, 105, 165, 225, 57, 117, 177, 237, 59, 119, 179, 239, 58, 118, 178, 238)(48, 108, 168, 228, 51, 111, 171, 231, 60, 120, 180, 240, 54, 114, 174, 234, 53, 113, 173, 233) L = (1, 62)(2, 65)(3, 72)(4, 73)(5, 61)(6, 81)(7, 78)(8, 83)(9, 85)(10, 88)(11, 64)(12, 74)(13, 71)(14, 63)(15, 94)(16, 79)(17, 90)(18, 84)(19, 97)(20, 69)(21, 82)(22, 66)(23, 86)(24, 67)(25, 80)(26, 68)(27, 103)(28, 89)(29, 70)(30, 98)(31, 107)(32, 95)(33, 109)(34, 96)(35, 110)(36, 75)(37, 76)(38, 77)(39, 115)(40, 116)(41, 104)(42, 100)(43, 105)(44, 117)(45, 87)(46, 119)(47, 108)(48, 91)(49, 111)(50, 92)(51, 93)(52, 120)(53, 99)(54, 106)(55, 113)(56, 102)(57, 101)(58, 112)(59, 114)(60, 118)(121, 183)(122, 188)(123, 186)(124, 196)(125, 197)(126, 181)(127, 191)(128, 190)(129, 202)(130, 182)(131, 200)(132, 204)(133, 212)(134, 213)(135, 184)(136, 195)(137, 199)(138, 209)(139, 185)(140, 187)(141, 216)(142, 207)(143, 193)(144, 211)(145, 221)(146, 222)(147, 189)(148, 225)(149, 219)(150, 205)(151, 192)(152, 203)(153, 215)(154, 228)(155, 194)(156, 220)(157, 233)(158, 234)(159, 198)(160, 201)(161, 210)(162, 224)(163, 230)(164, 206)(165, 226)(166, 208)(167, 218)(168, 232)(169, 217)(170, 238)(171, 239)(172, 214)(173, 229)(174, 227)(175, 237)(176, 231)(177, 240)(178, 223)(179, 236)(180, 235) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E20.842 Transitivity :: VT+ Graph:: v = 12 e = 120 f = 70 degree seq :: [ 20^12 ] E20.844 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 3, 3, 5}) Quotient :: loop^2 Aut^+ = A5 (small group id <60, 5>) Aut = C2 x A5 (small group id <120, 35>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, Y1^3, Y2^3, (R * Y3)^2, R * Y2 * R * Y1, (Y1^-1 * Y3)^5, (Y1^-1 * Y3 * Y2^-1)^5, (Y3 * Y1 * Y3 * Y1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 121, 181, 3, 63, 123, 183)(2, 62, 122, 182, 5, 65, 125, 185)(4, 64, 124, 184, 8, 68, 128, 188)(6, 66, 126, 186, 11, 71, 131, 191)(7, 67, 127, 187, 12, 72, 132, 192)(9, 69, 129, 189, 15, 75, 135, 195)(10, 70, 130, 190, 16, 76, 136, 196)(13, 73, 133, 193, 21, 81, 141, 201)(14, 74, 134, 194, 22, 82, 142, 202)(17, 77, 137, 197, 27, 87, 147, 207)(18, 78, 138, 198, 28, 88, 148, 208)(19, 79, 139, 199, 29, 89, 149, 209)(20, 80, 140, 200, 23, 83, 143, 203)(24, 84, 144, 204, 33, 93, 153, 213)(25, 85, 145, 205, 34, 94, 154, 214)(26, 86, 146, 206, 30, 90, 150, 210)(31, 91, 151, 211, 39, 99, 159, 219)(32, 92, 152, 212, 40, 100, 160, 220)(35, 95, 155, 215, 45, 105, 165, 225)(36, 96, 156, 216, 37, 97, 157, 217)(38, 98, 158, 218, 46, 106, 166, 226)(41, 101, 161, 221, 51, 111, 171, 231)(42, 102, 162, 222, 43, 103, 163, 223)(44, 104, 164, 224, 52, 112, 172, 232)(47, 107, 167, 227, 56, 116, 176, 236)(48, 108, 168, 228, 49, 109, 169, 229)(50, 110, 170, 230, 53, 113, 173, 233)(54, 114, 174, 234, 58, 118, 178, 238)(55, 115, 175, 235, 59, 119, 179, 239)(57, 117, 177, 237, 60, 120, 180, 240) L = (1, 62)(2, 64)(3, 66)(4, 61)(5, 69)(6, 67)(7, 63)(8, 73)(9, 70)(10, 65)(11, 77)(12, 79)(13, 74)(14, 68)(15, 83)(16, 85)(17, 78)(18, 71)(19, 80)(20, 72)(21, 90)(22, 92)(23, 84)(24, 75)(25, 86)(26, 76)(27, 82)(28, 95)(29, 97)(30, 91)(31, 81)(32, 87)(33, 101)(34, 103)(35, 96)(36, 88)(37, 98)(38, 89)(39, 107)(40, 109)(41, 102)(42, 93)(43, 104)(44, 94)(45, 113)(46, 115)(47, 108)(48, 99)(49, 110)(50, 100)(51, 106)(52, 117)(53, 114)(54, 105)(55, 111)(56, 112)(57, 116)(58, 120)(59, 118)(60, 119)(121, 182)(122, 184)(123, 186)(124, 181)(125, 189)(126, 187)(127, 183)(128, 193)(129, 190)(130, 185)(131, 197)(132, 199)(133, 194)(134, 188)(135, 203)(136, 205)(137, 198)(138, 191)(139, 200)(140, 192)(141, 210)(142, 212)(143, 204)(144, 195)(145, 206)(146, 196)(147, 202)(148, 215)(149, 217)(150, 211)(151, 201)(152, 207)(153, 221)(154, 223)(155, 216)(156, 208)(157, 218)(158, 209)(159, 227)(160, 229)(161, 222)(162, 213)(163, 224)(164, 214)(165, 233)(166, 235)(167, 228)(168, 219)(169, 230)(170, 220)(171, 226)(172, 237)(173, 234)(174, 225)(175, 231)(176, 232)(177, 236)(178, 240)(179, 238)(180, 239) local type(s) :: { ( 3, 10, 3, 10, 3, 10, 3, 10 ) } Outer automorphisms :: reflexible Dual of E20.841 Transitivity :: VT+ Graph:: v = 30 e = 120 f = 52 degree seq :: [ 8^30 ] E20.845 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 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 * Y3, Y2^3, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^3, (Y3^-1 * Y1)^5, Y2 * Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 8, 68)(5, 65, 9, 69)(6, 66, 10, 70)(11, 71, 19, 79)(12, 72, 20, 80)(13, 73, 21, 81)(14, 74, 22, 82)(15, 75, 23, 83)(16, 76, 24, 84)(17, 77, 25, 85)(18, 78, 26, 86)(27, 87, 37, 97)(28, 88, 38, 98)(29, 89, 30, 90)(31, 91, 39, 99)(32, 92, 40, 100)(33, 93, 41, 101)(34, 94, 35, 95)(36, 96, 42, 102)(43, 103, 54, 114)(44, 104, 45, 105)(46, 106, 55, 115)(47, 107, 56, 116)(48, 108, 49, 109)(50, 110, 51, 111)(52, 112, 57, 117)(53, 113, 58, 118)(59, 119, 60, 120)(121, 181, 123, 183, 124, 184)(122, 182, 125, 185, 126, 186)(127, 187, 131, 191, 132, 192)(128, 188, 133, 193, 134, 194)(129, 189, 135, 195, 136, 196)(130, 190, 137, 197, 138, 198)(139, 199, 146, 206, 147, 207)(140, 200, 148, 208, 149, 209)(141, 201, 150, 210, 151, 211)(142, 202, 152, 212, 143, 203)(144, 204, 153, 213, 154, 214)(145, 205, 155, 215, 156, 216)(157, 217, 163, 223, 164, 224)(158, 218, 165, 225, 166, 226)(159, 219, 167, 227, 168, 228)(160, 220, 169, 229, 170, 230)(161, 221, 171, 231, 172, 232)(162, 222, 173, 233, 174, 234)(175, 235, 179, 239, 176, 236)(177, 237, 180, 240, 178, 238) L = (1, 124)(2, 126)(3, 121)(4, 123)(5, 122)(6, 125)(7, 132)(8, 134)(9, 136)(10, 138)(11, 127)(12, 131)(13, 128)(14, 133)(15, 129)(16, 135)(17, 130)(18, 137)(19, 147)(20, 149)(21, 151)(22, 143)(23, 152)(24, 154)(25, 156)(26, 139)(27, 146)(28, 140)(29, 148)(30, 141)(31, 150)(32, 142)(33, 144)(34, 153)(35, 145)(36, 155)(37, 164)(38, 166)(39, 168)(40, 170)(41, 172)(42, 174)(43, 157)(44, 163)(45, 158)(46, 165)(47, 159)(48, 167)(49, 160)(50, 169)(51, 161)(52, 171)(53, 162)(54, 173)(55, 176)(56, 179)(57, 178)(58, 180)(59, 175)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6, 10, 6, 10 ), ( 6, 10, 6, 10, 6, 10 ) } Outer automorphisms :: reflexible Dual of E20.849 Graph:: bipartite v = 50 e = 120 f = 32 degree seq :: [ 4^30, 6^20 ] E20.846 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 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, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^2 * Y2^-1 * Y3, Y3^5, Y1 * Y3 * Y2 * Y3^-1 * Y2, Y2 * Y3^-2 * Y1 * Y3^-1, R * Y2 * Y1 * R * Y2^-1, (Y2^-1 * Y3^-2)^2, Y2^-1 * Y3^2 * Y2 * Y1 * Y3^-1, (Y1 * Y2^-1)^3, Y1 * Y3 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y2^-1, (Y2 * Y3^-1 * Y2^-1 * Y1)^2 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 11, 71)(4, 64, 14, 74)(5, 65, 18, 78)(6, 66, 21, 81)(7, 67, 25, 85)(8, 68, 28, 88)(9, 69, 30, 90)(10, 70, 32, 92)(12, 72, 33, 93)(13, 73, 40, 100)(15, 75, 34, 94)(16, 76, 31, 91)(17, 77, 45, 105)(19, 79, 24, 84)(20, 80, 22, 82)(23, 83, 26, 86)(27, 87, 53, 113)(29, 89, 56, 116)(35, 95, 46, 106)(36, 96, 44, 104)(37, 97, 48, 108)(38, 98, 57, 117)(39, 99, 54, 114)(41, 101, 52, 112)(42, 102, 58, 118)(43, 103, 49, 109)(47, 107, 50, 110)(51, 111, 59, 119)(55, 115, 60, 120)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 135, 195, 137, 197)(126, 186, 142, 202, 143, 203)(128, 188, 139, 199, 149, 209)(130, 190, 136, 196, 153, 213)(131, 191, 150, 210, 155, 215)(132, 192, 157, 217, 159, 219)(133, 193, 141, 201, 161, 221)(134, 194, 162, 222, 163, 223)(138, 198, 166, 226, 145, 205)(140, 200, 160, 220, 167, 227)(144, 204, 156, 216, 158, 218)(146, 206, 170, 230, 172, 232)(147, 207, 152, 212, 174, 234)(148, 208, 175, 235, 164, 224)(151, 211, 173, 233, 168, 228)(154, 214, 169, 229, 171, 231)(165, 225, 179, 239, 178, 238)(176, 236, 177, 237, 180, 240) L = (1, 124)(2, 128)(3, 132)(4, 136)(5, 139)(6, 121)(7, 146)(8, 142)(9, 135)(10, 122)(11, 137)(12, 158)(13, 123)(14, 133)(15, 164)(16, 144)(17, 141)(18, 159)(19, 163)(20, 125)(21, 168)(22, 154)(23, 151)(24, 126)(25, 149)(26, 171)(27, 127)(28, 147)(29, 152)(30, 172)(31, 129)(32, 167)(33, 140)(34, 130)(35, 157)(36, 131)(37, 178)(38, 134)(39, 160)(40, 176)(41, 177)(42, 138)(43, 153)(44, 143)(45, 175)(46, 170)(47, 169)(48, 156)(49, 145)(50, 180)(51, 148)(52, 173)(53, 165)(54, 179)(55, 150)(56, 162)(57, 155)(58, 161)(59, 166)(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) :: { ( 6, 10, 6, 10 ), ( 6, 10, 6, 10, 6, 10 ) } Outer automorphisms :: reflexible Dual of E20.850 Graph:: simple bipartite v = 50 e = 120 f = 32 degree seq :: [ 4^30, 6^20 ] E20.847 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 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, Y2^3, Y1^3, (R * Y3)^2, (Y1 * R)^2, (Y3^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y2^-1)^2, Y2 * Y3^-2 * Y1 * Y3^-1, Y3^5, Y1^-1 * R * Y3^-1 * Y2^-1 * R * Y2^-1, Y3^-1 * R * Y2 * R * Y2^-1 * Y3^-1, (Y2 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2 * Y3^-1 * Y1^-1 * Y3 * Y1, Y1 * Y2^-1 * Y3^2 * Y1^-1 * Y2 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 5, 65)(3, 63, 12, 72, 14, 74)(4, 64, 16, 76, 19, 79)(6, 66, 23, 83, 8, 68)(7, 67, 25, 85, 9, 69)(10, 70, 33, 93, 21, 81)(11, 71, 35, 95, 22, 82)(13, 73, 39, 99, 41, 101)(15, 75, 43, 103, 37, 97)(17, 77, 46, 106, 47, 107)(18, 78, 40, 100, 48, 108)(20, 80, 50, 110, 31, 91)(24, 84, 29, 89, 27, 87)(26, 86, 32, 92, 54, 114)(28, 88, 52, 112, 55, 115)(30, 90, 53, 113, 57, 117)(34, 94, 51, 111, 36, 96)(38, 98, 59, 119, 42, 102)(44, 104, 60, 120, 56, 116)(45, 105, 58, 118, 49, 109)(121, 181, 123, 183, 126, 186)(122, 182, 128, 188, 130, 190)(124, 184, 137, 197, 140, 200)(125, 185, 141, 201, 132, 192)(127, 187, 146, 206, 133, 193)(129, 189, 150, 210, 152, 212)(131, 191, 138, 198, 148, 208)(134, 194, 153, 213, 143, 203)(135, 195, 164, 224, 144, 204)(136, 196, 151, 211, 165, 225)(139, 199, 169, 229, 166, 226)(142, 202, 158, 218, 160, 220)(145, 205, 161, 221, 173, 233)(147, 207, 156, 216, 163, 223)(149, 209, 176, 236, 154, 214)(155, 215, 175, 235, 179, 239)(157, 217, 171, 231, 180, 240)(159, 219, 174, 234, 177, 237)(162, 222, 172, 232, 168, 228)(167, 227, 178, 238, 170, 230) L = (1, 124)(2, 129)(3, 133)(4, 138)(5, 142)(6, 144)(7, 121)(8, 148)(9, 151)(10, 154)(11, 122)(12, 157)(13, 160)(14, 162)(15, 123)(16, 125)(17, 126)(18, 147)(19, 135)(20, 145)(21, 165)(22, 146)(23, 167)(24, 168)(25, 149)(26, 163)(27, 127)(28, 140)(29, 128)(30, 130)(31, 156)(32, 155)(33, 177)(34, 170)(35, 171)(36, 131)(37, 174)(38, 132)(39, 134)(40, 139)(41, 137)(42, 164)(43, 136)(44, 166)(45, 152)(46, 159)(47, 176)(48, 161)(49, 158)(50, 175)(51, 141)(52, 143)(53, 172)(54, 169)(55, 150)(56, 173)(57, 180)(58, 153)(59, 178)(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) :: { ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E20.848 Graph:: simple bipartite v = 40 e = 120 f = 42 degree seq :: [ 6^40 ] E20.848 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 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, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, R * Y2 * Y1^-1 * R * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y3, Y1^5, Y3^5, Y2 * Y3^-2 * Y1 * Y3^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1, (Y1^-1 * Y3^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 5, 65)(3, 63, 11, 71, 36, 96, 25, 85, 8, 68)(4, 64, 14, 74, 42, 102, 46, 106, 17, 77)(6, 66, 21, 81, 50, 110, 26, 86, 23, 83)(9, 69, 29, 89, 20, 80, 40, 100, 32, 92)(10, 70, 33, 93, 59, 119, 48, 108, 34, 94)(12, 72, 39, 99, 52, 112, 31, 91, 24, 84)(13, 73, 22, 82, 51, 111, 53, 113, 41, 101)(15, 75, 44, 104, 60, 120, 54, 114, 35, 95)(16, 76, 45, 105, 37, 97, 57, 117, 28, 88)(18, 78, 43, 103, 27, 87, 55, 115, 47, 107)(30, 90, 58, 118, 38, 98, 49, 109, 56, 116)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 135, 195)(125, 185, 131, 191)(126, 186, 142, 202)(127, 187, 145, 205)(129, 189, 150, 210)(130, 190, 136, 196)(132, 192, 138, 198)(133, 193, 141, 201)(134, 194, 155, 215)(137, 197, 164, 224)(139, 199, 156, 216)(140, 200, 169, 229)(143, 203, 171, 231)(144, 204, 163, 223)(146, 206, 173, 233)(147, 207, 151, 211)(148, 208, 153, 213)(149, 209, 176, 236)(152, 212, 178, 238)(154, 214, 165, 225)(157, 217, 168, 228)(158, 218, 160, 220)(159, 219, 167, 227)(161, 221, 170, 230)(162, 222, 174, 234)(166, 226, 180, 240)(172, 232, 175, 235)(177, 237, 179, 239) L = (1, 124)(2, 129)(3, 132)(4, 136)(5, 138)(6, 121)(7, 146)(8, 135)(9, 151)(10, 122)(11, 157)(12, 160)(13, 123)(14, 149)(15, 141)(16, 144)(17, 133)(18, 142)(19, 168)(20, 125)(21, 152)(22, 165)(23, 154)(24, 126)(25, 150)(26, 174)(27, 127)(28, 128)(29, 143)(30, 153)(31, 155)(32, 148)(33, 170)(34, 163)(35, 130)(36, 173)(37, 166)(38, 131)(39, 177)(40, 137)(41, 178)(42, 139)(43, 134)(44, 159)(45, 140)(46, 167)(47, 158)(48, 169)(49, 171)(50, 172)(51, 162)(52, 145)(53, 175)(54, 176)(55, 179)(56, 147)(57, 161)(58, 164)(59, 180)(60, 156)(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) :: { ( 6^4 ), ( 6^10 ) } Outer automorphisms :: reflexible Dual of E20.847 Graph:: simple bipartite v = 42 e = 120 f = 40 degree seq :: [ 4^30, 10^12 ] E20.849 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 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, Y3^-1 * Y1, Y1^3, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y2^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^2 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 61, 2, 62, 4, 64)(3, 63, 8, 68, 7, 67)(5, 65, 10, 70, 12, 72)(6, 66, 14, 74, 11, 71)(9, 69, 19, 79, 18, 78)(13, 73, 22, 82, 24, 84)(15, 75, 27, 87, 26, 86)(16, 76, 17, 77, 28, 88)(20, 80, 32, 92, 23, 83)(21, 81, 25, 85, 33, 93)(29, 89, 41, 101, 40, 100)(30, 90, 31, 91, 42, 102)(34, 94, 46, 106, 36, 96)(35, 95, 44, 104, 47, 107)(37, 97, 48, 108, 45, 105)(38, 98, 39, 99, 49, 109)(43, 103, 53, 113, 52, 112)(50, 110, 51, 111, 57, 117)(54, 114, 56, 116, 55, 115)(58, 118, 59, 119, 60, 120)(121, 181, 123, 183, 129, 189, 133, 193, 125, 185)(122, 182, 126, 186, 135, 195, 136, 196, 127, 187)(124, 184, 130, 190, 140, 200, 141, 201, 131, 191)(128, 188, 137, 197, 149, 209, 150, 210, 138, 198)(132, 192, 142, 202, 154, 214, 155, 215, 143, 203)(134, 194, 145, 205, 157, 217, 158, 218, 146, 206)(139, 199, 151, 211, 163, 223, 156, 216, 144, 204)(147, 207, 159, 219, 170, 230, 160, 220, 148, 208)(152, 212, 164, 224, 174, 234, 165, 225, 153, 213)(161, 221, 171, 231, 178, 238, 172, 232, 162, 222)(166, 226, 173, 233, 179, 239, 175, 235, 167, 227)(168, 228, 176, 236, 180, 240, 177, 237, 169, 229) L = (1, 122)(2, 124)(3, 128)(4, 121)(5, 130)(6, 134)(7, 123)(8, 127)(9, 139)(10, 132)(11, 126)(12, 125)(13, 142)(14, 131)(15, 147)(16, 137)(17, 148)(18, 129)(19, 138)(20, 152)(21, 145)(22, 144)(23, 140)(24, 133)(25, 153)(26, 135)(27, 146)(28, 136)(29, 161)(30, 151)(31, 162)(32, 143)(33, 141)(34, 166)(35, 164)(36, 154)(37, 168)(38, 159)(39, 169)(40, 149)(41, 160)(42, 150)(43, 173)(44, 167)(45, 157)(46, 156)(47, 155)(48, 165)(49, 158)(50, 171)(51, 177)(52, 163)(53, 172)(54, 176)(55, 174)(56, 175)(57, 170)(58, 179)(59, 180)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E20.845 Graph:: bipartite v = 32 e = 120 f = 50 degree seq :: [ 6^20, 10^12 ] E20.850 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 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, Y3^-1 * Y1 * Y2^-1, Y1^3, (R * Y1^-1)^2, (R * Y3)^2, (Y2 * Y3^-1)^2, Y3^5, Y2^5, (Y2^-1 * Y1^-1)^3, (Y3^-1 * Y1^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^2 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 5, 65)(3, 63, 11, 71, 7, 67)(4, 64, 15, 75, 17, 77)(6, 66, 20, 80, 22, 82)(8, 68, 26, 86, 10, 70)(9, 69, 30, 90, 32, 92)(12, 72, 35, 95, 14, 74)(13, 73, 38, 98, 40, 100)(16, 76, 44, 104, 34, 94)(18, 78, 42, 102, 19, 79)(21, 81, 51, 111, 25, 85)(23, 83, 46, 106, 37, 97)(24, 84, 52, 112, 28, 88)(27, 87, 53, 113, 29, 89)(31, 91, 55, 115, 48, 108)(33, 93, 57, 117, 47, 107)(36, 96, 43, 103, 41, 101)(39, 99, 45, 105, 54, 114)(49, 109, 56, 116, 50, 110)(58, 118, 59, 119, 60, 120)(121, 181, 123, 183, 132, 192, 143, 203, 126, 186)(122, 182, 128, 188, 147, 207, 134, 194, 124, 184)(125, 185, 138, 198, 166, 226, 149, 209, 129, 189)(127, 187, 141, 201, 140, 200, 169, 229, 144, 204)(130, 190, 136, 196, 135, 195, 161, 221, 153, 213)(131, 191, 152, 212, 176, 236, 157, 217, 133, 193)(137, 197, 165, 225, 173, 233, 167, 227, 162, 222)(139, 199, 151, 211, 150, 210, 159, 219, 158, 218)(142, 202, 156, 216, 155, 215, 148, 208, 146, 206)(145, 205, 164, 224, 172, 232, 178, 238, 163, 223)(154, 214, 175, 235, 177, 237, 180, 240, 174, 234)(160, 220, 179, 239, 170, 230, 168, 228, 171, 231) L = (1, 124)(2, 129)(3, 133)(4, 136)(5, 126)(6, 141)(7, 121)(8, 148)(9, 151)(10, 122)(11, 144)(12, 156)(13, 159)(14, 123)(15, 162)(16, 145)(17, 134)(18, 167)(19, 125)(20, 146)(21, 168)(22, 143)(23, 138)(24, 164)(25, 127)(26, 153)(27, 165)(28, 169)(29, 128)(30, 131)(31, 154)(32, 149)(33, 175)(34, 130)(35, 147)(36, 178)(37, 132)(38, 171)(39, 137)(40, 157)(41, 142)(42, 158)(43, 135)(44, 174)(45, 180)(46, 176)(47, 161)(48, 139)(49, 152)(50, 140)(51, 163)(52, 155)(53, 166)(54, 150)(55, 170)(56, 179)(57, 173)(58, 160)(59, 177)(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, 4, 6 ) } Outer automorphisms :: reflexible Dual of E20.846 Graph:: bipartite v = 32 e = 120 f = 50 degree seq :: [ 6^20, 10^12 ] E20.851 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^5, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y3^2 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 12, 72)(5, 65, 14, 74)(6, 66, 16, 76)(7, 67, 19, 79)(8, 68, 21, 81)(10, 70, 18, 78)(11, 71, 17, 77)(13, 73, 22, 82)(15, 75, 20, 80)(23, 83, 37, 97)(24, 84, 38, 98)(25, 85, 40, 100)(26, 86, 41, 101)(27, 87, 39, 99)(28, 88, 42, 102)(29, 89, 43, 103)(30, 90, 44, 104)(31, 91, 45, 105)(32, 92, 47, 107)(33, 93, 48, 108)(34, 94, 46, 106)(35, 95, 49, 109)(36, 96, 50, 110)(51, 111, 56, 116)(52, 112, 58, 118)(53, 113, 57, 117)(54, 114, 60, 120)(55, 115, 59, 119)(121, 181, 123, 183)(122, 182, 126, 186)(124, 184, 130, 190)(125, 185, 131, 191)(127, 187, 137, 197)(128, 188, 138, 198)(129, 189, 143, 203)(132, 192, 145, 205)(133, 193, 146, 206)(134, 194, 144, 204)(135, 195, 147, 207)(136, 196, 150, 210)(139, 199, 152, 212)(140, 200, 153, 213)(141, 201, 151, 211)(142, 202, 154, 214)(148, 208, 161, 221)(149, 209, 159, 219)(155, 215, 168, 228)(156, 216, 166, 226)(157, 217, 171, 231)(158, 218, 173, 233)(160, 220, 172, 232)(162, 222, 175, 235)(163, 223, 174, 234)(164, 224, 176, 236)(165, 225, 178, 238)(167, 227, 177, 237)(169, 229, 180, 240)(170, 230, 179, 239) L = (1, 124)(2, 127)(3, 130)(4, 133)(5, 121)(6, 137)(7, 140)(8, 122)(9, 144)(10, 146)(11, 123)(12, 143)(13, 147)(14, 149)(15, 125)(16, 151)(17, 153)(18, 126)(19, 150)(20, 154)(21, 156)(22, 128)(23, 134)(24, 159)(25, 129)(26, 135)(27, 131)(28, 132)(29, 161)(30, 141)(31, 166)(32, 136)(33, 142)(34, 138)(35, 139)(36, 168)(37, 172)(38, 171)(39, 148)(40, 175)(41, 145)(42, 174)(43, 173)(44, 177)(45, 176)(46, 155)(47, 180)(48, 152)(49, 179)(50, 178)(51, 160)(52, 162)(53, 157)(54, 158)(55, 163)(56, 167)(57, 169)(58, 164)(59, 165)(60, 170)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E20.856 Graph:: simple bipartite v = 60 e = 120 f = 22 degree seq :: [ 4^60 ] E20.852 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, R^2, R * Y2 * R * Y2^-1, Y3^-1 * Y2 * Y3 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^5, Y3^6 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 10, 70)(5, 65, 9, 69)(6, 66, 8, 68)(11, 71, 19, 79)(12, 72, 21, 81)(13, 73, 20, 80)(14, 74, 25, 85)(15, 75, 26, 86)(16, 76, 24, 84)(17, 77, 22, 82)(18, 78, 23, 83)(27, 87, 37, 97)(28, 88, 36, 96)(29, 89, 39, 99)(30, 90, 38, 98)(31, 91, 43, 103)(32, 92, 44, 104)(33, 93, 42, 102)(34, 94, 40, 100)(35, 95, 41, 101)(45, 105, 52, 112)(46, 106, 51, 111)(47, 107, 53, 113)(48, 108, 56, 116)(49, 109, 55, 115)(50, 110, 54, 114)(57, 117, 59, 119)(58, 118, 60, 120)(121, 181, 123, 183, 131, 191, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 144, 204, 129, 189)(124, 184, 134, 194, 151, 211, 147, 207, 132, 192)(126, 186, 137, 197, 154, 214, 148, 208, 133, 193)(128, 188, 142, 202, 160, 220, 156, 216, 140, 200)(130, 190, 145, 205, 163, 223, 157, 217, 141, 201)(135, 195, 149, 209, 165, 225, 168, 228, 152, 212)(138, 198, 150, 210, 166, 226, 170, 230, 155, 215)(143, 203, 158, 218, 171, 231, 174, 234, 161, 221)(146, 206, 159, 219, 172, 232, 176, 236, 164, 224)(153, 213, 169, 229, 178, 238, 177, 237, 167, 227)(162, 222, 175, 235, 180, 240, 179, 239, 173, 233) L = (1, 124)(2, 128)(3, 132)(4, 135)(5, 134)(6, 121)(7, 140)(8, 143)(9, 142)(10, 122)(11, 147)(12, 149)(13, 123)(14, 152)(15, 153)(16, 151)(17, 125)(18, 126)(19, 156)(20, 158)(21, 127)(22, 161)(23, 162)(24, 160)(25, 129)(26, 130)(27, 165)(28, 131)(29, 167)(30, 133)(31, 168)(32, 169)(33, 138)(34, 136)(35, 137)(36, 171)(37, 139)(38, 173)(39, 141)(40, 174)(41, 175)(42, 146)(43, 144)(44, 145)(45, 177)(46, 148)(47, 150)(48, 178)(49, 155)(50, 154)(51, 179)(52, 157)(53, 159)(54, 180)(55, 164)(56, 163)(57, 166)(58, 170)(59, 172)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E20.855 Graph:: simple bipartite v = 42 e = 120 f = 40 degree seq :: [ 4^30, 10^12 ] E20.853 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, R^2, R * Y2 * R * Y2^-1, Y3^-1 * Y2 * Y3 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y2^5, Y3^6 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 24, 84)(12, 72, 25, 85)(13, 73, 22, 82)(14, 74, 21, 81)(15, 75, 26, 86)(16, 76, 19, 79)(17, 77, 20, 80)(18, 78, 23, 83)(27, 87, 43, 103)(28, 88, 40, 100)(29, 89, 44, 104)(30, 90, 41, 101)(31, 91, 37, 97)(32, 92, 39, 99)(33, 93, 42, 102)(34, 94, 36, 96)(35, 95, 38, 98)(45, 105, 56, 116)(46, 106, 54, 114)(47, 107, 55, 115)(48, 108, 52, 112)(49, 109, 53, 113)(50, 110, 51, 111)(57, 117, 60, 120)(58, 118, 59, 119)(121, 181, 123, 183, 131, 191, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 144, 204, 129, 189)(124, 184, 134, 194, 151, 211, 147, 207, 132, 192)(126, 186, 137, 197, 154, 214, 148, 208, 133, 193)(128, 188, 142, 202, 160, 220, 156, 216, 140, 200)(130, 190, 145, 205, 163, 223, 157, 217, 141, 201)(135, 195, 149, 209, 165, 225, 168, 228, 152, 212)(138, 198, 150, 210, 166, 226, 170, 230, 155, 215)(143, 203, 158, 218, 171, 231, 174, 234, 161, 221)(146, 206, 159, 219, 172, 232, 176, 236, 164, 224)(153, 213, 169, 229, 178, 238, 177, 237, 167, 227)(162, 222, 175, 235, 180, 240, 179, 239, 173, 233) L = (1, 124)(2, 128)(3, 132)(4, 135)(5, 134)(6, 121)(7, 140)(8, 143)(9, 142)(10, 122)(11, 147)(12, 149)(13, 123)(14, 152)(15, 153)(16, 151)(17, 125)(18, 126)(19, 156)(20, 158)(21, 127)(22, 161)(23, 162)(24, 160)(25, 129)(26, 130)(27, 165)(28, 131)(29, 167)(30, 133)(31, 168)(32, 169)(33, 138)(34, 136)(35, 137)(36, 171)(37, 139)(38, 173)(39, 141)(40, 174)(41, 175)(42, 146)(43, 144)(44, 145)(45, 177)(46, 148)(47, 150)(48, 178)(49, 155)(50, 154)(51, 179)(52, 157)(53, 159)(54, 180)(55, 164)(56, 163)(57, 166)(58, 170)(59, 172)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E20.854 Graph:: simple bipartite v = 42 e = 120 f = 40 degree seq :: [ 4^30, 10^12 ] E20.854 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^-2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, Y3^-1 * Y1^4 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 15, 75, 5, 65)(3, 63, 11, 71, 27, 87, 35, 95, 20, 80, 8, 68)(4, 64, 14, 74, 6, 66, 18, 78, 21, 81, 16, 76)(9, 69, 24, 84, 10, 70, 26, 86, 17, 77, 25, 85)(12, 72, 29, 89, 13, 73, 31, 91, 36, 96, 30, 90)(22, 82, 37, 97, 23, 83, 39, 99, 28, 88, 38, 98)(32, 92, 46, 106, 33, 93, 48, 108, 34, 94, 47, 107)(40, 100, 52, 112, 41, 101, 54, 114, 42, 102, 53, 113)(43, 103, 55, 115, 44, 104, 57, 117, 45, 105, 56, 116)(49, 109, 58, 118, 50, 110, 60, 120, 51, 111, 59, 119)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 143, 203)(130, 190, 142, 202)(134, 194, 149, 209)(135, 195, 147, 207)(136, 196, 151, 211)(137, 197, 148, 208)(138, 198, 150, 210)(139, 199, 155, 215)(141, 201, 156, 216)(144, 204, 157, 217)(145, 205, 159, 219)(146, 206, 158, 218)(152, 212, 164, 224)(153, 213, 163, 223)(154, 214, 165, 225)(160, 220, 170, 230)(161, 221, 169, 229)(162, 222, 171, 231)(166, 226, 175, 235)(167, 227, 177, 237)(168, 228, 176, 236)(172, 232, 178, 238)(173, 233, 180, 240)(174, 234, 179, 239) L = (1, 124)(2, 129)(3, 132)(4, 135)(5, 137)(6, 121)(7, 126)(8, 142)(9, 125)(10, 122)(11, 143)(12, 140)(13, 123)(14, 152)(15, 141)(16, 154)(17, 139)(18, 153)(19, 130)(20, 156)(21, 127)(22, 155)(23, 128)(24, 160)(25, 162)(26, 161)(27, 133)(28, 131)(29, 163)(30, 165)(31, 164)(32, 136)(33, 134)(34, 138)(35, 148)(36, 147)(37, 169)(38, 171)(39, 170)(40, 145)(41, 144)(42, 146)(43, 150)(44, 149)(45, 151)(46, 173)(47, 174)(48, 172)(49, 158)(50, 157)(51, 159)(52, 166)(53, 167)(54, 168)(55, 178)(56, 179)(57, 180)(58, 176)(59, 177)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E20.853 Graph:: simple bipartite v = 40 e = 120 f = 42 degree seq :: [ 4^30, 12^10 ] E20.855 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y3^6, Y3^-1 * Y1^4 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y2 * Y1^-2 * Y3 * Y1 * Y2, Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 21, 81, 16, 76, 5, 65)(3, 63, 11, 71, 31, 91, 42, 102, 22, 82, 13, 73)(4, 64, 15, 75, 6, 66, 20, 80, 23, 83, 17, 77)(8, 68, 24, 84, 18, 78, 39, 99, 40, 100, 26, 86)(9, 69, 28, 88, 10, 70, 30, 90, 19, 79, 29, 89)(12, 72, 27, 87, 14, 74, 37, 97, 41, 101, 25, 85)(32, 92, 49, 109, 35, 95, 54, 114, 38, 98, 50, 110)(33, 93, 51, 111, 34, 94, 53, 113, 36, 96, 52, 112)(43, 103, 55, 115, 46, 106, 60, 120, 48, 108, 56, 116)(44, 104, 57, 117, 45, 105, 59, 119, 47, 107, 58, 118)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 134, 194)(125, 185, 138, 198)(126, 186, 132, 192)(127, 187, 142, 202)(129, 189, 147, 207)(130, 190, 145, 205)(131, 191, 152, 212)(133, 193, 155, 215)(135, 195, 153, 213)(136, 196, 151, 211)(137, 197, 154, 214)(139, 199, 157, 217)(140, 200, 156, 216)(141, 201, 160, 220)(143, 203, 161, 221)(144, 204, 163, 223)(146, 206, 166, 226)(148, 208, 164, 224)(149, 209, 165, 225)(150, 210, 167, 227)(158, 218, 162, 222)(159, 219, 168, 228)(169, 229, 177, 237)(170, 230, 179, 239)(171, 231, 176, 236)(172, 232, 175, 235)(173, 233, 180, 240)(174, 234, 178, 238) L = (1, 124)(2, 129)(3, 132)(4, 136)(5, 139)(6, 121)(7, 126)(8, 145)(9, 125)(10, 122)(11, 153)(12, 142)(13, 156)(14, 123)(15, 152)(16, 143)(17, 158)(18, 147)(19, 141)(20, 155)(21, 130)(22, 161)(23, 127)(24, 164)(25, 160)(26, 167)(27, 128)(28, 163)(29, 168)(30, 166)(31, 134)(32, 137)(33, 133)(34, 131)(35, 135)(36, 162)(37, 138)(38, 140)(39, 165)(40, 157)(41, 151)(42, 154)(43, 149)(44, 146)(45, 144)(46, 148)(47, 159)(48, 150)(49, 176)(50, 180)(51, 177)(52, 178)(53, 179)(54, 175)(55, 169)(56, 170)(57, 172)(58, 173)(59, 171)(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, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E20.852 Graph:: simple bipartite v = 40 e = 120 f = 42 degree seq :: [ 4^30, 12^10 ] E20.856 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y3^2, R^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y2^-1 * Y3)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y1^5, Y2^6 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 16, 76, 5, 65)(3, 63, 11, 71, 26, 86, 19, 79, 8, 68)(4, 64, 14, 74, 31, 91, 20, 80, 9, 69)(6, 66, 17, 77, 34, 94, 21, 81, 10, 70)(12, 72, 22, 82, 36, 96, 43, 103, 27, 87)(13, 73, 23, 83, 37, 97, 44, 104, 28, 88)(15, 75, 24, 84, 38, 98, 48, 108, 32, 92)(18, 78, 25, 85, 39, 99, 50, 110, 35, 95)(29, 89, 45, 105, 55, 115, 51, 111, 40, 100)(30, 90, 46, 106, 56, 116, 52, 112, 41, 101)(33, 93, 49, 109, 58, 118, 53, 113, 42, 102)(47, 107, 54, 114, 59, 119, 60, 120, 57, 117)(121, 181, 123, 183, 132, 192, 149, 209, 138, 198, 126, 186)(122, 182, 128, 188, 142, 202, 160, 220, 145, 205, 130, 190)(124, 184, 135, 195, 153, 213, 167, 227, 150, 210, 133, 193)(125, 185, 131, 191, 147, 207, 165, 225, 155, 215, 137, 197)(127, 187, 139, 199, 156, 216, 171, 231, 159, 219, 141, 201)(129, 189, 144, 204, 162, 222, 174, 234, 161, 221, 143, 203)(134, 194, 152, 212, 169, 229, 177, 237, 166, 226, 148, 208)(136, 196, 146, 206, 163, 223, 175, 235, 170, 230, 154, 214)(140, 200, 158, 218, 173, 233, 179, 239, 172, 232, 157, 217)(151, 211, 168, 228, 178, 238, 180, 240, 176, 236, 164, 224) L = (1, 124)(2, 129)(3, 133)(4, 121)(5, 134)(6, 135)(7, 140)(8, 143)(9, 122)(10, 144)(11, 148)(12, 150)(13, 123)(14, 125)(15, 126)(16, 151)(17, 152)(18, 153)(19, 157)(20, 127)(21, 158)(22, 161)(23, 128)(24, 130)(25, 162)(26, 164)(27, 166)(28, 131)(29, 167)(30, 132)(31, 136)(32, 137)(33, 138)(34, 168)(35, 169)(36, 172)(37, 139)(38, 141)(39, 173)(40, 174)(41, 142)(42, 145)(43, 176)(44, 146)(45, 177)(46, 147)(47, 149)(48, 154)(49, 155)(50, 178)(51, 179)(52, 156)(53, 159)(54, 160)(55, 180)(56, 163)(57, 165)(58, 170)(59, 171)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4^10 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E20.851 Graph:: simple bipartite v = 22 e = 120 f = 60 degree seq :: [ 10^12, 12^10 ] E20.857 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2^5, Y3^-6 * Y2, Y2^-1 * Y3^-2 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 24, 84)(12, 72, 25, 85)(13, 73, 23, 83)(14, 74, 26, 86)(15, 75, 21, 81)(16, 76, 19, 79)(17, 77, 20, 80)(18, 78, 22, 82)(27, 87, 44, 104)(28, 88, 43, 103)(29, 89, 45, 105)(30, 90, 42, 102)(31, 91, 46, 106)(32, 92, 40, 100)(33, 93, 38, 98)(34, 94, 37, 97)(35, 95, 39, 99)(36, 96, 41, 101)(47, 107, 57, 117)(48, 108, 56, 116)(49, 109, 58, 118)(50, 110, 54, 114)(51, 111, 53, 113)(52, 112, 55, 115)(59, 119, 60, 120)(121, 181, 123, 183, 131, 191, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 144, 204, 129, 189)(124, 184, 132, 192, 147, 207, 153, 213, 135, 195)(126, 186, 133, 193, 148, 208, 154, 214, 137, 197)(128, 188, 140, 200, 157, 217, 163, 223, 143, 203)(130, 190, 141, 201, 158, 218, 164, 224, 145, 205)(134, 194, 149, 209, 167, 227, 170, 230, 152, 212)(138, 198, 150, 210, 168, 228, 171, 231, 155, 215)(142, 202, 159, 219, 173, 233, 176, 236, 162, 222)(146, 206, 160, 220, 174, 234, 177, 237, 165, 225)(151, 211, 169, 229, 179, 239, 172, 232, 156, 216)(161, 221, 175, 235, 180, 240, 178, 238, 166, 226) L = (1, 124)(2, 128)(3, 132)(4, 134)(5, 135)(6, 121)(7, 140)(8, 142)(9, 143)(10, 122)(11, 147)(12, 149)(13, 123)(14, 151)(15, 152)(16, 153)(17, 125)(18, 126)(19, 157)(20, 159)(21, 127)(22, 161)(23, 162)(24, 163)(25, 129)(26, 130)(27, 167)(28, 131)(29, 169)(30, 133)(31, 150)(32, 156)(33, 170)(34, 136)(35, 137)(36, 138)(37, 173)(38, 139)(39, 175)(40, 141)(41, 160)(42, 166)(43, 176)(44, 144)(45, 145)(46, 146)(47, 179)(48, 148)(49, 168)(50, 172)(51, 154)(52, 155)(53, 180)(54, 158)(55, 174)(56, 178)(57, 164)(58, 165)(59, 171)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E20.858 Graph:: simple bipartite v = 42 e = 120 f = 40 degree seq :: [ 4^30, 10^12 ] E20.858 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 6}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^5 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 16, 76, 5, 65)(3, 63, 11, 71, 27, 87, 36, 96, 20, 80, 8, 68)(4, 64, 9, 69, 21, 81, 37, 97, 33, 93, 15, 75)(6, 66, 10, 70, 22, 82, 38, 98, 34, 94, 17, 77)(12, 72, 28, 88, 45, 105, 51, 111, 39, 99, 23, 83)(13, 73, 29, 89, 46, 106, 52, 112, 40, 100, 24, 84)(14, 74, 25, 85, 41, 101, 53, 113, 49, 109, 32, 92)(18, 78, 26, 86, 42, 102, 54, 114, 50, 110, 35, 95)(30, 90, 47, 107, 57, 117, 59, 119, 55, 115, 43, 103)(31, 91, 48, 108, 58, 118, 60, 120, 56, 116, 44, 104)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 144, 204)(130, 190, 143, 203)(134, 194, 151, 211)(135, 195, 149, 209)(136, 196, 147, 207)(137, 197, 148, 208)(138, 198, 150, 210)(139, 199, 156, 216)(141, 201, 160, 220)(142, 202, 159, 219)(145, 205, 164, 224)(146, 206, 163, 223)(152, 212, 168, 228)(153, 213, 166, 226)(154, 214, 165, 225)(155, 215, 167, 227)(157, 217, 172, 232)(158, 218, 171, 231)(161, 221, 176, 236)(162, 222, 175, 235)(169, 229, 178, 238)(170, 230, 177, 237)(173, 233, 180, 240)(174, 234, 179, 239) L = (1, 124)(2, 129)(3, 132)(4, 134)(5, 135)(6, 121)(7, 141)(8, 143)(9, 145)(10, 122)(11, 148)(12, 150)(13, 123)(14, 146)(15, 152)(16, 153)(17, 125)(18, 126)(19, 157)(20, 159)(21, 161)(22, 127)(23, 163)(24, 128)(25, 162)(26, 130)(27, 165)(28, 167)(29, 131)(30, 168)(31, 133)(32, 138)(33, 169)(34, 136)(35, 137)(36, 171)(37, 173)(38, 139)(39, 175)(40, 140)(41, 174)(42, 142)(43, 151)(44, 144)(45, 177)(46, 147)(47, 178)(48, 149)(49, 155)(50, 154)(51, 179)(52, 156)(53, 170)(54, 158)(55, 164)(56, 160)(57, 180)(58, 166)(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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E20.857 Graph:: simple bipartite v = 40 e = 120 f = 42 degree seq :: [ 4^30, 12^10 ] E20.859 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 10, 10}) Quotient :: edge Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^6, T2^10 ] Map:: non-degenerate R = (1, 3, 10, 21, 33, 45, 36, 24, 13, 5)(2, 7, 17, 29, 41, 52, 42, 30, 18, 8)(4, 9, 20, 32, 44, 54, 47, 35, 23, 12)(6, 15, 27, 39, 50, 58, 51, 40, 28, 16)(11, 19, 31, 43, 53, 59, 55, 46, 34, 22)(14, 25, 37, 48, 56, 60, 57, 49, 38, 26)(61, 62, 66, 74, 71, 64)(63, 69, 79, 85, 75, 67)(65, 72, 82, 86, 76, 68)(70, 77, 87, 97, 91, 80)(73, 78, 88, 98, 94, 83)(81, 92, 103, 108, 99, 89)(84, 95, 106, 109, 100, 90)(93, 101, 110, 116, 113, 104)(96, 102, 111, 117, 115, 107)(105, 114, 119, 120, 118, 112) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20^6 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E20.860 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 60 f = 6 degree seq :: [ 6^10, 10^6 ] E20.860 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 10, 10}) Quotient :: loop Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^6, T2^10 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 21, 81, 33, 93, 45, 105, 36, 96, 24, 84, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 29, 89, 41, 101, 52, 112, 42, 102, 30, 90, 18, 78, 8, 68)(4, 64, 9, 69, 20, 80, 32, 92, 44, 104, 54, 114, 47, 107, 35, 95, 23, 83, 12, 72)(6, 66, 15, 75, 27, 87, 39, 99, 50, 110, 58, 118, 51, 111, 40, 100, 28, 88, 16, 76)(11, 71, 19, 79, 31, 91, 43, 103, 53, 113, 59, 119, 55, 115, 46, 106, 34, 94, 22, 82)(14, 74, 25, 85, 37, 97, 48, 108, 56, 116, 60, 120, 57, 117, 49, 109, 38, 98, 26, 86) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 72)(6, 74)(7, 63)(8, 65)(9, 79)(10, 77)(11, 64)(12, 82)(13, 78)(14, 71)(15, 67)(16, 68)(17, 87)(18, 88)(19, 85)(20, 70)(21, 92)(22, 86)(23, 73)(24, 95)(25, 75)(26, 76)(27, 97)(28, 98)(29, 81)(30, 84)(31, 80)(32, 103)(33, 101)(34, 83)(35, 106)(36, 102)(37, 91)(38, 94)(39, 89)(40, 90)(41, 110)(42, 111)(43, 108)(44, 93)(45, 114)(46, 109)(47, 96)(48, 99)(49, 100)(50, 116)(51, 117)(52, 105)(53, 104)(54, 119)(55, 107)(56, 113)(57, 115)(58, 112)(59, 120)(60, 118) local type(s) :: { ( 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 E20.859 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 60 f = 16 degree seq :: [ 20^6 ] E20.861 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 10, 10}) Quotient :: dipole Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, Y2^10, (Y2^-1 * Y1)^10 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 11, 71, 4, 64)(3, 63, 9, 69, 19, 79, 25, 85, 15, 75, 7, 67)(5, 65, 12, 72, 22, 82, 26, 86, 16, 76, 8, 68)(10, 70, 17, 77, 27, 87, 37, 97, 31, 91, 20, 80)(13, 73, 18, 78, 28, 88, 38, 98, 34, 94, 23, 83)(21, 81, 32, 92, 43, 103, 48, 108, 39, 99, 29, 89)(24, 84, 35, 95, 46, 106, 49, 109, 40, 100, 30, 90)(33, 93, 41, 101, 50, 110, 56, 116, 53, 113, 44, 104)(36, 96, 42, 102, 51, 111, 57, 117, 55, 115, 47, 107)(45, 105, 54, 114, 59, 119, 60, 120, 58, 118, 52, 112)(121, 181, 123, 183, 130, 190, 141, 201, 153, 213, 165, 225, 156, 216, 144, 204, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 149, 209, 161, 221, 172, 232, 162, 222, 150, 210, 138, 198, 128, 188)(124, 184, 129, 189, 140, 200, 152, 212, 164, 224, 174, 234, 167, 227, 155, 215, 143, 203, 132, 192)(126, 186, 135, 195, 147, 207, 159, 219, 170, 230, 178, 238, 171, 231, 160, 220, 148, 208, 136, 196)(131, 191, 139, 199, 151, 211, 163, 223, 173, 233, 179, 239, 175, 235, 166, 226, 154, 214, 142, 202)(134, 194, 145, 205, 157, 217, 168, 228, 176, 236, 180, 240, 177, 237, 169, 229, 158, 218, 146, 206) L = (1, 124)(2, 121)(3, 127)(4, 131)(5, 128)(6, 122)(7, 135)(8, 136)(9, 123)(10, 140)(11, 134)(12, 125)(13, 143)(14, 126)(15, 145)(16, 146)(17, 130)(18, 133)(19, 129)(20, 151)(21, 149)(22, 132)(23, 154)(24, 150)(25, 139)(26, 142)(27, 137)(28, 138)(29, 159)(30, 160)(31, 157)(32, 141)(33, 164)(34, 158)(35, 144)(36, 167)(37, 147)(38, 148)(39, 168)(40, 169)(41, 153)(42, 156)(43, 152)(44, 173)(45, 172)(46, 155)(47, 175)(48, 163)(49, 166)(50, 161)(51, 162)(52, 178)(53, 176)(54, 165)(55, 177)(56, 170)(57, 171)(58, 180)(59, 174)(60, 179)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E20.862 Graph:: bipartite v = 16 e = 120 f = 66 degree seq :: [ 12^10, 20^6 ] E20.862 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 10, 10}) Quotient :: dipole Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-4 * Y1^-1, Y1^10, (Y3 * Y2^-1)^6 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 25, 85, 37, 97, 36, 96, 24, 84, 12, 72, 4, 64)(3, 63, 8, 68, 15, 75, 27, 87, 38, 98, 49, 109, 45, 105, 33, 93, 21, 81, 10, 70)(5, 65, 7, 67, 16, 76, 26, 86, 39, 99, 48, 108, 47, 107, 35, 95, 23, 83, 11, 71)(9, 69, 18, 78, 28, 88, 41, 101, 50, 110, 57, 117, 54, 114, 44, 104, 32, 92, 20, 80)(13, 73, 17, 77, 29, 89, 40, 100, 51, 111, 56, 116, 55, 115, 46, 106, 34, 94, 22, 82)(19, 79, 30, 90, 42, 102, 52, 112, 58, 118, 60, 120, 59, 119, 53, 113, 43, 103, 31, 91)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 124)(11, 142)(12, 141)(13, 125)(14, 146)(15, 148)(16, 126)(17, 150)(18, 128)(19, 133)(20, 130)(21, 152)(22, 151)(23, 132)(24, 155)(25, 158)(26, 160)(27, 134)(28, 162)(29, 136)(30, 138)(31, 140)(32, 163)(33, 144)(34, 143)(35, 166)(36, 165)(37, 168)(38, 170)(39, 145)(40, 172)(41, 147)(42, 149)(43, 154)(44, 153)(45, 174)(46, 173)(47, 156)(48, 176)(49, 157)(50, 178)(51, 159)(52, 161)(53, 164)(54, 179)(55, 167)(56, 180)(57, 169)(58, 171)(59, 175)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12, 20 ), ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E20.861 Graph:: simple bipartite v = 66 e = 120 f = 16 degree seq :: [ 2^60, 20^6 ] E20.863 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 12, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^5, T2^12 ] Map:: non-degenerate R = (1, 3, 10, 20, 30, 40, 50, 43, 33, 23, 13, 5)(2, 7, 16, 26, 36, 46, 55, 47, 37, 27, 17, 8)(4, 9, 19, 29, 39, 49, 57, 52, 42, 32, 22, 12)(6, 14, 24, 34, 44, 53, 59, 54, 45, 35, 25, 15)(11, 18, 28, 38, 48, 56, 60, 58, 51, 41, 31, 21)(61, 62, 66, 71, 64)(63, 69, 78, 74, 67)(65, 72, 81, 75, 68)(70, 76, 84, 88, 79)(73, 77, 85, 91, 82)(80, 89, 98, 94, 86)(83, 92, 101, 95, 87)(90, 96, 104, 108, 99)(93, 97, 105, 111, 102)(100, 109, 116, 113, 106)(103, 112, 118, 114, 107)(110, 115, 119, 120, 117) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^5 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E20.864 Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 60 f = 5 degree seq :: [ 5^12, 12^5 ] E20.864 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 12, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^5, T2^12 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 20, 80, 30, 90, 40, 100, 50, 110, 43, 103, 33, 93, 23, 83, 13, 73, 5, 65)(2, 62, 7, 67, 16, 76, 26, 86, 36, 96, 46, 106, 55, 115, 47, 107, 37, 97, 27, 87, 17, 77, 8, 68)(4, 64, 9, 69, 19, 79, 29, 89, 39, 99, 49, 109, 57, 117, 52, 112, 42, 102, 32, 92, 22, 82, 12, 72)(6, 66, 14, 74, 24, 84, 34, 94, 44, 104, 53, 113, 59, 119, 54, 114, 45, 105, 35, 95, 25, 85, 15, 75)(11, 71, 18, 78, 28, 88, 38, 98, 48, 108, 56, 116, 60, 120, 58, 118, 51, 111, 41, 101, 31, 91, 21, 81) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 72)(6, 71)(7, 63)(8, 65)(9, 78)(10, 76)(11, 64)(12, 81)(13, 77)(14, 67)(15, 68)(16, 84)(17, 85)(18, 74)(19, 70)(20, 89)(21, 75)(22, 73)(23, 92)(24, 88)(25, 91)(26, 80)(27, 83)(28, 79)(29, 98)(30, 96)(31, 82)(32, 101)(33, 97)(34, 86)(35, 87)(36, 104)(37, 105)(38, 94)(39, 90)(40, 109)(41, 95)(42, 93)(43, 112)(44, 108)(45, 111)(46, 100)(47, 103)(48, 99)(49, 116)(50, 115)(51, 102)(52, 118)(53, 106)(54, 107)(55, 119)(56, 113)(57, 110)(58, 114)(59, 120)(60, 117) local type(s) :: { ( 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12 ) } Outer automorphisms :: reflexible Dual of E20.863 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 60 f = 17 degree seq :: [ 24^5 ] E20.865 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y2^12, (Y2^-1 * Y1)^12 ] Map:: R = (1, 61, 2, 62, 6, 66, 11, 71, 4, 64)(3, 63, 9, 69, 18, 78, 14, 74, 7, 67)(5, 65, 12, 72, 21, 81, 15, 75, 8, 68)(10, 70, 16, 76, 24, 84, 28, 88, 19, 79)(13, 73, 17, 77, 25, 85, 31, 91, 22, 82)(20, 80, 29, 89, 38, 98, 34, 94, 26, 86)(23, 83, 32, 92, 41, 101, 35, 95, 27, 87)(30, 90, 36, 96, 44, 104, 48, 108, 39, 99)(33, 93, 37, 97, 45, 105, 51, 111, 42, 102)(40, 100, 49, 109, 56, 116, 53, 113, 46, 106)(43, 103, 52, 112, 58, 118, 54, 114, 47, 107)(50, 110, 55, 115, 59, 119, 60, 120, 57, 117)(121, 181, 123, 183, 130, 190, 140, 200, 150, 210, 160, 220, 170, 230, 163, 223, 153, 213, 143, 203, 133, 193, 125, 185)(122, 182, 127, 187, 136, 196, 146, 206, 156, 216, 166, 226, 175, 235, 167, 227, 157, 217, 147, 207, 137, 197, 128, 188)(124, 184, 129, 189, 139, 199, 149, 209, 159, 219, 169, 229, 177, 237, 172, 232, 162, 222, 152, 212, 142, 202, 132, 192)(126, 186, 134, 194, 144, 204, 154, 214, 164, 224, 173, 233, 179, 239, 174, 234, 165, 225, 155, 215, 145, 205, 135, 195)(131, 191, 138, 198, 148, 208, 158, 218, 168, 228, 176, 236, 180, 240, 178, 238, 171, 231, 161, 221, 151, 211, 141, 201) L = (1, 124)(2, 121)(3, 127)(4, 131)(5, 128)(6, 122)(7, 134)(8, 135)(9, 123)(10, 139)(11, 126)(12, 125)(13, 142)(14, 138)(15, 141)(16, 130)(17, 133)(18, 129)(19, 148)(20, 146)(21, 132)(22, 151)(23, 147)(24, 136)(25, 137)(26, 154)(27, 155)(28, 144)(29, 140)(30, 159)(31, 145)(32, 143)(33, 162)(34, 158)(35, 161)(36, 150)(37, 153)(38, 149)(39, 168)(40, 166)(41, 152)(42, 171)(43, 167)(44, 156)(45, 157)(46, 173)(47, 174)(48, 164)(49, 160)(50, 177)(51, 165)(52, 163)(53, 176)(54, 178)(55, 170)(56, 169)(57, 180)(58, 172)(59, 175)(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, 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 E20.866 Graph:: bipartite v = 17 e = 120 f = 65 degree seq :: [ 10^12, 24^5 ] E20.866 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, Y1^12 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 24, 84, 34, 94, 44, 104, 43, 103, 33, 93, 23, 83, 12, 72, 4, 64)(3, 63, 8, 68, 15, 75, 26, 86, 35, 95, 46, 106, 53, 113, 50, 110, 40, 100, 30, 90, 20, 80, 10, 70)(5, 65, 7, 67, 16, 76, 25, 85, 36, 96, 45, 105, 54, 114, 52, 112, 42, 102, 32, 92, 22, 82, 11, 71)(9, 69, 18, 78, 27, 87, 38, 98, 47, 107, 56, 116, 59, 119, 57, 117, 49, 109, 39, 99, 29, 89, 19, 79)(13, 73, 17, 77, 28, 88, 37, 97, 48, 108, 55, 115, 60, 120, 58, 118, 51, 111, 41, 101, 31, 91, 21, 81)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 135)(7, 137)(8, 122)(9, 133)(10, 124)(11, 141)(12, 140)(13, 125)(14, 145)(15, 147)(16, 126)(17, 138)(18, 128)(19, 130)(20, 149)(21, 139)(22, 132)(23, 152)(24, 155)(25, 157)(26, 134)(27, 148)(28, 136)(29, 151)(30, 143)(31, 142)(32, 161)(33, 160)(34, 165)(35, 167)(36, 144)(37, 158)(38, 146)(39, 150)(40, 169)(41, 159)(42, 153)(43, 172)(44, 173)(45, 175)(46, 154)(47, 168)(48, 156)(49, 171)(50, 163)(51, 162)(52, 178)(53, 179)(54, 164)(55, 176)(56, 166)(57, 170)(58, 177)(59, 180)(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) :: { ( 10, 24 ), ( 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24, 10, 24 ) } Outer automorphisms :: reflexible Dual of E20.865 Graph:: simple bipartite v = 65 e = 120 f = 17 degree seq :: [ 2^60, 24^5 ] E20.867 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {5, 12, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X1^5, X1 * X2 * X1^2 * X2^-1, X1 * X2 * X1^-1 * X2^-1 * X1, X2^12, (X2^-1 * X1 * X2^-1)^6 ] Map:: non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 12, 7, 11)(5, 15, 8, 14, 16)(10, 21, 23, 20, 18)(17, 24, 25, 26, 19)(22, 32, 28, 31, 30)(27, 36, 34, 29, 35)(33, 38, 40, 42, 41)(37, 39, 46, 45, 44)(43, 50, 51, 48, 52)(47, 55, 49, 54, 56)(53, 59, 60, 58, 57)(61, 63, 70, 82, 93, 103, 113, 107, 97, 87, 77, 65)(62, 67, 78, 88, 98, 108, 117, 109, 99, 89, 79, 68)(64, 72, 81, 91, 101, 111, 119, 114, 104, 94, 84, 74)(66, 69, 80, 90, 100, 110, 118, 116, 106, 96, 86, 76)(71, 83, 92, 102, 112, 120, 115, 105, 95, 85, 75, 73) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^5 ), ( 24^12 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 60 f = 5 degree seq :: [ 5^12, 12^5 ] E20.868 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {5, 12, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C3 x (C5 : C4) (small group id <60, 6>) |r| :: 1 Presentation :: [ X2^-3 * X1^-1 * X2 * X1^-1, X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-1, X1^-2 * X2^-1 * X1 * X2^-1 * X1^-1, X1^-1 * X2^-1 * X1^-2 * X2^-2, X2^-1 * X1 * X2^-1 * X1^9, X1^-1 * X2 * X1^-1 * X2^9 ] Map:: non-degenerate R = (1, 61, 2, 62, 6, 66, 18, 78, 34, 94, 46, 106, 56, 116, 52, 112, 41, 101, 30, 90, 13, 73, 4, 64)(3, 63, 9, 69, 25, 85, 8, 68, 24, 84, 38, 98, 50, 110, 57, 117, 51, 111, 43, 103, 31, 91, 11, 71)(5, 65, 15, 75, 26, 86, 40, 100, 47, 107, 58, 118, 54, 114, 42, 102, 28, 88, 12, 72, 22, 82, 16, 76)(7, 67, 21, 81, 37, 97, 20, 80, 36, 96, 49, 109, 60, 120, 55, 115, 45, 105, 32, 92, 39, 99, 23, 83)(10, 70, 27, 87, 14, 74, 19, 79, 17, 77, 33, 93, 35, 95, 48, 108, 59, 119, 53, 113, 44, 104, 29, 89) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 79)(7, 82)(8, 62)(9, 83)(10, 88)(11, 90)(12, 92)(13, 89)(14, 64)(15, 81)(16, 87)(17, 65)(18, 75)(19, 69)(20, 66)(21, 74)(22, 71)(23, 73)(24, 77)(25, 76)(26, 68)(27, 99)(28, 101)(29, 103)(30, 105)(31, 102)(32, 104)(33, 97)(34, 84)(35, 78)(36, 86)(37, 85)(38, 80)(39, 91)(40, 93)(41, 111)(42, 113)(43, 115)(44, 112)(45, 114)(46, 96)(47, 94)(48, 98)(49, 95)(50, 100)(51, 119)(52, 118)(53, 120)(54, 117)(55, 116)(56, 108)(57, 106)(58, 109)(59, 107)(60, 110) local type(s) :: { ( 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12, 5, 12 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 5 e = 60 f = 17 degree seq :: [ 24^5 ] E20.869 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {5, 12, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C6 x (C5 : C4) (small group id <120, 40>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1^9, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 41, 51, 59, 47, 34, 24, 17, 5)(2, 7, 22, 11, 30, 44, 55, 57, 46, 37, 26, 8)(4, 12, 31, 45, 52, 58, 49, 35, 18, 15, 25, 14)(6, 19, 16, 23, 13, 32, 42, 53, 56, 48, 38, 20)(9, 27, 39, 29, 43, 54, 60, 50, 40, 33, 36, 21)(61, 62, 66, 78, 94, 106, 116, 112, 101, 90, 73, 64)(63, 69, 85, 68, 84, 100, 109, 117, 111, 103, 91, 71)(65, 75, 93, 98, 107, 118, 114, 102, 88, 72, 87, 76)(67, 81, 77, 80, 97, 110, 119, 113, 104, 89, 70, 83)(74, 79, 96, 86, 95, 108, 120, 115, 105, 92, 99, 82) 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) :: { ( 10^12 ) } Outer automorphisms :: reflexible Dual of E20.870 Transitivity :: ET+ VT AT Graph:: bipartite v = 10 e = 60 f = 12 degree seq :: [ 12^10 ] E20.870 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {5, 12, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C6 x (C5 : C4) (small group id <120, 40>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2 * T1^-1 * T2^-1 * T1 * T2, T1 * T2 * T1^-1 * T2^2, T2^5, T1^12, T1^-2 * T2^-1 * T1^-3 * T2^-1 * T1^-3 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2 ] Map:: polytopal non-degenerate R = (1, 61, 3, 63, 10, 70, 17, 77, 5, 65)(2, 62, 7, 67, 9, 69, 15, 75, 8, 68)(4, 64, 12, 72, 16, 76, 11, 71, 14, 74)(6, 66, 19, 79, 21, 81, 22, 82, 20, 80)(13, 73, 25, 85, 27, 87, 24, 84, 23, 83)(18, 78, 29, 89, 31, 91, 32, 92, 30, 90)(26, 86, 36, 96, 33, 93, 35, 95, 34, 94)(28, 88, 39, 99, 41, 101, 42, 102, 40, 100)(37, 97, 43, 103, 44, 104, 46, 106, 45, 105)(38, 98, 49, 109, 51, 111, 52, 112, 50, 110)(47, 107, 54, 114, 55, 115, 53, 113, 56, 116)(48, 108, 57, 117, 59, 119, 60, 120, 58, 118) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 81)(8, 82)(9, 80)(10, 68)(11, 63)(12, 70)(13, 64)(14, 77)(15, 79)(16, 65)(17, 67)(18, 88)(19, 91)(20, 92)(21, 90)(22, 89)(23, 71)(24, 72)(25, 76)(26, 73)(27, 74)(28, 98)(29, 101)(30, 102)(31, 100)(32, 99)(33, 83)(34, 84)(35, 85)(36, 87)(37, 86)(38, 108)(39, 111)(40, 112)(41, 110)(42, 109)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 107)(49, 119)(50, 120)(51, 118)(52, 117)(53, 103)(54, 104)(55, 105)(56, 106)(57, 115)(58, 113)(59, 116)(60, 114) local type(s) :: { ( 12^10 ) } Outer automorphisms :: reflexible Dual of E20.869 Transitivity :: ET+ VT+ Graph:: bipartite v = 12 e = 60 f = 10 degree seq :: [ 10^12 ] E20.871 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 12, 12}) Quotient :: edge^2 Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C6 x (C5 : C4) (small group id <120, 40>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2^2 * Y1^2 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y2^9, Y1^12, (Y1^-1 * Y3^-1 * Y2^-1)^5 ] Map:: polytopal R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 122, 126, 138, 154, 166, 176, 172, 161, 150, 133, 124)(123, 129, 145, 128, 144, 160, 169, 177, 171, 163, 151, 131)(125, 135, 153, 158, 167, 178, 174, 162, 148, 132, 147, 136)(127, 141, 137, 140, 157, 170, 179, 173, 164, 149, 130, 143)(134, 139, 156, 146, 155, 168, 180, 175, 165, 152, 159, 142)(181, 183, 190, 208, 221, 231, 239, 227, 214, 204, 197, 185)(182, 187, 202, 191, 210, 224, 235, 237, 226, 217, 206, 188)(184, 192, 211, 225, 232, 238, 229, 215, 198, 195, 205, 194)(186, 199, 196, 203, 193, 212, 222, 233, 236, 228, 218, 200)(189, 207, 219, 209, 223, 234, 240, 230, 220, 213, 216, 201) 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 ), ( 20^12 ) } Outer automorphisms :: reflexible Dual of E20.874 Graph:: simple bipartite v = 70 e = 120 f = 12 degree seq :: [ 2^60, 12^10 ] E20.872 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 12, 12}) Quotient :: edge^2 Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C6 x (C5 : C4) (small group id <120, 40>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2^-1 * Y3, Y3 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y1, R * Y2 * R * Y1, Y2 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^-2, Y1^-1 * Y2^-1 * Y3^3, Y2^12, Y1^12 ] Map:: polytopal non-degenerate R = (1, 61, 4, 64, 17, 77, 12, 72, 7, 67)(2, 62, 9, 69, 6, 66, 22, 82, 11, 71)(3, 63, 5, 65, 19, 79, 16, 76, 15, 75)(8, 68, 23, 83, 10, 70, 27, 87, 21, 81)(13, 73, 14, 74, 32, 92, 18, 78, 20, 80)(24, 84, 28, 88, 25, 85, 35, 95, 26, 86)(29, 89, 30, 90, 34, 94, 31, 91, 33, 93)(36, 96, 39, 99, 37, 97, 40, 100, 38, 98)(41, 101, 42, 102, 45, 105, 43, 103, 44, 104)(46, 106, 49, 109, 47, 107, 50, 110, 48, 108)(51, 111, 52, 112, 55, 115, 53, 113, 54, 114)(56, 116, 59, 119, 57, 117, 60, 120, 58, 118)(121, 122, 128, 144, 156, 166, 176, 172, 161, 151, 140, 125)(123, 132, 129, 130, 146, 160, 169, 177, 171, 163, 153, 134)(124, 126, 141, 155, 159, 167, 178, 174, 162, 149, 138, 135)(127, 142, 143, 145, 158, 170, 179, 173, 164, 150, 133, 136)(131, 147, 148, 157, 168, 180, 175, 165, 154, 152, 139, 137)(181, 183, 193, 209, 221, 231, 239, 227, 216, 206, 203, 186)(182, 187, 199, 194, 211, 224, 235, 237, 226, 218, 208, 190)(184, 196, 200, 214, 222, 233, 236, 228, 219, 205, 188, 191)(185, 198, 213, 225, 232, 238, 229, 217, 204, 201, 189, 197)(192, 195, 212, 210, 223, 234, 240, 230, 220, 215, 207, 202) 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) :: { ( 4^10 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E20.873 Graph:: simple bipartite v = 22 e = 120 f = 60 degree seq :: [ 10^12, 12^10 ] E20.873 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 12, 12}) Quotient :: loop^2 Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C6 x (C5 : C4) (small group id <120, 40>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2^2 * Y1^2 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y2^9, Y1^12, (Y1^-1 * Y3^-1 * Y2^-1)^5 ] Map:: polytopal non-degenerate R = (1, 61, 121, 181)(2, 62, 122, 182)(3, 63, 123, 183)(4, 64, 124, 184)(5, 65, 125, 185)(6, 66, 126, 186)(7, 67, 127, 187)(8, 68, 128, 188)(9, 69, 129, 189)(10, 70, 130, 190)(11, 71, 131, 191)(12, 72, 132, 192)(13, 73, 133, 193)(14, 74, 134, 194)(15, 75, 135, 195)(16, 76, 136, 196)(17, 77, 137, 197)(18, 78, 138, 198)(19, 79, 139, 199)(20, 80, 140, 200)(21, 81, 141, 201)(22, 82, 142, 202)(23, 83, 143, 203)(24, 84, 144, 204)(25, 85, 145, 205)(26, 86, 146, 206)(27, 87, 147, 207)(28, 88, 148, 208)(29, 89, 149, 209)(30, 90, 150, 210)(31, 91, 151, 211)(32, 92, 152, 212)(33, 93, 153, 213)(34, 94, 154, 214)(35, 95, 155, 215)(36, 96, 156, 216)(37, 97, 157, 217)(38, 98, 158, 218)(39, 99, 159, 219)(40, 100, 160, 220)(41, 101, 161, 221)(42, 102, 162, 222)(43, 103, 163, 223)(44, 104, 164, 224)(45, 105, 165, 225)(46, 106, 166, 226)(47, 107, 167, 227)(48, 108, 168, 228)(49, 109, 169, 229)(50, 110, 170, 230)(51, 111, 171, 231)(52, 112, 172, 232)(53, 113, 173, 233)(54, 114, 174, 234)(55, 115, 175, 235)(56, 116, 176, 236)(57, 117, 177, 237)(58, 118, 178, 238)(59, 119, 179, 239)(60, 120, 180, 240) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 81)(8, 84)(9, 85)(10, 83)(11, 63)(12, 87)(13, 64)(14, 79)(15, 93)(16, 65)(17, 80)(18, 94)(19, 96)(20, 97)(21, 77)(22, 74)(23, 67)(24, 100)(25, 68)(26, 95)(27, 76)(28, 72)(29, 70)(30, 73)(31, 71)(32, 99)(33, 98)(34, 106)(35, 108)(36, 86)(37, 110)(38, 107)(39, 82)(40, 109)(41, 90)(42, 88)(43, 91)(44, 89)(45, 92)(46, 116)(47, 118)(48, 120)(49, 117)(50, 119)(51, 103)(52, 101)(53, 104)(54, 102)(55, 105)(56, 112)(57, 111)(58, 114)(59, 113)(60, 115)(121, 183)(122, 187)(123, 190)(124, 192)(125, 181)(126, 199)(127, 202)(128, 182)(129, 207)(130, 208)(131, 210)(132, 211)(133, 212)(134, 184)(135, 205)(136, 203)(137, 185)(138, 195)(139, 196)(140, 186)(141, 189)(142, 191)(143, 193)(144, 197)(145, 194)(146, 188)(147, 219)(148, 221)(149, 223)(150, 224)(151, 225)(152, 222)(153, 216)(154, 204)(155, 198)(156, 201)(157, 206)(158, 200)(159, 209)(160, 213)(161, 231)(162, 233)(163, 234)(164, 235)(165, 232)(166, 217)(167, 214)(168, 218)(169, 215)(170, 220)(171, 239)(172, 238)(173, 236)(174, 240)(175, 237)(176, 228)(177, 226)(178, 229)(179, 227)(180, 230) local type(s) :: { ( 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E20.872 Transitivity :: VT+ Graph:: simple bipartite v = 60 e = 120 f = 22 degree seq :: [ 4^60 ] E20.874 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 12, 12}) Quotient :: loop^2 Aut^+ = C3 x (C5 : C4) (small group id <60, 6>) Aut = C6 x (C5 : C4) (small group id <120, 40>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2^-1 * Y3, Y3 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y1, R * Y2 * R * Y1, Y2 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^-2, Y1^-1 * Y2^-1 * Y3^3, Y2^12, Y1^12 ] Map:: R = (1, 61, 121, 181, 4, 64, 124, 184, 17, 77, 137, 197, 12, 72, 132, 192, 7, 67, 127, 187)(2, 62, 122, 182, 9, 69, 129, 189, 6, 66, 126, 186, 22, 82, 142, 202, 11, 71, 131, 191)(3, 63, 123, 183, 5, 65, 125, 185, 19, 79, 139, 199, 16, 76, 136, 196, 15, 75, 135, 195)(8, 68, 128, 188, 23, 83, 143, 203, 10, 70, 130, 190, 27, 87, 147, 207, 21, 81, 141, 201)(13, 73, 133, 193, 14, 74, 134, 194, 32, 92, 152, 212, 18, 78, 138, 198, 20, 80, 140, 200)(24, 84, 144, 204, 28, 88, 148, 208, 25, 85, 145, 205, 35, 95, 155, 215, 26, 86, 146, 206)(29, 89, 149, 209, 30, 90, 150, 210, 34, 94, 154, 214, 31, 91, 151, 211, 33, 93, 153, 213)(36, 96, 156, 216, 39, 99, 159, 219, 37, 97, 157, 217, 40, 100, 160, 220, 38, 98, 158, 218)(41, 101, 161, 221, 42, 102, 162, 222, 45, 105, 165, 225, 43, 103, 163, 223, 44, 104, 164, 224)(46, 106, 166, 226, 49, 109, 169, 229, 47, 107, 167, 227, 50, 110, 170, 230, 48, 108, 168, 228)(51, 111, 171, 231, 52, 112, 172, 232, 55, 115, 175, 235, 53, 113, 173, 233, 54, 114, 174, 234)(56, 116, 176, 236, 59, 119, 179, 239, 57, 117, 177, 237, 60, 120, 180, 240, 58, 118, 178, 238) L = (1, 62)(2, 68)(3, 72)(4, 66)(5, 61)(6, 81)(7, 82)(8, 84)(9, 70)(10, 86)(11, 87)(12, 69)(13, 76)(14, 63)(15, 64)(16, 67)(17, 71)(18, 75)(19, 77)(20, 65)(21, 95)(22, 83)(23, 85)(24, 96)(25, 98)(26, 100)(27, 88)(28, 97)(29, 78)(30, 73)(31, 80)(32, 79)(33, 74)(34, 92)(35, 99)(36, 106)(37, 108)(38, 110)(39, 107)(40, 109)(41, 91)(42, 89)(43, 93)(44, 90)(45, 94)(46, 116)(47, 118)(48, 120)(49, 117)(50, 119)(51, 103)(52, 101)(53, 104)(54, 102)(55, 105)(56, 112)(57, 111)(58, 114)(59, 113)(60, 115)(121, 183)(122, 187)(123, 193)(124, 196)(125, 198)(126, 181)(127, 199)(128, 191)(129, 197)(130, 182)(131, 184)(132, 195)(133, 209)(134, 211)(135, 212)(136, 200)(137, 185)(138, 213)(139, 194)(140, 214)(141, 189)(142, 192)(143, 186)(144, 201)(145, 188)(146, 203)(147, 202)(148, 190)(149, 221)(150, 223)(151, 224)(152, 210)(153, 225)(154, 222)(155, 207)(156, 206)(157, 204)(158, 208)(159, 205)(160, 215)(161, 231)(162, 233)(163, 234)(164, 235)(165, 232)(166, 218)(167, 216)(168, 219)(169, 217)(170, 220)(171, 239)(172, 238)(173, 236)(174, 240)(175, 237)(176, 228)(177, 226)(178, 229)(179, 227)(180, 230) local type(s) :: { ( 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 E20.871 Transitivity :: VT+ Graph:: bipartite v = 12 e = 120 f = 70 degree seq :: [ 20^12 ] E20.875 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 15, 20}) Quotient :: edge Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1 * T2 * T1^-1 * T2^3, T2 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^-1 * T1, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 28, 23, 50, 59, 46, 52, 60, 47, 21, 40, 16, 5)(2, 7, 20, 35, 14, 34, 54, 27, 38, 53, 26, 9, 25, 24, 8)(4, 12, 32, 37, 15, 36, 55, 29, 39, 56, 31, 11, 30, 33, 13)(6, 17, 41, 49, 22, 48, 58, 45, 51, 57, 44, 19, 43, 42, 18)(61, 62, 66, 64)(63, 69, 77, 71)(65, 74, 78, 75)(67, 79, 72, 81)(68, 82, 73, 83)(70, 87, 101, 89)(76, 98, 102, 99)(80, 105, 92, 106)(84, 111, 93, 112)(85, 103, 90, 100)(86, 108, 91, 110)(88, 95, 109, 97)(94, 104, 96, 107)(113, 117, 116, 120)(114, 118, 115, 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) :: { ( 40^4 ), ( 40^15 ) } Outer automorphisms :: reflexible Dual of E20.879 Transitivity :: ET+ Graph:: simple bipartite v = 19 e = 60 f = 3 degree seq :: [ 4^15, 15^4 ] E20.876 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 15, 20}) Quotient :: edge Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-1 * T2^-3 * T1, T1^3 * T2 * T1 * T2^-1 * T1, (T2^-1 * T1^-1)^4, T2^20 ] Map:: non-degenerate R = (1, 3, 10, 30, 57, 49, 52, 24, 38, 21, 50, 41, 18, 36, 58, 53, 60, 47, 17, 5)(2, 7, 22, 43, 55, 27, 54, 39, 13, 37, 46, 16, 34, 11, 32, 40, 56, 35, 26, 8)(4, 12, 31, 25, 51, 23, 44, 15, 29, 9, 28, 20, 6, 19, 48, 45, 59, 33, 42, 14)(61, 62, 66, 78, 94, 111, 117, 115, 119, 120, 116, 89, 98, 73, 64)(63, 69, 87, 96, 72, 95, 109, 79, 97, 107, 83, 67, 81, 93, 71)(65, 75, 103, 101, 74, 100, 90, 80, 99, 113, 85, 68, 84, 105, 76)(70, 82, 108, 118, 92, 104, 112, 114, 102, 77, 86, 88, 110, 106, 91) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^15 ), ( 8^20 ) } Outer automorphisms :: reflexible Dual of E20.880 Transitivity :: ET+ Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 15^4, 20^3 ] E20.877 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 15, 20}) Quotient :: edge Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^2, T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T1^2 * T2^2)^5, T1^20 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 27, 14)(6, 18, 39, 19)(9, 25, 15, 26)(11, 28, 16, 30)(13, 29, 49, 33)(17, 36, 54, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 40, 34, 38)(32, 45, 57, 47)(35, 52, 60, 53)(46, 51, 48, 58)(50, 55, 59, 56)(61, 62, 66, 77, 95, 111, 119, 117, 109, 87, 70, 81, 99, 114, 120, 118, 110, 92, 73, 64)(63, 69, 78, 98, 112, 104, 116, 102, 93, 76, 65, 75, 79, 100, 113, 103, 115, 101, 89, 71)(67, 80, 96, 90, 108, 86, 107, 94, 74, 84, 68, 83, 97, 88, 106, 85, 105, 91, 72, 82) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30^4 ), ( 30^20 ) } Outer automorphisms :: reflexible Dual of E20.878 Transitivity :: ET+ Graph:: bipartite v = 18 e = 60 f = 4 degree seq :: [ 4^15, 20^3 ] E20.878 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 15, 20}) Quotient :: loop Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1 * T2 * T1^-1 * T2^3, T2 * T1 * T2^-2 * T1 * T2^2 * T1 * T2^-1 * T1, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 28, 88, 23, 83, 50, 110, 59, 119, 46, 106, 52, 112, 60, 120, 47, 107, 21, 81, 40, 100, 16, 76, 5, 65)(2, 62, 7, 67, 20, 80, 35, 95, 14, 74, 34, 94, 54, 114, 27, 87, 38, 98, 53, 113, 26, 86, 9, 69, 25, 85, 24, 84, 8, 68)(4, 64, 12, 72, 32, 92, 37, 97, 15, 75, 36, 96, 55, 115, 29, 89, 39, 99, 56, 116, 31, 91, 11, 71, 30, 90, 33, 93, 13, 73)(6, 66, 17, 77, 41, 101, 49, 109, 22, 82, 48, 108, 58, 118, 45, 105, 51, 111, 57, 117, 44, 104, 19, 79, 43, 103, 42, 102, 18, 78) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 74)(6, 64)(7, 79)(8, 82)(9, 77)(10, 87)(11, 63)(12, 81)(13, 83)(14, 78)(15, 65)(16, 98)(17, 71)(18, 75)(19, 72)(20, 105)(21, 67)(22, 73)(23, 68)(24, 111)(25, 103)(26, 108)(27, 101)(28, 95)(29, 70)(30, 100)(31, 110)(32, 106)(33, 112)(34, 104)(35, 109)(36, 107)(37, 88)(38, 102)(39, 76)(40, 85)(41, 89)(42, 99)(43, 90)(44, 96)(45, 92)(46, 80)(47, 94)(48, 91)(49, 97)(50, 86)(51, 93)(52, 84)(53, 117)(54, 118)(55, 119)(56, 120)(57, 116)(58, 115)(59, 114)(60, 113) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.877 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 60 f = 18 degree seq :: [ 30^4 ] E20.879 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 15, 20}) Quotient :: loop Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-1 * T2^-3 * T1, T1^3 * T2 * T1 * T2^-1 * T1, (T2^-1 * T1^-1)^4, T2^20 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 30, 90, 57, 117, 49, 109, 52, 112, 24, 84, 38, 98, 21, 81, 50, 110, 41, 101, 18, 78, 36, 96, 58, 118, 53, 113, 60, 120, 47, 107, 17, 77, 5, 65)(2, 62, 7, 67, 22, 82, 43, 103, 55, 115, 27, 87, 54, 114, 39, 99, 13, 73, 37, 97, 46, 106, 16, 76, 34, 94, 11, 71, 32, 92, 40, 100, 56, 116, 35, 95, 26, 86, 8, 68)(4, 64, 12, 72, 31, 91, 25, 85, 51, 111, 23, 83, 44, 104, 15, 75, 29, 89, 9, 69, 28, 88, 20, 80, 6, 66, 19, 79, 48, 108, 45, 105, 59, 119, 33, 93, 42, 102, 14, 74) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 81)(8, 84)(9, 87)(10, 82)(11, 63)(12, 95)(13, 64)(14, 100)(15, 103)(16, 65)(17, 86)(18, 94)(19, 97)(20, 99)(21, 93)(22, 108)(23, 67)(24, 105)(25, 68)(26, 88)(27, 96)(28, 110)(29, 98)(30, 80)(31, 70)(32, 104)(33, 71)(34, 111)(35, 109)(36, 72)(37, 107)(38, 73)(39, 113)(40, 90)(41, 74)(42, 77)(43, 101)(44, 112)(45, 76)(46, 91)(47, 83)(48, 118)(49, 79)(50, 106)(51, 117)(52, 114)(53, 85)(54, 102)(55, 119)(56, 89)(57, 115)(58, 92)(59, 120)(60, 116) local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E20.875 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 60 f = 19 degree seq :: [ 40^3 ] E20.880 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 15, 20}) Quotient :: loop Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^2, T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T1^2 * T2^2)^5, T1^20 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 5, 65)(2, 62, 7, 67, 21, 81, 8, 68)(4, 64, 12, 72, 27, 87, 14, 74)(6, 66, 18, 78, 39, 99, 19, 79)(9, 69, 25, 85, 15, 75, 26, 86)(11, 71, 28, 88, 16, 76, 30, 90)(13, 73, 29, 89, 49, 109, 33, 93)(17, 77, 36, 96, 54, 114, 37, 97)(20, 80, 41, 101, 23, 83, 42, 102)(22, 82, 43, 103, 24, 84, 44, 104)(31, 91, 40, 100, 34, 94, 38, 98)(32, 92, 45, 105, 57, 117, 47, 107)(35, 95, 52, 112, 60, 120, 53, 113)(46, 106, 51, 111, 48, 108, 58, 118)(50, 110, 55, 115, 59, 119, 56, 116) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 77)(7, 80)(8, 83)(9, 78)(10, 81)(11, 63)(12, 82)(13, 64)(14, 84)(15, 79)(16, 65)(17, 95)(18, 98)(19, 100)(20, 96)(21, 99)(22, 67)(23, 97)(24, 68)(25, 105)(26, 107)(27, 70)(28, 106)(29, 71)(30, 108)(31, 72)(32, 73)(33, 76)(34, 74)(35, 111)(36, 90)(37, 88)(38, 112)(39, 114)(40, 113)(41, 89)(42, 93)(43, 115)(44, 116)(45, 91)(46, 85)(47, 94)(48, 86)(49, 87)(50, 92)(51, 119)(52, 104)(53, 103)(54, 120)(55, 101)(56, 102)(57, 109)(58, 110)(59, 117)(60, 118) local type(s) :: { ( 15, 20, 15, 20, 15, 20, 15, 20 ) } Outer automorphisms :: reflexible Dual of E20.876 Transitivity :: ET+ VT+ AT Graph:: v = 15 e = 60 f = 7 degree seq :: [ 8^15 ] E20.881 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 15, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^4, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^2 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^-4, Y2^3 * Y1 * Y2^-3 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-2)^2, Y2^2 * Y3 * Y2^-2 * Y3^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^20 ] Map:: R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 9, 69, 17, 77, 11, 71)(5, 65, 14, 74, 18, 78, 15, 75)(7, 67, 19, 79, 12, 72, 21, 81)(8, 68, 22, 82, 13, 73, 23, 83)(10, 70, 27, 87, 41, 101, 29, 89)(16, 76, 38, 98, 42, 102, 39, 99)(20, 80, 45, 105, 32, 92, 46, 106)(24, 84, 51, 111, 33, 93, 52, 112)(25, 85, 43, 103, 30, 90, 40, 100)(26, 86, 48, 108, 31, 91, 50, 110)(28, 88, 35, 95, 49, 109, 37, 97)(34, 94, 44, 104, 36, 96, 47, 107)(53, 113, 57, 117, 56, 116, 60, 120)(54, 114, 58, 118, 55, 115, 59, 119)(121, 181, 123, 183, 130, 190, 148, 208, 143, 203, 170, 230, 179, 239, 166, 226, 172, 232, 180, 240, 167, 227, 141, 201, 160, 220, 136, 196, 125, 185)(122, 182, 127, 187, 140, 200, 155, 215, 134, 194, 154, 214, 174, 234, 147, 207, 158, 218, 173, 233, 146, 206, 129, 189, 145, 205, 144, 204, 128, 188)(124, 184, 132, 192, 152, 212, 157, 217, 135, 195, 156, 216, 175, 235, 149, 209, 159, 219, 176, 236, 151, 211, 131, 191, 150, 210, 153, 213, 133, 193)(126, 186, 137, 197, 161, 221, 169, 229, 142, 202, 168, 228, 178, 238, 165, 225, 171, 231, 177, 237, 164, 224, 139, 199, 163, 223, 162, 222, 138, 198) L = (1, 124)(2, 121)(3, 131)(4, 126)(5, 135)(6, 122)(7, 141)(8, 143)(9, 123)(10, 149)(11, 137)(12, 139)(13, 142)(14, 125)(15, 138)(16, 159)(17, 129)(18, 134)(19, 127)(20, 166)(21, 132)(22, 128)(23, 133)(24, 172)(25, 160)(26, 170)(27, 130)(28, 157)(29, 161)(30, 163)(31, 168)(32, 165)(33, 171)(34, 167)(35, 148)(36, 164)(37, 169)(38, 136)(39, 162)(40, 150)(41, 147)(42, 158)(43, 145)(44, 154)(45, 140)(46, 152)(47, 156)(48, 146)(49, 155)(50, 151)(51, 144)(52, 153)(53, 180)(54, 179)(55, 178)(56, 177)(57, 173)(58, 174)(59, 175)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E20.884 Graph:: bipartite v = 19 e = 120 f = 63 degree seq :: [ 8^15, 30^4 ] E20.882 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 15, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1^-1 * Y2^2 * Y1, Y1^4 * Y2^-1 * Y1 * Y2, Y1 * Y2^-1 * Y1^-1 * Y2^-3 * Y1, (Y3^-1 * Y1^-1)^4, Y2^20 ] Map:: R = (1, 61, 2, 62, 6, 66, 18, 78, 34, 94, 51, 111, 57, 117, 55, 115, 59, 119, 60, 120, 56, 116, 29, 89, 38, 98, 13, 73, 4, 64)(3, 63, 9, 69, 27, 87, 36, 96, 12, 72, 35, 95, 49, 109, 19, 79, 37, 97, 47, 107, 23, 83, 7, 67, 21, 81, 33, 93, 11, 71)(5, 65, 15, 75, 43, 103, 41, 101, 14, 74, 40, 100, 30, 90, 20, 80, 39, 99, 53, 113, 25, 85, 8, 68, 24, 84, 45, 105, 16, 76)(10, 70, 22, 82, 48, 108, 58, 118, 32, 92, 44, 104, 52, 112, 54, 114, 42, 102, 17, 77, 26, 86, 28, 88, 50, 110, 46, 106, 31, 91)(121, 181, 123, 183, 130, 190, 150, 210, 177, 237, 169, 229, 172, 232, 144, 204, 158, 218, 141, 201, 170, 230, 161, 221, 138, 198, 156, 216, 178, 238, 173, 233, 180, 240, 167, 227, 137, 197, 125, 185)(122, 182, 127, 187, 142, 202, 163, 223, 175, 235, 147, 207, 174, 234, 159, 219, 133, 193, 157, 217, 166, 226, 136, 196, 154, 214, 131, 191, 152, 212, 160, 220, 176, 236, 155, 215, 146, 206, 128, 188)(124, 184, 132, 192, 151, 211, 145, 205, 171, 231, 143, 203, 164, 224, 135, 195, 149, 209, 129, 189, 148, 208, 140, 200, 126, 186, 139, 199, 168, 228, 165, 225, 179, 239, 153, 213, 162, 222, 134, 194) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 142)(8, 122)(9, 148)(10, 150)(11, 152)(12, 151)(13, 157)(14, 124)(15, 149)(16, 154)(17, 125)(18, 156)(19, 168)(20, 126)(21, 170)(22, 163)(23, 164)(24, 158)(25, 171)(26, 128)(27, 174)(28, 140)(29, 129)(30, 177)(31, 145)(32, 160)(33, 162)(34, 131)(35, 146)(36, 178)(37, 166)(38, 141)(39, 133)(40, 176)(41, 138)(42, 134)(43, 175)(44, 135)(45, 179)(46, 136)(47, 137)(48, 165)(49, 172)(50, 161)(51, 143)(52, 144)(53, 180)(54, 159)(55, 147)(56, 155)(57, 169)(58, 173)(59, 153)(60, 167)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E20.883 Graph:: bipartite v = 7 e = 120 f = 75 degree seq :: [ 30^4, 40^3 ] E20.883 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 15, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^2 * Y2^-1 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2 * Y3^3 * Y2^-1, Y3^-2 * Y2^-2 * Y3^-1 * Y2^-3 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^20 ] 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, 129, 189, 137, 197, 131, 191)(125, 185, 134, 194, 138, 198, 135, 195)(127, 187, 139, 199, 132, 192, 141, 201)(128, 188, 142, 202, 133, 193, 143, 203)(130, 190, 140, 200, 155, 215, 148, 208)(136, 196, 144, 204, 156, 216, 151, 211)(145, 205, 165, 225, 149, 209, 164, 224)(146, 206, 166, 226, 150, 210, 167, 227)(147, 207, 162, 222, 171, 231, 163, 223)(152, 212, 159, 219, 153, 213, 169, 229)(154, 214, 160, 220, 172, 232, 157, 217)(158, 218, 173, 233, 161, 221, 174, 234)(168, 228, 175, 235, 179, 239, 178, 238)(170, 230, 176, 236, 180, 240, 177, 237) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 137)(7, 140)(8, 122)(9, 145)(10, 147)(11, 149)(12, 148)(13, 124)(14, 146)(15, 150)(16, 125)(17, 155)(18, 126)(19, 157)(20, 159)(21, 160)(22, 158)(23, 161)(24, 128)(25, 162)(26, 129)(27, 168)(28, 169)(29, 163)(30, 131)(31, 133)(32, 134)(33, 135)(34, 136)(35, 171)(36, 138)(37, 153)(38, 139)(39, 175)(40, 152)(41, 141)(42, 142)(43, 143)(44, 144)(45, 151)(46, 177)(47, 176)(48, 174)(49, 178)(50, 154)(51, 179)(52, 156)(53, 170)(54, 180)(55, 166)(56, 164)(57, 165)(58, 167)(59, 173)(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) :: { ( 30, 40 ), ( 30, 40, 30, 40, 30, 40, 30, 40 ) } Outer automorphisms :: reflexible Dual of E20.882 Graph:: simple bipartite v = 75 e = 120 f = 7 degree seq :: [ 2^60, 8^15 ] E20.884 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 15, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3^2 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2^-1)^4, Y1^20, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 61, 2, 62, 6, 66, 17, 77, 35, 95, 51, 111, 59, 119, 57, 117, 49, 109, 27, 87, 10, 70, 21, 81, 39, 99, 54, 114, 60, 120, 58, 118, 50, 110, 32, 92, 13, 73, 4, 64)(3, 63, 9, 69, 18, 78, 38, 98, 52, 112, 44, 104, 56, 116, 42, 102, 33, 93, 16, 76, 5, 65, 15, 75, 19, 79, 40, 100, 53, 113, 43, 103, 55, 115, 41, 101, 29, 89, 11, 71)(7, 67, 20, 80, 36, 96, 30, 90, 48, 108, 26, 86, 47, 107, 34, 94, 14, 74, 24, 84, 8, 68, 23, 83, 37, 97, 28, 88, 46, 106, 25, 85, 45, 105, 31, 91, 12, 72, 22, 82)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 138)(7, 141)(8, 122)(9, 145)(10, 125)(11, 148)(12, 147)(13, 149)(14, 124)(15, 146)(16, 150)(17, 156)(18, 159)(19, 126)(20, 161)(21, 128)(22, 163)(23, 162)(24, 164)(25, 135)(26, 129)(27, 134)(28, 136)(29, 169)(30, 131)(31, 160)(32, 165)(33, 133)(34, 158)(35, 172)(36, 174)(37, 137)(38, 151)(39, 139)(40, 154)(41, 143)(42, 140)(43, 144)(44, 142)(45, 177)(46, 171)(47, 152)(48, 178)(49, 153)(50, 175)(51, 168)(52, 180)(53, 155)(54, 157)(55, 179)(56, 170)(57, 167)(58, 166)(59, 176)(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) :: { ( 8, 30 ), ( 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30, 8, 30 ) } Outer automorphisms :: reflexible Dual of E20.881 Graph:: simple bipartite v = 63 e = 120 f = 19 degree seq :: [ 2^60, 40^3 ] E20.885 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 15, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-3, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y2^2 * Y3 * Y2^-2 * Y3^-1, (Y2^-1 * R * Y2^-1)^2, Y1 * Y2^-3 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y2^20, (Y3 * Y2^-1)^15 ] Map:: R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 9, 69, 17, 77, 11, 71)(5, 65, 14, 74, 18, 78, 15, 75)(7, 67, 19, 79, 12, 72, 21, 81)(8, 68, 22, 82, 13, 73, 23, 83)(10, 70, 20, 80, 35, 95, 28, 88)(16, 76, 24, 84, 36, 96, 31, 91)(25, 85, 44, 104, 29, 89, 45, 105)(26, 86, 46, 106, 30, 90, 47, 107)(27, 87, 43, 103, 51, 111, 42, 102)(32, 92, 49, 109, 33, 93, 39, 99)(34, 94, 37, 97, 52, 112, 40, 100)(38, 98, 53, 113, 41, 101, 54, 114)(48, 108, 55, 115, 59, 119, 58, 118)(50, 110, 56, 116, 60, 120, 57, 117)(121, 181, 123, 183, 130, 190, 147, 207, 168, 228, 173, 233, 180, 240, 172, 232, 156, 216, 138, 198, 126, 186, 137, 197, 155, 215, 171, 231, 179, 239, 174, 234, 170, 230, 154, 214, 136, 196, 125, 185)(122, 182, 127, 187, 140, 200, 159, 219, 175, 235, 167, 227, 177, 237, 165, 225, 151, 211, 133, 193, 124, 184, 132, 192, 148, 208, 169, 229, 178, 238, 166, 226, 176, 236, 164, 224, 144, 204, 128, 188)(129, 189, 145, 205, 163, 223, 143, 203, 161, 221, 141, 201, 160, 220, 153, 213, 135, 195, 150, 210, 131, 191, 149, 209, 162, 222, 142, 202, 158, 218, 139, 199, 157, 217, 152, 212, 134, 194, 146, 206) L = (1, 124)(2, 121)(3, 131)(4, 126)(5, 135)(6, 122)(7, 141)(8, 143)(9, 123)(10, 148)(11, 137)(12, 139)(13, 142)(14, 125)(15, 138)(16, 151)(17, 129)(18, 134)(19, 127)(20, 130)(21, 132)(22, 128)(23, 133)(24, 136)(25, 165)(26, 167)(27, 162)(28, 155)(29, 164)(30, 166)(31, 156)(32, 159)(33, 169)(34, 160)(35, 140)(36, 144)(37, 154)(38, 174)(39, 153)(40, 172)(41, 173)(42, 171)(43, 147)(44, 145)(45, 149)(46, 146)(47, 150)(48, 178)(49, 152)(50, 177)(51, 163)(52, 157)(53, 158)(54, 161)(55, 168)(56, 170)(57, 180)(58, 179)(59, 175)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E20.886 Graph:: bipartite v = 18 e = 120 f = 64 degree seq :: [ 8^15, 40^3 ] E20.886 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 15, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^2 * Y1 * Y3^-1, Y1^3 * Y3 * Y1 * Y3^-1 * Y1, Y1 * Y3^-1 * Y1^-1 * Y3^-3 * Y1, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^20 ] Map:: R = (1, 61, 2, 62, 6, 66, 18, 78, 34, 94, 51, 111, 57, 117, 55, 115, 59, 119, 60, 120, 56, 116, 29, 89, 38, 98, 13, 73, 4, 64)(3, 63, 9, 69, 27, 87, 36, 96, 12, 72, 35, 95, 49, 109, 19, 79, 37, 97, 47, 107, 23, 83, 7, 67, 21, 81, 33, 93, 11, 71)(5, 65, 15, 75, 43, 103, 41, 101, 14, 74, 40, 100, 30, 90, 20, 80, 39, 99, 53, 113, 25, 85, 8, 68, 24, 84, 45, 105, 16, 76)(10, 70, 22, 82, 48, 108, 58, 118, 32, 92, 44, 104, 52, 112, 54, 114, 42, 102, 17, 77, 26, 86, 28, 88, 50, 110, 46, 106, 31, 91)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 142)(8, 122)(9, 148)(10, 150)(11, 152)(12, 151)(13, 157)(14, 124)(15, 149)(16, 154)(17, 125)(18, 156)(19, 168)(20, 126)(21, 170)(22, 163)(23, 164)(24, 158)(25, 171)(26, 128)(27, 174)(28, 140)(29, 129)(30, 177)(31, 145)(32, 160)(33, 162)(34, 131)(35, 146)(36, 178)(37, 166)(38, 141)(39, 133)(40, 176)(41, 138)(42, 134)(43, 175)(44, 135)(45, 179)(46, 136)(47, 137)(48, 165)(49, 172)(50, 161)(51, 143)(52, 144)(53, 180)(54, 159)(55, 147)(56, 155)(57, 169)(58, 173)(59, 153)(60, 167)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) } Outer automorphisms :: reflexible Dual of E20.885 Graph:: simple bipartite v = 64 e = 120 f = 18 degree seq :: [ 2^60, 30^4 ] E20.887 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 30}) Quotient :: dipole Aut^+ = C6 x D10 (small group id <60, 10>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^10 ] Map:: non-degenerate R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 10, 70)(5, 65, 9, 69)(6, 66, 8, 68)(11, 71, 18, 78)(12, 72, 17, 77)(13, 73, 22, 82)(14, 74, 21, 81)(15, 75, 20, 80)(16, 76, 19, 79)(23, 83, 30, 90)(24, 84, 29, 89)(25, 85, 34, 94)(26, 86, 33, 93)(27, 87, 32, 92)(28, 88, 31, 91)(35, 95, 42, 102)(36, 96, 41, 101)(37, 97, 46, 106)(38, 98, 45, 105)(39, 99, 44, 104)(40, 100, 43, 103)(47, 107, 53, 113)(48, 108, 52, 112)(49, 109, 54, 114)(50, 110, 56, 116)(51, 111, 55, 115)(57, 117, 59, 119)(58, 118, 60, 120)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 131, 191, 134, 194)(126, 186, 132, 192, 135, 195)(128, 188, 137, 197, 140, 200)(130, 190, 138, 198, 141, 201)(133, 193, 143, 203, 146, 206)(136, 196, 144, 204, 147, 207)(139, 199, 149, 209, 152, 212)(142, 202, 150, 210, 153, 213)(145, 205, 155, 215, 158, 218)(148, 208, 156, 216, 159, 219)(151, 211, 161, 221, 164, 224)(154, 214, 162, 222, 165, 225)(157, 217, 167, 227, 170, 230)(160, 220, 168, 228, 171, 231)(163, 223, 172, 232, 175, 235)(166, 226, 173, 233, 176, 236)(169, 229, 177, 237, 178, 238)(174, 234, 179, 239, 180, 240) L = (1, 124)(2, 128)(3, 131)(4, 133)(5, 134)(6, 121)(7, 137)(8, 139)(9, 140)(10, 122)(11, 143)(12, 123)(13, 145)(14, 146)(15, 125)(16, 126)(17, 149)(18, 127)(19, 151)(20, 152)(21, 129)(22, 130)(23, 155)(24, 132)(25, 157)(26, 158)(27, 135)(28, 136)(29, 161)(30, 138)(31, 163)(32, 164)(33, 141)(34, 142)(35, 167)(36, 144)(37, 169)(38, 170)(39, 147)(40, 148)(41, 172)(42, 150)(43, 174)(44, 175)(45, 153)(46, 154)(47, 177)(48, 156)(49, 160)(50, 178)(51, 159)(52, 179)(53, 162)(54, 166)(55, 180)(56, 165)(57, 168)(58, 171)(59, 173)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E20.888 Graph:: simple bipartite v = 50 e = 120 f = 32 degree seq :: [ 4^30, 6^20 ] E20.888 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 30}) Quotient :: dipole Aut^+ = C6 x D10 (small group id <60, 10>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1, Y3^-1), (Y2 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y1^-3 * Y3^-3, Y1^2 * Y2 * Y1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, Y3 * R * Y2 * Y1^-1 * Y2 * R * Y1^2, Y1^-6 * Y3^4, Y3^20 ] Map:: non-degenerate R = (1, 61, 2, 62, 7, 67, 21, 81, 37, 97, 49, 109, 46, 106, 36, 96, 16, 76, 4, 64, 9, 69, 23, 83, 20, 80, 30, 90, 42, 102, 54, 114, 48, 108, 35, 95, 15, 75, 29, 89, 19, 79, 6, 66, 10, 70, 24, 84, 39, 99, 51, 111, 47, 107, 34, 94, 18, 78, 5, 65)(3, 63, 11, 71, 31, 91, 43, 103, 55, 115, 58, 118, 52, 112, 41, 101, 22, 82, 12, 72, 28, 88, 17, 77, 33, 93, 45, 105, 57, 117, 60, 120, 50, 110, 40, 100, 27, 87, 8, 68, 25, 85, 14, 74, 32, 92, 44, 104, 56, 116, 59, 119, 53, 113, 38, 98, 26, 86, 13, 73)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 134, 194)(125, 185, 137, 197)(126, 186, 132, 192)(127, 187, 142, 202)(129, 189, 148, 208)(130, 190, 146, 206)(131, 191, 149, 209)(133, 193, 143, 203)(135, 195, 153, 213)(136, 196, 151, 211)(138, 198, 152, 212)(139, 199, 145, 205)(140, 200, 147, 207)(141, 201, 158, 218)(144, 204, 160, 220)(150, 210, 161, 221)(154, 214, 163, 223)(155, 215, 164, 224)(156, 216, 165, 225)(157, 217, 170, 230)(159, 219, 172, 232)(162, 222, 173, 233)(166, 226, 176, 236)(167, 227, 177, 237)(168, 228, 175, 235)(169, 229, 178, 238)(171, 231, 179, 239)(174, 234, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 135)(5, 136)(6, 121)(7, 143)(8, 146)(9, 149)(10, 122)(11, 148)(12, 147)(13, 142)(14, 123)(15, 154)(16, 155)(17, 145)(18, 156)(19, 125)(20, 126)(21, 140)(22, 160)(23, 139)(24, 127)(25, 133)(26, 161)(27, 158)(28, 128)(29, 138)(30, 130)(31, 137)(32, 131)(33, 134)(34, 166)(35, 167)(36, 168)(37, 150)(38, 172)(39, 141)(40, 173)(41, 170)(42, 144)(43, 153)(44, 151)(45, 152)(46, 174)(47, 169)(48, 171)(49, 162)(50, 179)(51, 157)(52, 180)(53, 178)(54, 159)(55, 165)(56, 163)(57, 164)(58, 177)(59, 175)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E20.887 Graph:: bipartite v = 32 e = 120 f = 50 degree seq :: [ 4^30, 60^2 ] E20.889 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 30}) Quotient :: halfedge^2 Aut^+ = D60 (small group id <60, 12>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y3)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2 * Y1)^2, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3, Y1^4 * Y2 * Y1^-5 * Y3, Y1^-1 * Y3 * Y1^2 * Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 ] Map:: non-degenerate R = (1, 62, 2, 66, 6, 74, 14, 86, 26, 102, 42, 110, 50, 98, 38, 83, 23, 72, 12, 78, 18, 90, 30, 96, 36, 107, 47, 116, 56, 120, 60, 119, 59, 112, 52, 100, 40, 94, 34, 80, 20, 70, 10, 77, 17, 89, 29, 105, 45, 113, 53, 101, 41, 85, 25, 73, 13, 65, 5, 61)(3, 69, 9, 79, 19, 93, 33, 108, 48, 117, 57, 115, 55, 106, 46, 91, 31, 81, 21, 95, 35, 92, 32, 84, 24, 99, 39, 111, 51, 118, 58, 114, 54, 104, 44, 88, 28, 76, 16, 68, 8, 64, 4, 71, 11, 82, 22, 97, 37, 109, 49, 103, 43, 87, 27, 75, 15, 67, 7, 63) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 43)(28, 36)(29, 46)(32, 34)(37, 50)(39, 52)(41, 48)(42, 49)(44, 47)(45, 55)(51, 59)(53, 57)(54, 56)(58, 60)(61, 64)(62, 68)(63, 70)(65, 71)(66, 76)(67, 77)(69, 80)(72, 84)(73, 82)(74, 88)(75, 89)(78, 92)(79, 94)(81, 96)(83, 99)(85, 97)(86, 104)(87, 105)(90, 95)(91, 107)(93, 100)(98, 111)(101, 109)(102, 114)(103, 113)(106, 116)(108, 112)(110, 118)(115, 120)(117, 119) local type(s) :: { ( 6^60 ) } Outer automorphisms :: reflexible Dual of E20.890 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 60 f = 20 degree seq :: [ 60^2 ] E20.890 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 30}) Quotient :: halfedge^2 Aut^+ = D60 (small group id <60, 12>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1)^2, (Y3 * Y2)^10, (Y2 * Y1 * Y3)^30 ] Map:: non-degenerate R = (1, 62, 2, 65, 5, 61)(3, 68, 8, 66, 6, 63)(4, 70, 10, 67, 7, 64)(9, 72, 12, 74, 14, 69)(11, 73, 13, 76, 16, 71)(15, 80, 20, 78, 18, 75)(17, 82, 22, 79, 19, 77)(21, 84, 24, 86, 26, 81)(23, 85, 25, 88, 28, 83)(27, 92, 32, 90, 30, 87)(29, 94, 34, 91, 31, 89)(33, 96, 36, 98, 38, 93)(35, 97, 37, 100, 40, 95)(39, 104, 44, 102, 42, 99)(41, 106, 46, 103, 43, 101)(45, 108, 48, 110, 50, 105)(47, 109, 49, 112, 52, 107)(51, 116, 56, 114, 54, 111)(53, 118, 58, 115, 55, 113)(57, 119, 59, 120, 60, 117) L = (1, 3)(2, 6)(4, 11)(5, 8)(7, 13)(9, 15)(10, 16)(12, 18)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 35)(31, 37)(33, 39)(34, 40)(36, 42)(38, 44)(41, 47)(43, 49)(45, 51)(46, 52)(48, 54)(50, 56)(53, 57)(55, 59)(58, 60)(61, 64)(62, 67)(63, 69)(65, 70)(66, 72)(68, 74)(71, 77)(73, 79)(75, 81)(76, 82)(78, 84)(80, 86)(83, 89)(85, 91)(87, 93)(88, 94)(90, 96)(92, 98)(95, 101)(97, 103)(99, 105)(100, 106)(102, 108)(104, 110)(107, 113)(109, 115)(111, 117)(112, 118)(114, 119)(116, 120) local type(s) :: { ( 60^6 ) } Outer automorphisms :: reflexible Dual of E20.889 Transitivity :: VT+ AT Graph:: bipartite v = 20 e = 60 f = 2 degree seq :: [ 6^20 ] E20.891 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 30}) Quotient :: edge^2 Aut^+ = D60 (small group id <60, 12>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, (Y2 * Y1)^10, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 61, 4, 64, 5, 65)(2, 62, 7, 67, 8, 68)(3, 63, 10, 70, 11, 71)(6, 66, 13, 73, 14, 74)(9, 69, 16, 76, 17, 77)(12, 72, 19, 79, 20, 80)(15, 75, 22, 82, 23, 83)(18, 78, 25, 85, 26, 86)(21, 81, 28, 88, 29, 89)(24, 84, 31, 91, 32, 92)(27, 87, 34, 94, 35, 95)(30, 90, 37, 97, 38, 98)(33, 93, 40, 100, 41, 101)(36, 96, 43, 103, 44, 104)(39, 99, 46, 106, 47, 107)(42, 102, 49, 109, 50, 110)(45, 105, 52, 112, 53, 113)(48, 108, 55, 115, 56, 116)(51, 111, 57, 117, 58, 118)(54, 114, 59, 119, 60, 120)(121, 122)(123, 129)(124, 128)(125, 127)(126, 132)(130, 137)(131, 136)(133, 140)(134, 139)(135, 141)(138, 144)(142, 149)(143, 148)(145, 152)(146, 151)(147, 153)(150, 156)(154, 161)(155, 160)(157, 164)(158, 163)(159, 165)(162, 168)(166, 173)(167, 172)(169, 176)(170, 175)(171, 174)(177, 180)(178, 179)(181, 183)(182, 186)(184, 191)(185, 190)(187, 194)(188, 193)(189, 195)(192, 198)(196, 203)(197, 202)(199, 206)(200, 205)(201, 207)(204, 210)(208, 215)(209, 214)(211, 218)(212, 217)(213, 219)(216, 222)(220, 227)(221, 226)(223, 230)(224, 229)(225, 231)(228, 234)(232, 238)(233, 237)(235, 240)(236, 239) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 120, 120 ), ( 120^6 ) } Outer automorphisms :: reflexible Dual of E20.894 Graph:: simple bipartite v = 80 e = 120 f = 2 degree seq :: [ 2^60, 6^20 ] E20.892 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 30}) Quotient :: edge^2 Aut^+ = D60 (small group id <60, 12>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, (Y3 * Y1 * Y2)^3, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3^8 ] Map:: R = (1, 61, 4, 64, 12, 72, 24, 84, 40, 100, 52, 112, 44, 104, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 33, 93, 47, 107, 57, 117, 60, 120, 54, 114, 42, 102, 26, 86, 37, 97, 21, 81, 9, 69, 20, 80, 36, 96, 49, 109, 53, 113, 41, 101, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 45, 105, 51, 111, 39, 99, 23, 83, 11, 71, 3, 63, 10, 70, 22, 82, 38, 98, 50, 110, 59, 119, 58, 118, 48, 108, 35, 95, 19, 79, 34, 94, 28, 88, 14, 74, 27, 87, 43, 103, 55, 115, 56, 116, 46, 106, 32, 92, 18, 78, 8, 68)(121, 122)(123, 129)(124, 128)(125, 127)(126, 134)(130, 141)(131, 140)(132, 138)(133, 137)(135, 148)(136, 147)(139, 153)(142, 157)(143, 156)(144, 152)(145, 151)(146, 158)(149, 154)(150, 163)(155, 167)(159, 169)(160, 166)(161, 165)(162, 170)(164, 175)(168, 177)(171, 173)(172, 176)(174, 179)(178, 180)(181, 183)(182, 186)(184, 191)(185, 190)(187, 196)(188, 195)(189, 199)(192, 203)(193, 202)(194, 206)(197, 210)(198, 209)(200, 215)(201, 214)(204, 219)(205, 218)(207, 222)(208, 217)(211, 224)(212, 213)(216, 228)(220, 231)(221, 230)(223, 234)(225, 232)(226, 227)(229, 238)(233, 239)(235, 240)(236, 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) :: { ( 12, 12 ), ( 12^60 ) } Outer automorphisms :: reflexible Dual of E20.893 Graph:: simple bipartite v = 62 e = 120 f = 20 degree seq :: [ 2^60, 60^2 ] E20.893 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 30}) Quotient :: loop^2 Aut^+ = D60 (small group id <60, 12>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, (Y2 * Y1)^10, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] 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, 13, 73, 133, 193, 14, 74, 134, 194)(9, 69, 129, 189, 16, 76, 136, 196, 17, 77, 137, 197)(12, 72, 132, 192, 19, 79, 139, 199, 20, 80, 140, 200)(15, 75, 135, 195, 22, 82, 142, 202, 23, 83, 143, 203)(18, 78, 138, 198, 25, 85, 145, 205, 26, 86, 146, 206)(21, 81, 141, 201, 28, 88, 148, 208, 29, 89, 149, 209)(24, 84, 144, 204, 31, 91, 151, 211, 32, 92, 152, 212)(27, 87, 147, 207, 34, 94, 154, 214, 35, 95, 155, 215)(30, 90, 150, 210, 37, 97, 157, 217, 38, 98, 158, 218)(33, 93, 153, 213, 40, 100, 160, 220, 41, 101, 161, 221)(36, 96, 156, 216, 43, 103, 163, 223, 44, 104, 164, 224)(39, 99, 159, 219, 46, 106, 166, 226, 47, 107, 167, 227)(42, 102, 162, 222, 49, 109, 169, 229, 50, 110, 170, 230)(45, 105, 165, 225, 52, 112, 172, 232, 53, 113, 173, 233)(48, 108, 168, 228, 55, 115, 175, 235, 56, 116, 176, 236)(51, 111, 171, 231, 57, 117, 177, 237, 58, 118, 178, 238)(54, 114, 174, 234, 59, 119, 179, 239, 60, 120, 180, 240) L = (1, 62)(2, 61)(3, 69)(4, 68)(5, 67)(6, 72)(7, 65)(8, 64)(9, 63)(10, 77)(11, 76)(12, 66)(13, 80)(14, 79)(15, 81)(16, 71)(17, 70)(18, 84)(19, 74)(20, 73)(21, 75)(22, 89)(23, 88)(24, 78)(25, 92)(26, 91)(27, 93)(28, 83)(29, 82)(30, 96)(31, 86)(32, 85)(33, 87)(34, 101)(35, 100)(36, 90)(37, 104)(38, 103)(39, 105)(40, 95)(41, 94)(42, 108)(43, 98)(44, 97)(45, 99)(46, 113)(47, 112)(48, 102)(49, 116)(50, 115)(51, 114)(52, 107)(53, 106)(54, 111)(55, 110)(56, 109)(57, 120)(58, 119)(59, 118)(60, 117)(121, 183)(122, 186)(123, 181)(124, 191)(125, 190)(126, 182)(127, 194)(128, 193)(129, 195)(130, 185)(131, 184)(132, 198)(133, 188)(134, 187)(135, 189)(136, 203)(137, 202)(138, 192)(139, 206)(140, 205)(141, 207)(142, 197)(143, 196)(144, 210)(145, 200)(146, 199)(147, 201)(148, 215)(149, 214)(150, 204)(151, 218)(152, 217)(153, 219)(154, 209)(155, 208)(156, 222)(157, 212)(158, 211)(159, 213)(160, 227)(161, 226)(162, 216)(163, 230)(164, 229)(165, 231)(166, 221)(167, 220)(168, 234)(169, 224)(170, 223)(171, 225)(172, 238)(173, 237)(174, 228)(175, 240)(176, 239)(177, 233)(178, 232)(179, 236)(180, 235) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E20.892 Transitivity :: VT+ Graph:: bipartite v = 20 e = 120 f = 62 degree seq :: [ 12^20 ] E20.894 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 30}) Quotient :: loop^2 Aut^+ = D60 (small group id <60, 12>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, (Y3 * Y1 * Y2)^3, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3^8 ] Map:: R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 24, 84, 144, 204, 40, 100, 160, 220, 52, 112, 172, 232, 44, 104, 164, 224, 30, 90, 150, 210, 16, 76, 136, 196, 6, 66, 126, 186, 15, 75, 135, 195, 29, 89, 149, 209, 33, 93, 153, 213, 47, 107, 167, 227, 57, 117, 177, 237, 60, 120, 180, 240, 54, 114, 174, 234, 42, 102, 162, 222, 26, 86, 146, 206, 37, 97, 157, 217, 21, 81, 141, 201, 9, 69, 129, 189, 20, 80, 140, 200, 36, 96, 156, 216, 49, 109, 169, 229, 53, 113, 173, 233, 41, 101, 161, 221, 25, 85, 145, 205, 13, 73, 133, 193, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 17, 77, 137, 197, 31, 91, 151, 211, 45, 105, 165, 225, 51, 111, 171, 231, 39, 99, 159, 219, 23, 83, 143, 203, 11, 71, 131, 191, 3, 63, 123, 183, 10, 70, 130, 190, 22, 82, 142, 202, 38, 98, 158, 218, 50, 110, 170, 230, 59, 119, 179, 239, 58, 118, 178, 238, 48, 108, 168, 228, 35, 95, 155, 215, 19, 79, 139, 199, 34, 94, 154, 214, 28, 88, 148, 208, 14, 74, 134, 194, 27, 87, 147, 207, 43, 103, 163, 223, 55, 115, 175, 235, 56, 116, 176, 236, 46, 106, 166, 226, 32, 92, 152, 212, 18, 78, 138, 198, 8, 68, 128, 188) L = (1, 62)(2, 61)(3, 69)(4, 68)(5, 67)(6, 74)(7, 65)(8, 64)(9, 63)(10, 81)(11, 80)(12, 78)(13, 77)(14, 66)(15, 88)(16, 87)(17, 73)(18, 72)(19, 93)(20, 71)(21, 70)(22, 97)(23, 96)(24, 92)(25, 91)(26, 98)(27, 76)(28, 75)(29, 94)(30, 103)(31, 85)(32, 84)(33, 79)(34, 89)(35, 107)(36, 83)(37, 82)(38, 86)(39, 109)(40, 106)(41, 105)(42, 110)(43, 90)(44, 115)(45, 101)(46, 100)(47, 95)(48, 117)(49, 99)(50, 102)(51, 113)(52, 116)(53, 111)(54, 119)(55, 104)(56, 112)(57, 108)(58, 120)(59, 114)(60, 118)(121, 183)(122, 186)(123, 181)(124, 191)(125, 190)(126, 182)(127, 196)(128, 195)(129, 199)(130, 185)(131, 184)(132, 203)(133, 202)(134, 206)(135, 188)(136, 187)(137, 210)(138, 209)(139, 189)(140, 215)(141, 214)(142, 193)(143, 192)(144, 219)(145, 218)(146, 194)(147, 222)(148, 217)(149, 198)(150, 197)(151, 224)(152, 213)(153, 212)(154, 201)(155, 200)(156, 228)(157, 208)(158, 205)(159, 204)(160, 231)(161, 230)(162, 207)(163, 234)(164, 211)(165, 232)(166, 227)(167, 226)(168, 216)(169, 238)(170, 221)(171, 220)(172, 225)(173, 239)(174, 223)(175, 240)(176, 237)(177, 236)(178, 229)(179, 233)(180, 235) 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 ) } Outer automorphisms :: reflexible Dual of E20.891 Transitivity :: VT+ Graph:: bipartite v = 2 e = 120 f = 80 degree seq :: [ 120^2 ] E20.895 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 30}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y3^10 ] Map:: non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 21, 81)(12, 72, 20, 80)(13, 73, 22, 82)(14, 74, 18, 78)(15, 75, 17, 77)(16, 76, 19, 79)(23, 83, 33, 93)(24, 84, 32, 92)(25, 85, 34, 94)(26, 86, 30, 90)(27, 87, 29, 89)(28, 88, 31, 91)(35, 95, 45, 105)(36, 96, 44, 104)(37, 97, 46, 106)(38, 98, 42, 102)(39, 99, 41, 101)(40, 100, 43, 103)(47, 107, 56, 116)(48, 108, 55, 115)(49, 109, 54, 114)(50, 110, 53, 113)(51, 111, 52, 112)(57, 117, 60, 120)(58, 118, 59, 119)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 131, 191, 134, 194)(126, 186, 132, 192, 135, 195)(128, 188, 137, 197, 140, 200)(130, 190, 138, 198, 141, 201)(133, 193, 143, 203, 146, 206)(136, 196, 144, 204, 147, 207)(139, 199, 149, 209, 152, 212)(142, 202, 150, 210, 153, 213)(145, 205, 155, 215, 158, 218)(148, 208, 156, 216, 159, 219)(151, 211, 161, 221, 164, 224)(154, 214, 162, 222, 165, 225)(157, 217, 167, 227, 170, 230)(160, 220, 168, 228, 171, 231)(163, 223, 172, 232, 175, 235)(166, 226, 173, 233, 176, 236)(169, 229, 177, 237, 178, 238)(174, 234, 179, 239, 180, 240) L = (1, 124)(2, 128)(3, 131)(4, 133)(5, 134)(6, 121)(7, 137)(8, 139)(9, 140)(10, 122)(11, 143)(12, 123)(13, 145)(14, 146)(15, 125)(16, 126)(17, 149)(18, 127)(19, 151)(20, 152)(21, 129)(22, 130)(23, 155)(24, 132)(25, 157)(26, 158)(27, 135)(28, 136)(29, 161)(30, 138)(31, 163)(32, 164)(33, 141)(34, 142)(35, 167)(36, 144)(37, 169)(38, 170)(39, 147)(40, 148)(41, 172)(42, 150)(43, 174)(44, 175)(45, 153)(46, 154)(47, 177)(48, 156)(49, 160)(50, 178)(51, 159)(52, 179)(53, 162)(54, 166)(55, 180)(56, 165)(57, 168)(58, 171)(59, 173)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E20.897 Graph:: simple bipartite v = 50 e = 120 f = 32 degree seq :: [ 4^30, 6^20 ] E20.896 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 30}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y3^10 * Y2, (Y2^-1 * Y3)^30 ] Map:: non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 21, 81)(12, 72, 20, 80)(13, 73, 22, 82)(14, 74, 18, 78)(15, 75, 17, 77)(16, 76, 19, 79)(23, 83, 33, 93)(24, 84, 32, 92)(25, 85, 34, 94)(26, 86, 30, 90)(27, 87, 29, 89)(28, 88, 31, 91)(35, 95, 45, 105)(36, 96, 44, 104)(37, 97, 46, 106)(38, 98, 42, 102)(39, 99, 41, 101)(40, 100, 43, 103)(47, 107, 57, 117)(48, 108, 56, 116)(49, 109, 58, 118)(50, 110, 54, 114)(51, 111, 53, 113)(52, 112, 55, 115)(59, 119, 60, 120)(121, 181, 123, 183, 125, 185)(122, 182, 127, 187, 129, 189)(124, 184, 131, 191, 134, 194)(126, 186, 132, 192, 135, 195)(128, 188, 137, 197, 140, 200)(130, 190, 138, 198, 141, 201)(133, 193, 143, 203, 146, 206)(136, 196, 144, 204, 147, 207)(139, 199, 149, 209, 152, 212)(142, 202, 150, 210, 153, 213)(145, 205, 155, 215, 158, 218)(148, 208, 156, 216, 159, 219)(151, 211, 161, 221, 164, 224)(154, 214, 162, 222, 165, 225)(157, 217, 167, 227, 170, 230)(160, 220, 168, 228, 171, 231)(163, 223, 173, 233, 176, 236)(166, 226, 174, 234, 177, 237)(169, 229, 172, 232, 179, 239)(175, 235, 178, 238, 180, 240) L = (1, 124)(2, 128)(3, 131)(4, 133)(5, 134)(6, 121)(7, 137)(8, 139)(9, 140)(10, 122)(11, 143)(12, 123)(13, 145)(14, 146)(15, 125)(16, 126)(17, 149)(18, 127)(19, 151)(20, 152)(21, 129)(22, 130)(23, 155)(24, 132)(25, 157)(26, 158)(27, 135)(28, 136)(29, 161)(30, 138)(31, 163)(32, 164)(33, 141)(34, 142)(35, 167)(36, 144)(37, 169)(38, 170)(39, 147)(40, 148)(41, 173)(42, 150)(43, 175)(44, 176)(45, 153)(46, 154)(47, 172)(48, 156)(49, 171)(50, 179)(51, 159)(52, 160)(53, 178)(54, 162)(55, 177)(56, 180)(57, 165)(58, 166)(59, 168)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60 ) } Outer automorphisms :: reflexible Dual of E20.898 Graph:: simple bipartite v = 50 e = 120 f = 32 degree seq :: [ 4^30, 6^20 ] E20.897 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 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, Y1), (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^3 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^4 * Y1^-6, Y3^20 ] Map:: non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 35, 95, 49, 109, 46, 106, 34, 94, 15, 75, 4, 64, 9, 69, 21, 81, 18, 78, 26, 86, 40, 100, 53, 113, 48, 108, 33, 93, 14, 74, 25, 85, 17, 77, 6, 66, 10, 70, 22, 82, 37, 97, 51, 111, 47, 107, 32, 92, 16, 76, 5, 65)(3, 63, 11, 71, 27, 87, 43, 103, 55, 115, 59, 119, 52, 112, 38, 98, 23, 83, 12, 72, 28, 88, 42, 102, 31, 91, 45, 105, 57, 117, 60, 120, 54, 114, 41, 101, 30, 90, 39, 99, 24, 84, 13, 73, 29, 89, 44, 104, 56, 116, 58, 118, 50, 110, 36, 96, 20, 80, 8, 68)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 144, 204)(130, 190, 143, 203)(134, 194, 151, 211)(135, 195, 149, 209)(136, 196, 147, 207)(137, 197, 148, 208)(138, 198, 150, 210)(139, 199, 156, 216)(141, 201, 159, 219)(142, 202, 158, 218)(145, 205, 162, 222)(146, 206, 161, 221)(152, 212, 163, 223)(153, 213, 165, 225)(154, 214, 164, 224)(155, 215, 170, 230)(157, 217, 172, 232)(160, 220, 174, 234)(166, 226, 176, 236)(167, 227, 175, 235)(168, 228, 177, 237)(169, 229, 178, 238)(171, 231, 179, 239)(173, 233, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 134)(5, 135)(6, 121)(7, 141)(8, 143)(9, 145)(10, 122)(11, 148)(12, 150)(13, 123)(14, 152)(15, 153)(16, 154)(17, 125)(18, 126)(19, 138)(20, 158)(21, 137)(22, 127)(23, 161)(24, 128)(25, 136)(26, 130)(27, 162)(28, 159)(29, 131)(30, 156)(31, 133)(32, 166)(33, 167)(34, 168)(35, 146)(36, 172)(37, 139)(38, 174)(39, 140)(40, 142)(41, 170)(42, 144)(43, 151)(44, 147)(45, 149)(46, 173)(47, 169)(48, 171)(49, 160)(50, 179)(51, 155)(52, 180)(53, 157)(54, 178)(55, 165)(56, 163)(57, 164)(58, 175)(59, 177)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E20.895 Graph:: bipartite v = 32 e = 120 f = 50 degree seq :: [ 4^30, 60^2 ] E20.898 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 30}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y3)^2, Y3^3 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^5 * Y1^-5, Y1^30 ] Map:: non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 35, 95, 49, 109, 48, 108, 33, 93, 14, 74, 25, 85, 17, 77, 6, 66, 10, 70, 22, 82, 37, 97, 51, 111, 46, 106, 34, 94, 15, 75, 4, 64, 9, 69, 21, 81, 18, 78, 26, 86, 40, 100, 53, 113, 47, 107, 32, 92, 16, 76, 5, 65)(3, 63, 11, 71, 27, 87, 43, 103, 55, 115, 60, 120, 54, 114, 41, 101, 30, 90, 39, 99, 24, 84, 13, 73, 29, 89, 44, 104, 56, 116, 59, 119, 52, 112, 38, 98, 23, 83, 12, 72, 28, 88, 42, 102, 31, 91, 45, 105, 57, 117, 58, 118, 50, 110, 36, 96, 20, 80, 8, 68)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 144, 204)(130, 190, 143, 203)(134, 194, 151, 211)(135, 195, 149, 209)(136, 196, 147, 207)(137, 197, 148, 208)(138, 198, 150, 210)(139, 199, 156, 216)(141, 201, 159, 219)(142, 202, 158, 218)(145, 205, 162, 222)(146, 206, 161, 221)(152, 212, 163, 223)(153, 213, 165, 225)(154, 214, 164, 224)(155, 215, 170, 230)(157, 217, 172, 232)(160, 220, 174, 234)(166, 226, 176, 236)(167, 227, 175, 235)(168, 228, 177, 237)(169, 229, 178, 238)(171, 231, 179, 239)(173, 233, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 134)(5, 135)(6, 121)(7, 141)(8, 143)(9, 145)(10, 122)(11, 148)(12, 150)(13, 123)(14, 152)(15, 153)(16, 154)(17, 125)(18, 126)(19, 138)(20, 158)(21, 137)(22, 127)(23, 161)(24, 128)(25, 136)(26, 130)(27, 162)(28, 159)(29, 131)(30, 156)(31, 133)(32, 166)(33, 167)(34, 168)(35, 146)(36, 172)(37, 139)(38, 174)(39, 140)(40, 142)(41, 170)(42, 144)(43, 151)(44, 147)(45, 149)(46, 169)(47, 171)(48, 173)(49, 160)(50, 179)(51, 155)(52, 180)(53, 157)(54, 178)(55, 165)(56, 163)(57, 164)(58, 176)(59, 175)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 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 E20.896 Graph:: bipartite v = 32 e = 120 f = 50 degree seq :: [ 4^30, 60^2 ] E20.899 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 6, 30}) Quotient :: edge Aut^+ = C6 x D10 (small group id <60, 10>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^-3 * T2 * T1, (T2 * T1 * T2)^2, T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-8 * T1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 25, 37, 49, 55, 43, 31, 19, 12, 21, 33, 45, 57, 60, 54, 42, 30, 18, 6, 17, 29, 41, 53, 52, 40, 28, 15, 5)(2, 7, 20, 32, 44, 56, 48, 36, 24, 13, 4, 11, 26, 38, 50, 59, 47, 35, 23, 9, 16, 14, 27, 39, 51, 58, 46, 34, 22, 8)(61, 62, 66, 76, 72, 64)(63, 69, 77, 73, 81, 68)(65, 71, 78, 67, 79, 74)(70, 84, 89, 82, 93, 83)(75, 87, 90, 86, 91, 80)(85, 94, 101, 95, 105, 96)(88, 92, 102, 99, 103, 98)(97, 107, 113, 108, 117, 106)(100, 110, 114, 104, 115, 111)(109, 116, 112, 118, 120, 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) :: { ( 12^6 ), ( 12^30 ) } Outer automorphisms :: reflexible Dual of E20.900 Transitivity :: ET+ Graph:: bipartite v = 12 e = 60 f = 10 degree seq :: [ 6^10, 30^2 ] E20.900 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 6, 30}) Quotient :: loop Aut^+ = C6 x D10 (small group id <60, 10>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^-2, (F * T2)^2, (F * T1)^2, T1^6, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^30 ] Map:: non-degenerate R = (1, 61, 3, 63, 6, 66, 15, 75, 11, 71, 5, 65)(2, 62, 7, 67, 14, 74, 12, 72, 4, 64, 8, 68)(9, 69, 19, 79, 13, 73, 21, 81, 10, 70, 20, 80)(16, 76, 22, 82, 18, 78, 24, 84, 17, 77, 23, 83)(25, 85, 31, 91, 27, 87, 33, 93, 26, 86, 32, 92)(28, 88, 34, 94, 30, 90, 36, 96, 29, 89, 35, 95)(37, 97, 43, 103, 39, 99, 45, 105, 38, 98, 44, 104)(40, 100, 46, 106, 42, 102, 48, 108, 41, 101, 47, 107)(49, 109, 55, 115, 51, 111, 57, 117, 50, 110, 56, 116)(52, 112, 58, 118, 54, 114, 60, 120, 53, 113, 59, 119) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 70)(6, 74)(7, 76)(8, 77)(9, 75)(10, 63)(11, 64)(12, 78)(13, 65)(14, 71)(15, 73)(16, 72)(17, 67)(18, 68)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 81)(26, 79)(27, 80)(28, 84)(29, 82)(30, 83)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 93)(38, 91)(39, 92)(40, 96)(41, 94)(42, 95)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 105)(50, 103)(51, 104)(52, 108)(53, 106)(54, 107)(55, 118)(56, 119)(57, 120)(58, 117)(59, 115)(60, 116) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E20.899 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 60 f = 12 degree seq :: [ 12^10 ] E20.901 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 30}) Quotient :: dipole Aut^+ = C6 x D10 (small group id <60, 10>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^3 * Y2 * Y1, Y2^-1 * Y1^3 * Y2^-1 * Y1^-1, Y2^3 * Y1^-1 * Y2^-7 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 61, 2, 62, 6, 66, 16, 76, 12, 72, 4, 64)(3, 63, 9, 69, 17, 77, 13, 73, 21, 81, 8, 68)(5, 65, 11, 71, 18, 78, 7, 67, 19, 79, 14, 74)(10, 70, 24, 84, 29, 89, 22, 82, 33, 93, 23, 83)(15, 75, 27, 87, 30, 90, 26, 86, 31, 91, 20, 80)(25, 85, 34, 94, 41, 101, 35, 95, 45, 105, 36, 96)(28, 88, 32, 92, 42, 102, 39, 99, 43, 103, 38, 98)(37, 97, 47, 107, 53, 113, 48, 108, 57, 117, 46, 106)(40, 100, 50, 110, 54, 114, 44, 104, 55, 115, 51, 111)(49, 109, 56, 116, 52, 112, 58, 118, 60, 120, 59, 119)(121, 181, 123, 183, 130, 190, 145, 205, 157, 217, 169, 229, 175, 235, 163, 223, 151, 211, 139, 199, 132, 192, 141, 201, 153, 213, 165, 225, 177, 237, 180, 240, 174, 234, 162, 222, 150, 210, 138, 198, 126, 186, 137, 197, 149, 209, 161, 221, 173, 233, 172, 232, 160, 220, 148, 208, 135, 195, 125, 185)(122, 182, 127, 187, 140, 200, 152, 212, 164, 224, 176, 236, 168, 228, 156, 216, 144, 204, 133, 193, 124, 184, 131, 191, 146, 206, 158, 218, 170, 230, 179, 239, 167, 227, 155, 215, 143, 203, 129, 189, 136, 196, 134, 194, 147, 207, 159, 219, 171, 231, 178, 238, 166, 226, 154, 214, 142, 202, 128, 188) L = (1, 123)(2, 127)(3, 130)(4, 131)(5, 121)(6, 137)(7, 140)(8, 122)(9, 136)(10, 145)(11, 146)(12, 141)(13, 124)(14, 147)(15, 125)(16, 134)(17, 149)(18, 126)(19, 132)(20, 152)(21, 153)(22, 128)(23, 129)(24, 133)(25, 157)(26, 158)(27, 159)(28, 135)(29, 161)(30, 138)(31, 139)(32, 164)(33, 165)(34, 142)(35, 143)(36, 144)(37, 169)(38, 170)(39, 171)(40, 148)(41, 173)(42, 150)(43, 151)(44, 176)(45, 177)(46, 154)(47, 155)(48, 156)(49, 175)(50, 179)(51, 178)(52, 160)(53, 172)(54, 162)(55, 163)(56, 168)(57, 180)(58, 166)(59, 167)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E20.902 Graph:: bipartite v = 12 e = 120 f = 70 degree seq :: [ 12^10, 60^2 ] E20.902 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 30}) Quotient :: dipole Aut^+ = C6 x D10 (small group id <60, 10>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2^3, (Y3^2 * Y2^-1)^2, Y2 * Y3^-10 * Y2, (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, 136, 196, 133, 193, 124, 184)(123, 183, 129, 189, 137, 197, 128, 188, 141, 201, 131, 191)(125, 185, 134, 194, 138, 198, 132, 192, 140, 200, 127, 187)(130, 190, 144, 204, 149, 209, 143, 203, 153, 213, 142, 202)(135, 195, 146, 206, 150, 210, 139, 199, 151, 211, 147, 207)(145, 205, 154, 214, 161, 221, 156, 216, 165, 225, 155, 215)(148, 208, 152, 212, 162, 222, 159, 219, 163, 223, 158, 218)(157, 217, 167, 227, 173, 233, 166, 226, 177, 237, 168, 228)(160, 220, 171, 231, 174, 234, 170, 230, 175, 235, 164, 224)(169, 229, 176, 236, 180, 240, 179, 239, 172, 232, 178, 238) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 137)(7, 139)(8, 122)(9, 124)(10, 145)(11, 136)(12, 146)(13, 141)(14, 147)(15, 125)(16, 134)(17, 149)(18, 126)(19, 152)(20, 133)(21, 153)(22, 128)(23, 129)(24, 131)(25, 157)(26, 158)(27, 159)(28, 135)(29, 161)(30, 138)(31, 140)(32, 164)(33, 165)(34, 142)(35, 143)(36, 144)(37, 169)(38, 170)(39, 171)(40, 148)(41, 173)(42, 150)(43, 151)(44, 176)(45, 177)(46, 154)(47, 155)(48, 156)(49, 174)(50, 178)(51, 179)(52, 160)(53, 180)(54, 162)(55, 163)(56, 168)(57, 172)(58, 166)(59, 167)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12, 60 ), ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) } Outer automorphisms :: reflexible Dual of E20.901 Graph:: simple bipartite v = 70 e = 120 f = 12 degree seq :: [ 2^60, 12^10 ] E20.903 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 30}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-2 * T1 * T2^2 * T1^-1, T1^-1 * T2^4 * T1^-1 * T2^2, T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T1 * T2^-2 * T1)^3 ] Map:: non-degenerate R = (1, 3, 10, 27, 36, 18, 6, 17, 35, 34, 16, 5)(2, 7, 20, 39, 31, 13, 4, 12, 28, 44, 24, 8)(9, 25, 46, 33, 15, 30, 11, 29, 50, 32, 14, 26)(19, 37, 54, 43, 23, 41, 21, 40, 58, 42, 22, 38)(45, 57, 52, 55, 49, 59, 47, 56, 51, 53, 48, 60)(61, 62, 66, 64)(63, 69, 77, 71)(65, 74, 78, 75)(67, 79, 72, 81)(68, 82, 73, 83)(70, 80, 95, 88)(76, 84, 96, 91)(85, 105, 89, 107)(86, 108, 90, 109)(87, 106, 94, 110)(92, 111, 93, 112)(97, 113, 100, 115)(98, 116, 101, 117)(99, 114, 104, 118)(102, 119, 103, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 60^4 ), ( 60^12 ) } Outer automorphisms :: reflexible Dual of E20.907 Transitivity :: ET+ Graph:: bipartite v = 20 e = 60 f = 2 degree seq :: [ 4^15, 12^5 ] E20.904 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 30}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1^-2 * T2^-1 * T1, T2 * T1^2 * T2^4, T2^2 * T1 * T2^-3 * T1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4 ] Map:: non-degenerate R = (1, 3, 10, 30, 35, 13, 24, 52, 50, 60, 54, 25, 53, 49, 21, 48, 36, 55, 51, 23, 44, 59, 56, 47, 20, 6, 19, 43, 17, 5)(2, 7, 22, 37, 14, 4, 12, 33, 29, 58, 34, 15, 38, 31, 46, 40, 16, 39, 28, 9, 27, 57, 41, 32, 11, 18, 45, 42, 26, 8)(61, 62, 66, 78, 104, 87, 108, 100, 114, 94, 73, 64)(63, 69, 79, 106, 119, 118, 96, 74, 85, 68, 84, 71)(65, 75, 80, 72, 83, 67, 81, 105, 120, 117, 95, 76)(70, 89, 103, 97, 116, 86, 115, 92, 113, 88, 112, 91)(77, 101, 107, 99, 111, 98, 109, 93, 110, 82, 90, 102) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 8^12 ), ( 8^30 ) } Outer automorphisms :: reflexible Dual of E20.908 Transitivity :: ET+ Graph:: bipartite v = 7 e = 60 f = 15 degree seq :: [ 12^5, 30^2 ] E20.905 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 12, 30}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^2 * T1^-1 * T2, T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^2, T2^-1 * T1^-2 * T2^-2 * T1^2 * T2^-1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 42, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 52, 36)(17, 37, 51, 32)(20, 45, 23, 46)(22, 35, 24, 47)(25, 49, 39, 50)(30, 54, 40, 55)(33, 53, 38, 56)(41, 57, 43, 58)(44, 59, 48, 60)(61, 62, 66, 77, 86, 105, 117, 114, 110, 120, 116, 91, 107, 112, 88, 70, 81, 102, 111, 87, 106, 118, 115, 109, 119, 113, 89, 95, 73, 64)(63, 69, 85, 84, 68, 83, 108, 96, 78, 101, 93, 72, 92, 100, 76, 65, 75, 99, 82, 67, 80, 104, 94, 79, 103, 98, 74, 97, 90, 71) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^4 ), ( 24^30 ) } Outer automorphisms :: reflexible Dual of E20.906 Transitivity :: ET+ Graph:: bipartite v = 17 e = 60 f = 5 degree seq :: [ 4^15, 30^2 ] E20.906 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 30}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-2 * T1 * T2^2 * T1^-1, T1^-1 * T2^4 * T1^-1 * T2^2, T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T1 * T2^-2 * T1)^3 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 27, 87, 36, 96, 18, 78, 6, 66, 17, 77, 35, 95, 34, 94, 16, 76, 5, 65)(2, 62, 7, 67, 20, 80, 39, 99, 31, 91, 13, 73, 4, 64, 12, 72, 28, 88, 44, 104, 24, 84, 8, 68)(9, 69, 25, 85, 46, 106, 33, 93, 15, 75, 30, 90, 11, 71, 29, 89, 50, 110, 32, 92, 14, 74, 26, 86)(19, 79, 37, 97, 54, 114, 43, 103, 23, 83, 41, 101, 21, 81, 40, 100, 58, 118, 42, 102, 22, 82, 38, 98)(45, 105, 57, 117, 52, 112, 55, 115, 49, 109, 59, 119, 47, 107, 56, 116, 51, 111, 53, 113, 48, 108, 60, 120) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 74)(6, 64)(7, 79)(8, 82)(9, 77)(10, 80)(11, 63)(12, 81)(13, 83)(14, 78)(15, 65)(16, 84)(17, 71)(18, 75)(19, 72)(20, 95)(21, 67)(22, 73)(23, 68)(24, 96)(25, 105)(26, 108)(27, 106)(28, 70)(29, 107)(30, 109)(31, 76)(32, 111)(33, 112)(34, 110)(35, 88)(36, 91)(37, 113)(38, 116)(39, 114)(40, 115)(41, 117)(42, 119)(43, 120)(44, 118)(45, 89)(46, 94)(47, 85)(48, 90)(49, 86)(50, 87)(51, 93)(52, 92)(53, 100)(54, 104)(55, 97)(56, 101)(57, 98)(58, 99)(59, 103)(60, 102) local type(s) :: { ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E20.905 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 60 f = 17 degree seq :: [ 24^5 ] E20.907 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 30}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1^-2 * T2^-1 * T1, T2 * T1^2 * T2^4, T2^2 * T1 * T2^-3 * T1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 30, 90, 35, 95, 13, 73, 24, 84, 52, 112, 50, 110, 60, 120, 54, 114, 25, 85, 53, 113, 49, 109, 21, 81, 48, 108, 36, 96, 55, 115, 51, 111, 23, 83, 44, 104, 59, 119, 56, 116, 47, 107, 20, 80, 6, 66, 19, 79, 43, 103, 17, 77, 5, 65)(2, 62, 7, 67, 22, 82, 37, 97, 14, 74, 4, 64, 12, 72, 33, 93, 29, 89, 58, 118, 34, 94, 15, 75, 38, 98, 31, 91, 46, 106, 40, 100, 16, 76, 39, 99, 28, 88, 9, 69, 27, 87, 57, 117, 41, 101, 32, 92, 11, 71, 18, 78, 45, 105, 42, 102, 26, 86, 8, 68) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 81)(8, 84)(9, 79)(10, 89)(11, 63)(12, 83)(13, 64)(14, 85)(15, 80)(16, 65)(17, 101)(18, 104)(19, 106)(20, 72)(21, 105)(22, 90)(23, 67)(24, 71)(25, 68)(26, 115)(27, 108)(28, 112)(29, 103)(30, 102)(31, 70)(32, 113)(33, 110)(34, 73)(35, 76)(36, 74)(37, 116)(38, 109)(39, 111)(40, 114)(41, 107)(42, 77)(43, 97)(44, 87)(45, 120)(46, 119)(47, 99)(48, 100)(49, 93)(50, 82)(51, 98)(52, 91)(53, 88)(54, 94)(55, 92)(56, 86)(57, 95)(58, 96)(59, 118)(60, 117) 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 ) } Outer automorphisms :: reflexible Dual of E20.903 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 60 f = 20 degree seq :: [ 60^2 ] E20.908 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 12, 30}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^2 * T1^-1 * T2, T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^2, T2^-1 * T1^-2 * T2^-2 * T1^2 * T2^-1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 5, 65)(2, 62, 7, 67, 21, 81, 8, 68)(4, 64, 12, 72, 28, 88, 14, 74)(6, 66, 18, 78, 42, 102, 19, 79)(9, 69, 26, 86, 15, 75, 27, 87)(11, 71, 29, 89, 16, 76, 31, 91)(13, 73, 34, 94, 52, 112, 36, 96)(17, 77, 37, 97, 51, 111, 32, 92)(20, 80, 45, 105, 23, 83, 46, 106)(22, 82, 35, 95, 24, 84, 47, 107)(25, 85, 49, 109, 39, 99, 50, 110)(30, 90, 54, 114, 40, 100, 55, 115)(33, 93, 53, 113, 38, 98, 56, 116)(41, 101, 57, 117, 43, 103, 58, 118)(44, 104, 59, 119, 48, 108, 60, 120) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 77)(7, 80)(8, 83)(9, 85)(10, 81)(11, 63)(12, 92)(13, 64)(14, 97)(15, 99)(16, 65)(17, 86)(18, 101)(19, 103)(20, 104)(21, 102)(22, 67)(23, 108)(24, 68)(25, 84)(26, 105)(27, 106)(28, 70)(29, 95)(30, 71)(31, 107)(32, 100)(33, 72)(34, 79)(35, 73)(36, 78)(37, 90)(38, 74)(39, 82)(40, 76)(41, 93)(42, 111)(43, 98)(44, 94)(45, 117)(46, 118)(47, 112)(48, 96)(49, 119)(50, 120)(51, 87)(52, 88)(53, 89)(54, 110)(55, 109)(56, 91)(57, 114)(58, 115)(59, 113)(60, 116) local type(s) :: { ( 12, 30, 12, 30, 12, 30, 12, 30 ) } Outer automorphisms :: reflexible Dual of E20.904 Transitivity :: ET+ VT+ AT Graph:: v = 15 e = 60 f = 7 degree seq :: [ 8^15 ] E20.909 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 30}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, (Y1 * Y3^-1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y1^2 * Y2 * Y3 * Y2^-2 * Y1^-1 * Y2, Y2^-3 * Y1 * Y3^-1 * Y2^-3, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^30 ] Map:: R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 9, 69, 17, 77, 11, 71)(5, 65, 14, 74, 18, 78, 15, 75)(7, 67, 19, 79, 12, 72, 21, 81)(8, 68, 22, 82, 13, 73, 23, 83)(10, 70, 20, 80, 35, 95, 28, 88)(16, 76, 24, 84, 36, 96, 31, 91)(25, 85, 45, 105, 29, 89, 47, 107)(26, 86, 48, 108, 30, 90, 49, 109)(27, 87, 46, 106, 34, 94, 50, 110)(32, 92, 51, 111, 33, 93, 52, 112)(37, 97, 53, 113, 40, 100, 55, 115)(38, 98, 56, 116, 41, 101, 57, 117)(39, 99, 54, 114, 44, 104, 58, 118)(42, 102, 59, 119, 43, 103, 60, 120)(121, 181, 123, 183, 130, 190, 147, 207, 156, 216, 138, 198, 126, 186, 137, 197, 155, 215, 154, 214, 136, 196, 125, 185)(122, 182, 127, 187, 140, 200, 159, 219, 151, 211, 133, 193, 124, 184, 132, 192, 148, 208, 164, 224, 144, 204, 128, 188)(129, 189, 145, 205, 166, 226, 153, 213, 135, 195, 150, 210, 131, 191, 149, 209, 170, 230, 152, 212, 134, 194, 146, 206)(139, 199, 157, 217, 174, 234, 163, 223, 143, 203, 161, 221, 141, 201, 160, 220, 178, 238, 162, 222, 142, 202, 158, 218)(165, 225, 177, 237, 172, 232, 175, 235, 169, 229, 179, 239, 167, 227, 176, 236, 171, 231, 173, 233, 168, 228, 180, 240) L = (1, 124)(2, 121)(3, 131)(4, 126)(5, 135)(6, 122)(7, 141)(8, 143)(9, 123)(10, 148)(11, 137)(12, 139)(13, 142)(14, 125)(15, 138)(16, 151)(17, 129)(18, 134)(19, 127)(20, 130)(21, 132)(22, 128)(23, 133)(24, 136)(25, 167)(26, 169)(27, 170)(28, 155)(29, 165)(30, 168)(31, 156)(32, 172)(33, 171)(34, 166)(35, 140)(36, 144)(37, 175)(38, 177)(39, 178)(40, 173)(41, 176)(42, 180)(43, 179)(44, 174)(45, 145)(46, 147)(47, 149)(48, 146)(49, 150)(50, 154)(51, 152)(52, 153)(53, 157)(54, 159)(55, 160)(56, 158)(57, 161)(58, 164)(59, 162)(60, 163)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E20.912 Graph:: bipartite v = 20 e = 120 f = 62 degree seq :: [ 8^15, 24^5 ] E20.910 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 30}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2 * Y1^-3, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^2 * Y2^5, Y1 * Y2^2 * Y1 * Y2^-3, (Y3^-1 * Y1^-1)^4, (Y2^-1 * Y1 * Y2^-1)^4 ] Map:: R = (1, 61, 2, 62, 6, 66, 18, 78, 44, 104, 27, 87, 48, 108, 40, 100, 54, 114, 34, 94, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 46, 106, 59, 119, 58, 118, 36, 96, 14, 74, 25, 85, 8, 68, 24, 84, 11, 71)(5, 65, 15, 75, 20, 80, 12, 72, 23, 83, 7, 67, 21, 81, 45, 105, 60, 120, 57, 117, 35, 95, 16, 76)(10, 70, 29, 89, 43, 103, 37, 97, 56, 116, 26, 86, 55, 115, 32, 92, 53, 113, 28, 88, 52, 112, 31, 91)(17, 77, 41, 101, 47, 107, 39, 99, 51, 111, 38, 98, 49, 109, 33, 93, 50, 110, 22, 82, 30, 90, 42, 102)(121, 181, 123, 183, 130, 190, 150, 210, 155, 215, 133, 193, 144, 204, 172, 232, 170, 230, 180, 240, 174, 234, 145, 205, 173, 233, 169, 229, 141, 201, 168, 228, 156, 216, 175, 235, 171, 231, 143, 203, 164, 224, 179, 239, 176, 236, 167, 227, 140, 200, 126, 186, 139, 199, 163, 223, 137, 197, 125, 185)(122, 182, 127, 187, 142, 202, 157, 217, 134, 194, 124, 184, 132, 192, 153, 213, 149, 209, 178, 238, 154, 214, 135, 195, 158, 218, 151, 211, 166, 226, 160, 220, 136, 196, 159, 219, 148, 208, 129, 189, 147, 207, 177, 237, 161, 221, 152, 212, 131, 191, 138, 198, 165, 225, 162, 222, 146, 206, 128, 188) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 142)(8, 122)(9, 147)(10, 150)(11, 138)(12, 153)(13, 144)(14, 124)(15, 158)(16, 159)(17, 125)(18, 165)(19, 163)(20, 126)(21, 168)(22, 157)(23, 164)(24, 172)(25, 173)(26, 128)(27, 177)(28, 129)(29, 178)(30, 155)(31, 166)(32, 131)(33, 149)(34, 135)(35, 133)(36, 175)(37, 134)(38, 151)(39, 148)(40, 136)(41, 152)(42, 146)(43, 137)(44, 179)(45, 162)(46, 160)(47, 140)(48, 156)(49, 141)(50, 180)(51, 143)(52, 170)(53, 169)(54, 145)(55, 171)(56, 167)(57, 161)(58, 154)(59, 176)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E20.911 Graph:: bipartite v = 7 e = 120 f = 75 degree seq :: [ 24^5, 60^2 ] E20.911 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 30}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-4 * Y2^-1 * Y3, Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1, (Y3 * Y2)^12, (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, 129, 189, 137, 197, 131, 191)(125, 185, 134, 194, 138, 198, 135, 195)(127, 187, 139, 199, 132, 192, 141, 201)(128, 188, 142, 202, 133, 193, 143, 203)(130, 190, 147, 207, 161, 221, 149, 209)(136, 196, 158, 218, 162, 222, 159, 219)(140, 200, 164, 224, 152, 212, 165, 225)(144, 204, 171, 231, 153, 213, 172, 232)(145, 205, 163, 223, 150, 210, 166, 226)(146, 206, 160, 220, 151, 211, 169, 229)(148, 208, 156, 216, 167, 227, 154, 214)(155, 215, 168, 228, 157, 217, 170, 230)(173, 233, 178, 238, 176, 236, 179, 239)(174, 234, 177, 237, 175, 235, 180, 240) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 137)(7, 140)(8, 122)(9, 145)(10, 148)(11, 150)(12, 152)(13, 124)(14, 154)(15, 156)(16, 125)(17, 161)(18, 126)(19, 163)(20, 151)(21, 166)(22, 160)(23, 169)(24, 128)(25, 173)(26, 129)(27, 174)(28, 139)(29, 175)(30, 176)(31, 131)(32, 146)(33, 133)(34, 153)(35, 134)(36, 144)(37, 135)(38, 149)(39, 147)(40, 136)(41, 167)(42, 138)(43, 177)(44, 178)(45, 179)(46, 180)(47, 141)(48, 142)(49, 162)(50, 143)(51, 165)(52, 164)(53, 158)(54, 155)(55, 157)(56, 159)(57, 171)(58, 168)(59, 170)(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) :: { ( 24, 60 ), ( 24, 60, 24, 60, 24, 60, 24, 60 ) } Outer automorphisms :: reflexible Dual of E20.910 Graph:: simple bipartite v = 75 e = 120 f = 7 degree seq :: [ 2^60, 8^15 ] E20.912 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 30}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1^-1 * Y3^-2 * Y1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2, Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^4, Y3 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1, (Y1^2 * Y3^-1 * Y1)^4 ] Map:: R = (1, 61, 2, 62, 6, 66, 17, 77, 26, 86, 45, 105, 57, 117, 54, 114, 50, 110, 60, 120, 56, 116, 31, 91, 47, 107, 52, 112, 28, 88, 10, 70, 21, 81, 42, 102, 51, 111, 27, 87, 46, 106, 58, 118, 55, 115, 49, 109, 59, 119, 53, 113, 29, 89, 35, 95, 13, 73, 4, 64)(3, 63, 9, 69, 25, 85, 24, 84, 8, 68, 23, 83, 48, 108, 36, 96, 18, 78, 41, 101, 33, 93, 12, 72, 32, 92, 40, 100, 16, 76, 5, 65, 15, 75, 39, 99, 22, 82, 7, 67, 20, 80, 44, 104, 34, 94, 19, 79, 43, 103, 38, 98, 14, 74, 37, 97, 30, 90, 11, 71)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 138)(7, 141)(8, 122)(9, 146)(10, 125)(11, 149)(12, 148)(13, 154)(14, 124)(15, 147)(16, 151)(17, 157)(18, 162)(19, 126)(20, 165)(21, 128)(22, 155)(23, 166)(24, 167)(25, 169)(26, 135)(27, 129)(28, 134)(29, 136)(30, 174)(31, 131)(32, 137)(33, 173)(34, 172)(35, 144)(36, 133)(37, 171)(38, 176)(39, 170)(40, 175)(41, 177)(42, 139)(43, 178)(44, 179)(45, 143)(46, 140)(47, 142)(48, 180)(49, 159)(50, 145)(51, 152)(52, 156)(53, 158)(54, 160)(55, 150)(56, 153)(57, 163)(58, 161)(59, 168)(60, 164)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E20.909 Graph:: simple bipartite v = 62 e = 120 f = 20 degree seq :: [ 2^60, 60^2 ] E20.913 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 30}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, Y1 * Y3^-1 * Y1^2, (R * Y3)^2, Y3 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y1^-1 * Y2^4, Y1^-1 * Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1, Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * R * Y2^3 * R * Y2^-2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^4 * Y3^-1 * Y1 * Y2^2 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 61, 2, 62, 6, 66, 4, 64)(3, 63, 9, 69, 17, 77, 11, 71)(5, 65, 14, 74, 18, 78, 15, 75)(7, 67, 19, 79, 12, 72, 21, 81)(8, 68, 22, 82, 13, 73, 23, 83)(10, 70, 27, 87, 41, 101, 29, 89)(16, 76, 38, 98, 42, 102, 39, 99)(20, 80, 44, 104, 32, 92, 45, 105)(24, 84, 51, 111, 33, 93, 52, 112)(25, 85, 43, 103, 30, 90, 46, 106)(26, 86, 40, 100, 31, 91, 49, 109)(28, 88, 36, 96, 47, 107, 34, 94)(35, 95, 48, 108, 37, 97, 50, 110)(53, 113, 58, 118, 56, 116, 59, 119)(54, 114, 57, 117, 55, 115, 60, 120)(121, 181, 123, 183, 130, 190, 148, 208, 139, 199, 163, 223, 177, 237, 171, 231, 165, 225, 179, 239, 170, 230, 143, 203, 169, 229, 162, 222, 138, 198, 126, 186, 137, 197, 161, 221, 167, 227, 141, 201, 166, 226, 180, 240, 172, 232, 164, 224, 178, 238, 168, 228, 142, 202, 160, 220, 136, 196, 125, 185)(122, 182, 127, 187, 140, 200, 151, 211, 131, 191, 150, 210, 176, 236, 159, 219, 147, 207, 174, 234, 155, 215, 134, 194, 154, 214, 153, 213, 133, 193, 124, 184, 132, 192, 152, 212, 146, 206, 129, 189, 145, 205, 173, 233, 158, 218, 149, 209, 175, 235, 157, 217, 135, 195, 156, 216, 144, 204, 128, 188) L = (1, 124)(2, 121)(3, 131)(4, 126)(5, 135)(6, 122)(7, 141)(8, 143)(9, 123)(10, 149)(11, 137)(12, 139)(13, 142)(14, 125)(15, 138)(16, 159)(17, 129)(18, 134)(19, 127)(20, 165)(21, 132)(22, 128)(23, 133)(24, 172)(25, 166)(26, 169)(27, 130)(28, 154)(29, 161)(30, 163)(31, 160)(32, 164)(33, 171)(34, 167)(35, 170)(36, 148)(37, 168)(38, 136)(39, 162)(40, 146)(41, 147)(42, 158)(43, 145)(44, 140)(45, 152)(46, 150)(47, 156)(48, 155)(49, 151)(50, 157)(51, 144)(52, 153)(53, 179)(54, 180)(55, 177)(56, 178)(57, 174)(58, 173)(59, 176)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 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 E20.914 Graph:: bipartite v = 17 e = 120 f = 65 degree seq :: [ 8^15, 60^2 ] E20.914 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 12, 30}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-3 * Y3 * Y1^-1, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1, Y3 * Y1^2 * Y3^4, Y3 * Y1 * Y3^-3 * Y1 * Y3, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^30 ] Map:: R = (1, 61, 2, 62, 6, 66, 18, 78, 44, 104, 27, 87, 48, 108, 40, 100, 54, 114, 34, 94, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 46, 106, 59, 119, 58, 118, 36, 96, 14, 74, 25, 85, 8, 68, 24, 84, 11, 71)(5, 65, 15, 75, 20, 80, 12, 72, 23, 83, 7, 67, 21, 81, 45, 105, 60, 120, 57, 117, 35, 95, 16, 76)(10, 70, 29, 89, 43, 103, 37, 97, 56, 116, 26, 86, 55, 115, 32, 92, 53, 113, 28, 88, 52, 112, 31, 91)(17, 77, 41, 101, 47, 107, 39, 99, 51, 111, 38, 98, 49, 109, 33, 93, 50, 110, 22, 82, 30, 90, 42, 102)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 142)(8, 122)(9, 147)(10, 150)(11, 138)(12, 153)(13, 144)(14, 124)(15, 158)(16, 159)(17, 125)(18, 165)(19, 163)(20, 126)(21, 168)(22, 157)(23, 164)(24, 172)(25, 173)(26, 128)(27, 177)(28, 129)(29, 178)(30, 155)(31, 166)(32, 131)(33, 149)(34, 135)(35, 133)(36, 175)(37, 134)(38, 151)(39, 148)(40, 136)(41, 152)(42, 146)(43, 137)(44, 179)(45, 162)(46, 160)(47, 140)(48, 156)(49, 141)(50, 180)(51, 143)(52, 170)(53, 169)(54, 145)(55, 171)(56, 167)(57, 161)(58, 154)(59, 176)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 8, 60 ), ( 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60, 8, 60 ) } Outer automorphisms :: reflexible Dual of E20.913 Graph:: simple bipartite v = 65 e = 120 f = 17 degree seq :: [ 2^60, 24^5 ] E20.915 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 60, 60}) Quotient :: edge Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2^20, (T1^-1 * T2^-1)^60 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 50, 56, 58, 52, 46, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 60, 55, 49, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 48, 54, 59, 53, 47, 41, 35, 29, 23, 17, 11, 5)(61, 62, 64)(63, 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, 96, 99)(95, 97, 100)(98, 102, 105)(101, 103, 106)(104, 108, 111)(107, 109, 112)(110, 114, 117)(113, 115, 118)(116, 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) :: { ( 120^3 ), ( 120^60 ) } Outer automorphisms :: reflexible Dual of E20.916 Transitivity :: ET+ Graph:: bipartite v = 21 e = 60 f = 1 degree seq :: [ 3^20, 60 ] E20.916 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 60, 60}) Quotient :: loop Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2^20, (T1^-1 * T2^-1)^60 ] Map:: non-degenerate R = (1, 61, 3, 63, 8, 68, 14, 74, 20, 80, 26, 86, 32, 92, 38, 98, 44, 104, 50, 110, 56, 116, 58, 118, 52, 112, 46, 106, 40, 100, 34, 94, 28, 88, 22, 82, 16, 76, 10, 70, 4, 64, 9, 69, 15, 75, 21, 81, 27, 87, 33, 93, 39, 99, 45, 105, 51, 111, 57, 117, 60, 120, 55, 115, 49, 109, 43, 103, 37, 97, 31, 91, 25, 85, 19, 79, 13, 73, 7, 67, 2, 62, 6, 66, 12, 72, 18, 78, 24, 84, 30, 90, 36, 96, 42, 102, 48, 108, 54, 114, 59, 119, 53, 113, 47, 107, 41, 101, 35, 95, 29, 89, 23, 83, 17, 77, 11, 71, 5, 65) L = (1, 62)(2, 64)(3, 66)(4, 61)(5, 67)(6, 69)(7, 70)(8, 72)(9, 63)(10, 65)(11, 73)(12, 75)(13, 76)(14, 78)(15, 68)(16, 71)(17, 79)(18, 81)(19, 82)(20, 84)(21, 74)(22, 77)(23, 85)(24, 87)(25, 88)(26, 90)(27, 80)(28, 83)(29, 91)(30, 93)(31, 94)(32, 96)(33, 86)(34, 89)(35, 97)(36, 99)(37, 100)(38, 102)(39, 92)(40, 95)(41, 103)(42, 105)(43, 106)(44, 108)(45, 98)(46, 101)(47, 109)(48, 111)(49, 112)(50, 114)(51, 104)(52, 107)(53, 115)(54, 117)(55, 118)(56, 119)(57, 110)(58, 113)(59, 120)(60, 116) local type(s) :: { ( 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60, 3, 60 ) } Outer automorphisms :: reflexible Dual of E20.915 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 60 f = 21 degree seq :: [ 120 ] E20.917 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 60, 60}) Quotient :: dipole Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y1^-2, Y1^3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y2^20 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 61, 2, 62, 4, 64)(3, 63, 6, 66, 9, 69)(5, 65, 7, 67, 10, 70)(8, 68, 12, 72, 15, 75)(11, 71, 13, 73, 16, 76)(14, 74, 18, 78, 21, 81)(17, 77, 19, 79, 22, 82)(20, 80, 24, 84, 27, 87)(23, 83, 25, 85, 28, 88)(26, 86, 30, 90, 33, 93)(29, 89, 31, 91, 34, 94)(32, 92, 36, 96, 39, 99)(35, 95, 37, 97, 40, 100)(38, 98, 42, 102, 45, 105)(41, 101, 43, 103, 46, 106)(44, 104, 48, 108, 51, 111)(47, 107, 49, 109, 52, 112)(50, 110, 54, 114, 57, 117)(53, 113, 55, 115, 58, 118)(56, 116, 59, 119, 60, 120)(121, 181, 123, 183, 128, 188, 134, 194, 140, 200, 146, 206, 152, 212, 158, 218, 164, 224, 170, 230, 176, 236, 178, 238, 172, 232, 166, 226, 160, 220, 154, 214, 148, 208, 142, 202, 136, 196, 130, 190, 124, 184, 129, 189, 135, 195, 141, 201, 147, 207, 153, 213, 159, 219, 165, 225, 171, 231, 177, 237, 180, 240, 175, 235, 169, 229, 163, 223, 157, 217, 151, 211, 145, 205, 139, 199, 133, 193, 127, 187, 122, 182, 126, 186, 132, 192, 138, 198, 144, 204, 150, 210, 156, 216, 162, 222, 168, 228, 174, 234, 179, 239, 173, 233, 167, 227, 161, 221, 155, 215, 149, 209, 143, 203, 137, 197, 131, 191, 125, 185) L = (1, 124)(2, 121)(3, 129)(4, 122)(5, 130)(6, 123)(7, 125)(8, 135)(9, 126)(10, 127)(11, 136)(12, 128)(13, 131)(14, 141)(15, 132)(16, 133)(17, 142)(18, 134)(19, 137)(20, 147)(21, 138)(22, 139)(23, 148)(24, 140)(25, 143)(26, 153)(27, 144)(28, 145)(29, 154)(30, 146)(31, 149)(32, 159)(33, 150)(34, 151)(35, 160)(36, 152)(37, 155)(38, 165)(39, 156)(40, 157)(41, 166)(42, 158)(43, 161)(44, 171)(45, 162)(46, 163)(47, 172)(48, 164)(49, 167)(50, 177)(51, 168)(52, 169)(53, 178)(54, 170)(55, 173)(56, 180)(57, 174)(58, 175)(59, 176)(60, 179)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) } Outer automorphisms :: reflexible Dual of E20.918 Graph:: bipartite v = 21 e = 120 f = 61 degree seq :: [ 6^20, 120 ] E20.918 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 60, 60}) Quotient :: dipole Aut^+ = C60 (small group id <60, 4>) Aut = D120 (small group id <120, 28>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^20, (Y1^-1 * Y3^-1)^60 ] Map:: R = (1, 61, 2, 62, 6, 66, 12, 72, 18, 78, 24, 84, 30, 90, 36, 96, 42, 102, 48, 108, 54, 114, 59, 119, 53, 113, 47, 107, 41, 101, 35, 95, 29, 89, 23, 83, 17, 77, 11, 71, 5, 65, 8, 68, 14, 74, 20, 80, 26, 86, 32, 92, 38, 98, 44, 104, 50, 110, 56, 116, 60, 120, 57, 117, 51, 111, 45, 105, 39, 99, 33, 93, 27, 87, 21, 81, 15, 75, 9, 69, 3, 63, 7, 67, 13, 73, 19, 79, 25, 85, 31, 91, 37, 97, 43, 103, 49, 109, 55, 115, 58, 118, 52, 112, 46, 106, 40, 100, 34, 94, 28, 88, 22, 82, 16, 76, 10, 70, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 125)(4, 129)(5, 121)(6, 133)(7, 128)(8, 122)(9, 131)(10, 135)(11, 124)(12, 139)(13, 134)(14, 126)(15, 137)(16, 141)(17, 130)(18, 145)(19, 140)(20, 132)(21, 143)(22, 147)(23, 136)(24, 151)(25, 146)(26, 138)(27, 149)(28, 153)(29, 142)(30, 157)(31, 152)(32, 144)(33, 155)(34, 159)(35, 148)(36, 163)(37, 158)(38, 150)(39, 161)(40, 165)(41, 154)(42, 169)(43, 164)(44, 156)(45, 167)(46, 171)(47, 160)(48, 175)(49, 170)(50, 162)(51, 173)(52, 177)(53, 166)(54, 178)(55, 176)(56, 168)(57, 179)(58, 180)(59, 172)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 6, 120 ), ( 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120, 6, 120 ) } Outer automorphisms :: reflexible Dual of E20.917 Graph:: bipartite v = 61 e = 120 f = 21 degree seq :: [ 2^60, 120 ] E20.919 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 11}) Quotient :: dipole Aut^+ = D66 (small group id <66, 3>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y2 * Y1)^2, Y3^-11 * Y2^-1, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ] Map:: polytopal non-degenerate R = (1, 67, 2, 68)(3, 69, 9, 75)(4, 70, 10, 76)(5, 71, 7, 73)(6, 72, 8, 74)(11, 77, 21, 87)(12, 78, 20, 86)(13, 79, 22, 88)(14, 80, 18, 84)(15, 81, 17, 83)(16, 82, 19, 85)(23, 89, 33, 99)(24, 90, 32, 98)(25, 91, 34, 100)(26, 92, 30, 96)(27, 93, 29, 95)(28, 94, 31, 97)(35, 101, 45, 111)(36, 102, 44, 110)(37, 103, 46, 112)(38, 104, 42, 108)(39, 105, 41, 107)(40, 106, 43, 109)(47, 113, 57, 123)(48, 114, 56, 122)(49, 115, 58, 124)(50, 116, 54, 120)(51, 117, 53, 119)(52, 118, 55, 121)(59, 125, 65, 131)(60, 126, 66, 132)(61, 127, 63, 129)(62, 128, 64, 130)(133, 199, 135, 201, 137, 203)(134, 200, 139, 205, 141, 207)(136, 202, 143, 209, 146, 212)(138, 204, 144, 210, 147, 213)(140, 206, 149, 215, 152, 218)(142, 208, 150, 216, 153, 219)(145, 211, 155, 221, 158, 224)(148, 214, 156, 222, 159, 225)(151, 217, 161, 227, 164, 230)(154, 220, 162, 228, 165, 231)(157, 223, 167, 233, 170, 236)(160, 226, 168, 234, 171, 237)(163, 229, 173, 239, 176, 242)(166, 232, 174, 240, 177, 243)(169, 235, 179, 245, 182, 248)(172, 238, 180, 246, 183, 249)(175, 241, 185, 251, 188, 254)(178, 244, 186, 252, 189, 255)(181, 247, 191, 257, 194, 260)(184, 250, 192, 258, 193, 259)(187, 253, 195, 261, 198, 264)(190, 256, 196, 262, 197, 263) L = (1, 136)(2, 140)(3, 143)(4, 145)(5, 146)(6, 133)(7, 149)(8, 151)(9, 152)(10, 134)(11, 155)(12, 135)(13, 157)(14, 158)(15, 137)(16, 138)(17, 161)(18, 139)(19, 163)(20, 164)(21, 141)(22, 142)(23, 167)(24, 144)(25, 169)(26, 170)(27, 147)(28, 148)(29, 173)(30, 150)(31, 175)(32, 176)(33, 153)(34, 154)(35, 179)(36, 156)(37, 181)(38, 182)(39, 159)(40, 160)(41, 185)(42, 162)(43, 187)(44, 188)(45, 165)(46, 166)(47, 191)(48, 168)(49, 193)(50, 194)(51, 171)(52, 172)(53, 195)(54, 174)(55, 197)(56, 198)(57, 177)(58, 178)(59, 184)(60, 180)(61, 183)(62, 192)(63, 190)(64, 186)(65, 189)(66, 196)(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, 22, 4, 22 ), ( 4, 22, 4, 22, 4, 22 ) } Outer automorphisms :: reflexible Dual of E20.920 Graph:: simple bipartite v = 55 e = 132 f = 39 degree seq :: [ 4^33, 6^22 ] E20.920 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 11}) Quotient :: dipole Aut^+ = D66 (small group id <66, 3>) Aut = D132 (small group id <132, 9>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y3^-9 * Y1^2, Y1^4 * Y3^-1 * Y1 * Y3^-5, Y1^11 ] Map:: polytopal non-degenerate R = (1, 67, 2, 68, 7, 73, 19, 85, 35, 101, 49, 115, 60, 126, 47, 113, 32, 98, 16, 82, 5, 71)(3, 69, 11, 77, 27, 93, 43, 109, 55, 121, 64, 130, 61, 127, 50, 116, 36, 102, 20, 86, 8, 74)(4, 70, 9, 75, 21, 87, 18, 84, 26, 92, 40, 106, 53, 119, 59, 125, 46, 112, 34, 100, 15, 81)(6, 72, 10, 76, 22, 88, 37, 103, 51, 117, 58, 124, 48, 114, 33, 99, 14, 80, 25, 91, 17, 83)(12, 78, 28, 94, 42, 108, 31, 97, 45, 111, 57, 123, 66, 132, 62, 128, 52, 118, 38, 104, 23, 89)(13, 79, 29, 95, 44, 110, 56, 122, 65, 131, 63, 129, 54, 120, 41, 107, 30, 96, 39, 105, 24, 90)(133, 199, 135, 201)(134, 200, 140, 206)(136, 202, 145, 211)(137, 203, 143, 209)(138, 204, 144, 210)(139, 205, 152, 218)(141, 207, 156, 222)(142, 208, 155, 221)(146, 212, 163, 229)(147, 213, 161, 227)(148, 214, 159, 225)(149, 215, 160, 226)(150, 216, 162, 228)(151, 217, 168, 234)(153, 219, 171, 237)(154, 220, 170, 236)(157, 223, 174, 240)(158, 224, 173, 239)(164, 230, 175, 241)(165, 231, 177, 243)(166, 232, 176, 242)(167, 233, 182, 248)(169, 235, 184, 250)(172, 238, 186, 252)(178, 244, 188, 254)(179, 245, 187, 253)(180, 246, 189, 255)(181, 247, 193, 259)(183, 249, 194, 260)(185, 251, 195, 261)(190, 256, 198, 264)(191, 257, 197, 263)(192, 258, 196, 262) L = (1, 136)(2, 141)(3, 144)(4, 146)(5, 147)(6, 133)(7, 153)(8, 155)(9, 157)(10, 134)(11, 160)(12, 162)(13, 135)(14, 164)(15, 165)(16, 166)(17, 137)(18, 138)(19, 150)(20, 170)(21, 149)(22, 139)(23, 173)(24, 140)(25, 148)(26, 142)(27, 174)(28, 171)(29, 143)(30, 168)(31, 145)(32, 178)(33, 179)(34, 180)(35, 158)(36, 184)(37, 151)(38, 186)(39, 152)(40, 154)(41, 182)(42, 156)(43, 163)(44, 159)(45, 161)(46, 190)(47, 191)(48, 192)(49, 172)(50, 194)(51, 167)(52, 195)(53, 169)(54, 193)(55, 177)(56, 175)(57, 176)(58, 181)(59, 183)(60, 185)(61, 198)(62, 197)(63, 196)(64, 189)(65, 187)(66, 188)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4, 6, 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 E20.919 Graph:: simple bipartite v = 39 e = 132 f = 55 degree seq :: [ 4^33, 22^6 ] E20.921 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 6, 11}) Quotient :: edge Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^6, T2^11 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 43, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 54, 42, 30, 18, 8)(4, 11, 22, 34, 46, 57, 55, 44, 32, 20, 10)(6, 15, 27, 39, 51, 61, 62, 52, 40, 28, 16)(12, 21, 33, 45, 56, 63, 64, 58, 47, 35, 23)(14, 25, 37, 49, 59, 65, 66, 60, 50, 38, 26)(67, 68, 72, 80, 78, 70)(69, 74, 81, 92, 87, 76)(71, 73, 82, 91, 89, 77)(75, 84, 93, 104, 99, 86)(79, 83, 94, 103, 101, 88)(85, 96, 105, 116, 111, 98)(90, 95, 106, 115, 113, 100)(97, 108, 117, 126, 122, 110)(102, 107, 118, 125, 124, 112)(109, 120, 127, 132, 129, 121)(114, 119, 128, 131, 130, 123) L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132) local type(s) :: { ( 12^6 ), ( 12^11 ) } Outer automorphisms :: reflexible Dual of E20.922 Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 66 f = 11 degree seq :: [ 6^11, 11^6 ] E20.922 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 6, 11}) Quotient :: loop Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-2, (F * T2)^2, (F * T1)^2, T2^6, T2^-2 * T1^4, (T2 * T1)^11 ] Map:: non-degenerate R = (1, 67, 3, 69, 10, 76, 15, 81, 6, 72, 5, 71)(2, 68, 7, 73, 4, 70, 12, 78, 14, 80, 8, 74)(9, 75, 19, 85, 11, 77, 21, 87, 13, 79, 20, 86)(16, 82, 22, 88, 17, 83, 24, 90, 18, 84, 23, 89)(25, 91, 31, 97, 26, 92, 33, 99, 27, 93, 32, 98)(28, 94, 34, 100, 29, 95, 36, 102, 30, 96, 35, 101)(37, 103, 43, 109, 38, 104, 45, 111, 39, 105, 44, 110)(40, 106, 46, 112, 41, 107, 48, 114, 42, 108, 47, 113)(49, 115, 55, 121, 50, 116, 57, 123, 51, 117, 56, 122)(52, 118, 58, 124, 53, 119, 60, 126, 54, 120, 59, 125)(61, 127, 65, 131, 62, 128, 66, 132, 63, 129, 64, 130) L = (1, 68)(2, 72)(3, 75)(4, 67)(5, 79)(6, 80)(7, 82)(8, 84)(9, 71)(10, 70)(11, 69)(12, 83)(13, 81)(14, 76)(15, 77)(16, 74)(17, 73)(18, 78)(19, 91)(20, 93)(21, 92)(22, 94)(23, 96)(24, 95)(25, 86)(26, 85)(27, 87)(28, 89)(29, 88)(30, 90)(31, 103)(32, 105)(33, 104)(34, 106)(35, 108)(36, 107)(37, 98)(38, 97)(39, 99)(40, 101)(41, 100)(42, 102)(43, 115)(44, 117)(45, 116)(46, 118)(47, 120)(48, 119)(49, 110)(50, 109)(51, 111)(52, 113)(53, 112)(54, 114)(55, 127)(56, 129)(57, 128)(58, 130)(59, 132)(60, 131)(61, 122)(62, 121)(63, 123)(64, 125)(65, 124)(66, 126) local type(s) :: { ( 6, 11, 6, 11, 6, 11, 6, 11, 6, 11, 6, 11 ) } Outer automorphisms :: reflexible Dual of E20.921 Transitivity :: ET+ VT+ AT Graph:: v = 11 e = 66 f = 17 degree seq :: [ 12^11 ] E20.923 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 11}) Quotient :: dipole Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^6, Y2^11, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 67, 2, 68, 6, 72, 14, 80, 12, 78, 4, 70)(3, 69, 8, 74, 15, 81, 26, 92, 21, 87, 10, 76)(5, 71, 7, 73, 16, 82, 25, 91, 23, 89, 11, 77)(9, 75, 18, 84, 27, 93, 38, 104, 33, 99, 20, 86)(13, 79, 17, 83, 28, 94, 37, 103, 35, 101, 22, 88)(19, 85, 30, 96, 39, 105, 50, 116, 45, 111, 32, 98)(24, 90, 29, 95, 40, 106, 49, 115, 47, 113, 34, 100)(31, 97, 42, 108, 51, 117, 60, 126, 56, 122, 44, 110)(36, 102, 41, 107, 52, 118, 59, 125, 58, 124, 46, 112)(43, 109, 54, 120, 61, 127, 66, 132, 63, 129, 55, 121)(48, 114, 53, 119, 62, 128, 65, 131, 64, 130, 57, 123)(133, 199, 135, 201, 141, 207, 151, 217, 163, 229, 175, 241, 180, 246, 168, 234, 156, 222, 145, 211, 137, 203)(134, 200, 139, 205, 149, 215, 161, 227, 173, 239, 185, 251, 186, 252, 174, 240, 162, 228, 150, 216, 140, 206)(136, 202, 143, 209, 154, 220, 166, 232, 178, 244, 189, 255, 187, 253, 176, 242, 164, 230, 152, 218, 142, 208)(138, 204, 147, 213, 159, 225, 171, 237, 183, 249, 193, 259, 194, 260, 184, 250, 172, 238, 160, 226, 148, 214)(144, 210, 153, 219, 165, 231, 177, 243, 188, 254, 195, 261, 196, 262, 190, 256, 179, 245, 167, 233, 155, 221)(146, 212, 157, 223, 169, 235, 181, 247, 191, 257, 197, 263, 198, 264, 192, 258, 182, 248, 170, 236, 158, 224) L = (1, 135)(2, 139)(3, 141)(4, 143)(5, 133)(6, 147)(7, 149)(8, 134)(9, 151)(10, 136)(11, 154)(12, 153)(13, 137)(14, 157)(15, 159)(16, 138)(17, 161)(18, 140)(19, 163)(20, 142)(21, 165)(22, 166)(23, 144)(24, 145)(25, 169)(26, 146)(27, 171)(28, 148)(29, 173)(30, 150)(31, 175)(32, 152)(33, 177)(34, 178)(35, 155)(36, 156)(37, 181)(38, 158)(39, 183)(40, 160)(41, 185)(42, 162)(43, 180)(44, 164)(45, 188)(46, 189)(47, 167)(48, 168)(49, 191)(50, 170)(51, 193)(52, 172)(53, 186)(54, 174)(55, 176)(56, 195)(57, 187)(58, 179)(59, 197)(60, 182)(61, 194)(62, 184)(63, 196)(64, 190)(65, 198)(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, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E20.924 Graph:: bipartite v = 17 e = 132 f = 77 degree seq :: [ 12^11, 22^6 ] E20.924 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 11}) Quotient :: dipole Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^11 ] Map:: R = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)(133, 199, 134, 200, 138, 204, 146, 212, 144, 210, 136, 202)(135, 201, 140, 206, 147, 213, 158, 224, 153, 219, 142, 208)(137, 203, 139, 205, 148, 214, 157, 223, 155, 221, 143, 209)(141, 207, 150, 216, 159, 225, 170, 236, 165, 231, 152, 218)(145, 211, 149, 215, 160, 226, 169, 235, 167, 233, 154, 220)(151, 217, 162, 228, 171, 237, 182, 248, 177, 243, 164, 230)(156, 222, 161, 227, 172, 238, 181, 247, 179, 245, 166, 232)(163, 229, 174, 240, 183, 249, 192, 258, 188, 254, 176, 242)(168, 234, 173, 239, 184, 250, 191, 257, 190, 256, 178, 244)(175, 241, 186, 252, 193, 259, 198, 264, 195, 261, 187, 253)(180, 246, 185, 251, 194, 260, 197, 263, 196, 262, 189, 255) L = (1, 135)(2, 139)(3, 141)(4, 143)(5, 133)(6, 147)(7, 149)(8, 134)(9, 151)(10, 136)(11, 154)(12, 153)(13, 137)(14, 157)(15, 159)(16, 138)(17, 161)(18, 140)(19, 163)(20, 142)(21, 165)(22, 166)(23, 144)(24, 145)(25, 169)(26, 146)(27, 171)(28, 148)(29, 173)(30, 150)(31, 175)(32, 152)(33, 177)(34, 178)(35, 155)(36, 156)(37, 181)(38, 158)(39, 183)(40, 160)(41, 185)(42, 162)(43, 180)(44, 164)(45, 188)(46, 189)(47, 167)(48, 168)(49, 191)(50, 170)(51, 193)(52, 172)(53, 186)(54, 174)(55, 176)(56, 195)(57, 187)(58, 179)(59, 197)(60, 182)(61, 194)(62, 184)(63, 196)(64, 190)(65, 198)(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) :: { ( 12, 22 ), ( 12, 22, 12, 22, 12, 22, 12, 22, 12, 22, 12, 22 ) } Outer automorphisms :: reflexible Dual of E20.923 Graph:: simple bipartite v = 77 e = 132 f = 17 degree seq :: [ 2^66, 12^11 ] E20.925 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 22, 22}) 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, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^22 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 59, 53, 47, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 65, 61, 55, 49, 43, 37, 31, 25, 19, 13, 7)(4, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 66, 64, 58, 52, 46, 40, 34, 28, 22, 16, 10)(67, 68, 70)(69, 74, 72)(71, 76, 73)(75, 78, 80)(77, 79, 82)(81, 86, 84)(83, 88, 85)(87, 90, 92)(89, 91, 94)(93, 98, 96)(95, 100, 97)(99, 102, 104)(101, 103, 106)(105, 110, 108)(107, 112, 109)(111, 114, 116)(113, 115, 118)(117, 122, 120)(119, 124, 121)(123, 126, 128)(125, 127, 130)(129, 132, 131) 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) :: { ( 44^3 ), ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.926 Transitivity :: ET+ Graph:: simple bipartite v = 25 e = 66 f = 3 degree seq :: [ 3^22, 22^3 ] E20.926 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 22, 22}) 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, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^22 ] Map:: non-degenerate R = (1, 67, 3, 69, 9, 75, 15, 81, 21, 87, 27, 93, 33, 99, 39, 105, 45, 111, 51, 117, 57, 123, 63, 129, 59, 125, 53, 119, 47, 113, 41, 107, 35, 101, 29, 95, 23, 89, 17, 83, 11, 77, 5, 71)(2, 68, 6, 72, 12, 78, 18, 84, 24, 90, 30, 96, 36, 102, 42, 108, 48, 114, 54, 120, 60, 126, 65, 131, 61, 127, 55, 121, 49, 115, 43, 109, 37, 103, 31, 97, 25, 91, 19, 85, 13, 79, 7, 73)(4, 70, 8, 74, 14, 80, 20, 86, 26, 92, 32, 98, 38, 104, 44, 110, 50, 116, 56, 122, 62, 128, 66, 132, 64, 130, 58, 124, 52, 118, 46, 112, 40, 106, 34, 100, 28, 94, 22, 88, 16, 82, 10, 76) L = (1, 68)(2, 70)(3, 74)(4, 67)(5, 76)(6, 69)(7, 71)(8, 72)(9, 78)(10, 73)(11, 79)(12, 80)(13, 82)(14, 75)(15, 86)(16, 77)(17, 88)(18, 81)(19, 83)(20, 84)(21, 90)(22, 85)(23, 91)(24, 92)(25, 94)(26, 87)(27, 98)(28, 89)(29, 100)(30, 93)(31, 95)(32, 96)(33, 102)(34, 97)(35, 103)(36, 104)(37, 106)(38, 99)(39, 110)(40, 101)(41, 112)(42, 105)(43, 107)(44, 108)(45, 114)(46, 109)(47, 115)(48, 116)(49, 118)(50, 111)(51, 122)(52, 113)(53, 124)(54, 117)(55, 119)(56, 120)(57, 126)(58, 121)(59, 127)(60, 128)(61, 130)(62, 123)(63, 132)(64, 125)(65, 129)(66, 131) local type(s) :: { ( 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22, 3, 22 ) } Outer automorphisms :: reflexible Dual of E20.925 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 66 f = 25 degree seq :: [ 44^3 ] E20.927 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 22, 22}) 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^-1 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^22, 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 ] Map:: R = (1, 67, 2, 68, 4, 70)(3, 69, 8, 74, 6, 72)(5, 71, 10, 76, 7, 73)(9, 75, 12, 78, 14, 80)(11, 77, 13, 79, 16, 82)(15, 81, 20, 86, 18, 84)(17, 83, 22, 88, 19, 85)(21, 87, 24, 90, 26, 92)(23, 89, 25, 91, 28, 94)(27, 93, 32, 98, 30, 96)(29, 95, 34, 100, 31, 97)(33, 99, 36, 102, 38, 104)(35, 101, 37, 103, 40, 106)(39, 105, 44, 110, 42, 108)(41, 107, 46, 112, 43, 109)(45, 111, 48, 114, 50, 116)(47, 113, 49, 115, 52, 118)(51, 117, 56, 122, 54, 120)(53, 119, 58, 124, 55, 121)(57, 123, 60, 126, 62, 128)(59, 125, 61, 127, 64, 130)(63, 129, 66, 132, 65, 131)(133, 199, 135, 201, 141, 207, 147, 213, 153, 219, 159, 225, 165, 231, 171, 237, 177, 243, 183, 249, 189, 255, 195, 261, 191, 257, 185, 251, 179, 245, 173, 239, 167, 233, 161, 227, 155, 221, 149, 215, 143, 209, 137, 203)(134, 200, 138, 204, 144, 210, 150, 216, 156, 222, 162, 228, 168, 234, 174, 240, 180, 246, 186, 252, 192, 258, 197, 263, 193, 259, 187, 253, 181, 247, 175, 241, 169, 235, 163, 229, 157, 223, 151, 217, 145, 211, 139, 205)(136, 202, 140, 206, 146, 212, 152, 218, 158, 224, 164, 230, 170, 236, 176, 242, 182, 248, 188, 254, 194, 260, 198, 264, 196, 262, 190, 256, 184, 250, 178, 244, 172, 238, 166, 232, 160, 226, 154, 220, 148, 214, 142, 208) L = (1, 136)(2, 133)(3, 138)(4, 134)(5, 139)(6, 140)(7, 142)(8, 135)(9, 146)(10, 137)(11, 148)(12, 141)(13, 143)(14, 144)(15, 150)(16, 145)(17, 151)(18, 152)(19, 154)(20, 147)(21, 158)(22, 149)(23, 160)(24, 153)(25, 155)(26, 156)(27, 162)(28, 157)(29, 163)(30, 164)(31, 166)(32, 159)(33, 170)(34, 161)(35, 172)(36, 165)(37, 167)(38, 168)(39, 174)(40, 169)(41, 175)(42, 176)(43, 178)(44, 171)(45, 182)(46, 173)(47, 184)(48, 177)(49, 179)(50, 180)(51, 186)(52, 181)(53, 187)(54, 188)(55, 190)(56, 183)(57, 194)(58, 185)(59, 196)(60, 189)(61, 191)(62, 192)(63, 197)(64, 193)(65, 198)(66, 195)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 2, 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 E20.928 Graph:: bipartite v = 25 e = 132 f = 69 degree seq :: [ 6^22, 44^3 ] E20.928 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 22, 22}) 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, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^22 ] Map:: R = (1, 67, 2, 68, 6, 72, 12, 78, 18, 84, 24, 90, 30, 96, 36, 102, 42, 108, 48, 114, 54, 120, 60, 126, 59, 125, 53, 119, 47, 113, 41, 107, 35, 101, 29, 95, 23, 89, 17, 83, 11, 77, 4, 70)(3, 69, 8, 74, 13, 79, 20, 86, 25, 91, 32, 98, 37, 103, 44, 110, 49, 115, 56, 122, 61, 127, 66, 132, 63, 129, 57, 123, 51, 117, 45, 111, 39, 105, 33, 99, 27, 93, 21, 87, 15, 81, 9, 75)(5, 71, 7, 73, 14, 80, 19, 85, 26, 92, 31, 97, 38, 104, 43, 109, 50, 116, 55, 121, 62, 128, 65, 131, 64, 130, 58, 124, 52, 118, 46, 112, 40, 106, 34, 100, 28, 94, 22, 88, 16, 82, 10, 76)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264) L = (1, 135)(2, 139)(3, 137)(4, 142)(5, 133)(6, 145)(7, 140)(8, 134)(9, 136)(10, 141)(11, 147)(12, 151)(13, 146)(14, 138)(15, 148)(16, 143)(17, 154)(18, 157)(19, 152)(20, 144)(21, 149)(22, 153)(23, 159)(24, 163)(25, 158)(26, 150)(27, 160)(28, 155)(29, 166)(30, 169)(31, 164)(32, 156)(33, 161)(34, 165)(35, 171)(36, 175)(37, 170)(38, 162)(39, 172)(40, 167)(41, 178)(42, 181)(43, 176)(44, 168)(45, 173)(46, 177)(47, 183)(48, 187)(49, 182)(50, 174)(51, 184)(52, 179)(53, 190)(54, 193)(55, 188)(56, 180)(57, 185)(58, 189)(59, 195)(60, 197)(61, 194)(62, 186)(63, 196)(64, 191)(65, 198)(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) :: { ( 6, 44 ), ( 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44, 6, 44 ) } Outer automorphisms :: reflexible Dual of E20.927 Graph:: simple bipartite v = 69 e = 132 f = 25 degree seq :: [ 2^66, 44^3 ] E20.929 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 9, 9}) Quotient :: edge Aut^+ = Q8 : C9 (small group id <72, 3>) Aut = (Q8 : C9) : C2 (small group id <144, 32>) |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, T2^9 ] Map:: non-degenerate R = (1, 3, 10, 28, 47, 56, 40, 16, 5)(2, 7, 20, 43, 59, 60, 44, 24, 8)(4, 12, 32, 48, 64, 66, 51, 33, 13)(6, 17, 41, 57, 71, 72, 58, 42, 18)(9, 25, 45, 61, 69, 54, 38, 22, 26)(11, 30, 50, 63, 70, 55, 39, 23, 31)(14, 34, 21, 27, 46, 62, 67, 52, 35)(15, 36, 19, 29, 49, 65, 68, 53, 37)(73, 74, 78, 76)(75, 81, 89, 83)(77, 86, 90, 87)(79, 91, 84, 93)(80, 94, 85, 95)(82, 99, 113, 101)(88, 110, 114, 111)(92, 97, 104, 102)(96, 109, 105, 107)(98, 106, 103, 108)(100, 115, 129, 120)(112, 116, 130, 123)(117, 118, 122, 121)(119, 133, 143, 135)(124, 127, 125, 126)(128, 139, 144, 140)(131, 137, 136, 134)(132, 141, 138, 142) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 18^4 ), ( 18^9 ) } Outer automorphisms :: reflexible Dual of E20.930 Transitivity :: ET+ Graph:: simple bipartite v = 26 e = 72 f = 8 degree seq :: [ 4^18, 9^8 ] E20.930 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 9, 9}) Quotient :: loop Aut^+ = Q8 : C9 (small group id <72, 3>) Aut = (Q8 : C9) : C2 (small group id <144, 32>) |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, T2^9 ] Map:: non-degenerate R = (1, 73, 3, 75, 10, 82, 28, 100, 47, 119, 56, 128, 40, 112, 16, 88, 5, 77)(2, 74, 7, 79, 20, 92, 43, 115, 59, 131, 60, 132, 44, 116, 24, 96, 8, 80)(4, 76, 12, 84, 32, 104, 48, 120, 64, 136, 66, 138, 51, 123, 33, 105, 13, 85)(6, 78, 17, 89, 41, 113, 57, 129, 71, 143, 72, 144, 58, 130, 42, 114, 18, 90)(9, 81, 25, 97, 45, 117, 61, 133, 69, 141, 54, 126, 38, 110, 22, 94, 26, 98)(11, 83, 30, 102, 50, 122, 63, 135, 70, 142, 55, 127, 39, 111, 23, 95, 31, 103)(14, 86, 34, 106, 21, 93, 27, 99, 46, 118, 62, 134, 67, 139, 52, 124, 35, 107)(15, 87, 36, 108, 19, 91, 29, 101, 49, 121, 65, 137, 68, 140, 53, 125, 37, 109) L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 86)(6, 76)(7, 91)(8, 94)(9, 89)(10, 99)(11, 75)(12, 93)(13, 95)(14, 90)(15, 77)(16, 110)(17, 83)(18, 87)(19, 84)(20, 97)(21, 79)(22, 85)(23, 80)(24, 109)(25, 104)(26, 106)(27, 113)(28, 115)(29, 82)(30, 92)(31, 108)(32, 102)(33, 107)(34, 103)(35, 96)(36, 98)(37, 105)(38, 114)(39, 88)(40, 116)(41, 101)(42, 111)(43, 129)(44, 130)(45, 118)(46, 122)(47, 133)(48, 100)(49, 117)(50, 121)(51, 112)(52, 127)(53, 126)(54, 124)(55, 125)(56, 139)(57, 120)(58, 123)(59, 137)(60, 141)(61, 143)(62, 131)(63, 119)(64, 134)(65, 136)(66, 142)(67, 144)(68, 128)(69, 138)(70, 132)(71, 135)(72, 140) local type(s) :: { ( 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9 ) } Outer automorphisms :: reflexible Dual of E20.929 Transitivity :: ET+ VT+ AT Graph:: v = 8 e = 72 f = 26 degree seq :: [ 18^8 ] E20.931 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 9, 9}) Quotient :: dipole Aut^+ = Q8 : C9 (small group id <72, 3>) Aut = (Q8 : C9) : C2 (small group id <144, 32>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^2 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y2 * Y3 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-2, 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, Y2^9, (Y3 * Y2^-1)^9 ] Map:: R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 17, 89, 11, 83)(5, 77, 14, 86, 18, 90, 15, 87)(7, 79, 19, 91, 12, 84, 21, 93)(8, 80, 22, 94, 13, 85, 23, 95)(10, 82, 27, 99, 41, 113, 29, 101)(16, 88, 38, 110, 42, 114, 39, 111)(20, 92, 25, 97, 32, 104, 30, 102)(24, 96, 37, 109, 33, 105, 35, 107)(26, 98, 34, 106, 31, 103, 36, 108)(28, 100, 43, 115, 57, 129, 48, 120)(40, 112, 44, 116, 58, 130, 51, 123)(45, 117, 46, 118, 50, 122, 49, 121)(47, 119, 61, 133, 71, 143, 63, 135)(52, 124, 55, 127, 53, 125, 54, 126)(56, 128, 67, 139, 72, 144, 68, 140)(59, 131, 65, 137, 64, 136, 62, 134)(60, 132, 69, 141, 66, 138, 70, 142)(145, 217, 147, 219, 154, 226, 172, 244, 191, 263, 200, 272, 184, 256, 160, 232, 149, 221)(146, 218, 151, 223, 164, 236, 187, 259, 203, 275, 204, 276, 188, 260, 168, 240, 152, 224)(148, 220, 156, 228, 176, 248, 192, 264, 208, 280, 210, 282, 195, 267, 177, 249, 157, 229)(150, 222, 161, 233, 185, 257, 201, 273, 215, 287, 216, 288, 202, 274, 186, 258, 162, 234)(153, 225, 169, 241, 189, 261, 205, 277, 213, 285, 198, 270, 182, 254, 166, 238, 170, 242)(155, 227, 174, 246, 194, 266, 207, 279, 214, 286, 199, 271, 183, 255, 167, 239, 175, 247)(158, 230, 178, 250, 165, 237, 171, 243, 190, 262, 206, 278, 211, 283, 196, 268, 179, 251)(159, 231, 180, 252, 163, 235, 173, 245, 193, 265, 209, 281, 212, 284, 197, 269, 181, 253) L = (1, 148)(2, 145)(3, 155)(4, 150)(5, 159)(6, 146)(7, 165)(8, 167)(9, 147)(10, 173)(11, 161)(12, 163)(13, 166)(14, 149)(15, 162)(16, 183)(17, 153)(18, 158)(19, 151)(20, 174)(21, 156)(22, 152)(23, 157)(24, 179)(25, 164)(26, 180)(27, 154)(28, 192)(29, 185)(30, 176)(31, 178)(32, 169)(33, 181)(34, 170)(35, 177)(36, 175)(37, 168)(38, 160)(39, 186)(40, 195)(41, 171)(42, 182)(43, 172)(44, 184)(45, 193)(46, 189)(47, 207)(48, 201)(49, 194)(50, 190)(51, 202)(52, 198)(53, 199)(54, 197)(55, 196)(56, 212)(57, 187)(58, 188)(59, 206)(60, 214)(61, 191)(62, 208)(63, 215)(64, 209)(65, 203)(66, 213)(67, 200)(68, 216)(69, 204)(70, 210)(71, 205)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E20.932 Graph:: bipartite v = 26 e = 144 f = 80 degree seq :: [ 8^18, 18^8 ] E20.932 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 9, 9}) Quotient :: dipole Aut^+ = Q8 : C9 (small group id <72, 3>) Aut = (Q8 : C9) : C2 (small group id <144, 32>) |r| :: 2 Presentation :: [ Y2, R^2, 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 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^4, Y1^9 ] Map:: R = (1, 73, 2, 74, 6, 78, 17, 89, 41, 113, 53, 125, 35, 107, 13, 85, 4, 76)(3, 75, 9, 81, 25, 97, 42, 114, 59, 131, 65, 137, 50, 122, 30, 102, 11, 83)(5, 77, 15, 87, 39, 111, 43, 115, 61, 133, 69, 141, 54, 126, 40, 112, 16, 88)(7, 79, 20, 92, 47, 119, 57, 129, 67, 139, 52, 124, 34, 106, 29, 101, 22, 94)(8, 80, 23, 95, 48, 120, 58, 130, 70, 142, 55, 127, 36, 108, 31, 103, 24, 96)(10, 82, 21, 93, 45, 117, 60, 132, 71, 143, 72, 144, 64, 136, 49, 121, 28, 100)(12, 84, 32, 104, 27, 99, 18, 90, 44, 116, 62, 134, 66, 138, 51, 123, 33, 105)(14, 86, 37, 109, 26, 98, 19, 91, 46, 118, 63, 135, 68, 140, 56, 128, 38, 110)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288) L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 162)(7, 165)(8, 146)(9, 170)(10, 149)(11, 173)(12, 172)(13, 178)(14, 148)(15, 171)(16, 175)(17, 186)(18, 189)(19, 150)(20, 183)(21, 152)(22, 176)(23, 169)(24, 181)(25, 164)(26, 159)(27, 153)(28, 158)(29, 160)(30, 182)(31, 155)(32, 168)(33, 174)(34, 193)(35, 194)(36, 157)(37, 166)(38, 184)(39, 167)(40, 177)(41, 201)(42, 204)(43, 161)(44, 192)(45, 163)(46, 191)(47, 188)(48, 190)(49, 180)(50, 208)(51, 199)(52, 195)(53, 210)(54, 179)(55, 200)(56, 196)(57, 215)(58, 185)(59, 207)(60, 187)(61, 206)(62, 203)(63, 205)(64, 198)(65, 211)(66, 216)(67, 213)(68, 197)(69, 214)(70, 209)(71, 202)(72, 212)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ) } Outer automorphisms :: reflexible Dual of E20.931 Graph:: simple bipartite v = 80 e = 144 f = 26 degree seq :: [ 2^72, 18^8 ] E20.933 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 40}) Quotient :: dipole Aut^+ = D80 (small group id <80, 7>) Aut = C2 x D80 (small group id <160, 124>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 81, 2, 82)(3, 83, 5, 85)(4, 84, 8, 88)(6, 86, 10, 90)(7, 87, 11, 91)(9, 89, 13, 93)(12, 92, 16, 96)(14, 94, 18, 98)(15, 95, 19, 99)(17, 97, 21, 101)(20, 100, 24, 104)(22, 102, 26, 106)(23, 103, 27, 107)(25, 105, 29, 109)(28, 108, 32, 112)(30, 110, 55, 135)(31, 111, 57, 137)(33, 113, 59, 139)(34, 114, 62, 142)(35, 115, 65, 145)(36, 116, 68, 148)(37, 117, 70, 150)(38, 118, 69, 149)(39, 119, 73, 153)(40, 120, 60, 140)(41, 121, 74, 154)(42, 122, 63, 143)(43, 123, 66, 146)(44, 124, 61, 141)(45, 125, 71, 151)(46, 126, 64, 144)(47, 127, 67, 147)(48, 128, 75, 155)(49, 129, 72, 152)(50, 130, 76, 156)(51, 131, 77, 157)(52, 132, 78, 158)(53, 133, 79, 159)(54, 134, 80, 160)(56, 136, 58, 138)(161, 241, 163, 243)(162, 242, 165, 245)(164, 244, 167, 247)(166, 246, 169, 249)(168, 248, 171, 251)(170, 250, 173, 253)(172, 252, 175, 255)(174, 254, 177, 257)(176, 256, 179, 259)(178, 258, 181, 261)(180, 260, 183, 263)(182, 262, 185, 265)(184, 264, 187, 267)(186, 266, 189, 269)(188, 268, 191, 271)(190, 270, 208, 288)(192, 272, 217, 297)(193, 273, 195, 275)(194, 274, 197, 277)(196, 276, 199, 279)(198, 278, 201, 281)(200, 280, 203, 283)(202, 282, 205, 285)(204, 284, 207, 287)(206, 286, 209, 289)(210, 290, 212, 292)(211, 291, 213, 293)(214, 294, 218, 298)(215, 295, 235, 315)(216, 296, 240, 320)(219, 299, 225, 305)(220, 300, 226, 306)(221, 301, 227, 307)(222, 302, 230, 310)(223, 303, 231, 311)(224, 304, 232, 312)(228, 308, 233, 313)(229, 309, 234, 314)(236, 316, 238, 318)(237, 317, 239, 319) L = (1, 164)(2, 166)(3, 167)(4, 161)(5, 169)(6, 162)(7, 163)(8, 172)(9, 165)(10, 174)(11, 175)(12, 168)(13, 177)(14, 170)(15, 171)(16, 180)(17, 173)(18, 182)(19, 183)(20, 176)(21, 185)(22, 178)(23, 179)(24, 188)(25, 181)(26, 190)(27, 191)(28, 184)(29, 208)(30, 186)(31, 187)(32, 205)(33, 220)(34, 223)(35, 226)(36, 222)(37, 231)(38, 219)(39, 230)(40, 235)(41, 225)(42, 217)(43, 215)(44, 228)(45, 192)(46, 229)(47, 233)(48, 189)(49, 234)(50, 221)(51, 224)(52, 227)(53, 232)(54, 236)(55, 203)(56, 237)(57, 202)(58, 238)(59, 198)(60, 193)(61, 210)(62, 196)(63, 194)(64, 211)(65, 201)(66, 195)(67, 212)(68, 204)(69, 206)(70, 199)(71, 197)(72, 213)(73, 207)(74, 209)(75, 200)(76, 214)(77, 216)(78, 218)(79, 240)(80, 239)(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 ) } Outer automorphisms :: reflexible Dual of E20.934 Graph:: simple bipartite v = 80 e = 160 f = 42 degree seq :: [ 4^80 ] E20.934 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 40}) Quotient :: dipole Aut^+ = D80 (small group id <80, 7>) Aut = C2 x D80 (small group id <160, 124>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2 * Y3 * Y1^20, Y1^-1 * Y2 * Y1^9 * Y3 * Y1^-10 ] Map:: non-degenerate R = (1, 81, 2, 82, 6, 86, 13, 93, 21, 101, 29, 109, 37, 117, 45, 125, 53, 133, 61, 141, 69, 149, 77, 157, 74, 154, 66, 146, 58, 138, 50, 130, 42, 122, 34, 114, 26, 106, 18, 98, 10, 90, 16, 96, 24, 104, 32, 112, 40, 120, 48, 128, 56, 136, 64, 144, 72, 152, 80, 160, 76, 156, 68, 148, 60, 140, 52, 132, 44, 124, 36, 116, 28, 108, 20, 100, 12, 92, 5, 85)(3, 83, 9, 89, 17, 97, 25, 105, 33, 113, 41, 121, 49, 129, 57, 137, 65, 145, 73, 153, 79, 159, 71, 151, 63, 143, 55, 135, 47, 127, 39, 119, 31, 111, 23, 103, 15, 95, 8, 88, 4, 84, 11, 91, 19, 99, 27, 107, 35, 115, 43, 123, 51, 131, 59, 139, 67, 147, 75, 155, 78, 158, 70, 150, 62, 142, 54, 134, 46, 126, 38, 118, 30, 110, 22, 102, 14, 94, 7, 87)(161, 241, 163, 243)(162, 242, 167, 247)(164, 244, 170, 250)(165, 245, 169, 249)(166, 246, 174, 254)(168, 248, 176, 256)(171, 251, 178, 258)(172, 252, 177, 257)(173, 253, 182, 262)(175, 255, 184, 264)(179, 259, 186, 266)(180, 260, 185, 265)(181, 261, 190, 270)(183, 263, 192, 272)(187, 267, 194, 274)(188, 268, 193, 273)(189, 269, 198, 278)(191, 271, 200, 280)(195, 275, 202, 282)(196, 276, 201, 281)(197, 277, 206, 286)(199, 279, 208, 288)(203, 283, 210, 290)(204, 284, 209, 289)(205, 285, 214, 294)(207, 287, 216, 296)(211, 291, 218, 298)(212, 292, 217, 297)(213, 293, 222, 302)(215, 295, 224, 304)(219, 299, 226, 306)(220, 300, 225, 305)(221, 301, 230, 310)(223, 303, 232, 312)(227, 307, 234, 314)(228, 308, 233, 313)(229, 309, 238, 318)(231, 311, 240, 320)(235, 315, 237, 317)(236, 316, 239, 319) L = (1, 164)(2, 168)(3, 170)(4, 161)(5, 171)(6, 175)(7, 176)(8, 162)(9, 178)(10, 163)(11, 165)(12, 179)(13, 183)(14, 184)(15, 166)(16, 167)(17, 186)(18, 169)(19, 172)(20, 187)(21, 191)(22, 192)(23, 173)(24, 174)(25, 194)(26, 177)(27, 180)(28, 195)(29, 199)(30, 200)(31, 181)(32, 182)(33, 202)(34, 185)(35, 188)(36, 203)(37, 207)(38, 208)(39, 189)(40, 190)(41, 210)(42, 193)(43, 196)(44, 211)(45, 215)(46, 216)(47, 197)(48, 198)(49, 218)(50, 201)(51, 204)(52, 219)(53, 223)(54, 224)(55, 205)(56, 206)(57, 226)(58, 209)(59, 212)(60, 227)(61, 231)(62, 232)(63, 213)(64, 214)(65, 234)(66, 217)(67, 220)(68, 235)(69, 239)(70, 240)(71, 221)(72, 222)(73, 237)(74, 225)(75, 228)(76, 238)(77, 233)(78, 236)(79, 229)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4^4 ), ( 4^80 ) } Outer automorphisms :: reflexible Dual of E20.933 Graph:: bipartite v = 42 e = 160 f = 80 degree seq :: [ 4^40, 80^2 ] E20.935 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 40}) Quotient :: edge Aut^+ = C5 : Q16 (small group id <80, 8>) Aut = (C40 x C2) : C2 (small group id <160, 125>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1^4, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^9 * T1^-1 * T2^-11 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 78, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 74, 66, 58, 50, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(81, 82, 86, 84)(83, 88, 93, 90)(85, 87, 94, 91)(89, 96, 101, 98)(92, 95, 102, 99)(97, 104, 109, 106)(100, 103, 110, 107)(105, 112, 117, 114)(108, 111, 118, 115)(113, 120, 125, 122)(116, 119, 126, 123)(121, 128, 133, 130)(124, 127, 134, 131)(129, 136, 141, 138)(132, 135, 142, 139)(137, 144, 149, 146)(140, 143, 150, 147)(145, 152, 157, 154)(148, 151, 158, 155)(153, 160, 156, 159) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8^4 ), ( 8^40 ) } Outer automorphisms :: reflexible Dual of E20.936 Transitivity :: ET+ Graph:: bipartite v = 22 e = 80 f = 20 degree seq :: [ 4^20, 40^2 ] E20.936 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 40}) Quotient :: loop Aut^+ = C5 : Q16 (small group id <80, 8>) Aut = (C40 x C2) : C2 (small group id <160, 125>) |r| :: 2 Presentation :: [ F^2, T1^4, T2^4, (F * T2)^2, T2 * T1^2 * T2, (F * T1)^2, T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-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 * 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^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 81, 3, 83, 6, 86, 5, 85)(2, 82, 7, 87, 4, 84, 8, 88)(9, 89, 13, 93, 10, 90, 14, 94)(11, 91, 15, 95, 12, 92, 16, 96)(17, 97, 21, 101, 18, 98, 22, 102)(19, 99, 23, 103, 20, 100, 24, 104)(25, 105, 29, 109, 26, 106, 30, 110)(27, 107, 31, 111, 28, 108, 32, 112)(33, 113, 35, 115, 34, 114, 38, 118)(36, 116, 52, 132, 37, 117, 51, 131)(39, 119, 56, 136, 40, 120, 55, 135)(41, 121, 58, 138, 42, 122, 57, 137)(43, 123, 60, 140, 44, 124, 59, 139)(45, 125, 62, 142, 46, 126, 61, 141)(47, 127, 64, 144, 48, 128, 63, 143)(49, 129, 66, 146, 50, 130, 65, 145)(53, 133, 68, 148, 54, 134, 67, 147)(69, 149, 71, 151, 70, 150, 72, 152)(73, 153, 75, 155, 74, 154, 76, 156)(77, 157, 80, 160, 78, 158, 79, 159) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 90)(6, 84)(7, 91)(8, 92)(9, 85)(10, 83)(11, 88)(12, 87)(13, 97)(14, 98)(15, 99)(16, 100)(17, 94)(18, 93)(19, 96)(20, 95)(21, 105)(22, 106)(23, 107)(24, 108)(25, 102)(26, 101)(27, 104)(28, 103)(29, 113)(30, 114)(31, 131)(32, 132)(33, 110)(34, 109)(35, 135)(36, 137)(37, 138)(38, 136)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 144)(45, 145)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 112)(52, 111)(53, 153)(54, 154)(55, 118)(56, 115)(57, 117)(58, 116)(59, 120)(60, 119)(61, 122)(62, 121)(63, 124)(64, 123)(65, 126)(66, 125)(67, 128)(68, 127)(69, 130)(70, 129)(71, 159)(72, 160)(73, 134)(74, 133)(75, 158)(76, 157)(77, 155)(78, 156)(79, 152)(80, 151) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E20.935 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 20 e = 80 f = 22 degree seq :: [ 8^20 ] E20.937 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 40}) Quotient :: dipole Aut^+ = C5 : Q16 (small group id <80, 8>) Aut = (C40 x C2) : C2 (small group id <160, 125>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (Y3^-1 * Y1^-1)^4, Y2^19 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 81, 2, 82, 6, 86, 4, 84)(3, 83, 8, 88, 13, 93, 10, 90)(5, 85, 7, 87, 14, 94, 11, 91)(9, 89, 16, 96, 21, 101, 18, 98)(12, 92, 15, 95, 22, 102, 19, 99)(17, 97, 24, 104, 29, 109, 26, 106)(20, 100, 23, 103, 30, 110, 27, 107)(25, 105, 32, 112, 37, 117, 34, 114)(28, 108, 31, 111, 38, 118, 35, 115)(33, 113, 40, 120, 45, 125, 42, 122)(36, 116, 39, 119, 46, 126, 43, 123)(41, 121, 48, 128, 53, 133, 50, 130)(44, 124, 47, 127, 54, 134, 51, 131)(49, 129, 56, 136, 61, 141, 58, 138)(52, 132, 55, 135, 62, 142, 59, 139)(57, 137, 64, 144, 69, 149, 66, 146)(60, 140, 63, 143, 70, 150, 67, 147)(65, 145, 72, 152, 77, 157, 74, 154)(68, 148, 71, 151, 78, 158, 75, 155)(73, 153, 80, 160, 76, 156, 79, 159)(161, 241, 163, 243, 169, 249, 177, 257, 185, 265, 193, 273, 201, 281, 209, 289, 217, 297, 225, 305, 233, 313, 238, 318, 230, 310, 222, 302, 214, 294, 206, 286, 198, 278, 190, 270, 182, 262, 174, 254, 166, 246, 173, 253, 181, 261, 189, 269, 197, 277, 205, 285, 213, 293, 221, 301, 229, 309, 237, 317, 236, 316, 228, 308, 220, 300, 212, 292, 204, 284, 196, 276, 188, 268, 180, 260, 172, 252, 165, 245)(162, 242, 167, 247, 175, 255, 183, 263, 191, 271, 199, 279, 207, 287, 215, 295, 223, 303, 231, 311, 239, 319, 234, 314, 226, 306, 218, 298, 210, 290, 202, 282, 194, 274, 186, 266, 178, 258, 170, 250, 164, 244, 171, 251, 179, 259, 187, 267, 195, 275, 203, 283, 211, 291, 219, 299, 227, 307, 235, 315, 240, 320, 232, 312, 224, 304, 216, 296, 208, 288, 200, 280, 192, 272, 184, 264, 176, 256, 168, 248) L = (1, 163)(2, 167)(3, 169)(4, 171)(5, 161)(6, 173)(7, 175)(8, 162)(9, 177)(10, 164)(11, 179)(12, 165)(13, 181)(14, 166)(15, 183)(16, 168)(17, 185)(18, 170)(19, 187)(20, 172)(21, 189)(22, 174)(23, 191)(24, 176)(25, 193)(26, 178)(27, 195)(28, 180)(29, 197)(30, 182)(31, 199)(32, 184)(33, 201)(34, 186)(35, 203)(36, 188)(37, 205)(38, 190)(39, 207)(40, 192)(41, 209)(42, 194)(43, 211)(44, 196)(45, 213)(46, 198)(47, 215)(48, 200)(49, 217)(50, 202)(51, 219)(52, 204)(53, 221)(54, 206)(55, 223)(56, 208)(57, 225)(58, 210)(59, 227)(60, 212)(61, 229)(62, 214)(63, 231)(64, 216)(65, 233)(66, 218)(67, 235)(68, 220)(69, 237)(70, 222)(71, 239)(72, 224)(73, 238)(74, 226)(75, 240)(76, 228)(77, 236)(78, 230)(79, 234)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E20.938 Graph:: bipartite v = 22 e = 160 f = 100 degree seq :: [ 8^20, 80^2 ] E20.938 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 40}) Quotient :: dipole Aut^+ = C5 : Q16 (small group id <80, 8>) Aut = (C40 x C2) : C2 (small group id <160, 125>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^19 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^40 ] Map:: R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242, 166, 246, 164, 244)(163, 243, 168, 248, 173, 253, 170, 250)(165, 245, 167, 247, 174, 254, 171, 251)(169, 249, 176, 256, 181, 261, 178, 258)(172, 252, 175, 255, 182, 262, 179, 259)(177, 257, 184, 264, 189, 269, 186, 266)(180, 260, 183, 263, 190, 270, 187, 267)(185, 265, 192, 272, 197, 277, 194, 274)(188, 268, 191, 271, 198, 278, 195, 275)(193, 273, 200, 280, 205, 285, 202, 282)(196, 276, 199, 279, 206, 286, 203, 283)(201, 281, 208, 288, 213, 293, 210, 290)(204, 284, 207, 287, 214, 294, 211, 291)(209, 289, 216, 296, 221, 301, 218, 298)(212, 292, 215, 295, 222, 302, 219, 299)(217, 297, 224, 304, 229, 309, 226, 306)(220, 300, 223, 303, 230, 310, 227, 307)(225, 305, 232, 312, 237, 317, 234, 314)(228, 308, 231, 311, 238, 318, 235, 315)(233, 313, 240, 320, 236, 316, 239, 319) L = (1, 163)(2, 167)(3, 169)(4, 171)(5, 161)(6, 173)(7, 175)(8, 162)(9, 177)(10, 164)(11, 179)(12, 165)(13, 181)(14, 166)(15, 183)(16, 168)(17, 185)(18, 170)(19, 187)(20, 172)(21, 189)(22, 174)(23, 191)(24, 176)(25, 193)(26, 178)(27, 195)(28, 180)(29, 197)(30, 182)(31, 199)(32, 184)(33, 201)(34, 186)(35, 203)(36, 188)(37, 205)(38, 190)(39, 207)(40, 192)(41, 209)(42, 194)(43, 211)(44, 196)(45, 213)(46, 198)(47, 215)(48, 200)(49, 217)(50, 202)(51, 219)(52, 204)(53, 221)(54, 206)(55, 223)(56, 208)(57, 225)(58, 210)(59, 227)(60, 212)(61, 229)(62, 214)(63, 231)(64, 216)(65, 233)(66, 218)(67, 235)(68, 220)(69, 237)(70, 222)(71, 239)(72, 224)(73, 238)(74, 226)(75, 240)(76, 228)(77, 236)(78, 230)(79, 234)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 8, 80 ), ( 8, 80, 8, 80, 8, 80, 8, 80 ) } Outer automorphisms :: reflexible Dual of E20.937 Graph:: simple bipartite v = 100 e = 160 f = 22 degree seq :: [ 2^80, 8^20 ] E20.939 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 80, 80}) Quotient :: regular Aut^+ = C80 (small group id <80, 2>) Aut = D160 (small group id <160, 6>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^40 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 36, 38, 40, 42, 44, 46, 48, 50, 51, 52, 54, 56, 58, 60, 62, 64, 70, 72, 74, 76, 78, 80, 66, 49, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 33, 34, 35, 37, 39, 41, 43, 45, 47, 53, 55, 57, 59, 61, 63, 65, 67, 68, 69, 71, 73, 75, 77, 79, 32, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 33)(32, 49)(34, 36)(35, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(51, 53)(52, 55)(54, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 79)(68, 70)(69, 72)(71, 74)(73, 76)(75, 78)(77, 80) local type(s) :: { ( 80^80 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 40 f = 1 degree seq :: [ 80 ] E20.940 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 80, 80}) Quotient :: edge Aut^+ = C80 (small group id <80, 2>) Aut = D160 (small group id <160, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^40 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 36, 33, 35, 39, 42, 44, 46, 48, 50, 52, 57, 54, 56, 60, 63, 65, 67, 69, 71, 73, 77, 75, 74, 53, 30, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 29, 41, 38, 34, 37, 40, 43, 45, 47, 49, 51, 62, 59, 55, 58, 61, 64, 66, 68, 70, 72, 80, 79, 76, 78, 32, 28, 24, 20, 16, 12, 8, 4)(81, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 97)(96, 98)(99, 101)(100, 102)(103, 105)(104, 106)(107, 109)(108, 110)(111, 121)(112, 133)(113, 114)(115, 117)(116, 118)(119, 120)(122, 123)(124, 125)(126, 127)(128, 129)(130, 131)(132, 142)(134, 135)(136, 138)(137, 139)(140, 141)(143, 144)(145, 146)(147, 148)(149, 150)(151, 152)(153, 160)(154, 158)(155, 156)(157, 159) L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 160, 160 ), ( 160^80 ) } Outer automorphisms :: reflexible Dual of E20.941 Transitivity :: ET+ Graph:: bipartite v = 41 e = 80 f = 1 degree seq :: [ 2^40, 80 ] E20.941 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 80, 80}) Quotient :: loop Aut^+ = C80 (small group id <80, 2>) Aut = D160 (small group id <160, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^40 * T1 ] Map:: R = (1, 81, 3, 83, 7, 87, 11, 91, 15, 95, 19, 99, 23, 103, 27, 107, 31, 111, 33, 113, 35, 115, 38, 118, 40, 120, 42, 122, 44, 124, 46, 126, 48, 128, 50, 130, 52, 132, 54, 134, 57, 137, 59, 139, 61, 141, 63, 143, 65, 145, 67, 147, 69, 149, 71, 151, 73, 153, 76, 156, 78, 158, 70, 150, 51, 131, 30, 110, 26, 106, 22, 102, 18, 98, 14, 94, 10, 90, 6, 86, 2, 82, 5, 85, 9, 89, 13, 93, 17, 97, 21, 101, 25, 105, 29, 109, 37, 117, 34, 114, 36, 116, 39, 119, 41, 121, 43, 123, 45, 125, 47, 127, 49, 129, 56, 136, 53, 133, 55, 135, 58, 138, 60, 140, 62, 142, 64, 144, 66, 146, 68, 148, 75, 155, 72, 152, 74, 154, 77, 157, 79, 159, 80, 160, 32, 112, 28, 108, 24, 104, 20, 100, 16, 96, 12, 92, 8, 88, 4, 84) L = (1, 82)(2, 81)(3, 85)(4, 86)(5, 83)(6, 84)(7, 89)(8, 90)(9, 87)(10, 88)(11, 93)(12, 94)(13, 91)(14, 92)(15, 97)(16, 98)(17, 95)(18, 96)(19, 101)(20, 102)(21, 99)(22, 100)(23, 105)(24, 106)(25, 103)(26, 104)(27, 109)(28, 110)(29, 107)(30, 108)(31, 117)(32, 131)(33, 114)(34, 113)(35, 116)(36, 115)(37, 111)(38, 119)(39, 118)(40, 121)(41, 120)(42, 123)(43, 122)(44, 125)(45, 124)(46, 127)(47, 126)(48, 129)(49, 128)(50, 136)(51, 112)(52, 133)(53, 132)(54, 135)(55, 134)(56, 130)(57, 138)(58, 137)(59, 140)(60, 139)(61, 142)(62, 141)(63, 144)(64, 143)(65, 146)(66, 145)(67, 148)(68, 147)(69, 155)(70, 160)(71, 152)(72, 151)(73, 154)(74, 153)(75, 149)(76, 157)(77, 156)(78, 159)(79, 158)(80, 150) 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, 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 E20.940 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 80 f = 41 degree seq :: [ 160 ] E20.942 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 80, 80}) Quotient :: dipole Aut^+ = C80 (small group id <80, 2>) Aut = D160 (small group id <160, 6>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^40 * Y1, (Y3 * Y2^-1)^80 ] Map:: R = (1, 81, 2, 82)(3, 83, 5, 85)(4, 84, 6, 86)(7, 87, 9, 89)(8, 88, 10, 90)(11, 91, 13, 93)(12, 92, 14, 94)(15, 95, 17, 97)(16, 96, 18, 98)(19, 99, 21, 101)(20, 100, 22, 102)(23, 103, 25, 105)(24, 104, 26, 106)(27, 107, 29, 109)(28, 108, 30, 110)(31, 111, 45, 125)(32, 112, 55, 135)(33, 113, 34, 114)(35, 115, 37, 117)(36, 116, 38, 118)(39, 119, 41, 121)(40, 120, 42, 122)(43, 123, 44, 124)(46, 126, 47, 127)(48, 128, 49, 129)(50, 130, 51, 131)(52, 132, 53, 133)(54, 134, 68, 148)(56, 136, 57, 137)(58, 138, 60, 140)(59, 139, 61, 141)(62, 142, 64, 144)(63, 143, 65, 145)(66, 146, 67, 147)(69, 149, 70, 150)(71, 151, 72, 152)(73, 153, 74, 154)(75, 155, 76, 156)(77, 157, 80, 160)(78, 158, 79, 159)(161, 241, 163, 243, 167, 247, 171, 251, 175, 255, 179, 259, 183, 263, 187, 267, 191, 271, 200, 280, 196, 276, 193, 273, 195, 275, 199, 279, 203, 283, 206, 286, 208, 288, 210, 290, 212, 292, 214, 294, 223, 303, 219, 299, 216, 296, 218, 298, 222, 302, 226, 306, 229, 309, 231, 311, 233, 313, 235, 315, 237, 317, 238, 318, 215, 295, 190, 270, 186, 266, 182, 262, 178, 258, 174, 254, 170, 250, 166, 246, 162, 242, 165, 245, 169, 249, 173, 253, 177, 257, 181, 261, 185, 265, 189, 269, 205, 285, 202, 282, 198, 278, 194, 274, 197, 277, 201, 281, 204, 284, 207, 287, 209, 289, 211, 291, 213, 293, 228, 308, 225, 305, 221, 301, 217, 297, 220, 300, 224, 304, 227, 307, 230, 310, 232, 312, 234, 314, 236, 316, 240, 320, 239, 319, 192, 272, 188, 268, 184, 264, 180, 260, 176, 256, 172, 252, 168, 248, 164, 244) L = (1, 162)(2, 161)(3, 165)(4, 166)(5, 163)(6, 164)(7, 169)(8, 170)(9, 167)(10, 168)(11, 173)(12, 174)(13, 171)(14, 172)(15, 177)(16, 178)(17, 175)(18, 176)(19, 181)(20, 182)(21, 179)(22, 180)(23, 185)(24, 186)(25, 183)(26, 184)(27, 189)(28, 190)(29, 187)(30, 188)(31, 205)(32, 215)(33, 194)(34, 193)(35, 197)(36, 198)(37, 195)(38, 196)(39, 201)(40, 202)(41, 199)(42, 200)(43, 204)(44, 203)(45, 191)(46, 207)(47, 206)(48, 209)(49, 208)(50, 211)(51, 210)(52, 213)(53, 212)(54, 228)(55, 192)(56, 217)(57, 216)(58, 220)(59, 221)(60, 218)(61, 219)(62, 224)(63, 225)(64, 222)(65, 223)(66, 227)(67, 226)(68, 214)(69, 230)(70, 229)(71, 232)(72, 231)(73, 234)(74, 233)(75, 236)(76, 235)(77, 240)(78, 239)(79, 238)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 2, 160, 2, 160 ), ( 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160, 2, 160 ) } Outer automorphisms :: reflexible Dual of E20.943 Graph:: bipartite v = 41 e = 160 f = 81 degree seq :: [ 4^40, 160 ] E20.943 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 80, 80}) Quotient :: dipole Aut^+ = C80 (small group id <80, 2>) Aut = D160 (small group id <160, 6>) |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 * Y1^40 ] Map:: R = (1, 81, 2, 82, 5, 85, 9, 89, 13, 93, 17, 97, 21, 101, 25, 105, 29, 109, 36, 116, 38, 118, 40, 120, 42, 122, 44, 124, 46, 126, 48, 128, 50, 130, 51, 131, 52, 132, 54, 134, 56, 136, 58, 138, 60, 140, 62, 142, 64, 144, 70, 150, 72, 152, 74, 154, 76, 156, 78, 158, 80, 160, 66, 146, 49, 129, 31, 111, 27, 107, 23, 103, 19, 99, 15, 95, 11, 91, 7, 87, 3, 83, 6, 86, 10, 90, 14, 94, 18, 98, 22, 102, 26, 106, 30, 110, 33, 113, 34, 114, 35, 115, 37, 117, 39, 119, 41, 121, 43, 123, 45, 125, 47, 127, 53, 133, 55, 135, 57, 137, 59, 139, 61, 141, 63, 143, 65, 145, 67, 147, 68, 148, 69, 149, 71, 151, 73, 153, 75, 155, 77, 157, 79, 159, 32, 112, 28, 108, 24, 104, 20, 100, 16, 96, 12, 92, 8, 88, 4, 84)(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, 167)(5, 170)(6, 162)(7, 164)(8, 171)(9, 174)(10, 165)(11, 168)(12, 175)(13, 178)(14, 169)(15, 172)(16, 179)(17, 182)(18, 173)(19, 176)(20, 183)(21, 186)(22, 177)(23, 180)(24, 187)(25, 190)(26, 181)(27, 184)(28, 191)(29, 193)(30, 185)(31, 188)(32, 209)(33, 189)(34, 196)(35, 198)(36, 194)(37, 200)(38, 195)(39, 202)(40, 197)(41, 204)(42, 199)(43, 206)(44, 201)(45, 208)(46, 203)(47, 210)(48, 205)(49, 192)(50, 207)(51, 213)(52, 215)(53, 211)(54, 217)(55, 212)(56, 219)(57, 214)(58, 221)(59, 216)(60, 223)(61, 218)(62, 225)(63, 220)(64, 227)(65, 222)(66, 239)(67, 224)(68, 230)(69, 232)(70, 228)(71, 234)(72, 229)(73, 236)(74, 231)(75, 238)(76, 233)(77, 240)(78, 235)(79, 226)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4, 160 ), ( 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160, 4, 160 ) } Outer automorphisms :: reflexible Dual of E20.942 Graph:: bipartite v = 81 e = 160 f = 41 degree seq :: [ 2^80, 160 ] E20.944 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 41, 82}) Quotient :: regular Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-41 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 36, 33, 34, 37, 40, 43, 45, 47, 49, 51, 57, 54, 55, 58, 61, 64, 66, 68, 70, 72, 78, 75, 76, 74, 53, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 42, 39, 35, 38, 41, 44, 46, 48, 50, 52, 63, 60, 56, 59, 62, 65, 67, 69, 71, 73, 82, 80, 77, 79, 81, 32, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 42)(32, 53)(33, 35)(34, 38)(36, 39)(37, 41)(40, 44)(43, 46)(45, 48)(47, 50)(49, 52)(51, 63)(54, 56)(55, 59)(57, 60)(58, 62)(61, 65)(64, 67)(66, 69)(68, 71)(70, 73)(72, 82)(74, 81)(75, 77)(76, 79)(78, 80) local type(s) :: { ( 41^82 ) } Outer automorphisms :: reflexible Dual of E20.945 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 41 f = 2 degree seq :: [ 82 ] E20.945 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 41, 82}) Quotient :: regular Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^41 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 47, 43, 39, 35, 38, 42, 46, 50, 52, 54, 56, 73, 69, 65, 61, 58, 59, 62, 66, 70, 74, 76, 78, 80, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 48, 44, 40, 36, 33, 34, 37, 41, 45, 49, 51, 53, 55, 72, 68, 64, 60, 63, 67, 71, 75, 77, 79, 81, 82, 57, 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, 48)(32, 57)(33, 35)(34, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 50)(49, 52)(51, 54)(53, 56)(55, 73)(58, 60)(59, 63)(61, 64)(62, 67)(65, 68)(66, 71)(69, 72)(70, 75)(74, 77)(76, 79)(78, 81)(80, 82) local type(s) :: { ( 82^41 ) } Outer automorphisms :: reflexible Dual of E20.944 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 41 f = 1 degree seq :: [ 41^2 ] E20.946 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 41, 82}) Quotient :: edge Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^41 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 33, 35, 38, 40, 42, 44, 46, 48, 50, 52, 54, 57, 59, 61, 63, 65, 67, 69, 71, 73, 76, 78, 80, 82, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 37, 34, 36, 39, 41, 43, 45, 47, 49, 56, 53, 55, 58, 60, 62, 64, 66, 68, 75, 72, 74, 77, 79, 81, 70, 51, 30, 26, 22, 18, 14, 10, 6)(83, 84)(85, 87)(86, 88)(89, 91)(90, 92)(93, 95)(94, 96)(97, 99)(98, 100)(101, 103)(102, 104)(105, 107)(106, 108)(109, 111)(110, 112)(113, 119)(114, 133)(115, 116)(117, 118)(120, 121)(122, 123)(124, 125)(126, 127)(128, 129)(130, 131)(132, 138)(134, 135)(136, 137)(139, 140)(141, 142)(143, 144)(145, 146)(147, 148)(149, 150)(151, 157)(152, 164)(153, 154)(155, 156)(158, 159)(160, 161)(162, 163) L = (1, 83)(2, 84)(3, 85)(4, 86)(5, 87)(6, 88)(7, 89)(8, 90)(9, 91)(10, 92)(11, 93)(12, 94)(13, 95)(14, 96)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 102)(21, 103)(22, 104)(23, 105)(24, 106)(25, 107)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 114)(33, 115)(34, 116)(35, 117)(36, 118)(37, 119)(38, 120)(39, 121)(40, 122)(41, 123)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 164, 164 ), ( 164^41 ) } Outer automorphisms :: reflexible Dual of E20.950 Transitivity :: ET+ Graph:: simple bipartite v = 43 e = 82 f = 1 degree seq :: [ 2^41, 41^2 ] E20.947 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 41, 82}) Quotient :: edge Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^18 * T2^-1 * T1 * T2^-19, T2^-2 * T1^39, T2^17 * T1^16 * T2^-1 * T1^19 * T2^-1 * T1^19 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 33, 61, 81, 78, 73, 70, 64, 69, 66, 72, 76, 80, 59, 58, 55, 54, 49, 46, 40, 39, 35, 37, 43, 47, 51, 32, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 34, 62, 82, 77, 74, 68, 67, 63, 65, 71, 75, 79, 60, 57, 56, 53, 50, 45, 42, 36, 41, 38, 44, 48, 52, 31, 28, 23, 20, 15, 12, 6, 5)(83, 84, 88, 93, 97, 101, 105, 109, 113, 133, 130, 125, 120, 117, 118, 122, 127, 131, 135, 137, 139, 141, 161, 158, 153, 148, 145, 146, 150, 155, 159, 163, 144, 115, 112, 107, 104, 99, 96, 91, 86)(85, 89, 87, 90, 94, 98, 102, 106, 110, 114, 134, 129, 126, 119, 123, 121, 124, 128, 132, 136, 138, 140, 142, 162, 157, 154, 147, 151, 149, 152, 156, 160, 164, 143, 116, 111, 108, 103, 100, 95, 92) L = (1, 83)(2, 84)(3, 85)(4, 86)(5, 87)(6, 88)(7, 89)(8, 90)(9, 91)(10, 92)(11, 93)(12, 94)(13, 95)(14, 96)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 102)(21, 103)(22, 104)(23, 105)(24, 106)(25, 107)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 114)(33, 115)(34, 116)(35, 117)(36, 118)(37, 119)(38, 120)(39, 121)(40, 122)(41, 123)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 4^41 ), ( 4^82 ) } Outer automorphisms :: reflexible Dual of E20.951 Transitivity :: ET+ Graph:: bipartite v = 3 e = 82 f = 41 degree seq :: [ 41^2, 82 ] E20.948 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 41, 82}) Quotient :: edge Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-41 ] Map:: R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 38)(32, 51)(33, 35)(34, 37)(36, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 57)(52, 54)(53, 56)(55, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 76)(70, 82)(71, 73)(72, 75)(74, 78)(77, 80)(79, 81)(83, 84, 87, 91, 95, 99, 103, 107, 111, 115, 116, 118, 121, 123, 125, 127, 129, 131, 134, 135, 137, 140, 142, 144, 146, 148, 150, 153, 154, 156, 159, 161, 152, 133, 113, 109, 105, 101, 97, 93, 89, 85, 88, 92, 96, 100, 104, 108, 112, 120, 117, 119, 122, 124, 126, 128, 130, 132, 139, 136, 138, 141, 143, 145, 147, 149, 151, 158, 155, 157, 160, 162, 163, 164, 114, 110, 106, 102, 98, 94, 90, 86) L = (1, 83)(2, 84)(3, 85)(4, 86)(5, 87)(6, 88)(7, 89)(8, 90)(9, 91)(10, 92)(11, 93)(12, 94)(13, 95)(14, 96)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 102)(21, 103)(22, 104)(23, 105)(24, 106)(25, 107)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 114)(33, 115)(34, 116)(35, 117)(36, 118)(37, 119)(38, 120)(39, 121)(40, 122)(41, 123)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164) local type(s) :: { ( 82, 82 ), ( 82^82 ) } Outer automorphisms :: reflexible Dual of E20.949 Transitivity :: ET+ Graph:: bipartite v = 42 e = 82 f = 2 degree seq :: [ 2^41, 82 ] E20.949 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 41, 82}) Quotient :: loop Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^41 ] Map:: R = (1, 83, 3, 85, 7, 89, 11, 93, 15, 97, 19, 101, 23, 105, 27, 109, 31, 113, 34, 116, 37, 119, 39, 121, 41, 123, 43, 125, 45, 127, 47, 129, 49, 131, 55, 137, 52, 134, 54, 136, 57, 139, 59, 141, 61, 143, 63, 145, 65, 147, 67, 149, 69, 151, 72, 154, 75, 157, 77, 159, 79, 161, 81, 163, 82, 164, 32, 114, 28, 110, 24, 106, 20, 102, 16, 98, 12, 94, 8, 90, 4, 86)(2, 84, 5, 87, 9, 91, 13, 95, 17, 99, 21, 103, 25, 107, 29, 111, 36, 118, 33, 115, 35, 117, 38, 120, 40, 122, 42, 124, 44, 126, 46, 128, 48, 130, 50, 132, 53, 135, 56, 138, 58, 140, 60, 142, 62, 144, 64, 146, 66, 148, 68, 150, 74, 156, 71, 153, 73, 155, 76, 158, 78, 160, 80, 162, 70, 152, 51, 133, 30, 112, 26, 108, 22, 104, 18, 100, 14, 96, 10, 92, 6, 88) L = (1, 84)(2, 83)(3, 87)(4, 88)(5, 85)(6, 86)(7, 91)(8, 92)(9, 89)(10, 90)(11, 95)(12, 96)(13, 93)(14, 94)(15, 99)(16, 100)(17, 97)(18, 98)(19, 103)(20, 104)(21, 101)(22, 102)(23, 107)(24, 108)(25, 105)(26, 106)(27, 111)(28, 112)(29, 109)(30, 110)(31, 118)(32, 133)(33, 116)(34, 115)(35, 119)(36, 113)(37, 117)(38, 121)(39, 120)(40, 123)(41, 122)(42, 125)(43, 124)(44, 127)(45, 126)(46, 129)(47, 128)(48, 131)(49, 130)(50, 137)(51, 114)(52, 135)(53, 134)(54, 138)(55, 132)(56, 136)(57, 140)(58, 139)(59, 142)(60, 141)(61, 144)(62, 143)(63, 146)(64, 145)(65, 148)(66, 147)(67, 150)(68, 149)(69, 156)(70, 164)(71, 154)(72, 153)(73, 157)(74, 151)(75, 155)(76, 159)(77, 158)(78, 161)(79, 160)(80, 163)(81, 162)(82, 152) local type(s) :: { ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.948 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 82 f = 42 degree seq :: [ 82^2 ] E20.950 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 41, 82}) Quotient :: loop Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^18 * T2^-1 * T1 * T2^-19, T2^-2 * T1^39, T2^17 * T1^16 * T2^-1 * T1^19 * T2^-1 * T1^19 * T2^-1 * T1 ] Map:: R = (1, 83, 3, 85, 9, 91, 13, 95, 17, 99, 21, 103, 25, 107, 29, 111, 33, 115, 53, 135, 73, 155, 82, 164, 78, 160, 77, 159, 75, 157, 72, 154, 69, 151, 68, 150, 65, 147, 64, 146, 61, 143, 60, 142, 56, 138, 59, 141, 51, 133, 50, 132, 47, 129, 46, 128, 43, 125, 42, 124, 38, 120, 37, 119, 35, 117, 32, 114, 27, 109, 24, 106, 19, 101, 16, 98, 11, 93, 8, 90, 2, 84, 7, 89, 4, 86, 10, 92, 14, 96, 18, 100, 22, 104, 26, 108, 30, 112, 34, 116, 54, 136, 74, 156, 81, 163, 80, 162, 76, 158, 79, 161, 71, 153, 70, 152, 67, 149, 66, 148, 63, 145, 62, 144, 58, 140, 57, 139, 55, 137, 52, 134, 49, 131, 48, 130, 45, 127, 44, 126, 41, 123, 40, 122, 36, 118, 39, 121, 31, 113, 28, 110, 23, 105, 20, 102, 15, 97, 12, 94, 6, 88, 5, 87) L = (1, 84)(2, 88)(3, 89)(4, 83)(5, 90)(6, 93)(7, 87)(8, 94)(9, 86)(10, 85)(11, 97)(12, 98)(13, 92)(14, 91)(15, 101)(16, 102)(17, 96)(18, 95)(19, 105)(20, 106)(21, 100)(22, 99)(23, 109)(24, 110)(25, 104)(26, 103)(27, 113)(28, 114)(29, 108)(30, 107)(31, 117)(32, 121)(33, 112)(34, 111)(35, 118)(36, 120)(37, 122)(38, 123)(39, 119)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 137)(52, 141)(53, 116)(54, 115)(55, 138)(56, 140)(57, 142)(58, 143)(59, 139)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 157)(72, 161)(73, 136)(74, 135)(75, 158)(76, 160)(77, 162)(78, 163)(79, 159)(80, 164)(81, 155)(82, 156) local type(s) :: { ( 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41, 2, 41 ) } Outer automorphisms :: reflexible Dual of E20.946 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 82 f = 43 degree seq :: [ 164 ] E20.951 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 41, 82}) Quotient :: loop Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-41 ] Map:: non-degenerate R = (1, 83, 3, 85)(2, 84, 6, 88)(4, 86, 7, 89)(5, 87, 10, 92)(8, 90, 11, 93)(9, 91, 14, 96)(12, 94, 15, 97)(13, 95, 18, 100)(16, 98, 19, 101)(17, 99, 22, 104)(20, 102, 23, 105)(21, 103, 26, 108)(24, 106, 27, 109)(25, 107, 30, 112)(28, 110, 31, 113)(29, 111, 36, 118)(32, 114, 51, 133)(33, 115, 35, 117)(34, 116, 38, 120)(37, 119, 40, 122)(39, 121, 42, 124)(41, 123, 44, 126)(43, 125, 46, 128)(45, 127, 48, 130)(47, 129, 50, 132)(49, 131, 55, 137)(52, 134, 54, 136)(53, 135, 57, 139)(56, 138, 59, 141)(58, 140, 61, 143)(60, 142, 63, 145)(62, 144, 65, 147)(64, 146, 67, 149)(66, 148, 69, 151)(68, 150, 74, 156)(70, 152, 81, 163)(71, 153, 73, 155)(72, 154, 76, 158)(75, 157, 78, 160)(77, 159, 80, 162)(79, 161, 82, 164) L = (1, 84)(2, 87)(3, 88)(4, 83)(5, 91)(6, 92)(7, 85)(8, 86)(9, 95)(10, 96)(11, 89)(12, 90)(13, 99)(14, 100)(15, 93)(16, 94)(17, 103)(18, 104)(19, 97)(20, 98)(21, 107)(22, 108)(23, 101)(24, 102)(25, 111)(26, 112)(27, 105)(28, 106)(29, 117)(30, 118)(31, 109)(32, 110)(33, 116)(34, 119)(35, 120)(36, 115)(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, 136)(50, 137)(51, 113)(52, 135)(53, 138)(54, 139)(55, 134)(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, 155)(69, 156)(70, 133)(71, 154)(72, 157)(73, 158)(74, 153)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 114)(82, 152) local type(s) :: { ( 41, 82, 41, 82 ) } Outer automorphisms :: reflexible Dual of E20.947 Transitivity :: ET+ VT+ AT Graph:: v = 41 e = 82 f = 3 degree seq :: [ 4^41 ] E20.952 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 41, 82}) Quotient :: dipole Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |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, Y2^41, (Y3 * Y2^-1)^82 ] Map:: R = (1, 83, 2, 84)(3, 85, 5, 87)(4, 86, 6, 88)(7, 89, 9, 91)(8, 90, 10, 92)(11, 93, 13, 95)(12, 94, 14, 96)(15, 97, 17, 99)(16, 98, 18, 100)(19, 101, 21, 103)(20, 102, 22, 104)(23, 105, 25, 107)(24, 106, 26, 108)(27, 109, 29, 111)(28, 110, 30, 112)(31, 113, 36, 118)(32, 114, 51, 133)(33, 115, 34, 116)(35, 117, 37, 119)(38, 120, 39, 121)(40, 122, 41, 123)(42, 124, 43, 125)(44, 126, 45, 127)(46, 128, 47, 129)(48, 130, 49, 131)(50, 132, 55, 137)(52, 134, 53, 135)(54, 136, 56, 138)(57, 139, 58, 140)(59, 141, 60, 142)(61, 143, 62, 144)(63, 145, 64, 146)(65, 147, 66, 148)(67, 149, 68, 150)(69, 151, 74, 156)(70, 152, 82, 164)(71, 153, 72, 154)(73, 155, 75, 157)(76, 158, 77, 159)(78, 160, 79, 161)(80, 162, 81, 163)(165, 247, 167, 249, 171, 253, 175, 257, 179, 261, 183, 265, 187, 269, 191, 273, 195, 277, 198, 280, 201, 283, 203, 285, 205, 287, 207, 289, 209, 291, 211, 293, 213, 295, 219, 301, 216, 298, 218, 300, 221, 303, 223, 305, 225, 307, 227, 309, 229, 311, 231, 313, 233, 315, 236, 318, 239, 321, 241, 323, 243, 325, 245, 327, 246, 328, 196, 278, 192, 274, 188, 270, 184, 266, 180, 262, 176, 258, 172, 254, 168, 250)(166, 248, 169, 251, 173, 255, 177, 259, 181, 263, 185, 267, 189, 271, 193, 275, 200, 282, 197, 279, 199, 281, 202, 284, 204, 286, 206, 288, 208, 290, 210, 292, 212, 294, 214, 296, 217, 299, 220, 302, 222, 304, 224, 306, 226, 308, 228, 310, 230, 312, 232, 314, 238, 320, 235, 317, 237, 319, 240, 322, 242, 324, 244, 326, 234, 316, 215, 297, 194, 276, 190, 272, 186, 268, 182, 264, 178, 260, 174, 256, 170, 252) L = (1, 166)(2, 165)(3, 169)(4, 170)(5, 167)(6, 168)(7, 173)(8, 174)(9, 171)(10, 172)(11, 177)(12, 178)(13, 175)(14, 176)(15, 181)(16, 182)(17, 179)(18, 180)(19, 185)(20, 186)(21, 183)(22, 184)(23, 189)(24, 190)(25, 187)(26, 188)(27, 193)(28, 194)(29, 191)(30, 192)(31, 200)(32, 215)(33, 198)(34, 197)(35, 201)(36, 195)(37, 199)(38, 203)(39, 202)(40, 205)(41, 204)(42, 207)(43, 206)(44, 209)(45, 208)(46, 211)(47, 210)(48, 213)(49, 212)(50, 219)(51, 196)(52, 217)(53, 216)(54, 220)(55, 214)(56, 218)(57, 222)(58, 221)(59, 224)(60, 223)(61, 226)(62, 225)(63, 228)(64, 227)(65, 230)(66, 229)(67, 232)(68, 231)(69, 238)(70, 246)(71, 236)(72, 235)(73, 239)(74, 233)(75, 237)(76, 241)(77, 240)(78, 243)(79, 242)(80, 245)(81, 244)(82, 234)(83, 247)(84, 248)(85, 249)(86, 250)(87, 251)(88, 252)(89, 253)(90, 254)(91, 255)(92, 256)(93, 257)(94, 258)(95, 259)(96, 260)(97, 261)(98, 262)(99, 263)(100, 264)(101, 265)(102, 266)(103, 267)(104, 268)(105, 269)(106, 270)(107, 271)(108, 272)(109, 273)(110, 274)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 283)(120, 284)(121, 285)(122, 286)(123, 287)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 298)(135, 299)(136, 300)(137, 301)(138, 302)(139, 303)(140, 304)(141, 305)(142, 306)(143, 307)(144, 308)(145, 309)(146, 310)(147, 311)(148, 312)(149, 313)(150, 314)(151, 315)(152, 316)(153, 317)(154, 318)(155, 319)(156, 320)(157, 321)(158, 322)(159, 323)(160, 324)(161, 325)(162, 326)(163, 327)(164, 328) local type(s) :: { ( 2, 164, 2, 164 ), ( 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164, 2, 164 ) } Outer automorphisms :: reflexible Dual of E20.955 Graph:: bipartite v = 43 e = 164 f = 83 degree seq :: [ 4^41, 82^2 ] E20.953 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 41, 82}) Quotient :: dipole Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y2^2 * Y1^2, R * Y2 * R * Y3, (R * Y1)^2, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^-20 * Y2^-20, Y1^-1 * Y2^40, Y1^41 ] Map:: R = (1, 83, 2, 84, 6, 88, 11, 93, 15, 97, 19, 101, 23, 105, 27, 109, 31, 113, 53, 135, 75, 157, 79, 161, 80, 162, 77, 159, 74, 156, 71, 153, 70, 152, 67, 149, 66, 148, 63, 145, 60, 142, 57, 139, 58, 140, 55, 137, 52, 134, 49, 131, 48, 130, 45, 127, 44, 126, 41, 123, 38, 120, 35, 117, 36, 118, 33, 115, 30, 112, 25, 107, 22, 104, 17, 99, 14, 96, 9, 91, 4, 86)(3, 85, 7, 89, 5, 87, 8, 90, 12, 94, 16, 98, 20, 102, 24, 106, 28, 110, 32, 114, 54, 136, 76, 158, 82, 164, 81, 163, 78, 160, 73, 155, 72, 154, 69, 151, 68, 150, 65, 147, 64, 146, 59, 141, 62, 144, 61, 143, 56, 138, 51, 133, 50, 132, 47, 129, 46, 128, 43, 125, 42, 124, 37, 119, 40, 122, 39, 121, 34, 116, 29, 111, 26, 108, 21, 103, 18, 100, 13, 95, 10, 92)(165, 247, 167, 249, 173, 255, 177, 259, 181, 263, 185, 267, 189, 271, 193, 275, 197, 279, 203, 285, 199, 281, 201, 283, 205, 287, 207, 289, 209, 291, 211, 293, 213, 295, 215, 297, 219, 301, 225, 307, 221, 303, 223, 305, 227, 309, 229, 311, 231, 313, 233, 315, 235, 317, 237, 319, 241, 323, 245, 327, 243, 325, 240, 322, 217, 299, 196, 278, 191, 273, 188, 270, 183, 265, 180, 262, 175, 257, 172, 254, 166, 248, 171, 253, 168, 250, 174, 256, 178, 260, 182, 264, 186, 268, 190, 272, 194, 276, 198, 280, 200, 282, 204, 286, 202, 284, 206, 288, 208, 290, 210, 292, 212, 294, 214, 296, 216, 298, 220, 302, 222, 304, 226, 308, 224, 306, 228, 310, 230, 312, 232, 314, 234, 316, 236, 318, 238, 320, 242, 324, 244, 326, 246, 328, 239, 321, 218, 300, 195, 277, 192, 274, 187, 269, 184, 266, 179, 261, 176, 258, 170, 252, 169, 251) L = (1, 167)(2, 171)(3, 173)(4, 174)(5, 165)(6, 169)(7, 168)(8, 166)(9, 177)(10, 178)(11, 172)(12, 170)(13, 181)(14, 182)(15, 176)(16, 175)(17, 185)(18, 186)(19, 180)(20, 179)(21, 189)(22, 190)(23, 184)(24, 183)(25, 193)(26, 194)(27, 188)(28, 187)(29, 197)(30, 198)(31, 192)(32, 191)(33, 203)(34, 200)(35, 201)(36, 204)(37, 205)(38, 206)(39, 199)(40, 202)(41, 207)(42, 208)(43, 209)(44, 210)(45, 211)(46, 212)(47, 213)(48, 214)(49, 215)(50, 216)(51, 219)(52, 220)(53, 196)(54, 195)(55, 225)(56, 222)(57, 223)(58, 226)(59, 227)(60, 228)(61, 221)(62, 224)(63, 229)(64, 230)(65, 231)(66, 232)(67, 233)(68, 234)(69, 235)(70, 236)(71, 237)(72, 238)(73, 241)(74, 242)(75, 218)(76, 217)(77, 245)(78, 244)(79, 240)(80, 246)(81, 243)(82, 239)(83, 247)(84, 248)(85, 249)(86, 250)(87, 251)(88, 252)(89, 253)(90, 254)(91, 255)(92, 256)(93, 257)(94, 258)(95, 259)(96, 260)(97, 261)(98, 262)(99, 263)(100, 264)(101, 265)(102, 266)(103, 267)(104, 268)(105, 269)(106, 270)(107, 271)(108, 272)(109, 273)(110, 274)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 283)(120, 284)(121, 285)(122, 286)(123, 287)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 298)(135, 299)(136, 300)(137, 301)(138, 302)(139, 303)(140, 304)(141, 305)(142, 306)(143, 307)(144, 308)(145, 309)(146, 310)(147, 311)(148, 312)(149, 313)(150, 314)(151, 315)(152, 316)(153, 317)(154, 318)(155, 319)(156, 320)(157, 321)(158, 322)(159, 323)(160, 324)(161, 325)(162, 326)(163, 327)(164, 328) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E20.954 Graph:: bipartite v = 3 e = 164 f = 123 degree seq :: [ 82^2, 164 ] E20.954 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 41, 82}) Quotient :: dipole Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^41 * Y2, (Y3^-1 * Y1^-1)^82 ] Map:: R = (1, 83)(2, 84)(3, 85)(4, 86)(5, 87)(6, 88)(7, 89)(8, 90)(9, 91)(10, 92)(11, 93)(12, 94)(13, 95)(14, 96)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 102)(21, 103)(22, 104)(23, 105)(24, 106)(25, 107)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 114)(33, 115)(34, 116)(35, 117)(36, 118)(37, 119)(38, 120)(39, 121)(40, 122)(41, 123)(42, 124)(43, 125)(44, 126)(45, 127)(46, 128)(47, 129)(48, 130)(49, 131)(50, 132)(51, 133)(52, 134)(53, 135)(54, 136)(55, 137)(56, 138)(57, 139)(58, 140)(59, 141)(60, 142)(61, 143)(62, 144)(63, 145)(64, 146)(65, 147)(66, 148)(67, 149)(68, 150)(69, 151)(70, 152)(71, 153)(72, 154)(73, 155)(74, 156)(75, 157)(76, 158)(77, 159)(78, 160)(79, 161)(80, 162)(81, 163)(82, 164)(165, 247, 166, 248)(167, 249, 169, 251)(168, 250, 170, 252)(171, 253, 173, 255)(172, 254, 174, 256)(175, 257, 177, 259)(176, 258, 178, 260)(179, 261, 181, 263)(180, 262, 182, 264)(183, 265, 185, 267)(184, 266, 186, 268)(187, 269, 189, 271)(188, 270, 190, 272)(191, 273, 193, 275)(192, 274, 194, 276)(195, 277, 197, 279)(196, 278, 213, 295)(198, 280, 199, 281)(200, 282, 201, 283)(202, 284, 203, 285)(204, 286, 205, 287)(206, 288, 207, 289)(208, 290, 209, 291)(210, 292, 211, 293)(212, 294, 214, 296)(215, 297, 216, 298)(217, 299, 218, 300)(219, 301, 220, 302)(221, 303, 222, 304)(223, 305, 224, 306)(225, 307, 226, 308)(227, 309, 228, 310)(229, 311, 232, 314)(230, 312, 246, 328)(231, 313, 233, 315)(234, 316, 235, 317)(236, 318, 237, 319)(238, 320, 239, 321)(240, 322, 241, 323)(242, 324, 243, 325)(244, 326, 245, 327) L = (1, 167)(2, 169)(3, 171)(4, 165)(5, 173)(6, 166)(7, 175)(8, 168)(9, 177)(10, 170)(11, 179)(12, 172)(13, 181)(14, 174)(15, 183)(16, 176)(17, 185)(18, 178)(19, 187)(20, 180)(21, 189)(22, 182)(23, 191)(24, 184)(25, 193)(26, 186)(27, 195)(28, 188)(29, 197)(30, 190)(31, 199)(32, 192)(33, 198)(34, 200)(35, 201)(36, 202)(37, 203)(38, 204)(39, 205)(40, 206)(41, 207)(42, 208)(43, 209)(44, 210)(45, 211)(46, 212)(47, 214)(48, 216)(49, 194)(50, 215)(51, 217)(52, 218)(53, 219)(54, 220)(55, 221)(56, 222)(57, 223)(58, 224)(59, 225)(60, 226)(61, 227)(62, 228)(63, 229)(64, 232)(65, 233)(66, 213)(67, 234)(68, 231)(69, 235)(70, 236)(71, 237)(72, 238)(73, 239)(74, 240)(75, 241)(76, 242)(77, 243)(78, 244)(79, 245)(80, 246)(81, 230)(82, 196)(83, 247)(84, 248)(85, 249)(86, 250)(87, 251)(88, 252)(89, 253)(90, 254)(91, 255)(92, 256)(93, 257)(94, 258)(95, 259)(96, 260)(97, 261)(98, 262)(99, 263)(100, 264)(101, 265)(102, 266)(103, 267)(104, 268)(105, 269)(106, 270)(107, 271)(108, 272)(109, 273)(110, 274)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 283)(120, 284)(121, 285)(122, 286)(123, 287)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 298)(135, 299)(136, 300)(137, 301)(138, 302)(139, 303)(140, 304)(141, 305)(142, 306)(143, 307)(144, 308)(145, 309)(146, 310)(147, 311)(148, 312)(149, 313)(150, 314)(151, 315)(152, 316)(153, 317)(154, 318)(155, 319)(156, 320)(157, 321)(158, 322)(159, 323)(160, 324)(161, 325)(162, 326)(163, 327)(164, 328) local type(s) :: { ( 82, 164 ), ( 82, 164, 82, 164 ) } Outer automorphisms :: reflexible Dual of E20.953 Graph:: simple bipartite v = 123 e = 164 f = 3 degree seq :: [ 2^82, 4^41 ] E20.955 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 41, 82}) Quotient :: dipole Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-41 ] Map:: R = (1, 83, 2, 84, 5, 87, 9, 91, 13, 95, 17, 99, 21, 103, 25, 107, 29, 111, 39, 121, 35, 117, 38, 120, 42, 124, 44, 126, 46, 128, 48, 130, 50, 132, 52, 134, 61, 143, 57, 139, 54, 136, 55, 137, 58, 140, 62, 144, 64, 146, 66, 148, 68, 150, 70, 152, 72, 154, 81, 163, 77, 159, 80, 162, 74, 156, 53, 135, 31, 113, 27, 109, 23, 105, 19, 101, 15, 97, 11, 93, 7, 89, 3, 85, 6, 88, 10, 92, 14, 96, 18, 100, 22, 104, 26, 108, 30, 112, 40, 122, 36, 118, 33, 115, 34, 116, 37, 119, 41, 123, 43, 125, 45, 127, 47, 129, 49, 131, 51, 133, 60, 142, 56, 138, 59, 141, 63, 145, 65, 147, 67, 149, 69, 151, 71, 153, 73, 155, 82, 164, 78, 160, 75, 157, 76, 158, 79, 161, 32, 114, 28, 110, 24, 106, 20, 102, 16, 98, 12, 94, 8, 90, 4, 86)(165, 247)(166, 248)(167, 249)(168, 250)(169, 251)(170, 252)(171, 253)(172, 254)(173, 255)(174, 256)(175, 257)(176, 258)(177, 259)(178, 260)(179, 261)(180, 262)(181, 263)(182, 264)(183, 265)(184, 266)(185, 267)(186, 268)(187, 269)(188, 270)(189, 271)(190, 272)(191, 273)(192, 274)(193, 275)(194, 276)(195, 277)(196, 278)(197, 279)(198, 280)(199, 281)(200, 282)(201, 283)(202, 284)(203, 285)(204, 286)(205, 287)(206, 288)(207, 289)(208, 290)(209, 291)(210, 292)(211, 293)(212, 294)(213, 295)(214, 296)(215, 297)(216, 298)(217, 299)(218, 300)(219, 301)(220, 302)(221, 303)(222, 304)(223, 305)(224, 306)(225, 307)(226, 308)(227, 309)(228, 310)(229, 311)(230, 312)(231, 313)(232, 314)(233, 315)(234, 316)(235, 317)(236, 318)(237, 319)(238, 320)(239, 321)(240, 322)(241, 323)(242, 324)(243, 325)(244, 326)(245, 327)(246, 328) L = (1, 167)(2, 170)(3, 165)(4, 171)(5, 174)(6, 166)(7, 168)(8, 175)(9, 178)(10, 169)(11, 172)(12, 179)(13, 182)(14, 173)(15, 176)(16, 183)(17, 186)(18, 177)(19, 180)(20, 187)(21, 190)(22, 181)(23, 184)(24, 191)(25, 194)(26, 185)(27, 188)(28, 195)(29, 204)(30, 189)(31, 192)(32, 217)(33, 199)(34, 202)(35, 197)(36, 203)(37, 206)(38, 198)(39, 200)(40, 193)(41, 208)(42, 201)(43, 210)(44, 205)(45, 212)(46, 207)(47, 214)(48, 209)(49, 216)(50, 211)(51, 225)(52, 213)(53, 196)(54, 220)(55, 223)(56, 218)(57, 224)(58, 227)(59, 219)(60, 221)(61, 215)(62, 229)(63, 222)(64, 231)(65, 226)(66, 233)(67, 228)(68, 235)(69, 230)(70, 237)(71, 232)(72, 246)(73, 234)(74, 243)(75, 241)(76, 244)(77, 239)(78, 245)(79, 238)(80, 240)(81, 242)(82, 236)(83, 247)(84, 248)(85, 249)(86, 250)(87, 251)(88, 252)(89, 253)(90, 254)(91, 255)(92, 256)(93, 257)(94, 258)(95, 259)(96, 260)(97, 261)(98, 262)(99, 263)(100, 264)(101, 265)(102, 266)(103, 267)(104, 268)(105, 269)(106, 270)(107, 271)(108, 272)(109, 273)(110, 274)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 283)(120, 284)(121, 285)(122, 286)(123, 287)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 298)(135, 299)(136, 300)(137, 301)(138, 302)(139, 303)(140, 304)(141, 305)(142, 306)(143, 307)(144, 308)(145, 309)(146, 310)(147, 311)(148, 312)(149, 313)(150, 314)(151, 315)(152, 316)(153, 317)(154, 318)(155, 319)(156, 320)(157, 321)(158, 322)(159, 323)(160, 324)(161, 325)(162, 326)(163, 327)(164, 328) local type(s) :: { ( 4, 82 ), ( 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82, 4, 82 ) } Outer automorphisms :: reflexible Dual of E20.952 Graph:: bipartite v = 83 e = 164 f = 43 degree seq :: [ 2^82, 164 ] E20.956 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 41, 82}) Quotient :: dipole Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |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, Y2^41 * Y1, (Y3 * Y2^-1)^41 ] Map:: R = (1, 83, 2, 84)(3, 85, 5, 87)(4, 86, 6, 88)(7, 89, 9, 91)(8, 90, 10, 92)(11, 93, 13, 95)(12, 94, 14, 96)(15, 97, 17, 99)(16, 98, 18, 100)(19, 101, 21, 103)(20, 102, 22, 104)(23, 105, 25, 107)(24, 106, 26, 108)(27, 109, 29, 111)(28, 110, 30, 112)(31, 113, 52, 134)(32, 114, 59, 141)(33, 115, 34, 116)(35, 117, 37, 119)(36, 118, 38, 120)(39, 121, 41, 123)(40, 122, 42, 124)(43, 125, 45, 127)(44, 126, 46, 128)(47, 129, 49, 131)(48, 130, 50, 132)(51, 133, 53, 135)(54, 136, 55, 137)(56, 138, 57, 139)(58, 140, 79, 161)(60, 142, 61, 143)(62, 144, 64, 146)(63, 145, 65, 147)(66, 148, 68, 150)(67, 149, 69, 151)(70, 152, 72, 154)(71, 153, 73, 155)(74, 156, 76, 158)(75, 157, 77, 159)(78, 160, 80, 162)(81, 163, 82, 164)(165, 247, 167, 249, 171, 253, 175, 257, 179, 261, 183, 265, 187, 269, 191, 273, 195, 277, 214, 296, 210, 292, 206, 288, 202, 284, 198, 280, 201, 283, 205, 287, 209, 291, 213, 295, 217, 299, 219, 301, 221, 303, 243, 325, 239, 321, 235, 317, 231, 313, 227, 309, 224, 306, 226, 308, 230, 312, 234, 316, 238, 320, 242, 324, 245, 327, 223, 305, 194, 276, 190, 272, 186, 268, 182, 264, 178, 260, 174, 256, 170, 252, 166, 248, 169, 251, 173, 255, 177, 259, 181, 263, 185, 267, 189, 271, 193, 275, 216, 298, 212, 294, 208, 290, 204, 286, 200, 282, 197, 279, 199, 281, 203, 285, 207, 289, 211, 293, 215, 297, 218, 300, 220, 302, 222, 304, 241, 323, 237, 319, 233, 315, 229, 311, 225, 307, 228, 310, 232, 314, 236, 318, 240, 322, 244, 326, 246, 328, 196, 278, 192, 274, 188, 270, 184, 266, 180, 262, 176, 258, 172, 254, 168, 250) L = (1, 166)(2, 165)(3, 169)(4, 170)(5, 167)(6, 168)(7, 173)(8, 174)(9, 171)(10, 172)(11, 177)(12, 178)(13, 175)(14, 176)(15, 181)(16, 182)(17, 179)(18, 180)(19, 185)(20, 186)(21, 183)(22, 184)(23, 189)(24, 190)(25, 187)(26, 188)(27, 193)(28, 194)(29, 191)(30, 192)(31, 216)(32, 223)(33, 198)(34, 197)(35, 201)(36, 202)(37, 199)(38, 200)(39, 205)(40, 206)(41, 203)(42, 204)(43, 209)(44, 210)(45, 207)(46, 208)(47, 213)(48, 214)(49, 211)(50, 212)(51, 217)(52, 195)(53, 215)(54, 219)(55, 218)(56, 221)(57, 220)(58, 243)(59, 196)(60, 225)(61, 224)(62, 228)(63, 229)(64, 226)(65, 227)(66, 232)(67, 233)(68, 230)(69, 231)(70, 236)(71, 237)(72, 234)(73, 235)(74, 240)(75, 241)(76, 238)(77, 239)(78, 244)(79, 222)(80, 242)(81, 246)(82, 245)(83, 247)(84, 248)(85, 249)(86, 250)(87, 251)(88, 252)(89, 253)(90, 254)(91, 255)(92, 256)(93, 257)(94, 258)(95, 259)(96, 260)(97, 261)(98, 262)(99, 263)(100, 264)(101, 265)(102, 266)(103, 267)(104, 268)(105, 269)(106, 270)(107, 271)(108, 272)(109, 273)(110, 274)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 283)(120, 284)(121, 285)(122, 286)(123, 287)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 298)(135, 299)(136, 300)(137, 301)(138, 302)(139, 303)(140, 304)(141, 305)(142, 306)(143, 307)(144, 308)(145, 309)(146, 310)(147, 311)(148, 312)(149, 313)(150, 314)(151, 315)(152, 316)(153, 317)(154, 318)(155, 319)(156, 320)(157, 321)(158, 322)(159, 323)(160, 324)(161, 325)(162, 326)(163, 327)(164, 328) local type(s) :: { ( 2, 82, 2, 82 ), ( 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82, 2, 82 ) } Outer automorphisms :: reflexible Dual of E20.957 Graph:: bipartite v = 42 e = 164 f = 84 degree seq :: [ 4^41, 164 ] E20.957 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 41, 82}) Quotient :: dipole Aut^+ = C82 (small group id <82, 2>) Aut = D164 (small group id <164, 4>) |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 * Y1^18 * Y3^-1 * Y1 * Y3^-19, Y3^-2 * Y1^39, (Y3 * Y2^-1)^82 ] Map:: R = (1, 83, 2, 84, 6, 88, 11, 93, 15, 97, 19, 101, 23, 105, 27, 109, 31, 113, 51, 133, 71, 153, 81, 163, 80, 162, 76, 158, 78, 160, 73, 155, 70, 152, 67, 149, 66, 148, 63, 145, 62, 144, 59, 141, 57, 139, 55, 137, 54, 136, 49, 131, 48, 130, 45, 127, 44, 126, 41, 123, 40, 122, 36, 118, 38, 120, 33, 115, 30, 112, 25, 107, 22, 104, 17, 99, 14, 96, 9, 91, 4, 86)(3, 85, 7, 89, 5, 87, 8, 90, 12, 94, 16, 98, 20, 102, 24, 106, 28, 110, 32, 114, 52, 134, 72, 154, 82, 164, 79, 161, 77, 159, 75, 157, 74, 156, 69, 151, 68, 150, 65, 147, 64, 146, 61, 143, 60, 142, 56, 138, 58, 140, 53, 135, 50, 132, 47, 129, 46, 128, 43, 125, 42, 124, 39, 121, 37, 119, 35, 117, 34, 116, 29, 111, 26, 108, 21, 103, 18, 100, 13, 95, 10, 92)(165, 247)(166, 248)(167, 249)(168, 250)(169, 251)(170, 252)(171, 253)(172, 254)(173, 255)(174, 256)(175, 257)(176, 258)(177, 259)(178, 260)(179, 261)(180, 262)(181, 263)(182, 264)(183, 265)(184, 266)(185, 267)(186, 268)(187, 269)(188, 270)(189, 271)(190, 272)(191, 273)(192, 274)(193, 275)(194, 276)(195, 277)(196, 278)(197, 279)(198, 280)(199, 281)(200, 282)(201, 283)(202, 284)(203, 285)(204, 286)(205, 287)(206, 288)(207, 289)(208, 290)(209, 291)(210, 292)(211, 293)(212, 294)(213, 295)(214, 296)(215, 297)(216, 298)(217, 299)(218, 300)(219, 301)(220, 302)(221, 303)(222, 304)(223, 305)(224, 306)(225, 307)(226, 308)(227, 309)(228, 310)(229, 311)(230, 312)(231, 313)(232, 314)(233, 315)(234, 316)(235, 317)(236, 318)(237, 319)(238, 320)(239, 321)(240, 322)(241, 323)(242, 324)(243, 325)(244, 326)(245, 327)(246, 328) L = (1, 167)(2, 171)(3, 173)(4, 174)(5, 165)(6, 169)(7, 168)(8, 166)(9, 177)(10, 178)(11, 172)(12, 170)(13, 181)(14, 182)(15, 176)(16, 175)(17, 185)(18, 186)(19, 180)(20, 179)(21, 189)(22, 190)(23, 184)(24, 183)(25, 193)(26, 194)(27, 188)(28, 187)(29, 197)(30, 198)(31, 192)(32, 191)(33, 199)(34, 202)(35, 200)(36, 203)(37, 204)(38, 201)(39, 205)(40, 206)(41, 207)(42, 208)(43, 209)(44, 210)(45, 211)(46, 212)(47, 213)(48, 214)(49, 217)(50, 218)(51, 196)(52, 195)(53, 219)(54, 222)(55, 220)(56, 223)(57, 224)(58, 221)(59, 225)(60, 226)(61, 227)(62, 228)(63, 229)(64, 230)(65, 231)(66, 232)(67, 233)(68, 234)(69, 237)(70, 238)(71, 216)(72, 215)(73, 239)(74, 242)(75, 240)(76, 243)(77, 244)(78, 241)(79, 245)(80, 246)(81, 236)(82, 235)(83, 247)(84, 248)(85, 249)(86, 250)(87, 251)(88, 252)(89, 253)(90, 254)(91, 255)(92, 256)(93, 257)(94, 258)(95, 259)(96, 260)(97, 261)(98, 262)(99, 263)(100, 264)(101, 265)(102, 266)(103, 267)(104, 268)(105, 269)(106, 270)(107, 271)(108, 272)(109, 273)(110, 274)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 283)(120, 284)(121, 285)(122, 286)(123, 287)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 298)(135, 299)(136, 300)(137, 301)(138, 302)(139, 303)(140, 304)(141, 305)(142, 306)(143, 307)(144, 308)(145, 309)(146, 310)(147, 311)(148, 312)(149, 313)(150, 314)(151, 315)(152, 316)(153, 317)(154, 318)(155, 319)(156, 320)(157, 321)(158, 322)(159, 323)(160, 324)(161, 325)(162, 326)(163, 327)(164, 328) local type(s) :: { ( 4, 164 ), ( 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164, 4, 164 ) } Outer automorphisms :: reflexible Dual of E20.956 Graph:: simple bipartite v = 84 e = 164 f = 42 degree seq :: [ 2^82, 82^2 ] E20.958 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) 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 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y1 * Y3 * Y2 * Y1 * Y2)^2, (Y2 * Y1)^6, (Y1 * Y3 * Y1 * Y3 * Y1 * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * 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, 34, 118)(26, 110, 32, 116)(27, 111, 44, 128)(29, 113, 45, 129)(35, 119, 53, 137)(37, 121, 54, 138)(39, 123, 48, 132)(40, 124, 50, 134)(41, 125, 49, 133)(42, 126, 55, 139)(43, 127, 58, 142)(46, 130, 51, 135)(47, 131, 63, 147)(52, 136, 65, 149)(56, 140, 70, 154)(57, 141, 66, 150)(59, 143, 64, 148)(60, 144, 73, 157)(61, 145, 74, 158)(62, 146, 75, 159)(67, 151, 79, 163)(68, 152, 80, 164)(69, 153, 81, 165)(71, 155, 83, 167)(72, 156, 82, 166)(76, 160, 78, 162)(77, 161, 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, 209, 293)(195, 279, 211, 295)(196, 280, 208, 292)(198, 282, 214, 298)(199, 283, 216, 300)(201, 285, 218, 302)(203, 287, 220, 304)(204, 288, 217, 301)(206, 290, 223, 307)(210, 294, 225, 309)(212, 296, 227, 311)(213, 297, 226, 310)(215, 299, 230, 314)(219, 303, 232, 316)(221, 305, 234, 318)(222, 306, 233, 317)(224, 308, 237, 321)(228, 312, 240, 324)(229, 313, 239, 323)(231, 315, 241, 325)(235, 319, 246, 330)(236, 320, 245, 329)(238, 322, 247, 331)(242, 326, 250, 334)(243, 327, 251, 335)(244, 328, 248, 332)(249, 333, 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, 210)(26, 211)(27, 183)(28, 207)(29, 184)(30, 215)(31, 217)(32, 186)(33, 219)(34, 220)(35, 188)(36, 216)(37, 189)(38, 224)(39, 196)(40, 191)(41, 225)(42, 193)(43, 194)(44, 228)(45, 229)(46, 230)(47, 198)(48, 204)(49, 199)(50, 232)(51, 201)(52, 202)(53, 235)(54, 236)(55, 237)(56, 206)(57, 209)(58, 239)(59, 240)(60, 212)(61, 213)(62, 214)(63, 244)(64, 218)(65, 245)(66, 246)(67, 221)(68, 222)(69, 223)(70, 250)(71, 226)(72, 227)(73, 248)(74, 247)(75, 249)(76, 231)(77, 233)(78, 234)(79, 242)(80, 241)(81, 243)(82, 238)(83, 252)(84, 251)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.962 Graph:: simple bipartite v = 84 e = 168 f = 46 degree seq :: [ 4^84 ] E20.959 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) 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, (Y2 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^6, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86)(3, 87, 6, 90)(4, 88, 11, 95)(5, 89, 13, 97)(7, 91, 17, 101)(8, 92, 19, 103)(9, 93, 21, 105)(10, 94, 23, 107)(12, 96, 18, 102)(14, 98, 20, 104)(15, 99, 29, 113)(16, 100, 31, 115)(22, 106, 30, 114)(24, 108, 32, 116)(25, 109, 41, 125)(26, 110, 43, 127)(27, 111, 42, 126)(28, 112, 44, 128)(33, 117, 49, 133)(34, 118, 51, 135)(35, 119, 50, 134)(36, 120, 52, 136)(37, 121, 53, 137)(38, 122, 55, 139)(39, 123, 54, 138)(40, 124, 56, 140)(45, 129, 60, 144)(46, 130, 62, 146)(47, 131, 61, 145)(48, 132, 63, 147)(57, 141, 70, 154)(58, 142, 71, 155)(59, 143, 72, 156)(64, 148, 76, 160)(65, 149, 77, 161)(66, 150, 78, 162)(67, 151, 79, 163)(68, 152, 80, 164)(69, 153, 81, 165)(73, 157, 82, 166)(74, 158, 83, 167)(75, 159, 84, 168)(169, 253, 171, 255)(170, 254, 174, 258)(172, 256, 178, 262)(173, 257, 177, 261)(175, 259, 184, 268)(176, 260, 183, 267)(179, 263, 191, 275)(180, 264, 192, 276)(181, 265, 189, 273)(182, 266, 190, 274)(185, 269, 199, 283)(186, 270, 200, 284)(187, 271, 197, 281)(188, 272, 198, 282)(193, 277, 208, 292)(194, 278, 206, 290)(195, 279, 207, 291)(196, 280, 205, 289)(201, 285, 216, 300)(202, 286, 214, 298)(203, 287, 215, 299)(204, 288, 213, 297)(209, 293, 224, 308)(210, 294, 222, 306)(211, 295, 223, 307)(212, 296, 221, 305)(217, 301, 231, 315)(218, 302, 229, 313)(219, 303, 230, 314)(220, 304, 228, 312)(225, 309, 235, 319)(226, 310, 237, 321)(227, 311, 236, 320)(232, 316, 241, 325)(233, 317, 243, 327)(234, 318, 242, 326)(238, 322, 247, 331)(239, 323, 249, 333)(240, 324, 248, 332)(244, 328, 250, 334)(245, 329, 252, 336)(246, 330, 251, 335) L = (1, 172)(2, 175)(3, 177)(4, 180)(5, 169)(6, 183)(7, 186)(8, 170)(9, 190)(10, 171)(11, 193)(12, 195)(13, 194)(14, 173)(15, 198)(16, 174)(17, 201)(18, 203)(19, 202)(20, 176)(21, 205)(22, 207)(23, 206)(24, 178)(25, 210)(26, 179)(27, 182)(28, 181)(29, 213)(30, 215)(31, 214)(32, 184)(33, 218)(34, 185)(35, 188)(36, 187)(37, 222)(38, 189)(39, 192)(40, 191)(41, 225)(42, 196)(43, 226)(44, 227)(45, 229)(46, 197)(47, 200)(48, 199)(49, 232)(50, 204)(51, 233)(52, 234)(53, 235)(54, 208)(55, 236)(56, 237)(57, 212)(58, 209)(59, 211)(60, 241)(61, 216)(62, 242)(63, 243)(64, 220)(65, 217)(66, 219)(67, 224)(68, 221)(69, 223)(70, 245)(71, 246)(72, 244)(73, 231)(74, 228)(75, 230)(76, 239)(77, 240)(78, 238)(79, 251)(80, 252)(81, 250)(82, 248)(83, 249)(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, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.963 Graph:: simple bipartite v = 84 e = 168 f = 46 degree seq :: [ 4^84 ] E20.960 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) 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, (Y2 * Y1 * Y2 * Y3 * Y1)^2, (Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1, Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * 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, 34, 118)(26, 110, 32, 116)(27, 111, 44, 128)(29, 113, 45, 129)(35, 119, 53, 137)(37, 121, 54, 138)(39, 123, 57, 141)(40, 124, 58, 142)(41, 125, 59, 143)(42, 126, 61, 145)(43, 127, 62, 146)(46, 130, 66, 150)(47, 131, 68, 152)(48, 132, 69, 153)(49, 133, 70, 154)(50, 134, 71, 155)(51, 135, 73, 157)(52, 136, 74, 158)(55, 139, 78, 162)(56, 140, 80, 164)(60, 144, 75, 159)(63, 147, 72, 156)(64, 148, 79, 163)(65, 149, 77, 161)(67, 151, 76, 160)(81, 165, 84, 168)(82, 166, 83, 167)(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, 209, 293)(195, 279, 211, 295)(196, 280, 208, 292)(198, 282, 214, 298)(199, 283, 216, 300)(201, 285, 218, 302)(203, 287, 220, 304)(204, 288, 217, 301)(206, 290, 223, 307)(210, 294, 228, 312)(212, 296, 231, 315)(213, 297, 230, 314)(215, 299, 235, 319)(219, 303, 240, 324)(221, 305, 243, 327)(222, 306, 242, 326)(224, 308, 247, 331)(225, 309, 248, 332)(226, 310, 246, 330)(227, 311, 241, 325)(229, 313, 239, 323)(232, 316, 250, 334)(233, 317, 249, 333)(234, 318, 238, 322)(236, 320, 237, 321)(244, 328, 252, 336)(245, 329, 251, 335) 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, 210)(26, 211)(27, 183)(28, 207)(29, 184)(30, 215)(31, 217)(32, 186)(33, 219)(34, 220)(35, 188)(36, 216)(37, 189)(38, 224)(39, 196)(40, 191)(41, 228)(42, 193)(43, 194)(44, 232)(45, 233)(46, 235)(47, 198)(48, 204)(49, 199)(50, 240)(51, 201)(52, 202)(53, 244)(54, 245)(55, 247)(56, 206)(57, 241)(58, 238)(59, 248)(60, 209)(61, 237)(62, 249)(63, 250)(64, 212)(65, 213)(66, 246)(67, 214)(68, 239)(69, 229)(70, 226)(71, 236)(72, 218)(73, 225)(74, 251)(75, 252)(76, 221)(77, 222)(78, 234)(79, 223)(80, 227)(81, 230)(82, 231)(83, 242)(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, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.961 Graph:: simple bipartite v = 84 e = 168 f = 46 degree seq :: [ 4^84 ] E20.961 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) 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, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y2 * Y1^3 * Y2 * Y1^-3, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y1^2 * Y2 * Y1^2 * Y2 * Y1^3 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 6, 90, 15, 99, 33, 117, 52, 136, 71, 155, 48, 132, 22, 106, 40, 124, 63, 147, 77, 161, 51, 135, 25, 109, 43, 127, 66, 150, 45, 129, 60, 144, 32, 116, 14, 98, 5, 89)(3, 87, 9, 93, 21, 105, 34, 118, 59, 143, 31, 115, 44, 128, 20, 104, 7, 91, 18, 102, 39, 123, 58, 142, 30, 114, 13, 97, 29, 113, 38, 122, 16, 100, 36, 120, 53, 137, 26, 110, 11, 95)(4, 88, 12, 96, 27, 111, 54, 138, 78, 162, 72, 156, 82, 166, 70, 154, 50, 134, 76, 160, 84, 168, 81, 165, 68, 152, 47, 131, 73, 157, 83, 167, 75, 159, 61, 145, 35, 119, 17, 101, 8, 92)(10, 94, 24, 108, 49, 133, 74, 158, 64, 148, 37, 121, 65, 149, 57, 141, 28, 112, 56, 140, 80, 164, 67, 151, 41, 125, 19, 103, 42, 126, 69, 153, 55, 139, 79, 163, 62, 146, 46, 130, 23, 107)(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, 196, 280)(182, 266, 199, 283)(183, 267, 202, 286)(185, 269, 205, 289)(186, 270, 208, 292)(188, 272, 211, 295)(189, 273, 213, 297)(191, 275, 215, 299)(192, 276, 218, 302)(194, 278, 220, 304)(195, 279, 223, 307)(197, 281, 216, 300)(198, 282, 219, 303)(200, 284, 221, 305)(201, 285, 226, 310)(203, 287, 230, 314)(204, 288, 231, 315)(206, 290, 234, 318)(207, 291, 228, 312)(209, 293, 236, 320)(210, 294, 238, 322)(212, 296, 239, 323)(214, 298, 240, 324)(217, 301, 243, 327)(222, 306, 242, 326)(224, 308, 244, 328)(225, 309, 241, 325)(227, 311, 245, 329)(229, 313, 248, 332)(232, 316, 249, 333)(233, 317, 250, 334)(235, 319, 246, 330)(237, 321, 251, 335)(247, 331, 252, 336) 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, 196)(14, 195)(15, 203)(16, 205)(17, 174)(18, 209)(19, 175)(20, 210)(21, 214)(22, 215)(23, 177)(24, 179)(25, 218)(26, 217)(27, 182)(28, 181)(29, 225)(30, 224)(31, 223)(32, 222)(33, 229)(34, 230)(35, 183)(36, 232)(37, 184)(38, 233)(39, 235)(40, 236)(41, 186)(42, 188)(43, 238)(44, 237)(45, 240)(46, 189)(47, 190)(48, 241)(49, 194)(50, 193)(51, 244)(52, 243)(53, 242)(54, 200)(55, 199)(56, 198)(57, 197)(58, 248)(59, 247)(60, 246)(61, 201)(62, 202)(63, 249)(64, 204)(65, 206)(66, 250)(67, 207)(68, 208)(69, 212)(70, 211)(71, 251)(72, 213)(73, 216)(74, 221)(75, 220)(76, 219)(77, 252)(78, 228)(79, 227)(80, 226)(81, 231)(82, 234)(83, 239)(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 ), ( 4^42 ) } Outer automorphisms :: reflexible Dual of E20.960 Graph:: simple bipartite v = 46 e = 168 f = 84 degree seq :: [ 4^42, 42^4 ] E20.962 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) 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, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y1^-1 * Y2 * Y1^-2)^2, Y1^2 * Y2 * Y1^-5 * Y2 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 6, 90, 15, 99, 33, 117, 46, 130, 67, 151, 52, 136, 25, 109, 43, 127, 66, 150, 75, 159, 49, 133, 22, 106, 40, 124, 63, 147, 53, 137, 60, 144, 32, 116, 14, 98, 5, 89)(3, 87, 9, 93, 21, 105, 45, 129, 38, 122, 16, 100, 36, 120, 30, 114, 13, 97, 29, 113, 58, 142, 44, 128, 20, 104, 7, 91, 18, 102, 39, 123, 31, 115, 59, 143, 34, 118, 26, 110, 11, 95)(4, 88, 12, 96, 27, 111, 54, 138, 78, 162, 76, 160, 81, 165, 69, 153, 48, 132, 74, 158, 84, 168, 82, 166, 71, 155, 51, 135, 77, 161, 83, 167, 73, 157, 61, 145, 35, 119, 17, 101, 8, 92)(10, 94, 24, 108, 50, 134, 62, 146, 79, 163, 55, 139, 68, 152, 41, 125, 19, 103, 42, 126, 70, 154, 80, 164, 57, 141, 28, 112, 56, 140, 64, 148, 37, 121, 65, 149, 72, 156, 47, 131, 23, 107)(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, 196, 280)(182, 266, 199, 283)(183, 267, 202, 286)(185, 269, 205, 289)(186, 270, 208, 292)(188, 272, 211, 295)(189, 273, 214, 298)(191, 275, 216, 300)(192, 276, 219, 303)(194, 278, 221, 305)(195, 279, 223, 307)(197, 281, 217, 301)(198, 282, 220, 304)(200, 284, 213, 297)(201, 285, 226, 310)(203, 287, 230, 314)(204, 288, 231, 315)(206, 290, 234, 318)(207, 291, 235, 319)(209, 293, 237, 321)(210, 294, 239, 323)(212, 296, 228, 312)(215, 299, 241, 325)(218, 302, 244, 328)(222, 306, 240, 324)(224, 308, 245, 329)(225, 309, 242, 326)(227, 311, 243, 327)(229, 313, 248, 332)(232, 316, 249, 333)(233, 317, 250, 334)(236, 320, 251, 335)(238, 322, 246, 330)(247, 331, 252, 336) 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, 196)(14, 195)(15, 203)(16, 205)(17, 174)(18, 209)(19, 175)(20, 210)(21, 215)(22, 216)(23, 177)(24, 179)(25, 219)(26, 218)(27, 182)(28, 181)(29, 225)(30, 224)(31, 223)(32, 222)(33, 229)(34, 230)(35, 183)(36, 232)(37, 184)(38, 233)(39, 236)(40, 237)(41, 186)(42, 188)(43, 239)(44, 238)(45, 240)(46, 241)(47, 189)(48, 190)(49, 242)(50, 194)(51, 193)(52, 245)(53, 244)(54, 200)(55, 199)(56, 198)(57, 197)(58, 248)(59, 247)(60, 246)(61, 201)(62, 202)(63, 249)(64, 204)(65, 206)(66, 250)(67, 251)(68, 207)(69, 208)(70, 212)(71, 211)(72, 213)(73, 214)(74, 217)(75, 252)(76, 221)(77, 220)(78, 228)(79, 227)(80, 226)(81, 231)(82, 234)(83, 235)(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) :: { ( 4^4 ), ( 4^42 ) } Outer automorphisms :: reflexible Dual of E20.958 Graph:: simple bipartite v = 46 e = 168 f = 84 degree seq :: [ 4^42, 42^4 ] E20.963 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) 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, (Y1 * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-2 * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^-1 * Y3 * Y1^-1, Y1^2 * Y3 * Y1^-5 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 7, 91, 21, 105, 44, 128, 65, 149, 40, 124, 15, 99, 27, 111, 50, 134, 72, 156, 82, 166, 64, 148, 39, 123, 20, 104, 30, 114, 52, 136, 68, 152, 43, 127, 18, 102, 5, 89)(3, 87, 11, 95, 31, 115, 57, 141, 76, 160, 73, 157, 53, 137, 34, 118, 60, 144, 79, 163, 84, 168, 83, 167, 75, 159, 56, 140, 37, 121, 62, 146, 81, 165, 69, 153, 45, 129, 22, 106, 8, 92)(4, 88, 14, 98, 38, 122, 63, 147, 51, 135, 23, 107, 10, 94, 29, 113, 17, 101, 41, 125, 66, 150, 47, 131, 28, 112, 9, 93, 6, 90, 19, 103, 42, 126, 67, 151, 46, 130, 24, 108, 16, 100)(12, 96, 26, 110, 55, 139, 70, 154, 80, 164, 58, 142, 33, 117, 54, 138, 25, 109, 49, 133, 74, 158, 78, 162, 61, 145, 32, 116, 13, 97, 36, 120, 48, 132, 71, 155, 77, 161, 59, 143, 35, 119)(169, 253, 171, 255)(170, 254, 176, 260)(172, 256, 181, 265)(173, 257, 179, 263)(174, 258, 180, 264)(175, 259, 190, 274)(177, 261, 194, 278)(178, 262, 193, 277)(182, 266, 200, 284)(183, 267, 205, 289)(184, 268, 204, 288)(185, 269, 201, 285)(186, 270, 199, 283)(187, 271, 203, 287)(188, 272, 202, 286)(189, 273, 213, 297)(191, 275, 217, 301)(192, 276, 216, 300)(195, 279, 224, 308)(196, 280, 223, 307)(197, 281, 222, 306)(198, 282, 221, 305)(206, 290, 229, 313)(207, 291, 228, 312)(208, 292, 230, 314)(209, 293, 226, 310)(210, 294, 227, 311)(211, 295, 225, 309)(212, 296, 237, 321)(214, 298, 239, 323)(215, 299, 238, 322)(218, 302, 243, 327)(219, 303, 242, 326)(220, 304, 241, 325)(231, 315, 246, 330)(232, 316, 247, 331)(233, 317, 249, 333)(234, 318, 248, 332)(235, 319, 245, 329)(236, 320, 244, 328)(240, 324, 251, 335)(250, 334, 252, 336) L = (1, 172)(2, 177)(3, 180)(4, 183)(5, 185)(6, 169)(7, 191)(8, 193)(9, 195)(10, 170)(11, 200)(12, 202)(13, 171)(14, 173)(15, 197)(16, 198)(17, 208)(18, 210)(19, 207)(20, 174)(21, 214)(22, 216)(23, 218)(24, 175)(25, 221)(26, 176)(27, 184)(28, 220)(29, 188)(30, 178)(31, 226)(32, 228)(33, 179)(34, 222)(35, 230)(36, 224)(37, 181)(38, 232)(39, 182)(40, 187)(41, 186)(42, 233)(43, 231)(44, 234)(45, 238)(46, 240)(47, 189)(48, 241)(49, 190)(50, 196)(51, 236)(52, 192)(53, 204)(54, 205)(55, 243)(56, 194)(57, 245)(58, 247)(59, 199)(60, 203)(61, 249)(62, 201)(63, 212)(64, 209)(65, 206)(66, 250)(67, 211)(68, 215)(69, 246)(70, 244)(71, 213)(72, 219)(73, 223)(74, 251)(75, 217)(76, 242)(77, 252)(78, 225)(79, 229)(80, 237)(81, 227)(82, 235)(83, 239)(84, 248)(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 ), ( 4^42 ) } Outer automorphisms :: reflexible Dual of E20.959 Graph:: simple bipartite v = 46 e = 168 f = 84 degree seq :: [ 4^42, 42^4 ] E20.964 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) Quotient :: dipole Aut^+ = D84 (small group id <84, 14>) Aut = C2 x C2 x D42 (small group id <168, 56>) |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)^21 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86)(3, 87, 5, 89)(4, 88, 8, 92)(6, 90, 10, 94)(7, 91, 11, 95)(9, 93, 13, 97)(12, 96, 16, 100)(14, 98, 18, 102)(15, 99, 19, 103)(17, 101, 21, 105)(20, 104, 24, 108)(22, 106, 26, 110)(23, 107, 27, 111)(25, 109, 29, 113)(28, 112, 32, 116)(30, 114, 35, 119)(31, 115, 33, 117)(34, 118, 47, 131)(36, 120, 51, 135)(37, 121, 53, 137)(38, 122, 49, 133)(39, 123, 55, 139)(40, 124, 57, 141)(41, 125, 59, 143)(42, 126, 61, 145)(43, 127, 63, 147)(44, 128, 65, 149)(45, 129, 67, 151)(46, 130, 69, 153)(48, 132, 71, 155)(50, 134, 73, 157)(52, 136, 77, 161)(54, 138, 79, 163)(56, 140, 75, 159)(58, 142, 83, 167)(60, 144, 82, 166)(62, 146, 81, 165)(64, 148, 84, 168)(66, 150, 76, 160)(68, 152, 74, 158)(70, 154, 80, 164)(72, 156, 78, 162)(169, 253, 171, 255)(170, 254, 173, 257)(172, 256, 175, 259)(174, 258, 177, 261)(176, 260, 179, 263)(178, 262, 181, 265)(180, 264, 183, 267)(182, 266, 185, 269)(184, 268, 187, 271)(186, 270, 189, 273)(188, 272, 191, 275)(190, 274, 193, 277)(192, 276, 195, 279)(194, 278, 197, 281)(196, 280, 199, 283)(198, 282, 215, 299)(200, 284, 201, 285)(202, 286, 203, 287)(204, 288, 206, 290)(205, 289, 207, 291)(208, 292, 210, 294)(209, 293, 211, 295)(212, 296, 214, 298)(213, 297, 216, 300)(217, 301, 219, 303)(218, 302, 220, 304)(221, 305, 223, 307)(222, 306, 224, 308)(225, 309, 229, 313)(226, 310, 230, 314)(227, 311, 231, 315)(228, 312, 232, 316)(233, 317, 237, 321)(234, 318, 238, 322)(235, 319, 239, 323)(236, 320, 240, 324)(241, 325, 245, 329)(242, 326, 246, 330)(243, 327, 247, 331)(244, 328, 248, 332)(249, 333, 251, 335)(250, 334, 252, 336) L = (1, 172)(2, 174)(3, 175)(4, 169)(5, 177)(6, 170)(7, 171)(8, 180)(9, 173)(10, 182)(11, 183)(12, 176)(13, 185)(14, 178)(15, 179)(16, 188)(17, 181)(18, 190)(19, 191)(20, 184)(21, 193)(22, 186)(23, 187)(24, 196)(25, 189)(26, 198)(27, 199)(28, 192)(29, 215)(30, 194)(31, 195)(32, 217)(33, 219)(34, 221)(35, 223)(36, 225)(37, 227)(38, 229)(39, 231)(40, 233)(41, 235)(42, 237)(43, 239)(44, 241)(45, 243)(46, 245)(47, 197)(48, 247)(49, 200)(50, 249)(51, 201)(52, 251)(53, 202)(54, 250)(55, 203)(56, 252)(57, 204)(58, 244)(59, 205)(60, 242)(61, 206)(62, 248)(63, 207)(64, 246)(65, 208)(66, 236)(67, 209)(68, 234)(69, 210)(70, 240)(71, 211)(72, 238)(73, 212)(74, 228)(75, 213)(76, 226)(77, 214)(78, 232)(79, 216)(80, 230)(81, 218)(82, 222)(83, 220)(84, 224)(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, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.965 Graph:: simple bipartite v = 84 e = 168 f = 46 degree seq :: [ 4^84 ] E20.965 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 21}) Quotient :: dipole Aut^+ = D84 (small group id <84, 14>) Aut = C2 x C2 x D42 (small group id <168, 56>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y1^21 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 6, 90, 13, 97, 21, 105, 29, 113, 37, 121, 45, 129, 53, 137, 61, 145, 69, 153, 76, 160, 68, 152, 60, 144, 52, 136, 44, 128, 36, 120, 28, 112, 20, 104, 12, 96, 5, 89)(3, 87, 9, 93, 17, 101, 25, 109, 33, 117, 41, 125, 49, 133, 57, 141, 65, 149, 73, 157, 80, 164, 77, 161, 70, 154, 62, 146, 54, 138, 46, 130, 38, 122, 30, 114, 22, 106, 14, 98, 7, 91)(4, 88, 11, 95, 19, 103, 27, 111, 35, 119, 43, 127, 51, 135, 59, 143, 67, 151, 75, 159, 82, 166, 78, 162, 71, 155, 63, 147, 55, 139, 47, 131, 39, 123, 31, 115, 23, 107, 15, 99, 8, 92)(10, 94, 16, 100, 24, 108, 32, 116, 40, 124, 48, 132, 56, 140, 64, 148, 72, 156, 79, 163, 83, 167, 84, 168, 81, 165, 74, 158, 66, 150, 58, 142, 50, 134, 42, 126, 34, 118, 26, 110, 18, 102)(169, 253, 171, 255)(170, 254, 175, 259)(172, 256, 178, 262)(173, 257, 177, 261)(174, 258, 182, 266)(176, 260, 184, 268)(179, 263, 186, 270)(180, 264, 185, 269)(181, 265, 190, 274)(183, 267, 192, 276)(187, 271, 194, 278)(188, 272, 193, 277)(189, 273, 198, 282)(191, 275, 200, 284)(195, 279, 202, 286)(196, 280, 201, 285)(197, 281, 206, 290)(199, 283, 208, 292)(203, 287, 210, 294)(204, 288, 209, 293)(205, 289, 214, 298)(207, 291, 216, 300)(211, 295, 218, 302)(212, 296, 217, 301)(213, 297, 222, 306)(215, 299, 224, 308)(219, 303, 226, 310)(220, 304, 225, 309)(221, 305, 230, 314)(223, 307, 232, 316)(227, 311, 234, 318)(228, 312, 233, 317)(229, 313, 238, 322)(231, 315, 240, 324)(235, 319, 242, 326)(236, 320, 241, 325)(237, 321, 245, 329)(239, 323, 247, 331)(243, 327, 249, 333)(244, 328, 248, 332)(246, 330, 251, 335)(250, 334, 252, 336) L = (1, 172)(2, 176)(3, 178)(4, 169)(5, 179)(6, 183)(7, 184)(8, 170)(9, 186)(10, 171)(11, 173)(12, 187)(13, 191)(14, 192)(15, 174)(16, 175)(17, 194)(18, 177)(19, 180)(20, 195)(21, 199)(22, 200)(23, 181)(24, 182)(25, 202)(26, 185)(27, 188)(28, 203)(29, 207)(30, 208)(31, 189)(32, 190)(33, 210)(34, 193)(35, 196)(36, 211)(37, 215)(38, 216)(39, 197)(40, 198)(41, 218)(42, 201)(43, 204)(44, 219)(45, 223)(46, 224)(47, 205)(48, 206)(49, 226)(50, 209)(51, 212)(52, 227)(53, 231)(54, 232)(55, 213)(56, 214)(57, 234)(58, 217)(59, 220)(60, 235)(61, 239)(62, 240)(63, 221)(64, 222)(65, 242)(66, 225)(67, 228)(68, 243)(69, 246)(70, 247)(71, 229)(72, 230)(73, 249)(74, 233)(75, 236)(76, 250)(77, 251)(78, 237)(79, 238)(80, 252)(81, 241)(82, 244)(83, 245)(84, 248)(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 ), ( 4^42 ) } Outer automorphisms :: reflexible Dual of E20.964 Graph:: simple bipartite v = 46 e = 168 f = 84 degree seq :: [ 4^42, 42^4 ] E20.966 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 21}) Quotient :: edge Aut^+ = C21 : C4 (small group id <84, 5>) Aut = (C42 x C2) : C2 (small group id <168, 38>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^4, T2^21 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 82, 81, 74, 66, 58, 50, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 83, 84, 78, 70, 62, 54, 46, 38, 30, 22, 14)(85, 86, 90, 88)(87, 92, 97, 94)(89, 91, 98, 95)(93, 100, 105, 102)(96, 99, 106, 103)(101, 108, 113, 110)(104, 107, 114, 111)(109, 116, 121, 118)(112, 115, 122, 119)(117, 124, 129, 126)(120, 123, 130, 127)(125, 132, 137, 134)(128, 131, 138, 135)(133, 140, 145, 142)(136, 139, 146, 143)(141, 148, 153, 150)(144, 147, 154, 151)(149, 156, 161, 158)(152, 155, 162, 159)(157, 164, 167, 165)(160, 163, 168, 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 ), ( 8^21 ) } Outer automorphisms :: reflexible Dual of E20.967 Transitivity :: ET+ Graph:: simple bipartite v = 25 e = 84 f = 21 degree seq :: [ 4^21, 21^4 ] E20.967 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 21}) Quotient :: loop Aut^+ = C21 : C4 (small group id <84, 5>) Aut = (C42 x C2) : C2 (small group id <168, 38>) |r| :: 2 Presentation :: [ F^2, T1^-1 * T2^-2 * T1^-1, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^21 ] Map:: non-degenerate R = (1, 85, 3, 87, 6, 90, 5, 89)(2, 86, 7, 91, 4, 88, 8, 92)(9, 93, 13, 97, 10, 94, 14, 98)(11, 95, 15, 99, 12, 96, 16, 100)(17, 101, 21, 105, 18, 102, 22, 106)(19, 103, 23, 107, 20, 104, 24, 108)(25, 109, 29, 113, 26, 110, 30, 114)(27, 111, 31, 115, 28, 112, 32, 116)(33, 117, 36, 120, 34, 118, 38, 122)(35, 119, 53, 137, 40, 124, 55, 139)(37, 121, 60, 144, 39, 123, 62, 146)(41, 125, 59, 143, 42, 126, 57, 141)(43, 127, 65, 149, 44, 128, 63, 147)(45, 129, 71, 155, 46, 130, 69, 153)(47, 131, 75, 159, 48, 132, 73, 157)(49, 133, 79, 163, 50, 134, 77, 161)(51, 135, 83, 167, 52, 136, 81, 165)(54, 138, 84, 168, 56, 140, 82, 166)(58, 142, 74, 158, 68, 152, 76, 160)(61, 145, 78, 162, 66, 150, 80, 164)(64, 148, 72, 156, 67, 151, 70, 154) L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 94)(6, 88)(7, 95)(8, 96)(9, 89)(10, 87)(11, 92)(12, 91)(13, 101)(14, 102)(15, 103)(16, 104)(17, 98)(18, 97)(19, 100)(20, 99)(21, 109)(22, 110)(23, 111)(24, 112)(25, 106)(26, 105)(27, 108)(28, 107)(29, 117)(30, 118)(31, 137)(32, 139)(33, 114)(34, 113)(35, 141)(36, 144)(37, 147)(38, 146)(39, 149)(40, 143)(41, 153)(42, 155)(43, 157)(44, 159)(45, 161)(46, 163)(47, 165)(48, 167)(49, 166)(50, 168)(51, 164)(52, 162)(53, 116)(54, 158)(55, 115)(56, 160)(57, 124)(58, 151)(59, 119)(60, 122)(61, 156)(62, 120)(63, 123)(64, 142)(65, 121)(66, 154)(67, 152)(68, 148)(69, 126)(70, 145)(71, 125)(72, 150)(73, 128)(74, 140)(75, 127)(76, 138)(77, 130)(78, 135)(79, 129)(80, 136)(81, 132)(82, 134)(83, 131)(84, 133) local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21 ) } Outer automorphisms :: reflexible Dual of E20.966 Transitivity :: ET+ VT+ AT Graph:: v = 21 e = 84 f = 25 degree seq :: [ 8^21 ] E20.968 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 21}) Quotient :: dipole Aut^+ = C21 : C4 (small group id <84, 5>) Aut = (C42 x C2) : C2 (small group id <168, 38>) |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, Y2^21 ] Map:: R = (1, 85, 2, 86, 6, 90, 4, 88)(3, 87, 8, 92, 13, 97, 10, 94)(5, 89, 7, 91, 14, 98, 11, 95)(9, 93, 16, 100, 21, 105, 18, 102)(12, 96, 15, 99, 22, 106, 19, 103)(17, 101, 24, 108, 29, 113, 26, 110)(20, 104, 23, 107, 30, 114, 27, 111)(25, 109, 32, 116, 37, 121, 34, 118)(28, 112, 31, 115, 38, 122, 35, 119)(33, 117, 40, 124, 45, 129, 42, 126)(36, 120, 39, 123, 46, 130, 43, 127)(41, 125, 48, 132, 53, 137, 50, 134)(44, 128, 47, 131, 54, 138, 51, 135)(49, 133, 56, 140, 61, 145, 58, 142)(52, 136, 55, 139, 62, 146, 59, 143)(57, 141, 64, 148, 69, 153, 66, 150)(60, 144, 63, 147, 70, 154, 67, 151)(65, 149, 72, 156, 77, 161, 74, 158)(68, 152, 71, 155, 78, 162, 75, 159)(73, 157, 80, 164, 83, 167, 81, 165)(76, 160, 79, 163, 84, 168, 82, 166)(169, 253, 171, 255, 177, 261, 185, 269, 193, 277, 201, 285, 209, 293, 217, 301, 225, 309, 233, 317, 241, 325, 244, 328, 236, 320, 228, 312, 220, 304, 212, 296, 204, 288, 196, 280, 188, 272, 180, 264, 173, 257)(170, 254, 175, 259, 183, 267, 191, 275, 199, 283, 207, 291, 215, 299, 223, 307, 231, 315, 239, 323, 247, 331, 248, 332, 240, 324, 232, 316, 224, 308, 216, 300, 208, 292, 200, 284, 192, 276, 184, 268, 176, 260)(172, 256, 179, 263, 187, 271, 195, 279, 203, 287, 211, 295, 219, 303, 227, 311, 235, 319, 243, 327, 250, 334, 249, 333, 242, 326, 234, 318, 226, 310, 218, 302, 210, 294, 202, 286, 194, 278, 186, 270, 178, 262)(174, 258, 181, 265, 189, 273, 197, 281, 205, 289, 213, 297, 221, 305, 229, 313, 237, 321, 245, 329, 251, 335, 252, 336, 246, 330, 238, 322, 230, 314, 222, 306, 214, 298, 206, 290, 198, 282, 190, 274, 182, 266) L = (1, 171)(2, 175)(3, 177)(4, 179)(5, 169)(6, 181)(7, 183)(8, 170)(9, 185)(10, 172)(11, 187)(12, 173)(13, 189)(14, 174)(15, 191)(16, 176)(17, 193)(18, 178)(19, 195)(20, 180)(21, 197)(22, 182)(23, 199)(24, 184)(25, 201)(26, 186)(27, 203)(28, 188)(29, 205)(30, 190)(31, 207)(32, 192)(33, 209)(34, 194)(35, 211)(36, 196)(37, 213)(38, 198)(39, 215)(40, 200)(41, 217)(42, 202)(43, 219)(44, 204)(45, 221)(46, 206)(47, 223)(48, 208)(49, 225)(50, 210)(51, 227)(52, 212)(53, 229)(54, 214)(55, 231)(56, 216)(57, 233)(58, 218)(59, 235)(60, 220)(61, 237)(62, 222)(63, 239)(64, 224)(65, 241)(66, 226)(67, 243)(68, 228)(69, 245)(70, 230)(71, 247)(72, 232)(73, 244)(74, 234)(75, 250)(76, 236)(77, 251)(78, 238)(79, 248)(80, 240)(81, 242)(82, 249)(83, 252)(84, 246)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E20.969 Graph:: bipartite v = 25 e = 168 f = 105 degree seq :: [ 8^21, 42^4 ] E20.969 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 21}) Quotient :: dipole Aut^+ = C21 : C4 (small group id <84, 5>) Aut = (C42 x C2) : C2 (small group id <168, 38>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^21 ] Map:: R = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)(169, 253, 170, 254, 174, 258, 172, 256)(171, 255, 176, 260, 181, 265, 178, 262)(173, 257, 175, 259, 182, 266, 179, 263)(177, 261, 184, 268, 189, 273, 186, 270)(180, 264, 183, 267, 190, 274, 187, 271)(185, 269, 192, 276, 197, 281, 194, 278)(188, 272, 191, 275, 198, 282, 195, 279)(193, 277, 200, 284, 205, 289, 202, 286)(196, 280, 199, 283, 206, 290, 203, 287)(201, 285, 208, 292, 213, 297, 210, 294)(204, 288, 207, 291, 214, 298, 211, 295)(209, 293, 216, 300, 221, 305, 218, 302)(212, 296, 215, 299, 222, 306, 219, 303)(217, 301, 224, 308, 229, 313, 226, 310)(220, 304, 223, 307, 230, 314, 227, 311)(225, 309, 232, 316, 237, 321, 234, 318)(228, 312, 231, 315, 238, 322, 235, 319)(233, 317, 240, 324, 245, 329, 242, 326)(236, 320, 239, 323, 246, 330, 243, 327)(241, 325, 248, 332, 251, 335, 249, 333)(244, 328, 247, 331, 252, 336, 250, 334) L = (1, 171)(2, 175)(3, 177)(4, 179)(5, 169)(6, 181)(7, 183)(8, 170)(9, 185)(10, 172)(11, 187)(12, 173)(13, 189)(14, 174)(15, 191)(16, 176)(17, 193)(18, 178)(19, 195)(20, 180)(21, 197)(22, 182)(23, 199)(24, 184)(25, 201)(26, 186)(27, 203)(28, 188)(29, 205)(30, 190)(31, 207)(32, 192)(33, 209)(34, 194)(35, 211)(36, 196)(37, 213)(38, 198)(39, 215)(40, 200)(41, 217)(42, 202)(43, 219)(44, 204)(45, 221)(46, 206)(47, 223)(48, 208)(49, 225)(50, 210)(51, 227)(52, 212)(53, 229)(54, 214)(55, 231)(56, 216)(57, 233)(58, 218)(59, 235)(60, 220)(61, 237)(62, 222)(63, 239)(64, 224)(65, 241)(66, 226)(67, 243)(68, 228)(69, 245)(70, 230)(71, 247)(72, 232)(73, 244)(74, 234)(75, 250)(76, 236)(77, 251)(78, 238)(79, 248)(80, 240)(81, 242)(82, 249)(83, 252)(84, 246)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 8, 42 ), ( 8, 42, 8, 42, 8, 42, 8, 42 ) } Outer automorphisms :: reflexible Dual of E20.968 Graph:: simple bipartite v = 105 e = 168 f = 25 degree seq :: [ 2^84, 8^21 ] E20.970 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 42, 42}) Quotient :: regular Aut^+ = C42 x C2 (small group id <84, 15>) Aut = C2 x C2 x D42 (small group id <168, 56>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^42 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 39, 35, 38, 42, 44, 46, 48, 50, 52, 61, 57, 54, 55, 58, 62, 64, 66, 68, 70, 72, 81, 77, 80, 83, 84, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 40, 36, 33, 34, 37, 41, 43, 45, 47, 49, 51, 60, 56, 59, 63, 65, 67, 69, 71, 73, 82, 78, 75, 76, 79, 74, 53, 31, 27, 23, 19, 15, 11, 7) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 40)(32, 53)(33, 35)(34, 38)(36, 39)(37, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 52)(51, 61)(54, 56)(55, 59)(57, 60)(58, 63)(62, 65)(64, 67)(66, 69)(68, 71)(70, 73)(72, 82)(74, 84)(75, 77)(76, 80)(78, 81)(79, 83) local type(s) :: { ( 42^42 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 42 f = 2 degree seq :: [ 42^2 ] E20.971 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 42, 42}) Quotient :: edge Aut^+ = C42 x C2 (small group id <84, 15>) Aut = C2 x C2 x D42 (small group id <168, 56>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^42 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 37, 39, 41, 43, 45, 47, 50, 51, 53, 55, 57, 59, 61, 63, 65, 70, 67, 73, 75, 77, 79, 81, 84, 83, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 33, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 64, 68, 69, 71, 72, 74, 76, 78, 80, 82, 66, 49, 30, 26, 22, 18, 14, 10, 6)(85, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 97)(96, 98)(99, 101)(100, 102)(103, 105)(104, 106)(107, 109)(108, 110)(111, 113)(112, 114)(115, 117)(116, 133)(118, 119)(120, 121)(122, 123)(124, 125)(126, 127)(128, 129)(130, 131)(132, 134)(135, 136)(137, 138)(139, 140)(141, 142)(143, 144)(145, 146)(147, 148)(149, 152)(150, 167)(151, 155)(153, 154)(156, 157)(158, 159)(160, 161)(162, 163)(164, 165)(166, 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) :: { ( 84, 84 ), ( 84^42 ) } Outer automorphisms :: reflexible Dual of E20.972 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 84 f = 2 degree seq :: [ 2^42, 42^2 ] E20.972 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 42, 42}) Quotient :: loop Aut^+ = C42 x C2 (small group id <84, 15>) Aut = C2 x C2 x D42 (small group id <168, 56>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^42 ] Map:: R = (1, 85, 3, 87, 7, 91, 11, 95, 15, 99, 19, 103, 23, 107, 27, 111, 31, 115, 38, 122, 34, 118, 37, 121, 41, 125, 43, 127, 45, 129, 47, 131, 49, 133, 51, 135, 61, 145, 57, 141, 54, 138, 56, 140, 60, 144, 63, 147, 65, 149, 67, 151, 69, 153, 71, 155, 73, 157, 80, 164, 76, 160, 79, 163, 83, 167, 84, 168, 32, 116, 28, 112, 24, 108, 20, 104, 16, 100, 12, 96, 8, 92, 4, 88)(2, 86, 5, 89, 9, 93, 13, 97, 17, 101, 21, 105, 25, 109, 29, 113, 40, 124, 36, 120, 33, 117, 35, 119, 39, 123, 42, 126, 44, 128, 46, 130, 48, 132, 50, 134, 52, 136, 59, 143, 55, 139, 58, 142, 62, 146, 64, 148, 66, 150, 68, 152, 70, 154, 72, 156, 82, 166, 78, 162, 75, 159, 77, 161, 81, 165, 74, 158, 53, 137, 30, 114, 26, 110, 22, 106, 18, 102, 14, 98, 10, 94, 6, 90) L = (1, 86)(2, 85)(3, 89)(4, 90)(5, 87)(6, 88)(7, 93)(8, 94)(9, 91)(10, 92)(11, 97)(12, 98)(13, 95)(14, 96)(15, 101)(16, 102)(17, 99)(18, 100)(19, 105)(20, 106)(21, 103)(22, 104)(23, 109)(24, 110)(25, 107)(26, 108)(27, 113)(28, 114)(29, 111)(30, 112)(31, 124)(32, 137)(33, 118)(34, 117)(35, 121)(36, 122)(37, 119)(38, 120)(39, 125)(40, 115)(41, 123)(42, 127)(43, 126)(44, 129)(45, 128)(46, 131)(47, 130)(48, 133)(49, 132)(50, 135)(51, 134)(52, 145)(53, 116)(54, 139)(55, 138)(56, 142)(57, 143)(58, 140)(59, 141)(60, 146)(61, 136)(62, 144)(63, 148)(64, 147)(65, 150)(66, 149)(67, 152)(68, 151)(69, 154)(70, 153)(71, 156)(72, 155)(73, 166)(74, 168)(75, 160)(76, 159)(77, 163)(78, 164)(79, 161)(80, 162)(81, 167)(82, 157)(83, 165)(84, 158) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.971 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 84 f = 44 degree seq :: [ 84^2 ] E20.973 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 42, 42}) Quotient :: dipole Aut^+ = C42 x C2 (small group id <84, 15>) Aut = C2 x C2 x D42 (small group id <168, 56>) |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, Y2^42, (Y3 * Y2^-1)^42 ] Map:: R = (1, 85, 2, 86)(3, 87, 5, 89)(4, 88, 6, 90)(7, 91, 9, 93)(8, 92, 10, 94)(11, 95, 13, 97)(12, 96, 14, 98)(15, 99, 17, 101)(16, 100, 18, 102)(19, 103, 21, 105)(20, 104, 22, 106)(23, 107, 25, 109)(24, 108, 26, 110)(27, 111, 29, 113)(28, 112, 30, 114)(31, 115, 37, 121)(32, 116, 51, 135)(33, 117, 34, 118)(35, 119, 36, 120)(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, 56, 140)(52, 136, 53, 137)(54, 138, 55, 139)(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, 75, 159)(70, 154, 84, 168)(71, 155, 72, 156)(73, 157, 74, 158)(76, 160, 77, 161)(78, 162, 79, 163)(80, 164, 81, 165)(82, 166, 83, 167)(169, 253, 171, 255, 175, 259, 179, 263, 183, 267, 187, 271, 191, 275, 195, 279, 199, 283, 201, 285, 203, 287, 206, 290, 208, 292, 210, 294, 212, 296, 214, 298, 216, 300, 218, 302, 220, 304, 222, 306, 225, 309, 227, 311, 229, 313, 231, 315, 233, 317, 235, 319, 237, 321, 239, 323, 241, 325, 244, 328, 246, 330, 248, 332, 250, 334, 252, 336, 200, 284, 196, 280, 192, 276, 188, 272, 184, 268, 180, 264, 176, 260, 172, 256)(170, 254, 173, 257, 177, 261, 181, 265, 185, 269, 189, 273, 193, 277, 197, 281, 205, 289, 202, 286, 204, 288, 207, 291, 209, 293, 211, 295, 213, 297, 215, 299, 217, 301, 224, 308, 221, 305, 223, 307, 226, 310, 228, 312, 230, 314, 232, 316, 234, 318, 236, 320, 243, 327, 240, 324, 242, 326, 245, 329, 247, 331, 249, 333, 251, 335, 238, 322, 219, 303, 198, 282, 194, 278, 190, 274, 186, 270, 182, 266, 178, 262, 174, 258) L = (1, 170)(2, 169)(3, 173)(4, 174)(5, 171)(6, 172)(7, 177)(8, 178)(9, 175)(10, 176)(11, 181)(12, 182)(13, 179)(14, 180)(15, 185)(16, 186)(17, 183)(18, 184)(19, 189)(20, 190)(21, 187)(22, 188)(23, 193)(24, 194)(25, 191)(26, 192)(27, 197)(28, 198)(29, 195)(30, 196)(31, 205)(32, 219)(33, 202)(34, 201)(35, 204)(36, 203)(37, 199)(38, 207)(39, 206)(40, 209)(41, 208)(42, 211)(43, 210)(44, 213)(45, 212)(46, 215)(47, 214)(48, 217)(49, 216)(50, 224)(51, 200)(52, 221)(53, 220)(54, 223)(55, 222)(56, 218)(57, 226)(58, 225)(59, 228)(60, 227)(61, 230)(62, 229)(63, 232)(64, 231)(65, 234)(66, 233)(67, 236)(68, 235)(69, 243)(70, 252)(71, 240)(72, 239)(73, 242)(74, 241)(75, 237)(76, 245)(77, 244)(78, 247)(79, 246)(80, 249)(81, 248)(82, 251)(83, 250)(84, 238)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 2, 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, 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, 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, 2, 84, 2, 84, 2, 84, 2, 84, 2, 84 ) } Outer automorphisms :: reflexible Dual of E20.974 Graph:: bipartite v = 44 e = 168 f = 86 degree seq :: [ 4^42, 84^2 ] E20.974 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 42, 42}) Quotient :: dipole Aut^+ = C42 x C2 (small group id <84, 15>) Aut = C2 x C2 x D42 (small group id <168, 56>) |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^-42, Y1^42 ] Map:: R = (1, 85, 2, 86, 5, 89, 9, 93, 13, 97, 17, 101, 21, 105, 25, 109, 29, 113, 55, 139, 51, 135, 47, 131, 43, 127, 39, 123, 35, 119, 38, 122, 42, 126, 46, 130, 50, 134, 54, 138, 58, 142, 60, 144, 84, 168, 81, 165, 77, 161, 73, 157, 69, 153, 65, 149, 62, 146, 63, 147, 66, 150, 70, 154, 74, 158, 78, 162, 32, 116, 28, 112, 24, 108, 20, 104, 16, 100, 12, 96, 8, 92, 4, 88)(3, 87, 6, 90, 10, 94, 14, 98, 18, 102, 22, 106, 26, 110, 30, 114, 56, 140, 52, 136, 48, 132, 44, 128, 40, 124, 36, 120, 33, 117, 34, 118, 37, 121, 41, 125, 45, 129, 49, 133, 53, 137, 57, 141, 59, 143, 83, 167, 80, 164, 76, 160, 72, 156, 68, 152, 64, 148, 67, 151, 71, 155, 75, 159, 79, 163, 82, 166, 61, 145, 31, 115, 27, 111, 23, 107, 19, 103, 15, 99, 11, 95, 7, 91)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336) L = (1, 171)(2, 174)(3, 169)(4, 175)(5, 178)(6, 170)(7, 172)(8, 179)(9, 182)(10, 173)(11, 176)(12, 183)(13, 186)(14, 177)(15, 180)(16, 187)(17, 190)(18, 181)(19, 184)(20, 191)(21, 194)(22, 185)(23, 188)(24, 195)(25, 198)(26, 189)(27, 192)(28, 199)(29, 224)(30, 193)(31, 196)(32, 229)(33, 203)(34, 206)(35, 201)(36, 207)(37, 210)(38, 202)(39, 204)(40, 211)(41, 214)(42, 205)(43, 208)(44, 215)(45, 218)(46, 209)(47, 212)(48, 219)(49, 222)(50, 213)(51, 216)(52, 223)(53, 226)(54, 217)(55, 220)(56, 197)(57, 228)(58, 221)(59, 252)(60, 225)(61, 200)(62, 232)(63, 235)(64, 230)(65, 236)(66, 239)(67, 231)(68, 233)(69, 240)(70, 243)(71, 234)(72, 237)(73, 244)(74, 247)(75, 238)(76, 241)(77, 248)(78, 250)(79, 242)(80, 245)(81, 251)(82, 246)(83, 249)(84, 227)(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, 84 ), ( 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84 ) } Outer automorphisms :: reflexible Dual of E20.973 Graph:: simple bipartite v = 86 e = 168 f = 44 degree seq :: [ 2^84, 84^2 ] E20.975 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 22, 44}) Quotient :: regular Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2, (T1 * T2 * T1^-1 * T2)^2, T1^-2 * T2 * T1^-19 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 81, 73, 65, 57, 49, 41, 33, 25, 16, 24, 15, 23, 32, 40, 48, 56, 64, 72, 80, 88, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 71, 78, 87, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 14, 6, 13, 21, 31, 38, 47, 54, 63, 70, 79, 86, 82, 74, 66, 58, 50, 42, 34, 26, 17, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 73)(68, 75)(69, 78)(71, 80)(74, 81)(76, 82)(77, 86)(79, 88)(83, 85)(84, 87) local type(s) :: { ( 22^44 ) } Outer automorphisms :: reflexible Dual of E20.976 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 44 f = 4 degree seq :: [ 44^2 ] E20.976 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 22, 44}) Quotient :: regular Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, (T1 * T2 * T1^-1 * T2)^2, T1^22, T1^-1 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 71, 78, 85, 82, 74, 66, 58, 50, 42, 34, 26, 17, 8)(6, 13, 21, 31, 38, 47, 54, 63, 70, 79, 84, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 14)(15, 23, 32, 40, 48, 56, 64, 72, 80, 86, 88, 87, 81, 73, 65, 57, 49, 41, 33, 25, 16, 24) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 73)(68, 75)(69, 78)(71, 80)(74, 81)(76, 82)(77, 84)(79, 86)(83, 87)(85, 88) local type(s) :: { ( 44^22 ) } Outer automorphisms :: reflexible Dual of E20.975 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 44 f = 2 degree seq :: [ 22^4 ] E20.977 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 22, 44}) Quotient :: edge Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2^-1 * T1 * T2 * T1)^2, T2^22, T2^-1 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-4 * T1 * T2^2 * T1 * T2^-1 * T1 ] Map:: R = (1, 3, 8, 17, 26, 34, 42, 50, 58, 66, 74, 82, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(2, 5, 12, 22, 30, 38, 46, 54, 62, 70, 78, 85, 80, 72, 64, 56, 48, 40, 32, 24, 14, 6)(7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 87, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 16)(11, 20, 29, 37, 45, 53, 61, 69, 77, 84, 88, 86, 79, 71, 63, 55, 47, 39, 31, 23, 13, 21)(89, 90)(91, 95)(92, 97)(93, 99)(94, 101)(96, 100)(98, 102)(103, 108)(104, 109)(105, 113)(106, 111)(107, 115)(110, 117)(112, 119)(114, 118)(116, 120)(121, 125)(122, 129)(123, 127)(124, 131)(126, 133)(128, 135)(130, 134)(132, 136)(137, 141)(138, 145)(139, 143)(140, 147)(142, 149)(144, 151)(146, 150)(148, 152)(153, 157)(154, 161)(155, 159)(156, 163)(158, 165)(160, 167)(162, 166)(164, 168)(169, 172)(170, 175)(171, 174)(173, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 88, 88 ), ( 88^22 ) } Outer automorphisms :: reflexible Dual of E20.981 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 88 f = 2 degree seq :: [ 2^44, 22^4 ] E20.978 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 22, 44}) Quotient :: edge Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-3 * T1^-1 * T2 * T1^-1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T2 * T1^-2 * T2^9 * T1^-5 * T2 * T1^-2 * T2 * T1^-1, T2^-1 * T1^2 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 33, 41, 49, 57, 65, 73, 81, 86, 77, 71, 64, 54, 45, 39, 32, 18, 6, 17, 30, 20, 13, 27, 36, 44, 52, 60, 68, 76, 84, 87, 80, 70, 61, 55, 48, 38, 28, 21, 15, 5)(2, 7, 19, 11, 26, 34, 43, 50, 59, 66, 75, 82, 85, 79, 72, 62, 53, 47, 40, 29, 16, 14, 23, 9, 4, 12, 25, 35, 42, 51, 58, 67, 74, 83, 88, 78, 69, 63, 56, 46, 37, 31, 22, 8)(89, 90, 94, 104, 116, 125, 133, 141, 149, 157, 165, 173, 172, 162, 153, 147, 140, 130, 121, 114, 101, 92)(91, 97, 105, 96, 109, 117, 127, 134, 143, 150, 159, 166, 175, 170, 161, 155, 148, 138, 129, 123, 115, 99)(93, 102, 106, 119, 126, 135, 142, 151, 158, 167, 174, 171, 164, 154, 145, 139, 132, 122, 112, 100, 108, 95)(98, 107, 118, 111, 103, 110, 120, 128, 136, 144, 152, 160, 168, 176, 169, 163, 156, 146, 137, 131, 124, 113) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 4^22 ), ( 4^44 ) } Outer automorphisms :: reflexible Dual of E20.982 Transitivity :: ET+ Graph:: bipartite v = 6 e = 88 f = 44 degree seq :: [ 22^4, 44^2 ] E20.979 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 22, 44}) Quotient :: edge Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1 * T2 * T1^-1 * T2)^2, T1^-2 * T2 * T1^-19 * T2 * T1^-1 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 73)(68, 75)(69, 78)(71, 80)(74, 81)(76, 82)(77, 86)(79, 88)(83, 85)(84, 87)(89, 90, 93, 99, 108, 117, 125, 133, 141, 149, 157, 165, 173, 169, 161, 153, 145, 137, 129, 121, 113, 104, 112, 103, 111, 120, 128, 136, 144, 152, 160, 168, 176, 172, 164, 156, 148, 140, 132, 124, 116, 107, 98, 92)(91, 95, 100, 110, 118, 127, 134, 143, 150, 159, 166, 175, 171, 163, 155, 147, 139, 131, 123, 115, 106, 97, 102, 94, 101, 109, 119, 126, 135, 142, 151, 158, 167, 174, 170, 162, 154, 146, 138, 130, 122, 114, 105, 96) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 44, 44 ), ( 44^44 ) } Outer automorphisms :: reflexible Dual of E20.980 Transitivity :: ET+ Graph:: simple bipartite v = 46 e = 88 f = 4 degree seq :: [ 2^44, 44^2 ] E20.980 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 22, 44}) Quotient :: loop Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2^-1 * T1 * T2 * T1)^2, T2^22, T2^-1 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-4 * T1 * T2^2 * T1 * T2^-1 * T1 ] Map:: R = (1, 89, 3, 91, 8, 96, 17, 105, 26, 114, 34, 122, 42, 130, 50, 138, 58, 146, 66, 154, 74, 162, 82, 170, 76, 164, 68, 156, 60, 148, 52, 140, 44, 132, 36, 124, 28, 116, 19, 107, 10, 98, 4, 92)(2, 90, 5, 93, 12, 100, 22, 110, 30, 118, 38, 126, 46, 134, 54, 142, 62, 150, 70, 158, 78, 166, 85, 173, 80, 168, 72, 160, 64, 152, 56, 144, 48, 136, 40, 128, 32, 120, 24, 112, 14, 102, 6, 94)(7, 95, 15, 103, 25, 113, 33, 121, 41, 129, 49, 137, 57, 145, 65, 153, 73, 161, 81, 169, 87, 175, 83, 171, 75, 163, 67, 155, 59, 147, 51, 139, 43, 131, 35, 123, 27, 115, 18, 106, 9, 97, 16, 104)(11, 99, 20, 108, 29, 117, 37, 125, 45, 133, 53, 141, 61, 149, 69, 157, 77, 165, 84, 172, 88, 176, 86, 174, 79, 167, 71, 159, 63, 151, 55, 143, 47, 135, 39, 127, 31, 119, 23, 111, 13, 101, 21, 109) L = (1, 90)(2, 89)(3, 95)(4, 97)(5, 99)(6, 101)(7, 91)(8, 100)(9, 92)(10, 102)(11, 93)(12, 96)(13, 94)(14, 98)(15, 108)(16, 109)(17, 113)(18, 111)(19, 115)(20, 103)(21, 104)(22, 117)(23, 106)(24, 119)(25, 105)(26, 118)(27, 107)(28, 120)(29, 110)(30, 114)(31, 112)(32, 116)(33, 125)(34, 129)(35, 127)(36, 131)(37, 121)(38, 133)(39, 123)(40, 135)(41, 122)(42, 134)(43, 124)(44, 136)(45, 126)(46, 130)(47, 128)(48, 132)(49, 141)(50, 145)(51, 143)(52, 147)(53, 137)(54, 149)(55, 139)(56, 151)(57, 138)(58, 150)(59, 140)(60, 152)(61, 142)(62, 146)(63, 144)(64, 148)(65, 157)(66, 161)(67, 159)(68, 163)(69, 153)(70, 165)(71, 155)(72, 167)(73, 154)(74, 166)(75, 156)(76, 168)(77, 158)(78, 162)(79, 160)(80, 164)(81, 172)(82, 175)(83, 174)(84, 169)(85, 176)(86, 171)(87, 170)(88, 173) 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 ) } Outer automorphisms :: reflexible Dual of E20.979 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 88 f = 46 degree seq :: [ 44^4 ] E20.981 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 22, 44}) Quotient :: loop Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-3 * T1^-1 * T2 * T1^-1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T2 * T1^-2 * T2^9 * T1^-5 * T2 * T1^-2 * T2 * T1^-1, T2^-1 * T1^2 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-1 * T1 * T2^-1 * T1^3 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1 ] Map:: R = (1, 89, 3, 91, 10, 98, 24, 112, 33, 121, 41, 129, 49, 137, 57, 145, 65, 153, 73, 161, 81, 169, 86, 174, 77, 165, 71, 159, 64, 152, 54, 142, 45, 133, 39, 127, 32, 120, 18, 106, 6, 94, 17, 105, 30, 118, 20, 108, 13, 101, 27, 115, 36, 124, 44, 132, 52, 140, 60, 148, 68, 156, 76, 164, 84, 172, 87, 175, 80, 168, 70, 158, 61, 149, 55, 143, 48, 136, 38, 126, 28, 116, 21, 109, 15, 103, 5, 93)(2, 90, 7, 95, 19, 107, 11, 99, 26, 114, 34, 122, 43, 131, 50, 138, 59, 147, 66, 154, 75, 163, 82, 170, 85, 173, 79, 167, 72, 160, 62, 150, 53, 141, 47, 135, 40, 128, 29, 117, 16, 104, 14, 102, 23, 111, 9, 97, 4, 92, 12, 100, 25, 113, 35, 123, 42, 130, 51, 139, 58, 146, 67, 155, 74, 162, 83, 171, 88, 176, 78, 166, 69, 157, 63, 151, 56, 144, 46, 134, 37, 125, 31, 119, 22, 110, 8, 96) L = (1, 90)(2, 94)(3, 97)(4, 89)(5, 102)(6, 104)(7, 93)(8, 109)(9, 105)(10, 107)(11, 91)(12, 108)(13, 92)(14, 106)(15, 110)(16, 116)(17, 96)(18, 119)(19, 118)(20, 95)(21, 117)(22, 120)(23, 103)(24, 100)(25, 98)(26, 101)(27, 99)(28, 125)(29, 127)(30, 111)(31, 126)(32, 128)(33, 114)(34, 112)(35, 115)(36, 113)(37, 133)(38, 135)(39, 134)(40, 136)(41, 123)(42, 121)(43, 124)(44, 122)(45, 141)(46, 143)(47, 142)(48, 144)(49, 131)(50, 129)(51, 132)(52, 130)(53, 149)(54, 151)(55, 150)(56, 152)(57, 139)(58, 137)(59, 140)(60, 138)(61, 157)(62, 159)(63, 158)(64, 160)(65, 147)(66, 145)(67, 148)(68, 146)(69, 165)(70, 167)(71, 166)(72, 168)(73, 155)(74, 153)(75, 156)(76, 154)(77, 173)(78, 175)(79, 174)(80, 176)(81, 163)(82, 161)(83, 164)(84, 162)(85, 172)(86, 171)(87, 170)(88, 169) 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 ) } Outer automorphisms :: reflexible Dual of E20.977 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 88 f = 48 degree seq :: [ 88^2 ] E20.982 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 22, 44}) Quotient :: loop Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1 * T2 * T1^-1 * T2)^2, T1^-2 * T2 * T1^-19 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 89, 3, 91)(2, 90, 6, 94)(4, 92, 9, 97)(5, 93, 12, 100)(7, 95, 15, 103)(8, 96, 16, 104)(10, 98, 17, 105)(11, 99, 21, 109)(13, 101, 23, 111)(14, 102, 24, 112)(18, 106, 25, 113)(19, 107, 27, 115)(20, 108, 30, 118)(22, 110, 32, 120)(26, 114, 33, 121)(28, 116, 34, 122)(29, 117, 38, 126)(31, 119, 40, 128)(35, 123, 41, 129)(36, 124, 43, 131)(37, 125, 46, 134)(39, 127, 48, 136)(42, 130, 49, 137)(44, 132, 50, 138)(45, 133, 54, 142)(47, 135, 56, 144)(51, 139, 57, 145)(52, 140, 59, 147)(53, 141, 62, 150)(55, 143, 64, 152)(58, 146, 65, 153)(60, 148, 66, 154)(61, 149, 70, 158)(63, 151, 72, 160)(67, 155, 73, 161)(68, 156, 75, 163)(69, 157, 78, 166)(71, 159, 80, 168)(74, 162, 81, 169)(76, 164, 82, 170)(77, 165, 86, 174)(79, 167, 88, 176)(83, 171, 85, 173)(84, 172, 87, 175) L = (1, 90)(2, 93)(3, 95)(4, 89)(5, 99)(6, 101)(7, 100)(8, 91)(9, 102)(10, 92)(11, 108)(12, 110)(13, 109)(14, 94)(15, 111)(16, 112)(17, 96)(18, 97)(19, 98)(20, 117)(21, 119)(22, 118)(23, 120)(24, 103)(25, 104)(26, 105)(27, 106)(28, 107)(29, 125)(30, 127)(31, 126)(32, 128)(33, 113)(34, 114)(35, 115)(36, 116)(37, 133)(38, 135)(39, 134)(40, 136)(41, 121)(42, 122)(43, 123)(44, 124)(45, 141)(46, 143)(47, 142)(48, 144)(49, 129)(50, 130)(51, 131)(52, 132)(53, 149)(54, 151)(55, 150)(56, 152)(57, 137)(58, 138)(59, 139)(60, 140)(61, 157)(62, 159)(63, 158)(64, 160)(65, 145)(66, 146)(67, 147)(68, 148)(69, 165)(70, 167)(71, 166)(72, 168)(73, 153)(74, 154)(75, 155)(76, 156)(77, 173)(78, 175)(79, 174)(80, 176)(81, 161)(82, 162)(83, 163)(84, 164)(85, 169)(86, 170)(87, 171)(88, 172) local type(s) :: { ( 22, 44, 22, 44 ) } Outer automorphisms :: reflexible Dual of E20.978 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 44 e = 88 f = 6 degree seq :: [ 4^44 ] E20.983 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 44}) Quotient :: dipole Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^22, (Y3 * Y2^-1)^44 ] Map:: R = (1, 89, 2, 90)(3, 91, 7, 95)(4, 92, 9, 97)(5, 93, 11, 99)(6, 94, 13, 101)(8, 96, 12, 100)(10, 98, 14, 102)(15, 103, 20, 108)(16, 104, 21, 109)(17, 105, 25, 113)(18, 106, 23, 111)(19, 107, 27, 115)(22, 110, 29, 117)(24, 112, 31, 119)(26, 114, 30, 118)(28, 116, 32, 120)(33, 121, 37, 125)(34, 122, 41, 129)(35, 123, 39, 127)(36, 124, 43, 131)(38, 126, 45, 133)(40, 128, 47, 135)(42, 130, 46, 134)(44, 132, 48, 136)(49, 137, 53, 141)(50, 138, 57, 145)(51, 139, 55, 143)(52, 140, 59, 147)(54, 142, 61, 149)(56, 144, 63, 151)(58, 146, 62, 150)(60, 148, 64, 152)(65, 153, 69, 157)(66, 154, 73, 161)(67, 155, 71, 159)(68, 156, 75, 163)(70, 158, 77, 165)(72, 160, 79, 167)(74, 162, 78, 166)(76, 164, 80, 168)(81, 169, 84, 172)(82, 170, 87, 175)(83, 171, 86, 174)(85, 173, 88, 176)(177, 265, 179, 267, 184, 272, 193, 281, 202, 290, 210, 298, 218, 306, 226, 314, 234, 322, 242, 330, 250, 338, 258, 346, 252, 340, 244, 332, 236, 324, 228, 316, 220, 308, 212, 300, 204, 292, 195, 283, 186, 274, 180, 268)(178, 266, 181, 269, 188, 276, 198, 286, 206, 294, 214, 302, 222, 310, 230, 318, 238, 326, 246, 334, 254, 342, 261, 349, 256, 344, 248, 336, 240, 328, 232, 320, 224, 312, 216, 304, 208, 296, 200, 288, 190, 278, 182, 270)(183, 271, 191, 279, 201, 289, 209, 297, 217, 305, 225, 313, 233, 321, 241, 329, 249, 337, 257, 345, 263, 351, 259, 347, 251, 339, 243, 331, 235, 323, 227, 315, 219, 307, 211, 299, 203, 291, 194, 282, 185, 273, 192, 280)(187, 275, 196, 284, 205, 293, 213, 301, 221, 309, 229, 317, 237, 325, 245, 333, 253, 341, 260, 348, 264, 352, 262, 350, 255, 343, 247, 335, 239, 327, 231, 319, 223, 311, 215, 303, 207, 295, 199, 287, 189, 277, 197, 285) L = (1, 178)(2, 177)(3, 183)(4, 185)(5, 187)(6, 189)(7, 179)(8, 188)(9, 180)(10, 190)(11, 181)(12, 184)(13, 182)(14, 186)(15, 196)(16, 197)(17, 201)(18, 199)(19, 203)(20, 191)(21, 192)(22, 205)(23, 194)(24, 207)(25, 193)(26, 206)(27, 195)(28, 208)(29, 198)(30, 202)(31, 200)(32, 204)(33, 213)(34, 217)(35, 215)(36, 219)(37, 209)(38, 221)(39, 211)(40, 223)(41, 210)(42, 222)(43, 212)(44, 224)(45, 214)(46, 218)(47, 216)(48, 220)(49, 229)(50, 233)(51, 231)(52, 235)(53, 225)(54, 237)(55, 227)(56, 239)(57, 226)(58, 238)(59, 228)(60, 240)(61, 230)(62, 234)(63, 232)(64, 236)(65, 245)(66, 249)(67, 247)(68, 251)(69, 241)(70, 253)(71, 243)(72, 255)(73, 242)(74, 254)(75, 244)(76, 256)(77, 246)(78, 250)(79, 248)(80, 252)(81, 260)(82, 263)(83, 262)(84, 257)(85, 264)(86, 259)(87, 258)(88, 261)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 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, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88, 2, 88 ) } Outer automorphisms :: reflexible Dual of E20.986 Graph:: bipartite v = 48 e = 176 f = 90 degree seq :: [ 4^44, 44^4 ] E20.984 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 44}) Quotient :: dipole Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y2^6 * Y1 * Y2^2 * Y1^7, Y2^8 * Y1^-1 * Y2^2 * Y1^-9 * Y2^2, Y1^22 ] Map:: R = (1, 89, 2, 90, 6, 94, 16, 104, 28, 116, 37, 125, 45, 133, 53, 141, 61, 149, 69, 157, 77, 165, 85, 173, 84, 172, 74, 162, 65, 153, 59, 147, 52, 140, 42, 130, 33, 121, 26, 114, 13, 101, 4, 92)(3, 91, 9, 97, 17, 105, 8, 96, 21, 109, 29, 117, 39, 127, 46, 134, 55, 143, 62, 150, 71, 159, 78, 166, 87, 175, 82, 170, 73, 161, 67, 155, 60, 148, 50, 138, 41, 129, 35, 123, 27, 115, 11, 99)(5, 93, 14, 102, 18, 106, 31, 119, 38, 126, 47, 135, 54, 142, 63, 151, 70, 158, 79, 167, 86, 174, 83, 171, 76, 164, 66, 154, 57, 145, 51, 139, 44, 132, 34, 122, 24, 112, 12, 100, 20, 108, 7, 95)(10, 98, 19, 107, 30, 118, 23, 111, 15, 103, 22, 110, 32, 120, 40, 128, 48, 136, 56, 144, 64, 152, 72, 160, 80, 168, 88, 176, 81, 169, 75, 163, 68, 156, 58, 146, 49, 137, 43, 131, 36, 124, 25, 113)(177, 265, 179, 267, 186, 274, 200, 288, 209, 297, 217, 305, 225, 313, 233, 321, 241, 329, 249, 337, 257, 345, 262, 350, 253, 341, 247, 335, 240, 328, 230, 318, 221, 309, 215, 303, 208, 296, 194, 282, 182, 270, 193, 281, 206, 294, 196, 284, 189, 277, 203, 291, 212, 300, 220, 308, 228, 316, 236, 324, 244, 332, 252, 340, 260, 348, 263, 351, 256, 344, 246, 334, 237, 325, 231, 319, 224, 312, 214, 302, 204, 292, 197, 285, 191, 279, 181, 269)(178, 266, 183, 271, 195, 283, 187, 275, 202, 290, 210, 298, 219, 307, 226, 314, 235, 323, 242, 330, 251, 339, 258, 346, 261, 349, 255, 343, 248, 336, 238, 326, 229, 317, 223, 311, 216, 304, 205, 293, 192, 280, 190, 278, 199, 287, 185, 273, 180, 268, 188, 276, 201, 289, 211, 299, 218, 306, 227, 315, 234, 322, 243, 331, 250, 338, 259, 347, 264, 352, 254, 342, 245, 333, 239, 327, 232, 320, 222, 310, 213, 301, 207, 295, 198, 286, 184, 272) L = (1, 179)(2, 183)(3, 186)(4, 188)(5, 177)(6, 193)(7, 195)(8, 178)(9, 180)(10, 200)(11, 202)(12, 201)(13, 203)(14, 199)(15, 181)(16, 190)(17, 206)(18, 182)(19, 187)(20, 189)(21, 191)(22, 184)(23, 185)(24, 209)(25, 211)(26, 210)(27, 212)(28, 197)(29, 192)(30, 196)(31, 198)(32, 194)(33, 217)(34, 219)(35, 218)(36, 220)(37, 207)(38, 204)(39, 208)(40, 205)(41, 225)(42, 227)(43, 226)(44, 228)(45, 215)(46, 213)(47, 216)(48, 214)(49, 233)(50, 235)(51, 234)(52, 236)(53, 223)(54, 221)(55, 224)(56, 222)(57, 241)(58, 243)(59, 242)(60, 244)(61, 231)(62, 229)(63, 232)(64, 230)(65, 249)(66, 251)(67, 250)(68, 252)(69, 239)(70, 237)(71, 240)(72, 238)(73, 257)(74, 259)(75, 258)(76, 260)(77, 247)(78, 245)(79, 248)(80, 246)(81, 262)(82, 261)(83, 264)(84, 263)(85, 255)(86, 253)(87, 256)(88, 254)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.985 Graph:: bipartite v = 6 e = 176 f = 132 degree seq :: [ 44^4, 88^2 ] E20.985 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 44}) Quotient :: dipole Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |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 * Y3^-1 * Y2)^2, Y3^21 * Y2 * Y3 * Y2, Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^7, (Y3^-1 * Y1^-1)^44 ] Map:: polytopal R = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)(177, 265, 178, 266)(179, 267, 183, 271)(180, 268, 185, 273)(181, 269, 187, 275)(182, 270, 189, 277)(184, 272, 188, 276)(186, 274, 190, 278)(191, 279, 196, 284)(192, 280, 197, 285)(193, 281, 201, 289)(194, 282, 199, 287)(195, 283, 203, 291)(198, 286, 205, 293)(200, 288, 207, 295)(202, 290, 206, 294)(204, 292, 208, 296)(209, 297, 213, 301)(210, 298, 217, 305)(211, 299, 215, 303)(212, 300, 219, 307)(214, 302, 221, 309)(216, 304, 223, 311)(218, 306, 222, 310)(220, 308, 224, 312)(225, 313, 229, 317)(226, 314, 233, 321)(227, 315, 231, 319)(228, 316, 235, 323)(230, 318, 237, 325)(232, 320, 239, 327)(234, 322, 238, 326)(236, 324, 240, 328)(241, 329, 245, 333)(242, 330, 249, 337)(243, 331, 247, 335)(244, 332, 251, 339)(246, 334, 253, 341)(248, 336, 255, 343)(250, 338, 254, 342)(252, 340, 256, 344)(257, 345, 261, 349)(258, 346, 264, 352)(259, 347, 263, 351)(260, 348, 262, 350) L = (1, 179)(2, 181)(3, 184)(4, 177)(5, 188)(6, 178)(7, 191)(8, 193)(9, 192)(10, 180)(11, 196)(12, 198)(13, 197)(14, 182)(15, 201)(16, 183)(17, 202)(18, 185)(19, 186)(20, 205)(21, 187)(22, 206)(23, 189)(24, 190)(25, 209)(26, 210)(27, 194)(28, 195)(29, 213)(30, 214)(31, 199)(32, 200)(33, 217)(34, 218)(35, 203)(36, 204)(37, 221)(38, 222)(39, 207)(40, 208)(41, 225)(42, 226)(43, 211)(44, 212)(45, 229)(46, 230)(47, 215)(48, 216)(49, 233)(50, 234)(51, 219)(52, 220)(53, 237)(54, 238)(55, 223)(56, 224)(57, 241)(58, 242)(59, 227)(60, 228)(61, 245)(62, 246)(63, 231)(64, 232)(65, 249)(66, 250)(67, 235)(68, 236)(69, 253)(70, 254)(71, 239)(72, 240)(73, 257)(74, 258)(75, 243)(76, 244)(77, 261)(78, 262)(79, 247)(80, 248)(81, 264)(82, 263)(83, 251)(84, 252)(85, 260)(86, 259)(87, 255)(88, 256)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 44, 88 ), ( 44, 88, 44, 88 ) } Outer automorphisms :: reflexible Dual of E20.984 Graph:: simple bipartite v = 132 e = 176 f = 6 degree seq :: [ 2^88, 4^44 ] E20.986 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 44}) Quotient :: dipole Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3^2 * Y1^-1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-20, Y1^-4 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * 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, 89, 2, 90, 5, 93, 11, 99, 20, 108, 29, 117, 37, 125, 45, 133, 53, 141, 61, 149, 69, 157, 77, 165, 85, 173, 81, 169, 73, 161, 65, 153, 57, 145, 49, 137, 41, 129, 33, 121, 25, 113, 16, 104, 24, 112, 15, 103, 23, 111, 32, 120, 40, 128, 48, 136, 56, 144, 64, 152, 72, 160, 80, 168, 88, 176, 84, 172, 76, 164, 68, 156, 60, 148, 52, 140, 44, 132, 36, 124, 28, 116, 19, 107, 10, 98, 4, 92)(3, 91, 7, 95, 12, 100, 22, 110, 30, 118, 39, 127, 46, 134, 55, 143, 62, 150, 71, 159, 78, 166, 87, 175, 83, 171, 75, 163, 67, 155, 59, 147, 51, 139, 43, 131, 35, 123, 27, 115, 18, 106, 9, 97, 14, 102, 6, 94, 13, 101, 21, 109, 31, 119, 38, 126, 47, 135, 54, 142, 63, 151, 70, 158, 79, 167, 86, 174, 82, 170, 74, 162, 66, 154, 58, 146, 50, 138, 42, 130, 34, 122, 26, 114, 17, 105, 8, 96)(177, 265)(178, 266)(179, 267)(180, 268)(181, 269)(182, 270)(183, 271)(184, 272)(185, 273)(186, 274)(187, 275)(188, 276)(189, 277)(190, 278)(191, 279)(192, 280)(193, 281)(194, 282)(195, 283)(196, 284)(197, 285)(198, 286)(199, 287)(200, 288)(201, 289)(202, 290)(203, 291)(204, 292)(205, 293)(206, 294)(207, 295)(208, 296)(209, 297)(210, 298)(211, 299)(212, 300)(213, 301)(214, 302)(215, 303)(216, 304)(217, 305)(218, 306)(219, 307)(220, 308)(221, 309)(222, 310)(223, 311)(224, 312)(225, 313)(226, 314)(227, 315)(228, 316)(229, 317)(230, 318)(231, 319)(232, 320)(233, 321)(234, 322)(235, 323)(236, 324)(237, 325)(238, 326)(239, 327)(240, 328)(241, 329)(242, 330)(243, 331)(244, 332)(245, 333)(246, 334)(247, 335)(248, 336)(249, 337)(250, 338)(251, 339)(252, 340)(253, 341)(254, 342)(255, 343)(256, 344)(257, 345)(258, 346)(259, 347)(260, 348)(261, 349)(262, 350)(263, 351)(264, 352) L = (1, 179)(2, 182)(3, 177)(4, 185)(5, 188)(6, 178)(7, 191)(8, 192)(9, 180)(10, 193)(11, 197)(12, 181)(13, 199)(14, 200)(15, 183)(16, 184)(17, 186)(18, 201)(19, 203)(20, 206)(21, 187)(22, 208)(23, 189)(24, 190)(25, 194)(26, 209)(27, 195)(28, 210)(29, 214)(30, 196)(31, 216)(32, 198)(33, 202)(34, 204)(35, 217)(36, 219)(37, 222)(38, 205)(39, 224)(40, 207)(41, 211)(42, 225)(43, 212)(44, 226)(45, 230)(46, 213)(47, 232)(48, 215)(49, 218)(50, 220)(51, 233)(52, 235)(53, 238)(54, 221)(55, 240)(56, 223)(57, 227)(58, 241)(59, 228)(60, 242)(61, 246)(62, 229)(63, 248)(64, 231)(65, 234)(66, 236)(67, 249)(68, 251)(69, 254)(70, 237)(71, 256)(72, 239)(73, 243)(74, 257)(75, 244)(76, 258)(77, 262)(78, 245)(79, 264)(80, 247)(81, 250)(82, 252)(83, 261)(84, 263)(85, 259)(86, 253)(87, 260)(88, 255)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.983 Graph:: simple bipartite v = 90 e = 176 f = 48 degree seq :: [ 2^88, 88^2 ] E20.987 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 44}) Quotient :: dipole Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y1 * Y2 * Y1)^2, Y2^21 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^22 ] Map:: R = (1, 89, 2, 90)(3, 91, 7, 95)(4, 92, 9, 97)(5, 93, 11, 99)(6, 94, 13, 101)(8, 96, 12, 100)(10, 98, 14, 102)(15, 103, 20, 108)(16, 104, 21, 109)(17, 105, 25, 113)(18, 106, 23, 111)(19, 107, 27, 115)(22, 110, 29, 117)(24, 112, 31, 119)(26, 114, 30, 118)(28, 116, 32, 120)(33, 121, 37, 125)(34, 122, 41, 129)(35, 123, 39, 127)(36, 124, 43, 131)(38, 126, 45, 133)(40, 128, 47, 135)(42, 130, 46, 134)(44, 132, 48, 136)(49, 137, 53, 141)(50, 138, 57, 145)(51, 139, 55, 143)(52, 140, 59, 147)(54, 142, 61, 149)(56, 144, 63, 151)(58, 146, 62, 150)(60, 148, 64, 152)(65, 153, 69, 157)(66, 154, 73, 161)(67, 155, 71, 159)(68, 156, 75, 163)(70, 158, 77, 165)(72, 160, 79, 167)(74, 162, 78, 166)(76, 164, 80, 168)(81, 169, 85, 173)(82, 170, 88, 176)(83, 171, 87, 175)(84, 172, 86, 174)(177, 265, 179, 267, 184, 272, 193, 281, 202, 290, 210, 298, 218, 306, 226, 314, 234, 322, 242, 330, 250, 338, 258, 346, 263, 351, 255, 343, 247, 335, 239, 327, 231, 319, 223, 311, 215, 303, 207, 295, 199, 287, 189, 277, 197, 285, 187, 275, 196, 284, 205, 293, 213, 301, 221, 309, 229, 317, 237, 325, 245, 333, 253, 341, 261, 349, 260, 348, 252, 340, 244, 332, 236, 324, 228, 316, 220, 308, 212, 300, 204, 292, 195, 283, 186, 274, 180, 268)(178, 266, 181, 269, 188, 276, 198, 286, 206, 294, 214, 302, 222, 310, 230, 318, 238, 326, 246, 334, 254, 342, 262, 350, 259, 347, 251, 339, 243, 331, 235, 323, 227, 315, 219, 307, 211, 299, 203, 291, 194, 282, 185, 273, 192, 280, 183, 271, 191, 279, 201, 289, 209, 297, 217, 305, 225, 313, 233, 321, 241, 329, 249, 337, 257, 345, 264, 352, 256, 344, 248, 336, 240, 328, 232, 320, 224, 312, 216, 304, 208, 296, 200, 288, 190, 278, 182, 270) L = (1, 178)(2, 177)(3, 183)(4, 185)(5, 187)(6, 189)(7, 179)(8, 188)(9, 180)(10, 190)(11, 181)(12, 184)(13, 182)(14, 186)(15, 196)(16, 197)(17, 201)(18, 199)(19, 203)(20, 191)(21, 192)(22, 205)(23, 194)(24, 207)(25, 193)(26, 206)(27, 195)(28, 208)(29, 198)(30, 202)(31, 200)(32, 204)(33, 213)(34, 217)(35, 215)(36, 219)(37, 209)(38, 221)(39, 211)(40, 223)(41, 210)(42, 222)(43, 212)(44, 224)(45, 214)(46, 218)(47, 216)(48, 220)(49, 229)(50, 233)(51, 231)(52, 235)(53, 225)(54, 237)(55, 227)(56, 239)(57, 226)(58, 238)(59, 228)(60, 240)(61, 230)(62, 234)(63, 232)(64, 236)(65, 245)(66, 249)(67, 247)(68, 251)(69, 241)(70, 253)(71, 243)(72, 255)(73, 242)(74, 254)(75, 244)(76, 256)(77, 246)(78, 250)(79, 248)(80, 252)(81, 261)(82, 264)(83, 263)(84, 262)(85, 257)(86, 260)(87, 259)(88, 258)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 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, 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 E20.988 Graph:: bipartite v = 46 e = 176 f = 92 degree seq :: [ 4^44, 88^2 ] E20.988 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 22, 44}) Quotient :: dipole Aut^+ = C11 x D8 (small group id <88, 9>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-3, Y1^-1 * Y3 * Y1^-1 * Y3^9 * Y1^-10, (Y3 * Y2^-1)^44 ] Map:: R = (1, 89, 2, 90, 6, 94, 16, 104, 28, 116, 37, 125, 45, 133, 53, 141, 61, 149, 69, 157, 77, 165, 85, 173, 84, 172, 74, 162, 65, 153, 59, 147, 52, 140, 42, 130, 33, 121, 26, 114, 13, 101, 4, 92)(3, 91, 9, 97, 17, 105, 8, 96, 21, 109, 29, 117, 39, 127, 46, 134, 55, 143, 62, 150, 71, 159, 78, 166, 87, 175, 82, 170, 73, 161, 67, 155, 60, 148, 50, 138, 41, 129, 35, 123, 27, 115, 11, 99)(5, 93, 14, 102, 18, 106, 31, 119, 38, 126, 47, 135, 54, 142, 63, 151, 70, 158, 79, 167, 86, 174, 83, 171, 76, 164, 66, 154, 57, 145, 51, 139, 44, 132, 34, 122, 24, 112, 12, 100, 20, 108, 7, 95)(10, 98, 19, 107, 30, 118, 23, 111, 15, 103, 22, 110, 32, 120, 40, 128, 48, 136, 56, 144, 64, 152, 72, 160, 80, 168, 88, 176, 81, 169, 75, 163, 68, 156, 58, 146, 49, 137, 43, 131, 36, 124, 25, 113)(177, 265)(178, 266)(179, 267)(180, 268)(181, 269)(182, 270)(183, 271)(184, 272)(185, 273)(186, 274)(187, 275)(188, 276)(189, 277)(190, 278)(191, 279)(192, 280)(193, 281)(194, 282)(195, 283)(196, 284)(197, 285)(198, 286)(199, 287)(200, 288)(201, 289)(202, 290)(203, 291)(204, 292)(205, 293)(206, 294)(207, 295)(208, 296)(209, 297)(210, 298)(211, 299)(212, 300)(213, 301)(214, 302)(215, 303)(216, 304)(217, 305)(218, 306)(219, 307)(220, 308)(221, 309)(222, 310)(223, 311)(224, 312)(225, 313)(226, 314)(227, 315)(228, 316)(229, 317)(230, 318)(231, 319)(232, 320)(233, 321)(234, 322)(235, 323)(236, 324)(237, 325)(238, 326)(239, 327)(240, 328)(241, 329)(242, 330)(243, 331)(244, 332)(245, 333)(246, 334)(247, 335)(248, 336)(249, 337)(250, 338)(251, 339)(252, 340)(253, 341)(254, 342)(255, 343)(256, 344)(257, 345)(258, 346)(259, 347)(260, 348)(261, 349)(262, 350)(263, 351)(264, 352) L = (1, 179)(2, 183)(3, 186)(4, 188)(5, 177)(6, 193)(7, 195)(8, 178)(9, 180)(10, 200)(11, 202)(12, 201)(13, 203)(14, 199)(15, 181)(16, 190)(17, 206)(18, 182)(19, 187)(20, 189)(21, 191)(22, 184)(23, 185)(24, 209)(25, 211)(26, 210)(27, 212)(28, 197)(29, 192)(30, 196)(31, 198)(32, 194)(33, 217)(34, 219)(35, 218)(36, 220)(37, 207)(38, 204)(39, 208)(40, 205)(41, 225)(42, 227)(43, 226)(44, 228)(45, 215)(46, 213)(47, 216)(48, 214)(49, 233)(50, 235)(51, 234)(52, 236)(53, 223)(54, 221)(55, 224)(56, 222)(57, 241)(58, 243)(59, 242)(60, 244)(61, 231)(62, 229)(63, 232)(64, 230)(65, 249)(66, 251)(67, 250)(68, 252)(69, 239)(70, 237)(71, 240)(72, 238)(73, 257)(74, 259)(75, 258)(76, 260)(77, 247)(78, 245)(79, 248)(80, 246)(81, 262)(82, 261)(83, 264)(84, 263)(85, 255)(86, 253)(87, 256)(88, 254)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 88 ), ( 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88 ) } Outer automorphisms :: reflexible Dual of E20.987 Graph:: simple bipartite v = 92 e = 176 f = 46 degree seq :: [ 2^88, 44^4 ] E20.989 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 18, 45}) Quotient :: regular Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^7 * T2 * T1^2 * T2, T1^4 * T2 * T1^-5 * T2 * T1, T2 * T1^2 * T2 * T1^-3 * T2 * T1^3 * T2 * T1^-2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 60, 35, 53, 75, 88, 81, 56, 77, 86, 90, 83, 58, 33, 16, 28, 48, 72, 84, 59, 34, 17, 29, 49, 73, 87, 80, 85, 61, 78, 89, 82, 57, 32, 52, 70, 42, 22, 10, 4)(3, 7, 15, 31, 55, 66, 40, 21, 39, 65, 74, 46, 24, 45, 69, 79, 54, 30, 14, 6, 13, 27, 51, 64, 38, 20, 9, 19, 37, 63, 71, 44, 68, 41, 67, 76, 50, 26, 12, 25, 47, 62, 36, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 69)(43, 66)(45, 72)(46, 73)(47, 70)(50, 75)(51, 77)(54, 78)(55, 80)(62, 86)(63, 81)(64, 85)(65, 82)(67, 83)(68, 84)(71, 87)(74, 88)(76, 89)(79, 90) local type(s) :: { ( 18^45 ) } Outer automorphisms :: reflexible Dual of E20.990 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 45 f = 5 degree seq :: [ 45^2 ] E20.990 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 18, 45}) Quotient :: regular Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^-4 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^18 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 65, 80, 88, 87, 79, 64, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 66, 82, 89, 84, 90, 83, 78, 60, 43, 28, 17, 8)(6, 13, 21, 34, 48, 67, 81, 77, 86, 76, 85, 75, 63, 45, 30, 18, 9, 14)(15, 25, 35, 51, 68, 61, 74, 54, 73, 53, 72, 52, 71, 59, 42, 27, 16, 26)(23, 36, 50, 69, 58, 41, 57, 40, 56, 39, 55, 70, 62, 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, 61)(45, 62)(46, 63)(47, 66)(49, 68)(51, 70)(55, 75)(56, 76)(57, 77)(58, 67)(59, 69)(60, 71)(64, 78)(65, 81)(72, 83)(73, 84)(74, 82)(79, 85)(80, 89)(86, 88)(87, 90) local type(s) :: { ( 45^18 ) } Outer automorphisms :: reflexible Dual of E20.989 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 5 e = 45 f = 2 degree seq :: [ 18^5 ] E20.991 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 45}) Quotient :: edge Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 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 * T2^2, T2^18 ] Map:: R = (1, 3, 8, 17, 28, 43, 60, 78, 86, 88, 87, 79, 64, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 70, 83, 89, 85, 90, 84, 74, 54, 38, 24, 14, 6)(7, 15, 26, 41, 58, 71, 82, 69, 81, 67, 80, 65, 63, 45, 30, 18, 9, 16)(11, 20, 33, 49, 68, 61, 77, 59, 76, 57, 75, 55, 73, 53, 37, 23, 13, 21)(25, 39, 56, 72, 52, 36, 50, 34, 48, 32, 47, 66, 62, 44, 29, 42, 27, 40)(91, 92)(93, 97)(94, 99)(95, 101)(96, 103)(98, 102)(100, 104)(105, 115)(106, 117)(107, 116)(108, 119)(109, 120)(110, 122)(111, 124)(112, 123)(113, 126)(114, 127)(118, 125)(121, 128)(129, 145)(130, 147)(131, 146)(132, 149)(133, 148)(134, 151)(135, 152)(136, 153)(137, 155)(138, 157)(139, 156)(140, 159)(141, 158)(142, 161)(143, 162)(144, 163)(150, 160)(154, 164)(165, 174)(166, 175)(167, 173)(168, 172)(169, 170)(171, 178)(176, 179)(177, 180) L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(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 ), ( 90^18 ) } Outer automorphisms :: reflexible Dual of E20.995 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 90 f = 2 degree seq :: [ 2^45, 18^5 ] E20.992 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 45}) Quotient :: edge Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ F^2, (T1 * T2)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1^2 * T2 * T1^-2, T1^2 * T2^-1 * T1^2 * T2^-4, T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1, T1^18 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 34, 21, 42, 67, 83, 90, 82, 66, 55, 74, 88, 80, 63, 39, 20, 13, 28, 51, 38, 18, 6, 17, 36, 62, 79, 78, 61, 43, 68, 84, 89, 81, 64, 41, 30, 53, 59, 33, 15, 5)(2, 7, 19, 40, 65, 60, 37, 32, 57, 76, 86, 71, 47, 26, 50, 73, 69, 45, 23, 9, 4, 12, 29, 54, 35, 16, 14, 31, 56, 75, 87, 72, 49, 58, 77, 85, 70, 46, 24, 11, 27, 52, 44, 22, 8)(91, 92, 96, 106, 124, 150, 168, 177, 180, 176, 179, 175, 178, 163, 143, 117, 103, 94)(93, 99, 107, 98, 111, 125, 151, 155, 172, 165, 171, 166, 170, 167, 149, 140, 118, 101)(95, 104, 108, 127, 138, 162, 169, 161, 173, 160, 174, 159, 164, 142, 120, 102, 110, 97)(100, 114, 126, 113, 132, 112, 133, 144, 156, 130, 154, 146, 153, 147, 123, 148, 141, 116)(105, 122, 128, 139, 115, 137, 152, 136, 157, 135, 158, 134, 145, 119, 131, 109, 129, 121) L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(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) :: { ( 4^18 ), ( 4^45 ) } Outer automorphisms :: reflexible Dual of E20.996 Transitivity :: ET+ Graph:: bipartite v = 7 e = 90 f = 45 degree seq :: [ 18^5, 45^2 ] E20.993 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 18, 45}) Quotient :: edge Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^7 * T2 * T1^2 * T2, T1^4 * T2 * T1^-5 * T2 * T1, T2 * T1^2 * T2 * T1^-3 * T2 * T1^3 * T2 * T1^-2 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 69)(43, 66)(45, 72)(46, 73)(47, 70)(50, 75)(51, 77)(54, 78)(55, 80)(62, 86)(63, 81)(64, 85)(65, 82)(67, 83)(68, 84)(71, 87)(74, 88)(76, 89)(79, 90)(91, 92, 95, 101, 113, 133, 150, 125, 143, 165, 178, 171, 146, 167, 176, 180, 173, 148, 123, 106, 118, 138, 162, 174, 149, 124, 107, 119, 139, 163, 177, 170, 175, 151, 168, 179, 172, 147, 122, 142, 160, 132, 112, 100, 94)(93, 97, 105, 121, 145, 156, 130, 111, 129, 155, 164, 136, 114, 135, 159, 169, 144, 120, 104, 96, 103, 117, 141, 154, 128, 110, 99, 109, 127, 153, 161, 134, 158, 131, 157, 166, 140, 116, 102, 115, 137, 152, 126, 108, 98) L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(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) :: { ( 36, 36 ), ( 36^45 ) } Outer automorphisms :: reflexible Dual of E20.994 Transitivity :: ET+ Graph:: simple bipartite v = 47 e = 90 f = 5 degree seq :: [ 2^45, 45^2 ] E20.994 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 45}) Quotient :: loop Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 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 * T2^2, T2^18 ] Map:: R = (1, 91, 3, 93, 8, 98, 17, 107, 28, 118, 43, 133, 60, 150, 78, 168, 86, 176, 88, 178, 87, 177, 79, 169, 64, 154, 46, 136, 31, 121, 19, 109, 10, 100, 4, 94)(2, 92, 5, 95, 12, 102, 22, 112, 35, 125, 51, 141, 70, 160, 83, 173, 89, 179, 85, 175, 90, 180, 84, 174, 74, 164, 54, 144, 38, 128, 24, 114, 14, 104, 6, 96)(7, 97, 15, 105, 26, 116, 41, 131, 58, 148, 71, 161, 82, 172, 69, 159, 81, 171, 67, 157, 80, 170, 65, 155, 63, 153, 45, 135, 30, 120, 18, 108, 9, 99, 16, 106)(11, 101, 20, 110, 33, 123, 49, 139, 68, 158, 61, 151, 77, 167, 59, 149, 76, 166, 57, 147, 75, 165, 55, 145, 73, 163, 53, 143, 37, 127, 23, 113, 13, 103, 21, 111)(25, 115, 39, 129, 56, 146, 72, 162, 52, 142, 36, 126, 50, 140, 34, 124, 48, 138, 32, 122, 47, 137, 66, 156, 62, 152, 44, 134, 29, 119, 42, 132, 27, 117, 40, 130) L = (1, 92)(2, 91)(3, 97)(4, 99)(5, 101)(6, 103)(7, 93)(8, 102)(9, 94)(10, 104)(11, 95)(12, 98)(13, 96)(14, 100)(15, 115)(16, 117)(17, 116)(18, 119)(19, 120)(20, 122)(21, 124)(22, 123)(23, 126)(24, 127)(25, 105)(26, 107)(27, 106)(28, 125)(29, 108)(30, 109)(31, 128)(32, 110)(33, 112)(34, 111)(35, 118)(36, 113)(37, 114)(38, 121)(39, 145)(40, 147)(41, 146)(42, 149)(43, 148)(44, 151)(45, 152)(46, 153)(47, 155)(48, 157)(49, 156)(50, 159)(51, 158)(52, 161)(53, 162)(54, 163)(55, 129)(56, 131)(57, 130)(58, 133)(59, 132)(60, 160)(61, 134)(62, 135)(63, 136)(64, 164)(65, 137)(66, 139)(67, 138)(68, 141)(69, 140)(70, 150)(71, 142)(72, 143)(73, 144)(74, 154)(75, 174)(76, 175)(77, 173)(78, 172)(79, 170)(80, 169)(81, 178)(82, 168)(83, 167)(84, 165)(85, 166)(86, 179)(87, 180)(88, 171)(89, 176)(90, 177) local type(s) :: { ( 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45, 2, 45 ) } Outer automorphisms :: reflexible Dual of E20.993 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 90 f = 47 degree seq :: [ 36^5 ] E20.995 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 45}) Quotient :: loop Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ F^2, (T1 * T2)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1^2 * T2 * T1^-2, T1^2 * T2^-1 * T1^2 * T2^-4, T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1, T1^18 ] Map:: R = (1, 91, 3, 93, 10, 100, 25, 115, 48, 138, 34, 124, 21, 111, 42, 132, 67, 157, 83, 173, 90, 180, 82, 172, 66, 156, 55, 145, 74, 164, 88, 178, 80, 170, 63, 153, 39, 129, 20, 110, 13, 103, 28, 118, 51, 141, 38, 128, 18, 108, 6, 96, 17, 107, 36, 126, 62, 152, 79, 169, 78, 168, 61, 151, 43, 133, 68, 158, 84, 174, 89, 179, 81, 171, 64, 154, 41, 131, 30, 120, 53, 143, 59, 149, 33, 123, 15, 105, 5, 95)(2, 92, 7, 97, 19, 109, 40, 130, 65, 155, 60, 150, 37, 127, 32, 122, 57, 147, 76, 166, 86, 176, 71, 161, 47, 137, 26, 116, 50, 140, 73, 163, 69, 159, 45, 135, 23, 113, 9, 99, 4, 94, 12, 102, 29, 119, 54, 144, 35, 125, 16, 106, 14, 104, 31, 121, 56, 146, 75, 165, 87, 177, 72, 162, 49, 139, 58, 148, 77, 167, 85, 175, 70, 160, 46, 136, 24, 114, 11, 101, 27, 117, 52, 142, 44, 134, 22, 112, 8, 98) L = (1, 92)(2, 96)(3, 99)(4, 91)(5, 104)(6, 106)(7, 95)(8, 111)(9, 107)(10, 114)(11, 93)(12, 110)(13, 94)(14, 108)(15, 122)(16, 124)(17, 98)(18, 127)(19, 129)(20, 97)(21, 125)(22, 133)(23, 132)(24, 126)(25, 137)(26, 100)(27, 103)(28, 101)(29, 131)(30, 102)(31, 105)(32, 128)(33, 148)(34, 150)(35, 151)(36, 113)(37, 138)(38, 139)(39, 121)(40, 154)(41, 109)(42, 112)(43, 144)(44, 145)(45, 158)(46, 157)(47, 152)(48, 162)(49, 115)(50, 118)(51, 116)(52, 120)(53, 117)(54, 156)(55, 119)(56, 153)(57, 123)(58, 141)(59, 140)(60, 168)(61, 155)(62, 136)(63, 147)(64, 146)(65, 172)(66, 130)(67, 135)(68, 134)(69, 164)(70, 174)(71, 173)(72, 169)(73, 143)(74, 142)(75, 171)(76, 170)(77, 149)(78, 177)(79, 161)(80, 167)(81, 166)(82, 165)(83, 160)(84, 159)(85, 178)(86, 179)(87, 180)(88, 163)(89, 175)(90, 176) 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 ) } Outer automorphisms :: reflexible Dual of E20.991 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 90 f = 50 degree seq :: [ 90^2 ] E20.996 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 18, 45}) Quotient :: loop Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^7 * T2 * T1^2 * T2, T1^4 * T2 * T1^-5 * T2 * T1, T2 * T1^2 * T2 * T1^-3 * T2 * T1^3 * T2 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 91, 3, 93)(2, 92, 6, 96)(4, 94, 9, 99)(5, 95, 12, 102)(7, 97, 16, 106)(8, 98, 17, 107)(10, 100, 21, 111)(11, 101, 24, 114)(13, 103, 28, 118)(14, 104, 29, 119)(15, 105, 32, 122)(18, 108, 35, 125)(19, 109, 33, 123)(20, 110, 34, 124)(22, 112, 41, 131)(23, 113, 44, 134)(25, 115, 48, 138)(26, 116, 49, 139)(27, 117, 52, 142)(30, 120, 53, 143)(31, 121, 56, 146)(36, 126, 61, 151)(37, 127, 57, 147)(38, 128, 60, 150)(39, 129, 58, 148)(40, 130, 59, 149)(42, 132, 69, 159)(43, 133, 66, 156)(45, 135, 72, 162)(46, 136, 73, 163)(47, 137, 70, 160)(50, 140, 75, 165)(51, 141, 77, 167)(54, 144, 78, 168)(55, 145, 80, 170)(62, 152, 86, 176)(63, 153, 81, 171)(64, 154, 85, 175)(65, 155, 82, 172)(67, 157, 83, 173)(68, 158, 84, 174)(71, 161, 87, 177)(74, 164, 88, 178)(76, 166, 89, 179)(79, 169, 90, 180) L = (1, 92)(2, 95)(3, 97)(4, 91)(5, 101)(6, 103)(7, 105)(8, 93)(9, 109)(10, 94)(11, 113)(12, 115)(13, 117)(14, 96)(15, 121)(16, 118)(17, 119)(18, 98)(19, 127)(20, 99)(21, 129)(22, 100)(23, 133)(24, 135)(25, 137)(26, 102)(27, 141)(28, 138)(29, 139)(30, 104)(31, 145)(32, 142)(33, 106)(34, 107)(35, 143)(36, 108)(37, 153)(38, 110)(39, 155)(40, 111)(41, 157)(42, 112)(43, 150)(44, 158)(45, 159)(46, 114)(47, 152)(48, 162)(49, 163)(50, 116)(51, 154)(52, 160)(53, 165)(54, 120)(55, 156)(56, 167)(57, 122)(58, 123)(59, 124)(60, 125)(61, 168)(62, 126)(63, 161)(64, 128)(65, 164)(66, 130)(67, 166)(68, 131)(69, 169)(70, 132)(71, 134)(72, 174)(73, 177)(74, 136)(75, 178)(76, 140)(77, 176)(78, 179)(79, 144)(80, 175)(81, 146)(82, 147)(83, 148)(84, 149)(85, 151)(86, 180)(87, 170)(88, 171)(89, 172)(90, 173) local type(s) :: { ( 18, 45, 18, 45 ) } Outer automorphisms :: reflexible Dual of E20.992 Transitivity :: ET+ VT+ AT Graph:: simple v = 45 e = 90 f = 7 degree seq :: [ 4^45 ] E20.997 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 45}) Quotient :: dipole Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2^-3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2, Y2^18, (Y3 * Y2^-1)^45 ] Map:: R = (1, 91, 2, 92)(3, 93, 7, 97)(4, 94, 9, 99)(5, 95, 11, 101)(6, 96, 13, 103)(8, 98, 12, 102)(10, 100, 14, 104)(15, 105, 25, 115)(16, 106, 27, 117)(17, 107, 26, 116)(18, 108, 29, 119)(19, 109, 30, 120)(20, 110, 32, 122)(21, 111, 34, 124)(22, 112, 33, 123)(23, 113, 36, 126)(24, 114, 37, 127)(28, 118, 35, 125)(31, 121, 38, 128)(39, 129, 55, 145)(40, 130, 57, 147)(41, 131, 56, 146)(42, 132, 59, 149)(43, 133, 58, 148)(44, 134, 61, 151)(45, 135, 62, 152)(46, 136, 63, 153)(47, 137, 65, 155)(48, 138, 67, 157)(49, 139, 66, 156)(50, 140, 69, 159)(51, 141, 68, 158)(52, 142, 71, 161)(53, 143, 72, 162)(54, 144, 73, 163)(60, 150, 70, 160)(64, 154, 74, 164)(75, 165, 84, 174)(76, 166, 85, 175)(77, 167, 83, 173)(78, 168, 82, 172)(79, 169, 80, 170)(81, 171, 88, 178)(86, 176, 89, 179)(87, 177, 90, 180)(181, 271, 183, 273, 188, 278, 197, 287, 208, 298, 223, 313, 240, 330, 258, 348, 266, 356, 268, 358, 267, 357, 259, 349, 244, 334, 226, 316, 211, 301, 199, 289, 190, 280, 184, 274)(182, 272, 185, 275, 192, 282, 202, 292, 215, 305, 231, 321, 250, 340, 263, 353, 269, 359, 265, 355, 270, 360, 264, 354, 254, 344, 234, 324, 218, 308, 204, 294, 194, 284, 186, 276)(187, 277, 195, 285, 206, 296, 221, 311, 238, 328, 251, 341, 262, 352, 249, 339, 261, 351, 247, 337, 260, 350, 245, 335, 243, 333, 225, 315, 210, 300, 198, 288, 189, 279, 196, 286)(191, 281, 200, 290, 213, 303, 229, 319, 248, 338, 241, 331, 257, 347, 239, 329, 256, 346, 237, 327, 255, 345, 235, 325, 253, 343, 233, 323, 217, 307, 203, 293, 193, 283, 201, 291)(205, 295, 219, 309, 236, 326, 252, 342, 232, 322, 216, 306, 230, 320, 214, 304, 228, 318, 212, 302, 227, 317, 246, 336, 242, 332, 224, 314, 209, 299, 222, 312, 207, 297, 220, 310) L = (1, 182)(2, 181)(3, 187)(4, 189)(5, 191)(6, 193)(7, 183)(8, 192)(9, 184)(10, 194)(11, 185)(12, 188)(13, 186)(14, 190)(15, 205)(16, 207)(17, 206)(18, 209)(19, 210)(20, 212)(21, 214)(22, 213)(23, 216)(24, 217)(25, 195)(26, 197)(27, 196)(28, 215)(29, 198)(30, 199)(31, 218)(32, 200)(33, 202)(34, 201)(35, 208)(36, 203)(37, 204)(38, 211)(39, 235)(40, 237)(41, 236)(42, 239)(43, 238)(44, 241)(45, 242)(46, 243)(47, 245)(48, 247)(49, 246)(50, 249)(51, 248)(52, 251)(53, 252)(54, 253)(55, 219)(56, 221)(57, 220)(58, 223)(59, 222)(60, 250)(61, 224)(62, 225)(63, 226)(64, 254)(65, 227)(66, 229)(67, 228)(68, 231)(69, 230)(70, 240)(71, 232)(72, 233)(73, 234)(74, 244)(75, 264)(76, 265)(77, 263)(78, 262)(79, 260)(80, 259)(81, 268)(82, 258)(83, 257)(84, 255)(85, 256)(86, 269)(87, 270)(88, 261)(89, 266)(90, 267)(91, 271)(92, 272)(93, 273)(94, 274)(95, 275)(96, 276)(97, 277)(98, 278)(99, 279)(100, 280)(101, 281)(102, 282)(103, 283)(104, 284)(105, 285)(106, 286)(107, 287)(108, 288)(109, 289)(110, 290)(111, 291)(112, 292)(113, 293)(114, 294)(115, 295)(116, 296)(117, 297)(118, 298)(119, 299)(120, 300)(121, 301)(122, 302)(123, 303)(124, 304)(125, 305)(126, 306)(127, 307)(128, 308)(129, 309)(130, 310)(131, 311)(132, 312)(133, 313)(134, 314)(135, 315)(136, 316)(137, 317)(138, 318)(139, 319)(140, 320)(141, 321)(142, 322)(143, 323)(144, 324)(145, 325)(146, 326)(147, 327)(148, 328)(149, 329)(150, 330)(151, 331)(152, 332)(153, 333)(154, 334)(155, 335)(156, 336)(157, 337)(158, 338)(159, 339)(160, 340)(161, 341)(162, 342)(163, 343)(164, 344)(165, 345)(166, 346)(167, 347)(168, 348)(169, 349)(170, 350)(171, 351)(172, 352)(173, 353)(174, 354)(175, 355)(176, 356)(177, 357)(178, 358)(179, 359)(180, 360) 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 ) } Outer automorphisms :: reflexible Dual of E20.1000 Graph:: bipartite v = 50 e = 180 f = 92 degree seq :: [ 4^45, 36^5 ] E20.998 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 45}) Quotient :: dipole Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2 * Y1^3 * Y2 * Y1^-1, Y1^2 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^2, Y1^2 * Y2^-1 * Y1^2 * Y2^-4, Y1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y1 * Y2^-2, Y1^18 ] Map:: R = (1, 91, 2, 92, 6, 96, 16, 106, 34, 124, 60, 150, 78, 168, 87, 177, 90, 180, 86, 176, 89, 179, 85, 175, 88, 178, 73, 163, 53, 143, 27, 117, 13, 103, 4, 94)(3, 93, 9, 99, 17, 107, 8, 98, 21, 111, 35, 125, 61, 151, 65, 155, 82, 172, 75, 165, 81, 171, 76, 166, 80, 170, 77, 167, 59, 149, 50, 140, 28, 118, 11, 101)(5, 95, 14, 104, 18, 108, 37, 127, 48, 138, 72, 162, 79, 169, 71, 161, 83, 173, 70, 160, 84, 174, 69, 159, 74, 164, 52, 142, 30, 120, 12, 102, 20, 110, 7, 97)(10, 100, 24, 114, 36, 126, 23, 113, 42, 132, 22, 112, 43, 133, 54, 144, 66, 156, 40, 130, 64, 154, 56, 146, 63, 153, 57, 147, 33, 123, 58, 148, 51, 141, 26, 116)(15, 105, 32, 122, 38, 128, 49, 139, 25, 115, 47, 137, 62, 152, 46, 136, 67, 157, 45, 135, 68, 158, 44, 134, 55, 145, 29, 119, 41, 131, 19, 109, 39, 129, 31, 121)(181, 271, 183, 273, 190, 280, 205, 295, 228, 318, 214, 304, 201, 291, 222, 312, 247, 337, 263, 353, 270, 360, 262, 352, 246, 336, 235, 325, 254, 344, 268, 358, 260, 350, 243, 333, 219, 309, 200, 290, 193, 283, 208, 298, 231, 321, 218, 308, 198, 288, 186, 276, 197, 287, 216, 306, 242, 332, 259, 349, 258, 348, 241, 331, 223, 313, 248, 338, 264, 354, 269, 359, 261, 351, 244, 334, 221, 311, 210, 300, 233, 323, 239, 329, 213, 303, 195, 285, 185, 275)(182, 272, 187, 277, 199, 289, 220, 310, 245, 335, 240, 330, 217, 307, 212, 302, 237, 327, 256, 346, 266, 356, 251, 341, 227, 317, 206, 296, 230, 320, 253, 343, 249, 339, 225, 315, 203, 293, 189, 279, 184, 274, 192, 282, 209, 299, 234, 324, 215, 305, 196, 286, 194, 284, 211, 301, 236, 326, 255, 345, 267, 357, 252, 342, 229, 319, 238, 328, 257, 347, 265, 355, 250, 340, 226, 316, 204, 294, 191, 281, 207, 297, 232, 322, 224, 314, 202, 292, 188, 278) L = (1, 183)(2, 187)(3, 190)(4, 192)(5, 181)(6, 197)(7, 199)(8, 182)(9, 184)(10, 205)(11, 207)(12, 209)(13, 208)(14, 211)(15, 185)(16, 194)(17, 216)(18, 186)(19, 220)(20, 193)(21, 222)(22, 188)(23, 189)(24, 191)(25, 228)(26, 230)(27, 232)(28, 231)(29, 234)(30, 233)(31, 236)(32, 237)(33, 195)(34, 201)(35, 196)(36, 242)(37, 212)(38, 198)(39, 200)(40, 245)(41, 210)(42, 247)(43, 248)(44, 202)(45, 203)(46, 204)(47, 206)(48, 214)(49, 238)(50, 253)(51, 218)(52, 224)(53, 239)(54, 215)(55, 254)(56, 255)(57, 256)(58, 257)(59, 213)(60, 217)(61, 223)(62, 259)(63, 219)(64, 221)(65, 240)(66, 235)(67, 263)(68, 264)(69, 225)(70, 226)(71, 227)(72, 229)(73, 249)(74, 268)(75, 267)(76, 266)(77, 265)(78, 241)(79, 258)(80, 243)(81, 244)(82, 246)(83, 270)(84, 269)(85, 250)(86, 251)(87, 252)(88, 260)(89, 261)(90, 262)(91, 271)(92, 272)(93, 273)(94, 274)(95, 275)(96, 276)(97, 277)(98, 278)(99, 279)(100, 280)(101, 281)(102, 282)(103, 283)(104, 284)(105, 285)(106, 286)(107, 287)(108, 288)(109, 289)(110, 290)(111, 291)(112, 292)(113, 293)(114, 294)(115, 295)(116, 296)(117, 297)(118, 298)(119, 299)(120, 300)(121, 301)(122, 302)(123, 303)(124, 304)(125, 305)(126, 306)(127, 307)(128, 308)(129, 309)(130, 310)(131, 311)(132, 312)(133, 313)(134, 314)(135, 315)(136, 316)(137, 317)(138, 318)(139, 319)(140, 320)(141, 321)(142, 322)(143, 323)(144, 324)(145, 325)(146, 326)(147, 327)(148, 328)(149, 329)(150, 330)(151, 331)(152, 332)(153, 333)(154, 334)(155, 335)(156, 336)(157, 337)(158, 338)(159, 339)(160, 340)(161, 341)(162, 342)(163, 343)(164, 344)(165, 345)(166, 346)(167, 347)(168, 348)(169, 349)(170, 350)(171, 351)(172, 352)(173, 353)(174, 354)(175, 355)(176, 356)(177, 357)(178, 358)(179, 359)(180, 360) 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 ) } Outer automorphisms :: reflexible Dual of E20.999 Graph:: bipartite v = 7 e = 180 f = 135 degree seq :: [ 36^5, 90^2 ] E20.999 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 45}) Quotient :: dipole Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 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, Y2 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3, Y2 * Y3^2 * Y2 * Y3^7, (Y3^-1 * Y1^-1)^45 ] Map:: polytopal R = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(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)(181, 271, 182, 272)(183, 273, 187, 277)(184, 274, 189, 279)(185, 275, 191, 281)(186, 276, 193, 283)(188, 278, 197, 287)(190, 280, 201, 291)(192, 282, 205, 295)(194, 284, 209, 299)(195, 285, 203, 293)(196, 286, 207, 297)(198, 288, 215, 305)(199, 289, 204, 294)(200, 290, 208, 298)(202, 292, 221, 311)(206, 296, 227, 317)(210, 300, 233, 323)(211, 301, 225, 315)(212, 302, 231, 321)(213, 303, 223, 313)(214, 304, 229, 319)(216, 306, 241, 331)(217, 307, 226, 316)(218, 308, 232, 322)(219, 309, 224, 314)(220, 310, 230, 320)(222, 312, 249, 339)(228, 318, 256, 346)(234, 324, 262, 352)(235, 325, 254, 344)(236, 326, 260, 350)(237, 327, 250, 340)(238, 328, 259, 349)(239, 329, 251, 341)(240, 330, 257, 347)(242, 332, 246, 336)(243, 333, 255, 345)(244, 334, 261, 351)(245, 335, 253, 343)(247, 337, 252, 342)(248, 338, 258, 348)(263, 353, 267, 357)(264, 354, 268, 358)(265, 355, 269, 359)(266, 356, 270, 360) L = (1, 183)(2, 185)(3, 188)(4, 181)(5, 192)(6, 182)(7, 195)(8, 198)(9, 199)(10, 184)(11, 203)(12, 206)(13, 207)(14, 186)(15, 211)(16, 187)(17, 213)(18, 216)(19, 217)(20, 189)(21, 219)(22, 190)(23, 223)(24, 191)(25, 225)(26, 228)(27, 229)(28, 193)(29, 231)(30, 194)(31, 235)(32, 196)(33, 237)(34, 197)(35, 239)(36, 242)(37, 243)(38, 200)(39, 245)(40, 201)(41, 247)(42, 202)(43, 251)(44, 204)(45, 250)(46, 205)(47, 254)(48, 246)(49, 257)(50, 208)(51, 259)(52, 209)(53, 260)(54, 210)(55, 244)(56, 212)(57, 234)(58, 214)(59, 249)(60, 215)(61, 248)(62, 232)(63, 266)(64, 218)(65, 265)(66, 220)(67, 264)(68, 221)(69, 263)(70, 222)(71, 258)(72, 224)(73, 226)(74, 262)(75, 227)(76, 261)(77, 270)(78, 230)(79, 269)(80, 268)(81, 233)(82, 267)(83, 236)(84, 238)(85, 240)(86, 241)(87, 252)(88, 253)(89, 255)(90, 256)(91, 271)(92, 272)(93, 273)(94, 274)(95, 275)(96, 276)(97, 277)(98, 278)(99, 279)(100, 280)(101, 281)(102, 282)(103, 283)(104, 284)(105, 285)(106, 286)(107, 287)(108, 288)(109, 289)(110, 290)(111, 291)(112, 292)(113, 293)(114, 294)(115, 295)(116, 296)(117, 297)(118, 298)(119, 299)(120, 300)(121, 301)(122, 302)(123, 303)(124, 304)(125, 305)(126, 306)(127, 307)(128, 308)(129, 309)(130, 310)(131, 311)(132, 312)(133, 313)(134, 314)(135, 315)(136, 316)(137, 317)(138, 318)(139, 319)(140, 320)(141, 321)(142, 322)(143, 323)(144, 324)(145, 325)(146, 326)(147, 327)(148, 328)(149, 329)(150, 330)(151, 331)(152, 332)(153, 333)(154, 334)(155, 335)(156, 336)(157, 337)(158, 338)(159, 339)(160, 340)(161, 341)(162, 342)(163, 343)(164, 344)(165, 345)(166, 346)(167, 347)(168, 348)(169, 349)(170, 350)(171, 351)(172, 352)(173, 353)(174, 354)(175, 355)(176, 356)(177, 357)(178, 358)(179, 359)(180, 360) local type(s) :: { ( 36, 90 ), ( 36, 90, 36, 90 ) } Outer automorphisms :: reflexible Dual of E20.998 Graph:: simple bipartite v = 135 e = 180 f = 7 degree seq :: [ 2^90, 4^45 ] E20.1000 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 45}) Quotient :: dipole Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |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 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y1^7 * Y3 * Y1^2 * Y3, Y1^4 * Y3 * Y1^-5 * Y3 * Y1, Y3 * Y1^3 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-3 ] Map:: R = (1, 91, 2, 92, 5, 95, 11, 101, 23, 113, 43, 133, 60, 150, 35, 125, 53, 143, 75, 165, 88, 178, 81, 171, 56, 146, 77, 167, 86, 176, 90, 180, 83, 173, 58, 148, 33, 123, 16, 106, 28, 118, 48, 138, 72, 162, 84, 174, 59, 149, 34, 124, 17, 107, 29, 119, 49, 139, 73, 163, 87, 177, 80, 170, 85, 175, 61, 151, 78, 168, 89, 179, 82, 172, 57, 147, 32, 122, 52, 142, 70, 160, 42, 132, 22, 112, 10, 100, 4, 94)(3, 93, 7, 97, 15, 105, 31, 121, 55, 145, 66, 156, 40, 130, 21, 111, 39, 129, 65, 155, 74, 164, 46, 136, 24, 114, 45, 135, 69, 159, 79, 169, 54, 144, 30, 120, 14, 104, 6, 96, 13, 103, 27, 117, 51, 141, 64, 154, 38, 128, 20, 110, 9, 99, 19, 109, 37, 127, 63, 153, 71, 161, 44, 134, 68, 158, 41, 131, 67, 157, 76, 166, 50, 140, 26, 116, 12, 102, 25, 115, 47, 137, 62, 152, 36, 126, 18, 108, 8, 98)(181, 271)(182, 272)(183, 273)(184, 274)(185, 275)(186, 276)(187, 277)(188, 278)(189, 279)(190, 280)(191, 281)(192, 282)(193, 283)(194, 284)(195, 285)(196, 286)(197, 287)(198, 288)(199, 289)(200, 290)(201, 291)(202, 292)(203, 293)(204, 294)(205, 295)(206, 296)(207, 297)(208, 298)(209, 299)(210, 300)(211, 301)(212, 302)(213, 303)(214, 304)(215, 305)(216, 306)(217, 307)(218, 308)(219, 309)(220, 310)(221, 311)(222, 312)(223, 313)(224, 314)(225, 315)(226, 316)(227, 317)(228, 318)(229, 319)(230, 320)(231, 321)(232, 322)(233, 323)(234, 324)(235, 325)(236, 326)(237, 327)(238, 328)(239, 329)(240, 330)(241, 331)(242, 332)(243, 333)(244, 334)(245, 335)(246, 336)(247, 337)(248, 338)(249, 339)(250, 340)(251, 341)(252, 342)(253, 343)(254, 344)(255, 345)(256, 346)(257, 347)(258, 348)(259, 349)(260, 350)(261, 351)(262, 352)(263, 353)(264, 354)(265, 355)(266, 356)(267, 357)(268, 358)(269, 359)(270, 360) L = (1, 183)(2, 186)(3, 181)(4, 189)(5, 192)(6, 182)(7, 196)(8, 197)(9, 184)(10, 201)(11, 204)(12, 185)(13, 208)(14, 209)(15, 212)(16, 187)(17, 188)(18, 215)(19, 213)(20, 214)(21, 190)(22, 221)(23, 224)(24, 191)(25, 228)(26, 229)(27, 232)(28, 193)(29, 194)(30, 233)(31, 236)(32, 195)(33, 199)(34, 200)(35, 198)(36, 241)(37, 237)(38, 240)(39, 238)(40, 239)(41, 202)(42, 249)(43, 246)(44, 203)(45, 252)(46, 253)(47, 250)(48, 205)(49, 206)(50, 255)(51, 257)(52, 207)(53, 210)(54, 258)(55, 260)(56, 211)(57, 217)(58, 219)(59, 220)(60, 218)(61, 216)(62, 266)(63, 261)(64, 265)(65, 262)(66, 223)(67, 263)(68, 264)(69, 222)(70, 227)(71, 267)(72, 225)(73, 226)(74, 268)(75, 230)(76, 269)(77, 231)(78, 234)(79, 270)(80, 235)(81, 243)(82, 245)(83, 247)(84, 248)(85, 244)(86, 242)(87, 251)(88, 254)(89, 256)(90, 259)(91, 271)(92, 272)(93, 273)(94, 274)(95, 275)(96, 276)(97, 277)(98, 278)(99, 279)(100, 280)(101, 281)(102, 282)(103, 283)(104, 284)(105, 285)(106, 286)(107, 287)(108, 288)(109, 289)(110, 290)(111, 291)(112, 292)(113, 293)(114, 294)(115, 295)(116, 296)(117, 297)(118, 298)(119, 299)(120, 300)(121, 301)(122, 302)(123, 303)(124, 304)(125, 305)(126, 306)(127, 307)(128, 308)(129, 309)(130, 310)(131, 311)(132, 312)(133, 313)(134, 314)(135, 315)(136, 316)(137, 317)(138, 318)(139, 319)(140, 320)(141, 321)(142, 322)(143, 323)(144, 324)(145, 325)(146, 326)(147, 327)(148, 328)(149, 329)(150, 330)(151, 331)(152, 332)(153, 333)(154, 334)(155, 335)(156, 336)(157, 337)(158, 338)(159, 339)(160, 340)(161, 341)(162, 342)(163, 343)(164, 344)(165, 345)(166, 346)(167, 347)(168, 348)(169, 349)(170, 350)(171, 351)(172, 352)(173, 353)(174, 354)(175, 355)(176, 356)(177, 357)(178, 358)(179, 359)(180, 360) local type(s) :: { ( 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E20.997 Graph:: simple bipartite v = 92 e = 180 f = 50 degree seq :: [ 2^90, 90^2 ] E20.1001 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 45}) Quotient :: dipole Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1 * R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^2 * Y1 * Y2^2 * Y1 * Y2^5, (Y2^-1 * R * Y2^-4)^2, Y2^2 * Y1 * Y2^-3 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^18 ] Map:: R = (1, 91, 2, 92)(3, 93, 7, 97)(4, 94, 9, 99)(5, 95, 11, 101)(6, 96, 13, 103)(8, 98, 17, 107)(10, 100, 21, 111)(12, 102, 25, 115)(14, 104, 29, 119)(15, 105, 23, 113)(16, 106, 27, 117)(18, 108, 35, 125)(19, 109, 24, 114)(20, 110, 28, 118)(22, 112, 41, 131)(26, 116, 47, 137)(30, 120, 53, 143)(31, 121, 45, 135)(32, 122, 51, 141)(33, 123, 43, 133)(34, 124, 49, 139)(36, 126, 61, 151)(37, 127, 46, 136)(38, 128, 52, 142)(39, 129, 44, 134)(40, 130, 50, 140)(42, 132, 69, 159)(48, 138, 76, 166)(54, 144, 82, 172)(55, 145, 74, 164)(56, 146, 80, 170)(57, 147, 70, 160)(58, 148, 79, 169)(59, 149, 71, 161)(60, 150, 77, 167)(62, 152, 66, 156)(63, 153, 75, 165)(64, 154, 81, 171)(65, 155, 73, 163)(67, 157, 72, 162)(68, 158, 78, 168)(83, 173, 87, 177)(84, 174, 88, 178)(85, 175, 89, 179)(86, 176, 90, 180)(181, 271, 183, 273, 188, 278, 198, 288, 216, 306, 242, 332, 232, 322, 209, 299, 231, 321, 259, 349, 269, 359, 255, 345, 227, 317, 254, 344, 262, 352, 267, 357, 252, 342, 224, 314, 204, 294, 191, 281, 203, 293, 223, 313, 251, 341, 258, 348, 230, 320, 208, 298, 193, 283, 207, 297, 229, 319, 257, 347, 270, 360, 256, 346, 261, 351, 233, 323, 260, 350, 268, 358, 253, 343, 226, 316, 205, 295, 225, 315, 250, 340, 222, 312, 202, 292, 190, 280, 184, 274)(182, 272, 185, 275, 192, 282, 206, 296, 228, 318, 246, 336, 220, 310, 201, 291, 219, 309, 245, 335, 265, 355, 240, 330, 215, 305, 239, 329, 249, 339, 263, 353, 236, 326, 212, 302, 196, 286, 187, 277, 195, 285, 211, 301, 235, 325, 244, 334, 218, 308, 200, 290, 189, 279, 199, 289, 217, 307, 243, 333, 266, 356, 241, 331, 248, 338, 221, 311, 247, 337, 264, 354, 238, 328, 214, 304, 197, 287, 213, 303, 237, 327, 234, 324, 210, 300, 194, 284, 186, 276) L = (1, 182)(2, 181)(3, 187)(4, 189)(5, 191)(6, 193)(7, 183)(8, 197)(9, 184)(10, 201)(11, 185)(12, 205)(13, 186)(14, 209)(15, 203)(16, 207)(17, 188)(18, 215)(19, 204)(20, 208)(21, 190)(22, 221)(23, 195)(24, 199)(25, 192)(26, 227)(27, 196)(28, 200)(29, 194)(30, 233)(31, 225)(32, 231)(33, 223)(34, 229)(35, 198)(36, 241)(37, 226)(38, 232)(39, 224)(40, 230)(41, 202)(42, 249)(43, 213)(44, 219)(45, 211)(46, 217)(47, 206)(48, 256)(49, 214)(50, 220)(51, 212)(52, 218)(53, 210)(54, 262)(55, 254)(56, 260)(57, 250)(58, 259)(59, 251)(60, 257)(61, 216)(62, 246)(63, 255)(64, 261)(65, 253)(66, 242)(67, 252)(68, 258)(69, 222)(70, 237)(71, 239)(72, 247)(73, 245)(74, 235)(75, 243)(76, 228)(77, 240)(78, 248)(79, 238)(80, 236)(81, 244)(82, 234)(83, 267)(84, 268)(85, 269)(86, 270)(87, 263)(88, 264)(89, 265)(90, 266)(91, 271)(92, 272)(93, 273)(94, 274)(95, 275)(96, 276)(97, 277)(98, 278)(99, 279)(100, 280)(101, 281)(102, 282)(103, 283)(104, 284)(105, 285)(106, 286)(107, 287)(108, 288)(109, 289)(110, 290)(111, 291)(112, 292)(113, 293)(114, 294)(115, 295)(116, 296)(117, 297)(118, 298)(119, 299)(120, 300)(121, 301)(122, 302)(123, 303)(124, 304)(125, 305)(126, 306)(127, 307)(128, 308)(129, 309)(130, 310)(131, 311)(132, 312)(133, 313)(134, 314)(135, 315)(136, 316)(137, 317)(138, 318)(139, 319)(140, 320)(141, 321)(142, 322)(143, 323)(144, 324)(145, 325)(146, 326)(147, 327)(148, 328)(149, 329)(150, 330)(151, 331)(152, 332)(153, 333)(154, 334)(155, 335)(156, 336)(157, 337)(158, 338)(159, 339)(160, 340)(161, 341)(162, 342)(163, 343)(164, 344)(165, 345)(166, 346)(167, 347)(168, 348)(169, 349)(170, 350)(171, 351)(172, 352)(173, 353)(174, 354)(175, 355)(176, 356)(177, 357)(178, 358)(179, 359)(180, 360) local type(s) :: { ( 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E20.1002 Graph:: bipartite v = 47 e = 180 f = 95 degree seq :: [ 4^45, 90^2 ] E20.1002 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 18, 45}) Quotient :: dipole Aut^+ = C9 x D10 (small group id <90, 2>) Aut = D10 x D18 (small group id <180, 7>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^3 * Y3 * Y1^-1, Y3^-1 * Y1^2 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^2 * Y3^-1 * Y1^2 * Y3^-4, Y1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-2 * Y1 * Y3^-2, Y1^18, (Y3 * Y2^-1)^45 ] Map:: R = (1, 91, 2, 92, 6, 96, 16, 106, 34, 124, 60, 150, 78, 168, 87, 177, 90, 180, 86, 176, 89, 179, 85, 175, 88, 178, 73, 163, 53, 143, 27, 117, 13, 103, 4, 94)(3, 93, 9, 99, 17, 107, 8, 98, 21, 111, 35, 125, 61, 151, 65, 155, 82, 172, 75, 165, 81, 171, 76, 166, 80, 170, 77, 167, 59, 149, 50, 140, 28, 118, 11, 101)(5, 95, 14, 104, 18, 108, 37, 127, 48, 138, 72, 162, 79, 169, 71, 161, 83, 173, 70, 160, 84, 174, 69, 159, 74, 164, 52, 142, 30, 120, 12, 102, 20, 110, 7, 97)(10, 100, 24, 114, 36, 126, 23, 113, 42, 132, 22, 112, 43, 133, 54, 144, 66, 156, 40, 130, 64, 154, 56, 146, 63, 153, 57, 147, 33, 123, 58, 148, 51, 141, 26, 116)(15, 105, 32, 122, 38, 128, 49, 139, 25, 115, 47, 137, 62, 152, 46, 136, 67, 157, 45, 135, 68, 158, 44, 134, 55, 145, 29, 119, 41, 131, 19, 109, 39, 129, 31, 121)(181, 271)(182, 272)(183, 273)(184, 274)(185, 275)(186, 276)(187, 277)(188, 278)(189, 279)(190, 280)(191, 281)(192, 282)(193, 283)(194, 284)(195, 285)(196, 286)(197, 287)(198, 288)(199, 289)(200, 290)(201, 291)(202, 292)(203, 293)(204, 294)(205, 295)(206, 296)(207, 297)(208, 298)(209, 299)(210, 300)(211, 301)(212, 302)(213, 303)(214, 304)(215, 305)(216, 306)(217, 307)(218, 308)(219, 309)(220, 310)(221, 311)(222, 312)(223, 313)(224, 314)(225, 315)(226, 316)(227, 317)(228, 318)(229, 319)(230, 320)(231, 321)(232, 322)(233, 323)(234, 324)(235, 325)(236, 326)(237, 327)(238, 328)(239, 329)(240, 330)(241, 331)(242, 332)(243, 333)(244, 334)(245, 335)(246, 336)(247, 337)(248, 338)(249, 339)(250, 340)(251, 341)(252, 342)(253, 343)(254, 344)(255, 345)(256, 346)(257, 347)(258, 348)(259, 349)(260, 350)(261, 351)(262, 352)(263, 353)(264, 354)(265, 355)(266, 356)(267, 357)(268, 358)(269, 359)(270, 360) L = (1, 183)(2, 187)(3, 190)(4, 192)(5, 181)(6, 197)(7, 199)(8, 182)(9, 184)(10, 205)(11, 207)(12, 209)(13, 208)(14, 211)(15, 185)(16, 194)(17, 216)(18, 186)(19, 220)(20, 193)(21, 222)(22, 188)(23, 189)(24, 191)(25, 228)(26, 230)(27, 232)(28, 231)(29, 234)(30, 233)(31, 236)(32, 237)(33, 195)(34, 201)(35, 196)(36, 242)(37, 212)(38, 198)(39, 200)(40, 245)(41, 210)(42, 247)(43, 248)(44, 202)(45, 203)(46, 204)(47, 206)(48, 214)(49, 238)(50, 253)(51, 218)(52, 224)(53, 239)(54, 215)(55, 254)(56, 255)(57, 256)(58, 257)(59, 213)(60, 217)(61, 223)(62, 259)(63, 219)(64, 221)(65, 240)(66, 235)(67, 263)(68, 264)(69, 225)(70, 226)(71, 227)(72, 229)(73, 249)(74, 268)(75, 267)(76, 266)(77, 265)(78, 241)(79, 258)(80, 243)(81, 244)(82, 246)(83, 270)(84, 269)(85, 250)(86, 251)(87, 252)(88, 260)(89, 261)(90, 262)(91, 271)(92, 272)(93, 273)(94, 274)(95, 275)(96, 276)(97, 277)(98, 278)(99, 279)(100, 280)(101, 281)(102, 282)(103, 283)(104, 284)(105, 285)(106, 286)(107, 287)(108, 288)(109, 289)(110, 290)(111, 291)(112, 292)(113, 293)(114, 294)(115, 295)(116, 296)(117, 297)(118, 298)(119, 299)(120, 300)(121, 301)(122, 302)(123, 303)(124, 304)(125, 305)(126, 306)(127, 307)(128, 308)(129, 309)(130, 310)(131, 311)(132, 312)(133, 313)(134, 314)(135, 315)(136, 316)(137, 317)(138, 318)(139, 319)(140, 320)(141, 321)(142, 322)(143, 323)(144, 324)(145, 325)(146, 326)(147, 327)(148, 328)(149, 329)(150, 330)(151, 331)(152, 332)(153, 333)(154, 334)(155, 335)(156, 336)(157, 337)(158, 338)(159, 339)(160, 340)(161, 341)(162, 342)(163, 343)(164, 344)(165, 345)(166, 346)(167, 347)(168, 348)(169, 349)(170, 350)(171, 351)(172, 352)(173, 353)(174, 354)(175, 355)(176, 356)(177, 357)(178, 358)(179, 359)(180, 360) local type(s) :: { ( 4, 90 ), ( 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90, 4, 90 ) } Outer automorphisms :: reflexible Dual of E20.1001 Graph:: simple bipartite v = 95 e = 180 f = 47 degree seq :: [ 2^90, 36^5 ] E20.1003 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 12, 48}) Quotient :: regular Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^6 * T2 * T1^-1 * T2 * T1, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2, (T1^-2 * T2 * T1^-1)^4 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 33, 16, 28, 48, 67, 84, 76, 56, 32, 52, 70, 86, 94, 91, 75, 55, 73, 89, 95, 93, 79, 59, 74, 90, 96, 92, 78, 58, 35, 53, 71, 87, 77, 57, 34, 17, 29, 49, 42, 22, 10, 4)(3, 7, 15, 31, 54, 30, 14, 6, 13, 27, 51, 72, 50, 26, 12, 25, 47, 69, 88, 68, 46, 24, 45, 66, 85, 82, 64, 41, 44, 65, 83, 81, 63, 40, 21, 39, 62, 80, 61, 38, 20, 9, 19, 37, 60, 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, 55)(36, 59)(37, 56)(38, 58)(39, 43)(40, 57)(42, 46)(45, 67)(47, 70)(50, 71)(51, 73)(54, 74)(60, 75)(61, 79)(62, 76)(63, 78)(64, 77)(65, 84)(66, 86)(68, 87)(69, 89)(72, 90)(80, 91)(81, 93)(82, 92)(83, 94)(85, 95)(88, 96) local type(s) :: { ( 12^48 ) } Outer automorphisms :: reflexible Dual of E20.1004 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 48 f = 8 degree seq :: [ 48^2 ] E20.1004 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 12, 48}) Quotient :: regular Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1, T1^12, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 64, 60, 43, 28, 17, 8)(6, 13, 21, 34, 48, 65, 63, 45, 30, 18, 9, 14)(15, 25, 35, 51, 66, 82, 78, 59, 42, 27, 16, 26)(23, 36, 50, 67, 81, 80, 62, 44, 29, 38, 24, 37)(39, 55, 68, 84, 93, 91, 77, 58, 41, 57, 40, 56)(52, 69, 83, 94, 92, 79, 61, 72, 54, 71, 53, 70)(73, 88, 95, 87, 96, 86, 76, 85, 75, 90, 74, 89) 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, 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, 89)(80, 92)(82, 93)(84, 95)(90, 94)(91, 96) local type(s) :: { ( 48^12 ) } Outer automorphisms :: reflexible Dual of E20.1003 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 48 f = 2 degree seq :: [ 12^8 ] E20.1005 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 48}) Quotient :: edge Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^12, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 ] Map:: R = (1, 3, 8, 17, 28, 43, 60, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 69, 54, 38, 24, 14, 6)(7, 15, 26, 41, 58, 77, 63, 45, 30, 18, 9, 16)(11, 20, 33, 49, 67, 85, 72, 53, 37, 23, 13, 21)(25, 39, 56, 75, 90, 80, 62, 44, 29, 42, 27, 40)(32, 47, 65, 83, 94, 88, 71, 52, 36, 50, 34, 48)(55, 73, 89, 95, 92, 79, 61, 78, 59, 76, 57, 74)(64, 81, 93, 91, 96, 87, 70, 86, 68, 84, 66, 82)(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, 128)(117, 130)(118, 129)(119, 132)(120, 133)(124, 131)(127, 134)(135, 151)(136, 153)(137, 152)(138, 155)(139, 154)(140, 157)(141, 158)(142, 159)(143, 160)(144, 162)(145, 161)(146, 164)(147, 163)(148, 166)(149, 167)(150, 168)(156, 165)(169, 182)(170, 183)(171, 185)(172, 187)(173, 186)(174, 177)(175, 178)(176, 188)(179, 189)(180, 191)(181, 190)(184, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^12 ) } Outer automorphisms :: reflexible Dual of E20.1009 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 96 f = 2 degree seq :: [ 2^48, 12^8 ] E20.1006 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 48}) Quotient :: edge Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2^-1 * T1 * T2^-1, T1 * T2 * T1^-1 * T2 * T1^2, T2^-6 * T1^-1 * T2 * T1 * T2^-1, T2^2 * T1^-3 * T2^2 * T1^-5, (T2^-1 * T1 * T2^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 67, 39, 20, 13, 28, 51, 80, 94, 68, 41, 30, 53, 82, 90, 73, 95, 70, 55, 84, 86, 62, 43, 72, 96, 85, 89, 61, 34, 21, 42, 71, 93, 66, 38, 18, 6, 17, 36, 64, 59, 33, 15, 5)(2, 7, 19, 40, 69, 45, 23, 9, 4, 12, 29, 54, 75, 46, 24, 11, 27, 52, 83, 92, 76, 47, 26, 50, 81, 88, 65, 58, 77, 49, 79, 87, 60, 37, 32, 57, 78, 91, 63, 35, 16, 14, 31, 56, 74, 44, 22, 8)(97, 98, 102, 112, 130, 156, 182, 177, 149, 123, 109, 100)(99, 105, 113, 104, 117, 131, 158, 183, 178, 146, 124, 107)(101, 110, 114, 133, 157, 184, 180, 148, 126, 108, 116, 103)(106, 120, 132, 119, 138, 118, 139, 159, 186, 175, 147, 122)(111, 128, 134, 161, 185, 179, 151, 125, 137, 115, 135, 127)(121, 143, 160, 142, 167, 141, 168, 140, 169, 187, 176, 145)(129, 154, 162, 188, 181, 150, 166, 136, 164, 152, 163, 153)(144, 173, 155, 172, 189, 171, 192, 165, 191, 170, 190, 174) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^12 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E20.1010 Transitivity :: ET+ Graph:: bipartite v = 10 e = 96 f = 48 degree seq :: [ 12^8, 48^2 ] E20.1007 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 48}) Quotient :: edge Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^6 * T2 * T1^-1 * T2 * T1, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2, (T1^-2 * T2 * T1^-1)^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, 55)(36, 59)(37, 56)(38, 58)(39, 43)(40, 57)(42, 46)(45, 67)(47, 70)(50, 71)(51, 73)(54, 74)(60, 75)(61, 79)(62, 76)(63, 78)(64, 77)(65, 84)(66, 86)(68, 87)(69, 89)(72, 90)(80, 91)(81, 93)(82, 92)(83, 94)(85, 95)(88, 96)(97, 98, 101, 107, 119, 139, 129, 112, 124, 144, 163, 180, 172, 152, 128, 148, 166, 182, 190, 187, 171, 151, 169, 185, 191, 189, 175, 155, 170, 186, 192, 188, 174, 154, 131, 149, 167, 183, 173, 153, 130, 113, 125, 145, 138, 118, 106, 100)(99, 103, 111, 127, 150, 126, 110, 102, 109, 123, 147, 168, 146, 122, 108, 121, 143, 165, 184, 164, 142, 120, 141, 162, 181, 178, 160, 137, 140, 161, 179, 177, 159, 136, 117, 135, 158, 176, 157, 134, 116, 105, 115, 133, 156, 132, 114, 104) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 24, 24 ), ( 24^48 ) } Outer automorphisms :: reflexible Dual of E20.1008 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 96 f = 8 degree seq :: [ 2^48, 48^2 ] E20.1008 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 48}) Quotient :: loop Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^12, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 ] Map:: R = (1, 97, 3, 99, 8, 104, 17, 113, 28, 124, 43, 139, 60, 156, 46, 142, 31, 127, 19, 115, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 22, 118, 35, 131, 51, 147, 69, 165, 54, 150, 38, 134, 24, 120, 14, 110, 6, 102)(7, 103, 15, 111, 26, 122, 41, 137, 58, 154, 77, 173, 63, 159, 45, 141, 30, 126, 18, 114, 9, 105, 16, 112)(11, 107, 20, 116, 33, 129, 49, 145, 67, 163, 85, 181, 72, 168, 53, 149, 37, 133, 23, 119, 13, 109, 21, 117)(25, 121, 39, 135, 56, 152, 75, 171, 90, 186, 80, 176, 62, 158, 44, 140, 29, 125, 42, 138, 27, 123, 40, 136)(32, 128, 47, 143, 65, 161, 83, 179, 94, 190, 88, 184, 71, 167, 52, 148, 36, 132, 50, 146, 34, 130, 48, 144)(55, 151, 73, 169, 89, 185, 95, 191, 92, 188, 79, 175, 61, 157, 78, 174, 59, 155, 76, 172, 57, 153, 74, 170)(64, 160, 81, 177, 93, 189, 91, 187, 96, 192, 87, 183, 70, 166, 86, 182, 68, 164, 84, 180, 66, 162, 82, 178) 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, 128)(21, 130)(22, 129)(23, 132)(24, 133)(25, 111)(26, 113)(27, 112)(28, 131)(29, 114)(30, 115)(31, 134)(32, 116)(33, 118)(34, 117)(35, 124)(36, 119)(37, 120)(38, 127)(39, 151)(40, 153)(41, 152)(42, 155)(43, 154)(44, 157)(45, 158)(46, 159)(47, 160)(48, 162)(49, 161)(50, 164)(51, 163)(52, 166)(53, 167)(54, 168)(55, 135)(56, 137)(57, 136)(58, 139)(59, 138)(60, 165)(61, 140)(62, 141)(63, 142)(64, 143)(65, 145)(66, 144)(67, 147)(68, 146)(69, 156)(70, 148)(71, 149)(72, 150)(73, 182)(74, 183)(75, 185)(76, 187)(77, 186)(78, 177)(79, 178)(80, 188)(81, 174)(82, 175)(83, 189)(84, 191)(85, 190)(86, 169)(87, 170)(88, 192)(89, 171)(90, 173)(91, 172)(92, 176)(93, 179)(94, 181)(95, 180)(96, 184) 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 E20.1007 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 96 f = 50 degree seq :: [ 24^8 ] E20.1009 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 48}) Quotient :: loop Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2^-1 * T1 * T2^-1, T1 * T2 * T1^-1 * T2 * T1^2, T2^-6 * T1^-1 * T2 * T1 * T2^-1, T2^2 * T1^-3 * T2^2 * T1^-5, (T2^-1 * T1 * T2^-1)^4 ] Map:: R = (1, 97, 3, 99, 10, 106, 25, 121, 48, 144, 67, 163, 39, 135, 20, 116, 13, 109, 28, 124, 51, 147, 80, 176, 94, 190, 68, 164, 41, 137, 30, 126, 53, 149, 82, 178, 90, 186, 73, 169, 95, 191, 70, 166, 55, 151, 84, 180, 86, 182, 62, 158, 43, 139, 72, 168, 96, 192, 85, 181, 89, 185, 61, 157, 34, 130, 21, 117, 42, 138, 71, 167, 93, 189, 66, 162, 38, 134, 18, 114, 6, 102, 17, 113, 36, 132, 64, 160, 59, 155, 33, 129, 15, 111, 5, 101)(2, 98, 7, 103, 19, 115, 40, 136, 69, 165, 45, 141, 23, 119, 9, 105, 4, 100, 12, 108, 29, 125, 54, 150, 75, 171, 46, 142, 24, 120, 11, 107, 27, 123, 52, 148, 83, 179, 92, 188, 76, 172, 47, 143, 26, 122, 50, 146, 81, 177, 88, 184, 65, 161, 58, 154, 77, 173, 49, 145, 79, 175, 87, 183, 60, 156, 37, 133, 32, 128, 57, 153, 78, 174, 91, 187, 63, 159, 35, 131, 16, 112, 14, 110, 31, 127, 56, 152, 74, 170, 44, 140, 22, 118, 8, 104) 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, 154)(34, 156)(35, 158)(36, 119)(37, 157)(38, 161)(39, 127)(40, 164)(41, 115)(42, 118)(43, 159)(44, 169)(45, 168)(46, 167)(47, 160)(48, 173)(49, 121)(50, 124)(51, 122)(52, 126)(53, 123)(54, 166)(55, 125)(56, 163)(57, 129)(58, 162)(59, 172)(60, 182)(61, 184)(62, 183)(63, 186)(64, 142)(65, 185)(66, 188)(67, 153)(68, 152)(69, 191)(70, 136)(71, 141)(72, 140)(73, 187)(74, 190)(75, 192)(76, 189)(77, 155)(78, 144)(79, 147)(80, 145)(81, 149)(82, 146)(83, 151)(84, 148)(85, 150)(86, 177)(87, 178)(88, 180)(89, 179)(90, 175)(91, 176)(92, 181)(93, 171)(94, 174)(95, 170)(96, 165) 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 ) } Outer automorphisms :: reflexible Dual of E20.1005 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 96 f = 56 degree seq :: [ 96^2 ] E20.1010 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 48}) Quotient :: loop Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^6 * T2 * T1^-1 * T2 * T1, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2, (T1^-2 * T2 * T1^-1)^4 ] 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, 55, 151)(36, 132, 59, 155)(37, 133, 56, 152)(38, 134, 58, 154)(39, 135, 43, 139)(40, 136, 57, 153)(42, 138, 46, 142)(45, 141, 67, 163)(47, 143, 70, 166)(50, 146, 71, 167)(51, 147, 73, 169)(54, 150, 74, 170)(60, 156, 75, 171)(61, 157, 79, 175)(62, 158, 76, 172)(63, 159, 78, 174)(64, 160, 77, 173)(65, 161, 84, 180)(66, 162, 86, 182)(68, 164, 87, 183)(69, 165, 89, 185)(72, 168, 90, 186)(80, 176, 91, 187)(81, 177, 93, 189)(82, 178, 92, 188)(83, 179, 94, 190)(85, 181, 95, 191)(88, 184, 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, 150)(32, 148)(33, 112)(34, 113)(35, 149)(36, 114)(37, 156)(38, 116)(39, 158)(40, 117)(41, 140)(42, 118)(43, 129)(44, 161)(45, 162)(46, 120)(47, 165)(48, 163)(49, 138)(50, 122)(51, 168)(52, 166)(53, 167)(54, 126)(55, 169)(56, 128)(57, 130)(58, 131)(59, 170)(60, 132)(61, 134)(62, 176)(63, 136)(64, 137)(65, 179)(66, 181)(67, 180)(68, 142)(69, 184)(70, 182)(71, 183)(72, 146)(73, 185)(74, 186)(75, 151)(76, 152)(77, 153)(78, 154)(79, 155)(80, 157)(81, 159)(82, 160)(83, 177)(84, 172)(85, 178)(86, 190)(87, 173)(88, 164)(89, 191)(90, 192)(91, 171)(92, 174)(93, 175)(94, 187)(95, 189)(96, 188) local type(s) :: { ( 12, 48, 12, 48 ) } Outer automorphisms :: reflexible Dual of E20.1006 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 10 degree seq :: [ 4^48 ] E20.1011 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 48}) Quotient :: dipole Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, Y2^12, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 12, 108)(10, 106, 14, 110)(15, 111, 25, 121)(16, 112, 27, 123)(17, 113, 26, 122)(18, 114, 29, 125)(19, 115, 30, 126)(20, 116, 32, 128)(21, 117, 34, 130)(22, 118, 33, 129)(23, 119, 36, 132)(24, 120, 37, 133)(28, 124, 35, 131)(31, 127, 38, 134)(39, 135, 55, 151)(40, 136, 57, 153)(41, 137, 56, 152)(42, 138, 59, 155)(43, 139, 58, 154)(44, 140, 61, 157)(45, 141, 62, 158)(46, 142, 63, 159)(47, 143, 64, 160)(48, 144, 66, 162)(49, 145, 65, 161)(50, 146, 68, 164)(51, 147, 67, 163)(52, 148, 70, 166)(53, 149, 71, 167)(54, 150, 72, 168)(60, 156, 69, 165)(73, 169, 86, 182)(74, 170, 87, 183)(75, 171, 89, 185)(76, 172, 91, 187)(77, 173, 90, 186)(78, 174, 81, 177)(79, 175, 82, 178)(80, 176, 92, 188)(83, 179, 93, 189)(84, 180, 95, 191)(85, 181, 94, 190)(88, 184, 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, 218, 314, 233, 329, 250, 346, 269, 365, 255, 351, 237, 333, 222, 318, 210, 306, 201, 297, 208, 304)(203, 299, 212, 308, 225, 321, 241, 337, 259, 355, 277, 373, 264, 360, 245, 341, 229, 325, 215, 311, 205, 301, 213, 309)(217, 313, 231, 327, 248, 344, 267, 363, 282, 378, 272, 368, 254, 350, 236, 332, 221, 317, 234, 330, 219, 315, 232, 328)(224, 320, 239, 335, 257, 353, 275, 371, 286, 382, 280, 376, 263, 359, 244, 340, 228, 324, 242, 338, 226, 322, 240, 336)(247, 343, 265, 361, 281, 377, 287, 383, 284, 380, 271, 367, 253, 349, 270, 366, 251, 347, 268, 364, 249, 345, 266, 362)(256, 352, 273, 369, 285, 381, 283, 379, 288, 384, 279, 375, 262, 358, 278, 374, 260, 356, 276, 372, 258, 354, 274, 370) 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, 224)(21, 226)(22, 225)(23, 228)(24, 229)(25, 207)(26, 209)(27, 208)(28, 227)(29, 210)(30, 211)(31, 230)(32, 212)(33, 214)(34, 213)(35, 220)(36, 215)(37, 216)(38, 223)(39, 247)(40, 249)(41, 248)(42, 251)(43, 250)(44, 253)(45, 254)(46, 255)(47, 256)(48, 258)(49, 257)(50, 260)(51, 259)(52, 262)(53, 263)(54, 264)(55, 231)(56, 233)(57, 232)(58, 235)(59, 234)(60, 261)(61, 236)(62, 237)(63, 238)(64, 239)(65, 241)(66, 240)(67, 243)(68, 242)(69, 252)(70, 244)(71, 245)(72, 246)(73, 278)(74, 279)(75, 281)(76, 283)(77, 282)(78, 273)(79, 274)(80, 284)(81, 270)(82, 271)(83, 285)(84, 287)(85, 286)(86, 265)(87, 266)(88, 288)(89, 267)(90, 269)(91, 268)(92, 272)(93, 275)(94, 277)(95, 276)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 96, 2, 96 ), ( 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 E20.1014 Graph:: bipartite v = 56 e = 192 f = 98 degree seq :: [ 4^48, 24^8 ] E20.1012 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 48}) Quotient :: dipole Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y1 * Y2)^2, R * Y2 * R * Y3, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2 * Y1^-1 * Y2 * Y1^2, Y1 * Y2^-6 * Y1 * Y2^2, (Y2^-1 * Y1 * Y2^-1)^4, (Y2^3 * Y1^-3)^2, Y2 * Y1^-3 * Y2 * Y1^-7 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 34, 130, 60, 156, 86, 182, 81, 177, 53, 149, 27, 123, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 8, 104, 21, 117, 35, 131, 62, 158, 87, 183, 82, 178, 50, 146, 28, 124, 11, 107)(5, 101, 14, 110, 18, 114, 37, 133, 61, 157, 88, 184, 84, 180, 52, 148, 30, 126, 12, 108, 20, 116, 7, 103)(10, 106, 24, 120, 36, 132, 23, 119, 42, 138, 22, 118, 43, 139, 63, 159, 90, 186, 79, 175, 51, 147, 26, 122)(15, 111, 32, 128, 38, 134, 65, 161, 89, 185, 83, 179, 55, 151, 29, 125, 41, 137, 19, 115, 39, 135, 31, 127)(25, 121, 47, 143, 64, 160, 46, 142, 71, 167, 45, 141, 72, 168, 44, 140, 73, 169, 91, 187, 80, 176, 49, 145)(33, 129, 58, 154, 66, 162, 92, 188, 85, 181, 54, 150, 70, 166, 40, 136, 68, 164, 56, 152, 67, 163, 57, 153)(48, 144, 77, 173, 59, 155, 76, 172, 93, 189, 75, 171, 96, 192, 69, 165, 95, 191, 74, 170, 94, 190, 78, 174)(193, 289, 195, 291, 202, 298, 217, 313, 240, 336, 259, 355, 231, 327, 212, 308, 205, 301, 220, 316, 243, 339, 272, 368, 286, 382, 260, 356, 233, 329, 222, 318, 245, 341, 274, 370, 282, 378, 265, 361, 287, 383, 262, 358, 247, 343, 276, 372, 278, 374, 254, 350, 235, 331, 264, 360, 288, 384, 277, 373, 281, 377, 253, 349, 226, 322, 213, 309, 234, 330, 263, 359, 285, 381, 258, 354, 230, 326, 210, 306, 198, 294, 209, 305, 228, 324, 256, 352, 251, 347, 225, 321, 207, 303, 197, 293)(194, 290, 199, 295, 211, 307, 232, 328, 261, 357, 237, 333, 215, 311, 201, 297, 196, 292, 204, 300, 221, 317, 246, 342, 267, 363, 238, 334, 216, 312, 203, 299, 219, 315, 244, 340, 275, 371, 284, 380, 268, 364, 239, 335, 218, 314, 242, 338, 273, 369, 280, 376, 257, 353, 250, 346, 269, 365, 241, 337, 271, 367, 279, 375, 252, 348, 229, 325, 224, 320, 249, 345, 270, 366, 283, 379, 255, 351, 227, 323, 208, 304, 206, 302, 223, 319, 248, 344, 266, 362, 236, 332, 214, 310, 200, 296) 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, 242)(27, 244)(28, 243)(29, 246)(30, 245)(31, 248)(32, 249)(33, 207)(34, 213)(35, 208)(36, 256)(37, 224)(38, 210)(39, 212)(40, 261)(41, 222)(42, 263)(43, 264)(44, 214)(45, 215)(46, 216)(47, 218)(48, 259)(49, 271)(50, 273)(51, 272)(52, 275)(53, 274)(54, 267)(55, 276)(56, 266)(57, 270)(58, 269)(59, 225)(60, 229)(61, 226)(62, 235)(63, 227)(64, 251)(65, 250)(66, 230)(67, 231)(68, 233)(69, 237)(70, 247)(71, 285)(72, 288)(73, 287)(74, 236)(75, 238)(76, 239)(77, 241)(78, 283)(79, 279)(80, 286)(81, 280)(82, 282)(83, 284)(84, 278)(85, 281)(86, 254)(87, 252)(88, 257)(89, 253)(90, 265)(91, 255)(92, 268)(93, 258)(94, 260)(95, 262)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.1013 Graph:: bipartite v = 10 e = 192 f = 144 degree seq :: [ 24^8, 96^2 ] E20.1013 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 48}) Quotient :: dipole Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |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^-2 * Y2 * Y3 * Y2 * Y3^-5, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, (Y3^2 * Y2 * Y3)^4, (Y3^-1 * Y1^-1)^48 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 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, 252, 348)(229, 325, 238, 334)(230, 326, 244, 340)(231, 327, 236, 332)(232, 328, 242, 338)(234, 330, 251, 347)(240, 336, 262, 358)(246, 342, 261, 357)(247, 343, 260, 356)(248, 344, 258, 354)(249, 345, 264, 360)(250, 346, 257, 353)(253, 349, 266, 362)(254, 350, 259, 355)(255, 351, 265, 361)(256, 352, 263, 359)(267, 363, 279, 375)(268, 364, 277, 373)(269, 365, 276, 372)(270, 366, 280, 376)(271, 367, 275, 371)(272, 368, 278, 374)(273, 369, 282, 378)(274, 370, 281, 377)(283, 379, 288, 384)(284, 380, 287, 383)(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, 248)(34, 209)(35, 250)(36, 236)(37, 246)(38, 212)(39, 254)(40, 213)(41, 252)(42, 214)(43, 257)(44, 216)(45, 258)(46, 217)(47, 260)(48, 224)(49, 234)(50, 220)(51, 264)(52, 221)(53, 262)(54, 222)(55, 267)(56, 268)(57, 226)(58, 269)(59, 227)(60, 271)(61, 230)(62, 272)(63, 232)(64, 233)(65, 275)(66, 276)(67, 238)(68, 277)(69, 239)(70, 279)(71, 242)(72, 280)(73, 244)(74, 245)(75, 249)(76, 283)(77, 284)(78, 251)(79, 285)(80, 253)(81, 255)(82, 256)(83, 259)(84, 286)(85, 287)(86, 261)(87, 288)(88, 263)(89, 265)(90, 266)(91, 270)(92, 274)(93, 273)(94, 278)(95, 282)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 24, 96 ), ( 24, 96, 24, 96 ) } Outer automorphisms :: reflexible Dual of E20.1012 Graph:: simple bipartite v = 144 e = 192 f = 10 degree seq :: [ 2^96, 4^48 ] E20.1014 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 48}) Quotient :: dipole Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y1^6 * Y3 * Y1^-1 * Y3 * Y1, Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3, (Y1^-2 * Y3 * Y1^-1)^4 ] Map:: R = (1, 97, 2, 98, 5, 101, 11, 107, 23, 119, 43, 139, 33, 129, 16, 112, 28, 124, 48, 144, 67, 163, 84, 180, 76, 172, 56, 152, 32, 128, 52, 148, 70, 166, 86, 182, 94, 190, 91, 187, 75, 171, 55, 151, 73, 169, 89, 185, 95, 191, 93, 189, 79, 175, 59, 155, 74, 170, 90, 186, 96, 192, 92, 188, 78, 174, 58, 154, 35, 131, 53, 149, 71, 167, 87, 183, 77, 173, 57, 153, 34, 130, 17, 113, 29, 125, 49, 145, 42, 138, 22, 118, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 31, 127, 54, 150, 30, 126, 14, 110, 6, 102, 13, 109, 27, 123, 51, 147, 72, 168, 50, 146, 26, 122, 12, 108, 25, 121, 47, 143, 69, 165, 88, 184, 68, 164, 46, 142, 24, 120, 45, 141, 66, 162, 85, 181, 82, 178, 64, 160, 41, 137, 44, 140, 65, 161, 83, 179, 81, 177, 63, 159, 40, 136, 21, 117, 39, 135, 62, 158, 80, 176, 61, 157, 38, 134, 20, 116, 9, 105, 19, 115, 37, 133, 60, 156, 36, 132, 18, 114, 8, 104)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 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, 247)(32, 207)(33, 211)(34, 212)(35, 210)(36, 251)(37, 248)(38, 250)(39, 235)(40, 249)(41, 214)(42, 238)(43, 231)(44, 215)(45, 259)(46, 234)(47, 262)(48, 217)(49, 218)(50, 263)(51, 265)(52, 219)(53, 222)(54, 266)(55, 223)(56, 229)(57, 232)(58, 230)(59, 228)(60, 267)(61, 271)(62, 268)(63, 270)(64, 269)(65, 276)(66, 278)(67, 237)(68, 279)(69, 281)(70, 239)(71, 242)(72, 282)(73, 243)(74, 246)(75, 252)(76, 254)(77, 256)(78, 255)(79, 253)(80, 283)(81, 285)(82, 284)(83, 286)(84, 257)(85, 287)(86, 258)(87, 260)(88, 288)(89, 261)(90, 264)(91, 272)(92, 274)(93, 273)(94, 275)(95, 277)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E20.1011 Graph:: simple bipartite v = 98 e = 192 f = 56 degree seq :: [ 2^96, 96^2 ] E20.1015 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 48}) Quotient :: dipole Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1 * R)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y1 * Y2^-7 * Y1 * Y2, Y2^-2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * 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, 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, 60, 156)(37, 133, 46, 142)(38, 134, 52, 148)(39, 135, 44, 140)(40, 136, 50, 146)(42, 138, 59, 155)(48, 144, 70, 166)(54, 150, 69, 165)(55, 151, 68, 164)(56, 152, 66, 162)(57, 153, 72, 168)(58, 154, 65, 161)(61, 157, 74, 170)(62, 158, 67, 163)(63, 159, 73, 169)(64, 160, 71, 167)(75, 171, 87, 183)(76, 172, 85, 181)(77, 173, 84, 180)(78, 174, 88, 184)(79, 175, 83, 179)(80, 176, 86, 182)(81, 177, 90, 186)(82, 178, 89, 185)(91, 187, 96, 192)(92, 188, 95, 191)(93, 189, 94, 190)(193, 289, 195, 291, 200, 296, 210, 306, 228, 324, 236, 332, 216, 312, 203, 299, 215, 311, 235, 331, 257, 353, 275, 371, 259, 355, 238, 334, 217, 313, 237, 333, 258, 354, 276, 372, 286, 382, 278, 374, 261, 357, 239, 335, 260, 356, 277, 373, 287, 383, 282, 378, 266, 362, 245, 341, 262, 358, 279, 375, 288, 384, 281, 377, 265, 361, 244, 340, 221, 317, 243, 339, 264, 360, 280, 376, 263, 359, 242, 338, 220, 316, 205, 301, 219, 315, 241, 337, 234, 330, 214, 310, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 218, 314, 240, 336, 224, 320, 208, 304, 199, 295, 207, 303, 223, 319, 247, 343, 267, 363, 249, 345, 226, 322, 209, 305, 225, 321, 248, 344, 268, 364, 283, 379, 270, 366, 251, 347, 227, 323, 250, 346, 269, 365, 284, 380, 274, 370, 256, 352, 233, 329, 252, 348, 271, 367, 285, 381, 273, 369, 255, 351, 232, 328, 213, 309, 231, 327, 254, 350, 272, 368, 253, 349, 230, 326, 212, 308, 201, 297, 211, 307, 229, 325, 246, 342, 222, 318, 206, 302, 198, 294) 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, 252)(37, 238)(38, 244)(39, 236)(40, 242)(41, 214)(42, 251)(43, 225)(44, 231)(45, 223)(46, 229)(47, 218)(48, 262)(49, 226)(50, 232)(51, 224)(52, 230)(53, 222)(54, 261)(55, 260)(56, 258)(57, 264)(58, 257)(59, 234)(60, 228)(61, 266)(62, 259)(63, 265)(64, 263)(65, 250)(66, 248)(67, 254)(68, 247)(69, 246)(70, 240)(71, 256)(72, 249)(73, 255)(74, 253)(75, 279)(76, 277)(77, 276)(78, 280)(79, 275)(80, 278)(81, 282)(82, 281)(83, 271)(84, 269)(85, 268)(86, 272)(87, 267)(88, 270)(89, 274)(90, 273)(91, 288)(92, 287)(93, 286)(94, 285)(95, 284)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E20.1016 Graph:: bipartite v = 50 e = 192 f = 104 degree seq :: [ 4^48, 96^2 ] E20.1016 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 48}) Quotient :: dipole Aut^+ = C3 x QD32 (small group id <96, 62>) Aut = $<192, 473>$ (small group id <192, 473>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^-3 * Y3^-1 * Y1 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-3, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-3, Y1^-1 * Y3^-3 * Y1^2 * Y3^3 * Y1^-1, Y3^8 * Y1^2, Y3 * Y1^-3 * Y3^2 * Y1^-1 * Y3 * Y1^-4, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98, 6, 102, 16, 112, 34, 130, 60, 156, 86, 182, 81, 177, 53, 149, 27, 123, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 8, 104, 21, 117, 35, 131, 62, 158, 87, 183, 82, 178, 50, 146, 28, 124, 11, 107)(5, 101, 14, 110, 18, 114, 37, 133, 61, 157, 88, 184, 84, 180, 52, 148, 30, 126, 12, 108, 20, 116, 7, 103)(10, 106, 24, 120, 36, 132, 23, 119, 42, 138, 22, 118, 43, 139, 63, 159, 90, 186, 79, 175, 51, 147, 26, 122)(15, 111, 32, 128, 38, 134, 65, 161, 89, 185, 83, 179, 55, 151, 29, 125, 41, 137, 19, 115, 39, 135, 31, 127)(25, 121, 47, 143, 64, 160, 46, 142, 71, 167, 45, 141, 72, 168, 44, 140, 73, 169, 91, 187, 80, 176, 49, 145)(33, 129, 58, 154, 66, 162, 92, 188, 85, 181, 54, 150, 70, 166, 40, 136, 68, 164, 56, 152, 67, 163, 57, 153)(48, 144, 77, 173, 59, 155, 76, 172, 93, 189, 75, 171, 96, 192, 69, 165, 95, 191, 74, 170, 94, 190, 78, 174)(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, 242)(27, 244)(28, 243)(29, 246)(30, 245)(31, 248)(32, 249)(33, 207)(34, 213)(35, 208)(36, 256)(37, 224)(38, 210)(39, 212)(40, 261)(41, 222)(42, 263)(43, 264)(44, 214)(45, 215)(46, 216)(47, 218)(48, 259)(49, 271)(50, 273)(51, 272)(52, 275)(53, 274)(54, 267)(55, 276)(56, 266)(57, 270)(58, 269)(59, 225)(60, 229)(61, 226)(62, 235)(63, 227)(64, 251)(65, 250)(66, 230)(67, 231)(68, 233)(69, 237)(70, 247)(71, 285)(72, 288)(73, 287)(74, 236)(75, 238)(76, 239)(77, 241)(78, 283)(79, 279)(80, 286)(81, 280)(82, 282)(83, 284)(84, 278)(85, 281)(86, 254)(87, 252)(88, 257)(89, 253)(90, 265)(91, 255)(92, 268)(93, 258)(94, 260)(95, 262)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 96 ), ( 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96 ) } Outer automorphisms :: reflexible Dual of E20.1015 Graph:: simple bipartite v = 104 e = 192 f = 50 degree seq :: [ 2^96, 24^8 ] E20.1017 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 28}) Quotient :: regular Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T2 * T1^-4 * T2 * T1 * T2 * T1^4 * T2 * T1^-1, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^-2 * T2 * T1 * T2 * T1^-3 * T2 * T1 * T2 * T1^-7 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 65, 86, 105, 100, 80, 95, 78, 93, 79, 94, 81, 96, 112, 104, 85, 64, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 75, 97, 111, 91, 74, 54, 72, 52, 71, 53, 73, 63, 84, 103, 106, 88, 66, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 61, 82, 101, 110, 92, 70, 60, 43, 58, 41, 57, 42, 59, 77, 99, 107, 87, 67, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 68, 90, 108, 102, 83, 62, 45, 30, 37, 23, 36, 24, 38, 50, 69, 89, 109, 98, 76, 56, 40, 27) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 102)(83, 103)(84, 100)(85, 101)(86, 106)(88, 108)(90, 110)(92, 112)(97, 109)(98, 107)(99, 105)(104, 111) local type(s) :: { ( 8^28 ) } Outer automorphisms :: reflexible Dual of E20.1018 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 56 f = 14 degree seq :: [ 28^4 ] E20.1018 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 28}) Quotient :: regular Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, T1^8, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^3, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 15, 25, 31, 22, 12, 8)(6, 13, 9, 18, 29, 32, 21, 14)(16, 26, 17, 28, 33, 43, 37, 27)(23, 34, 24, 36, 42, 41, 30, 35)(38, 47, 39, 49, 52, 50, 40, 48)(44, 53, 45, 55, 51, 56, 46, 54)(57, 65, 58, 67, 60, 68, 59, 66)(61, 69, 62, 71, 64, 72, 63, 70)(73, 81, 74, 83, 76, 84, 75, 82)(77, 85, 78, 87, 80, 88, 79, 86)(89, 97, 90, 99, 92, 100, 91, 98)(93, 101, 94, 103, 96, 104, 95, 102)(105, 111, 106, 109, 108, 110, 107, 112) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) local type(s) :: { ( 28^8 ) } Outer automorphisms :: reflexible Dual of E20.1017 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 14 e = 56 f = 4 degree seq :: [ 8^14 ] E20.1019 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 28}) Quotient :: edge Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1, T2^-2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 ] Map:: R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 9, 18, 30, 40, 27, 16)(11, 20, 13, 23, 36, 45, 33, 21)(25, 37, 26, 39, 50, 41, 29, 38)(31, 42, 32, 44, 55, 46, 35, 43)(47, 57, 48, 59, 51, 60, 49, 58)(52, 61, 53, 63, 56, 64, 54, 62)(65, 73, 66, 75, 68, 76, 67, 74)(69, 77, 70, 79, 72, 80, 71, 78)(81, 89, 82, 91, 84, 92, 83, 90)(85, 93, 86, 95, 88, 96, 87, 94)(97, 105, 98, 107, 100, 108, 99, 106)(101, 109, 102, 111, 104, 112, 103, 110)(113, 114)(115, 119)(116, 121)(117, 123)(118, 125)(120, 126)(122, 124)(127, 137)(128, 138)(129, 139)(130, 141)(131, 142)(132, 143)(133, 144)(134, 145)(135, 147)(136, 148)(140, 146)(149, 159)(150, 160)(151, 161)(152, 162)(153, 163)(154, 164)(155, 165)(156, 166)(157, 167)(158, 168)(169, 177)(170, 178)(171, 179)(172, 180)(173, 181)(174, 182)(175, 183)(176, 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, 223)(218, 224)(219, 221)(220, 222) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 56, 56 ), ( 56^8 ) } Outer automorphisms :: reflexible Dual of E20.1023 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 112 f = 4 degree seq :: [ 2^56, 8^14 ] E20.1020 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 28}) Quotient :: edge Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^2, (T2 * T1^-1)^2, T1^8, T1^-1 * T2^-1 * T1^2 * T2^-13 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 52, 68, 84, 100, 106, 90, 74, 58, 42, 26, 41, 57, 73, 89, 105, 104, 88, 72, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 63, 79, 95, 111, 97, 81, 65, 49, 33, 24, 37, 53, 69, 85, 101, 112, 96, 80, 64, 48, 32, 18, 8)(4, 11, 23, 39, 55, 71, 87, 103, 108, 92, 76, 60, 44, 28, 14, 27, 43, 59, 75, 91, 107, 99, 83, 67, 51, 35, 20, 9)(6, 15, 29, 45, 61, 77, 93, 109, 102, 86, 70, 54, 38, 22, 12, 19, 34, 50, 66, 82, 98, 110, 94, 78, 62, 46, 30, 16)(113, 114, 118, 126, 138, 136, 124, 116)(115, 121, 131, 145, 153, 140, 127, 120)(117, 123, 134, 149, 154, 139, 128, 119)(122, 130, 141, 156, 169, 161, 146, 132)(125, 129, 142, 155, 170, 165, 150, 135)(133, 147, 162, 177, 185, 172, 157, 144)(137, 151, 166, 181, 186, 171, 158, 143)(148, 160, 173, 188, 201, 193, 178, 163)(152, 159, 174, 187, 202, 197, 182, 167)(164, 179, 194, 209, 217, 204, 189, 176)(168, 183, 198, 213, 218, 203, 190, 175)(180, 192, 205, 220, 216, 223, 210, 195)(184, 191, 206, 219, 212, 224, 214, 199)(196, 211, 222, 207, 200, 215, 221, 208) 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 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E20.1024 Transitivity :: ET+ Graph:: bipartite v = 18 e = 112 f = 56 degree seq :: [ 8^14, 28^4 ] E20.1021 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 28}) Quotient :: edge Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T2 * T1^-4 * T2 * T1 * T2 * T1^4 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^-2 * T2 * T1 * T2 * T1^-3 * T2 * T1 * T2 * T1^-7 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 102)(83, 103)(84, 100)(85, 101)(86, 106)(88, 108)(90, 110)(92, 112)(97, 109)(98, 107)(99, 105)(104, 111)(113, 114, 117, 123, 132, 144, 159, 177, 198, 217, 212, 192, 207, 190, 205, 191, 206, 193, 208, 224, 216, 197, 176, 158, 143, 131, 122, 116)(115, 119, 127, 137, 151, 167, 187, 209, 223, 203, 186, 166, 184, 164, 183, 165, 185, 175, 196, 215, 218, 200, 178, 161, 145, 134, 124, 120)(118, 125, 121, 130, 141, 156, 173, 194, 213, 222, 204, 182, 172, 155, 170, 153, 169, 154, 171, 189, 211, 219, 199, 179, 160, 146, 133, 126)(128, 138, 129, 140, 147, 163, 180, 202, 220, 214, 195, 174, 157, 142, 149, 135, 148, 136, 150, 162, 181, 201, 221, 210, 188, 168, 152, 139) 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 ), ( 16^28 ) } Outer automorphisms :: reflexible Dual of E20.1022 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 112 f = 14 degree seq :: [ 2^56, 28^4 ] E20.1022 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 28}) Quotient :: loop Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1, T2^-2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 ] Map:: R = (1, 113, 3, 115, 8, 120, 17, 129, 28, 140, 19, 131, 10, 122, 4, 116)(2, 114, 5, 117, 12, 124, 22, 134, 34, 146, 24, 136, 14, 126, 6, 118)(7, 119, 15, 127, 9, 121, 18, 130, 30, 142, 40, 152, 27, 139, 16, 128)(11, 123, 20, 132, 13, 125, 23, 135, 36, 148, 45, 157, 33, 145, 21, 133)(25, 137, 37, 149, 26, 138, 39, 151, 50, 162, 41, 153, 29, 141, 38, 150)(31, 143, 42, 154, 32, 144, 44, 156, 55, 167, 46, 158, 35, 147, 43, 155)(47, 159, 57, 169, 48, 160, 59, 171, 51, 163, 60, 172, 49, 161, 58, 170)(52, 164, 61, 173, 53, 165, 63, 175, 56, 168, 64, 176, 54, 166, 62, 174)(65, 177, 73, 185, 66, 178, 75, 187, 68, 180, 76, 188, 67, 179, 74, 186)(69, 181, 77, 189, 70, 182, 79, 191, 72, 184, 80, 192, 71, 183, 78, 190)(81, 193, 89, 201, 82, 194, 91, 203, 84, 196, 92, 204, 83, 195, 90, 202)(85, 197, 93, 205, 86, 198, 95, 207, 88, 200, 96, 208, 87, 199, 94, 206)(97, 209, 105, 217, 98, 210, 107, 219, 100, 212, 108, 220, 99, 211, 106, 218)(101, 213, 109, 221, 102, 214, 111, 223, 104, 216, 112, 224, 103, 215, 110, 222) L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 123)(6, 125)(7, 115)(8, 126)(9, 116)(10, 124)(11, 117)(12, 122)(13, 118)(14, 120)(15, 137)(16, 138)(17, 139)(18, 141)(19, 142)(20, 143)(21, 144)(22, 145)(23, 147)(24, 148)(25, 127)(26, 128)(27, 129)(28, 146)(29, 130)(30, 131)(31, 132)(32, 133)(33, 134)(34, 140)(35, 135)(36, 136)(37, 159)(38, 160)(39, 161)(40, 162)(41, 163)(42, 164)(43, 165)(44, 166)(45, 167)(46, 168)(47, 149)(48, 150)(49, 151)(50, 152)(51, 153)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)(105, 223)(106, 224)(107, 221)(108, 222)(109, 219)(110, 220)(111, 217)(112, 218) local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E20.1021 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 14 e = 112 f = 60 degree seq :: [ 16^14 ] E20.1023 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 28}) Quotient :: loop Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^2, (T2 * T1^-1)^2, T1^8, T1^-1 * T2^-1 * T1^2 * T2^-13 * T1^-1 ] Map:: R = (1, 113, 3, 115, 10, 122, 21, 133, 36, 148, 52, 164, 68, 180, 84, 196, 100, 212, 106, 218, 90, 202, 74, 186, 58, 170, 42, 154, 26, 138, 41, 153, 57, 169, 73, 185, 89, 201, 105, 217, 104, 216, 88, 200, 72, 184, 56, 168, 40, 152, 25, 137, 13, 125, 5, 117)(2, 114, 7, 119, 17, 129, 31, 143, 47, 159, 63, 175, 79, 191, 95, 207, 111, 223, 97, 209, 81, 193, 65, 177, 49, 161, 33, 145, 24, 136, 37, 149, 53, 165, 69, 181, 85, 197, 101, 213, 112, 224, 96, 208, 80, 192, 64, 176, 48, 160, 32, 144, 18, 130, 8, 120)(4, 116, 11, 123, 23, 135, 39, 151, 55, 167, 71, 183, 87, 199, 103, 215, 108, 220, 92, 204, 76, 188, 60, 172, 44, 156, 28, 140, 14, 126, 27, 139, 43, 155, 59, 171, 75, 187, 91, 203, 107, 219, 99, 211, 83, 195, 67, 179, 51, 163, 35, 147, 20, 132, 9, 121)(6, 118, 15, 127, 29, 141, 45, 157, 61, 173, 77, 189, 93, 205, 109, 221, 102, 214, 86, 198, 70, 182, 54, 166, 38, 150, 22, 134, 12, 124, 19, 131, 34, 146, 50, 162, 66, 178, 82, 194, 98, 210, 110, 222, 94, 206, 78, 190, 62, 174, 46, 158, 30, 142, 16, 128) L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 123)(6, 126)(7, 117)(8, 115)(9, 131)(10, 130)(11, 134)(12, 116)(13, 129)(14, 138)(15, 120)(16, 119)(17, 142)(18, 141)(19, 145)(20, 122)(21, 147)(22, 149)(23, 125)(24, 124)(25, 151)(26, 136)(27, 128)(28, 127)(29, 156)(30, 155)(31, 137)(32, 133)(33, 153)(34, 132)(35, 162)(36, 160)(37, 154)(38, 135)(39, 166)(40, 159)(41, 140)(42, 139)(43, 170)(44, 169)(45, 144)(46, 143)(47, 174)(48, 173)(49, 146)(50, 177)(51, 148)(52, 179)(53, 150)(54, 181)(55, 152)(56, 183)(57, 161)(58, 165)(59, 158)(60, 157)(61, 188)(62, 187)(63, 168)(64, 164)(65, 185)(66, 163)(67, 194)(68, 192)(69, 186)(70, 167)(71, 198)(72, 191)(73, 172)(74, 171)(75, 202)(76, 201)(77, 176)(78, 175)(79, 206)(80, 205)(81, 178)(82, 209)(83, 180)(84, 211)(85, 182)(86, 213)(87, 184)(88, 215)(89, 193)(90, 197)(91, 190)(92, 189)(93, 220)(94, 219)(95, 200)(96, 196)(97, 217)(98, 195)(99, 222)(100, 224)(101, 218)(102, 199)(103, 221)(104, 223)(105, 204)(106, 203)(107, 212)(108, 216)(109, 208)(110, 207)(111, 210)(112, 214) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E20.1019 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 112 f = 70 degree seq :: [ 56^4 ] E20.1024 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 28}) Quotient :: loop Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T2 * T1^-4 * T2 * T1 * T2 * T1^4 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^-2 * T2 * T1 * T2 * T1^-3 * T2 * T1 * T2 * T1^-7 ] Map:: polytopal non-degenerate R = (1, 113, 3, 115)(2, 114, 6, 118)(4, 116, 9, 121)(5, 117, 12, 124)(7, 119, 16, 128)(8, 120, 17, 129)(10, 122, 15, 127)(11, 123, 21, 133)(13, 125, 23, 135)(14, 126, 24, 136)(18, 130, 30, 142)(19, 131, 29, 141)(20, 132, 33, 145)(22, 134, 35, 147)(25, 137, 40, 152)(26, 138, 41, 153)(27, 139, 42, 154)(28, 140, 43, 155)(31, 143, 39, 151)(32, 144, 48, 160)(34, 146, 50, 162)(36, 148, 52, 164)(37, 149, 53, 165)(38, 150, 54, 166)(44, 156, 62, 174)(45, 157, 63, 175)(46, 158, 61, 173)(47, 159, 66, 178)(49, 161, 68, 180)(51, 163, 70, 182)(55, 167, 76, 188)(56, 168, 77, 189)(57, 169, 78, 190)(58, 170, 79, 191)(59, 171, 80, 192)(60, 172, 81, 193)(64, 176, 75, 187)(65, 177, 87, 199)(67, 179, 89, 201)(69, 181, 91, 203)(71, 183, 93, 205)(72, 184, 94, 206)(73, 185, 95, 207)(74, 186, 96, 208)(82, 194, 102, 214)(83, 195, 103, 215)(84, 196, 100, 212)(85, 197, 101, 213)(86, 198, 106, 218)(88, 200, 108, 220)(90, 202, 110, 222)(92, 204, 112, 224)(97, 209, 109, 221)(98, 210, 107, 219)(99, 211, 105, 217)(104, 216, 111, 223) L = (1, 114)(2, 117)(3, 119)(4, 113)(5, 123)(6, 125)(7, 127)(8, 115)(9, 130)(10, 116)(11, 132)(12, 120)(13, 121)(14, 118)(15, 137)(16, 138)(17, 140)(18, 141)(19, 122)(20, 144)(21, 126)(22, 124)(23, 148)(24, 150)(25, 151)(26, 129)(27, 128)(28, 147)(29, 156)(30, 149)(31, 131)(32, 159)(33, 134)(34, 133)(35, 163)(36, 136)(37, 135)(38, 162)(39, 167)(40, 139)(41, 169)(42, 171)(43, 170)(44, 173)(45, 142)(46, 143)(47, 177)(48, 146)(49, 145)(50, 181)(51, 180)(52, 183)(53, 185)(54, 184)(55, 187)(56, 152)(57, 154)(58, 153)(59, 189)(60, 155)(61, 194)(62, 157)(63, 196)(64, 158)(65, 198)(66, 161)(67, 160)(68, 202)(69, 201)(70, 172)(71, 165)(72, 164)(73, 175)(74, 166)(75, 209)(76, 168)(77, 211)(78, 205)(79, 206)(80, 207)(81, 208)(82, 213)(83, 174)(84, 215)(85, 176)(86, 217)(87, 179)(88, 178)(89, 221)(90, 220)(91, 186)(92, 182)(93, 191)(94, 193)(95, 190)(96, 224)(97, 223)(98, 188)(99, 219)(100, 192)(101, 222)(102, 195)(103, 218)(104, 197)(105, 212)(106, 200)(107, 199)(108, 214)(109, 210)(110, 204)(111, 203)(112, 216) local type(s) :: { ( 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E20.1020 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 56 e = 112 f = 18 degree seq :: [ 4^56 ] E20.1025 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 28}) Quotient :: dipole Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^28 ] Map:: R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 11, 123)(6, 118, 13, 125)(8, 120, 14, 126)(10, 122, 12, 124)(15, 127, 25, 137)(16, 128, 26, 138)(17, 129, 27, 139)(18, 130, 29, 141)(19, 131, 30, 142)(20, 132, 31, 143)(21, 133, 32, 144)(22, 134, 33, 145)(23, 135, 35, 147)(24, 136, 36, 148)(28, 140, 34, 146)(37, 149, 47, 159)(38, 150, 48, 160)(39, 151, 49, 161)(40, 152, 50, 162)(41, 153, 51, 163)(42, 154, 52, 164)(43, 155, 53, 165)(44, 156, 54, 166)(45, 157, 55, 167)(46, 158, 56, 168)(57, 169, 65, 177)(58, 170, 66, 178)(59, 171, 67, 179)(60, 172, 68, 180)(61, 173, 69, 181)(62, 174, 70, 182)(63, 175, 71, 183)(64, 176, 72, 184)(73, 185, 81, 193)(74, 186, 82, 194)(75, 187, 83, 195)(76, 188, 84, 196)(77, 189, 85, 197)(78, 190, 86, 198)(79, 191, 87, 199)(80, 192, 88, 200)(89, 201, 97, 209)(90, 202, 98, 210)(91, 203, 99, 211)(92, 204, 100, 212)(93, 205, 101, 213)(94, 206, 102, 214)(95, 207, 103, 215)(96, 208, 104, 216)(105, 217, 111, 223)(106, 218, 112, 224)(107, 219, 109, 221)(108, 220, 110, 222)(225, 337, 227, 339, 232, 344, 241, 353, 252, 364, 243, 355, 234, 346, 228, 340)(226, 338, 229, 341, 236, 348, 246, 358, 258, 370, 248, 360, 238, 350, 230, 342)(231, 343, 239, 351, 233, 345, 242, 354, 254, 366, 264, 376, 251, 363, 240, 352)(235, 347, 244, 356, 237, 349, 247, 359, 260, 372, 269, 381, 257, 369, 245, 357)(249, 361, 261, 373, 250, 362, 263, 375, 274, 386, 265, 377, 253, 365, 262, 374)(255, 367, 266, 378, 256, 368, 268, 380, 279, 391, 270, 382, 259, 371, 267, 379)(271, 383, 281, 393, 272, 384, 283, 395, 275, 387, 284, 396, 273, 385, 282, 394)(276, 388, 285, 397, 277, 389, 287, 399, 280, 392, 288, 400, 278, 390, 286, 398)(289, 401, 297, 409, 290, 402, 299, 411, 292, 404, 300, 412, 291, 403, 298, 410)(293, 405, 301, 413, 294, 406, 303, 415, 296, 408, 304, 416, 295, 407, 302, 414)(305, 417, 313, 425, 306, 418, 315, 427, 308, 420, 316, 428, 307, 419, 314, 426)(309, 421, 317, 429, 310, 422, 319, 431, 312, 424, 320, 432, 311, 423, 318, 430)(321, 433, 329, 441, 322, 434, 331, 443, 324, 436, 332, 444, 323, 435, 330, 442)(325, 437, 333, 445, 326, 438, 335, 447, 328, 440, 336, 448, 327, 439, 334, 446) L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 235)(6, 237)(7, 227)(8, 238)(9, 228)(10, 236)(11, 229)(12, 234)(13, 230)(14, 232)(15, 249)(16, 250)(17, 251)(18, 253)(19, 254)(20, 255)(21, 256)(22, 257)(23, 259)(24, 260)(25, 239)(26, 240)(27, 241)(28, 258)(29, 242)(30, 243)(31, 244)(32, 245)(33, 246)(34, 252)(35, 247)(36, 248)(37, 271)(38, 272)(39, 273)(40, 274)(41, 275)(42, 276)(43, 277)(44, 278)(45, 279)(46, 280)(47, 261)(48, 262)(49, 263)(50, 264)(51, 265)(52, 266)(53, 267)(54, 268)(55, 269)(56, 270)(57, 289)(58, 290)(59, 291)(60, 292)(61, 293)(62, 294)(63, 295)(64, 296)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 305)(74, 306)(75, 307)(76, 308)(77, 309)(78, 310)(79, 311)(80, 312)(81, 297)(82, 298)(83, 299)(84, 300)(85, 301)(86, 302)(87, 303)(88, 304)(89, 321)(90, 322)(91, 323)(92, 324)(93, 325)(94, 326)(95, 327)(96, 328)(97, 313)(98, 314)(99, 315)(100, 316)(101, 317)(102, 318)(103, 319)(104, 320)(105, 335)(106, 336)(107, 333)(108, 334)(109, 331)(110, 332)(111, 329)(112, 330)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) } Outer automorphisms :: reflexible Dual of E20.1028 Graph:: bipartite v = 70 e = 224 f = 116 degree seq :: [ 4^56, 16^14 ] E20.1026 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 28}) Quotient :: dipole Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, Y1^8, Y1^-1 * Y2^-1 * Y1^2 * Y2^-13 * Y1^-1 ] Map:: R = (1, 113, 2, 114, 6, 118, 14, 126, 26, 138, 24, 136, 12, 124, 4, 116)(3, 115, 9, 121, 19, 131, 33, 145, 41, 153, 28, 140, 15, 127, 8, 120)(5, 117, 11, 123, 22, 134, 37, 149, 42, 154, 27, 139, 16, 128, 7, 119)(10, 122, 18, 130, 29, 141, 44, 156, 57, 169, 49, 161, 34, 146, 20, 132)(13, 125, 17, 129, 30, 142, 43, 155, 58, 170, 53, 165, 38, 150, 23, 135)(21, 133, 35, 147, 50, 162, 65, 177, 73, 185, 60, 172, 45, 157, 32, 144)(25, 137, 39, 151, 54, 166, 69, 181, 74, 186, 59, 171, 46, 158, 31, 143)(36, 148, 48, 160, 61, 173, 76, 188, 89, 201, 81, 193, 66, 178, 51, 163)(40, 152, 47, 159, 62, 174, 75, 187, 90, 202, 85, 197, 70, 182, 55, 167)(52, 164, 67, 179, 82, 194, 97, 209, 105, 217, 92, 204, 77, 189, 64, 176)(56, 168, 71, 183, 86, 198, 101, 213, 106, 218, 91, 203, 78, 190, 63, 175)(68, 180, 80, 192, 93, 205, 108, 220, 104, 216, 111, 223, 98, 210, 83, 195)(72, 184, 79, 191, 94, 206, 107, 219, 100, 212, 112, 224, 102, 214, 87, 199)(84, 196, 99, 211, 110, 222, 95, 207, 88, 200, 103, 215, 109, 221, 96, 208)(225, 337, 227, 339, 234, 346, 245, 357, 260, 372, 276, 388, 292, 404, 308, 420, 324, 436, 330, 442, 314, 426, 298, 410, 282, 394, 266, 378, 250, 362, 265, 377, 281, 393, 297, 409, 313, 425, 329, 441, 328, 440, 312, 424, 296, 408, 280, 392, 264, 376, 249, 361, 237, 349, 229, 341)(226, 338, 231, 343, 241, 353, 255, 367, 271, 383, 287, 399, 303, 415, 319, 431, 335, 447, 321, 433, 305, 417, 289, 401, 273, 385, 257, 369, 248, 360, 261, 373, 277, 389, 293, 405, 309, 421, 325, 437, 336, 448, 320, 432, 304, 416, 288, 400, 272, 384, 256, 368, 242, 354, 232, 344)(228, 340, 235, 347, 247, 359, 263, 375, 279, 391, 295, 407, 311, 423, 327, 439, 332, 444, 316, 428, 300, 412, 284, 396, 268, 380, 252, 364, 238, 350, 251, 363, 267, 379, 283, 395, 299, 411, 315, 427, 331, 443, 323, 435, 307, 419, 291, 403, 275, 387, 259, 371, 244, 356, 233, 345)(230, 342, 239, 351, 253, 365, 269, 381, 285, 397, 301, 413, 317, 429, 333, 445, 326, 438, 310, 422, 294, 406, 278, 390, 262, 374, 246, 358, 236, 348, 243, 355, 258, 370, 274, 386, 290, 402, 306, 418, 322, 434, 334, 446, 318, 430, 302, 414, 286, 398, 270, 382, 254, 366, 240, 352) L = (1, 227)(2, 231)(3, 234)(4, 235)(5, 225)(6, 239)(7, 241)(8, 226)(9, 228)(10, 245)(11, 247)(12, 243)(13, 229)(14, 251)(15, 253)(16, 230)(17, 255)(18, 232)(19, 258)(20, 233)(21, 260)(22, 236)(23, 263)(24, 261)(25, 237)(26, 265)(27, 267)(28, 238)(29, 269)(30, 240)(31, 271)(32, 242)(33, 248)(34, 274)(35, 244)(36, 276)(37, 277)(38, 246)(39, 279)(40, 249)(41, 281)(42, 250)(43, 283)(44, 252)(45, 285)(46, 254)(47, 287)(48, 256)(49, 257)(50, 290)(51, 259)(52, 292)(53, 293)(54, 262)(55, 295)(56, 264)(57, 297)(58, 266)(59, 299)(60, 268)(61, 301)(62, 270)(63, 303)(64, 272)(65, 273)(66, 306)(67, 275)(68, 308)(69, 309)(70, 278)(71, 311)(72, 280)(73, 313)(74, 282)(75, 315)(76, 284)(77, 317)(78, 286)(79, 319)(80, 288)(81, 289)(82, 322)(83, 291)(84, 324)(85, 325)(86, 294)(87, 327)(88, 296)(89, 329)(90, 298)(91, 331)(92, 300)(93, 333)(94, 302)(95, 335)(96, 304)(97, 305)(98, 334)(99, 307)(100, 330)(101, 336)(102, 310)(103, 332)(104, 312)(105, 328)(106, 314)(107, 323)(108, 316)(109, 326)(110, 318)(111, 321)(112, 320)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.1027 Graph:: bipartite v = 18 e = 224 f = 168 degree seq :: [ 16^14, 56^4 ] E20.1027 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 28}) Quotient :: dipole Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, (Y3^-1 * Y2)^8, Y3 * Y2 * Y3^-11 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^28 ] Map:: polytopal R = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)(225, 337, 226, 338)(227, 339, 231, 343)(228, 340, 233, 345)(229, 341, 235, 347)(230, 342, 237, 349)(232, 344, 238, 350)(234, 346, 236, 348)(239, 351, 249, 361)(240, 352, 250, 362)(241, 353, 251, 363)(242, 354, 253, 365)(243, 355, 254, 366)(244, 356, 256, 368)(245, 357, 257, 369)(246, 358, 258, 370)(247, 359, 260, 372)(248, 360, 261, 373)(252, 364, 262, 374)(255, 367, 259, 371)(263, 375, 279, 391)(264, 376, 280, 392)(265, 377, 281, 393)(266, 378, 282, 394)(267, 379, 283, 395)(268, 380, 285, 397)(269, 381, 286, 398)(270, 382, 287, 399)(271, 383, 289, 401)(272, 384, 290, 402)(273, 385, 291, 403)(274, 386, 292, 404)(275, 387, 293, 405)(276, 388, 295, 407)(277, 389, 296, 408)(278, 390, 297, 409)(284, 396, 298, 410)(288, 400, 294, 406)(299, 411, 310, 422)(300, 412, 312, 424)(301, 413, 311, 423)(302, 414, 317, 429)(303, 415, 321, 433)(304, 416, 322, 434)(305, 417, 323, 435)(306, 418, 313, 425)(307, 419, 325, 437)(308, 420, 326, 438)(309, 421, 327, 439)(314, 426, 329, 441)(315, 427, 330, 442)(316, 428, 331, 443)(318, 430, 333, 445)(319, 431, 334, 446)(320, 432, 335, 447)(324, 436, 336, 448)(328, 440, 332, 444) L = (1, 227)(2, 229)(3, 232)(4, 225)(5, 236)(6, 226)(7, 239)(8, 241)(9, 242)(10, 228)(11, 244)(12, 246)(13, 247)(14, 230)(15, 233)(16, 231)(17, 252)(18, 254)(19, 234)(20, 237)(21, 235)(22, 259)(23, 261)(24, 238)(25, 263)(26, 265)(27, 240)(28, 267)(29, 264)(30, 269)(31, 243)(32, 271)(33, 273)(34, 245)(35, 275)(36, 272)(37, 277)(38, 248)(39, 250)(40, 249)(41, 282)(42, 251)(43, 284)(44, 253)(45, 287)(46, 255)(47, 257)(48, 256)(49, 292)(50, 258)(51, 294)(52, 260)(53, 297)(54, 262)(55, 299)(56, 301)(57, 300)(58, 303)(59, 266)(60, 305)(61, 306)(62, 268)(63, 308)(64, 270)(65, 310)(66, 312)(67, 311)(68, 314)(69, 274)(70, 316)(71, 317)(72, 276)(73, 319)(74, 278)(75, 280)(76, 279)(77, 285)(78, 281)(79, 322)(80, 283)(81, 324)(82, 325)(83, 286)(84, 327)(85, 288)(86, 290)(87, 289)(88, 295)(89, 291)(90, 330)(91, 293)(92, 332)(93, 333)(94, 296)(95, 335)(96, 298)(97, 302)(98, 331)(99, 304)(100, 329)(101, 336)(102, 307)(103, 334)(104, 309)(105, 313)(106, 323)(107, 315)(108, 321)(109, 328)(110, 318)(111, 326)(112, 320)(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, 56 ), ( 16, 56, 16, 56 ) } Outer automorphisms :: reflexible Dual of E20.1026 Graph:: simple bipartite v = 168 e = 224 f = 18 degree seq :: [ 2^112, 4^56 ] E20.1028 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 28}) Quotient :: dipole Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y1^2 * Y3)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^-8 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-3 ] Map:: R = (1, 113, 2, 114, 5, 117, 11, 123, 20, 132, 32, 144, 47, 159, 65, 177, 86, 198, 105, 217, 100, 212, 80, 192, 95, 207, 78, 190, 93, 205, 79, 191, 94, 206, 81, 193, 96, 208, 112, 224, 104, 216, 85, 197, 64, 176, 46, 158, 31, 143, 19, 131, 10, 122, 4, 116)(3, 115, 7, 119, 15, 127, 25, 137, 39, 151, 55, 167, 75, 187, 97, 209, 111, 223, 91, 203, 74, 186, 54, 166, 72, 184, 52, 164, 71, 183, 53, 165, 73, 185, 63, 175, 84, 196, 103, 215, 106, 218, 88, 200, 66, 178, 49, 161, 33, 145, 22, 134, 12, 124, 8, 120)(6, 118, 13, 125, 9, 121, 18, 130, 29, 141, 44, 156, 61, 173, 82, 194, 101, 213, 110, 222, 92, 204, 70, 182, 60, 172, 43, 155, 58, 170, 41, 153, 57, 169, 42, 154, 59, 171, 77, 189, 99, 211, 107, 219, 87, 199, 67, 179, 48, 160, 34, 146, 21, 133, 14, 126)(16, 128, 26, 138, 17, 129, 28, 140, 35, 147, 51, 163, 68, 180, 90, 202, 108, 220, 102, 214, 83, 195, 62, 174, 45, 157, 30, 142, 37, 149, 23, 135, 36, 148, 24, 136, 38, 150, 50, 162, 69, 181, 89, 201, 109, 221, 98, 210, 76, 188, 56, 168, 40, 152, 27, 139)(225, 337)(226, 338)(227, 339)(228, 340)(229, 341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237, 349)(238, 350)(239, 351)(240, 352)(241, 353)(242, 354)(243, 355)(244, 356)(245, 357)(246, 358)(247, 359)(248, 360)(249, 361)(250, 362)(251, 363)(252, 364)(253, 365)(254, 366)(255, 367)(256, 368)(257, 369)(258, 370)(259, 371)(260, 372)(261, 373)(262, 374)(263, 375)(264, 376)(265, 377)(266, 378)(267, 379)(268, 380)(269, 381)(270, 382)(271, 383)(272, 384)(273, 385)(274, 386)(275, 387)(276, 388)(277, 389)(278, 390)(279, 391)(280, 392)(281, 393)(282, 394)(283, 395)(284, 396)(285, 397)(286, 398)(287, 399)(288, 400)(289, 401)(290, 402)(291, 403)(292, 404)(293, 405)(294, 406)(295, 407)(296, 408)(297, 409)(298, 410)(299, 411)(300, 412)(301, 413)(302, 414)(303, 415)(304, 416)(305, 417)(306, 418)(307, 419)(308, 420)(309, 421)(310, 422)(311, 423)(312, 424)(313, 425)(314, 426)(315, 427)(316, 428)(317, 429)(318, 430)(319, 431)(320, 432)(321, 433)(322, 434)(323, 435)(324, 436)(325, 437)(326, 438)(327, 439)(328, 440)(329, 441)(330, 442)(331, 443)(332, 444)(333, 445)(334, 446)(335, 447)(336, 448) L = (1, 227)(2, 230)(3, 225)(4, 233)(5, 236)(6, 226)(7, 240)(8, 241)(9, 228)(10, 239)(11, 245)(12, 229)(13, 247)(14, 248)(15, 234)(16, 231)(17, 232)(18, 254)(19, 253)(20, 257)(21, 235)(22, 259)(23, 237)(24, 238)(25, 264)(26, 265)(27, 266)(28, 267)(29, 243)(30, 242)(31, 263)(32, 272)(33, 244)(34, 274)(35, 246)(36, 276)(37, 277)(38, 278)(39, 255)(40, 249)(41, 250)(42, 251)(43, 252)(44, 286)(45, 287)(46, 285)(47, 290)(48, 256)(49, 292)(50, 258)(51, 294)(52, 260)(53, 261)(54, 262)(55, 300)(56, 301)(57, 302)(58, 303)(59, 304)(60, 305)(61, 270)(62, 268)(63, 269)(64, 299)(65, 311)(66, 271)(67, 313)(68, 273)(69, 315)(70, 275)(71, 317)(72, 318)(73, 319)(74, 320)(75, 288)(76, 279)(77, 280)(78, 281)(79, 282)(80, 283)(81, 284)(82, 326)(83, 327)(84, 324)(85, 325)(86, 330)(87, 289)(88, 332)(89, 291)(90, 334)(91, 293)(92, 336)(93, 295)(94, 296)(95, 297)(96, 298)(97, 333)(98, 331)(99, 329)(100, 308)(101, 309)(102, 306)(103, 307)(104, 335)(105, 323)(106, 310)(107, 322)(108, 312)(109, 321)(110, 314)(111, 328)(112, 316)(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, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 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 E20.1025 Graph:: simple bipartite v = 116 e = 224 f = 70 degree seq :: [ 2^112, 56^4 ] E20.1029 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 28}) Quotient :: dipole Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^8, Y2 * Y1 * Y2^-1 * Y1 * Y2^3 * Y1 * Y2^-9 * Y1 ] Map:: R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 11, 123)(6, 118, 13, 125)(8, 120, 14, 126)(10, 122, 12, 124)(15, 127, 25, 137)(16, 128, 26, 138)(17, 129, 27, 139)(18, 130, 29, 141)(19, 131, 30, 142)(20, 132, 32, 144)(21, 133, 33, 145)(22, 134, 34, 146)(23, 135, 36, 148)(24, 136, 37, 149)(28, 140, 38, 150)(31, 143, 35, 147)(39, 151, 55, 167)(40, 152, 56, 168)(41, 153, 57, 169)(42, 154, 58, 170)(43, 155, 59, 171)(44, 156, 61, 173)(45, 157, 62, 174)(46, 158, 63, 175)(47, 159, 65, 177)(48, 160, 66, 178)(49, 161, 67, 179)(50, 162, 68, 180)(51, 163, 69, 181)(52, 164, 71, 183)(53, 165, 72, 184)(54, 166, 73, 185)(60, 172, 74, 186)(64, 176, 70, 182)(75, 187, 86, 198)(76, 188, 88, 200)(77, 189, 87, 199)(78, 190, 93, 205)(79, 191, 97, 209)(80, 192, 98, 210)(81, 193, 99, 211)(82, 194, 89, 201)(83, 195, 101, 213)(84, 196, 102, 214)(85, 197, 103, 215)(90, 202, 105, 217)(91, 203, 106, 218)(92, 204, 107, 219)(94, 206, 109, 221)(95, 207, 110, 222)(96, 208, 111, 223)(100, 212, 112, 224)(104, 216, 108, 220)(225, 337, 227, 339, 232, 344, 241, 353, 252, 364, 267, 379, 284, 396, 305, 417, 324, 436, 329, 441, 313, 425, 291, 403, 311, 423, 289, 401, 310, 422, 290, 402, 312, 424, 295, 407, 317, 429, 333, 445, 328, 440, 309, 421, 288, 400, 270, 382, 255, 367, 243, 355, 234, 346, 228, 340)(226, 338, 229, 341, 236, 348, 246, 358, 259, 371, 275, 387, 294, 406, 316, 428, 332, 444, 321, 433, 302, 414, 281, 393, 300, 412, 279, 391, 299, 411, 280, 392, 301, 413, 285, 397, 306, 418, 325, 437, 336, 448, 320, 432, 298, 410, 278, 390, 262, 374, 248, 360, 238, 350, 230, 342)(231, 343, 239, 351, 233, 345, 242, 354, 254, 366, 269, 381, 287, 399, 308, 420, 327, 439, 334, 446, 318, 430, 296, 408, 276, 388, 260, 372, 272, 384, 256, 368, 271, 383, 257, 369, 273, 385, 292, 404, 314, 426, 330, 442, 323, 435, 304, 416, 283, 395, 266, 378, 251, 363, 240, 352)(235, 347, 244, 356, 237, 349, 247, 359, 261, 373, 277, 389, 297, 409, 319, 431, 335, 447, 326, 438, 307, 419, 286, 398, 268, 380, 253, 365, 264, 376, 249, 361, 263, 375, 250, 362, 265, 377, 282, 394, 303, 415, 322, 434, 331, 443, 315, 427, 293, 405, 274, 386, 258, 370, 245, 357) L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 235)(6, 237)(7, 227)(8, 238)(9, 228)(10, 236)(11, 229)(12, 234)(13, 230)(14, 232)(15, 249)(16, 250)(17, 251)(18, 253)(19, 254)(20, 256)(21, 257)(22, 258)(23, 260)(24, 261)(25, 239)(26, 240)(27, 241)(28, 262)(29, 242)(30, 243)(31, 259)(32, 244)(33, 245)(34, 246)(35, 255)(36, 247)(37, 248)(38, 252)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 285)(45, 286)(46, 287)(47, 289)(48, 290)(49, 291)(50, 292)(51, 293)(52, 295)(53, 296)(54, 297)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 298)(61, 268)(62, 269)(63, 270)(64, 294)(65, 271)(66, 272)(67, 273)(68, 274)(69, 275)(70, 288)(71, 276)(72, 277)(73, 278)(74, 284)(75, 310)(76, 312)(77, 311)(78, 317)(79, 321)(80, 322)(81, 323)(82, 313)(83, 325)(84, 326)(85, 327)(86, 299)(87, 301)(88, 300)(89, 306)(90, 329)(91, 330)(92, 331)(93, 302)(94, 333)(95, 334)(96, 335)(97, 303)(98, 304)(99, 305)(100, 336)(101, 307)(102, 308)(103, 309)(104, 332)(105, 314)(106, 315)(107, 316)(108, 328)(109, 318)(110, 319)(111, 320)(112, 324)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E20.1030 Graph:: bipartite v = 60 e = 224 f = 126 degree seq :: [ 4^56, 56^4 ] E20.1030 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 28}) Quotient :: dipole Aut^+ = (C7 x Q8) : C2 (small group id <112, 16>) Aut = (D8 x D14) : C2 (small group id <224, 109>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3 * Y1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^8, Y1^-1 * Y3^-1 * Y1^2 * Y3^-13 * Y1^-1, (Y3 * Y2^-1)^28 ] Map:: R = (1, 113, 2, 114, 6, 118, 14, 126, 26, 138, 24, 136, 12, 124, 4, 116)(3, 115, 9, 121, 19, 131, 33, 145, 41, 153, 28, 140, 15, 127, 8, 120)(5, 117, 11, 123, 22, 134, 37, 149, 42, 154, 27, 139, 16, 128, 7, 119)(10, 122, 18, 130, 29, 141, 44, 156, 57, 169, 49, 161, 34, 146, 20, 132)(13, 125, 17, 129, 30, 142, 43, 155, 58, 170, 53, 165, 38, 150, 23, 135)(21, 133, 35, 147, 50, 162, 65, 177, 73, 185, 60, 172, 45, 157, 32, 144)(25, 137, 39, 151, 54, 166, 69, 181, 74, 186, 59, 171, 46, 158, 31, 143)(36, 148, 48, 160, 61, 173, 76, 188, 89, 201, 81, 193, 66, 178, 51, 163)(40, 152, 47, 159, 62, 174, 75, 187, 90, 202, 85, 197, 70, 182, 55, 167)(52, 164, 67, 179, 82, 194, 97, 209, 105, 217, 92, 204, 77, 189, 64, 176)(56, 168, 71, 183, 86, 198, 101, 213, 106, 218, 91, 203, 78, 190, 63, 175)(68, 180, 80, 192, 93, 205, 108, 220, 104, 216, 111, 223, 98, 210, 83, 195)(72, 184, 79, 191, 94, 206, 107, 219, 100, 212, 112, 224, 102, 214, 87, 199)(84, 196, 99, 211, 110, 222, 95, 207, 88, 200, 103, 215, 109, 221, 96, 208)(225, 337)(226, 338)(227, 339)(228, 340)(229, 341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237, 349)(238, 350)(239, 351)(240, 352)(241, 353)(242, 354)(243, 355)(244, 356)(245, 357)(246, 358)(247, 359)(248, 360)(249, 361)(250, 362)(251, 363)(252, 364)(253, 365)(254, 366)(255, 367)(256, 368)(257, 369)(258, 370)(259, 371)(260, 372)(261, 373)(262, 374)(263, 375)(264, 376)(265, 377)(266, 378)(267, 379)(268, 380)(269, 381)(270, 382)(271, 383)(272, 384)(273, 385)(274, 386)(275, 387)(276, 388)(277, 389)(278, 390)(279, 391)(280, 392)(281, 393)(282, 394)(283, 395)(284, 396)(285, 397)(286, 398)(287, 399)(288, 400)(289, 401)(290, 402)(291, 403)(292, 404)(293, 405)(294, 406)(295, 407)(296, 408)(297, 409)(298, 410)(299, 411)(300, 412)(301, 413)(302, 414)(303, 415)(304, 416)(305, 417)(306, 418)(307, 419)(308, 420)(309, 421)(310, 422)(311, 423)(312, 424)(313, 425)(314, 426)(315, 427)(316, 428)(317, 429)(318, 430)(319, 431)(320, 432)(321, 433)(322, 434)(323, 435)(324, 436)(325, 437)(326, 438)(327, 439)(328, 440)(329, 441)(330, 442)(331, 443)(332, 444)(333, 445)(334, 446)(335, 447)(336, 448) L = (1, 227)(2, 231)(3, 234)(4, 235)(5, 225)(6, 239)(7, 241)(8, 226)(9, 228)(10, 245)(11, 247)(12, 243)(13, 229)(14, 251)(15, 253)(16, 230)(17, 255)(18, 232)(19, 258)(20, 233)(21, 260)(22, 236)(23, 263)(24, 261)(25, 237)(26, 265)(27, 267)(28, 238)(29, 269)(30, 240)(31, 271)(32, 242)(33, 248)(34, 274)(35, 244)(36, 276)(37, 277)(38, 246)(39, 279)(40, 249)(41, 281)(42, 250)(43, 283)(44, 252)(45, 285)(46, 254)(47, 287)(48, 256)(49, 257)(50, 290)(51, 259)(52, 292)(53, 293)(54, 262)(55, 295)(56, 264)(57, 297)(58, 266)(59, 299)(60, 268)(61, 301)(62, 270)(63, 303)(64, 272)(65, 273)(66, 306)(67, 275)(68, 308)(69, 309)(70, 278)(71, 311)(72, 280)(73, 313)(74, 282)(75, 315)(76, 284)(77, 317)(78, 286)(79, 319)(80, 288)(81, 289)(82, 322)(83, 291)(84, 324)(85, 325)(86, 294)(87, 327)(88, 296)(89, 329)(90, 298)(91, 331)(92, 300)(93, 333)(94, 302)(95, 335)(96, 304)(97, 305)(98, 334)(99, 307)(100, 330)(101, 336)(102, 310)(103, 332)(104, 312)(105, 328)(106, 314)(107, 323)(108, 316)(109, 326)(110, 318)(111, 321)(112, 320)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448) local type(s) :: { ( 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) } Outer automorphisms :: reflexible Dual of E20.1029 Graph:: simple bipartite v = 126 e = 224 f = 60 degree seq :: [ 2^112, 16^14 ] E20.1031 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 3}) Quotient :: edge^2 Aut^+ = (C19 : C3) : C2 (small group id <114, 1>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, Y2^3, Y1^2 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 115, 4, 118)(2, 116, 5, 119)(3, 117, 6, 120)(7, 121, 13, 127)(8, 122, 14, 128)(9, 123, 15, 129)(10, 124, 16, 130)(11, 125, 17, 131)(12, 126, 18, 132)(19, 133, 31, 145)(20, 134, 32, 146)(21, 135, 33, 147)(22, 136, 34, 148)(23, 137, 35, 149)(24, 138, 36, 150)(25, 139, 37, 151)(26, 140, 38, 152)(27, 141, 39, 153)(28, 142, 40, 154)(29, 143, 41, 155)(30, 144, 42, 156)(43, 157, 58, 172)(44, 158, 59, 173)(45, 159, 60, 174)(46, 160, 61, 175)(47, 161, 62, 176)(48, 162, 63, 177)(49, 163, 64, 178)(50, 164, 65, 179)(51, 165, 66, 180)(52, 166, 67, 181)(53, 167, 68, 182)(54, 168, 69, 183)(55, 169, 70, 184)(56, 170, 71, 185)(57, 171, 72, 186)(73, 187, 94, 208)(74, 188, 95, 209)(75, 189, 96, 210)(76, 190, 97, 211)(77, 191, 98, 212)(78, 192, 99, 213)(79, 193, 100, 214)(80, 194, 101, 215)(81, 195, 102, 216)(82, 196, 103, 217)(83, 197, 104, 218)(84, 198, 105, 219)(85, 199, 106, 220)(86, 200, 107, 221)(87, 201, 108, 222)(88, 202, 109, 223)(89, 203, 110, 224)(90, 204, 111, 225)(91, 205, 112, 226)(92, 206, 113, 227)(93, 207, 114, 228)(229, 230, 231)(232, 235, 236)(233, 237, 238)(234, 239, 240)(241, 247, 248)(242, 249, 250)(243, 251, 252)(244, 253, 254)(245, 255, 256)(246, 257, 258)(259, 270, 271)(260, 272, 273)(261, 274, 275)(262, 276, 263)(264, 277, 278)(265, 279, 280)(266, 281, 267)(268, 282, 283)(269, 284, 285)(286, 301, 302)(287, 303, 304)(288, 305, 289)(290, 306, 307)(291, 308, 309)(292, 310, 311)(293, 312, 294)(295, 313, 314)(296, 315, 316)(297, 317, 318)(298, 319, 299)(300, 320, 321)(322, 342, 334)(323, 333, 324)(325, 332, 339)(326, 338, 337)(327, 336, 335)(328, 341, 329)(330, 340, 331)(343, 345, 344)(346, 350, 349)(347, 352, 351)(348, 354, 353)(355, 362, 361)(356, 364, 363)(357, 366, 365)(358, 368, 367)(359, 370, 369)(360, 372, 371)(373, 385, 384)(374, 387, 386)(375, 389, 388)(376, 377, 390)(378, 392, 391)(379, 394, 393)(380, 381, 395)(382, 397, 396)(383, 399, 398)(400, 416, 415)(401, 418, 417)(402, 403, 419)(404, 421, 420)(405, 423, 422)(406, 425, 424)(407, 408, 426)(409, 428, 427)(410, 430, 429)(411, 432, 431)(412, 413, 433)(414, 435, 434)(436, 448, 456)(437, 438, 447)(439, 453, 446)(440, 451, 452)(441, 449, 450)(442, 443, 455)(444, 445, 454) L = (1, 229)(2, 230)(3, 231)(4, 232)(5, 233)(6, 234)(7, 235)(8, 236)(9, 237)(10, 238)(11, 239)(12, 240)(13, 241)(14, 242)(15, 243)(16, 244)(17, 245)(18, 246)(19, 247)(20, 248)(21, 249)(22, 250)(23, 251)(24, 252)(25, 253)(26, 254)(27, 255)(28, 256)(29, 257)(30, 258)(31, 259)(32, 260)(33, 261)(34, 262)(35, 263)(36, 264)(37, 265)(38, 266)(39, 267)(40, 268)(41, 269)(42, 270)(43, 271)(44, 272)(45, 273)(46, 274)(47, 275)(48, 276)(49, 277)(50, 278)(51, 279)(52, 280)(53, 281)(54, 282)(55, 283)(56, 284)(57, 285)(58, 286)(59, 287)(60, 288)(61, 289)(62, 290)(63, 291)(64, 292)(65, 293)(66, 294)(67, 295)(68, 296)(69, 297)(70, 298)(71, 299)(72, 300)(73, 301)(74, 302)(75, 303)(76, 304)(77, 305)(78, 306)(79, 307)(80, 308)(81, 309)(82, 310)(83, 311)(84, 312)(85, 313)(86, 314)(87, 315)(88, 316)(89, 317)(90, 318)(91, 319)(92, 320)(93, 321)(94, 322)(95, 323)(96, 324)(97, 325)(98, 326)(99, 327)(100, 328)(101, 329)(102, 330)(103, 331)(104, 332)(105, 333)(106, 334)(107, 335)(108, 336)(109, 337)(110, 338)(111, 339)(112, 340)(113, 341)(114, 342)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456) local type(s) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E20.1034 Graph:: simple bipartite v = 133 e = 228 f = 57 degree seq :: [ 3^76, 4^57 ] E20.1032 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 3}) Quotient :: edge^2 Aut^+ = (C19 : C3) : C2 (small group id <114, 1>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y2^3, Y1^2 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 115, 4, 118)(2, 116, 5, 119)(3, 117, 6, 120)(7, 121, 13, 127)(8, 122, 14, 128)(9, 123, 15, 129)(10, 124, 16, 130)(11, 125, 17, 131)(12, 126, 18, 132)(19, 133, 31, 145)(20, 134, 32, 146)(21, 135, 33, 147)(22, 136, 34, 148)(23, 137, 35, 149)(24, 138, 36, 150)(25, 139, 37, 151)(26, 140, 38, 152)(27, 141, 39, 153)(28, 142, 40, 154)(29, 143, 41, 155)(30, 144, 42, 156)(43, 157, 58, 172)(44, 158, 59, 173)(45, 159, 60, 174)(46, 160, 61, 175)(47, 161, 62, 176)(48, 162, 63, 177)(49, 163, 64, 178)(50, 164, 65, 179)(51, 165, 66, 180)(52, 166, 67, 181)(53, 167, 68, 182)(54, 168, 69, 183)(55, 169, 70, 184)(56, 170, 71, 185)(57, 171, 72, 186)(73, 187, 94, 208)(74, 188, 95, 209)(75, 189, 96, 210)(76, 190, 97, 211)(77, 191, 98, 212)(78, 192, 99, 213)(79, 193, 100, 214)(80, 194, 101, 215)(81, 195, 102, 216)(82, 196, 103, 217)(83, 197, 104, 218)(84, 198, 105, 219)(85, 199, 106, 220)(86, 200, 107, 221)(87, 201, 108, 222)(88, 202, 109, 223)(89, 203, 110, 224)(90, 204, 111, 225)(91, 205, 112, 226)(92, 206, 113, 227)(93, 207, 114, 228)(229, 230, 231)(232, 235, 236)(233, 237, 238)(234, 239, 240)(241, 247, 248)(242, 249, 250)(243, 251, 252)(244, 253, 254)(245, 255, 256)(246, 257, 258)(259, 270, 271)(260, 272, 273)(261, 274, 275)(262, 276, 263)(264, 277, 278)(265, 279, 280)(266, 281, 267)(268, 282, 283)(269, 284, 285)(286, 301, 302)(287, 303, 304)(288, 305, 289)(290, 306, 307)(291, 308, 309)(292, 310, 311)(293, 312, 294)(295, 313, 314)(296, 315, 316)(297, 317, 318)(298, 319, 299)(300, 320, 321)(322, 342, 333)(323, 332, 324)(325, 338, 337)(326, 336, 335)(327, 334, 341)(328, 340, 329)(330, 339, 331)(343, 345, 344)(346, 350, 349)(347, 352, 351)(348, 354, 353)(355, 362, 361)(356, 364, 363)(357, 366, 365)(358, 368, 367)(359, 370, 369)(360, 372, 371)(373, 385, 384)(374, 387, 386)(375, 389, 388)(376, 377, 390)(378, 392, 391)(379, 394, 393)(380, 381, 395)(382, 397, 396)(383, 399, 398)(400, 416, 415)(401, 418, 417)(402, 403, 419)(404, 421, 420)(405, 423, 422)(406, 425, 424)(407, 408, 426)(409, 428, 427)(410, 430, 429)(411, 432, 431)(412, 413, 433)(414, 435, 434)(436, 447, 456)(437, 438, 446)(439, 451, 452)(440, 449, 450)(441, 455, 448)(442, 443, 454)(444, 445, 453) L = (1, 229)(2, 230)(3, 231)(4, 232)(5, 233)(6, 234)(7, 235)(8, 236)(9, 237)(10, 238)(11, 239)(12, 240)(13, 241)(14, 242)(15, 243)(16, 244)(17, 245)(18, 246)(19, 247)(20, 248)(21, 249)(22, 250)(23, 251)(24, 252)(25, 253)(26, 254)(27, 255)(28, 256)(29, 257)(30, 258)(31, 259)(32, 260)(33, 261)(34, 262)(35, 263)(36, 264)(37, 265)(38, 266)(39, 267)(40, 268)(41, 269)(42, 270)(43, 271)(44, 272)(45, 273)(46, 274)(47, 275)(48, 276)(49, 277)(50, 278)(51, 279)(52, 280)(53, 281)(54, 282)(55, 283)(56, 284)(57, 285)(58, 286)(59, 287)(60, 288)(61, 289)(62, 290)(63, 291)(64, 292)(65, 293)(66, 294)(67, 295)(68, 296)(69, 297)(70, 298)(71, 299)(72, 300)(73, 301)(74, 302)(75, 303)(76, 304)(77, 305)(78, 306)(79, 307)(80, 308)(81, 309)(82, 310)(83, 311)(84, 312)(85, 313)(86, 314)(87, 315)(88, 316)(89, 317)(90, 318)(91, 319)(92, 320)(93, 321)(94, 322)(95, 323)(96, 324)(97, 325)(98, 326)(99, 327)(100, 328)(101, 329)(102, 330)(103, 331)(104, 332)(105, 333)(106, 334)(107, 335)(108, 336)(109, 337)(110, 338)(111, 339)(112, 340)(113, 341)(114, 342)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456) local type(s) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E20.1033 Graph:: simple bipartite v = 133 e = 228 f = 57 degree seq :: [ 3^76, 4^57 ] E20.1033 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 3}) Quotient :: loop^2 Aut^+ = (C19 : C3) : C2 (small group id <114, 1>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, Y2^3, Y1^2 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 115, 229, 343, 4, 118, 232, 346)(2, 116, 230, 344, 5, 119, 233, 347)(3, 117, 231, 345, 6, 120, 234, 348)(7, 121, 235, 349, 13, 127, 241, 355)(8, 122, 236, 350, 14, 128, 242, 356)(9, 123, 237, 351, 15, 129, 243, 357)(10, 124, 238, 352, 16, 130, 244, 358)(11, 125, 239, 353, 17, 131, 245, 359)(12, 126, 240, 354, 18, 132, 246, 360)(19, 133, 247, 361, 31, 145, 259, 373)(20, 134, 248, 362, 32, 146, 260, 374)(21, 135, 249, 363, 33, 147, 261, 375)(22, 136, 250, 364, 34, 148, 262, 376)(23, 137, 251, 365, 35, 149, 263, 377)(24, 138, 252, 366, 36, 150, 264, 378)(25, 139, 253, 367, 37, 151, 265, 379)(26, 140, 254, 368, 38, 152, 266, 380)(27, 141, 255, 369, 39, 153, 267, 381)(28, 142, 256, 370, 40, 154, 268, 382)(29, 143, 257, 371, 41, 155, 269, 383)(30, 144, 258, 372, 42, 156, 270, 384)(43, 157, 271, 385, 58, 172, 286, 400)(44, 158, 272, 386, 59, 173, 287, 401)(45, 159, 273, 387, 60, 174, 288, 402)(46, 160, 274, 388, 61, 175, 289, 403)(47, 161, 275, 389, 62, 176, 290, 404)(48, 162, 276, 390, 63, 177, 291, 405)(49, 163, 277, 391, 64, 178, 292, 406)(50, 164, 278, 392, 65, 179, 293, 407)(51, 165, 279, 393, 66, 180, 294, 408)(52, 166, 280, 394, 67, 181, 295, 409)(53, 167, 281, 395, 68, 182, 296, 410)(54, 168, 282, 396, 69, 183, 297, 411)(55, 169, 283, 397, 70, 184, 298, 412)(56, 170, 284, 398, 71, 185, 299, 413)(57, 171, 285, 399, 72, 186, 300, 414)(73, 187, 301, 415, 94, 208, 322, 436)(74, 188, 302, 416, 95, 209, 323, 437)(75, 189, 303, 417, 96, 210, 324, 438)(76, 190, 304, 418, 97, 211, 325, 439)(77, 191, 305, 419, 98, 212, 326, 440)(78, 192, 306, 420, 99, 213, 327, 441)(79, 193, 307, 421, 100, 214, 328, 442)(80, 194, 308, 422, 101, 215, 329, 443)(81, 195, 309, 423, 102, 216, 330, 444)(82, 196, 310, 424, 103, 217, 331, 445)(83, 197, 311, 425, 104, 218, 332, 446)(84, 198, 312, 426, 105, 219, 333, 447)(85, 199, 313, 427, 106, 220, 334, 448)(86, 200, 314, 428, 107, 221, 335, 449)(87, 201, 315, 429, 108, 222, 336, 450)(88, 202, 316, 430, 109, 223, 337, 451)(89, 203, 317, 431, 110, 224, 338, 452)(90, 204, 318, 432, 111, 225, 339, 453)(91, 205, 319, 433, 112, 226, 340, 454)(92, 206, 320, 434, 113, 227, 341, 455)(93, 207, 321, 435, 114, 228, 342, 456) L = (1, 116)(2, 117)(3, 115)(4, 121)(5, 123)(6, 125)(7, 122)(8, 118)(9, 124)(10, 119)(11, 126)(12, 120)(13, 133)(14, 135)(15, 137)(16, 139)(17, 141)(18, 143)(19, 134)(20, 127)(21, 136)(22, 128)(23, 138)(24, 129)(25, 140)(26, 130)(27, 142)(28, 131)(29, 144)(30, 132)(31, 156)(32, 158)(33, 160)(34, 162)(35, 148)(36, 163)(37, 165)(38, 167)(39, 152)(40, 168)(41, 170)(42, 157)(43, 145)(44, 159)(45, 146)(46, 161)(47, 147)(48, 149)(49, 164)(50, 150)(51, 166)(52, 151)(53, 153)(54, 169)(55, 154)(56, 171)(57, 155)(58, 187)(59, 189)(60, 191)(61, 174)(62, 192)(63, 194)(64, 196)(65, 198)(66, 179)(67, 199)(68, 201)(69, 203)(70, 205)(71, 184)(72, 206)(73, 188)(74, 172)(75, 190)(76, 173)(77, 175)(78, 193)(79, 176)(80, 195)(81, 177)(82, 197)(83, 178)(84, 180)(85, 200)(86, 181)(87, 202)(88, 182)(89, 204)(90, 183)(91, 185)(92, 207)(93, 186)(94, 228)(95, 219)(96, 209)(97, 218)(98, 224)(99, 222)(100, 227)(101, 214)(102, 226)(103, 216)(104, 225)(105, 210)(106, 208)(107, 213)(108, 221)(109, 212)(110, 223)(111, 211)(112, 217)(113, 215)(114, 220)(229, 345)(230, 343)(231, 344)(232, 350)(233, 352)(234, 354)(235, 346)(236, 349)(237, 347)(238, 351)(239, 348)(240, 353)(241, 362)(242, 364)(243, 366)(244, 368)(245, 370)(246, 372)(247, 355)(248, 361)(249, 356)(250, 363)(251, 357)(252, 365)(253, 358)(254, 367)(255, 359)(256, 369)(257, 360)(258, 371)(259, 385)(260, 387)(261, 389)(262, 377)(263, 390)(264, 392)(265, 394)(266, 381)(267, 395)(268, 397)(269, 399)(270, 373)(271, 384)(272, 374)(273, 386)(274, 375)(275, 388)(276, 376)(277, 378)(278, 391)(279, 379)(280, 393)(281, 380)(282, 382)(283, 396)(284, 383)(285, 398)(286, 416)(287, 418)(288, 403)(289, 419)(290, 421)(291, 423)(292, 425)(293, 408)(294, 426)(295, 428)(296, 430)(297, 432)(298, 413)(299, 433)(300, 435)(301, 400)(302, 415)(303, 401)(304, 417)(305, 402)(306, 404)(307, 420)(308, 405)(309, 422)(310, 406)(311, 424)(312, 407)(313, 409)(314, 427)(315, 410)(316, 429)(317, 411)(318, 431)(319, 412)(320, 414)(321, 434)(322, 448)(323, 438)(324, 447)(325, 453)(326, 451)(327, 449)(328, 443)(329, 455)(330, 445)(331, 454)(332, 439)(333, 437)(334, 456)(335, 450)(336, 441)(337, 452)(338, 440)(339, 446)(340, 444)(341, 442)(342, 436) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E20.1032 Transitivity :: VT+ Graph:: v = 57 e = 228 f = 133 degree seq :: [ 8^57 ] E20.1034 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 3}) Quotient :: loop^2 Aut^+ = (C19 : C3) : C2 (small group id <114, 1>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, Y2^3, Y1^2 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 115, 229, 343, 4, 118, 232, 346)(2, 116, 230, 344, 5, 119, 233, 347)(3, 117, 231, 345, 6, 120, 234, 348)(7, 121, 235, 349, 13, 127, 241, 355)(8, 122, 236, 350, 14, 128, 242, 356)(9, 123, 237, 351, 15, 129, 243, 357)(10, 124, 238, 352, 16, 130, 244, 358)(11, 125, 239, 353, 17, 131, 245, 359)(12, 126, 240, 354, 18, 132, 246, 360)(19, 133, 247, 361, 31, 145, 259, 373)(20, 134, 248, 362, 32, 146, 260, 374)(21, 135, 249, 363, 33, 147, 261, 375)(22, 136, 250, 364, 34, 148, 262, 376)(23, 137, 251, 365, 35, 149, 263, 377)(24, 138, 252, 366, 36, 150, 264, 378)(25, 139, 253, 367, 37, 151, 265, 379)(26, 140, 254, 368, 38, 152, 266, 380)(27, 141, 255, 369, 39, 153, 267, 381)(28, 142, 256, 370, 40, 154, 268, 382)(29, 143, 257, 371, 41, 155, 269, 383)(30, 144, 258, 372, 42, 156, 270, 384)(43, 157, 271, 385, 58, 172, 286, 400)(44, 158, 272, 386, 59, 173, 287, 401)(45, 159, 273, 387, 60, 174, 288, 402)(46, 160, 274, 388, 61, 175, 289, 403)(47, 161, 275, 389, 62, 176, 290, 404)(48, 162, 276, 390, 63, 177, 291, 405)(49, 163, 277, 391, 64, 178, 292, 406)(50, 164, 278, 392, 65, 179, 293, 407)(51, 165, 279, 393, 66, 180, 294, 408)(52, 166, 280, 394, 67, 181, 295, 409)(53, 167, 281, 395, 68, 182, 296, 410)(54, 168, 282, 396, 69, 183, 297, 411)(55, 169, 283, 397, 70, 184, 298, 412)(56, 170, 284, 398, 71, 185, 299, 413)(57, 171, 285, 399, 72, 186, 300, 414)(73, 187, 301, 415, 94, 208, 322, 436)(74, 188, 302, 416, 95, 209, 323, 437)(75, 189, 303, 417, 96, 210, 324, 438)(76, 190, 304, 418, 97, 211, 325, 439)(77, 191, 305, 419, 98, 212, 326, 440)(78, 192, 306, 420, 99, 213, 327, 441)(79, 193, 307, 421, 100, 214, 328, 442)(80, 194, 308, 422, 101, 215, 329, 443)(81, 195, 309, 423, 102, 216, 330, 444)(82, 196, 310, 424, 103, 217, 331, 445)(83, 197, 311, 425, 104, 218, 332, 446)(84, 198, 312, 426, 105, 219, 333, 447)(85, 199, 313, 427, 106, 220, 334, 448)(86, 200, 314, 428, 107, 221, 335, 449)(87, 201, 315, 429, 108, 222, 336, 450)(88, 202, 316, 430, 109, 223, 337, 451)(89, 203, 317, 431, 110, 224, 338, 452)(90, 204, 318, 432, 111, 225, 339, 453)(91, 205, 319, 433, 112, 226, 340, 454)(92, 206, 320, 434, 113, 227, 341, 455)(93, 207, 321, 435, 114, 228, 342, 456) L = (1, 116)(2, 117)(3, 115)(4, 121)(5, 123)(6, 125)(7, 122)(8, 118)(9, 124)(10, 119)(11, 126)(12, 120)(13, 133)(14, 135)(15, 137)(16, 139)(17, 141)(18, 143)(19, 134)(20, 127)(21, 136)(22, 128)(23, 138)(24, 129)(25, 140)(26, 130)(27, 142)(28, 131)(29, 144)(30, 132)(31, 156)(32, 158)(33, 160)(34, 162)(35, 148)(36, 163)(37, 165)(38, 167)(39, 152)(40, 168)(41, 170)(42, 157)(43, 145)(44, 159)(45, 146)(46, 161)(47, 147)(48, 149)(49, 164)(50, 150)(51, 166)(52, 151)(53, 153)(54, 169)(55, 154)(56, 171)(57, 155)(58, 187)(59, 189)(60, 191)(61, 174)(62, 192)(63, 194)(64, 196)(65, 198)(66, 179)(67, 199)(68, 201)(69, 203)(70, 205)(71, 184)(72, 206)(73, 188)(74, 172)(75, 190)(76, 173)(77, 175)(78, 193)(79, 176)(80, 195)(81, 177)(82, 197)(83, 178)(84, 180)(85, 200)(86, 181)(87, 202)(88, 182)(89, 204)(90, 183)(91, 185)(92, 207)(93, 186)(94, 228)(95, 218)(96, 209)(97, 224)(98, 222)(99, 220)(100, 226)(101, 214)(102, 225)(103, 216)(104, 210)(105, 208)(106, 227)(107, 212)(108, 221)(109, 211)(110, 223)(111, 217)(112, 215)(113, 213)(114, 219)(229, 345)(230, 343)(231, 344)(232, 350)(233, 352)(234, 354)(235, 346)(236, 349)(237, 347)(238, 351)(239, 348)(240, 353)(241, 362)(242, 364)(243, 366)(244, 368)(245, 370)(246, 372)(247, 355)(248, 361)(249, 356)(250, 363)(251, 357)(252, 365)(253, 358)(254, 367)(255, 359)(256, 369)(257, 360)(258, 371)(259, 385)(260, 387)(261, 389)(262, 377)(263, 390)(264, 392)(265, 394)(266, 381)(267, 395)(268, 397)(269, 399)(270, 373)(271, 384)(272, 374)(273, 386)(274, 375)(275, 388)(276, 376)(277, 378)(278, 391)(279, 379)(280, 393)(281, 380)(282, 382)(283, 396)(284, 383)(285, 398)(286, 416)(287, 418)(288, 403)(289, 419)(290, 421)(291, 423)(292, 425)(293, 408)(294, 426)(295, 428)(296, 430)(297, 432)(298, 413)(299, 433)(300, 435)(301, 400)(302, 415)(303, 401)(304, 417)(305, 402)(306, 404)(307, 420)(308, 405)(309, 422)(310, 406)(311, 424)(312, 407)(313, 409)(314, 427)(315, 410)(316, 429)(317, 411)(318, 431)(319, 412)(320, 414)(321, 434)(322, 447)(323, 438)(324, 446)(325, 451)(326, 449)(327, 455)(328, 443)(329, 454)(330, 445)(331, 453)(332, 437)(333, 456)(334, 441)(335, 450)(336, 440)(337, 452)(338, 439)(339, 444)(340, 442)(341, 448)(342, 436) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E20.1031 Transitivity :: VT+ Graph:: v = 57 e = 228 f = 133 degree seq :: [ 8^57 ] E20.1035 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 6, 6}) Quotient :: edge Aut^+ = (C19 : C3) : C2 (small group id <114, 1>) Aut = (C19 : C3) : C2 (small group id <114, 1>) |r| :: 1 Presentation :: [ X1^3, (X2 * X1^-1)^2, X2^6, (X2^-1 * X1^-1)^6, X1 * X2 * X1 * X2^2 * X1 * X2^-3 * X1 * X2 * X1 * X2^-3 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 7)(5, 10, 12)(6, 14, 11)(9, 19, 18)(13, 23, 25)(15, 28, 27)(16, 17, 30)(20, 35, 34)(21, 36, 24)(22, 26, 38)(29, 46, 45)(31, 48, 47)(32, 33, 50)(37, 56, 55)(39, 58, 41)(40, 54, 60)(42, 62, 57)(43, 44, 64)(49, 71, 70)(51, 73, 72)(52, 53, 75)(59, 83, 82)(61, 81, 85)(63, 88, 87)(65, 90, 89)(66, 67, 92)(68, 69, 94)(74, 101, 100)(76, 103, 102)(77, 104, 84)(78, 79, 106)(80, 86, 108)(91, 110, 111)(93, 113, 109)(95, 107, 114)(96, 97, 105)(98, 99, 112)(115, 117, 123, 134, 127, 119)(116, 120, 129, 143, 130, 121)(118, 124, 135, 151, 136, 125)(122, 131, 145, 163, 146, 132)(126, 137, 153, 173, 154, 138)(128, 140, 156, 177, 157, 141)(133, 147, 165, 188, 166, 148)(139, 149, 167, 190, 175, 155)(142, 158, 179, 205, 180, 159)(144, 160, 181, 207, 182, 161)(150, 168, 191, 219, 192, 169)(152, 170, 193, 221, 194, 171)(162, 183, 209, 220, 210, 184)(164, 185, 211, 218, 212, 186)(172, 195, 223, 206, 224, 196)(174, 197, 225, 204, 226, 198)(176, 200, 216, 189, 215, 201)(178, 202, 214, 187, 213, 203)(199, 217, 222, 228, 208, 227) L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228) local type(s) :: { ( 12^3 ), ( 12^6 ) } Outer automorphisms :: chiral Dual of E20.1036 Transitivity :: ET+ Graph:: simple bipartite v = 57 e = 114 f = 19 degree seq :: [ 3^38, 6^19 ] E20.1036 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 6, 6}) Quotient :: loop Aut^+ = (C19 : C3) : C2 (small group id <114, 1>) Aut = (C19 : C3) : C2 (small group id <114, 1>) |r| :: 1 Presentation :: [ (X1 * X2 * X1)^2, X2 * X1 * X2 * X1^-1 * X2^-1 * X1^-1, X2^6, X1^6, X2 * X1^-1 * X2^2 * X1^-2 * X2^2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 115, 2, 116, 6, 120, 18, 132, 13, 127, 4, 118)(3, 117, 9, 123, 27, 141, 55, 169, 33, 147, 11, 125)(5, 119, 15, 129, 38, 152, 44, 158, 19, 133, 16, 130)(7, 121, 21, 135, 14, 128, 34, 148, 51, 165, 23, 137)(8, 122, 24, 138, 52, 166, 74, 188, 41, 155, 25, 139)(10, 124, 29, 143, 57, 171, 94, 208, 61, 175, 31, 145)(12, 126, 28, 142, 42, 156, 75, 189, 66, 180, 36, 150)(17, 131, 40, 154, 71, 185, 84, 198, 49, 163, 22, 136)(20, 134, 45, 159, 80, 194, 68, 182, 37, 151, 46, 160)(26, 140, 54, 168, 89, 203, 109, 223, 78, 192, 43, 157)(30, 144, 59, 173, 96, 210, 114, 228, 86, 200, 50, 164)(32, 146, 58, 172, 91, 205, 113, 227, 99, 213, 63, 177)(35, 149, 56, 170, 92, 206, 110, 224, 90, 204, 64, 178)(39, 153, 69, 183, 100, 214, 111, 225, 79, 193, 48, 162)(47, 161, 82, 196, 62, 176, 95, 209, 104, 218, 73, 187)(53, 167, 87, 201, 60, 174, 97, 211, 105, 219, 77, 191)(65, 179, 93, 207, 106, 220, 98, 212, 108, 222, 88, 202)(67, 181, 76, 190, 107, 221, 85, 199, 72, 186, 101, 215)(70, 184, 102, 216, 103, 217, 81, 195, 112, 226, 83, 197) L = (1, 117)(2, 121)(3, 124)(4, 126)(5, 115)(6, 133)(7, 136)(8, 116)(9, 135)(10, 144)(11, 146)(12, 149)(13, 151)(14, 118)(15, 137)(16, 139)(17, 119)(18, 155)(19, 157)(20, 120)(21, 130)(22, 162)(23, 164)(24, 158)(25, 160)(26, 122)(27, 127)(28, 123)(29, 128)(30, 131)(31, 174)(32, 176)(33, 178)(34, 125)(35, 172)(36, 179)(37, 181)(38, 163)(39, 129)(40, 165)(41, 187)(42, 132)(43, 191)(44, 193)(45, 188)(46, 142)(47, 134)(48, 140)(49, 197)(50, 199)(51, 145)(52, 192)(53, 138)(54, 152)(55, 150)(56, 141)(57, 147)(58, 143)(59, 148)(60, 212)(61, 196)(62, 211)(63, 195)(64, 214)(65, 203)(66, 215)(67, 207)(68, 216)(69, 198)(70, 153)(71, 200)(72, 154)(73, 217)(74, 219)(75, 182)(76, 156)(77, 161)(78, 222)(79, 224)(80, 218)(81, 159)(82, 166)(83, 227)(84, 221)(85, 184)(86, 220)(87, 223)(88, 167)(89, 225)(90, 168)(91, 169)(92, 180)(93, 170)(94, 177)(95, 171)(96, 175)(97, 173)(98, 186)(99, 183)(100, 226)(101, 228)(102, 185)(103, 190)(104, 213)(105, 208)(106, 189)(107, 194)(108, 210)(109, 206)(110, 202)(111, 205)(112, 209)(113, 204)(114, 201) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E20.1035 Transitivity :: ET+ VT+ Graph:: v = 19 e = 114 f = 57 degree seq :: [ 12^19 ] E20.1037 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 6, 6}) Quotient :: edge Aut^+ = C2 x (C19 : C3) (small group id <114, 2>) Aut = C2 x (C19 : C3) (small group id <114, 2>) |r| :: 1 Presentation :: [ X1^3, X2^6, X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1, X2^2 * X1^-2 * X2^3 * X1^-1 * X2, X2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2, X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^2 ] Map:: 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, 33)(15, 39, 40)(17, 41, 43)(21, 38, 50)(22, 30, 52)(23, 53, 54)(25, 42, 57)(27, 59, 61)(28, 62, 35)(34, 49, 68)(36, 69, 70)(37, 71, 72)(44, 76, 78)(45, 79, 46)(47, 81, 82)(48, 83, 84)(51, 85, 86)(55, 60, 93)(56, 94, 95)(58, 96, 97)(63, 92, 102)(64, 103, 105)(65, 106, 66)(67, 108, 109)(73, 77, 91)(74, 90, 111)(75, 110, 101)(80, 114, 98)(87, 104, 113)(88, 112, 89)(99, 107, 100)(115, 117, 123, 139, 129, 119)(116, 120, 131, 156, 135, 121)(118, 125, 144, 171, 148, 126)(122, 136, 165, 153, 147, 137)(124, 141, 174, 154, 177, 142)(127, 149, 170, 138, 169, 150)(128, 151, 130, 140, 172, 152)(132, 158, 191, 164, 194, 159)(133, 160, 188, 155, 187, 161)(134, 162, 143, 157, 189, 163)(145, 178, 218, 182, 221, 179)(146, 180, 202, 166, 201, 181)(167, 203, 195, 199, 223, 204)(168, 205, 173, 200, 193, 206)(175, 212, 219, 216, 192, 213)(176, 214, 198, 207, 217, 215)(183, 224, 196, 208, 197, 225)(184, 226, 185, 209, 222, 210)(186, 227, 190, 211, 220, 228) L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228) local type(s) :: { ( 12^3 ), ( 12^6 ) } Outer automorphisms :: chiral Dual of E20.1038 Transitivity :: ET+ Graph:: simple bipartite v = 57 e = 114 f = 19 degree seq :: [ 3^38, 6^19 ] E20.1038 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 6, 6}) Quotient :: loop Aut^+ = C2 x (C19 : C3) (small group id <114, 2>) Aut = C2 x (C19 : C3) (small group id <114, 2>) |r| :: 1 Presentation :: [ X2^6, X2^3 * X1^3, X1^6, X2^3 * X1^-3, (X2^-1 * X1^-1)^3, X2^2 * X1^-1 * X2^-1 * X1^-1 * X2^2 * X1^-1, X2 * X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1 * X2^-1 * X1^-1 ] Map:: non-degenerate R = (1, 115, 2, 116, 6, 120, 18, 132, 13, 127, 4, 118)(3, 117, 9, 123, 27, 141, 17, 131, 33, 147, 11, 125)(5, 119, 15, 129, 31, 145, 10, 124, 30, 144, 16, 130)(7, 121, 21, 135, 45, 159, 26, 140, 50, 164, 23, 137)(8, 122, 24, 138, 48, 162, 22, 136, 47, 161, 25, 139)(12, 126, 35, 149, 42, 156, 19, 133, 41, 155, 36, 150)(14, 128, 37, 151, 44, 158, 20, 134, 43, 157, 28, 142)(29, 143, 58, 172, 95, 209, 57, 171, 94, 208, 59, 173)(32, 146, 62, 176, 92, 206, 55, 169, 91, 205, 63, 177)(34, 148, 64, 178, 38, 152, 56, 170, 93, 207, 60, 174)(39, 153, 69, 183, 98, 212, 61, 175, 97, 211, 70, 184)(40, 154, 71, 185, 81, 195, 46, 160, 80, 194, 72, 186)(49, 163, 84, 198, 111, 225, 78, 192, 110, 224, 85, 199)(51, 165, 86, 200, 52, 166, 79, 193, 112, 226, 82, 196)(53, 167, 87, 201, 114, 228, 83, 197, 113, 227, 88, 202)(54, 168, 89, 203, 104, 218, 73, 187, 103, 217, 90, 204)(65, 179, 100, 214, 106, 220, 74, 188, 105, 219, 99, 213)(66, 180, 101, 215, 67, 181, 75, 189, 107, 221, 76, 190)(68, 182, 102, 216, 109, 223, 77, 191, 108, 222, 96, 210) L = (1, 117)(2, 121)(3, 124)(4, 126)(5, 115)(6, 133)(7, 136)(8, 116)(9, 142)(10, 132)(11, 146)(12, 134)(13, 140)(14, 118)(15, 152)(16, 154)(17, 119)(18, 131)(19, 128)(20, 120)(21, 130)(22, 127)(23, 163)(24, 166)(25, 168)(26, 122)(27, 169)(28, 171)(29, 123)(30, 174)(31, 160)(32, 170)(33, 158)(34, 125)(35, 162)(36, 179)(37, 181)(38, 175)(39, 129)(40, 164)(41, 139)(42, 188)(43, 190)(44, 143)(45, 192)(46, 135)(47, 196)(48, 187)(49, 193)(50, 145)(51, 137)(52, 197)(53, 138)(54, 149)(55, 148)(56, 141)(57, 147)(58, 210)(59, 200)(60, 153)(61, 144)(62, 209)(63, 199)(64, 214)(65, 189)(66, 150)(67, 191)(68, 151)(69, 203)(70, 216)(71, 212)(72, 215)(73, 155)(74, 180)(75, 156)(76, 182)(77, 157)(78, 165)(79, 159)(80, 184)(81, 221)(82, 167)(83, 161)(84, 186)(85, 220)(86, 176)(87, 172)(88, 183)(89, 228)(90, 178)(91, 173)(92, 225)(93, 219)(94, 223)(95, 226)(96, 227)(97, 217)(98, 222)(99, 177)(100, 218)(101, 224)(102, 185)(103, 202)(104, 207)(105, 204)(106, 206)(107, 198)(108, 194)(109, 201)(110, 195)(111, 213)(112, 205)(113, 208)(114, 211) local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: chiral Dual of E20.1037 Transitivity :: ET+ VT+ Graph:: v = 19 e = 114 f = 57 degree seq :: [ 12^19 ] E20.1039 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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 * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, (T2 * T1^-1)^5, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: 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, 45, 40, 47)(46, 65, 48, 66)(49, 67, 51, 68)(50, 59, 52, 61)(60, 77, 62, 78)(63, 79, 64, 80)(69, 89, 71, 90)(70, 73, 72, 75)(74, 91, 76, 92)(81, 101, 83, 102)(82, 85, 84, 87)(86, 103, 88, 104)(93, 111, 95, 112)(94, 97, 96, 99)(98, 107, 100, 105)(106, 115, 108, 116)(109, 117, 110, 118)(113, 119, 114, 120)(121, 122, 124)(123, 128, 130)(125, 133, 134)(126, 135, 137)(127, 138, 139)(129, 136, 142)(131, 145, 146)(132, 147, 148)(140, 153, 154)(141, 155, 156)(143, 157, 158)(144, 159, 160)(149, 165, 166)(150, 167, 168)(151, 169, 170)(152, 171, 172)(161, 179, 180)(162, 181, 182)(163, 183, 174)(164, 184, 173)(175, 189, 190)(176, 191, 192)(177, 193, 194)(178, 195, 196)(185, 201, 202)(186, 203, 204)(187, 205, 206)(188, 207, 208)(197, 213, 214)(198, 215, 216)(199, 217, 218)(200, 219, 220)(209, 225, 226)(210, 227, 228)(211, 229, 222)(212, 230, 221)(223, 233, 232)(224, 234, 231)(235, 240, 238)(236, 239, 237) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 20^3 ), ( 20^4 ) } Outer automorphisms :: reflexible Dual of E20.1043 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 120 f = 12 degree seq :: [ 3^40, 4^30 ] E20.1040 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 10}) Quotient :: edge Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2 * T1^-1 * T2 * T1 * T2, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, (T2^-1 * T1^-1)^3, T2 * T1^2 * T2^4 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 18, 6, 17, 36, 16, 5)(2, 7, 20, 31, 13, 4, 12, 30, 24, 8)(9, 22, 41, 50, 29, 11, 23, 42, 47, 25)(14, 32, 52, 37, 19, 15, 33, 54, 40, 21)(26, 45, 65, 70, 49, 28, 46, 66, 69, 48)(34, 55, 75, 71, 51, 35, 56, 76, 74, 53)(38, 57, 77, 80, 60, 39, 58, 78, 79, 59)(43, 63, 83, 81, 61, 44, 64, 84, 82, 62)(67, 87, 103, 101, 85, 68, 88, 104, 102, 86)(72, 91, 107, 110, 94, 73, 92, 108, 109, 93)(89, 105, 117, 112, 96, 90, 106, 118, 111, 95)(97, 113, 119, 116, 100, 98, 114, 120, 115, 99)(121, 122, 126, 124)(123, 129, 137, 131)(125, 134, 138, 135)(127, 139, 132, 141)(128, 142, 133, 143)(130, 146, 156, 148)(136, 154, 147, 155)(140, 158, 150, 159)(144, 163, 151, 164)(145, 165, 149, 166)(152, 171, 153, 173)(157, 177, 160, 178)(161, 181, 162, 182)(167, 187, 170, 188)(168, 176, 169, 175)(172, 192, 174, 193)(179, 184, 180, 183)(185, 205, 186, 206)(189, 209, 190, 210)(191, 211, 194, 212)(195, 215, 196, 216)(197, 214, 198, 213)(199, 217, 200, 218)(201, 208, 202, 207)(203, 219, 204, 220)(221, 226, 222, 225)(223, 235, 224, 236)(227, 232, 228, 231)(229, 233, 230, 234)(237, 240, 238, 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) :: { ( 6^4 ), ( 6^10 ) } Outer automorphisms :: reflexible Dual of E20.1044 Transitivity :: ET+ Graph:: bipartite v = 42 e = 120 f = 40 degree seq :: [ 4^30, 10^12 ] E20.1041 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 10}) Quotient :: edge Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T2 * T1^-4 * T2 * T1, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^5 ] Map:: 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, 42, 29)(19, 45, 35)(20, 46, 47)(21, 40, 49)(22, 50, 32)(23, 30, 53)(27, 57, 58)(34, 54, 64)(36, 56, 65)(43, 68, 69)(44, 51, 71)(48, 73, 75)(52, 77, 55)(59, 66, 72)(60, 62, 84)(61, 85, 86)(63, 67, 88)(70, 92, 93)(74, 76, 91)(78, 79, 101)(80, 82, 102)(81, 103, 95)(83, 99, 105)(87, 94, 107)(89, 90, 108)(96, 113, 109)(97, 98, 114)(100, 106, 115)(104, 116, 117)(110, 119, 118)(111, 112, 120)(121, 122, 126, 136, 144, 165, 161, 152, 132, 124)(123, 129, 143, 172, 157, 155, 133, 154, 147, 130)(125, 134, 156, 140, 127, 139, 148, 179, 160, 135)(128, 141, 168, 163, 137, 159, 167, 194, 171, 142)(131, 149, 180, 199, 174, 145, 153, 183, 181, 150)(138, 164, 190, 187, 162, 170, 189, 207, 182, 151)(146, 175, 200, 210, 186, 158, 178, 203, 201, 176)(166, 192, 215, 218, 196, 169, 185, 209, 216, 193)(173, 198, 220, 219, 197, 184, 206, 224, 202, 177)(188, 211, 229, 232, 214, 191, 195, 217, 230, 212)(204, 213, 231, 236, 221, 208, 227, 238, 226, 205)(222, 235, 240, 234, 228, 225, 237, 239, 233, 223) 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) :: { ( 8^3 ), ( 8^10 ) } Outer automorphisms :: reflexible Dual of E20.1042 Transitivity :: ET+ Graph:: simple bipartite v = 52 e = 120 f = 30 degree seq :: [ 3^40, 10^12 ] E20.1042 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 10}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, (T2 * T1^-1)^5, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 121, 3, 123, 9, 129, 5, 125)(2, 122, 6, 126, 16, 136, 7, 127)(4, 124, 11, 131, 22, 142, 12, 132)(8, 128, 20, 140, 13, 133, 21, 141)(10, 130, 23, 143, 14, 134, 24, 144)(15, 135, 29, 149, 18, 138, 30, 150)(17, 137, 31, 151, 19, 139, 32, 152)(25, 145, 41, 161, 27, 147, 42, 162)(26, 146, 43, 163, 28, 148, 44, 164)(33, 153, 53, 173, 35, 155, 54, 174)(34, 154, 55, 175, 36, 156, 56, 176)(37, 157, 57, 177, 39, 159, 58, 178)(38, 158, 45, 165, 40, 160, 47, 167)(46, 166, 65, 185, 48, 168, 66, 186)(49, 169, 67, 187, 51, 171, 68, 188)(50, 170, 59, 179, 52, 172, 61, 181)(60, 180, 77, 197, 62, 182, 78, 198)(63, 183, 79, 199, 64, 184, 80, 200)(69, 189, 89, 209, 71, 191, 90, 210)(70, 190, 73, 193, 72, 192, 75, 195)(74, 194, 91, 211, 76, 196, 92, 212)(81, 201, 101, 221, 83, 203, 102, 222)(82, 202, 85, 205, 84, 204, 87, 207)(86, 206, 103, 223, 88, 208, 104, 224)(93, 213, 111, 231, 95, 215, 112, 232)(94, 214, 97, 217, 96, 216, 99, 219)(98, 218, 107, 227, 100, 220, 105, 225)(106, 226, 115, 235, 108, 228, 116, 236)(109, 229, 117, 237, 110, 230, 118, 238)(113, 233, 119, 239, 114, 234, 120, 240) L = (1, 122)(2, 124)(3, 128)(4, 121)(5, 133)(6, 135)(7, 138)(8, 130)(9, 136)(10, 123)(11, 145)(12, 147)(13, 134)(14, 125)(15, 137)(16, 142)(17, 126)(18, 139)(19, 127)(20, 153)(21, 155)(22, 129)(23, 157)(24, 159)(25, 146)(26, 131)(27, 148)(28, 132)(29, 165)(30, 167)(31, 169)(32, 171)(33, 154)(34, 140)(35, 156)(36, 141)(37, 158)(38, 143)(39, 160)(40, 144)(41, 179)(42, 181)(43, 183)(44, 184)(45, 166)(46, 149)(47, 168)(48, 150)(49, 170)(50, 151)(51, 172)(52, 152)(53, 164)(54, 163)(55, 189)(56, 191)(57, 193)(58, 195)(59, 180)(60, 161)(61, 182)(62, 162)(63, 174)(64, 173)(65, 201)(66, 203)(67, 205)(68, 207)(69, 190)(70, 175)(71, 192)(72, 176)(73, 194)(74, 177)(75, 196)(76, 178)(77, 213)(78, 215)(79, 217)(80, 219)(81, 202)(82, 185)(83, 204)(84, 186)(85, 206)(86, 187)(87, 208)(88, 188)(89, 225)(90, 227)(91, 229)(92, 230)(93, 214)(94, 197)(95, 216)(96, 198)(97, 218)(98, 199)(99, 220)(100, 200)(101, 212)(102, 211)(103, 233)(104, 234)(105, 226)(106, 209)(107, 228)(108, 210)(109, 222)(110, 221)(111, 224)(112, 223)(113, 232)(114, 231)(115, 240)(116, 239)(117, 236)(118, 235)(119, 237)(120, 238) local type(s) :: { ( 3, 10, 3, 10, 3, 10, 3, 10 ) } Outer automorphisms :: reflexible Dual of E20.1041 Transitivity :: ET+ VT+ AT Graph:: v = 30 e = 120 f = 52 degree seq :: [ 8^30 ] E20.1043 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 10}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2 * T1^-1 * T2 * T1 * T2, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, (T2^-1 * T1^-1)^3, T2 * T1^2 * T2^4 ] Map:: non-degenerate R = (1, 121, 3, 123, 10, 130, 27, 147, 18, 138, 6, 126, 17, 137, 36, 156, 16, 136, 5, 125)(2, 122, 7, 127, 20, 140, 31, 151, 13, 133, 4, 124, 12, 132, 30, 150, 24, 144, 8, 128)(9, 129, 22, 142, 41, 161, 50, 170, 29, 149, 11, 131, 23, 143, 42, 162, 47, 167, 25, 145)(14, 134, 32, 152, 52, 172, 37, 157, 19, 139, 15, 135, 33, 153, 54, 174, 40, 160, 21, 141)(26, 146, 45, 165, 65, 185, 70, 190, 49, 169, 28, 148, 46, 166, 66, 186, 69, 189, 48, 168)(34, 154, 55, 175, 75, 195, 71, 191, 51, 171, 35, 155, 56, 176, 76, 196, 74, 194, 53, 173)(38, 158, 57, 177, 77, 197, 80, 200, 60, 180, 39, 159, 58, 178, 78, 198, 79, 199, 59, 179)(43, 163, 63, 183, 83, 203, 81, 201, 61, 181, 44, 164, 64, 184, 84, 204, 82, 202, 62, 182)(67, 187, 87, 207, 103, 223, 101, 221, 85, 205, 68, 188, 88, 208, 104, 224, 102, 222, 86, 206)(72, 192, 91, 211, 107, 227, 110, 230, 94, 214, 73, 193, 92, 212, 108, 228, 109, 229, 93, 213)(89, 209, 105, 225, 117, 237, 112, 232, 96, 216, 90, 210, 106, 226, 118, 238, 111, 231, 95, 215)(97, 217, 113, 233, 119, 239, 116, 236, 100, 220, 98, 218, 114, 234, 120, 240, 115, 235, 99, 219) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 124)(7, 139)(8, 142)(9, 137)(10, 146)(11, 123)(12, 141)(13, 143)(14, 138)(15, 125)(16, 154)(17, 131)(18, 135)(19, 132)(20, 158)(21, 127)(22, 133)(23, 128)(24, 163)(25, 165)(26, 156)(27, 155)(28, 130)(29, 166)(30, 159)(31, 164)(32, 171)(33, 173)(34, 147)(35, 136)(36, 148)(37, 177)(38, 150)(39, 140)(40, 178)(41, 181)(42, 182)(43, 151)(44, 144)(45, 149)(46, 145)(47, 187)(48, 176)(49, 175)(50, 188)(51, 153)(52, 192)(53, 152)(54, 193)(55, 168)(56, 169)(57, 160)(58, 157)(59, 184)(60, 183)(61, 162)(62, 161)(63, 179)(64, 180)(65, 205)(66, 206)(67, 170)(68, 167)(69, 209)(70, 210)(71, 211)(72, 174)(73, 172)(74, 212)(75, 215)(76, 216)(77, 214)(78, 213)(79, 217)(80, 218)(81, 208)(82, 207)(83, 219)(84, 220)(85, 186)(86, 185)(87, 201)(88, 202)(89, 190)(90, 189)(91, 194)(92, 191)(93, 197)(94, 198)(95, 196)(96, 195)(97, 200)(98, 199)(99, 204)(100, 203)(101, 226)(102, 225)(103, 235)(104, 236)(105, 221)(106, 222)(107, 232)(108, 231)(109, 233)(110, 234)(111, 227)(112, 228)(113, 230)(114, 229)(115, 224)(116, 223)(117, 240)(118, 239)(119, 237)(120, 238) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E20.1039 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 120 f = 70 degree seq :: [ 20^12 ] E20.1044 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 10}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T2 * T1^-4 * T2 * T1, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^5 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 5, 125)(2, 122, 7, 127, 8, 128)(4, 124, 11, 131, 13, 133)(6, 126, 17, 137, 18, 138)(9, 129, 24, 144, 25, 145)(10, 130, 26, 146, 28, 148)(12, 132, 31, 151, 33, 153)(14, 134, 37, 157, 38, 158)(15, 135, 39, 159, 41, 161)(16, 136, 42, 162, 29, 149)(19, 139, 45, 165, 35, 155)(20, 140, 46, 166, 47, 167)(21, 141, 40, 160, 49, 169)(22, 142, 50, 170, 32, 152)(23, 143, 30, 150, 53, 173)(27, 147, 57, 177, 58, 178)(34, 154, 54, 174, 64, 184)(36, 156, 56, 176, 65, 185)(43, 163, 68, 188, 69, 189)(44, 164, 51, 171, 71, 191)(48, 168, 73, 193, 75, 195)(52, 172, 77, 197, 55, 175)(59, 179, 66, 186, 72, 192)(60, 180, 62, 182, 84, 204)(61, 181, 85, 205, 86, 206)(63, 183, 67, 187, 88, 208)(70, 190, 92, 212, 93, 213)(74, 194, 76, 196, 91, 211)(78, 198, 79, 199, 101, 221)(80, 200, 82, 202, 102, 222)(81, 201, 103, 223, 95, 215)(83, 203, 99, 219, 105, 225)(87, 207, 94, 214, 107, 227)(89, 209, 90, 210, 108, 228)(96, 216, 113, 233, 109, 229)(97, 217, 98, 218, 114, 234)(100, 220, 106, 226, 115, 235)(104, 224, 116, 236, 117, 237)(110, 230, 119, 239, 118, 238)(111, 231, 112, 232, 120, 240) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 139)(8, 141)(9, 143)(10, 123)(11, 149)(12, 124)(13, 154)(14, 156)(15, 125)(16, 144)(17, 159)(18, 164)(19, 148)(20, 127)(21, 168)(22, 128)(23, 172)(24, 165)(25, 153)(26, 175)(27, 130)(28, 179)(29, 180)(30, 131)(31, 138)(32, 132)(33, 183)(34, 147)(35, 133)(36, 140)(37, 155)(38, 178)(39, 167)(40, 135)(41, 152)(42, 170)(43, 137)(44, 190)(45, 161)(46, 192)(47, 194)(48, 163)(49, 185)(50, 189)(51, 142)(52, 157)(53, 198)(54, 145)(55, 200)(56, 146)(57, 173)(58, 203)(59, 160)(60, 199)(61, 150)(62, 151)(63, 181)(64, 206)(65, 209)(66, 158)(67, 162)(68, 211)(69, 207)(70, 187)(71, 195)(72, 215)(73, 166)(74, 171)(75, 217)(76, 169)(77, 184)(78, 220)(79, 174)(80, 210)(81, 176)(82, 177)(83, 201)(84, 213)(85, 204)(86, 224)(87, 182)(88, 227)(89, 216)(90, 186)(91, 229)(92, 188)(93, 231)(94, 191)(95, 218)(96, 193)(97, 230)(98, 196)(99, 197)(100, 219)(101, 208)(102, 235)(103, 222)(104, 202)(105, 237)(106, 205)(107, 238)(108, 225)(109, 232)(110, 212)(111, 236)(112, 214)(113, 223)(114, 228)(115, 240)(116, 221)(117, 239)(118, 226)(119, 233)(120, 234) local type(s) :: { ( 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E20.1040 Transitivity :: ET+ VT+ AT Graph:: simple v = 40 e = 120 f = 42 degree seq :: [ 6^40 ] E20.1045 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^2 * Y3^-1, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2^2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^10 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 15, 135, 17, 137)(7, 127, 18, 138, 19, 139)(9, 129, 16, 136, 22, 142)(11, 131, 25, 145, 26, 146)(12, 132, 27, 147, 28, 148)(20, 140, 33, 153, 34, 154)(21, 141, 35, 155, 36, 156)(23, 143, 37, 157, 38, 158)(24, 144, 39, 159, 40, 160)(29, 149, 45, 165, 46, 166)(30, 150, 47, 167, 48, 168)(31, 151, 49, 169, 50, 170)(32, 152, 51, 171, 52, 172)(41, 161, 59, 179, 60, 180)(42, 162, 61, 181, 62, 182)(43, 163, 63, 183, 54, 174)(44, 164, 64, 184, 53, 173)(55, 175, 69, 189, 70, 190)(56, 176, 71, 191, 72, 192)(57, 177, 73, 193, 74, 194)(58, 178, 75, 195, 76, 196)(65, 185, 81, 201, 82, 202)(66, 186, 83, 203, 84, 204)(67, 187, 85, 205, 86, 206)(68, 188, 87, 207, 88, 208)(77, 197, 93, 213, 94, 214)(78, 198, 95, 215, 96, 216)(79, 199, 97, 217, 98, 218)(80, 200, 99, 219, 100, 220)(89, 209, 105, 225, 106, 226)(90, 210, 107, 227, 108, 228)(91, 211, 109, 229, 102, 222)(92, 212, 110, 230, 101, 221)(103, 223, 113, 233, 112, 232)(104, 224, 114, 234, 111, 231)(115, 235, 120, 240, 118, 238)(116, 236, 119, 239, 117, 237)(241, 361, 243, 363, 249, 369, 245, 365)(242, 362, 246, 366, 256, 376, 247, 367)(244, 364, 251, 371, 262, 382, 252, 372)(248, 368, 260, 380, 253, 373, 261, 381)(250, 370, 263, 383, 254, 374, 264, 384)(255, 375, 269, 389, 258, 378, 270, 390)(257, 377, 271, 391, 259, 379, 272, 392)(265, 385, 281, 401, 267, 387, 282, 402)(266, 386, 283, 403, 268, 388, 284, 404)(273, 393, 293, 413, 275, 395, 294, 414)(274, 394, 295, 415, 276, 396, 296, 416)(277, 397, 297, 417, 279, 399, 298, 418)(278, 398, 285, 405, 280, 400, 287, 407)(286, 406, 305, 425, 288, 408, 306, 426)(289, 409, 307, 427, 291, 411, 308, 428)(290, 410, 299, 419, 292, 412, 301, 421)(300, 420, 317, 437, 302, 422, 318, 438)(303, 423, 319, 439, 304, 424, 320, 440)(309, 429, 329, 449, 311, 431, 330, 450)(310, 430, 313, 433, 312, 432, 315, 435)(314, 434, 331, 451, 316, 436, 332, 452)(321, 441, 341, 461, 323, 443, 342, 462)(322, 442, 325, 445, 324, 444, 327, 447)(326, 446, 343, 463, 328, 448, 344, 464)(333, 453, 351, 471, 335, 455, 352, 472)(334, 454, 337, 457, 336, 456, 339, 459)(338, 458, 347, 467, 340, 460, 345, 465)(346, 466, 355, 475, 348, 468, 356, 476)(349, 469, 357, 477, 350, 470, 358, 478)(353, 473, 359, 479, 354, 474, 360, 480) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 257)(7, 259)(8, 243)(9, 262)(10, 248)(11, 266)(12, 268)(13, 245)(14, 253)(15, 246)(16, 249)(17, 255)(18, 247)(19, 258)(20, 274)(21, 276)(22, 256)(23, 278)(24, 280)(25, 251)(26, 265)(27, 252)(28, 267)(29, 286)(30, 288)(31, 290)(32, 292)(33, 260)(34, 273)(35, 261)(36, 275)(37, 263)(38, 277)(39, 264)(40, 279)(41, 300)(42, 302)(43, 294)(44, 293)(45, 269)(46, 285)(47, 270)(48, 287)(49, 271)(50, 289)(51, 272)(52, 291)(53, 304)(54, 303)(55, 310)(56, 312)(57, 314)(58, 316)(59, 281)(60, 299)(61, 282)(62, 301)(63, 283)(64, 284)(65, 322)(66, 324)(67, 326)(68, 328)(69, 295)(70, 309)(71, 296)(72, 311)(73, 297)(74, 313)(75, 298)(76, 315)(77, 334)(78, 336)(79, 338)(80, 340)(81, 305)(82, 321)(83, 306)(84, 323)(85, 307)(86, 325)(87, 308)(88, 327)(89, 346)(90, 348)(91, 342)(92, 341)(93, 317)(94, 333)(95, 318)(96, 335)(97, 319)(98, 337)(99, 320)(100, 339)(101, 350)(102, 349)(103, 352)(104, 351)(105, 329)(106, 345)(107, 330)(108, 347)(109, 331)(110, 332)(111, 354)(112, 353)(113, 343)(114, 344)(115, 358)(116, 357)(117, 359)(118, 360)(119, 356)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E20.1048 Graph:: bipartite v = 70 e = 240 f = 132 degree seq :: [ 6^40, 8^30 ] E20.1046 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2, (Y3^-1 * Y1^-1)^3, Y2 * Y1^2 * Y2^4 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 17, 137, 11, 131)(5, 125, 14, 134, 18, 138, 15, 135)(7, 127, 19, 139, 12, 132, 21, 141)(8, 128, 22, 142, 13, 133, 23, 143)(10, 130, 26, 146, 36, 156, 28, 148)(16, 136, 34, 154, 27, 147, 35, 155)(20, 140, 38, 158, 30, 150, 39, 159)(24, 144, 43, 163, 31, 151, 44, 164)(25, 145, 45, 165, 29, 149, 46, 166)(32, 152, 51, 171, 33, 153, 53, 173)(37, 157, 57, 177, 40, 160, 58, 178)(41, 161, 61, 181, 42, 162, 62, 182)(47, 167, 67, 187, 50, 170, 68, 188)(48, 168, 56, 176, 49, 169, 55, 175)(52, 172, 72, 192, 54, 174, 73, 193)(59, 179, 64, 184, 60, 180, 63, 183)(65, 185, 85, 205, 66, 186, 86, 206)(69, 189, 89, 209, 70, 190, 90, 210)(71, 191, 91, 211, 74, 194, 92, 212)(75, 195, 95, 215, 76, 196, 96, 216)(77, 197, 94, 214, 78, 198, 93, 213)(79, 199, 97, 217, 80, 200, 98, 218)(81, 201, 88, 208, 82, 202, 87, 207)(83, 203, 99, 219, 84, 204, 100, 220)(101, 221, 106, 226, 102, 222, 105, 225)(103, 223, 115, 235, 104, 224, 116, 236)(107, 227, 112, 232, 108, 228, 111, 231)(109, 229, 113, 233, 110, 230, 114, 234)(117, 237, 120, 240, 118, 238, 119, 239)(241, 361, 243, 363, 250, 370, 267, 387, 258, 378, 246, 366, 257, 377, 276, 396, 256, 376, 245, 365)(242, 362, 247, 367, 260, 380, 271, 391, 253, 373, 244, 364, 252, 372, 270, 390, 264, 384, 248, 368)(249, 369, 262, 382, 281, 401, 290, 410, 269, 389, 251, 371, 263, 383, 282, 402, 287, 407, 265, 385)(254, 374, 272, 392, 292, 412, 277, 397, 259, 379, 255, 375, 273, 393, 294, 414, 280, 400, 261, 381)(266, 386, 285, 405, 305, 425, 310, 430, 289, 409, 268, 388, 286, 406, 306, 426, 309, 429, 288, 408)(274, 394, 295, 415, 315, 435, 311, 431, 291, 411, 275, 395, 296, 416, 316, 436, 314, 434, 293, 413)(278, 398, 297, 417, 317, 437, 320, 440, 300, 420, 279, 399, 298, 418, 318, 438, 319, 439, 299, 419)(283, 403, 303, 423, 323, 443, 321, 441, 301, 421, 284, 404, 304, 424, 324, 444, 322, 442, 302, 422)(307, 427, 327, 447, 343, 463, 341, 461, 325, 445, 308, 428, 328, 448, 344, 464, 342, 462, 326, 446)(312, 432, 331, 451, 347, 467, 350, 470, 334, 454, 313, 433, 332, 452, 348, 468, 349, 469, 333, 453)(329, 449, 345, 465, 357, 477, 352, 472, 336, 456, 330, 450, 346, 466, 358, 478, 351, 471, 335, 455)(337, 457, 353, 473, 359, 479, 356, 476, 340, 460, 338, 458, 354, 474, 360, 480, 355, 475, 339, 459) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 260)(8, 242)(9, 262)(10, 267)(11, 263)(12, 270)(13, 244)(14, 272)(15, 273)(16, 245)(17, 276)(18, 246)(19, 255)(20, 271)(21, 254)(22, 281)(23, 282)(24, 248)(25, 249)(26, 285)(27, 258)(28, 286)(29, 251)(30, 264)(31, 253)(32, 292)(33, 294)(34, 295)(35, 296)(36, 256)(37, 259)(38, 297)(39, 298)(40, 261)(41, 290)(42, 287)(43, 303)(44, 304)(45, 305)(46, 306)(47, 265)(48, 266)(49, 268)(50, 269)(51, 275)(52, 277)(53, 274)(54, 280)(55, 315)(56, 316)(57, 317)(58, 318)(59, 278)(60, 279)(61, 284)(62, 283)(63, 323)(64, 324)(65, 310)(66, 309)(67, 327)(68, 328)(69, 288)(70, 289)(71, 291)(72, 331)(73, 332)(74, 293)(75, 311)(76, 314)(77, 320)(78, 319)(79, 299)(80, 300)(81, 301)(82, 302)(83, 321)(84, 322)(85, 308)(86, 307)(87, 343)(88, 344)(89, 345)(90, 346)(91, 347)(92, 348)(93, 312)(94, 313)(95, 329)(96, 330)(97, 353)(98, 354)(99, 337)(100, 338)(101, 325)(102, 326)(103, 341)(104, 342)(105, 357)(106, 358)(107, 350)(108, 349)(109, 333)(110, 334)(111, 335)(112, 336)(113, 359)(114, 360)(115, 339)(116, 340)(117, 352)(118, 351)(119, 356)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 6, 2, 6, 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 E20.1047 Graph:: bipartite v = 42 e = 240 f = 160 degree seq :: [ 8^30, 20^12 ] E20.1047 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-2 * Y2, Y3^4 * Y2 * Y3^-1 * Y2, (Y3 * Y2^-1)^4, (Y3 * Y2)^5, (Y3 * Y2 * Y3)^5, (Y3^-1 * Y1^-1)^10 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362, 244, 364)(243, 363, 248, 368, 250, 370)(245, 365, 253, 373, 254, 374)(246, 366, 256, 376, 258, 378)(247, 367, 259, 379, 260, 380)(249, 369, 264, 384, 266, 386)(251, 371, 269, 389, 271, 391)(252, 372, 272, 392, 273, 393)(255, 375, 279, 399, 280, 400)(257, 377, 284, 404, 285, 405)(261, 381, 262, 382, 289, 409)(263, 383, 281, 401, 292, 412)(265, 385, 277, 397, 295, 415)(267, 387, 276, 396, 287, 407)(268, 388, 288, 408, 297, 417)(270, 390, 299, 419, 278, 398)(274, 394, 282, 402, 301, 421)(275, 395, 302, 422, 298, 418)(283, 403, 290, 410, 308, 428)(286, 406, 300, 420, 312, 432)(291, 411, 315, 435, 316, 436)(293, 413, 294, 414, 318, 438)(296, 416, 317, 437, 321, 441)(303, 423, 327, 447, 306, 426)(304, 424, 326, 446, 328, 448)(305, 425, 329, 449, 320, 440)(307, 427, 331, 451, 332, 452)(309, 429, 310, 430, 334, 454)(311, 431, 333, 453, 336, 456)(313, 433, 337, 457, 314, 434)(319, 439, 341, 461, 342, 462)(322, 442, 323, 443, 343, 463)(324, 444, 345, 465, 325, 445)(330, 450, 348, 468, 340, 460)(335, 455, 351, 471, 352, 472)(338, 458, 339, 459, 350, 470)(344, 464, 357, 477, 347, 467)(346, 466, 349, 469, 356, 476)(353, 473, 358, 478, 359, 479)(354, 474, 355, 475, 360, 480) L = (1, 243)(2, 246)(3, 249)(4, 251)(5, 241)(6, 257)(7, 242)(8, 262)(9, 265)(10, 267)(11, 270)(12, 244)(13, 275)(14, 277)(15, 245)(16, 282)(17, 268)(18, 276)(19, 281)(20, 288)(21, 247)(22, 291)(23, 248)(24, 294)(25, 271)(26, 260)(27, 272)(28, 250)(29, 279)(30, 286)(31, 287)(32, 290)(33, 300)(34, 252)(35, 274)(36, 253)(37, 303)(38, 254)(39, 305)(40, 264)(41, 255)(42, 307)(43, 256)(44, 310)(45, 273)(46, 258)(47, 259)(48, 313)(49, 284)(50, 261)(51, 296)(52, 317)(53, 263)(54, 319)(55, 292)(56, 266)(57, 308)(58, 269)(59, 323)(60, 324)(61, 299)(62, 326)(63, 322)(64, 278)(65, 304)(66, 280)(67, 311)(68, 333)(69, 283)(70, 335)(71, 285)(72, 302)(73, 293)(74, 289)(75, 339)(76, 297)(77, 330)(78, 315)(79, 320)(80, 295)(81, 337)(82, 298)(83, 344)(84, 309)(85, 301)(86, 346)(87, 341)(88, 327)(89, 348)(90, 306)(91, 349)(92, 312)(93, 338)(94, 331)(95, 316)(96, 345)(97, 351)(98, 314)(99, 353)(100, 318)(101, 355)(102, 321)(103, 329)(104, 332)(105, 357)(106, 325)(107, 328)(108, 358)(109, 359)(110, 334)(111, 354)(112, 336)(113, 342)(114, 340)(115, 356)(116, 343)(117, 360)(118, 347)(119, 352)(120, 350)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 8, 20 ), ( 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E20.1046 Graph:: simple bipartite v = 160 e = 240 f = 42 degree seq :: [ 2^120, 6^40 ] E20.1048 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1, Y1^4 * Y3^-1 * Y1^-1 * Y3^-1, (Y3^-1 * Y1^-1)^4, (Y1 * Y3^-1)^5 ] Map:: R = (1, 121, 2, 122, 6, 126, 16, 136, 24, 144, 45, 165, 41, 161, 32, 152, 12, 132, 4, 124)(3, 123, 9, 129, 23, 143, 52, 172, 37, 157, 35, 155, 13, 133, 34, 154, 27, 147, 10, 130)(5, 125, 14, 134, 36, 156, 20, 140, 7, 127, 19, 139, 28, 148, 59, 179, 40, 160, 15, 135)(8, 128, 21, 141, 48, 168, 43, 163, 17, 137, 39, 159, 47, 167, 74, 194, 51, 171, 22, 142)(11, 131, 29, 149, 60, 180, 79, 199, 54, 174, 25, 145, 33, 153, 63, 183, 61, 181, 30, 150)(18, 138, 44, 164, 70, 190, 67, 187, 42, 162, 50, 170, 69, 189, 87, 207, 62, 182, 31, 151)(26, 146, 55, 175, 80, 200, 90, 210, 66, 186, 38, 158, 58, 178, 83, 203, 81, 201, 56, 176)(46, 166, 72, 192, 95, 215, 98, 218, 76, 196, 49, 169, 65, 185, 89, 209, 96, 216, 73, 193)(53, 173, 78, 198, 100, 220, 99, 219, 77, 197, 64, 184, 86, 206, 104, 224, 82, 202, 57, 177)(68, 188, 91, 211, 109, 229, 112, 232, 94, 214, 71, 191, 75, 195, 97, 217, 110, 230, 92, 212)(84, 204, 93, 213, 111, 231, 116, 236, 101, 221, 88, 208, 107, 227, 118, 238, 106, 226, 85, 205)(102, 222, 115, 235, 120, 240, 114, 234, 108, 228, 105, 225, 117, 237, 119, 239, 113, 233, 103, 223)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 245)(4, 251)(5, 241)(6, 257)(7, 248)(8, 242)(9, 264)(10, 266)(11, 253)(12, 271)(13, 244)(14, 277)(15, 279)(16, 282)(17, 258)(18, 246)(19, 285)(20, 286)(21, 280)(22, 290)(23, 270)(24, 265)(25, 249)(26, 268)(27, 297)(28, 250)(29, 256)(30, 293)(31, 273)(32, 262)(33, 252)(34, 294)(35, 259)(36, 296)(37, 278)(38, 254)(39, 281)(40, 289)(41, 255)(42, 269)(43, 308)(44, 291)(45, 275)(46, 287)(47, 260)(48, 313)(49, 261)(50, 272)(51, 311)(52, 317)(53, 263)(54, 304)(55, 292)(56, 305)(57, 298)(58, 267)(59, 306)(60, 302)(61, 325)(62, 324)(63, 307)(64, 274)(65, 276)(66, 312)(67, 328)(68, 309)(69, 283)(70, 332)(71, 284)(72, 299)(73, 315)(74, 316)(75, 288)(76, 331)(77, 295)(78, 319)(79, 341)(80, 322)(81, 343)(82, 342)(83, 339)(84, 300)(85, 326)(86, 301)(87, 334)(88, 303)(89, 330)(90, 348)(91, 314)(92, 333)(93, 310)(94, 347)(95, 321)(96, 353)(97, 338)(98, 354)(99, 345)(100, 346)(101, 318)(102, 320)(103, 335)(104, 356)(105, 323)(106, 355)(107, 327)(108, 329)(109, 336)(110, 359)(111, 352)(112, 360)(113, 349)(114, 337)(115, 340)(116, 357)(117, 344)(118, 350)(119, 358)(120, 351)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 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 E20.1045 Graph:: simple bipartite v = 132 e = 240 f = 70 degree seq :: [ 2^120, 20^12 ] E20.1049 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^3, Y3^2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-2 * Y3, Y2 * Y1 * Y2^-4 * Y3^-1, Y2 * Y1^-1 * Y2 * Y3^-1 * Y2^2 * Y1, Y1 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, R * Y2 * Y1^-1 * Y2 * Y1^-1 * R * Y2^-2, Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2^3 * R * Y3 * Y2^-1 * Y1 * Y2 * R, Y2^-1 * Y1 * Y2^2 * Y3 * Y2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2, Y2^2 * R * Y2^-2 * R * Y1 * Y2^-2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 16, 136, 18, 138)(7, 127, 19, 139, 20, 140)(9, 129, 24, 144, 26, 146)(11, 131, 29, 149, 31, 151)(12, 132, 32, 152, 33, 153)(15, 135, 39, 159, 40, 160)(17, 137, 36, 156, 44, 164)(21, 141, 49, 169, 50, 170)(22, 142, 42, 162, 38, 158)(23, 143, 51, 171, 52, 172)(25, 145, 54, 174, 35, 155)(27, 147, 34, 154, 57, 177)(28, 148, 58, 178, 41, 161)(30, 150, 47, 167, 60, 180)(37, 157, 45, 165, 64, 184)(43, 163, 67, 187, 46, 166)(48, 168, 61, 181, 72, 192)(53, 173, 77, 197, 78, 198)(55, 175, 59, 179, 81, 201)(56, 176, 75, 195, 82, 202)(62, 182, 65, 185, 86, 206)(63, 183, 87, 207, 88, 208)(66, 186, 79, 199, 90, 210)(68, 188, 69, 189, 93, 213)(70, 190, 73, 193, 94, 214)(71, 191, 95, 215, 96, 216)(74, 194, 91, 211, 98, 218)(76, 196, 83, 203, 100, 220)(80, 200, 101, 221, 102, 222)(84, 204, 85, 205, 106, 226)(89, 209, 103, 223, 108, 228)(92, 212, 107, 227, 109, 229)(97, 217, 110, 230, 112, 232)(99, 219, 111, 231, 113, 233)(104, 224, 105, 225, 117, 237)(114, 234, 120, 240, 118, 238)(115, 235, 116, 236, 119, 239)(241, 361, 243, 363, 249, 369, 265, 385, 256, 376, 282, 402, 273, 393, 281, 401, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 283, 403, 269, 389, 278, 398, 254, 374, 277, 397, 261, 381, 247, 367)(244, 364, 251, 371, 270, 390, 263, 383, 248, 368, 262, 382, 260, 380, 288, 408, 274, 394, 252, 372)(250, 370, 267, 387, 296, 416, 293, 413, 264, 384, 272, 392, 292, 412, 316, 436, 299, 419, 268, 388)(253, 373, 275, 395, 302, 422, 309, 429, 285, 405, 258, 378, 280, 400, 306, 426, 303, 423, 276, 396)(259, 379, 286, 406, 310, 430, 325, 445, 301, 421, 271, 391, 290, 410, 314, 434, 311, 431, 287, 407)(266, 386, 295, 415, 320, 440, 319, 439, 294, 414, 298, 418, 318, 438, 329, 449, 305, 425, 279, 399)(284, 404, 308, 428, 332, 452, 331, 451, 307, 427, 304, 424, 328, 448, 337, 457, 313, 433, 289, 409)(291, 411, 312, 432, 336, 456, 345, 465, 323, 443, 297, 417, 300, 420, 324, 444, 339, 459, 315, 435)(317, 437, 340, 460, 353, 473, 356, 476, 343, 463, 321, 441, 322, 442, 344, 464, 354, 474, 341, 461)(326, 446, 342, 462, 355, 475, 350, 470, 333, 453, 330, 450, 348, 468, 358, 478, 347, 467, 327, 447)(334, 454, 349, 469, 359, 479, 357, 477, 346, 466, 338, 458, 352, 472, 360, 480, 351, 471, 335, 455) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 258)(7, 260)(8, 243)(9, 266)(10, 248)(11, 271)(12, 273)(13, 245)(14, 253)(15, 280)(16, 246)(17, 284)(18, 256)(19, 247)(20, 259)(21, 290)(22, 278)(23, 292)(24, 249)(25, 275)(26, 264)(27, 297)(28, 281)(29, 251)(30, 300)(31, 269)(32, 252)(33, 272)(34, 267)(35, 294)(36, 257)(37, 304)(38, 282)(39, 255)(40, 279)(41, 298)(42, 262)(43, 286)(44, 276)(45, 277)(46, 307)(47, 270)(48, 312)(49, 261)(50, 289)(51, 263)(52, 291)(53, 318)(54, 265)(55, 321)(56, 322)(57, 274)(58, 268)(59, 295)(60, 287)(61, 288)(62, 326)(63, 328)(64, 285)(65, 302)(66, 330)(67, 283)(68, 333)(69, 308)(70, 334)(71, 336)(72, 301)(73, 310)(74, 338)(75, 296)(76, 340)(77, 293)(78, 317)(79, 306)(80, 342)(81, 299)(82, 315)(83, 316)(84, 346)(85, 324)(86, 305)(87, 303)(88, 327)(89, 348)(90, 319)(91, 314)(92, 349)(93, 309)(94, 313)(95, 311)(96, 335)(97, 352)(98, 331)(99, 353)(100, 323)(101, 320)(102, 341)(103, 329)(104, 357)(105, 344)(106, 325)(107, 332)(108, 343)(109, 347)(110, 337)(111, 339)(112, 350)(113, 351)(114, 358)(115, 359)(116, 355)(117, 345)(118, 360)(119, 356)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 8, 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 E20.1050 Graph:: bipartite v = 52 e = 240 f = 150 degree seq :: [ 6^40, 20^12 ] E20.1050 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^2 * Y3^4, (Y3 * Y2^-1)^10 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 17, 137, 11, 131)(5, 125, 14, 134, 18, 138, 15, 135)(7, 127, 19, 139, 12, 132, 21, 141)(8, 128, 22, 142, 13, 133, 23, 143)(10, 130, 26, 146, 36, 156, 28, 148)(16, 136, 34, 154, 27, 147, 35, 155)(20, 140, 38, 158, 30, 150, 39, 159)(24, 144, 43, 163, 31, 151, 44, 164)(25, 145, 45, 165, 29, 149, 46, 166)(32, 152, 51, 171, 33, 153, 53, 173)(37, 157, 57, 177, 40, 160, 58, 178)(41, 161, 61, 181, 42, 162, 62, 182)(47, 167, 67, 187, 50, 170, 68, 188)(48, 168, 56, 176, 49, 169, 55, 175)(52, 172, 72, 192, 54, 174, 73, 193)(59, 179, 64, 184, 60, 180, 63, 183)(65, 185, 85, 205, 66, 186, 86, 206)(69, 189, 89, 209, 70, 190, 90, 210)(71, 191, 91, 211, 74, 194, 92, 212)(75, 195, 95, 215, 76, 196, 96, 216)(77, 197, 94, 214, 78, 198, 93, 213)(79, 199, 97, 217, 80, 200, 98, 218)(81, 201, 88, 208, 82, 202, 87, 207)(83, 203, 99, 219, 84, 204, 100, 220)(101, 221, 106, 226, 102, 222, 105, 225)(103, 223, 115, 235, 104, 224, 116, 236)(107, 227, 112, 232, 108, 228, 111, 231)(109, 229, 113, 233, 110, 230, 114, 234)(117, 237, 120, 240, 118, 238, 119, 239)(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, 260)(8, 242)(9, 262)(10, 267)(11, 263)(12, 270)(13, 244)(14, 272)(15, 273)(16, 245)(17, 276)(18, 246)(19, 255)(20, 271)(21, 254)(22, 281)(23, 282)(24, 248)(25, 249)(26, 285)(27, 258)(28, 286)(29, 251)(30, 264)(31, 253)(32, 292)(33, 294)(34, 295)(35, 296)(36, 256)(37, 259)(38, 297)(39, 298)(40, 261)(41, 290)(42, 287)(43, 303)(44, 304)(45, 305)(46, 306)(47, 265)(48, 266)(49, 268)(50, 269)(51, 275)(52, 277)(53, 274)(54, 280)(55, 315)(56, 316)(57, 317)(58, 318)(59, 278)(60, 279)(61, 284)(62, 283)(63, 323)(64, 324)(65, 310)(66, 309)(67, 327)(68, 328)(69, 288)(70, 289)(71, 291)(72, 331)(73, 332)(74, 293)(75, 311)(76, 314)(77, 320)(78, 319)(79, 299)(80, 300)(81, 301)(82, 302)(83, 321)(84, 322)(85, 308)(86, 307)(87, 343)(88, 344)(89, 345)(90, 346)(91, 347)(92, 348)(93, 312)(94, 313)(95, 329)(96, 330)(97, 353)(98, 354)(99, 337)(100, 338)(101, 325)(102, 326)(103, 341)(104, 342)(105, 357)(106, 358)(107, 350)(108, 349)(109, 333)(110, 334)(111, 335)(112, 336)(113, 359)(114, 360)(115, 339)(116, 340)(117, 352)(118, 351)(119, 356)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E20.1049 Graph:: simple bipartite v = 150 e = 240 f = 52 degree seq :: [ 2^120, 8^30 ] E20.1051 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 12}) Quotient :: regular Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^12, 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 ] 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, 97, 84, 68, 60, 43, 58)(52, 69, 53, 71, 63, 80, 95, 98, 83, 72, 54, 70)(75, 90, 76, 92, 78, 94, 99, 113, 105, 93, 77, 91)(85, 100, 86, 102, 88, 104, 112, 111, 96, 103, 87, 101)(106, 115, 107, 117, 109, 119, 120, 118, 110, 116, 108, 114) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 64)(49, 66)(51, 68)(55, 73)(56, 74)(57, 75)(58, 76)(59, 77)(60, 78)(65, 81)(67, 83)(69, 85)(70, 86)(71, 87)(72, 88)(79, 95)(80, 96)(82, 97)(84, 99)(89, 105)(90, 106)(91, 107)(92, 108)(93, 109)(94, 110)(98, 112)(100, 114)(101, 115)(102, 116)(103, 117)(104, 118)(111, 119)(113, 120) local type(s) :: { ( 10^12 ) } Outer automorphisms :: reflexible Dual of E20.1052 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 60 f = 12 degree seq :: [ 12^10 ] E20.1052 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 12}) Quotient :: regular Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^10, T1 * T2 * T1^-6 * T2 * T1^3, (T1 * T2)^12 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 15, 25, 39, 47, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 46, 34, 21, 14)(16, 26, 17, 28, 35, 49, 60, 53, 40, 27)(23, 36, 24, 38, 48, 61, 58, 45, 30, 37)(41, 54, 42, 56, 67, 74, 62, 57, 43, 55)(50, 63, 51, 65, 59, 72, 73, 66, 52, 64)(68, 79, 69, 81, 71, 83, 85, 82, 70, 80)(75, 86, 76, 88, 78, 90, 84, 89, 77, 87)(91, 101, 92, 103, 94, 105, 95, 104, 93, 102)(96, 106, 97, 108, 99, 110, 100, 109, 98, 107)(111, 116, 112, 117, 114, 119, 115, 120, 113, 118) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 67)(54, 68)(55, 69)(56, 70)(57, 71)(61, 73)(63, 75)(64, 76)(65, 77)(66, 78)(72, 84)(74, 85)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(86, 96)(87, 97)(88, 98)(89, 99)(90, 100)(101, 111)(102, 112)(103, 113)(104, 114)(105, 115)(106, 116)(107, 117)(108, 118)(109, 119)(110, 120) local type(s) :: { ( 12^10 ) } Outer automorphisms :: reflexible Dual of E20.1051 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 12 e = 60 f = 10 degree seq :: [ 10^12 ] E20.1053 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 12}) Quotient :: edge Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1)^2, T2^10, 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 ] Map:: polytopal R = (1, 3, 8, 17, 28, 43, 31, 19, 10, 4)(2, 5, 12, 22, 35, 50, 38, 24, 14, 6)(7, 15, 9, 18, 30, 45, 57, 42, 27, 16)(11, 20, 13, 23, 37, 52, 64, 49, 34, 21)(25, 39, 26, 41, 56, 71, 59, 44, 29, 40)(32, 46, 33, 48, 63, 77, 66, 51, 36, 47)(53, 67, 54, 69, 58, 72, 83, 70, 55, 68)(60, 73, 61, 75, 65, 78, 89, 76, 62, 74)(79, 91, 80, 93, 82, 95, 84, 94, 81, 92)(85, 96, 86, 98, 88, 100, 90, 99, 87, 97)(101, 111, 102, 113, 104, 115, 105, 114, 103, 112)(106, 116, 107, 118, 109, 120, 110, 119, 108, 117)(121, 122)(123, 127)(124, 129)(125, 131)(126, 133)(128, 134)(130, 132)(135, 145)(136, 146)(137, 147)(138, 149)(139, 150)(140, 152)(141, 153)(142, 154)(143, 156)(144, 157)(148, 158)(151, 155)(159, 173)(160, 174)(161, 175)(162, 176)(163, 177)(164, 178)(165, 179)(166, 180)(167, 181)(168, 182)(169, 183)(170, 184)(171, 185)(172, 186)(187, 199)(188, 200)(189, 201)(190, 202)(191, 203)(192, 204)(193, 205)(194, 206)(195, 207)(196, 208)(197, 209)(198, 210)(211, 221)(212, 222)(213, 223)(214, 224)(215, 225)(216, 226)(217, 227)(218, 228)(219, 229)(220, 230)(231, 236)(232, 238)(233, 237)(234, 240)(235, 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) :: { ( 24, 24 ), ( 24^10 ) } Outer automorphisms :: reflexible Dual of E20.1057 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 120 f = 10 degree seq :: [ 2^60, 10^12 ] E20.1054 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 12}) Quotient :: edge Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^10, T2^12 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 55, 75, 60, 41, 25, 13, 5)(2, 7, 17, 31, 49, 69, 88, 70, 50, 32, 18, 8)(4, 11, 23, 39, 59, 79, 92, 74, 54, 35, 20, 9)(6, 15, 29, 47, 67, 86, 102, 87, 68, 48, 30, 16)(12, 19, 34, 53, 73, 91, 105, 95, 78, 58, 38, 22)(14, 27, 45, 65, 84, 100, 112, 101, 85, 66, 46, 28)(24, 37, 57, 77, 94, 107, 114, 104, 90, 72, 52, 33)(26, 43, 63, 82, 98, 110, 118, 111, 99, 83, 64, 44)(40, 51, 71, 89, 103, 113, 119, 115, 106, 93, 76, 56)(42, 61, 80, 96, 108, 116, 120, 117, 109, 97, 81, 62)(121, 122, 126, 134, 146, 162, 160, 144, 132, 124)(123, 129, 139, 153, 171, 182, 163, 148, 135, 128)(125, 131, 142, 157, 176, 181, 164, 147, 136, 127)(130, 138, 149, 166, 183, 201, 191, 172, 154, 140)(133, 137, 150, 165, 184, 200, 196, 177, 158, 143)(141, 155, 173, 192, 209, 217, 202, 186, 167, 152)(145, 159, 178, 197, 213, 216, 203, 185, 168, 151)(156, 170, 187, 205, 218, 229, 223, 210, 193, 174)(161, 169, 188, 204, 219, 228, 226, 214, 198, 179)(175, 194, 211, 224, 233, 237, 230, 221, 206, 190)(180, 199, 215, 227, 235, 236, 231, 220, 207, 189)(195, 208, 222, 232, 238, 240, 239, 234, 225, 212) 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) :: { ( 4^10 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E20.1058 Transitivity :: ET+ Graph:: simple bipartite v = 22 e = 120 f = 60 degree seq :: [ 10^12, 12^10 ] E20.1055 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 12}) Quotient :: edge Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^12, 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 ] 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, 95)(80, 96)(82, 97)(84, 99)(89, 105)(90, 106)(91, 107)(92, 108)(93, 109)(94, 110)(98, 112)(100, 114)(101, 115)(102, 116)(103, 117)(104, 118)(111, 119)(113, 120)(121, 122, 125, 131, 140, 152, 167, 166, 151, 139, 130, 124)(123, 127, 135, 145, 159, 175, 184, 169, 153, 142, 132, 128)(126, 133, 129, 138, 149, 164, 181, 185, 168, 154, 141, 134)(136, 146, 137, 148, 155, 171, 186, 202, 193, 176, 160, 147)(143, 156, 144, 158, 170, 187, 201, 199, 182, 165, 150, 157)(161, 177, 162, 179, 194, 209, 217, 204, 188, 180, 163, 178)(172, 189, 173, 191, 183, 200, 215, 218, 203, 192, 174, 190)(195, 210, 196, 212, 198, 214, 219, 233, 225, 213, 197, 211)(205, 220, 206, 222, 208, 224, 232, 231, 216, 223, 207, 221)(226, 235, 227, 237, 229, 239, 240, 238, 230, 236, 228, 234) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 20, 20 ), ( 20^12 ) } Outer automorphisms :: reflexible Dual of E20.1056 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 120 f = 12 degree seq :: [ 2^60, 12^10 ] E20.1056 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 12}) Quotient :: loop Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1)^2, T2^10, 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 ] Map:: R = (1, 121, 3, 123, 8, 128, 17, 137, 28, 148, 43, 163, 31, 151, 19, 139, 10, 130, 4, 124)(2, 122, 5, 125, 12, 132, 22, 142, 35, 155, 50, 170, 38, 158, 24, 144, 14, 134, 6, 126)(7, 127, 15, 135, 9, 129, 18, 138, 30, 150, 45, 165, 57, 177, 42, 162, 27, 147, 16, 136)(11, 131, 20, 140, 13, 133, 23, 143, 37, 157, 52, 172, 64, 184, 49, 169, 34, 154, 21, 141)(25, 145, 39, 159, 26, 146, 41, 161, 56, 176, 71, 191, 59, 179, 44, 164, 29, 149, 40, 160)(32, 152, 46, 166, 33, 153, 48, 168, 63, 183, 77, 197, 66, 186, 51, 171, 36, 156, 47, 167)(53, 173, 67, 187, 54, 174, 69, 189, 58, 178, 72, 192, 83, 203, 70, 190, 55, 175, 68, 188)(60, 180, 73, 193, 61, 181, 75, 195, 65, 185, 78, 198, 89, 209, 76, 196, 62, 182, 74, 194)(79, 199, 91, 211, 80, 200, 93, 213, 82, 202, 95, 215, 84, 204, 94, 214, 81, 201, 92, 212)(85, 205, 96, 216, 86, 206, 98, 218, 88, 208, 100, 220, 90, 210, 99, 219, 87, 207, 97, 217)(101, 221, 111, 231, 102, 222, 113, 233, 104, 224, 115, 235, 105, 225, 114, 234, 103, 223, 112, 232)(106, 226, 116, 236, 107, 227, 118, 238, 109, 229, 120, 240, 110, 230, 119, 239, 108, 228, 117, 237) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 134)(9, 124)(10, 132)(11, 125)(12, 130)(13, 126)(14, 128)(15, 145)(16, 146)(17, 147)(18, 149)(19, 150)(20, 152)(21, 153)(22, 154)(23, 156)(24, 157)(25, 135)(26, 136)(27, 137)(28, 158)(29, 138)(30, 139)(31, 155)(32, 140)(33, 141)(34, 142)(35, 151)(36, 143)(37, 144)(38, 148)(39, 173)(40, 174)(41, 175)(42, 176)(43, 177)(44, 178)(45, 179)(46, 180)(47, 181)(48, 182)(49, 183)(50, 184)(51, 185)(52, 186)(53, 159)(54, 160)(55, 161)(56, 162)(57, 163)(58, 164)(59, 165)(60, 166)(61, 167)(62, 168)(63, 169)(64, 170)(65, 171)(66, 172)(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, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 221)(92, 222)(93, 223)(94, 224)(95, 225)(96, 226)(97, 227)(98, 228)(99, 229)(100, 230)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)(111, 236)(112, 238)(113, 237)(114, 240)(115, 239)(116, 231)(117, 233)(118, 232)(119, 235)(120, 234) local type(s) :: { ( 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 E20.1055 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 120 f = 70 degree seq :: [ 20^12 ] E20.1057 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 12}) Quotient :: loop Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^10, T2^12 ] Map:: R = (1, 121, 3, 123, 10, 130, 21, 141, 36, 156, 55, 175, 75, 195, 60, 180, 41, 161, 25, 145, 13, 133, 5, 125)(2, 122, 7, 127, 17, 137, 31, 151, 49, 169, 69, 189, 88, 208, 70, 190, 50, 170, 32, 152, 18, 138, 8, 128)(4, 124, 11, 131, 23, 143, 39, 159, 59, 179, 79, 199, 92, 212, 74, 194, 54, 174, 35, 155, 20, 140, 9, 129)(6, 126, 15, 135, 29, 149, 47, 167, 67, 187, 86, 206, 102, 222, 87, 207, 68, 188, 48, 168, 30, 150, 16, 136)(12, 132, 19, 139, 34, 154, 53, 173, 73, 193, 91, 211, 105, 225, 95, 215, 78, 198, 58, 178, 38, 158, 22, 142)(14, 134, 27, 147, 45, 165, 65, 185, 84, 204, 100, 220, 112, 232, 101, 221, 85, 205, 66, 186, 46, 166, 28, 148)(24, 144, 37, 157, 57, 177, 77, 197, 94, 214, 107, 227, 114, 234, 104, 224, 90, 210, 72, 192, 52, 172, 33, 153)(26, 146, 43, 163, 63, 183, 82, 202, 98, 218, 110, 230, 118, 238, 111, 231, 99, 219, 83, 203, 64, 184, 44, 164)(40, 160, 51, 171, 71, 191, 89, 209, 103, 223, 113, 233, 119, 239, 115, 235, 106, 226, 93, 213, 76, 196, 56, 176)(42, 162, 61, 181, 80, 200, 96, 216, 108, 228, 116, 236, 120, 240, 117, 237, 109, 229, 97, 217, 81, 201, 62, 182) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 131)(6, 134)(7, 125)(8, 123)(9, 139)(10, 138)(11, 142)(12, 124)(13, 137)(14, 146)(15, 128)(16, 127)(17, 150)(18, 149)(19, 153)(20, 130)(21, 155)(22, 157)(23, 133)(24, 132)(25, 159)(26, 162)(27, 136)(28, 135)(29, 166)(30, 165)(31, 145)(32, 141)(33, 171)(34, 140)(35, 173)(36, 170)(37, 176)(38, 143)(39, 178)(40, 144)(41, 169)(42, 160)(43, 148)(44, 147)(45, 184)(46, 183)(47, 152)(48, 151)(49, 188)(50, 187)(51, 182)(52, 154)(53, 192)(54, 156)(55, 194)(56, 181)(57, 158)(58, 197)(59, 161)(60, 199)(61, 164)(62, 163)(63, 201)(64, 200)(65, 168)(66, 167)(67, 205)(68, 204)(69, 180)(70, 175)(71, 172)(72, 209)(73, 174)(74, 211)(75, 208)(76, 177)(77, 213)(78, 179)(79, 215)(80, 196)(81, 191)(82, 186)(83, 185)(84, 219)(85, 218)(86, 190)(87, 189)(88, 222)(89, 217)(90, 193)(91, 224)(92, 195)(93, 216)(94, 198)(95, 227)(96, 203)(97, 202)(98, 229)(99, 228)(100, 207)(101, 206)(102, 232)(103, 210)(104, 233)(105, 212)(106, 214)(107, 235)(108, 226)(109, 223)(110, 221)(111, 220)(112, 238)(113, 237)(114, 225)(115, 236)(116, 231)(117, 230)(118, 240)(119, 234)(120, 239) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E20.1053 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 120 f = 72 degree seq :: [ 24^10 ] E20.1058 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 12}) Quotient :: loop Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^12, 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 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 12, 132)(7, 127, 16, 136)(8, 128, 17, 137)(10, 130, 15, 135)(11, 131, 21, 141)(13, 133, 23, 143)(14, 134, 24, 144)(18, 138, 30, 150)(19, 139, 29, 149)(20, 140, 33, 153)(22, 142, 35, 155)(25, 145, 40, 160)(26, 146, 41, 161)(27, 147, 42, 162)(28, 148, 43, 163)(31, 151, 39, 159)(32, 152, 48, 168)(34, 154, 50, 170)(36, 156, 52, 172)(37, 157, 53, 173)(38, 158, 54, 174)(44, 164, 62, 182)(45, 165, 63, 183)(46, 166, 61, 181)(47, 167, 64, 184)(49, 169, 66, 186)(51, 171, 68, 188)(55, 175, 73, 193)(56, 176, 74, 194)(57, 177, 75, 195)(58, 178, 76, 196)(59, 179, 77, 197)(60, 180, 78, 198)(65, 185, 81, 201)(67, 187, 83, 203)(69, 189, 85, 205)(70, 190, 86, 206)(71, 191, 87, 207)(72, 192, 88, 208)(79, 199, 95, 215)(80, 200, 96, 216)(82, 202, 97, 217)(84, 204, 99, 219)(89, 209, 105, 225)(90, 210, 106, 226)(91, 211, 107, 227)(92, 212, 108, 228)(93, 213, 109, 229)(94, 214, 110, 230)(98, 218, 112, 232)(100, 220, 114, 234)(101, 221, 115, 235)(102, 222, 116, 236)(103, 223, 117, 237)(104, 224, 118, 238)(111, 231, 119, 239)(113, 233, 120, 240) L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 131)(6, 133)(7, 135)(8, 123)(9, 138)(10, 124)(11, 140)(12, 128)(13, 129)(14, 126)(15, 145)(16, 146)(17, 148)(18, 149)(19, 130)(20, 152)(21, 134)(22, 132)(23, 156)(24, 158)(25, 159)(26, 137)(27, 136)(28, 155)(29, 164)(30, 157)(31, 139)(32, 167)(33, 142)(34, 141)(35, 171)(36, 144)(37, 143)(38, 170)(39, 175)(40, 147)(41, 177)(42, 179)(43, 178)(44, 181)(45, 150)(46, 151)(47, 166)(48, 154)(49, 153)(50, 187)(51, 186)(52, 189)(53, 191)(54, 190)(55, 184)(56, 160)(57, 162)(58, 161)(59, 194)(60, 163)(61, 185)(62, 165)(63, 200)(64, 169)(65, 168)(66, 202)(67, 201)(68, 180)(69, 173)(70, 172)(71, 183)(72, 174)(73, 176)(74, 209)(75, 210)(76, 212)(77, 211)(78, 214)(79, 182)(80, 215)(81, 199)(82, 193)(83, 192)(84, 188)(85, 220)(86, 222)(87, 221)(88, 224)(89, 217)(90, 196)(91, 195)(92, 198)(93, 197)(94, 219)(95, 218)(96, 223)(97, 204)(98, 203)(99, 233)(100, 206)(101, 205)(102, 208)(103, 207)(104, 232)(105, 213)(106, 235)(107, 237)(108, 234)(109, 239)(110, 236)(111, 216)(112, 231)(113, 225)(114, 226)(115, 227)(116, 228)(117, 229)(118, 230)(119, 240)(120, 238) local type(s) :: { ( 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E20.1054 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 60 e = 120 f = 22 degree seq :: [ 4^60 ] E20.1059 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 12}) Quotient :: dipole Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^10, (Y3 * Y2^-1)^12 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 14, 134)(10, 130, 12, 132)(15, 135, 25, 145)(16, 136, 26, 146)(17, 137, 27, 147)(18, 138, 29, 149)(19, 139, 30, 150)(20, 140, 32, 152)(21, 141, 33, 153)(22, 142, 34, 154)(23, 143, 36, 156)(24, 144, 37, 157)(28, 148, 38, 158)(31, 151, 35, 155)(39, 159, 53, 173)(40, 160, 54, 174)(41, 161, 55, 175)(42, 162, 56, 176)(43, 163, 57, 177)(44, 164, 58, 178)(45, 165, 59, 179)(46, 166, 60, 180)(47, 167, 61, 181)(48, 168, 62, 182)(49, 169, 63, 183)(50, 170, 64, 184)(51, 171, 65, 185)(52, 172, 66, 186)(67, 187, 79, 199)(68, 188, 80, 200)(69, 189, 81, 201)(70, 190, 82, 202)(71, 191, 83, 203)(72, 192, 84, 204)(73, 193, 85, 205)(74, 194, 86, 206)(75, 195, 87, 207)(76, 196, 88, 208)(77, 197, 89, 209)(78, 198, 90, 210)(91, 211, 101, 221)(92, 212, 102, 222)(93, 213, 103, 223)(94, 214, 104, 224)(95, 215, 105, 225)(96, 216, 106, 226)(97, 217, 107, 227)(98, 218, 108, 228)(99, 219, 109, 229)(100, 220, 110, 230)(111, 231, 116, 236)(112, 232, 118, 238)(113, 233, 117, 237)(114, 234, 120, 240)(115, 235, 119, 239)(241, 361, 243, 363, 248, 368, 257, 377, 268, 388, 283, 403, 271, 391, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 275, 395, 290, 410, 278, 398, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 249, 369, 258, 378, 270, 390, 285, 405, 297, 417, 282, 402, 267, 387, 256, 376)(251, 371, 260, 380, 253, 373, 263, 383, 277, 397, 292, 412, 304, 424, 289, 409, 274, 394, 261, 381)(265, 385, 279, 399, 266, 386, 281, 401, 296, 416, 311, 431, 299, 419, 284, 404, 269, 389, 280, 400)(272, 392, 286, 406, 273, 393, 288, 408, 303, 423, 317, 437, 306, 426, 291, 411, 276, 396, 287, 407)(293, 413, 307, 427, 294, 414, 309, 429, 298, 418, 312, 432, 323, 443, 310, 430, 295, 415, 308, 428)(300, 420, 313, 433, 301, 421, 315, 435, 305, 425, 318, 438, 329, 449, 316, 436, 302, 422, 314, 434)(319, 439, 331, 451, 320, 440, 333, 453, 322, 442, 335, 455, 324, 444, 334, 454, 321, 441, 332, 452)(325, 445, 336, 456, 326, 446, 338, 458, 328, 448, 340, 460, 330, 450, 339, 459, 327, 447, 337, 457)(341, 461, 351, 471, 342, 462, 353, 473, 344, 464, 355, 475, 345, 465, 354, 474, 343, 463, 352, 472)(346, 466, 356, 476, 347, 467, 358, 478, 349, 469, 360, 480, 350, 470, 359, 479, 348, 468, 357, 477) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 254)(9, 244)(10, 252)(11, 245)(12, 250)(13, 246)(14, 248)(15, 265)(16, 266)(17, 267)(18, 269)(19, 270)(20, 272)(21, 273)(22, 274)(23, 276)(24, 277)(25, 255)(26, 256)(27, 257)(28, 278)(29, 258)(30, 259)(31, 275)(32, 260)(33, 261)(34, 262)(35, 271)(36, 263)(37, 264)(38, 268)(39, 293)(40, 294)(41, 295)(42, 296)(43, 297)(44, 298)(45, 299)(46, 300)(47, 301)(48, 302)(49, 303)(50, 304)(51, 305)(52, 306)(53, 279)(54, 280)(55, 281)(56, 282)(57, 283)(58, 284)(59, 285)(60, 286)(61, 287)(62, 288)(63, 289)(64, 290)(65, 291)(66, 292)(67, 319)(68, 320)(69, 321)(70, 322)(71, 323)(72, 324)(73, 325)(74, 326)(75, 327)(76, 328)(77, 329)(78, 330)(79, 307)(80, 308)(81, 309)(82, 310)(83, 311)(84, 312)(85, 313)(86, 314)(87, 315)(88, 316)(89, 317)(90, 318)(91, 341)(92, 342)(93, 343)(94, 344)(95, 345)(96, 346)(97, 347)(98, 348)(99, 349)(100, 350)(101, 331)(102, 332)(103, 333)(104, 334)(105, 335)(106, 336)(107, 337)(108, 338)(109, 339)(110, 340)(111, 356)(112, 358)(113, 357)(114, 360)(115, 359)(116, 351)(117, 353)(118, 352)(119, 355)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 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 E20.1062 Graph:: bipartite v = 72 e = 240 f = 130 degree seq :: [ 4^60, 20^12 ] E20.1060 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 12}) Quotient :: dipole Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^10, Y2^12 ] Map:: R = (1, 121, 2, 122, 6, 126, 14, 134, 26, 146, 42, 162, 40, 160, 24, 144, 12, 132, 4, 124)(3, 123, 9, 129, 19, 139, 33, 153, 51, 171, 62, 182, 43, 163, 28, 148, 15, 135, 8, 128)(5, 125, 11, 131, 22, 142, 37, 157, 56, 176, 61, 181, 44, 164, 27, 147, 16, 136, 7, 127)(10, 130, 18, 138, 29, 149, 46, 166, 63, 183, 81, 201, 71, 191, 52, 172, 34, 154, 20, 140)(13, 133, 17, 137, 30, 150, 45, 165, 64, 184, 80, 200, 76, 196, 57, 177, 38, 158, 23, 143)(21, 141, 35, 155, 53, 173, 72, 192, 89, 209, 97, 217, 82, 202, 66, 186, 47, 167, 32, 152)(25, 145, 39, 159, 58, 178, 77, 197, 93, 213, 96, 216, 83, 203, 65, 185, 48, 168, 31, 151)(36, 156, 50, 170, 67, 187, 85, 205, 98, 218, 109, 229, 103, 223, 90, 210, 73, 193, 54, 174)(41, 161, 49, 169, 68, 188, 84, 204, 99, 219, 108, 228, 106, 226, 94, 214, 78, 198, 59, 179)(55, 175, 74, 194, 91, 211, 104, 224, 113, 233, 117, 237, 110, 230, 101, 221, 86, 206, 70, 190)(60, 180, 79, 199, 95, 215, 107, 227, 115, 235, 116, 236, 111, 231, 100, 220, 87, 207, 69, 189)(75, 195, 88, 208, 102, 222, 112, 232, 118, 238, 120, 240, 119, 239, 114, 234, 105, 225, 92, 212)(241, 361, 243, 363, 250, 370, 261, 381, 276, 396, 295, 415, 315, 435, 300, 420, 281, 401, 265, 385, 253, 373, 245, 365)(242, 362, 247, 367, 257, 377, 271, 391, 289, 409, 309, 429, 328, 448, 310, 430, 290, 410, 272, 392, 258, 378, 248, 368)(244, 364, 251, 371, 263, 383, 279, 399, 299, 419, 319, 439, 332, 452, 314, 434, 294, 414, 275, 395, 260, 380, 249, 369)(246, 366, 255, 375, 269, 389, 287, 407, 307, 427, 326, 446, 342, 462, 327, 447, 308, 428, 288, 408, 270, 390, 256, 376)(252, 372, 259, 379, 274, 394, 293, 413, 313, 433, 331, 451, 345, 465, 335, 455, 318, 438, 298, 418, 278, 398, 262, 382)(254, 374, 267, 387, 285, 405, 305, 425, 324, 444, 340, 460, 352, 472, 341, 461, 325, 445, 306, 426, 286, 406, 268, 388)(264, 384, 277, 397, 297, 417, 317, 437, 334, 454, 347, 467, 354, 474, 344, 464, 330, 450, 312, 432, 292, 412, 273, 393)(266, 386, 283, 403, 303, 423, 322, 442, 338, 458, 350, 470, 358, 478, 351, 471, 339, 459, 323, 443, 304, 424, 284, 404)(280, 400, 291, 411, 311, 431, 329, 449, 343, 463, 353, 473, 359, 479, 355, 475, 346, 466, 333, 453, 316, 436, 296, 416)(282, 402, 301, 421, 320, 440, 336, 456, 348, 468, 356, 476, 360, 480, 357, 477, 349, 469, 337, 457, 321, 441, 302, 422) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 261)(11, 263)(12, 259)(13, 245)(14, 267)(15, 269)(16, 246)(17, 271)(18, 248)(19, 274)(20, 249)(21, 276)(22, 252)(23, 279)(24, 277)(25, 253)(26, 283)(27, 285)(28, 254)(29, 287)(30, 256)(31, 289)(32, 258)(33, 264)(34, 293)(35, 260)(36, 295)(37, 297)(38, 262)(39, 299)(40, 291)(41, 265)(42, 301)(43, 303)(44, 266)(45, 305)(46, 268)(47, 307)(48, 270)(49, 309)(50, 272)(51, 311)(52, 273)(53, 313)(54, 275)(55, 315)(56, 280)(57, 317)(58, 278)(59, 319)(60, 281)(61, 320)(62, 282)(63, 322)(64, 284)(65, 324)(66, 286)(67, 326)(68, 288)(69, 328)(70, 290)(71, 329)(72, 292)(73, 331)(74, 294)(75, 300)(76, 296)(77, 334)(78, 298)(79, 332)(80, 336)(81, 302)(82, 338)(83, 304)(84, 340)(85, 306)(86, 342)(87, 308)(88, 310)(89, 343)(90, 312)(91, 345)(92, 314)(93, 316)(94, 347)(95, 318)(96, 348)(97, 321)(98, 350)(99, 323)(100, 352)(101, 325)(102, 327)(103, 353)(104, 330)(105, 335)(106, 333)(107, 354)(108, 356)(109, 337)(110, 358)(111, 339)(112, 341)(113, 359)(114, 344)(115, 346)(116, 360)(117, 349)(118, 351)(119, 355)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 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 E20.1061 Graph:: bipartite v = 22 e = 240 f = 180 degree seq :: [ 20^12, 24^10 ] E20.1061 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 12}) Quotient :: dipole Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, Y3^12, (Y3^-1 * Y2)^10, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 254, 374)(250, 370, 252, 372)(255, 375, 265, 385)(256, 376, 266, 386)(257, 377, 267, 387)(258, 378, 269, 389)(259, 379, 270, 390)(260, 380, 272, 392)(261, 381, 273, 393)(262, 382, 274, 394)(263, 383, 276, 396)(264, 384, 277, 397)(268, 388, 278, 398)(271, 391, 275, 395)(279, 399, 295, 415)(280, 400, 296, 416)(281, 401, 297, 417)(282, 402, 298, 418)(283, 403, 299, 419)(284, 404, 301, 421)(285, 405, 302, 422)(286, 406, 303, 423)(287, 407, 304, 424)(288, 408, 305, 425)(289, 409, 306, 426)(290, 410, 307, 427)(291, 411, 308, 428)(292, 412, 310, 430)(293, 413, 311, 431)(294, 414, 312, 432)(300, 420, 309, 429)(313, 433, 329, 449)(314, 434, 330, 450)(315, 435, 331, 451)(316, 436, 332, 452)(317, 437, 333, 453)(318, 438, 334, 454)(319, 439, 335, 455)(320, 440, 336, 456)(321, 441, 337, 457)(322, 442, 338, 458)(323, 443, 339, 459)(324, 444, 340, 460)(325, 445, 341, 461)(326, 446, 342, 462)(327, 447, 343, 463)(328, 448, 344, 464)(345, 465, 353, 473)(346, 466, 352, 472)(347, 467, 355, 475)(348, 468, 354, 474)(349, 469, 358, 478)(350, 470, 359, 479)(351, 471, 356, 476)(357, 477, 360, 480) L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 257)(9, 258)(10, 244)(11, 260)(12, 262)(13, 263)(14, 246)(15, 249)(16, 247)(17, 268)(18, 270)(19, 250)(20, 253)(21, 251)(22, 275)(23, 277)(24, 254)(25, 279)(26, 281)(27, 256)(28, 283)(29, 280)(30, 285)(31, 259)(32, 287)(33, 289)(34, 261)(35, 291)(36, 288)(37, 293)(38, 264)(39, 266)(40, 265)(41, 298)(42, 267)(43, 300)(44, 269)(45, 303)(46, 271)(47, 273)(48, 272)(49, 307)(50, 274)(51, 309)(52, 276)(53, 312)(54, 278)(55, 313)(56, 315)(57, 314)(58, 317)(59, 282)(60, 286)(61, 319)(62, 284)(63, 318)(64, 321)(65, 323)(66, 322)(67, 325)(68, 290)(69, 294)(70, 327)(71, 292)(72, 326)(73, 296)(74, 295)(75, 301)(76, 297)(77, 334)(78, 299)(79, 336)(80, 302)(81, 305)(82, 304)(83, 310)(84, 306)(85, 342)(86, 308)(87, 344)(88, 311)(89, 345)(90, 347)(91, 346)(92, 349)(93, 316)(94, 320)(95, 348)(96, 350)(97, 352)(98, 354)(99, 353)(100, 356)(101, 324)(102, 328)(103, 355)(104, 357)(105, 330)(106, 329)(107, 332)(108, 331)(109, 359)(110, 333)(111, 335)(112, 338)(113, 337)(114, 340)(115, 339)(116, 360)(117, 341)(118, 343)(119, 351)(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) :: { ( 20, 24 ), ( 20, 24, 20, 24 ) } Outer automorphisms :: reflexible Dual of E20.1060 Graph:: simple bipartite v = 180 e = 240 f = 22 degree seq :: [ 2^120, 4^60 ] E20.1062 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 12}) Quotient :: dipole Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^-2 * Y3^-1, Y1^12, (Y3^-1 * Y1)^10 ] Map:: polytopal R = (1, 121, 2, 122, 5, 125, 11, 131, 20, 140, 32, 152, 47, 167, 46, 166, 31, 151, 19, 139, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 25, 145, 39, 159, 55, 175, 64, 184, 49, 169, 33, 153, 22, 142, 12, 132, 8, 128)(6, 126, 13, 133, 9, 129, 18, 138, 29, 149, 44, 164, 61, 181, 65, 185, 48, 168, 34, 154, 21, 141, 14, 134)(16, 136, 26, 146, 17, 137, 28, 148, 35, 155, 51, 171, 66, 186, 82, 202, 73, 193, 56, 176, 40, 160, 27, 147)(23, 143, 36, 156, 24, 144, 38, 158, 50, 170, 67, 187, 81, 201, 79, 199, 62, 182, 45, 165, 30, 150, 37, 157)(41, 161, 57, 177, 42, 162, 59, 179, 74, 194, 89, 209, 97, 217, 84, 204, 68, 188, 60, 180, 43, 163, 58, 178)(52, 172, 69, 189, 53, 173, 71, 191, 63, 183, 80, 200, 95, 215, 98, 218, 83, 203, 72, 192, 54, 174, 70, 190)(75, 195, 90, 210, 76, 196, 92, 212, 78, 198, 94, 214, 99, 219, 113, 233, 105, 225, 93, 213, 77, 197, 91, 211)(85, 205, 100, 220, 86, 206, 102, 222, 88, 208, 104, 224, 112, 232, 111, 231, 96, 216, 103, 223, 87, 207, 101, 221)(106, 226, 115, 235, 107, 227, 117, 237, 109, 229, 119, 239, 120, 240, 118, 238, 110, 230, 116, 236, 108, 228, 114, 234)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 255)(11, 261)(12, 245)(13, 263)(14, 264)(15, 250)(16, 247)(17, 248)(18, 270)(19, 269)(20, 273)(21, 251)(22, 275)(23, 253)(24, 254)(25, 280)(26, 281)(27, 282)(28, 283)(29, 259)(30, 258)(31, 279)(32, 288)(33, 260)(34, 290)(35, 262)(36, 292)(37, 293)(38, 294)(39, 271)(40, 265)(41, 266)(42, 267)(43, 268)(44, 302)(45, 303)(46, 301)(47, 304)(48, 272)(49, 306)(50, 274)(51, 308)(52, 276)(53, 277)(54, 278)(55, 313)(56, 314)(57, 315)(58, 316)(59, 317)(60, 318)(61, 286)(62, 284)(63, 285)(64, 287)(65, 321)(66, 289)(67, 323)(68, 291)(69, 325)(70, 326)(71, 327)(72, 328)(73, 295)(74, 296)(75, 297)(76, 298)(77, 299)(78, 300)(79, 335)(80, 336)(81, 305)(82, 337)(83, 307)(84, 339)(85, 309)(86, 310)(87, 311)(88, 312)(89, 345)(90, 346)(91, 347)(92, 348)(93, 349)(94, 350)(95, 319)(96, 320)(97, 322)(98, 352)(99, 324)(100, 354)(101, 355)(102, 356)(103, 357)(104, 358)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 359)(112, 338)(113, 360)(114, 340)(115, 341)(116, 342)(117, 343)(118, 344)(119, 351)(120, 353)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E20.1059 Graph:: simple bipartite v = 130 e = 240 f = 72 degree seq :: [ 2^120, 24^10 ] E20.1063 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 12}) Quotient :: dipole Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |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)^10 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 14, 134)(10, 130, 12, 132)(15, 135, 25, 145)(16, 136, 26, 146)(17, 137, 27, 147)(18, 138, 29, 149)(19, 139, 30, 150)(20, 140, 32, 152)(21, 141, 33, 153)(22, 142, 34, 154)(23, 143, 36, 156)(24, 144, 37, 157)(28, 148, 38, 158)(31, 151, 35, 155)(39, 159, 55, 175)(40, 160, 56, 176)(41, 161, 57, 177)(42, 162, 58, 178)(43, 163, 59, 179)(44, 164, 61, 181)(45, 165, 62, 182)(46, 166, 63, 183)(47, 167, 64, 184)(48, 168, 65, 185)(49, 169, 66, 186)(50, 170, 67, 187)(51, 171, 68, 188)(52, 172, 70, 190)(53, 173, 71, 191)(54, 174, 72, 192)(60, 180, 69, 189)(73, 193, 89, 209)(74, 194, 90, 210)(75, 195, 91, 211)(76, 196, 92, 212)(77, 197, 93, 213)(78, 198, 94, 214)(79, 199, 95, 215)(80, 200, 96, 216)(81, 201, 97, 217)(82, 202, 98, 218)(83, 203, 99, 219)(84, 204, 100, 220)(85, 205, 101, 221)(86, 206, 102, 222)(87, 207, 103, 223)(88, 208, 104, 224)(105, 225, 113, 233)(106, 226, 112, 232)(107, 227, 115, 235)(108, 228, 114, 234)(109, 229, 118, 238)(110, 230, 119, 239)(111, 231, 116, 236)(117, 237, 120, 240)(241, 361, 243, 363, 248, 368, 257, 377, 268, 388, 283, 403, 300, 420, 286, 406, 271, 391, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 275, 395, 291, 411, 309, 429, 294, 414, 278, 398, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 249, 369, 258, 378, 270, 390, 285, 405, 303, 423, 318, 438, 299, 419, 282, 402, 267, 387, 256, 376)(251, 371, 260, 380, 253, 373, 263, 383, 277, 397, 293, 413, 312, 432, 326, 446, 308, 428, 290, 410, 274, 394, 261, 381)(265, 385, 279, 399, 266, 386, 281, 401, 298, 418, 317, 437, 334, 454, 320, 440, 302, 422, 284, 404, 269, 389, 280, 400)(272, 392, 287, 407, 273, 393, 289, 409, 307, 427, 325, 445, 342, 462, 328, 448, 311, 431, 292, 412, 276, 396, 288, 408)(295, 415, 313, 433, 296, 416, 315, 435, 301, 421, 319, 439, 336, 456, 350, 470, 333, 453, 316, 436, 297, 417, 314, 434)(304, 424, 321, 441, 305, 425, 323, 443, 310, 430, 327, 447, 344, 464, 357, 477, 341, 461, 324, 444, 306, 426, 322, 442)(329, 449, 345, 465, 330, 450, 347, 467, 332, 452, 349, 469, 359, 479, 351, 471, 335, 455, 348, 468, 331, 451, 346, 466)(337, 457, 352, 472, 338, 458, 354, 474, 340, 460, 356, 476, 360, 480, 358, 478, 343, 463, 355, 475, 339, 459, 353, 473) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 254)(9, 244)(10, 252)(11, 245)(12, 250)(13, 246)(14, 248)(15, 265)(16, 266)(17, 267)(18, 269)(19, 270)(20, 272)(21, 273)(22, 274)(23, 276)(24, 277)(25, 255)(26, 256)(27, 257)(28, 278)(29, 258)(30, 259)(31, 275)(32, 260)(33, 261)(34, 262)(35, 271)(36, 263)(37, 264)(38, 268)(39, 295)(40, 296)(41, 297)(42, 298)(43, 299)(44, 301)(45, 302)(46, 303)(47, 304)(48, 305)(49, 306)(50, 307)(51, 308)(52, 310)(53, 311)(54, 312)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 309)(61, 284)(62, 285)(63, 286)(64, 287)(65, 288)(66, 289)(67, 290)(68, 291)(69, 300)(70, 292)(71, 293)(72, 294)(73, 329)(74, 330)(75, 331)(76, 332)(77, 333)(78, 334)(79, 335)(80, 336)(81, 337)(82, 338)(83, 339)(84, 340)(85, 341)(86, 342)(87, 343)(88, 344)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 353)(106, 352)(107, 355)(108, 354)(109, 358)(110, 359)(111, 356)(112, 346)(113, 345)(114, 348)(115, 347)(116, 351)(117, 360)(118, 349)(119, 350)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E20.1064 Graph:: bipartite v = 70 e = 240 f = 132 degree seq :: [ 4^60, 24^10 ] E20.1064 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 10, 12}) Quotient :: dipole Aut^+ = (C10 x S3) : C2 (small group id <120, 13>) Aut = D24 x D10 (small group id <240, 136>) |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, Y1^10, (Y3 * Y2^-1)^12 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 14, 134, 26, 146, 42, 162, 40, 160, 24, 144, 12, 132, 4, 124)(3, 123, 9, 129, 19, 139, 33, 153, 51, 171, 62, 182, 43, 163, 28, 148, 15, 135, 8, 128)(5, 125, 11, 131, 22, 142, 37, 157, 56, 176, 61, 181, 44, 164, 27, 147, 16, 136, 7, 127)(10, 130, 18, 138, 29, 149, 46, 166, 63, 183, 81, 201, 71, 191, 52, 172, 34, 154, 20, 140)(13, 133, 17, 137, 30, 150, 45, 165, 64, 184, 80, 200, 76, 196, 57, 177, 38, 158, 23, 143)(21, 141, 35, 155, 53, 173, 72, 192, 89, 209, 97, 217, 82, 202, 66, 186, 47, 167, 32, 152)(25, 145, 39, 159, 58, 178, 77, 197, 93, 213, 96, 216, 83, 203, 65, 185, 48, 168, 31, 151)(36, 156, 50, 170, 67, 187, 85, 205, 98, 218, 109, 229, 103, 223, 90, 210, 73, 193, 54, 174)(41, 161, 49, 169, 68, 188, 84, 204, 99, 219, 108, 228, 106, 226, 94, 214, 78, 198, 59, 179)(55, 175, 74, 194, 91, 211, 104, 224, 113, 233, 117, 237, 110, 230, 101, 221, 86, 206, 70, 190)(60, 180, 79, 199, 95, 215, 107, 227, 115, 235, 116, 236, 111, 231, 100, 220, 87, 207, 69, 189)(75, 195, 88, 208, 102, 222, 112, 232, 118, 238, 120, 240, 119, 239, 114, 234, 105, 225, 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, 255)(7, 257)(8, 242)(9, 244)(10, 261)(11, 263)(12, 259)(13, 245)(14, 267)(15, 269)(16, 246)(17, 271)(18, 248)(19, 274)(20, 249)(21, 276)(22, 252)(23, 279)(24, 277)(25, 253)(26, 283)(27, 285)(28, 254)(29, 287)(30, 256)(31, 289)(32, 258)(33, 264)(34, 293)(35, 260)(36, 295)(37, 297)(38, 262)(39, 299)(40, 291)(41, 265)(42, 301)(43, 303)(44, 266)(45, 305)(46, 268)(47, 307)(48, 270)(49, 309)(50, 272)(51, 311)(52, 273)(53, 313)(54, 275)(55, 315)(56, 280)(57, 317)(58, 278)(59, 319)(60, 281)(61, 320)(62, 282)(63, 322)(64, 284)(65, 324)(66, 286)(67, 326)(68, 288)(69, 328)(70, 290)(71, 329)(72, 292)(73, 331)(74, 294)(75, 300)(76, 296)(77, 334)(78, 298)(79, 332)(80, 336)(81, 302)(82, 338)(83, 304)(84, 340)(85, 306)(86, 342)(87, 308)(88, 310)(89, 343)(90, 312)(91, 345)(92, 314)(93, 316)(94, 347)(95, 318)(96, 348)(97, 321)(98, 350)(99, 323)(100, 352)(101, 325)(102, 327)(103, 353)(104, 330)(105, 335)(106, 333)(107, 354)(108, 356)(109, 337)(110, 358)(111, 339)(112, 341)(113, 359)(114, 344)(115, 346)(116, 360)(117, 349)(118, 351)(119, 355)(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, 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 E20.1063 Graph:: simple bipartite v = 132 e = 240 f = 70 degree seq :: [ 2^120, 20^12 ] E20.1065 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 60}) Quotient :: regular Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2 * T1^-1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^7 * T2 * T1^-10 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 89, 101, 113, 109, 96, 85, 73, 60, 49, 33, 16, 28, 42, 35, 46, 58, 70, 82, 94, 106, 118, 120, 119, 108, 97, 84, 72, 61, 48, 32, 45, 34, 17, 29, 43, 56, 68, 80, 92, 104, 116, 112, 100, 88, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 31, 47, 59, 71, 83, 95, 107, 114, 105, 91, 78, 69, 55, 40, 30, 14, 6, 13, 27, 21, 37, 51, 63, 75, 87, 99, 111, 117, 103, 90, 81, 67, 54, 44, 26, 12, 25, 20, 9, 19, 36, 50, 62, 74, 86, 98, 110, 115, 102, 93, 79, 66, 57, 41, 24, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 96)(87, 97)(88, 99)(89, 102)(91, 104)(93, 106)(95, 108)(98, 109)(100, 107)(101, 114)(103, 116)(105, 118)(110, 119)(111, 113)(112, 115)(117, 120) local type(s) :: { ( 6^60 ) } Outer automorphisms :: reflexible Dual of E20.1066 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 60 f = 20 degree seq :: [ 60^2 ] E20.1066 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 60}) Quotient :: regular Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * 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, (T1^-1 * T2)^60 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 23, 27, 25, 16, 24)(21, 28, 26, 30, 22, 29)(31, 37, 33, 39, 32, 38)(34, 40, 36, 42, 35, 41)(43, 49, 45, 51, 44, 50)(46, 82, 48, 84, 47, 83)(52, 88, 56, 96, 61, 90)(53, 91, 62, 95, 55, 93)(54, 92, 63, 102, 66, 94)(57, 97, 68, 101, 60, 89)(58, 98, 69, 100, 59, 99)(64, 103, 67, 105, 65, 104)(70, 106, 72, 108, 71, 107)(73, 109, 75, 111, 74, 110)(76, 112, 78, 114, 77, 113)(79, 115, 81, 117, 80, 116)(85, 118, 87, 120, 86, 119) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 68)(50, 57)(51, 60)(52, 89)(53, 92)(54, 84)(55, 94)(56, 97)(58, 88)(59, 90)(61, 101)(62, 102)(63, 83)(64, 91)(65, 93)(66, 82)(67, 95)(69, 96)(70, 98)(71, 99)(72, 100)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(85, 112)(86, 113)(87, 114)(115, 118)(116, 119)(117, 120) local type(s) :: { ( 60^6 ) } Outer automorphisms :: reflexible Dual of E20.1065 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 20 e = 60 f = 2 degree seq :: [ 6^20 ] E20.1067 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 60}) Quotient :: edge Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^60 ] Map:: R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 24, 18, 9, 16)(11, 19, 28, 22, 13, 20)(23, 31, 26, 33, 25, 32)(27, 34, 30, 36, 29, 35)(37, 43, 39, 45, 38, 44)(40, 46, 42, 48, 41, 47)(49, 55, 51, 57, 50, 52)(53, 76, 59, 78, 61, 77)(54, 85, 63, 87, 56, 82)(58, 89, 67, 91, 60, 83)(62, 93, 65, 86, 64, 84)(66, 97, 69, 90, 68, 88)(70, 95, 72, 94, 71, 92)(73, 99, 75, 98, 74, 96)(79, 102, 81, 101, 80, 100)(103, 106, 105, 108, 104, 107)(109, 115, 111, 117, 110, 112)(113, 114, 118, 120, 119, 116)(121, 122)(123, 127)(124, 129)(125, 131)(126, 133)(128, 132)(130, 134)(135, 143)(136, 145)(137, 144)(138, 146)(139, 147)(140, 149)(141, 148)(142, 150)(151, 157)(152, 158)(153, 159)(154, 160)(155, 161)(156, 162)(163, 169)(164, 170)(165, 171)(166, 196)(167, 197)(168, 198)(172, 202)(173, 203)(174, 204)(175, 205)(176, 206)(177, 207)(178, 208)(179, 209)(180, 210)(181, 211)(182, 212)(183, 213)(184, 214)(185, 215)(186, 216)(187, 217)(188, 218)(189, 219)(190, 220)(191, 221)(192, 222)(193, 223)(194, 224)(195, 225)(199, 229)(200, 230)(201, 231)(226, 234)(227, 236)(228, 240)(232, 233)(235, 238)(237, 239) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 120, 120 ), ( 120^6 ) } Outer automorphisms :: reflexible Dual of E20.1071 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 120 f = 2 degree seq :: [ 2^60, 6^20 ] E20.1068 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 60}) Quotient :: edge Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-1 * T1^-3, T2^-1 * T1 * T2^-1 * T1^3, (T2^-2 * T1)^2, T2^-2 * T1 * T2^17 * T1 * T2^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 49, 61, 73, 85, 97, 109, 115, 103, 91, 79, 67, 55, 43, 31, 20, 13, 21, 33, 45, 57, 69, 81, 93, 105, 117, 120, 114, 102, 90, 78, 66, 54, 42, 30, 18, 6, 17, 29, 41, 53, 65, 77, 89, 101, 113, 112, 100, 88, 76, 64, 52, 40, 28, 15, 5)(2, 7, 19, 32, 44, 56, 68, 80, 92, 104, 116, 107, 95, 83, 71, 59, 47, 35, 23, 9, 4, 12, 26, 38, 50, 62, 74, 86, 98, 110, 119, 108, 96, 84, 72, 60, 48, 36, 24, 11, 16, 14, 27, 39, 51, 63, 75, 87, 99, 111, 118, 106, 94, 82, 70, 58, 46, 34, 22, 8)(121, 122, 126, 136, 133, 124)(123, 129, 137, 128, 141, 131)(125, 134, 138, 132, 140, 127)(130, 144, 149, 143, 153, 142)(135, 146, 150, 139, 151, 147)(145, 154, 161, 156, 165, 155)(148, 152, 162, 159, 163, 158)(157, 167, 173, 166, 177, 168)(160, 171, 174, 170, 175, 164)(169, 180, 185, 179, 189, 178)(172, 182, 186, 176, 187, 183)(181, 190, 197, 192, 201, 191)(184, 188, 198, 195, 199, 194)(193, 203, 209, 202, 213, 204)(196, 207, 210, 206, 211, 200)(205, 216, 221, 215, 225, 214)(208, 218, 222, 212, 223, 219)(217, 226, 233, 228, 237, 227)(220, 224, 234, 231, 235, 230)(229, 236, 232, 238, 240, 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) :: { ( 4^6 ), ( 4^60 ) } Outer automorphisms :: reflexible Dual of E20.1072 Transitivity :: ET+ Graph:: bipartite v = 22 e = 120 f = 60 degree seq :: [ 6^20, 60^2 ] E20.1069 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 60}) Quotient :: edge Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-3 * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^7 * T2 * T1^-10 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 96)(87, 97)(88, 99)(89, 102)(91, 104)(93, 106)(95, 108)(98, 109)(100, 107)(101, 114)(103, 116)(105, 118)(110, 119)(111, 113)(112, 115)(117, 120)(121, 122, 125, 131, 143, 159, 173, 185, 197, 209, 221, 233, 229, 216, 205, 193, 180, 169, 153, 136, 148, 162, 155, 166, 178, 190, 202, 214, 226, 238, 240, 239, 228, 217, 204, 192, 181, 168, 152, 165, 154, 137, 149, 163, 176, 188, 200, 212, 224, 236, 232, 220, 208, 196, 184, 172, 158, 142, 130, 124)(123, 127, 135, 151, 167, 179, 191, 203, 215, 227, 234, 225, 211, 198, 189, 175, 160, 150, 134, 126, 133, 147, 141, 157, 171, 183, 195, 207, 219, 231, 237, 223, 210, 201, 187, 174, 164, 146, 132, 145, 140, 129, 139, 156, 170, 182, 194, 206, 218, 230, 235, 222, 213, 199, 186, 177, 161, 144, 138, 128) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12, 12 ), ( 12^60 ) } Outer automorphisms :: reflexible Dual of E20.1070 Transitivity :: ET+ Graph:: simple bipartite v = 62 e = 120 f = 20 degree seq :: [ 2^60, 60^2 ] E20.1070 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 60}) Quotient :: loop Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^60 ] Map:: R = (1, 121, 3, 123, 8, 128, 17, 137, 10, 130, 4, 124)(2, 122, 5, 125, 12, 132, 21, 141, 14, 134, 6, 126)(7, 127, 15, 135, 24, 144, 18, 138, 9, 129, 16, 136)(11, 131, 19, 139, 28, 148, 22, 142, 13, 133, 20, 140)(23, 143, 31, 151, 26, 146, 33, 153, 25, 145, 32, 152)(27, 147, 34, 154, 30, 150, 36, 156, 29, 149, 35, 155)(37, 157, 43, 163, 39, 159, 45, 165, 38, 158, 44, 164)(40, 160, 46, 166, 42, 162, 48, 168, 41, 161, 47, 167)(49, 169, 85, 205, 51, 171, 89, 209, 50, 170, 87, 207)(52, 172, 92, 212, 59, 179, 110, 230, 61, 181, 94, 214)(53, 173, 96, 216, 63, 183, 114, 234, 65, 185, 98, 218)(54, 174, 100, 220, 68, 188, 104, 224, 55, 175, 95, 215)(56, 176, 105, 225, 70, 190, 108, 228, 57, 177, 91, 211)(58, 178, 109, 229, 72, 192, 112, 232, 60, 180, 97, 217)(62, 182, 111, 231, 76, 196, 113, 233, 64, 184, 93, 213)(66, 186, 115, 235, 69, 189, 102, 222, 67, 187, 99, 219)(71, 191, 118, 238, 74, 194, 103, 223, 73, 193, 101, 221)(75, 195, 120, 240, 78, 198, 107, 227, 77, 197, 106, 226)(79, 199, 119, 239, 81, 201, 117, 237, 80, 200, 116, 236)(82, 202, 86, 206, 84, 204, 90, 210, 83, 203, 88, 208) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 132)(9, 124)(10, 134)(11, 125)(12, 128)(13, 126)(14, 130)(15, 143)(16, 145)(17, 144)(18, 146)(19, 147)(20, 149)(21, 148)(22, 150)(23, 135)(24, 137)(25, 136)(26, 138)(27, 139)(28, 141)(29, 140)(30, 142)(31, 157)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 169)(44, 170)(45, 171)(46, 189)(47, 186)(48, 187)(49, 163)(50, 164)(51, 165)(52, 211)(53, 215)(54, 219)(55, 222)(56, 209)(57, 205)(58, 212)(59, 225)(60, 214)(61, 228)(62, 216)(63, 220)(64, 218)(65, 224)(66, 167)(67, 168)(68, 235)(69, 166)(70, 207)(71, 229)(72, 230)(73, 217)(74, 232)(75, 231)(76, 234)(77, 213)(78, 233)(79, 238)(80, 221)(81, 223)(82, 240)(83, 226)(84, 227)(85, 177)(86, 239)(87, 190)(88, 236)(89, 176)(90, 237)(91, 172)(92, 178)(93, 197)(94, 180)(95, 173)(96, 182)(97, 193)(98, 184)(99, 174)(100, 183)(101, 200)(102, 175)(103, 201)(104, 185)(105, 179)(106, 203)(107, 204)(108, 181)(109, 191)(110, 192)(111, 195)(112, 194)(113, 198)(114, 196)(115, 188)(116, 208)(117, 210)(118, 199)(119, 206)(120, 202) local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) } Outer automorphisms :: reflexible Dual of E20.1069 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 20 e = 120 f = 62 degree seq :: [ 12^20 ] E20.1071 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 60}) Quotient :: loop Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-1 * T1^-3, T2^-1 * T1 * T2^-1 * T1^3, (T2^-2 * T1)^2, T2^-2 * T1 * T2^17 * T1 * T2^-1 ] Map:: R = (1, 121, 3, 123, 10, 130, 25, 145, 37, 157, 49, 169, 61, 181, 73, 193, 85, 205, 97, 217, 109, 229, 115, 235, 103, 223, 91, 211, 79, 199, 67, 187, 55, 175, 43, 163, 31, 151, 20, 140, 13, 133, 21, 141, 33, 153, 45, 165, 57, 177, 69, 189, 81, 201, 93, 213, 105, 225, 117, 237, 120, 240, 114, 234, 102, 222, 90, 210, 78, 198, 66, 186, 54, 174, 42, 162, 30, 150, 18, 138, 6, 126, 17, 137, 29, 149, 41, 161, 53, 173, 65, 185, 77, 197, 89, 209, 101, 221, 113, 233, 112, 232, 100, 220, 88, 208, 76, 196, 64, 184, 52, 172, 40, 160, 28, 148, 15, 135, 5, 125)(2, 122, 7, 127, 19, 139, 32, 152, 44, 164, 56, 176, 68, 188, 80, 200, 92, 212, 104, 224, 116, 236, 107, 227, 95, 215, 83, 203, 71, 191, 59, 179, 47, 167, 35, 155, 23, 143, 9, 129, 4, 124, 12, 132, 26, 146, 38, 158, 50, 170, 62, 182, 74, 194, 86, 206, 98, 218, 110, 230, 119, 239, 108, 228, 96, 216, 84, 204, 72, 192, 60, 180, 48, 168, 36, 156, 24, 144, 11, 131, 16, 136, 14, 134, 27, 147, 39, 159, 51, 171, 63, 183, 75, 195, 87, 207, 99, 219, 111, 231, 118, 238, 106, 226, 94, 214, 82, 202, 70, 190, 58, 178, 46, 166, 34, 154, 22, 142, 8, 128) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 125)(8, 141)(9, 137)(10, 144)(11, 123)(12, 140)(13, 124)(14, 138)(15, 146)(16, 133)(17, 128)(18, 132)(19, 151)(20, 127)(21, 131)(22, 130)(23, 153)(24, 149)(25, 154)(26, 150)(27, 135)(28, 152)(29, 143)(30, 139)(31, 147)(32, 162)(33, 142)(34, 161)(35, 145)(36, 165)(37, 167)(38, 148)(39, 163)(40, 171)(41, 156)(42, 159)(43, 158)(44, 160)(45, 155)(46, 177)(47, 173)(48, 157)(49, 180)(50, 175)(51, 174)(52, 182)(53, 166)(54, 170)(55, 164)(56, 187)(57, 168)(58, 169)(59, 189)(60, 185)(61, 190)(62, 186)(63, 172)(64, 188)(65, 179)(66, 176)(67, 183)(68, 198)(69, 178)(70, 197)(71, 181)(72, 201)(73, 203)(74, 184)(75, 199)(76, 207)(77, 192)(78, 195)(79, 194)(80, 196)(81, 191)(82, 213)(83, 209)(84, 193)(85, 216)(86, 211)(87, 210)(88, 218)(89, 202)(90, 206)(91, 200)(92, 223)(93, 204)(94, 205)(95, 225)(96, 221)(97, 226)(98, 222)(99, 208)(100, 224)(101, 215)(102, 212)(103, 219)(104, 234)(105, 214)(106, 233)(107, 217)(108, 237)(109, 236)(110, 220)(111, 235)(112, 238)(113, 228)(114, 231)(115, 230)(116, 232)(117, 227)(118, 240)(119, 229)(120, 239) 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 ) } Outer automorphisms :: reflexible Dual of E20.1067 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 120 f = 80 degree seq :: [ 120^2 ] E20.1072 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 60}) Quotient :: loop Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-3 * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-3 * T2 * T1^7 * T2 * T1^-10 ] 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, 35, 155)(19, 139, 33, 153)(20, 140, 34, 154)(22, 142, 31, 151)(23, 143, 40, 160)(25, 145, 42, 162)(26, 146, 43, 163)(27, 147, 45, 165)(30, 150, 46, 166)(36, 156, 48, 168)(37, 157, 49, 169)(38, 158, 50, 170)(39, 159, 54, 174)(41, 161, 56, 176)(44, 164, 58, 178)(47, 167, 60, 180)(51, 171, 61, 181)(52, 172, 63, 183)(53, 173, 66, 186)(55, 175, 68, 188)(57, 177, 70, 190)(59, 179, 72, 192)(62, 182, 73, 193)(64, 184, 71, 191)(65, 185, 78, 198)(67, 187, 80, 200)(69, 189, 82, 202)(74, 194, 84, 204)(75, 195, 85, 205)(76, 196, 86, 206)(77, 197, 90, 210)(79, 199, 92, 212)(81, 201, 94, 214)(83, 203, 96, 216)(87, 207, 97, 217)(88, 208, 99, 219)(89, 209, 102, 222)(91, 211, 104, 224)(93, 213, 106, 226)(95, 215, 108, 228)(98, 218, 109, 229)(100, 220, 107, 227)(101, 221, 114, 234)(103, 223, 116, 236)(105, 225, 118, 238)(110, 230, 119, 239)(111, 231, 113, 233)(112, 232, 115, 235)(117, 237, 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, 148)(17, 149)(18, 128)(19, 156)(20, 129)(21, 157)(22, 130)(23, 159)(24, 138)(25, 140)(26, 132)(27, 141)(28, 162)(29, 163)(30, 134)(31, 167)(32, 165)(33, 136)(34, 137)(35, 166)(36, 170)(37, 171)(38, 142)(39, 173)(40, 150)(41, 144)(42, 155)(43, 176)(44, 146)(45, 154)(46, 178)(47, 179)(48, 152)(49, 153)(50, 182)(51, 183)(52, 158)(53, 185)(54, 164)(55, 160)(56, 188)(57, 161)(58, 190)(59, 191)(60, 169)(61, 168)(62, 194)(63, 195)(64, 172)(65, 197)(66, 177)(67, 174)(68, 200)(69, 175)(70, 202)(71, 203)(72, 181)(73, 180)(74, 206)(75, 207)(76, 184)(77, 209)(78, 189)(79, 186)(80, 212)(81, 187)(82, 214)(83, 215)(84, 192)(85, 193)(86, 218)(87, 219)(88, 196)(89, 221)(90, 201)(91, 198)(92, 224)(93, 199)(94, 226)(95, 227)(96, 205)(97, 204)(98, 230)(99, 231)(100, 208)(101, 233)(102, 213)(103, 210)(104, 236)(105, 211)(106, 238)(107, 234)(108, 217)(109, 216)(110, 235)(111, 237)(112, 220)(113, 229)(114, 225)(115, 222)(116, 232)(117, 223)(118, 240)(119, 228)(120, 239) local type(s) :: { ( 6, 60, 6, 60 ) } Outer automorphisms :: reflexible Dual of E20.1068 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 60 e = 120 f = 22 degree seq :: [ 4^60 ] E20.1073 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 60}) Quotient :: dipole Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^60 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 12, 132)(10, 130, 14, 134)(15, 135, 23, 143)(16, 136, 25, 145)(17, 137, 24, 144)(18, 138, 26, 146)(19, 139, 27, 147)(20, 140, 29, 149)(21, 141, 28, 148)(22, 142, 30, 150)(31, 151, 37, 157)(32, 152, 38, 158)(33, 153, 39, 159)(34, 154, 40, 160)(35, 155, 41, 161)(36, 156, 42, 162)(43, 163, 49, 169)(44, 164, 50, 170)(45, 165, 51, 171)(46, 166, 76, 196)(47, 167, 77, 197)(48, 168, 78, 198)(52, 172, 82, 202)(53, 173, 83, 203)(54, 174, 84, 204)(55, 175, 85, 205)(56, 176, 86, 206)(57, 177, 87, 207)(58, 178, 88, 208)(59, 179, 89, 209)(60, 180, 90, 210)(61, 181, 91, 211)(62, 182, 92, 212)(63, 183, 93, 213)(64, 184, 94, 214)(65, 185, 95, 215)(66, 186, 96, 216)(67, 187, 97, 217)(68, 188, 98, 218)(69, 189, 99, 219)(70, 190, 100, 220)(71, 191, 101, 221)(72, 192, 102, 222)(73, 193, 103, 223)(74, 194, 104, 224)(75, 195, 105, 225)(79, 199, 109, 229)(80, 200, 110, 230)(81, 201, 111, 231)(106, 226, 119, 239)(107, 227, 116, 236)(108, 228, 117, 237)(112, 232, 114, 234)(113, 233, 115, 235)(118, 238, 120, 240)(241, 361, 243, 363, 248, 368, 257, 377, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 261, 381, 254, 374, 246, 366)(247, 367, 255, 375, 264, 384, 258, 378, 249, 369, 256, 376)(251, 371, 259, 379, 268, 388, 262, 382, 253, 373, 260, 380)(263, 383, 271, 391, 266, 386, 273, 393, 265, 385, 272, 392)(267, 387, 274, 394, 270, 390, 276, 396, 269, 389, 275, 395)(277, 397, 283, 403, 279, 399, 285, 405, 278, 398, 284, 404)(280, 400, 286, 406, 282, 402, 288, 408, 281, 401, 287, 407)(289, 409, 297, 417, 291, 411, 292, 412, 290, 410, 295, 415)(293, 413, 317, 437, 299, 419, 316, 436, 301, 421, 318, 438)(294, 414, 325, 445, 303, 423, 327, 447, 296, 416, 322, 442)(298, 418, 329, 449, 307, 427, 331, 451, 300, 420, 323, 443)(302, 422, 333, 453, 305, 425, 326, 446, 304, 424, 324, 444)(306, 426, 337, 457, 309, 429, 330, 450, 308, 428, 328, 448)(310, 430, 335, 455, 312, 432, 334, 454, 311, 431, 332, 452)(313, 433, 339, 459, 315, 435, 338, 458, 314, 434, 336, 456)(319, 439, 342, 462, 321, 441, 341, 461, 320, 440, 340, 460)(343, 463, 346, 466, 345, 465, 348, 468, 344, 464, 347, 467)(349, 469, 353, 473, 351, 471, 352, 472, 350, 470, 358, 478)(354, 474, 356, 476, 360, 480, 359, 479, 355, 475, 357, 477) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 252)(9, 244)(10, 254)(11, 245)(12, 248)(13, 246)(14, 250)(15, 263)(16, 265)(17, 264)(18, 266)(19, 267)(20, 269)(21, 268)(22, 270)(23, 255)(24, 257)(25, 256)(26, 258)(27, 259)(28, 261)(29, 260)(30, 262)(31, 277)(32, 278)(33, 279)(34, 280)(35, 281)(36, 282)(37, 271)(38, 272)(39, 273)(40, 274)(41, 275)(42, 276)(43, 289)(44, 290)(45, 291)(46, 316)(47, 317)(48, 318)(49, 283)(50, 284)(51, 285)(52, 322)(53, 323)(54, 324)(55, 325)(56, 326)(57, 327)(58, 328)(59, 329)(60, 330)(61, 331)(62, 332)(63, 333)(64, 334)(65, 335)(66, 336)(67, 337)(68, 338)(69, 339)(70, 340)(71, 341)(72, 342)(73, 343)(74, 344)(75, 345)(76, 286)(77, 287)(78, 288)(79, 349)(80, 350)(81, 351)(82, 292)(83, 293)(84, 294)(85, 295)(86, 296)(87, 297)(88, 298)(89, 299)(90, 300)(91, 301)(92, 302)(93, 303)(94, 304)(95, 305)(96, 306)(97, 307)(98, 308)(99, 309)(100, 310)(101, 311)(102, 312)(103, 313)(104, 314)(105, 315)(106, 359)(107, 356)(108, 357)(109, 319)(110, 320)(111, 321)(112, 354)(113, 355)(114, 352)(115, 353)(116, 347)(117, 348)(118, 360)(119, 346)(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) :: { ( 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) } Outer automorphisms :: reflexible Dual of E20.1076 Graph:: bipartite v = 80 e = 240 f = 122 degree seq :: [ 4^60, 12^20 ] E20.1074 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 60}) Quotient :: dipole Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-3, (Y2^2 * Y1^-1)^2, Y1^6, Y2^20 * Y1^2 ] Map:: R = (1, 121, 2, 122, 6, 126, 16, 136, 13, 133, 4, 124)(3, 123, 9, 129, 17, 137, 8, 128, 21, 141, 11, 131)(5, 125, 14, 134, 18, 138, 12, 132, 20, 140, 7, 127)(10, 130, 24, 144, 29, 149, 23, 143, 33, 153, 22, 142)(15, 135, 26, 146, 30, 150, 19, 139, 31, 151, 27, 147)(25, 145, 34, 154, 41, 161, 36, 156, 45, 165, 35, 155)(28, 148, 32, 152, 42, 162, 39, 159, 43, 163, 38, 158)(37, 157, 47, 167, 53, 173, 46, 166, 57, 177, 48, 168)(40, 160, 51, 171, 54, 174, 50, 170, 55, 175, 44, 164)(49, 169, 60, 180, 65, 185, 59, 179, 69, 189, 58, 178)(52, 172, 62, 182, 66, 186, 56, 176, 67, 187, 63, 183)(61, 181, 70, 190, 77, 197, 72, 192, 81, 201, 71, 191)(64, 184, 68, 188, 78, 198, 75, 195, 79, 199, 74, 194)(73, 193, 83, 203, 89, 209, 82, 202, 93, 213, 84, 204)(76, 196, 87, 207, 90, 210, 86, 206, 91, 211, 80, 200)(85, 205, 96, 216, 101, 221, 95, 215, 105, 225, 94, 214)(88, 208, 98, 218, 102, 222, 92, 212, 103, 223, 99, 219)(97, 217, 106, 226, 113, 233, 108, 228, 117, 237, 107, 227)(100, 220, 104, 224, 114, 234, 111, 231, 115, 235, 110, 230)(109, 229, 116, 236, 112, 232, 118, 238, 120, 240, 119, 239)(241, 361, 243, 363, 250, 370, 265, 385, 277, 397, 289, 409, 301, 421, 313, 433, 325, 445, 337, 457, 349, 469, 355, 475, 343, 463, 331, 451, 319, 439, 307, 427, 295, 415, 283, 403, 271, 391, 260, 380, 253, 373, 261, 381, 273, 393, 285, 405, 297, 417, 309, 429, 321, 441, 333, 453, 345, 465, 357, 477, 360, 480, 354, 474, 342, 462, 330, 450, 318, 438, 306, 426, 294, 414, 282, 402, 270, 390, 258, 378, 246, 366, 257, 377, 269, 389, 281, 401, 293, 413, 305, 425, 317, 437, 329, 449, 341, 461, 353, 473, 352, 472, 340, 460, 328, 448, 316, 436, 304, 424, 292, 412, 280, 400, 268, 388, 255, 375, 245, 365)(242, 362, 247, 367, 259, 379, 272, 392, 284, 404, 296, 416, 308, 428, 320, 440, 332, 452, 344, 464, 356, 476, 347, 467, 335, 455, 323, 443, 311, 431, 299, 419, 287, 407, 275, 395, 263, 383, 249, 369, 244, 364, 252, 372, 266, 386, 278, 398, 290, 410, 302, 422, 314, 434, 326, 446, 338, 458, 350, 470, 359, 479, 348, 468, 336, 456, 324, 444, 312, 432, 300, 420, 288, 408, 276, 396, 264, 384, 251, 371, 256, 376, 254, 374, 267, 387, 279, 399, 291, 411, 303, 423, 315, 435, 327, 447, 339, 459, 351, 471, 358, 478, 346, 466, 334, 454, 322, 442, 310, 430, 298, 418, 286, 406, 274, 394, 262, 382, 248, 368) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 259)(8, 242)(9, 244)(10, 265)(11, 256)(12, 266)(13, 261)(14, 267)(15, 245)(16, 254)(17, 269)(18, 246)(19, 272)(20, 253)(21, 273)(22, 248)(23, 249)(24, 251)(25, 277)(26, 278)(27, 279)(28, 255)(29, 281)(30, 258)(31, 260)(32, 284)(33, 285)(34, 262)(35, 263)(36, 264)(37, 289)(38, 290)(39, 291)(40, 268)(41, 293)(42, 270)(43, 271)(44, 296)(45, 297)(46, 274)(47, 275)(48, 276)(49, 301)(50, 302)(51, 303)(52, 280)(53, 305)(54, 282)(55, 283)(56, 308)(57, 309)(58, 286)(59, 287)(60, 288)(61, 313)(62, 314)(63, 315)(64, 292)(65, 317)(66, 294)(67, 295)(68, 320)(69, 321)(70, 298)(71, 299)(72, 300)(73, 325)(74, 326)(75, 327)(76, 304)(77, 329)(78, 306)(79, 307)(80, 332)(81, 333)(82, 310)(83, 311)(84, 312)(85, 337)(86, 338)(87, 339)(88, 316)(89, 341)(90, 318)(91, 319)(92, 344)(93, 345)(94, 322)(95, 323)(96, 324)(97, 349)(98, 350)(99, 351)(100, 328)(101, 353)(102, 330)(103, 331)(104, 356)(105, 357)(106, 334)(107, 335)(108, 336)(109, 355)(110, 359)(111, 358)(112, 340)(113, 352)(114, 342)(115, 343)(116, 347)(117, 360)(118, 346)(119, 348)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.1075 Graph:: bipartite v = 22 e = 240 f = 180 degree seq :: [ 12^20, 120^2 ] E20.1075 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 60}) Quotient :: dipole Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^3 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^4 * Y2 * Y3^-16 * Y2, (Y3^-1 * Y1^-1)^60 ] Map:: polytopal R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 257, 377)(250, 370, 261, 381)(252, 372, 265, 385)(254, 374, 269, 389)(255, 375, 263, 383)(256, 376, 267, 387)(258, 378, 270, 390)(259, 379, 264, 384)(260, 380, 268, 388)(262, 382, 266, 386)(271, 391, 281, 401)(272, 392, 285, 405)(273, 393, 279, 399)(274, 394, 284, 404)(275, 395, 287, 407)(276, 396, 282, 402)(277, 397, 280, 400)(278, 398, 290, 410)(283, 403, 293, 413)(286, 406, 296, 416)(288, 408, 297, 417)(289, 409, 300, 420)(291, 411, 294, 414)(292, 412, 303, 423)(295, 415, 306, 426)(298, 418, 309, 429)(299, 419, 308, 428)(301, 421, 310, 430)(302, 422, 305, 425)(304, 424, 307, 427)(311, 431, 321, 441)(312, 432, 320, 440)(313, 433, 323, 443)(314, 434, 318, 438)(315, 435, 317, 437)(316, 436, 326, 446)(319, 439, 329, 449)(322, 442, 332, 452)(324, 444, 333, 453)(325, 445, 336, 456)(327, 447, 330, 450)(328, 448, 339, 459)(331, 451, 342, 462)(334, 454, 345, 465)(335, 455, 344, 464)(337, 457, 346, 466)(338, 458, 341, 461)(340, 460, 343, 463)(347, 467, 357, 477)(348, 468, 356, 476)(349, 469, 355, 475)(350, 470, 354, 474)(351, 471, 353, 473)(352, 472, 358, 478)(359, 479, 360, 480) L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 258)(9, 259)(10, 244)(11, 263)(12, 266)(13, 267)(14, 246)(15, 271)(16, 247)(17, 273)(18, 275)(19, 276)(20, 249)(21, 277)(22, 250)(23, 279)(24, 251)(25, 281)(26, 283)(27, 284)(28, 253)(29, 285)(30, 254)(31, 261)(32, 256)(33, 260)(34, 257)(35, 289)(36, 290)(37, 291)(38, 262)(39, 269)(40, 264)(41, 268)(42, 265)(43, 295)(44, 296)(45, 297)(46, 270)(47, 272)(48, 274)(49, 301)(50, 302)(51, 303)(52, 278)(53, 280)(54, 282)(55, 307)(56, 308)(57, 309)(58, 286)(59, 287)(60, 288)(61, 313)(62, 314)(63, 315)(64, 292)(65, 293)(66, 294)(67, 319)(68, 320)(69, 321)(70, 298)(71, 299)(72, 300)(73, 325)(74, 326)(75, 327)(76, 304)(77, 305)(78, 306)(79, 331)(80, 332)(81, 333)(82, 310)(83, 311)(84, 312)(85, 337)(86, 338)(87, 339)(88, 316)(89, 317)(90, 318)(91, 343)(92, 344)(93, 345)(94, 322)(95, 323)(96, 324)(97, 349)(98, 350)(99, 351)(100, 328)(101, 329)(102, 330)(103, 355)(104, 356)(105, 357)(106, 334)(107, 335)(108, 336)(109, 353)(110, 358)(111, 359)(112, 340)(113, 341)(114, 342)(115, 347)(116, 352)(117, 360)(118, 346)(119, 348)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 12, 120 ), ( 12, 120, 12, 120 ) } Outer automorphisms :: reflexible Dual of E20.1074 Graph:: simple bipartite v = 180 e = 240 f = 22 degree seq :: [ 2^120, 4^60 ] E20.1076 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 60}) Quotient :: dipole Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y1^-2)^2, Y1^-3 * Y3 * Y1^13 * Y3 * Y1^-4 ] Map:: R = (1, 121, 2, 122, 5, 125, 11, 131, 23, 143, 39, 159, 53, 173, 65, 185, 77, 197, 89, 209, 101, 221, 113, 233, 109, 229, 96, 216, 85, 205, 73, 193, 60, 180, 49, 169, 33, 153, 16, 136, 28, 148, 42, 162, 35, 155, 46, 166, 58, 178, 70, 190, 82, 202, 94, 214, 106, 226, 118, 238, 120, 240, 119, 239, 108, 228, 97, 217, 84, 204, 72, 192, 61, 181, 48, 168, 32, 152, 45, 165, 34, 154, 17, 137, 29, 149, 43, 163, 56, 176, 68, 188, 80, 200, 92, 212, 104, 224, 116, 236, 112, 232, 100, 220, 88, 208, 76, 196, 64, 184, 52, 172, 38, 158, 22, 142, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 31, 151, 47, 167, 59, 179, 71, 191, 83, 203, 95, 215, 107, 227, 114, 234, 105, 225, 91, 211, 78, 198, 69, 189, 55, 175, 40, 160, 30, 150, 14, 134, 6, 126, 13, 133, 27, 147, 21, 141, 37, 157, 51, 171, 63, 183, 75, 195, 87, 207, 99, 219, 111, 231, 117, 237, 103, 223, 90, 210, 81, 201, 67, 187, 54, 174, 44, 164, 26, 146, 12, 132, 25, 145, 20, 140, 9, 129, 19, 139, 36, 156, 50, 170, 62, 182, 74, 194, 86, 206, 98, 218, 110, 230, 115, 235, 102, 222, 93, 213, 79, 199, 66, 186, 57, 177, 41, 161, 24, 144, 18, 138, 8, 128)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 261)(11, 264)(12, 245)(13, 268)(14, 269)(15, 272)(16, 247)(17, 248)(18, 275)(19, 273)(20, 274)(21, 250)(22, 271)(23, 280)(24, 251)(25, 282)(26, 283)(27, 285)(28, 253)(29, 254)(30, 286)(31, 262)(32, 255)(33, 259)(34, 260)(35, 258)(36, 288)(37, 289)(38, 290)(39, 294)(40, 263)(41, 296)(42, 265)(43, 266)(44, 298)(45, 267)(46, 270)(47, 300)(48, 276)(49, 277)(50, 278)(51, 301)(52, 303)(53, 306)(54, 279)(55, 308)(56, 281)(57, 310)(58, 284)(59, 312)(60, 287)(61, 291)(62, 313)(63, 292)(64, 311)(65, 318)(66, 293)(67, 320)(68, 295)(69, 322)(70, 297)(71, 304)(72, 299)(73, 302)(74, 324)(75, 325)(76, 326)(77, 330)(78, 305)(79, 332)(80, 307)(81, 334)(82, 309)(83, 336)(84, 314)(85, 315)(86, 316)(87, 337)(88, 339)(89, 342)(90, 317)(91, 344)(92, 319)(93, 346)(94, 321)(95, 348)(96, 323)(97, 327)(98, 349)(99, 328)(100, 347)(101, 354)(102, 329)(103, 356)(104, 331)(105, 358)(106, 333)(107, 340)(108, 335)(109, 338)(110, 359)(111, 353)(112, 355)(113, 351)(114, 341)(115, 352)(116, 343)(117, 360)(118, 345)(119, 350)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E20.1073 Graph:: simple bipartite v = 122 e = 240 f = 80 degree seq :: [ 2^120, 120^2 ] E20.1077 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 60}) Quotient :: dipole Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^3 * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^6, Y2^4 * Y1 * Y2^-16 * Y1, (Y2^-1 * R * Y2^-9)^2 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 17, 137)(10, 130, 21, 141)(12, 132, 25, 145)(14, 134, 29, 149)(15, 135, 23, 143)(16, 136, 27, 147)(18, 138, 30, 150)(19, 139, 24, 144)(20, 140, 28, 148)(22, 142, 26, 146)(31, 151, 41, 161)(32, 152, 45, 165)(33, 153, 39, 159)(34, 154, 44, 164)(35, 155, 47, 167)(36, 156, 42, 162)(37, 157, 40, 160)(38, 158, 50, 170)(43, 163, 53, 173)(46, 166, 56, 176)(48, 168, 57, 177)(49, 169, 60, 180)(51, 171, 54, 174)(52, 172, 63, 183)(55, 175, 66, 186)(58, 178, 69, 189)(59, 179, 68, 188)(61, 181, 70, 190)(62, 182, 65, 185)(64, 184, 67, 187)(71, 191, 81, 201)(72, 192, 80, 200)(73, 193, 83, 203)(74, 194, 78, 198)(75, 195, 77, 197)(76, 196, 86, 206)(79, 199, 89, 209)(82, 202, 92, 212)(84, 204, 93, 213)(85, 205, 96, 216)(87, 207, 90, 210)(88, 208, 99, 219)(91, 211, 102, 222)(94, 214, 105, 225)(95, 215, 104, 224)(97, 217, 106, 226)(98, 218, 101, 221)(100, 220, 103, 223)(107, 227, 117, 237)(108, 228, 116, 236)(109, 229, 115, 235)(110, 230, 114, 234)(111, 231, 113, 233)(112, 232, 118, 238)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 275, 395, 289, 409, 301, 421, 313, 433, 325, 445, 337, 457, 349, 469, 353, 473, 341, 461, 329, 449, 317, 437, 305, 425, 293, 413, 280, 400, 264, 384, 251, 371, 263, 383, 279, 399, 269, 389, 285, 405, 297, 417, 309, 429, 321, 441, 333, 453, 345, 465, 357, 477, 360, 480, 354, 474, 342, 462, 330, 450, 318, 438, 306, 426, 294, 414, 282, 402, 265, 385, 281, 401, 268, 388, 253, 373, 267, 387, 284, 404, 296, 416, 308, 428, 320, 440, 332, 452, 344, 464, 356, 476, 352, 472, 340, 460, 328, 448, 316, 436, 304, 424, 292, 412, 278, 398, 262, 382, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 266, 386, 283, 403, 295, 415, 307, 427, 319, 439, 331, 451, 343, 463, 355, 475, 347, 467, 335, 455, 323, 443, 311, 431, 299, 419, 287, 407, 272, 392, 256, 376, 247, 367, 255, 375, 271, 391, 261, 381, 277, 397, 291, 411, 303, 423, 315, 435, 327, 447, 339, 459, 351, 471, 359, 479, 348, 468, 336, 456, 324, 444, 312, 432, 300, 420, 288, 408, 274, 394, 257, 377, 273, 393, 260, 380, 249, 369, 259, 379, 276, 396, 290, 410, 302, 422, 314, 434, 326, 446, 338, 458, 350, 470, 358, 478, 346, 466, 334, 454, 322, 442, 310, 430, 298, 418, 286, 406, 270, 390, 254, 374, 246, 366) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 261)(11, 245)(12, 265)(13, 246)(14, 269)(15, 263)(16, 267)(17, 248)(18, 270)(19, 264)(20, 268)(21, 250)(22, 266)(23, 255)(24, 259)(25, 252)(26, 262)(27, 256)(28, 260)(29, 254)(30, 258)(31, 281)(32, 285)(33, 279)(34, 284)(35, 287)(36, 282)(37, 280)(38, 290)(39, 273)(40, 277)(41, 271)(42, 276)(43, 293)(44, 274)(45, 272)(46, 296)(47, 275)(48, 297)(49, 300)(50, 278)(51, 294)(52, 303)(53, 283)(54, 291)(55, 306)(56, 286)(57, 288)(58, 309)(59, 308)(60, 289)(61, 310)(62, 305)(63, 292)(64, 307)(65, 302)(66, 295)(67, 304)(68, 299)(69, 298)(70, 301)(71, 321)(72, 320)(73, 323)(74, 318)(75, 317)(76, 326)(77, 315)(78, 314)(79, 329)(80, 312)(81, 311)(82, 332)(83, 313)(84, 333)(85, 336)(86, 316)(87, 330)(88, 339)(89, 319)(90, 327)(91, 342)(92, 322)(93, 324)(94, 345)(95, 344)(96, 325)(97, 346)(98, 341)(99, 328)(100, 343)(101, 338)(102, 331)(103, 340)(104, 335)(105, 334)(106, 337)(107, 357)(108, 356)(109, 355)(110, 354)(111, 353)(112, 358)(113, 351)(114, 350)(115, 349)(116, 348)(117, 347)(118, 352)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E20.1078 Graph:: bipartite v = 62 e = 240 f = 140 degree seq :: [ 4^60, 120^2 ] E20.1078 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 60}) Quotient :: dipole Aut^+ = C3 x D40 (small group id <120, 18>) Aut = S3 x D40 (small group id <240, 137>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-2 * Y1)^2, Y1^-3 * Y3 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-3, Y1 * Y3^-19 * Y1^-1 * Y3, (Y3 * Y2^-1)^60 ] Map:: R = (1, 121, 2, 122, 6, 126, 16, 136, 13, 133, 4, 124)(3, 123, 9, 129, 17, 137, 8, 128, 21, 141, 11, 131)(5, 125, 14, 134, 18, 138, 12, 132, 20, 140, 7, 127)(10, 130, 24, 144, 29, 149, 23, 143, 33, 153, 22, 142)(15, 135, 26, 146, 30, 150, 19, 139, 31, 151, 27, 147)(25, 145, 34, 154, 41, 161, 36, 156, 45, 165, 35, 155)(28, 148, 32, 152, 42, 162, 39, 159, 43, 163, 38, 158)(37, 157, 47, 167, 53, 173, 46, 166, 57, 177, 48, 168)(40, 160, 51, 171, 54, 174, 50, 170, 55, 175, 44, 164)(49, 169, 60, 180, 65, 185, 59, 179, 69, 189, 58, 178)(52, 172, 62, 182, 66, 186, 56, 176, 67, 187, 63, 183)(61, 181, 70, 190, 77, 197, 72, 192, 81, 201, 71, 191)(64, 184, 68, 188, 78, 198, 75, 195, 79, 199, 74, 194)(73, 193, 83, 203, 89, 209, 82, 202, 93, 213, 84, 204)(76, 196, 87, 207, 90, 210, 86, 206, 91, 211, 80, 200)(85, 205, 96, 216, 101, 221, 95, 215, 105, 225, 94, 214)(88, 208, 98, 218, 102, 222, 92, 212, 103, 223, 99, 219)(97, 217, 106, 226, 113, 233, 108, 228, 117, 237, 107, 227)(100, 220, 104, 224, 114, 234, 111, 231, 115, 235, 110, 230)(109, 229, 116, 236, 112, 232, 118, 238, 120, 240, 119, 239)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 259)(8, 242)(9, 244)(10, 265)(11, 256)(12, 266)(13, 261)(14, 267)(15, 245)(16, 254)(17, 269)(18, 246)(19, 272)(20, 253)(21, 273)(22, 248)(23, 249)(24, 251)(25, 277)(26, 278)(27, 279)(28, 255)(29, 281)(30, 258)(31, 260)(32, 284)(33, 285)(34, 262)(35, 263)(36, 264)(37, 289)(38, 290)(39, 291)(40, 268)(41, 293)(42, 270)(43, 271)(44, 296)(45, 297)(46, 274)(47, 275)(48, 276)(49, 301)(50, 302)(51, 303)(52, 280)(53, 305)(54, 282)(55, 283)(56, 308)(57, 309)(58, 286)(59, 287)(60, 288)(61, 313)(62, 314)(63, 315)(64, 292)(65, 317)(66, 294)(67, 295)(68, 320)(69, 321)(70, 298)(71, 299)(72, 300)(73, 325)(74, 326)(75, 327)(76, 304)(77, 329)(78, 306)(79, 307)(80, 332)(81, 333)(82, 310)(83, 311)(84, 312)(85, 337)(86, 338)(87, 339)(88, 316)(89, 341)(90, 318)(91, 319)(92, 344)(93, 345)(94, 322)(95, 323)(96, 324)(97, 349)(98, 350)(99, 351)(100, 328)(101, 353)(102, 330)(103, 331)(104, 356)(105, 357)(106, 334)(107, 335)(108, 336)(109, 355)(110, 359)(111, 358)(112, 340)(113, 352)(114, 342)(115, 343)(116, 347)(117, 360)(118, 346)(119, 348)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 120 ), ( 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120 ) } Outer automorphisms :: reflexible Dual of E20.1077 Graph:: simple bipartite v = 140 e = 240 f = 62 degree seq :: [ 2^120, 12^20 ] E20.1079 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 22}) Quotient :: regular Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^6, T1^22 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 61, 73, 85, 97, 109, 108, 96, 84, 72, 60, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 67, 79, 91, 103, 115, 121, 110, 99, 86, 75, 62, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 58, 70, 82, 94, 106, 118, 120, 111, 98, 87, 74, 63, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 64, 77, 88, 101, 112, 123, 128, 125, 116, 104, 92, 80, 68, 56, 40, 27)(23, 36, 24, 38, 50, 65, 76, 89, 100, 113, 122, 129, 127, 119, 107, 95, 83, 71, 59, 45, 30, 37)(41, 53, 42, 57, 69, 81, 93, 105, 117, 126, 131, 132, 130, 124, 114, 102, 90, 78, 66, 54, 43, 52) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 59)(45, 57)(46, 58)(47, 62)(49, 64)(51, 66)(55, 68)(56, 69)(60, 67)(61, 74)(63, 76)(65, 78)(70, 83)(71, 81)(72, 82)(73, 86)(75, 88)(77, 90)(79, 92)(80, 93)(84, 91)(85, 98)(87, 100)(89, 102)(94, 107)(95, 105)(96, 106)(97, 110)(99, 112)(101, 114)(103, 116)(104, 117)(108, 115)(109, 120)(111, 122)(113, 124)(118, 127)(119, 126)(121, 128)(123, 130)(125, 131)(129, 132) local type(s) :: { ( 6^22 ) } Outer automorphisms :: reflexible Dual of E20.1080 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 66 f = 22 degree seq :: [ 22^6 ] E20.1080 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 22}) Quotient :: regular Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^6, (T1 * T2)^22 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 20, 12, 8)(6, 13, 9, 18, 19, 14)(16, 23, 17, 25, 27, 24)(21, 28, 22, 30, 26, 29)(31, 37, 32, 39, 33, 38)(34, 40, 35, 42, 36, 41)(43, 49, 44, 51, 45, 50)(46, 52, 47, 54, 48, 53)(55, 66, 56, 59, 57, 61)(58, 88, 65, 89, 62, 90)(60, 96, 67, 98, 68, 95)(63, 100, 71, 94, 64, 99)(69, 103, 75, 97, 70, 104)(72, 107, 74, 101, 73, 102)(76, 111, 78, 105, 77, 106)(79, 110, 81, 108, 80, 109)(82, 114, 84, 112, 83, 113)(85, 117, 87, 115, 86, 116)(91, 120, 93, 118, 92, 119)(121, 125, 122, 124, 123, 126)(127, 132, 128, 131, 129, 130) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 88)(53, 89)(54, 90)(58, 94)(59, 95)(60, 97)(61, 98)(62, 99)(63, 101)(64, 102)(65, 100)(66, 96)(67, 103)(68, 104)(69, 105)(70, 106)(71, 107)(72, 108)(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)(91, 127)(92, 128)(93, 129)(124, 130)(125, 132)(126, 131) local type(s) :: { ( 22^6 ) } Outer automorphisms :: reflexible Dual of E20.1079 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 22 e = 66 f = 6 degree seq :: [ 6^22 ] E20.1081 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 22}) Quotient :: edge Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^22 ] Map:: polytopal R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 9, 18, 25, 16)(11, 19, 13, 22, 29, 20)(23, 31, 24, 33, 26, 32)(27, 34, 28, 36, 30, 35)(37, 43, 38, 45, 39, 44)(40, 46, 41, 48, 42, 47)(49, 55, 50, 57, 51, 56)(52, 61, 53, 70, 54, 60)(58, 92, 65, 93, 63, 91)(59, 96, 69, 104, 67, 97)(62, 99, 73, 101, 64, 94)(66, 103, 77, 106, 68, 95)(71, 100, 74, 109, 72, 98)(75, 105, 78, 113, 76, 102)(79, 108, 81, 110, 80, 107)(82, 112, 84, 114, 83, 111)(85, 116, 87, 117, 86, 115)(88, 119, 90, 120, 89, 118)(121, 127, 122, 129, 123, 128)(124, 131, 125, 132, 126, 130)(133, 134)(135, 139)(136, 141)(137, 143)(138, 145)(140, 146)(142, 144)(147, 155)(148, 156)(149, 157)(150, 158)(151, 159)(152, 160)(153, 161)(154, 162)(163, 169)(164, 170)(165, 171)(166, 172)(167, 173)(168, 174)(175, 181)(176, 182)(177, 183)(178, 184)(179, 185)(180, 186)(187, 223)(188, 224)(189, 225)(190, 226)(191, 227)(192, 228)(193, 229)(194, 230)(195, 231)(196, 232)(197, 233)(198, 234)(199, 235)(200, 237)(201, 238)(202, 236)(203, 239)(204, 240)(205, 241)(206, 242)(207, 243)(208, 244)(209, 245)(210, 246)(211, 247)(212, 248)(213, 249)(214, 250)(215, 251)(216, 252)(217, 253)(218, 254)(219, 255)(220, 256)(221, 257)(222, 258)(259, 262)(260, 263)(261, 264) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 44, 44 ), ( 44^6 ) } Outer automorphisms :: reflexible Dual of E20.1085 Transitivity :: ET+ Graph:: simple bipartite v = 88 e = 132 f = 6 degree seq :: [ 2^66, 6^22 ] E20.1082 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 22}) Quotient :: edge Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T1^6, T2^22 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 33, 45, 57, 69, 81, 93, 105, 117, 108, 96, 84, 72, 60, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 65, 77, 89, 101, 113, 124, 114, 102, 90, 78, 66, 54, 42, 30, 18, 8)(4, 11, 23, 35, 47, 59, 71, 83, 95, 107, 119, 126, 116, 104, 92, 80, 68, 56, 44, 32, 20, 9)(6, 15, 27, 39, 51, 63, 75, 87, 99, 111, 122, 130, 123, 112, 100, 88, 76, 64, 52, 40, 28, 16)(12, 19, 31, 43, 55, 67, 79, 91, 103, 115, 125, 131, 127, 118, 106, 94, 82, 70, 58, 46, 34, 22)(14, 25, 37, 49, 61, 73, 85, 97, 109, 120, 128, 132, 129, 121, 110, 98, 86, 74, 62, 50, 38, 26)(133, 134, 138, 146, 144, 136)(135, 141, 151, 158, 147, 140)(137, 143, 154, 157, 148, 139)(142, 150, 159, 170, 163, 152)(145, 149, 160, 169, 166, 155)(153, 164, 175, 182, 171, 162)(156, 167, 178, 181, 172, 161)(165, 174, 183, 194, 187, 176)(168, 173, 184, 193, 190, 179)(177, 188, 199, 206, 195, 186)(180, 191, 202, 205, 196, 185)(189, 198, 207, 218, 211, 200)(192, 197, 208, 217, 214, 203)(201, 212, 223, 230, 219, 210)(204, 215, 226, 229, 220, 209)(213, 222, 231, 242, 235, 224)(216, 221, 232, 241, 238, 227)(225, 236, 247, 253, 243, 234)(228, 239, 250, 252, 244, 233)(237, 246, 254, 261, 257, 248)(240, 245, 255, 260, 259, 251)(249, 258, 263, 264, 262, 256) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4^6 ), ( 4^22 ) } Outer automorphisms :: reflexible Dual of E20.1086 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 132 f = 66 degree seq :: [ 6^22, 22^6 ] E20.1083 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 22}) Quotient :: edge Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T2 * T1)^6, T1^22 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 59)(45, 57)(46, 58)(47, 62)(49, 64)(51, 66)(55, 68)(56, 69)(60, 67)(61, 74)(63, 76)(65, 78)(70, 83)(71, 81)(72, 82)(73, 86)(75, 88)(77, 90)(79, 92)(80, 93)(84, 91)(85, 98)(87, 100)(89, 102)(94, 107)(95, 105)(96, 106)(97, 110)(99, 112)(101, 114)(103, 116)(104, 117)(108, 115)(109, 120)(111, 122)(113, 124)(118, 127)(119, 126)(121, 128)(123, 130)(125, 131)(129, 132)(133, 134, 137, 143, 152, 164, 179, 193, 205, 217, 229, 241, 240, 228, 216, 204, 192, 178, 163, 151, 142, 136)(135, 139, 147, 157, 171, 187, 199, 211, 223, 235, 247, 253, 242, 231, 218, 207, 194, 181, 165, 154, 144, 140)(138, 145, 141, 150, 161, 176, 190, 202, 214, 226, 238, 250, 252, 243, 230, 219, 206, 195, 180, 166, 153, 146)(148, 158, 149, 160, 167, 183, 196, 209, 220, 233, 244, 255, 260, 257, 248, 236, 224, 212, 200, 188, 172, 159)(155, 168, 156, 170, 182, 197, 208, 221, 232, 245, 254, 261, 259, 251, 239, 227, 215, 203, 191, 177, 162, 169)(173, 185, 174, 189, 201, 213, 225, 237, 249, 258, 263, 264, 262, 256, 246, 234, 222, 210, 198, 186, 175, 184) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 12, 12 ), ( 12^22 ) } Outer automorphisms :: reflexible Dual of E20.1084 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 132 f = 22 degree seq :: [ 2^66, 22^6 ] E20.1084 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 22}) Quotient :: loop Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^22 ] Map:: R = (1, 133, 3, 135, 8, 140, 17, 149, 10, 142, 4, 136)(2, 134, 5, 137, 12, 144, 21, 153, 14, 146, 6, 138)(7, 139, 15, 147, 9, 141, 18, 150, 25, 157, 16, 148)(11, 143, 19, 151, 13, 145, 22, 154, 29, 161, 20, 152)(23, 155, 31, 163, 24, 156, 33, 165, 26, 158, 32, 164)(27, 159, 34, 166, 28, 160, 36, 168, 30, 162, 35, 167)(37, 169, 43, 175, 38, 170, 45, 177, 39, 171, 44, 176)(40, 172, 46, 178, 41, 173, 48, 180, 42, 174, 47, 179)(49, 181, 55, 187, 50, 182, 57, 189, 51, 183, 56, 188)(52, 184, 63, 195, 53, 185, 58, 190, 54, 186, 64, 196)(59, 191, 89, 221, 60, 192, 85, 217, 67, 199, 87, 219)(61, 193, 91, 223, 62, 194, 101, 233, 71, 203, 99, 231)(65, 197, 93, 225, 66, 198, 108, 240, 68, 200, 95, 227)(69, 201, 97, 229, 70, 202, 116, 248, 72, 204, 100, 232)(73, 205, 105, 237, 74, 206, 111, 243, 75, 207, 107, 239)(76, 208, 113, 245, 77, 209, 119, 251, 78, 210, 115, 247)(79, 211, 121, 253, 80, 212, 125, 257, 81, 213, 123, 255)(82, 214, 127, 259, 83, 215, 131, 263, 84, 216, 129, 261)(86, 218, 132, 264, 88, 220, 130, 262, 90, 222, 128, 260)(92, 224, 122, 254, 103, 235, 126, 258, 104, 236, 124, 256)(94, 226, 120, 252, 110, 242, 117, 249, 96, 228, 114, 246)(98, 230, 112, 244, 118, 250, 109, 241, 102, 234, 106, 238) L = (1, 134)(2, 133)(3, 139)(4, 141)(5, 143)(6, 145)(7, 135)(8, 146)(9, 136)(10, 144)(11, 137)(12, 142)(13, 138)(14, 140)(15, 155)(16, 156)(17, 157)(18, 158)(19, 159)(20, 160)(21, 161)(22, 162)(23, 147)(24, 148)(25, 149)(26, 150)(27, 151)(28, 152)(29, 153)(30, 154)(31, 169)(32, 170)(33, 171)(34, 172)(35, 173)(36, 174)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 181)(44, 182)(45, 183)(46, 184)(47, 185)(48, 186)(49, 175)(50, 176)(51, 177)(52, 178)(53, 179)(54, 180)(55, 217)(56, 219)(57, 221)(58, 223)(59, 225)(60, 227)(61, 229)(62, 232)(63, 233)(64, 231)(65, 237)(66, 239)(67, 240)(68, 243)(69, 245)(70, 247)(71, 248)(72, 251)(73, 253)(74, 255)(75, 257)(76, 259)(77, 261)(78, 263)(79, 264)(80, 260)(81, 262)(82, 258)(83, 254)(84, 256)(85, 187)(86, 249)(87, 188)(88, 252)(89, 189)(90, 246)(91, 190)(92, 238)(93, 191)(94, 234)(95, 192)(96, 230)(97, 193)(98, 228)(99, 196)(100, 194)(101, 195)(102, 226)(103, 241)(104, 244)(105, 197)(106, 224)(107, 198)(108, 199)(109, 235)(110, 250)(111, 200)(112, 236)(113, 201)(114, 222)(115, 202)(116, 203)(117, 218)(118, 242)(119, 204)(120, 220)(121, 205)(122, 215)(123, 206)(124, 216)(125, 207)(126, 214)(127, 208)(128, 212)(129, 209)(130, 213)(131, 210)(132, 211) local type(s) :: { ( 2, 22, 2, 22, 2, 22, 2, 22, 2, 22, 2, 22 ) } Outer automorphisms :: reflexible Dual of E20.1083 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 22 e = 132 f = 72 degree seq :: [ 12^22 ] E20.1085 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 22}) Quotient :: loop Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T1^6, T2^22 ] Map:: R = (1, 133, 3, 135, 10, 142, 21, 153, 33, 165, 45, 177, 57, 189, 69, 201, 81, 213, 93, 225, 105, 237, 117, 249, 108, 240, 96, 228, 84, 216, 72, 204, 60, 192, 48, 180, 36, 168, 24, 156, 13, 145, 5, 137)(2, 134, 7, 139, 17, 149, 29, 161, 41, 173, 53, 185, 65, 197, 77, 209, 89, 221, 101, 233, 113, 245, 124, 256, 114, 246, 102, 234, 90, 222, 78, 210, 66, 198, 54, 186, 42, 174, 30, 162, 18, 150, 8, 140)(4, 136, 11, 143, 23, 155, 35, 167, 47, 179, 59, 191, 71, 203, 83, 215, 95, 227, 107, 239, 119, 251, 126, 258, 116, 248, 104, 236, 92, 224, 80, 212, 68, 200, 56, 188, 44, 176, 32, 164, 20, 152, 9, 141)(6, 138, 15, 147, 27, 159, 39, 171, 51, 183, 63, 195, 75, 207, 87, 219, 99, 231, 111, 243, 122, 254, 130, 262, 123, 255, 112, 244, 100, 232, 88, 220, 76, 208, 64, 196, 52, 184, 40, 172, 28, 160, 16, 148)(12, 144, 19, 151, 31, 163, 43, 175, 55, 187, 67, 199, 79, 211, 91, 223, 103, 235, 115, 247, 125, 257, 131, 263, 127, 259, 118, 250, 106, 238, 94, 226, 82, 214, 70, 202, 58, 190, 46, 178, 34, 166, 22, 154)(14, 146, 25, 157, 37, 169, 49, 181, 61, 193, 73, 205, 85, 217, 97, 229, 109, 241, 120, 252, 128, 260, 132, 264, 129, 261, 121, 253, 110, 242, 98, 230, 86, 218, 74, 206, 62, 194, 50, 182, 38, 170, 26, 158) L = (1, 134)(2, 138)(3, 141)(4, 133)(5, 143)(6, 146)(7, 137)(8, 135)(9, 151)(10, 150)(11, 154)(12, 136)(13, 149)(14, 144)(15, 140)(16, 139)(17, 160)(18, 159)(19, 158)(20, 142)(21, 164)(22, 157)(23, 145)(24, 167)(25, 148)(26, 147)(27, 170)(28, 169)(29, 156)(30, 153)(31, 152)(32, 175)(33, 174)(34, 155)(35, 178)(36, 173)(37, 166)(38, 163)(39, 162)(40, 161)(41, 184)(42, 183)(43, 182)(44, 165)(45, 188)(46, 181)(47, 168)(48, 191)(49, 172)(50, 171)(51, 194)(52, 193)(53, 180)(54, 177)(55, 176)(56, 199)(57, 198)(58, 179)(59, 202)(60, 197)(61, 190)(62, 187)(63, 186)(64, 185)(65, 208)(66, 207)(67, 206)(68, 189)(69, 212)(70, 205)(71, 192)(72, 215)(73, 196)(74, 195)(75, 218)(76, 217)(77, 204)(78, 201)(79, 200)(80, 223)(81, 222)(82, 203)(83, 226)(84, 221)(85, 214)(86, 211)(87, 210)(88, 209)(89, 232)(90, 231)(91, 230)(92, 213)(93, 236)(94, 229)(95, 216)(96, 239)(97, 220)(98, 219)(99, 242)(100, 241)(101, 228)(102, 225)(103, 224)(104, 247)(105, 246)(106, 227)(107, 250)(108, 245)(109, 238)(110, 235)(111, 234)(112, 233)(113, 255)(114, 254)(115, 253)(116, 237)(117, 258)(118, 252)(119, 240)(120, 244)(121, 243)(122, 261)(123, 260)(124, 249)(125, 248)(126, 263)(127, 251)(128, 259)(129, 257)(130, 256)(131, 264)(132, 262) 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 E20.1081 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 132 f = 88 degree seq :: [ 44^6 ] E20.1086 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 22}) Quotient :: loop Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T2 * T1)^6, T1^22 ] Map:: polytopal non-degenerate R = (1, 133, 3, 135)(2, 134, 6, 138)(4, 136, 9, 141)(5, 137, 12, 144)(7, 139, 16, 148)(8, 140, 17, 149)(10, 142, 15, 147)(11, 143, 21, 153)(13, 145, 23, 155)(14, 146, 24, 156)(18, 150, 30, 162)(19, 151, 29, 161)(20, 152, 33, 165)(22, 154, 35, 167)(25, 157, 40, 172)(26, 158, 41, 173)(27, 159, 42, 174)(28, 160, 43, 175)(31, 163, 39, 171)(32, 164, 48, 180)(34, 166, 50, 182)(36, 168, 52, 184)(37, 169, 53, 185)(38, 170, 54, 186)(44, 176, 59, 191)(45, 177, 57, 189)(46, 178, 58, 190)(47, 179, 62, 194)(49, 181, 64, 196)(51, 183, 66, 198)(55, 187, 68, 200)(56, 188, 69, 201)(60, 192, 67, 199)(61, 193, 74, 206)(63, 195, 76, 208)(65, 197, 78, 210)(70, 202, 83, 215)(71, 203, 81, 213)(72, 204, 82, 214)(73, 205, 86, 218)(75, 207, 88, 220)(77, 209, 90, 222)(79, 211, 92, 224)(80, 212, 93, 225)(84, 216, 91, 223)(85, 217, 98, 230)(87, 219, 100, 232)(89, 221, 102, 234)(94, 226, 107, 239)(95, 227, 105, 237)(96, 228, 106, 238)(97, 229, 110, 242)(99, 231, 112, 244)(101, 233, 114, 246)(103, 235, 116, 248)(104, 236, 117, 249)(108, 240, 115, 247)(109, 241, 120, 252)(111, 243, 122, 254)(113, 245, 124, 256)(118, 250, 127, 259)(119, 251, 126, 258)(121, 253, 128, 260)(123, 255, 130, 262)(125, 257, 131, 263)(129, 261, 132, 264) L = (1, 134)(2, 137)(3, 139)(4, 133)(5, 143)(6, 145)(7, 147)(8, 135)(9, 150)(10, 136)(11, 152)(12, 140)(13, 141)(14, 138)(15, 157)(16, 158)(17, 160)(18, 161)(19, 142)(20, 164)(21, 146)(22, 144)(23, 168)(24, 170)(25, 171)(26, 149)(27, 148)(28, 167)(29, 176)(30, 169)(31, 151)(32, 179)(33, 154)(34, 153)(35, 183)(36, 156)(37, 155)(38, 182)(39, 187)(40, 159)(41, 185)(42, 189)(43, 184)(44, 190)(45, 162)(46, 163)(47, 193)(48, 166)(49, 165)(50, 197)(51, 196)(52, 173)(53, 174)(54, 175)(55, 199)(56, 172)(57, 201)(58, 202)(59, 177)(60, 178)(61, 205)(62, 181)(63, 180)(64, 209)(65, 208)(66, 186)(67, 211)(68, 188)(69, 213)(70, 214)(71, 191)(72, 192)(73, 217)(74, 195)(75, 194)(76, 221)(77, 220)(78, 198)(79, 223)(80, 200)(81, 225)(82, 226)(83, 203)(84, 204)(85, 229)(86, 207)(87, 206)(88, 233)(89, 232)(90, 210)(91, 235)(92, 212)(93, 237)(94, 238)(95, 215)(96, 216)(97, 241)(98, 219)(99, 218)(100, 245)(101, 244)(102, 222)(103, 247)(104, 224)(105, 249)(106, 250)(107, 227)(108, 228)(109, 240)(110, 231)(111, 230)(112, 255)(113, 254)(114, 234)(115, 253)(116, 236)(117, 258)(118, 252)(119, 239)(120, 243)(121, 242)(122, 261)(123, 260)(124, 246)(125, 248)(126, 263)(127, 251)(128, 257)(129, 259)(130, 256)(131, 264)(132, 262) local type(s) :: { ( 6, 22, 6, 22 ) } Outer automorphisms :: reflexible Dual of E20.1082 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 66 e = 132 f = 28 degree seq :: [ 4^66 ] E20.1087 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 22}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^6, (Y3 * Y2^-1)^22 ] Map:: R = (1, 133, 2, 134)(3, 135, 7, 139)(4, 136, 9, 141)(5, 137, 11, 143)(6, 138, 13, 145)(8, 140, 14, 146)(10, 142, 12, 144)(15, 147, 23, 155)(16, 148, 24, 156)(17, 149, 25, 157)(18, 150, 26, 158)(19, 151, 27, 159)(20, 152, 28, 160)(21, 153, 29, 161)(22, 154, 30, 162)(31, 163, 37, 169)(32, 164, 38, 170)(33, 165, 39, 171)(34, 166, 40, 172)(35, 167, 41, 173)(36, 168, 42, 174)(43, 175, 49, 181)(44, 176, 50, 182)(45, 177, 51, 183)(46, 178, 52, 184)(47, 179, 53, 185)(48, 180, 54, 186)(55, 187, 73, 205)(56, 188, 63, 195)(57, 189, 62, 194)(58, 190, 97, 229)(59, 191, 101, 233)(60, 192, 93, 225)(61, 193, 95, 227)(64, 196, 113, 245)(65, 197, 110, 242)(66, 198, 98, 230)(67, 199, 112, 244)(68, 200, 121, 253)(69, 201, 106, 238)(70, 202, 102, 234)(71, 203, 108, 240)(72, 204, 91, 223)(74, 206, 118, 250)(75, 207, 114, 246)(76, 208, 100, 232)(77, 209, 116, 248)(78, 210, 126, 258)(79, 211, 122, 254)(80, 212, 104, 236)(81, 213, 124, 256)(82, 214, 127, 259)(83, 215, 123, 255)(84, 216, 131, 263)(85, 217, 119, 251)(86, 218, 115, 247)(87, 219, 132, 264)(88, 220, 103, 235)(89, 221, 128, 260)(90, 222, 125, 257)(92, 224, 99, 231)(94, 226, 120, 252)(96, 228, 117, 249)(105, 237, 130, 262)(107, 239, 111, 243)(109, 241, 129, 261)(265, 397, 267, 399, 272, 404, 281, 413, 274, 406, 268, 400)(266, 398, 269, 401, 276, 408, 285, 417, 278, 410, 270, 402)(271, 403, 279, 411, 273, 405, 282, 414, 289, 421, 280, 412)(275, 407, 283, 415, 277, 409, 286, 418, 293, 425, 284, 416)(287, 419, 295, 427, 288, 420, 297, 429, 290, 422, 296, 428)(291, 423, 298, 430, 292, 424, 300, 432, 294, 426, 299, 431)(301, 433, 307, 439, 302, 434, 309, 441, 303, 435, 308, 440)(304, 436, 310, 442, 305, 437, 312, 444, 306, 438, 311, 443)(313, 445, 319, 451, 314, 446, 321, 453, 315, 447, 320, 452)(316, 448, 355, 487, 317, 449, 357, 489, 318, 450, 359, 491)(322, 454, 362, 494, 329, 461, 377, 509, 331, 463, 364, 496)(323, 455, 366, 498, 333, 465, 385, 517, 335, 467, 368, 500)(324, 456, 365, 497, 336, 468, 372, 504, 325, 457, 370, 502)(326, 458, 361, 493, 337, 469, 376, 508, 327, 459, 374, 506)(328, 460, 378, 510, 330, 462, 382, 514, 340, 472, 380, 512)(332, 464, 386, 518, 334, 466, 390, 522, 344, 476, 388, 520)(338, 470, 387, 519, 339, 471, 391, 523, 341, 473, 395, 527)(342, 474, 379, 511, 343, 475, 383, 515, 345, 477, 396, 528)(346, 478, 392, 524, 347, 479, 367, 499, 348, 480, 389, 521)(349, 481, 384, 516, 350, 482, 363, 495, 351, 483, 381, 513)(352, 484, 371, 503, 353, 485, 369, 501, 354, 486, 393, 525)(356, 488, 375, 507, 358, 490, 373, 505, 360, 492, 394, 526) L = (1, 266)(2, 265)(3, 271)(4, 273)(5, 275)(6, 277)(7, 267)(8, 278)(9, 268)(10, 276)(11, 269)(12, 274)(13, 270)(14, 272)(15, 287)(16, 288)(17, 289)(18, 290)(19, 291)(20, 292)(21, 293)(22, 294)(23, 279)(24, 280)(25, 281)(26, 282)(27, 283)(28, 284)(29, 285)(30, 286)(31, 301)(32, 302)(33, 303)(34, 304)(35, 305)(36, 306)(37, 295)(38, 296)(39, 297)(40, 298)(41, 299)(42, 300)(43, 313)(44, 314)(45, 315)(46, 316)(47, 317)(48, 318)(49, 307)(50, 308)(51, 309)(52, 310)(53, 311)(54, 312)(55, 337)(56, 327)(57, 326)(58, 361)(59, 365)(60, 357)(61, 359)(62, 321)(63, 320)(64, 377)(65, 374)(66, 362)(67, 376)(68, 385)(69, 370)(70, 366)(71, 372)(72, 355)(73, 319)(74, 382)(75, 378)(76, 364)(77, 380)(78, 390)(79, 386)(80, 368)(81, 388)(82, 391)(83, 387)(84, 395)(85, 383)(86, 379)(87, 396)(88, 367)(89, 392)(90, 389)(91, 336)(92, 363)(93, 324)(94, 384)(95, 325)(96, 381)(97, 322)(98, 330)(99, 356)(100, 340)(101, 323)(102, 334)(103, 352)(104, 344)(105, 394)(106, 333)(107, 375)(108, 335)(109, 393)(110, 329)(111, 371)(112, 331)(113, 328)(114, 339)(115, 350)(116, 341)(117, 360)(118, 338)(119, 349)(120, 358)(121, 332)(122, 343)(123, 347)(124, 345)(125, 354)(126, 342)(127, 346)(128, 353)(129, 373)(130, 369)(131, 348)(132, 351)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 2, 44, 2, 44 ), ( 2, 44, 2, 44, 2, 44, 2, 44, 2, 44, 2, 44 ) } Outer automorphisms :: reflexible Dual of E20.1090 Graph:: bipartite v = 88 e = 264 f = 138 degree seq :: [ 4^66, 12^22 ] E20.1088 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 22}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^6, Y2^22 ] Map:: R = (1, 133, 2, 134, 6, 138, 14, 146, 12, 144, 4, 136)(3, 135, 9, 141, 19, 151, 26, 158, 15, 147, 8, 140)(5, 137, 11, 143, 22, 154, 25, 157, 16, 148, 7, 139)(10, 142, 18, 150, 27, 159, 38, 170, 31, 163, 20, 152)(13, 145, 17, 149, 28, 160, 37, 169, 34, 166, 23, 155)(21, 153, 32, 164, 43, 175, 50, 182, 39, 171, 30, 162)(24, 156, 35, 167, 46, 178, 49, 181, 40, 172, 29, 161)(33, 165, 42, 174, 51, 183, 62, 194, 55, 187, 44, 176)(36, 168, 41, 173, 52, 184, 61, 193, 58, 190, 47, 179)(45, 177, 56, 188, 67, 199, 74, 206, 63, 195, 54, 186)(48, 180, 59, 191, 70, 202, 73, 205, 64, 196, 53, 185)(57, 189, 66, 198, 75, 207, 86, 218, 79, 211, 68, 200)(60, 192, 65, 197, 76, 208, 85, 217, 82, 214, 71, 203)(69, 201, 80, 212, 91, 223, 98, 230, 87, 219, 78, 210)(72, 204, 83, 215, 94, 226, 97, 229, 88, 220, 77, 209)(81, 213, 90, 222, 99, 231, 110, 242, 103, 235, 92, 224)(84, 216, 89, 221, 100, 232, 109, 241, 106, 238, 95, 227)(93, 225, 104, 236, 115, 247, 121, 253, 111, 243, 102, 234)(96, 228, 107, 239, 118, 250, 120, 252, 112, 244, 101, 233)(105, 237, 114, 246, 122, 254, 129, 261, 125, 257, 116, 248)(108, 240, 113, 245, 123, 255, 128, 260, 127, 259, 119, 251)(117, 249, 126, 258, 131, 263, 132, 264, 130, 262, 124, 256)(265, 397, 267, 399, 274, 406, 285, 417, 297, 429, 309, 441, 321, 453, 333, 465, 345, 477, 357, 489, 369, 501, 381, 513, 372, 504, 360, 492, 348, 480, 336, 468, 324, 456, 312, 444, 300, 432, 288, 420, 277, 409, 269, 401)(266, 398, 271, 403, 281, 413, 293, 425, 305, 437, 317, 449, 329, 461, 341, 473, 353, 485, 365, 497, 377, 509, 388, 520, 378, 510, 366, 498, 354, 486, 342, 474, 330, 462, 318, 450, 306, 438, 294, 426, 282, 414, 272, 404)(268, 400, 275, 407, 287, 419, 299, 431, 311, 443, 323, 455, 335, 467, 347, 479, 359, 491, 371, 503, 383, 515, 390, 522, 380, 512, 368, 500, 356, 488, 344, 476, 332, 464, 320, 452, 308, 440, 296, 428, 284, 416, 273, 405)(270, 402, 279, 411, 291, 423, 303, 435, 315, 447, 327, 459, 339, 471, 351, 483, 363, 495, 375, 507, 386, 518, 394, 526, 387, 519, 376, 508, 364, 496, 352, 484, 340, 472, 328, 460, 316, 448, 304, 436, 292, 424, 280, 412)(276, 408, 283, 415, 295, 427, 307, 439, 319, 451, 331, 463, 343, 475, 355, 487, 367, 499, 379, 511, 389, 521, 395, 527, 391, 523, 382, 514, 370, 502, 358, 490, 346, 478, 334, 466, 322, 454, 310, 442, 298, 430, 286, 418)(278, 410, 289, 421, 301, 433, 313, 445, 325, 457, 337, 469, 349, 481, 361, 493, 373, 505, 384, 516, 392, 524, 396, 528, 393, 525, 385, 517, 374, 506, 362, 494, 350, 482, 338, 470, 326, 458, 314, 446, 302, 434, 290, 422) L = (1, 267)(2, 271)(3, 274)(4, 275)(5, 265)(6, 279)(7, 281)(8, 266)(9, 268)(10, 285)(11, 287)(12, 283)(13, 269)(14, 289)(15, 291)(16, 270)(17, 293)(18, 272)(19, 295)(20, 273)(21, 297)(22, 276)(23, 299)(24, 277)(25, 301)(26, 278)(27, 303)(28, 280)(29, 305)(30, 282)(31, 307)(32, 284)(33, 309)(34, 286)(35, 311)(36, 288)(37, 313)(38, 290)(39, 315)(40, 292)(41, 317)(42, 294)(43, 319)(44, 296)(45, 321)(46, 298)(47, 323)(48, 300)(49, 325)(50, 302)(51, 327)(52, 304)(53, 329)(54, 306)(55, 331)(56, 308)(57, 333)(58, 310)(59, 335)(60, 312)(61, 337)(62, 314)(63, 339)(64, 316)(65, 341)(66, 318)(67, 343)(68, 320)(69, 345)(70, 322)(71, 347)(72, 324)(73, 349)(74, 326)(75, 351)(76, 328)(77, 353)(78, 330)(79, 355)(80, 332)(81, 357)(82, 334)(83, 359)(84, 336)(85, 361)(86, 338)(87, 363)(88, 340)(89, 365)(90, 342)(91, 367)(92, 344)(93, 369)(94, 346)(95, 371)(96, 348)(97, 373)(98, 350)(99, 375)(100, 352)(101, 377)(102, 354)(103, 379)(104, 356)(105, 381)(106, 358)(107, 383)(108, 360)(109, 384)(110, 362)(111, 386)(112, 364)(113, 388)(114, 366)(115, 389)(116, 368)(117, 372)(118, 370)(119, 390)(120, 392)(121, 374)(122, 394)(123, 376)(124, 378)(125, 395)(126, 380)(127, 382)(128, 396)(129, 385)(130, 387)(131, 391)(132, 393)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.1089 Graph:: bipartite v = 28 e = 264 f = 198 degree seq :: [ 12^22, 44^6 ] E20.1089 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 22}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, (Y3^-1 * Y2)^6, (Y3^-1 * Y1^-1)^22 ] Map:: polytopal R = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)(265, 397, 266, 398)(267, 399, 271, 403)(268, 400, 273, 405)(269, 401, 275, 407)(270, 402, 277, 409)(272, 404, 278, 410)(274, 406, 276, 408)(279, 411, 289, 421)(280, 412, 290, 422)(281, 413, 291, 423)(282, 414, 293, 425)(283, 415, 294, 426)(284, 416, 296, 428)(285, 417, 297, 429)(286, 418, 298, 430)(287, 419, 300, 432)(288, 420, 301, 433)(292, 424, 302, 434)(295, 427, 299, 431)(303, 435, 312, 444)(304, 436, 311, 443)(305, 437, 316, 448)(306, 438, 319, 451)(307, 439, 320, 452)(308, 440, 313, 445)(309, 441, 322, 454)(310, 442, 323, 455)(314, 446, 325, 457)(315, 447, 326, 458)(317, 449, 328, 460)(318, 450, 329, 461)(321, 453, 330, 462)(324, 456, 327, 459)(331, 463, 340, 472)(332, 464, 343, 475)(333, 465, 344, 476)(334, 466, 337, 469)(335, 467, 346, 478)(336, 468, 347, 479)(338, 470, 349, 481)(339, 471, 350, 482)(341, 473, 352, 484)(342, 474, 353, 485)(345, 477, 354, 486)(348, 480, 351, 483)(355, 487, 364, 496)(356, 488, 367, 499)(357, 489, 368, 500)(358, 490, 361, 493)(359, 491, 370, 502)(360, 492, 371, 503)(362, 494, 373, 505)(363, 495, 374, 506)(365, 497, 376, 508)(366, 498, 377, 509)(369, 501, 378, 510)(372, 504, 375, 507)(379, 511, 387, 519)(380, 512, 389, 521)(381, 513, 390, 522)(382, 514, 384, 516)(383, 515, 391, 523)(385, 517, 392, 524)(386, 518, 393, 525)(388, 520, 394, 526)(395, 527, 396, 528) L = (1, 267)(2, 269)(3, 272)(4, 265)(5, 276)(6, 266)(7, 279)(8, 281)(9, 282)(10, 268)(11, 284)(12, 286)(13, 287)(14, 270)(15, 273)(16, 271)(17, 292)(18, 294)(19, 274)(20, 277)(21, 275)(22, 299)(23, 301)(24, 278)(25, 303)(26, 305)(27, 280)(28, 307)(29, 304)(30, 309)(31, 283)(32, 311)(33, 313)(34, 285)(35, 315)(36, 312)(37, 317)(38, 288)(39, 290)(40, 289)(41, 319)(42, 291)(43, 321)(44, 293)(45, 323)(46, 295)(47, 297)(48, 296)(49, 325)(50, 298)(51, 327)(52, 300)(53, 329)(54, 302)(55, 331)(56, 306)(57, 333)(58, 308)(59, 335)(60, 310)(61, 337)(62, 314)(63, 339)(64, 316)(65, 341)(66, 318)(67, 343)(68, 320)(69, 345)(70, 322)(71, 347)(72, 324)(73, 349)(74, 326)(75, 351)(76, 328)(77, 353)(78, 330)(79, 355)(80, 332)(81, 357)(82, 334)(83, 359)(84, 336)(85, 361)(86, 338)(87, 363)(88, 340)(89, 365)(90, 342)(91, 367)(92, 344)(93, 369)(94, 346)(95, 371)(96, 348)(97, 373)(98, 350)(99, 375)(100, 352)(101, 377)(102, 354)(103, 379)(104, 356)(105, 381)(106, 358)(107, 383)(108, 360)(109, 384)(110, 362)(111, 386)(112, 364)(113, 388)(114, 366)(115, 389)(116, 368)(117, 372)(118, 370)(119, 390)(120, 392)(121, 374)(122, 378)(123, 376)(124, 393)(125, 395)(126, 380)(127, 382)(128, 396)(129, 385)(130, 387)(131, 391)(132, 394)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 12, 44 ), ( 12, 44, 12, 44 ) } Outer automorphisms :: reflexible Dual of E20.1088 Graph:: simple bipartite v = 198 e = 264 f = 28 degree seq :: [ 2^132, 4^66 ] E20.1090 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 22}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^-2 * Y3^-1, (Y3^-1 * Y1)^6, Y1^22 ] Map:: polytopal R = (1, 133, 2, 134, 5, 137, 11, 143, 20, 152, 32, 164, 47, 179, 61, 193, 73, 205, 85, 217, 97, 229, 109, 241, 108, 240, 96, 228, 84, 216, 72, 204, 60, 192, 46, 178, 31, 163, 19, 151, 10, 142, 4, 136)(3, 135, 7, 139, 15, 147, 25, 157, 39, 171, 55, 187, 67, 199, 79, 211, 91, 223, 103, 235, 115, 247, 121, 253, 110, 242, 99, 231, 86, 218, 75, 207, 62, 194, 49, 181, 33, 165, 22, 154, 12, 144, 8, 140)(6, 138, 13, 145, 9, 141, 18, 150, 29, 161, 44, 176, 58, 190, 70, 202, 82, 214, 94, 226, 106, 238, 118, 250, 120, 252, 111, 243, 98, 230, 87, 219, 74, 206, 63, 195, 48, 180, 34, 166, 21, 153, 14, 146)(16, 148, 26, 158, 17, 149, 28, 160, 35, 167, 51, 183, 64, 196, 77, 209, 88, 220, 101, 233, 112, 244, 123, 255, 128, 260, 125, 257, 116, 248, 104, 236, 92, 224, 80, 212, 68, 200, 56, 188, 40, 172, 27, 159)(23, 155, 36, 168, 24, 156, 38, 170, 50, 182, 65, 197, 76, 208, 89, 221, 100, 232, 113, 245, 122, 254, 129, 261, 127, 259, 119, 251, 107, 239, 95, 227, 83, 215, 71, 203, 59, 191, 45, 177, 30, 162, 37, 169)(41, 173, 53, 185, 42, 174, 57, 189, 69, 201, 81, 213, 93, 225, 105, 237, 117, 249, 126, 258, 131, 263, 132, 264, 130, 262, 124, 256, 114, 246, 102, 234, 90, 222, 78, 210, 66, 198, 54, 186, 43, 175, 52, 184)(265, 397)(266, 398)(267, 399)(268, 400)(269, 401)(270, 402)(271, 403)(272, 404)(273, 405)(274, 406)(275, 407)(276, 408)(277, 409)(278, 410)(279, 411)(280, 412)(281, 413)(282, 414)(283, 415)(284, 416)(285, 417)(286, 418)(287, 419)(288, 420)(289, 421)(290, 422)(291, 423)(292, 424)(293, 425)(294, 426)(295, 427)(296, 428)(297, 429)(298, 430)(299, 431)(300, 432)(301, 433)(302, 434)(303, 435)(304, 436)(305, 437)(306, 438)(307, 439)(308, 440)(309, 441)(310, 442)(311, 443)(312, 444)(313, 445)(314, 446)(315, 447)(316, 448)(317, 449)(318, 450)(319, 451)(320, 452)(321, 453)(322, 454)(323, 455)(324, 456)(325, 457)(326, 458)(327, 459)(328, 460)(329, 461)(330, 462)(331, 463)(332, 464)(333, 465)(334, 466)(335, 467)(336, 468)(337, 469)(338, 470)(339, 471)(340, 472)(341, 473)(342, 474)(343, 475)(344, 476)(345, 477)(346, 478)(347, 479)(348, 480)(349, 481)(350, 482)(351, 483)(352, 484)(353, 485)(354, 486)(355, 487)(356, 488)(357, 489)(358, 490)(359, 491)(360, 492)(361, 493)(362, 494)(363, 495)(364, 496)(365, 497)(366, 498)(367, 499)(368, 500)(369, 501)(370, 502)(371, 503)(372, 504)(373, 505)(374, 506)(375, 507)(376, 508)(377, 509)(378, 510)(379, 511)(380, 512)(381, 513)(382, 514)(383, 515)(384, 516)(385, 517)(386, 518)(387, 519)(388, 520)(389, 521)(390, 522)(391, 523)(392, 524)(393, 525)(394, 526)(395, 527)(396, 528) L = (1, 267)(2, 270)(3, 265)(4, 273)(5, 276)(6, 266)(7, 280)(8, 281)(9, 268)(10, 279)(11, 285)(12, 269)(13, 287)(14, 288)(15, 274)(16, 271)(17, 272)(18, 294)(19, 293)(20, 297)(21, 275)(22, 299)(23, 277)(24, 278)(25, 304)(26, 305)(27, 306)(28, 307)(29, 283)(30, 282)(31, 303)(32, 312)(33, 284)(34, 314)(35, 286)(36, 316)(37, 317)(38, 318)(39, 295)(40, 289)(41, 290)(42, 291)(43, 292)(44, 323)(45, 321)(46, 322)(47, 326)(48, 296)(49, 328)(50, 298)(51, 330)(52, 300)(53, 301)(54, 302)(55, 332)(56, 333)(57, 309)(58, 310)(59, 308)(60, 331)(61, 338)(62, 311)(63, 340)(64, 313)(65, 342)(66, 315)(67, 324)(68, 319)(69, 320)(70, 347)(71, 345)(72, 346)(73, 350)(74, 325)(75, 352)(76, 327)(77, 354)(78, 329)(79, 356)(80, 357)(81, 335)(82, 336)(83, 334)(84, 355)(85, 362)(86, 337)(87, 364)(88, 339)(89, 366)(90, 341)(91, 348)(92, 343)(93, 344)(94, 371)(95, 369)(96, 370)(97, 374)(98, 349)(99, 376)(100, 351)(101, 378)(102, 353)(103, 380)(104, 381)(105, 359)(106, 360)(107, 358)(108, 379)(109, 384)(110, 361)(111, 386)(112, 363)(113, 388)(114, 365)(115, 372)(116, 367)(117, 368)(118, 391)(119, 390)(120, 373)(121, 392)(122, 375)(123, 394)(124, 377)(125, 395)(126, 383)(127, 382)(128, 385)(129, 396)(130, 387)(131, 389)(132, 393)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4, 12 ), ( 4, 12, 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 E20.1087 Graph:: simple bipartite v = 138 e = 264 f = 88 degree seq :: [ 2^132, 44^6 ] E20.1091 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 22}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^6, Y2^22 ] Map:: R = (1, 133, 2, 134)(3, 135, 7, 139)(4, 136, 9, 141)(5, 137, 11, 143)(6, 138, 13, 145)(8, 140, 14, 146)(10, 142, 12, 144)(15, 147, 25, 157)(16, 148, 26, 158)(17, 149, 27, 159)(18, 150, 29, 161)(19, 151, 30, 162)(20, 152, 32, 164)(21, 153, 33, 165)(22, 154, 34, 166)(23, 155, 36, 168)(24, 156, 37, 169)(28, 160, 38, 170)(31, 163, 35, 167)(39, 171, 48, 180)(40, 172, 47, 179)(41, 173, 52, 184)(42, 174, 55, 187)(43, 175, 56, 188)(44, 176, 49, 181)(45, 177, 58, 190)(46, 178, 59, 191)(50, 182, 61, 193)(51, 183, 62, 194)(53, 185, 64, 196)(54, 186, 65, 197)(57, 189, 66, 198)(60, 192, 63, 195)(67, 199, 76, 208)(68, 200, 79, 211)(69, 201, 80, 212)(70, 202, 73, 205)(71, 203, 82, 214)(72, 204, 83, 215)(74, 206, 85, 217)(75, 207, 86, 218)(77, 209, 88, 220)(78, 210, 89, 221)(81, 213, 90, 222)(84, 216, 87, 219)(91, 223, 100, 232)(92, 224, 103, 235)(93, 225, 104, 236)(94, 226, 97, 229)(95, 227, 106, 238)(96, 228, 107, 239)(98, 230, 109, 241)(99, 231, 110, 242)(101, 233, 112, 244)(102, 234, 113, 245)(105, 237, 114, 246)(108, 240, 111, 243)(115, 247, 123, 255)(116, 248, 125, 257)(117, 249, 126, 258)(118, 250, 120, 252)(119, 251, 127, 259)(121, 253, 128, 260)(122, 254, 129, 261)(124, 256, 130, 262)(131, 263, 132, 264)(265, 397, 267, 399, 272, 404, 281, 413, 292, 424, 307, 439, 321, 453, 333, 465, 345, 477, 357, 489, 369, 501, 381, 513, 372, 504, 360, 492, 348, 480, 336, 468, 324, 456, 310, 442, 295, 427, 283, 415, 274, 406, 268, 400)(266, 398, 269, 401, 276, 408, 286, 418, 299, 431, 315, 447, 327, 459, 339, 471, 351, 483, 363, 495, 375, 507, 386, 518, 378, 510, 366, 498, 354, 486, 342, 474, 330, 462, 318, 450, 302, 434, 288, 420, 278, 410, 270, 402)(271, 403, 279, 411, 273, 405, 282, 414, 294, 426, 309, 441, 323, 455, 335, 467, 347, 479, 359, 491, 371, 503, 383, 515, 390, 522, 380, 512, 368, 500, 356, 488, 344, 476, 332, 464, 320, 452, 306, 438, 291, 423, 280, 412)(275, 407, 284, 416, 277, 409, 287, 419, 301, 433, 317, 449, 329, 461, 341, 473, 353, 485, 365, 497, 377, 509, 388, 520, 393, 525, 385, 517, 374, 506, 362, 494, 350, 482, 338, 470, 326, 458, 314, 446, 298, 430, 285, 417)(289, 421, 303, 435, 290, 422, 305, 437, 319, 451, 331, 463, 343, 475, 355, 487, 367, 499, 379, 511, 389, 521, 395, 527, 391, 523, 382, 514, 370, 502, 358, 490, 346, 478, 334, 466, 322, 454, 308, 440, 293, 425, 304, 436)(296, 428, 311, 443, 297, 429, 313, 445, 325, 457, 337, 469, 349, 481, 361, 493, 373, 505, 384, 516, 392, 524, 396, 528, 394, 526, 387, 519, 376, 508, 364, 496, 352, 484, 340, 472, 328, 460, 316, 448, 300, 432, 312, 444) L = (1, 266)(2, 265)(3, 271)(4, 273)(5, 275)(6, 277)(7, 267)(8, 278)(9, 268)(10, 276)(11, 269)(12, 274)(13, 270)(14, 272)(15, 289)(16, 290)(17, 291)(18, 293)(19, 294)(20, 296)(21, 297)(22, 298)(23, 300)(24, 301)(25, 279)(26, 280)(27, 281)(28, 302)(29, 282)(30, 283)(31, 299)(32, 284)(33, 285)(34, 286)(35, 295)(36, 287)(37, 288)(38, 292)(39, 312)(40, 311)(41, 316)(42, 319)(43, 320)(44, 313)(45, 322)(46, 323)(47, 304)(48, 303)(49, 308)(50, 325)(51, 326)(52, 305)(53, 328)(54, 329)(55, 306)(56, 307)(57, 330)(58, 309)(59, 310)(60, 327)(61, 314)(62, 315)(63, 324)(64, 317)(65, 318)(66, 321)(67, 340)(68, 343)(69, 344)(70, 337)(71, 346)(72, 347)(73, 334)(74, 349)(75, 350)(76, 331)(77, 352)(78, 353)(79, 332)(80, 333)(81, 354)(82, 335)(83, 336)(84, 351)(85, 338)(86, 339)(87, 348)(88, 341)(89, 342)(90, 345)(91, 364)(92, 367)(93, 368)(94, 361)(95, 370)(96, 371)(97, 358)(98, 373)(99, 374)(100, 355)(101, 376)(102, 377)(103, 356)(104, 357)(105, 378)(106, 359)(107, 360)(108, 375)(109, 362)(110, 363)(111, 372)(112, 365)(113, 366)(114, 369)(115, 387)(116, 389)(117, 390)(118, 384)(119, 391)(120, 382)(121, 392)(122, 393)(123, 379)(124, 394)(125, 380)(126, 381)(127, 383)(128, 385)(129, 386)(130, 388)(131, 396)(132, 395)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 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 E20.1092 Graph:: bipartite v = 72 e = 264 f = 154 degree seq :: [ 4^66, 44^6 ] E20.1092 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 22}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^22 ] Map:: polytopal R = (1, 133, 2, 134, 6, 138, 14, 146, 12, 144, 4, 136)(3, 135, 9, 141, 19, 151, 26, 158, 15, 147, 8, 140)(5, 137, 11, 143, 22, 154, 25, 157, 16, 148, 7, 139)(10, 142, 18, 150, 27, 159, 38, 170, 31, 163, 20, 152)(13, 145, 17, 149, 28, 160, 37, 169, 34, 166, 23, 155)(21, 153, 32, 164, 43, 175, 50, 182, 39, 171, 30, 162)(24, 156, 35, 167, 46, 178, 49, 181, 40, 172, 29, 161)(33, 165, 42, 174, 51, 183, 62, 194, 55, 187, 44, 176)(36, 168, 41, 173, 52, 184, 61, 193, 58, 190, 47, 179)(45, 177, 56, 188, 67, 199, 74, 206, 63, 195, 54, 186)(48, 180, 59, 191, 70, 202, 73, 205, 64, 196, 53, 185)(57, 189, 66, 198, 75, 207, 86, 218, 79, 211, 68, 200)(60, 192, 65, 197, 76, 208, 85, 217, 82, 214, 71, 203)(69, 201, 80, 212, 91, 223, 98, 230, 87, 219, 78, 210)(72, 204, 83, 215, 94, 226, 97, 229, 88, 220, 77, 209)(81, 213, 90, 222, 99, 231, 110, 242, 103, 235, 92, 224)(84, 216, 89, 221, 100, 232, 109, 241, 106, 238, 95, 227)(93, 225, 104, 236, 115, 247, 121, 253, 111, 243, 102, 234)(96, 228, 107, 239, 118, 250, 120, 252, 112, 244, 101, 233)(105, 237, 114, 246, 122, 254, 129, 261, 125, 257, 116, 248)(108, 240, 113, 245, 123, 255, 128, 260, 127, 259, 119, 251)(117, 249, 126, 258, 131, 263, 132, 264, 130, 262, 124, 256)(265, 397)(266, 398)(267, 399)(268, 400)(269, 401)(270, 402)(271, 403)(272, 404)(273, 405)(274, 406)(275, 407)(276, 408)(277, 409)(278, 410)(279, 411)(280, 412)(281, 413)(282, 414)(283, 415)(284, 416)(285, 417)(286, 418)(287, 419)(288, 420)(289, 421)(290, 422)(291, 423)(292, 424)(293, 425)(294, 426)(295, 427)(296, 428)(297, 429)(298, 430)(299, 431)(300, 432)(301, 433)(302, 434)(303, 435)(304, 436)(305, 437)(306, 438)(307, 439)(308, 440)(309, 441)(310, 442)(311, 443)(312, 444)(313, 445)(314, 446)(315, 447)(316, 448)(317, 449)(318, 450)(319, 451)(320, 452)(321, 453)(322, 454)(323, 455)(324, 456)(325, 457)(326, 458)(327, 459)(328, 460)(329, 461)(330, 462)(331, 463)(332, 464)(333, 465)(334, 466)(335, 467)(336, 468)(337, 469)(338, 470)(339, 471)(340, 472)(341, 473)(342, 474)(343, 475)(344, 476)(345, 477)(346, 478)(347, 479)(348, 480)(349, 481)(350, 482)(351, 483)(352, 484)(353, 485)(354, 486)(355, 487)(356, 488)(357, 489)(358, 490)(359, 491)(360, 492)(361, 493)(362, 494)(363, 495)(364, 496)(365, 497)(366, 498)(367, 499)(368, 500)(369, 501)(370, 502)(371, 503)(372, 504)(373, 505)(374, 506)(375, 507)(376, 508)(377, 509)(378, 510)(379, 511)(380, 512)(381, 513)(382, 514)(383, 515)(384, 516)(385, 517)(386, 518)(387, 519)(388, 520)(389, 521)(390, 522)(391, 523)(392, 524)(393, 525)(394, 526)(395, 527)(396, 528) L = (1, 267)(2, 271)(3, 274)(4, 275)(5, 265)(6, 279)(7, 281)(8, 266)(9, 268)(10, 285)(11, 287)(12, 283)(13, 269)(14, 289)(15, 291)(16, 270)(17, 293)(18, 272)(19, 295)(20, 273)(21, 297)(22, 276)(23, 299)(24, 277)(25, 301)(26, 278)(27, 303)(28, 280)(29, 305)(30, 282)(31, 307)(32, 284)(33, 309)(34, 286)(35, 311)(36, 288)(37, 313)(38, 290)(39, 315)(40, 292)(41, 317)(42, 294)(43, 319)(44, 296)(45, 321)(46, 298)(47, 323)(48, 300)(49, 325)(50, 302)(51, 327)(52, 304)(53, 329)(54, 306)(55, 331)(56, 308)(57, 333)(58, 310)(59, 335)(60, 312)(61, 337)(62, 314)(63, 339)(64, 316)(65, 341)(66, 318)(67, 343)(68, 320)(69, 345)(70, 322)(71, 347)(72, 324)(73, 349)(74, 326)(75, 351)(76, 328)(77, 353)(78, 330)(79, 355)(80, 332)(81, 357)(82, 334)(83, 359)(84, 336)(85, 361)(86, 338)(87, 363)(88, 340)(89, 365)(90, 342)(91, 367)(92, 344)(93, 369)(94, 346)(95, 371)(96, 348)(97, 373)(98, 350)(99, 375)(100, 352)(101, 377)(102, 354)(103, 379)(104, 356)(105, 381)(106, 358)(107, 383)(108, 360)(109, 384)(110, 362)(111, 386)(112, 364)(113, 388)(114, 366)(115, 389)(116, 368)(117, 372)(118, 370)(119, 390)(120, 392)(121, 374)(122, 394)(123, 376)(124, 378)(125, 395)(126, 380)(127, 382)(128, 396)(129, 385)(130, 387)(131, 391)(132, 393)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) } Outer automorphisms :: reflexible Dual of E20.1091 Graph:: simple bipartite v = 154 e = 264 f = 72 degree seq :: [ 2^132, 12^22 ] E20.1093 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 9}) Quotient :: regular Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1^2)^2, T1^9, (T2 * T1^-1 * T2 * T1 * T2 * T1)^2, (T2 * T1 * T2 * T1 * T2 * T1^-1)^2, (T1^-1 * T2)^8 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 42, 22, 10, 4)(3, 7, 15, 31, 54, 44, 24, 18, 8)(6, 13, 27, 21, 41, 71, 43, 30, 14)(9, 19, 38, 65, 47, 26, 12, 25, 20)(16, 33, 57, 37, 64, 101, 89, 60, 34)(17, 35, 61, 73, 92, 56, 32, 55, 36)(28, 49, 81, 53, 88, 108, 72, 84, 50)(29, 51, 85, 107, 116, 80, 48, 79, 52)(39, 67, 75, 45, 74, 109, 78, 105, 68)(40, 69, 77, 46, 76, 104, 66, 103, 70)(58, 94, 115, 96, 129, 120, 102, 121, 87)(59, 95, 128, 132, 134, 117, 93, 111, 83)(62, 98, 114, 90, 123, 136, 126, 112, 86)(63, 99, 125, 91, 124, 130, 97, 110, 100)(82, 118, 106, 119, 138, 133, 122, 135, 113)(127, 137, 131, 139, 143, 142, 141, 144, 140) 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, 43)(25, 45)(26, 46)(27, 48)(30, 53)(33, 58)(34, 59)(35, 62)(36, 63)(38, 66)(41, 72)(42, 65)(44, 73)(47, 78)(49, 82)(50, 83)(51, 86)(52, 87)(54, 89)(55, 90)(56, 91)(57, 93)(60, 96)(61, 97)(64, 102)(67, 99)(68, 95)(69, 98)(70, 106)(71, 107)(74, 110)(75, 111)(76, 112)(77, 113)(79, 114)(80, 115)(81, 117)(84, 119)(85, 120)(88, 122)(92, 126)(94, 127)(100, 131)(101, 132)(103, 123)(104, 133)(105, 124)(108, 128)(109, 134)(116, 136)(118, 137)(121, 139)(125, 140)(129, 141)(130, 142)(135, 143)(138, 144) local type(s) :: { ( 8^9 ) } Outer automorphisms :: reflexible Dual of E20.1094 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 16 e = 72 f = 18 degree seq :: [ 9^16 ] E20.1094 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 9}) Quotient :: regular Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^8, (T2 * T1^-4)^2, (T2 * T1 * T2 * T1^-2)^2, (T1^-1 * T2 * T1^-1 * T2 * T1^-1)^2, (T1 * T2)^9 ] Map:: polytopal 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, 96, 74, 56)(29, 57, 40, 71, 79, 95, 73, 58)(32, 62, 78, 54, 37, 69, 75, 59)(64, 87, 68, 92, 98, 118, 105, 88)(65, 89, 67, 91, 106, 117, 97, 90)(80, 99, 83, 104, 116, 113, 93, 100)(81, 101, 82, 103, 94, 114, 115, 102)(107, 125, 110, 130, 136, 131, 111, 126)(108, 127, 109, 129, 112, 132, 135, 128)(119, 137, 122, 142, 133, 143, 123, 138)(120, 139, 121, 141, 124, 144, 134, 140) 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, 93)(72, 94)(76, 97)(77, 98)(85, 105)(86, 106)(87, 107)(88, 108)(89, 109)(90, 110)(91, 111)(92, 112)(95, 115)(96, 116)(99, 119)(100, 120)(101, 121)(102, 122)(103, 123)(104, 124)(113, 133)(114, 134)(117, 135)(118, 136)(125, 140)(126, 137)(127, 142)(128, 139)(129, 144)(130, 143)(131, 141)(132, 138) local type(s) :: { ( 9^8 ) } Outer automorphisms :: reflexible Dual of E20.1093 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 18 e = 72 f = 16 degree seq :: [ 8^18 ] E20.1095 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 9}) Quotient :: edge Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-3 * T1 * T2^-1)^2, (T2^-1 * T1 * T2 * T1 * T2^-1)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^9 ] Map:: polytopal 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, 92, 109, 87, 62)(33, 64, 39, 71, 88, 110, 91, 65)(46, 73, 56, 84, 102, 119, 97, 74)(48, 76, 54, 83, 98, 120, 101, 77)(85, 105, 90, 112, 130, 113, 93, 106)(86, 107, 89, 111, 94, 114, 129, 108)(95, 115, 100, 122, 140, 123, 103, 116)(96, 117, 99, 121, 104, 124, 139, 118)(125, 136, 128, 137, 133, 142, 131, 144)(126, 138, 127, 143, 132, 141, 134, 135)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 169)(158, 173)(159, 175)(160, 177)(162, 181)(163, 183)(164, 185)(166, 189)(167, 190)(168, 192)(170, 196)(171, 198)(172, 200)(174, 204)(176, 203)(178, 195)(179, 201)(180, 193)(182, 197)(184, 202)(186, 194)(187, 199)(188, 191)(205, 229)(206, 230)(207, 232)(208, 233)(209, 234)(210, 236)(211, 224)(212, 223)(213, 235)(214, 231)(215, 237)(216, 238)(217, 239)(218, 240)(219, 242)(220, 243)(221, 244)(222, 246)(225, 245)(226, 241)(227, 247)(228, 248)(249, 269)(250, 270)(251, 271)(252, 272)(253, 274)(254, 273)(255, 275)(256, 276)(257, 277)(258, 278)(259, 279)(260, 280)(261, 281)(262, 282)(263, 284)(264, 283)(265, 285)(266, 286)(267, 287)(268, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 18, 18 ), ( 18^8 ) } Outer automorphisms :: reflexible Dual of E20.1099 Transitivity :: ET+ Graph:: simple bipartite v = 90 e = 144 f = 16 degree seq :: [ 2^72, 8^18 ] E20.1096 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 9}) Quotient :: edge Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, (T2^2 * T1^-1)^2, (T1^-1 * T2 * T1^-2)^2, T1^8, T2^9, T1 * T2^-1 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2^-1, T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2^-2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 26, 58, 71, 36, 15, 5)(2, 7, 19, 45, 85, 92, 50, 22, 8)(4, 12, 30, 65, 103, 95, 55, 24, 9)(6, 17, 40, 78, 112, 114, 82, 43, 18)(11, 27, 14, 35, 69, 106, 99, 57, 25)(13, 32, 54, 94, 122, 127, 101, 63, 29)(16, 38, 74, 109, 133, 134, 110, 76, 39)(20, 46, 21, 49, 90, 120, 117, 84, 44)(23, 52, 93, 121, 128, 102, 64, 31, 53)(28, 61, 98, 125, 130, 105, 70, 75, 59)(33, 67, 100, 126, 142, 141, 123, 96, 66)(34, 60, 80, 56, 97, 124, 129, 104, 68)(37, 72, 107, 131, 143, 144, 132, 108, 73)(41, 79, 42, 81, 113, 136, 135, 111, 77)(47, 88, 116, 138, 140, 119, 91, 51, 86)(48, 87, 62, 83, 115, 137, 139, 118, 89)(145, 146, 150, 160, 181, 177, 157, 148)(147, 153, 167, 195, 216, 183, 172, 155)(149, 158, 178, 211, 217, 191, 164, 151)(152, 165, 192, 176, 210, 224, 185, 161)(154, 169, 200, 240, 251, 235, 193, 166)(156, 173, 206, 219, 182, 162, 186, 175)(159, 174, 208, 232, 252, 218, 214, 179)(163, 188, 227, 207, 244, 212, 225, 187)(168, 198, 233, 205, 220, 184, 221, 196)(170, 194, 222, 254, 275, 267, 238, 199)(171, 203, 231, 190, 230, 197, 223, 204)(180, 189, 226, 253, 276, 270, 245, 209)(201, 242, 262, 234, 263, 237, 255, 241)(202, 239, 265, 284, 287, 278, 269, 243)(213, 249, 259, 228, 260, 246, 257, 248)(215, 250, 273, 286, 288, 282, 261, 229)(236, 264, 283, 266, 285, 268, 279, 256)(247, 271, 281, 274, 277, 258, 280, 272) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 4^8 ), ( 4^9 ) } Outer automorphisms :: reflexible Dual of E20.1100 Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 144 f = 72 degree seq :: [ 8^18, 9^16 ] E20.1097 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 9}) Quotient :: edge Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1^2)^2, T1^9, (T2 * T1^-1 * T2 * T1 * T2 * T1)^2, (T2 * T1 * T2 * T1 * T2 * T1^-1)^2, (T2 * T1^-1)^8 ] 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, 37)(19, 39)(20, 40)(22, 31)(23, 43)(25, 45)(26, 46)(27, 48)(30, 53)(33, 58)(34, 59)(35, 62)(36, 63)(38, 66)(41, 72)(42, 65)(44, 73)(47, 78)(49, 82)(50, 83)(51, 86)(52, 87)(54, 89)(55, 90)(56, 91)(57, 93)(60, 96)(61, 97)(64, 102)(67, 99)(68, 95)(69, 98)(70, 106)(71, 107)(74, 110)(75, 111)(76, 112)(77, 113)(79, 114)(80, 115)(81, 117)(84, 119)(85, 120)(88, 122)(92, 126)(94, 127)(100, 131)(101, 132)(103, 123)(104, 133)(105, 124)(108, 128)(109, 134)(116, 136)(118, 137)(121, 139)(125, 140)(129, 141)(130, 142)(135, 143)(138, 144)(145, 146, 149, 155, 167, 186, 166, 154, 148)(147, 151, 159, 175, 198, 188, 168, 162, 152)(150, 157, 171, 165, 185, 215, 187, 174, 158)(153, 163, 182, 209, 191, 170, 156, 169, 164)(160, 177, 201, 181, 208, 245, 233, 204, 178)(161, 179, 205, 217, 236, 200, 176, 199, 180)(172, 193, 225, 197, 232, 252, 216, 228, 194)(173, 195, 229, 251, 260, 224, 192, 223, 196)(183, 211, 219, 189, 218, 253, 222, 249, 212)(184, 213, 221, 190, 220, 248, 210, 247, 214)(202, 238, 259, 240, 273, 264, 246, 265, 231)(203, 239, 272, 276, 278, 261, 237, 255, 227)(206, 242, 258, 234, 267, 280, 270, 256, 230)(207, 243, 269, 235, 268, 274, 241, 254, 244)(226, 262, 250, 263, 282, 277, 266, 279, 257)(271, 281, 275, 283, 287, 286, 285, 288, 284) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288) local type(s) :: { ( 16, 16 ), ( 16^9 ) } Outer automorphisms :: reflexible Dual of E20.1098 Transitivity :: ET+ Graph:: simple bipartite v = 88 e = 144 f = 18 degree seq :: [ 2^72, 9^16 ] E20.1098 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 9}) Quotient :: loop Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^8, (T2^-3 * T1 * T2^-1)^2, (T2^-1 * T1 * T2 * T1 * T2^-1)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^9 ] Map:: R = (1, 145, 3, 147, 8, 152, 18, 162, 38, 182, 22, 166, 10, 154, 4, 148)(2, 146, 5, 149, 12, 156, 26, 170, 53, 197, 30, 174, 14, 158, 6, 150)(7, 151, 15, 159, 32, 176, 63, 207, 45, 189, 66, 210, 34, 178, 16, 160)(9, 153, 19, 163, 40, 184, 70, 214, 37, 181, 69, 213, 42, 186, 20, 164)(11, 155, 23, 167, 47, 191, 75, 219, 60, 204, 78, 222, 49, 193, 24, 168)(13, 157, 27, 171, 55, 199, 82, 226, 52, 196, 81, 225, 57, 201, 28, 172)(17, 161, 35, 179, 67, 211, 44, 188, 21, 165, 43, 187, 68, 212, 36, 180)(25, 169, 50, 194, 79, 223, 59, 203, 29, 173, 58, 202, 80, 224, 51, 195)(31, 175, 61, 205, 41, 185, 72, 216, 92, 236, 109, 253, 87, 231, 62, 206)(33, 177, 64, 208, 39, 183, 71, 215, 88, 232, 110, 254, 91, 235, 65, 209)(46, 190, 73, 217, 56, 200, 84, 228, 102, 246, 119, 263, 97, 241, 74, 218)(48, 192, 76, 220, 54, 198, 83, 227, 98, 242, 120, 264, 101, 245, 77, 221)(85, 229, 105, 249, 90, 234, 112, 256, 130, 274, 113, 257, 93, 237, 106, 250)(86, 230, 107, 251, 89, 233, 111, 255, 94, 238, 114, 258, 129, 273, 108, 252)(95, 239, 115, 259, 100, 244, 122, 266, 140, 284, 123, 267, 103, 247, 116, 260)(96, 240, 117, 261, 99, 243, 121, 265, 104, 248, 124, 268, 139, 283, 118, 262)(125, 269, 136, 280, 128, 272, 137, 281, 133, 277, 142, 286, 131, 275, 144, 288)(126, 270, 138, 282, 127, 271, 143, 287, 132, 276, 141, 285, 134, 278, 135, 279) L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 161)(9, 148)(10, 165)(11, 149)(12, 169)(13, 150)(14, 173)(15, 175)(16, 177)(17, 152)(18, 181)(19, 183)(20, 185)(21, 154)(22, 189)(23, 190)(24, 192)(25, 156)(26, 196)(27, 198)(28, 200)(29, 158)(30, 204)(31, 159)(32, 203)(33, 160)(34, 195)(35, 201)(36, 193)(37, 162)(38, 197)(39, 163)(40, 202)(41, 164)(42, 194)(43, 199)(44, 191)(45, 166)(46, 167)(47, 188)(48, 168)(49, 180)(50, 186)(51, 178)(52, 170)(53, 182)(54, 171)(55, 187)(56, 172)(57, 179)(58, 184)(59, 176)(60, 174)(61, 229)(62, 230)(63, 232)(64, 233)(65, 234)(66, 236)(67, 224)(68, 223)(69, 235)(70, 231)(71, 237)(72, 238)(73, 239)(74, 240)(75, 242)(76, 243)(77, 244)(78, 246)(79, 212)(80, 211)(81, 245)(82, 241)(83, 247)(84, 248)(85, 205)(86, 206)(87, 214)(88, 207)(89, 208)(90, 209)(91, 213)(92, 210)(93, 215)(94, 216)(95, 217)(96, 218)(97, 226)(98, 219)(99, 220)(100, 221)(101, 225)(102, 222)(103, 227)(104, 228)(105, 269)(106, 270)(107, 271)(108, 272)(109, 274)(110, 273)(111, 275)(112, 276)(113, 277)(114, 278)(115, 279)(116, 280)(117, 281)(118, 282)(119, 284)(120, 283)(121, 285)(122, 286)(123, 287)(124, 288)(125, 249)(126, 250)(127, 251)(128, 252)(129, 254)(130, 253)(131, 255)(132, 256)(133, 257)(134, 258)(135, 259)(136, 260)(137, 261)(138, 262)(139, 264)(140, 263)(141, 265)(142, 266)(143, 267)(144, 268) local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9 ) } Outer automorphisms :: reflexible Dual of E20.1097 Transitivity :: ET+ VT+ AT Graph:: v = 18 e = 144 f = 88 degree seq :: [ 16^18 ] E20.1099 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 9}) Quotient :: loop Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, (T2^2 * T1^-1)^2, (T1^-1 * T2 * T1^-2)^2, T1^8, T2^9, T1 * T2^-1 * T1^2 * T2 * T1^-1 * T2 * T1^2 * T2^-1, T1^-1 * T2 * T1^2 * T2 * T1^-2 * T2^-2 * T1^-1 ] Map:: R = (1, 145, 3, 147, 10, 154, 26, 170, 58, 202, 71, 215, 36, 180, 15, 159, 5, 149)(2, 146, 7, 151, 19, 163, 45, 189, 85, 229, 92, 236, 50, 194, 22, 166, 8, 152)(4, 148, 12, 156, 30, 174, 65, 209, 103, 247, 95, 239, 55, 199, 24, 168, 9, 153)(6, 150, 17, 161, 40, 184, 78, 222, 112, 256, 114, 258, 82, 226, 43, 187, 18, 162)(11, 155, 27, 171, 14, 158, 35, 179, 69, 213, 106, 250, 99, 243, 57, 201, 25, 169)(13, 157, 32, 176, 54, 198, 94, 238, 122, 266, 127, 271, 101, 245, 63, 207, 29, 173)(16, 160, 38, 182, 74, 218, 109, 253, 133, 277, 134, 278, 110, 254, 76, 220, 39, 183)(20, 164, 46, 190, 21, 165, 49, 193, 90, 234, 120, 264, 117, 261, 84, 228, 44, 188)(23, 167, 52, 196, 93, 237, 121, 265, 128, 272, 102, 246, 64, 208, 31, 175, 53, 197)(28, 172, 61, 205, 98, 242, 125, 269, 130, 274, 105, 249, 70, 214, 75, 219, 59, 203)(33, 177, 67, 211, 100, 244, 126, 270, 142, 286, 141, 285, 123, 267, 96, 240, 66, 210)(34, 178, 60, 204, 80, 224, 56, 200, 97, 241, 124, 268, 129, 273, 104, 248, 68, 212)(37, 181, 72, 216, 107, 251, 131, 275, 143, 287, 144, 288, 132, 276, 108, 252, 73, 217)(41, 185, 79, 223, 42, 186, 81, 225, 113, 257, 136, 280, 135, 279, 111, 255, 77, 221)(47, 191, 88, 232, 116, 260, 138, 282, 140, 284, 119, 263, 91, 235, 51, 195, 86, 230)(48, 192, 87, 231, 62, 206, 83, 227, 115, 259, 137, 281, 139, 283, 118, 262, 89, 233) L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 158)(6, 160)(7, 149)(8, 165)(9, 167)(10, 169)(11, 147)(12, 173)(13, 148)(14, 178)(15, 174)(16, 181)(17, 152)(18, 186)(19, 188)(20, 151)(21, 192)(22, 154)(23, 195)(24, 198)(25, 200)(26, 194)(27, 203)(28, 155)(29, 206)(30, 208)(31, 156)(32, 210)(33, 157)(34, 211)(35, 159)(36, 189)(37, 177)(38, 162)(39, 172)(40, 221)(41, 161)(42, 175)(43, 163)(44, 227)(45, 226)(46, 230)(47, 164)(48, 176)(49, 166)(50, 222)(51, 216)(52, 168)(53, 223)(54, 233)(55, 170)(56, 240)(57, 242)(58, 239)(59, 231)(60, 171)(61, 220)(62, 219)(63, 244)(64, 232)(65, 180)(66, 224)(67, 217)(68, 225)(69, 249)(70, 179)(71, 250)(72, 183)(73, 191)(74, 214)(75, 182)(76, 184)(77, 196)(78, 254)(79, 204)(80, 185)(81, 187)(82, 253)(83, 207)(84, 260)(85, 215)(86, 197)(87, 190)(88, 252)(89, 205)(90, 263)(91, 193)(92, 264)(93, 255)(94, 199)(95, 265)(96, 251)(97, 201)(98, 262)(99, 202)(100, 212)(101, 209)(102, 257)(103, 271)(104, 213)(105, 259)(106, 273)(107, 235)(108, 218)(109, 276)(110, 275)(111, 241)(112, 236)(113, 248)(114, 280)(115, 228)(116, 246)(117, 229)(118, 234)(119, 237)(120, 283)(121, 284)(122, 285)(123, 238)(124, 279)(125, 243)(126, 245)(127, 281)(128, 247)(129, 286)(130, 277)(131, 267)(132, 270)(133, 258)(134, 269)(135, 256)(136, 272)(137, 274)(138, 261)(139, 266)(140, 287)(141, 268)(142, 288)(143, 278)(144, 282) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E20.1095 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 144 f = 90 degree seq :: [ 18^16 ] E20.1100 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 9}) Quotient :: loop Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1^2)^2, T1^9, (T2 * T1^-1 * T2 * T1 * T2 * T1)^2, (T2 * T1 * T2 * T1 * T2 * T1^-1)^2, (T2 * T1^-1)^8 ] 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, 37, 181)(19, 163, 39, 183)(20, 164, 40, 184)(22, 166, 31, 175)(23, 167, 43, 187)(25, 169, 45, 189)(26, 170, 46, 190)(27, 171, 48, 192)(30, 174, 53, 197)(33, 177, 58, 202)(34, 178, 59, 203)(35, 179, 62, 206)(36, 180, 63, 207)(38, 182, 66, 210)(41, 185, 72, 216)(42, 186, 65, 209)(44, 188, 73, 217)(47, 191, 78, 222)(49, 193, 82, 226)(50, 194, 83, 227)(51, 195, 86, 230)(52, 196, 87, 231)(54, 198, 89, 233)(55, 199, 90, 234)(56, 200, 91, 235)(57, 201, 93, 237)(60, 204, 96, 240)(61, 205, 97, 241)(64, 208, 102, 246)(67, 211, 99, 243)(68, 212, 95, 239)(69, 213, 98, 242)(70, 214, 106, 250)(71, 215, 107, 251)(74, 218, 110, 254)(75, 219, 111, 255)(76, 220, 112, 256)(77, 221, 113, 257)(79, 223, 114, 258)(80, 224, 115, 259)(81, 225, 117, 261)(84, 228, 119, 263)(85, 229, 120, 264)(88, 232, 122, 266)(92, 236, 126, 270)(94, 238, 127, 271)(100, 244, 131, 275)(101, 245, 132, 276)(103, 247, 123, 267)(104, 248, 133, 277)(105, 249, 124, 268)(108, 252, 128, 272)(109, 253, 134, 278)(116, 260, 136, 280)(118, 262, 137, 281)(121, 265, 139, 283)(125, 269, 140, 284)(129, 273, 141, 285)(130, 274, 142, 286)(135, 279, 143, 287)(138, 282, 144, 288) L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 163)(10, 148)(11, 167)(12, 169)(13, 171)(14, 150)(15, 175)(16, 177)(17, 179)(18, 152)(19, 182)(20, 153)(21, 185)(22, 154)(23, 186)(24, 162)(25, 164)(26, 156)(27, 165)(28, 193)(29, 195)(30, 158)(31, 198)(32, 199)(33, 201)(34, 160)(35, 205)(36, 161)(37, 208)(38, 209)(39, 211)(40, 213)(41, 215)(42, 166)(43, 174)(44, 168)(45, 218)(46, 220)(47, 170)(48, 223)(49, 225)(50, 172)(51, 229)(52, 173)(53, 232)(54, 188)(55, 180)(56, 176)(57, 181)(58, 238)(59, 239)(60, 178)(61, 217)(62, 242)(63, 243)(64, 245)(65, 191)(66, 247)(67, 219)(68, 183)(69, 221)(70, 184)(71, 187)(72, 228)(73, 236)(74, 253)(75, 189)(76, 248)(77, 190)(78, 249)(79, 196)(80, 192)(81, 197)(82, 262)(83, 203)(84, 194)(85, 251)(86, 206)(87, 202)(88, 252)(89, 204)(90, 267)(91, 268)(92, 200)(93, 255)(94, 259)(95, 272)(96, 273)(97, 254)(98, 258)(99, 269)(100, 207)(101, 233)(102, 265)(103, 214)(104, 210)(105, 212)(106, 263)(107, 260)(108, 216)(109, 222)(110, 244)(111, 227)(112, 230)(113, 226)(114, 234)(115, 240)(116, 224)(117, 237)(118, 250)(119, 282)(120, 246)(121, 231)(122, 279)(123, 280)(124, 274)(125, 235)(126, 256)(127, 281)(128, 276)(129, 264)(130, 241)(131, 283)(132, 278)(133, 266)(134, 261)(135, 257)(136, 270)(137, 275)(138, 277)(139, 287)(140, 271)(141, 288)(142, 285)(143, 286)(144, 284) local type(s) :: { ( 8, 9, 8, 9 ) } Outer automorphisms :: reflexible Dual of E20.1096 Transitivity :: ET+ VT+ AT Graph:: simple v = 72 e = 144 f = 34 degree seq :: [ 4^72 ] E20.1101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 9}) Quotient :: dipole Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^8, (Y2^-2 * R * Y2^-2)^2, (Y2^-3 * Y1 * Y2^-1)^2, (Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2, (Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^9 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 31, 175)(16, 160, 33, 177)(18, 162, 37, 181)(19, 163, 39, 183)(20, 164, 41, 185)(22, 166, 45, 189)(23, 167, 46, 190)(24, 168, 48, 192)(26, 170, 52, 196)(27, 171, 54, 198)(28, 172, 56, 200)(30, 174, 60, 204)(32, 176, 59, 203)(34, 178, 51, 195)(35, 179, 57, 201)(36, 180, 49, 193)(38, 182, 53, 197)(40, 184, 58, 202)(42, 186, 50, 194)(43, 187, 55, 199)(44, 188, 47, 191)(61, 205, 85, 229)(62, 206, 86, 230)(63, 207, 88, 232)(64, 208, 89, 233)(65, 209, 90, 234)(66, 210, 92, 236)(67, 211, 80, 224)(68, 212, 79, 223)(69, 213, 91, 235)(70, 214, 87, 231)(71, 215, 93, 237)(72, 216, 94, 238)(73, 217, 95, 239)(74, 218, 96, 240)(75, 219, 98, 242)(76, 220, 99, 243)(77, 221, 100, 244)(78, 222, 102, 246)(81, 225, 101, 245)(82, 226, 97, 241)(83, 227, 103, 247)(84, 228, 104, 248)(105, 249, 125, 269)(106, 250, 126, 270)(107, 251, 127, 271)(108, 252, 128, 272)(109, 253, 130, 274)(110, 254, 129, 273)(111, 255, 131, 275)(112, 256, 132, 276)(113, 257, 133, 277)(114, 258, 134, 278)(115, 259, 135, 279)(116, 260, 136, 280)(117, 261, 137, 281)(118, 262, 138, 282)(119, 263, 140, 284)(120, 264, 139, 283)(121, 265, 141, 285)(122, 266, 142, 286)(123, 267, 143, 287)(124, 268, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 326, 470, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 341, 485, 318, 462, 302, 446, 294, 438)(295, 439, 303, 447, 320, 464, 351, 495, 333, 477, 354, 498, 322, 466, 304, 448)(297, 441, 307, 451, 328, 472, 358, 502, 325, 469, 357, 501, 330, 474, 308, 452)(299, 443, 311, 455, 335, 479, 363, 507, 348, 492, 366, 510, 337, 481, 312, 456)(301, 445, 315, 459, 343, 487, 370, 514, 340, 484, 369, 513, 345, 489, 316, 460)(305, 449, 323, 467, 355, 499, 332, 476, 309, 453, 331, 475, 356, 500, 324, 468)(313, 457, 338, 482, 367, 511, 347, 491, 317, 461, 346, 490, 368, 512, 339, 483)(319, 463, 349, 493, 329, 473, 360, 504, 380, 524, 397, 541, 375, 519, 350, 494)(321, 465, 352, 496, 327, 471, 359, 503, 376, 520, 398, 542, 379, 523, 353, 497)(334, 478, 361, 505, 344, 488, 372, 516, 390, 534, 407, 551, 385, 529, 362, 506)(336, 480, 364, 508, 342, 486, 371, 515, 386, 530, 408, 552, 389, 533, 365, 509)(373, 517, 393, 537, 378, 522, 400, 544, 418, 562, 401, 545, 381, 525, 394, 538)(374, 518, 395, 539, 377, 521, 399, 543, 382, 526, 402, 546, 417, 561, 396, 540)(383, 527, 403, 547, 388, 532, 410, 554, 428, 572, 411, 555, 391, 535, 404, 548)(384, 528, 405, 549, 387, 531, 409, 553, 392, 536, 412, 556, 427, 571, 406, 550)(413, 557, 424, 568, 416, 560, 425, 569, 421, 565, 430, 574, 419, 563, 432, 576)(414, 558, 426, 570, 415, 559, 431, 575, 420, 564, 429, 573, 422, 566, 423, 567) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 319)(16, 321)(17, 296)(18, 325)(19, 327)(20, 329)(21, 298)(22, 333)(23, 334)(24, 336)(25, 300)(26, 340)(27, 342)(28, 344)(29, 302)(30, 348)(31, 303)(32, 347)(33, 304)(34, 339)(35, 345)(36, 337)(37, 306)(38, 341)(39, 307)(40, 346)(41, 308)(42, 338)(43, 343)(44, 335)(45, 310)(46, 311)(47, 332)(48, 312)(49, 324)(50, 330)(51, 322)(52, 314)(53, 326)(54, 315)(55, 331)(56, 316)(57, 323)(58, 328)(59, 320)(60, 318)(61, 373)(62, 374)(63, 376)(64, 377)(65, 378)(66, 380)(67, 368)(68, 367)(69, 379)(70, 375)(71, 381)(72, 382)(73, 383)(74, 384)(75, 386)(76, 387)(77, 388)(78, 390)(79, 356)(80, 355)(81, 389)(82, 385)(83, 391)(84, 392)(85, 349)(86, 350)(87, 358)(88, 351)(89, 352)(90, 353)(91, 357)(92, 354)(93, 359)(94, 360)(95, 361)(96, 362)(97, 370)(98, 363)(99, 364)(100, 365)(101, 369)(102, 366)(103, 371)(104, 372)(105, 413)(106, 414)(107, 415)(108, 416)(109, 418)(110, 417)(111, 419)(112, 420)(113, 421)(114, 422)(115, 423)(116, 424)(117, 425)(118, 426)(119, 428)(120, 427)(121, 429)(122, 430)(123, 431)(124, 432)(125, 393)(126, 394)(127, 395)(128, 396)(129, 398)(130, 397)(131, 399)(132, 400)(133, 401)(134, 402)(135, 403)(136, 404)(137, 405)(138, 406)(139, 408)(140, 407)(141, 409)(142, 410)(143, 411)(144, 412)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E20.1104 Graph:: bipartite v = 90 e = 288 f = 160 degree seq :: [ 4^72, 16^18 ] E20.1102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 9}) Quotient :: dipole Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1 * Y2)^2, (Y2 * Y1^-1 * Y2)^2, (Y1^-1 * Y2 * Y1^-2)^2, Y1^8, Y2^9, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2 * Y2 * Y1^2 * Y2^-1 ] Map:: R = (1, 145, 2, 146, 6, 150, 16, 160, 37, 181, 33, 177, 13, 157, 4, 148)(3, 147, 9, 153, 23, 167, 51, 195, 72, 216, 39, 183, 28, 172, 11, 155)(5, 149, 14, 158, 34, 178, 67, 211, 73, 217, 47, 191, 20, 164, 7, 151)(8, 152, 21, 165, 48, 192, 32, 176, 66, 210, 80, 224, 41, 185, 17, 161)(10, 154, 25, 169, 56, 200, 96, 240, 107, 251, 91, 235, 49, 193, 22, 166)(12, 156, 29, 173, 62, 206, 75, 219, 38, 182, 18, 162, 42, 186, 31, 175)(15, 159, 30, 174, 64, 208, 88, 232, 108, 252, 74, 218, 70, 214, 35, 179)(19, 163, 44, 188, 83, 227, 63, 207, 100, 244, 68, 212, 81, 225, 43, 187)(24, 168, 54, 198, 89, 233, 61, 205, 76, 220, 40, 184, 77, 221, 52, 196)(26, 170, 50, 194, 78, 222, 110, 254, 131, 275, 123, 267, 94, 238, 55, 199)(27, 171, 59, 203, 87, 231, 46, 190, 86, 230, 53, 197, 79, 223, 60, 204)(36, 180, 45, 189, 82, 226, 109, 253, 132, 276, 126, 270, 101, 245, 65, 209)(57, 201, 98, 242, 118, 262, 90, 234, 119, 263, 93, 237, 111, 255, 97, 241)(58, 202, 95, 239, 121, 265, 140, 284, 143, 287, 134, 278, 125, 269, 99, 243)(69, 213, 105, 249, 115, 259, 84, 228, 116, 260, 102, 246, 113, 257, 104, 248)(71, 215, 106, 250, 129, 273, 142, 286, 144, 288, 138, 282, 117, 261, 85, 229)(92, 236, 120, 264, 139, 283, 122, 266, 141, 285, 124, 268, 135, 279, 112, 256)(103, 247, 127, 271, 137, 281, 130, 274, 133, 277, 114, 258, 136, 280, 128, 272)(289, 433, 291, 435, 298, 442, 314, 458, 346, 490, 359, 503, 324, 468, 303, 447, 293, 437)(290, 434, 295, 439, 307, 451, 333, 477, 373, 517, 380, 524, 338, 482, 310, 454, 296, 440)(292, 436, 300, 444, 318, 462, 353, 497, 391, 535, 383, 527, 343, 487, 312, 456, 297, 441)(294, 438, 305, 449, 328, 472, 366, 510, 400, 544, 402, 546, 370, 514, 331, 475, 306, 450)(299, 443, 315, 459, 302, 446, 323, 467, 357, 501, 394, 538, 387, 531, 345, 489, 313, 457)(301, 445, 320, 464, 342, 486, 382, 526, 410, 554, 415, 559, 389, 533, 351, 495, 317, 461)(304, 448, 326, 470, 362, 506, 397, 541, 421, 565, 422, 566, 398, 542, 364, 508, 327, 471)(308, 452, 334, 478, 309, 453, 337, 481, 378, 522, 408, 552, 405, 549, 372, 516, 332, 476)(311, 455, 340, 484, 381, 525, 409, 553, 416, 560, 390, 534, 352, 496, 319, 463, 341, 485)(316, 460, 349, 493, 386, 530, 413, 557, 418, 562, 393, 537, 358, 502, 363, 507, 347, 491)(321, 465, 355, 499, 388, 532, 414, 558, 430, 574, 429, 573, 411, 555, 384, 528, 354, 498)(322, 466, 348, 492, 368, 512, 344, 488, 385, 529, 412, 556, 417, 561, 392, 536, 356, 500)(325, 469, 360, 504, 395, 539, 419, 563, 431, 575, 432, 576, 420, 564, 396, 540, 361, 505)(329, 473, 367, 511, 330, 474, 369, 513, 401, 545, 424, 568, 423, 567, 399, 543, 365, 509)(335, 479, 376, 520, 404, 548, 426, 570, 428, 572, 407, 551, 379, 523, 339, 483, 374, 518)(336, 480, 375, 519, 350, 494, 371, 515, 403, 547, 425, 569, 427, 571, 406, 550, 377, 521) L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 314)(11, 315)(12, 318)(13, 320)(14, 323)(15, 293)(16, 326)(17, 328)(18, 294)(19, 333)(20, 334)(21, 337)(22, 296)(23, 340)(24, 297)(25, 299)(26, 346)(27, 302)(28, 349)(29, 301)(30, 353)(31, 341)(32, 342)(33, 355)(34, 348)(35, 357)(36, 303)(37, 360)(38, 362)(39, 304)(40, 366)(41, 367)(42, 369)(43, 306)(44, 308)(45, 373)(46, 309)(47, 376)(48, 375)(49, 378)(50, 310)(51, 374)(52, 381)(53, 311)(54, 382)(55, 312)(56, 385)(57, 313)(58, 359)(59, 316)(60, 368)(61, 386)(62, 371)(63, 317)(64, 319)(65, 391)(66, 321)(67, 388)(68, 322)(69, 394)(70, 363)(71, 324)(72, 395)(73, 325)(74, 397)(75, 347)(76, 327)(77, 329)(78, 400)(79, 330)(80, 344)(81, 401)(82, 331)(83, 403)(84, 332)(85, 380)(86, 335)(87, 350)(88, 404)(89, 336)(90, 408)(91, 339)(92, 338)(93, 409)(94, 410)(95, 343)(96, 354)(97, 412)(98, 413)(99, 345)(100, 414)(101, 351)(102, 352)(103, 383)(104, 356)(105, 358)(106, 387)(107, 419)(108, 361)(109, 421)(110, 364)(111, 365)(112, 402)(113, 424)(114, 370)(115, 425)(116, 426)(117, 372)(118, 377)(119, 379)(120, 405)(121, 416)(122, 415)(123, 384)(124, 417)(125, 418)(126, 430)(127, 389)(128, 390)(129, 392)(130, 393)(131, 431)(132, 396)(133, 422)(134, 398)(135, 399)(136, 423)(137, 427)(138, 428)(139, 406)(140, 407)(141, 411)(142, 429)(143, 432)(144, 420)(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 ) } Outer automorphisms :: reflexible Dual of E20.1103 Graph:: bipartite v = 34 e = 288 f = 216 degree seq :: [ 16^18, 18^16 ] E20.1103 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 9}) Quotient :: dipole Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2 * Y3^-1)^2, Y3^9, (Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3)^2, (Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2)^2, (Y3 * Y2)^8, (Y3^-1 * Y1^-1)^9 ] Map:: polytopal R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 305, 449)(298, 442, 309, 453)(300, 444, 313, 457)(302, 446, 317, 461)(303, 447, 319, 463)(304, 448, 321, 465)(306, 450, 318, 462)(307, 451, 326, 470)(308, 452, 328, 472)(310, 454, 314, 458)(311, 455, 331, 475)(312, 456, 333, 477)(315, 459, 338, 482)(316, 460, 340, 484)(320, 464, 345, 489)(322, 466, 348, 492)(323, 467, 350, 494)(324, 468, 351, 495)(325, 469, 349, 493)(327, 471, 355, 499)(329, 473, 359, 503)(330, 474, 356, 500)(332, 476, 363, 507)(334, 478, 366, 510)(335, 479, 368, 512)(336, 480, 369, 513)(337, 481, 367, 511)(339, 483, 373, 517)(341, 485, 377, 521)(342, 486, 374, 518)(343, 487, 379, 523)(344, 488, 365, 509)(346, 490, 372, 516)(347, 491, 362, 506)(352, 496, 390, 534)(353, 497, 375, 519)(354, 498, 364, 508)(357, 501, 371, 515)(358, 502, 394, 538)(360, 504, 396, 540)(361, 505, 397, 541)(370, 514, 408, 552)(376, 520, 412, 556)(378, 522, 414, 558)(380, 524, 401, 545)(381, 525, 417, 561)(382, 526, 405, 549)(383, 527, 398, 542)(384, 528, 413, 557)(385, 529, 419, 563)(386, 530, 410, 554)(387, 531, 400, 544)(388, 532, 409, 553)(389, 533, 416, 560)(391, 535, 406, 550)(392, 536, 404, 548)(393, 537, 421, 565)(395, 539, 402, 546)(399, 543, 424, 568)(403, 547, 426, 570)(407, 551, 423, 567)(411, 555, 428, 572)(415, 559, 422, 566)(418, 562, 427, 571)(420, 564, 425, 569)(429, 573, 432, 576)(430, 574, 431, 575) L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 303)(8, 306)(9, 307)(10, 292)(11, 311)(12, 314)(13, 315)(14, 294)(15, 320)(16, 295)(17, 323)(18, 325)(19, 327)(20, 297)(21, 329)(22, 298)(23, 332)(24, 299)(25, 335)(26, 337)(27, 339)(28, 301)(29, 341)(30, 302)(31, 343)(32, 309)(33, 346)(34, 304)(35, 308)(36, 305)(37, 330)(38, 353)(39, 356)(40, 357)(41, 360)(42, 310)(43, 361)(44, 317)(45, 364)(46, 312)(47, 316)(48, 313)(49, 342)(50, 371)(51, 374)(52, 375)(53, 378)(54, 318)(55, 380)(56, 319)(57, 382)(58, 384)(59, 321)(60, 385)(61, 322)(62, 386)(63, 388)(64, 324)(65, 387)(66, 326)(67, 392)(68, 352)(69, 389)(70, 328)(71, 381)(72, 349)(73, 398)(74, 331)(75, 400)(76, 402)(77, 333)(78, 403)(79, 334)(80, 404)(81, 406)(82, 336)(83, 405)(84, 338)(85, 410)(86, 370)(87, 407)(88, 340)(89, 399)(90, 367)(91, 415)(92, 348)(93, 344)(94, 347)(95, 345)(96, 396)(97, 395)(98, 420)(99, 350)(100, 393)(101, 351)(102, 391)(103, 354)(104, 358)(105, 355)(106, 417)(107, 359)(108, 418)(109, 422)(110, 366)(111, 362)(112, 365)(113, 363)(114, 414)(115, 413)(116, 427)(117, 368)(118, 411)(119, 369)(120, 409)(121, 372)(122, 376)(123, 373)(124, 424)(125, 377)(126, 425)(127, 394)(128, 379)(129, 430)(130, 383)(131, 429)(132, 390)(133, 419)(134, 412)(135, 397)(136, 432)(137, 401)(138, 431)(139, 408)(140, 426)(141, 416)(142, 421)(143, 423)(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) :: { ( 16, 18 ), ( 16, 18, 16, 18 ) } Outer automorphisms :: reflexible Dual of E20.1102 Graph:: simple bipartite v = 216 e = 288 f = 34 degree seq :: [ 2^144, 4^72 ] E20.1104 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 9}) Quotient :: dipole Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |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, Y1^-1 * Y3 * Y1^-3 * Y3^-1 * Y1^-2, Y1^9, Y3 * Y1^-1 * Y3 * Y1^3 * Y3^-1 * Y1 * Y3^-1 * Y1^-3, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 145, 2, 146, 5, 149, 11, 155, 23, 167, 42, 186, 22, 166, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 31, 175, 54, 198, 44, 188, 24, 168, 18, 162, 8, 152)(6, 150, 13, 157, 27, 171, 21, 165, 41, 185, 71, 215, 43, 187, 30, 174, 14, 158)(9, 153, 19, 163, 38, 182, 65, 209, 47, 191, 26, 170, 12, 156, 25, 169, 20, 164)(16, 160, 33, 177, 57, 201, 37, 181, 64, 208, 101, 245, 89, 233, 60, 204, 34, 178)(17, 161, 35, 179, 61, 205, 73, 217, 92, 236, 56, 200, 32, 176, 55, 199, 36, 180)(28, 172, 49, 193, 81, 225, 53, 197, 88, 232, 108, 252, 72, 216, 84, 228, 50, 194)(29, 173, 51, 195, 85, 229, 107, 251, 116, 260, 80, 224, 48, 192, 79, 223, 52, 196)(39, 183, 67, 211, 75, 219, 45, 189, 74, 218, 109, 253, 78, 222, 105, 249, 68, 212)(40, 184, 69, 213, 77, 221, 46, 190, 76, 220, 104, 248, 66, 210, 103, 247, 70, 214)(58, 202, 94, 238, 115, 259, 96, 240, 129, 273, 120, 264, 102, 246, 121, 265, 87, 231)(59, 203, 95, 239, 128, 272, 132, 276, 134, 278, 117, 261, 93, 237, 111, 255, 83, 227)(62, 206, 98, 242, 114, 258, 90, 234, 123, 267, 136, 280, 126, 270, 112, 256, 86, 230)(63, 207, 99, 243, 125, 269, 91, 235, 124, 268, 130, 274, 97, 241, 110, 254, 100, 244)(82, 226, 118, 262, 106, 250, 119, 263, 138, 282, 133, 277, 122, 266, 135, 279, 113, 257)(127, 271, 137, 281, 131, 275, 139, 283, 143, 287, 142, 286, 141, 285, 144, 288, 140, 284)(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, 325)(19, 327)(20, 328)(21, 298)(22, 319)(23, 331)(24, 299)(25, 333)(26, 334)(27, 336)(28, 301)(29, 302)(30, 341)(31, 310)(32, 303)(33, 346)(34, 347)(35, 350)(36, 351)(37, 306)(38, 354)(39, 307)(40, 308)(41, 360)(42, 353)(43, 311)(44, 361)(45, 313)(46, 314)(47, 366)(48, 315)(49, 370)(50, 371)(51, 374)(52, 375)(53, 318)(54, 377)(55, 378)(56, 379)(57, 381)(58, 321)(59, 322)(60, 384)(61, 385)(62, 323)(63, 324)(64, 390)(65, 330)(66, 326)(67, 387)(68, 383)(69, 386)(70, 394)(71, 395)(72, 329)(73, 332)(74, 398)(75, 399)(76, 400)(77, 401)(78, 335)(79, 402)(80, 403)(81, 405)(82, 337)(83, 338)(84, 407)(85, 408)(86, 339)(87, 340)(88, 410)(89, 342)(90, 343)(91, 344)(92, 414)(93, 345)(94, 415)(95, 356)(96, 348)(97, 349)(98, 357)(99, 355)(100, 419)(101, 420)(102, 352)(103, 411)(104, 421)(105, 412)(106, 358)(107, 359)(108, 416)(109, 422)(110, 362)(111, 363)(112, 364)(113, 365)(114, 367)(115, 368)(116, 424)(117, 369)(118, 425)(119, 372)(120, 373)(121, 427)(122, 376)(123, 391)(124, 393)(125, 428)(126, 380)(127, 382)(128, 396)(129, 429)(130, 430)(131, 388)(132, 389)(133, 392)(134, 397)(135, 431)(136, 404)(137, 406)(138, 432)(139, 409)(140, 413)(141, 417)(142, 418)(143, 423)(144, 426)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E20.1101 Graph:: simple bipartite v = 160 e = 288 f = 90 degree seq :: [ 2^144, 18^16 ] E20.1105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 9}) Quotient :: dipole Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1 * Y2^-1)^2, Y2^-1 * R * Y2^3 * R * Y2^-2, Y2^9, (Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2)^2, (Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1)^2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 31, 175)(16, 160, 33, 177)(18, 162, 30, 174)(19, 163, 38, 182)(20, 164, 40, 184)(22, 166, 26, 170)(23, 167, 43, 187)(24, 168, 45, 189)(27, 171, 50, 194)(28, 172, 52, 196)(32, 176, 57, 201)(34, 178, 60, 204)(35, 179, 62, 206)(36, 180, 63, 207)(37, 181, 61, 205)(39, 183, 67, 211)(41, 185, 71, 215)(42, 186, 68, 212)(44, 188, 75, 219)(46, 190, 78, 222)(47, 191, 80, 224)(48, 192, 81, 225)(49, 193, 79, 223)(51, 195, 85, 229)(53, 197, 89, 233)(54, 198, 86, 230)(55, 199, 91, 235)(56, 200, 77, 221)(58, 202, 84, 228)(59, 203, 74, 218)(64, 208, 102, 246)(65, 209, 87, 231)(66, 210, 76, 220)(69, 213, 83, 227)(70, 214, 106, 250)(72, 216, 108, 252)(73, 217, 109, 253)(82, 226, 120, 264)(88, 232, 124, 268)(90, 234, 126, 270)(92, 236, 113, 257)(93, 237, 129, 273)(94, 238, 117, 261)(95, 239, 110, 254)(96, 240, 125, 269)(97, 241, 131, 275)(98, 242, 122, 266)(99, 243, 112, 256)(100, 244, 121, 265)(101, 245, 128, 272)(103, 247, 118, 262)(104, 248, 116, 260)(105, 249, 133, 277)(107, 251, 114, 258)(111, 255, 136, 280)(115, 259, 138, 282)(119, 263, 135, 279)(123, 267, 140, 284)(127, 271, 134, 278)(130, 274, 139, 283)(132, 276, 137, 281)(141, 285, 144, 288)(142, 286, 143, 287)(289, 433, 291, 435, 296, 440, 306, 450, 325, 469, 330, 474, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 337, 481, 342, 486, 318, 462, 302, 446, 294, 438)(295, 439, 303, 447, 320, 464, 309, 453, 329, 473, 360, 504, 349, 493, 322, 466, 304, 448)(297, 441, 307, 451, 327, 471, 356, 500, 352, 496, 324, 468, 305, 449, 323, 467, 308, 452)(299, 443, 311, 455, 332, 476, 317, 461, 341, 485, 378, 522, 367, 511, 334, 478, 312, 456)(301, 445, 315, 459, 339, 483, 374, 518, 370, 514, 336, 480, 313, 457, 335, 479, 316, 460)(319, 463, 343, 487, 380, 524, 348, 492, 385, 529, 395, 539, 359, 503, 381, 525, 344, 488)(321, 465, 346, 490, 384, 528, 396, 540, 418, 562, 383, 527, 345, 489, 382, 526, 347, 491)(326, 470, 353, 497, 387, 531, 350, 494, 386, 530, 420, 564, 390, 534, 391, 535, 354, 498)(328, 472, 357, 501, 389, 533, 351, 495, 388, 532, 393, 537, 355, 499, 392, 536, 358, 502)(331, 475, 361, 505, 398, 542, 366, 510, 403, 547, 413, 557, 377, 521, 399, 543, 362, 506)(333, 477, 364, 508, 402, 546, 414, 558, 425, 569, 401, 545, 363, 507, 400, 544, 365, 509)(338, 482, 371, 515, 405, 549, 368, 512, 404, 548, 427, 571, 408, 552, 409, 553, 372, 516)(340, 484, 375, 519, 407, 551, 369, 513, 406, 550, 411, 555, 373, 517, 410, 554, 376, 520)(379, 523, 415, 559, 394, 538, 417, 561, 430, 574, 421, 565, 419, 563, 429, 573, 416, 560)(397, 541, 422, 566, 412, 556, 424, 568, 432, 576, 428, 572, 426, 570, 431, 575, 423, 567) L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 319)(16, 321)(17, 296)(18, 318)(19, 326)(20, 328)(21, 298)(22, 314)(23, 331)(24, 333)(25, 300)(26, 310)(27, 338)(28, 340)(29, 302)(30, 306)(31, 303)(32, 345)(33, 304)(34, 348)(35, 350)(36, 351)(37, 349)(38, 307)(39, 355)(40, 308)(41, 359)(42, 356)(43, 311)(44, 363)(45, 312)(46, 366)(47, 368)(48, 369)(49, 367)(50, 315)(51, 373)(52, 316)(53, 377)(54, 374)(55, 379)(56, 365)(57, 320)(58, 372)(59, 362)(60, 322)(61, 325)(62, 323)(63, 324)(64, 390)(65, 375)(66, 364)(67, 327)(68, 330)(69, 371)(70, 394)(71, 329)(72, 396)(73, 397)(74, 347)(75, 332)(76, 354)(77, 344)(78, 334)(79, 337)(80, 335)(81, 336)(82, 408)(83, 357)(84, 346)(85, 339)(86, 342)(87, 353)(88, 412)(89, 341)(90, 414)(91, 343)(92, 401)(93, 417)(94, 405)(95, 398)(96, 413)(97, 419)(98, 410)(99, 400)(100, 409)(101, 416)(102, 352)(103, 406)(104, 404)(105, 421)(106, 358)(107, 402)(108, 360)(109, 361)(110, 383)(111, 424)(112, 387)(113, 380)(114, 395)(115, 426)(116, 392)(117, 382)(118, 391)(119, 423)(120, 370)(121, 388)(122, 386)(123, 428)(124, 376)(125, 384)(126, 378)(127, 422)(128, 389)(129, 381)(130, 427)(131, 385)(132, 425)(133, 393)(134, 415)(135, 407)(136, 399)(137, 420)(138, 403)(139, 418)(140, 411)(141, 432)(142, 431)(143, 430)(144, 429)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 2, 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 E20.1106 Graph:: bipartite v = 88 e = 288 f = 162 degree seq :: [ 4^72, 18^16 ] E20.1106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 9}) Quotient :: dipole Aut^+ = (Q8 : C9) : C2 (small group id <144, 32>) Aut = $<288, 340>$ (small group id <288, 340>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-1 * Y3)^2, (Y1^-1 * Y3 * Y1^-2)^2, Y1^8, Y1^-2 * Y3^-1 * Y1 * Y3 * Y1^-2 * Y3^-2 * Y1^-1, Y1 * Y3^-1 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3^-1, (Y3 * Y2^-1)^9 ] Map:: polytopal R = (1, 145, 2, 146, 6, 150, 16, 160, 37, 181, 33, 177, 13, 157, 4, 148)(3, 147, 9, 153, 23, 167, 51, 195, 72, 216, 39, 183, 28, 172, 11, 155)(5, 149, 14, 158, 34, 178, 67, 211, 73, 217, 47, 191, 20, 164, 7, 151)(8, 152, 21, 165, 48, 192, 32, 176, 66, 210, 80, 224, 41, 185, 17, 161)(10, 154, 25, 169, 56, 200, 96, 240, 107, 251, 91, 235, 49, 193, 22, 166)(12, 156, 29, 173, 62, 206, 75, 219, 38, 182, 18, 162, 42, 186, 31, 175)(15, 159, 30, 174, 64, 208, 88, 232, 108, 252, 74, 218, 70, 214, 35, 179)(19, 163, 44, 188, 83, 227, 63, 207, 100, 244, 68, 212, 81, 225, 43, 187)(24, 168, 54, 198, 89, 233, 61, 205, 76, 220, 40, 184, 77, 221, 52, 196)(26, 170, 50, 194, 78, 222, 110, 254, 131, 275, 123, 267, 94, 238, 55, 199)(27, 171, 59, 203, 87, 231, 46, 190, 86, 230, 53, 197, 79, 223, 60, 204)(36, 180, 45, 189, 82, 226, 109, 253, 132, 276, 126, 270, 101, 245, 65, 209)(57, 201, 98, 242, 118, 262, 90, 234, 119, 263, 93, 237, 111, 255, 97, 241)(58, 202, 95, 239, 121, 265, 140, 284, 143, 287, 134, 278, 125, 269, 99, 243)(69, 213, 105, 249, 115, 259, 84, 228, 116, 260, 102, 246, 113, 257, 104, 248)(71, 215, 106, 250, 129, 273, 142, 286, 144, 288, 138, 282, 117, 261, 85, 229)(92, 236, 120, 264, 139, 283, 122, 266, 141, 285, 124, 268, 135, 279, 112, 256)(103, 247, 127, 271, 137, 281, 130, 274, 133, 277, 114, 258, 136, 280, 128, 272)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576) L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 314)(11, 315)(12, 318)(13, 320)(14, 323)(15, 293)(16, 326)(17, 328)(18, 294)(19, 333)(20, 334)(21, 337)(22, 296)(23, 340)(24, 297)(25, 299)(26, 346)(27, 302)(28, 349)(29, 301)(30, 353)(31, 341)(32, 342)(33, 355)(34, 348)(35, 357)(36, 303)(37, 360)(38, 362)(39, 304)(40, 366)(41, 367)(42, 369)(43, 306)(44, 308)(45, 373)(46, 309)(47, 376)(48, 375)(49, 378)(50, 310)(51, 374)(52, 381)(53, 311)(54, 382)(55, 312)(56, 385)(57, 313)(58, 359)(59, 316)(60, 368)(61, 386)(62, 371)(63, 317)(64, 319)(65, 391)(66, 321)(67, 388)(68, 322)(69, 394)(70, 363)(71, 324)(72, 395)(73, 325)(74, 397)(75, 347)(76, 327)(77, 329)(78, 400)(79, 330)(80, 344)(81, 401)(82, 331)(83, 403)(84, 332)(85, 380)(86, 335)(87, 350)(88, 404)(89, 336)(90, 408)(91, 339)(92, 338)(93, 409)(94, 410)(95, 343)(96, 354)(97, 412)(98, 413)(99, 345)(100, 414)(101, 351)(102, 352)(103, 383)(104, 356)(105, 358)(106, 387)(107, 419)(108, 361)(109, 421)(110, 364)(111, 365)(112, 402)(113, 424)(114, 370)(115, 425)(116, 426)(117, 372)(118, 377)(119, 379)(120, 405)(121, 416)(122, 415)(123, 384)(124, 417)(125, 418)(126, 430)(127, 389)(128, 390)(129, 392)(130, 393)(131, 431)(132, 396)(133, 422)(134, 398)(135, 399)(136, 423)(137, 427)(138, 428)(139, 406)(140, 407)(141, 411)(142, 429)(143, 432)(144, 420)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576) local type(s) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) } Outer automorphisms :: reflexible Dual of E20.1105 Graph:: simple bipartite v = 162 e = 288 f = 88 degree seq :: [ 2^144, 16^18 ] E20.1107 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 80}) Quotient :: regular Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T2 * T1^-1 * T2 * T1^39, T1^-2 * T2 * T1^19 * T2 * T1^-19 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 78, 74, 79, 85, 90, 94, 98, 102, 107, 149, 154, 153, 146, 141, 136, 132, 128, 123, 118, 114, 111, 112, 109, 66, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 64, 80, 75, 71, 73, 77, 84, 89, 93, 97, 101, 106, 147, 157, 156, 158, 151, 144, 139, 135, 131, 127, 122, 126, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 70, 86, 72, 87, 83, 95, 92, 103, 100, 140, 110, 152, 159, 148, 143, 137, 134, 129, 125, 119, 116, 113, 105, 63, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 82, 69, 81, 76, 91, 88, 99, 96, 108, 104, 145, 160, 155, 150, 142, 138, 133, 130, 124, 121, 115, 120, 117, 62, 55, 46, 39, 30, 22, 12, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 105)(63, 80)(67, 109)(68, 82)(69, 111)(70, 112)(71, 113)(72, 114)(73, 115)(74, 116)(75, 117)(76, 118)(77, 119)(78, 120)(79, 121)(81, 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, 141)(101, 142)(102, 143)(103, 144)(104, 146)(106, 148)(107, 150)(108, 151)(110, 153)(140, 158)(145, 156)(147, 155)(149, 159)(152, 157)(154, 160) local type(s) :: { ( 4^80 ) } Outer automorphisms :: reflexible Dual of E20.1108 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 80 f = 40 degree seq :: [ 80^2 ] E20.1108 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 80}) Quotient :: regular Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 57, 38, 59)(39, 61, 41, 63)(40, 64, 44, 66)(42, 68, 43, 70)(45, 73, 46, 75)(47, 77, 48, 79)(49, 81, 50, 83)(51, 85, 52, 87)(53, 89, 54, 91)(55, 93, 56, 95)(58, 98, 60, 97)(62, 102, 67, 101)(65, 105, 72, 104)(69, 109, 71, 108)(74, 114, 76, 113)(78, 118, 80, 117)(82, 122, 84, 121)(86, 126, 88, 125)(90, 130, 92, 129)(94, 134, 96, 133)(99, 137, 100, 138)(103, 141, 107, 142)(106, 144, 112, 145)(110, 148, 111, 149)(115, 153, 116, 154)(119, 157, 120, 158)(123, 160, 124, 159)(127, 155, 128, 156)(131, 150, 132, 151)(135, 152, 136, 146)(139, 147, 140, 143) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 41)(40, 57)(42, 61)(43, 63)(44, 59)(45, 64)(46, 66)(47, 68)(48, 70)(49, 73)(50, 75)(51, 77)(52, 79)(53, 81)(54, 83)(55, 85)(56, 87)(58, 89)(60, 91)(62, 93)(65, 98)(67, 95)(69, 102)(71, 101)(72, 97)(74, 105)(76, 104)(78, 109)(80, 108)(82, 114)(84, 113)(86, 118)(88, 117)(90, 122)(92, 121)(94, 126)(96, 125)(99, 130)(100, 129)(103, 134)(106, 137)(107, 133)(110, 141)(111, 142)(112, 138)(115, 144)(116, 145)(119, 148)(120, 149)(123, 153)(124, 154)(127, 157)(128, 158)(131, 160)(132, 159)(135, 155)(136, 156)(139, 150)(140, 151)(143, 152)(146, 147) local type(s) :: { ( 80^4 ) } Outer automorphisms :: reflexible Dual of E20.1107 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 40 e = 80 f = 2 degree seq :: [ 4^40 ] E20.1109 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 80}) Quotient :: edge Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 64, 36, 63)(39, 74, 46, 76)(40, 78, 49, 80)(41, 82, 42, 77)(43, 87, 44, 73)(45, 91, 47, 93)(48, 96, 50, 98)(51, 84, 52, 81)(53, 89, 54, 86)(55, 109, 56, 111)(57, 71, 58, 69)(59, 103, 60, 101)(61, 107, 62, 105)(65, 117, 66, 115)(67, 121, 68, 119)(70, 127, 72, 125)(75, 138, 94, 140)(79, 142, 99, 144)(83, 139, 85, 141)(88, 143, 90, 137)(92, 149, 95, 150)(97, 151, 100, 152)(102, 146, 104, 145)(106, 148, 108, 147)(110, 157, 112, 158)(113, 135, 114, 133)(116, 154, 118, 153)(120, 156, 122, 155)(123, 129, 124, 131)(126, 160, 128, 159)(130, 136, 132, 134)(161, 162)(163, 167)(164, 169)(165, 170)(166, 172)(168, 171)(173, 177)(174, 178)(175, 179)(176, 180)(181, 185)(182, 186)(183, 187)(184, 188)(189, 193)(190, 194)(191, 195)(192, 196)(197, 229)(198, 231)(199, 233)(200, 237)(201, 241)(202, 244)(203, 246)(204, 249)(205, 234)(206, 247)(207, 236)(208, 238)(209, 242)(210, 240)(211, 261)(212, 263)(213, 265)(214, 267)(215, 251)(216, 253)(217, 256)(218, 258)(219, 275)(220, 277)(221, 279)(222, 281)(223, 269)(224, 271)(225, 285)(226, 287)(227, 289)(228, 291)(230, 293)(232, 295)(235, 297)(239, 301)(243, 305)(245, 306)(248, 307)(250, 308)(252, 298)(254, 303)(255, 300)(257, 302)(259, 299)(260, 304)(262, 313)(264, 314)(266, 315)(268, 316)(270, 309)(272, 310)(273, 311)(274, 312)(276, 319)(278, 320)(280, 294)(282, 296)(283, 317)(284, 318)(286, 292)(288, 290) L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 160, 160 ), ( 160^4 ) } Outer automorphisms :: reflexible Dual of E20.1113 Transitivity :: ET+ Graph:: simple bipartite v = 120 e = 160 f = 2 degree seq :: [ 2^80, 4^40 ] E20.1110 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 80}) Quotient :: edge Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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^-40 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 105, 113, 117, 121, 125, 129, 133, 138, 146, 157, 154, 149, 144, 104, 100, 94, 92, 86, 84, 78, 76, 70, 74, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 101, 109, 110, 114, 118, 122, 126, 130, 134, 139, 147, 158, 153, 150, 141, 108, 98, 96, 90, 88, 82, 80, 73, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 103, 111, 115, 119, 123, 127, 131, 136, 142, 159, 156, 151, 148, 106, 135, 95, 97, 87, 89, 79, 81, 71, 72, 65, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 67, 107, 112, 116, 120, 124, 128, 132, 137, 143, 160, 155, 152, 145, 140, 99, 102, 91, 93, 83, 85, 75, 77, 69, 64, 56, 48, 40, 32, 24, 16, 8)(161, 162, 166, 164)(163, 169, 173, 168)(165, 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, 261, 225)(220, 223, 234, 227)(226, 232, 269, 229)(228, 267, 230, 263)(231, 265, 237, 270)(233, 271, 236, 272)(235, 273, 241, 274)(238, 275, 240, 276)(239, 277, 245, 278)(242, 279, 244, 280)(243, 281, 249, 282)(246, 283, 248, 284)(247, 285, 253, 286)(250, 287, 252, 288)(251, 289, 257, 290)(254, 291, 256, 292)(255, 293, 262, 294)(258, 296, 260, 297)(259, 298, 295, 299)(264, 302, 268, 303)(266, 306, 300, 307)(301, 319, 304, 320)(305, 317, 308, 318)(309, 316, 310, 315)(311, 314, 312, 313) L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 4^4 ), ( 4^80 ) } Outer automorphisms :: reflexible Dual of E20.1114 Transitivity :: ET+ Graph:: bipartite v = 42 e = 160 f = 80 degree seq :: [ 4^40, 80^2 ] E20.1111 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 80}) Quotient :: edge Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^39, T1^-2 * T2 * T1^19 * T2 * T1^-19 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 105)(63, 78)(67, 109)(68, 76)(69, 111)(70, 113)(71, 115)(72, 117)(73, 119)(74, 121)(75, 123)(77, 126)(79, 129)(80, 131)(81, 133)(82, 135)(83, 137)(84, 139)(85, 141)(86, 143)(87, 145)(88, 147)(89, 149)(90, 151)(91, 153)(92, 155)(93, 154)(94, 157)(95, 159)(96, 150)(97, 148)(98, 160)(99, 140)(100, 158)(101, 134)(102, 156)(103, 152)(104, 130)(106, 127)(107, 146)(108, 120)(110, 144)(112, 132)(114, 125)(116, 142)(118, 124)(122, 136)(128, 138)(161, 162, 165, 171, 180, 189, 197, 205, 213, 221, 245, 242, 246, 250, 254, 258, 262, 267, 288, 278, 272, 274, 280, 290, 300, 310, 313, 307, 293, 286, 275, 281, 269, 226, 218, 210, 202, 194, 186, 176, 183, 177, 184, 192, 200, 208, 216, 224, 238, 232, 229, 230, 233, 239, 244, 249, 253, 257, 261, 266, 302, 296, 304, 312, 318, 319, 315, 305, 297, 283, 291, 228, 220, 212, 204, 196, 188, 179, 170, 164)(163, 167, 175, 185, 193, 201, 209, 217, 225, 234, 240, 237, 243, 248, 252, 256, 260, 264, 270, 285, 276, 284, 294, 306, 314, 320, 299, 311, 279, 295, 271, 265, 223, 214, 207, 198, 191, 181, 174, 166, 173, 169, 178, 187, 195, 203, 211, 219, 227, 236, 231, 235, 241, 247, 251, 255, 259, 263, 268, 282, 292, 287, 298, 308, 316, 309, 317, 289, 303, 273, 301, 277, 222, 215, 206, 199, 190, 182, 172, 168) L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320) local type(s) :: { ( 8, 8 ), ( 8^80 ) } Outer automorphisms :: reflexible Dual of E20.1112 Transitivity :: ET+ Graph:: simple bipartite v = 82 e = 160 f = 40 degree seq :: [ 2^80, 80^2 ] E20.1112 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 80}) Quotient :: loop Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 161, 3, 163, 8, 168, 4, 164)(2, 162, 5, 165, 11, 171, 6, 166)(7, 167, 13, 173, 9, 169, 14, 174)(10, 170, 15, 175, 12, 172, 16, 176)(17, 177, 21, 181, 18, 178, 22, 182)(19, 179, 23, 183, 20, 180, 24, 184)(25, 185, 29, 189, 26, 186, 30, 190)(27, 187, 31, 191, 28, 188, 32, 192)(33, 193, 37, 197, 34, 194, 38, 198)(35, 195, 39, 199, 36, 196, 44, 204)(40, 200, 59, 219, 41, 201, 57, 217)(42, 202, 68, 228, 43, 203, 61, 221)(45, 205, 65, 225, 46, 206, 63, 223)(47, 207, 70, 230, 48, 208, 67, 227)(49, 209, 75, 235, 50, 210, 73, 233)(51, 211, 79, 239, 52, 212, 77, 237)(53, 213, 83, 243, 54, 214, 81, 241)(55, 215, 87, 247, 56, 216, 85, 245)(58, 218, 91, 251, 60, 220, 89, 249)(62, 222, 95, 255, 72, 232, 93, 253)(64, 224, 97, 257, 66, 226, 98, 258)(69, 229, 101, 261, 71, 231, 102, 262)(74, 234, 104, 264, 76, 236, 105, 265)(78, 238, 108, 268, 80, 240, 109, 269)(82, 242, 113, 273, 84, 244, 114, 274)(86, 246, 117, 277, 88, 248, 118, 278)(90, 250, 121, 281, 92, 252, 122, 282)(94, 254, 125, 285, 96, 256, 126, 286)(99, 259, 129, 289, 100, 260, 130, 290)(103, 263, 133, 293, 112, 272, 134, 294)(106, 266, 138, 298, 107, 267, 137, 297)(110, 270, 142, 302, 111, 271, 141, 301)(115, 275, 145, 305, 116, 276, 144, 304)(119, 279, 149, 309, 120, 280, 148, 308)(123, 283, 154, 314, 124, 284, 153, 313)(127, 287, 158, 318, 128, 288, 157, 317)(131, 291, 159, 319, 132, 292, 160, 320)(135, 295, 155, 315, 136, 296, 156, 316)(139, 299, 151, 311, 140, 300, 150, 310)(143, 303, 147, 307, 152, 312, 146, 306) L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 170)(6, 172)(7, 163)(8, 171)(9, 164)(10, 165)(11, 168)(12, 166)(13, 177)(14, 178)(15, 179)(16, 180)(17, 173)(18, 174)(19, 175)(20, 176)(21, 185)(22, 186)(23, 187)(24, 188)(25, 181)(26, 182)(27, 183)(28, 184)(29, 193)(30, 194)(31, 195)(32, 196)(33, 189)(34, 190)(35, 191)(36, 192)(37, 217)(38, 219)(39, 221)(40, 223)(41, 225)(42, 227)(43, 230)(44, 228)(45, 233)(46, 235)(47, 237)(48, 239)(49, 241)(50, 243)(51, 245)(52, 247)(53, 249)(54, 251)(55, 253)(56, 255)(57, 197)(58, 258)(59, 198)(60, 257)(61, 199)(62, 262)(63, 200)(64, 265)(65, 201)(66, 264)(67, 202)(68, 204)(69, 269)(70, 203)(71, 268)(72, 261)(73, 205)(74, 274)(75, 206)(76, 273)(77, 207)(78, 278)(79, 208)(80, 277)(81, 209)(82, 282)(83, 210)(84, 281)(85, 211)(86, 286)(87, 212)(88, 285)(89, 213)(90, 290)(91, 214)(92, 289)(93, 215)(94, 294)(95, 216)(96, 293)(97, 220)(98, 218)(99, 297)(100, 298)(101, 232)(102, 222)(103, 301)(104, 226)(105, 224)(106, 304)(107, 305)(108, 231)(109, 229)(110, 308)(111, 309)(112, 302)(113, 236)(114, 234)(115, 313)(116, 314)(117, 240)(118, 238)(119, 317)(120, 318)(121, 244)(122, 242)(123, 320)(124, 319)(125, 248)(126, 246)(127, 316)(128, 315)(129, 252)(130, 250)(131, 310)(132, 311)(133, 256)(134, 254)(135, 306)(136, 307)(137, 259)(138, 260)(139, 312)(140, 303)(141, 263)(142, 272)(143, 300)(144, 266)(145, 267)(146, 295)(147, 296)(148, 270)(149, 271)(150, 291)(151, 292)(152, 299)(153, 275)(154, 276)(155, 288)(156, 287)(157, 279)(158, 280)(159, 284)(160, 283) local type(s) :: { ( 2, 80, 2, 80, 2, 80, 2, 80 ) } Outer automorphisms :: reflexible Dual of E20.1111 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 40 e = 160 f = 82 degree seq :: [ 8^40 ] E20.1113 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 80}) Quotient :: loop Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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^-40 * T1^-1 ] Map:: R = (1, 161, 3, 163, 10, 170, 18, 178, 26, 186, 34, 194, 42, 202, 50, 210, 58, 218, 66, 226, 103, 263, 91, 251, 87, 247, 75, 235, 72, 232, 76, 236, 85, 245, 92, 252, 101, 261, 107, 267, 115, 275, 118, 278, 124, 284, 149, 309, 141, 301, 133, 293, 127, 287, 131, 291, 139, 299, 147, 307, 154, 314, 159, 319, 122, 282, 62, 222, 54, 214, 46, 206, 38, 198, 30, 190, 22, 182, 14, 174, 6, 166, 13, 173, 21, 181, 29, 189, 37, 197, 45, 205, 53, 213, 61, 221, 113, 273, 109, 269, 99, 259, 95, 255, 83, 243, 79, 239, 70, 230, 77, 237, 84, 244, 93, 253, 100, 260, 108, 268, 114, 274, 119, 279, 123, 283, 150, 310, 142, 302, 134, 294, 128, 288, 132, 292, 140, 300, 148, 308, 155, 315, 68, 228, 60, 220, 52, 212, 44, 204, 36, 196, 28, 188, 20, 180, 12, 172, 5, 165)(2, 162, 7, 167, 15, 175, 23, 183, 31, 191, 39, 199, 47, 207, 55, 215, 63, 223, 111, 271, 94, 254, 97, 257, 78, 238, 81, 241, 69, 229, 82, 242, 80, 240, 98, 258, 96, 256, 112, 272, 110, 270, 121, 281, 120, 280, 153, 313, 145, 305, 137, 297, 129, 289, 135, 295, 143, 303, 151, 311, 156, 316, 125, 285, 65, 225, 57, 217, 49, 209, 41, 201, 33, 193, 25, 185, 17, 177, 9, 169, 4, 164, 11, 171, 19, 179, 27, 187, 35, 195, 43, 203, 51, 211, 59, 219, 67, 227, 102, 262, 105, 265, 86, 246, 89, 249, 71, 231, 74, 234, 73, 233, 90, 250, 88, 248, 106, 266, 104, 264, 117, 277, 116, 276, 158, 318, 126, 286, 146, 306, 138, 298, 130, 290, 136, 296, 144, 304, 152, 312, 157, 317, 160, 320, 64, 224, 56, 216, 48, 208, 40, 200, 32, 192, 24, 184, 16, 176, 8, 168) L = (1, 162)(2, 166)(3, 169)(4, 161)(5, 171)(6, 164)(7, 165)(8, 163)(9, 173)(10, 176)(11, 174)(12, 175)(13, 168)(14, 167)(15, 182)(16, 181)(17, 170)(18, 185)(19, 172)(20, 187)(21, 177)(22, 179)(23, 180)(24, 178)(25, 189)(26, 192)(27, 190)(28, 191)(29, 184)(30, 183)(31, 198)(32, 197)(33, 186)(34, 201)(35, 188)(36, 203)(37, 193)(38, 195)(39, 196)(40, 194)(41, 205)(42, 208)(43, 206)(44, 207)(45, 200)(46, 199)(47, 214)(48, 213)(49, 202)(50, 217)(51, 204)(52, 219)(53, 209)(54, 211)(55, 212)(56, 210)(57, 221)(58, 224)(59, 222)(60, 223)(61, 216)(62, 215)(63, 282)(64, 273)(65, 218)(66, 285)(67, 220)(68, 262)(69, 287)(70, 289)(71, 291)(72, 290)(73, 293)(74, 288)(75, 295)(76, 297)(77, 298)(78, 299)(79, 296)(80, 301)(81, 292)(82, 294)(83, 303)(84, 305)(85, 306)(86, 307)(87, 304)(88, 309)(89, 300)(90, 302)(91, 311)(92, 313)(93, 286)(94, 314)(95, 312)(96, 284)(97, 308)(98, 310)(99, 316)(100, 280)(101, 318)(102, 319)(103, 317)(104, 278)(105, 315)(106, 283)(107, 281)(108, 276)(109, 320)(110, 275)(111, 228)(112, 279)(113, 225)(114, 270)(115, 277)(116, 267)(117, 274)(118, 272)(119, 264)(120, 261)(121, 268)(122, 227)(123, 256)(124, 266)(125, 269)(126, 252)(127, 234)(128, 229)(129, 232)(130, 230)(131, 241)(132, 231)(133, 242)(134, 233)(135, 239)(136, 235)(137, 237)(138, 236)(139, 249)(140, 238)(141, 250)(142, 240)(143, 247)(144, 243)(145, 245)(146, 244)(147, 257)(148, 246)(149, 258)(150, 248)(151, 255)(152, 251)(153, 253)(154, 265)(155, 254)(156, 263)(157, 259)(158, 260)(159, 271)(160, 226) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E20.1109 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 160 f = 120 degree seq :: [ 160^2 ] E20.1114 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 80}) Quotient :: loop Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^39, T1^-2 * T2 * T1^19 * T2 * T1^-19 ] Map:: polytopal non-degenerate R = (1, 161, 3, 163)(2, 162, 6, 166)(4, 164, 9, 169)(5, 165, 12, 172)(7, 167, 16, 176)(8, 168, 17, 177)(10, 170, 15, 175)(11, 171, 21, 181)(13, 173, 23, 183)(14, 174, 24, 184)(18, 178, 26, 186)(19, 179, 27, 187)(20, 180, 30, 190)(22, 182, 32, 192)(25, 185, 34, 194)(28, 188, 33, 193)(29, 189, 38, 198)(31, 191, 40, 200)(35, 195, 42, 202)(36, 196, 43, 203)(37, 197, 46, 206)(39, 199, 48, 208)(41, 201, 50, 210)(44, 204, 49, 209)(45, 205, 54, 214)(47, 207, 56, 216)(51, 211, 58, 218)(52, 212, 59, 219)(53, 213, 62, 222)(55, 215, 64, 224)(57, 217, 66, 226)(60, 220, 65, 225)(61, 221, 81, 241)(63, 223, 107, 267)(67, 227, 78, 238)(68, 228, 111, 271)(69, 229, 113, 273)(70, 230, 114, 274)(71, 231, 115, 275)(72, 232, 116, 276)(73, 233, 117, 277)(74, 234, 109, 269)(75, 235, 118, 278)(76, 236, 119, 279)(77, 237, 120, 280)(79, 239, 121, 281)(80, 240, 122, 282)(82, 242, 123, 283)(83, 243, 124, 284)(84, 244, 125, 285)(85, 245, 105, 265)(86, 246, 126, 286)(87, 247, 127, 287)(88, 248, 128, 288)(89, 249, 129, 289)(90, 250, 130, 290)(91, 251, 131, 291)(92, 252, 132, 292)(93, 253, 133, 293)(94, 254, 134, 294)(95, 255, 135, 295)(96, 256, 136, 296)(97, 257, 137, 297)(98, 258, 139, 299)(99, 259, 140, 300)(100, 260, 141, 301)(101, 261, 142, 302)(102, 262, 144, 304)(103, 263, 145, 305)(104, 264, 146, 306)(106, 266, 148, 308)(108, 268, 150, 310)(110, 270, 152, 312)(112, 272, 154, 314)(138, 298, 160, 320)(143, 303, 157, 317)(147, 307, 156, 316)(149, 309, 158, 318)(151, 311, 159, 319)(153, 313, 155, 315) L = (1, 162)(2, 165)(3, 167)(4, 161)(5, 171)(6, 173)(7, 175)(8, 163)(9, 178)(10, 164)(11, 180)(12, 168)(13, 169)(14, 166)(15, 185)(16, 183)(17, 184)(18, 187)(19, 170)(20, 189)(21, 174)(22, 172)(23, 177)(24, 192)(25, 193)(26, 176)(27, 195)(28, 179)(29, 197)(30, 182)(31, 181)(32, 200)(33, 201)(34, 186)(35, 203)(36, 188)(37, 205)(38, 191)(39, 190)(40, 208)(41, 209)(42, 194)(43, 211)(44, 196)(45, 213)(46, 199)(47, 198)(48, 216)(49, 217)(50, 202)(51, 219)(52, 204)(53, 221)(54, 207)(55, 206)(56, 224)(57, 225)(58, 210)(59, 227)(60, 212)(61, 265)(62, 215)(63, 214)(64, 267)(65, 269)(66, 218)(67, 271)(68, 220)(69, 241)(70, 245)(71, 234)(72, 222)(73, 242)(74, 238)(75, 239)(76, 231)(77, 246)(78, 226)(79, 228)(80, 236)(81, 223)(82, 229)(83, 235)(84, 250)(85, 232)(86, 230)(87, 243)(88, 240)(89, 254)(90, 233)(91, 248)(92, 247)(93, 258)(94, 237)(95, 252)(96, 251)(97, 262)(98, 244)(99, 256)(100, 255)(101, 268)(102, 249)(103, 260)(104, 259)(105, 283)(106, 298)(107, 276)(108, 253)(109, 281)(110, 264)(111, 275)(112, 263)(113, 274)(114, 277)(115, 278)(116, 273)(117, 280)(118, 282)(119, 284)(120, 285)(121, 279)(122, 287)(123, 286)(124, 288)(125, 289)(126, 290)(127, 291)(128, 292)(129, 293)(130, 294)(131, 295)(132, 296)(133, 297)(134, 299)(135, 300)(136, 301)(137, 302)(138, 257)(139, 304)(140, 305)(141, 306)(142, 308)(143, 261)(144, 310)(145, 312)(146, 314)(147, 303)(148, 316)(149, 266)(150, 320)(151, 272)(152, 319)(153, 270)(154, 315)(155, 307)(156, 311)(157, 318)(158, 313)(159, 309)(160, 317) local type(s) :: { ( 4, 80, 4, 80 ) } Outer automorphisms :: reflexible Dual of E20.1110 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 80 e = 160 f = 42 degree seq :: [ 4^80 ] E20.1115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 80}) Quotient :: dipole Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^80 ] Map:: R = (1, 161, 2, 162)(3, 163, 7, 167)(4, 164, 9, 169)(5, 165, 10, 170)(6, 166, 12, 172)(8, 168, 11, 171)(13, 173, 17, 177)(14, 174, 18, 178)(15, 175, 19, 179)(16, 176, 20, 180)(21, 181, 25, 185)(22, 182, 26, 186)(23, 183, 27, 187)(24, 184, 28, 188)(29, 189, 33, 193)(30, 190, 34, 194)(31, 191, 35, 195)(32, 192, 36, 196)(37, 197, 44, 204)(38, 198, 43, 203)(39, 199, 65, 225)(40, 200, 69, 229)(41, 201, 63, 223)(42, 202, 61, 221)(45, 205, 66, 226)(46, 206, 76, 236)(47, 207, 68, 228)(48, 208, 70, 230)(49, 209, 73, 233)(50, 210, 72, 232)(51, 211, 79, 239)(52, 212, 81, 241)(53, 213, 84, 244)(54, 214, 86, 246)(55, 215, 89, 249)(56, 216, 91, 251)(57, 217, 93, 253)(58, 218, 95, 255)(59, 219, 97, 257)(60, 220, 99, 259)(62, 222, 101, 261)(64, 224, 103, 263)(67, 227, 113, 273)(71, 231, 117, 277)(74, 234, 111, 271)(75, 235, 109, 269)(77, 237, 107, 267)(78, 238, 105, 265)(80, 240, 114, 274)(82, 242, 124, 284)(83, 243, 116, 276)(85, 245, 118, 278)(87, 247, 121, 281)(88, 248, 120, 280)(90, 250, 127, 287)(92, 252, 129, 289)(94, 254, 132, 292)(96, 256, 134, 294)(98, 258, 137, 297)(100, 260, 139, 299)(102, 262, 141, 301)(104, 264, 143, 303)(106, 266, 145, 305)(108, 268, 147, 307)(110, 270, 149, 309)(112, 272, 151, 311)(115, 275, 160, 320)(119, 279, 156, 316)(122, 282, 159, 319)(123, 283, 157, 317)(125, 285, 155, 315)(126, 286, 153, 313)(128, 288, 150, 310)(130, 290, 158, 318)(131, 291, 152, 312)(133, 293, 146, 306)(135, 295, 154, 314)(136, 296, 148, 308)(138, 298, 144, 304)(140, 300, 142, 302)(321, 481, 323, 483, 328, 488, 324, 484)(322, 482, 325, 485, 331, 491, 326, 486)(327, 487, 333, 493, 329, 489, 334, 494)(330, 490, 335, 495, 332, 492, 336, 496)(337, 497, 341, 501, 338, 498, 342, 502)(339, 499, 343, 503, 340, 500, 344, 504)(345, 505, 349, 509, 346, 506, 350, 510)(347, 507, 351, 511, 348, 508, 352, 512)(353, 513, 357, 517, 354, 514, 358, 518)(355, 515, 381, 541, 356, 516, 383, 543)(359, 519, 386, 546, 366, 526, 388, 548)(360, 520, 390, 550, 369, 529, 392, 552)(361, 521, 393, 553, 362, 522, 389, 549)(363, 523, 396, 556, 364, 524, 385, 545)(365, 525, 399, 559, 367, 527, 401, 561)(368, 528, 404, 564, 370, 530, 406, 566)(371, 531, 409, 569, 372, 532, 411, 571)(373, 533, 413, 573, 374, 534, 415, 575)(375, 535, 417, 577, 376, 536, 419, 579)(377, 537, 421, 581, 378, 538, 423, 583)(379, 539, 425, 585, 380, 540, 427, 587)(382, 542, 429, 589, 384, 544, 431, 591)(387, 547, 434, 594, 402, 562, 436, 596)(391, 551, 438, 598, 407, 567, 440, 600)(394, 554, 441, 601, 395, 555, 437, 597)(397, 557, 444, 604, 398, 558, 433, 593)(400, 560, 447, 607, 403, 563, 449, 609)(405, 565, 452, 612, 408, 568, 454, 614)(410, 570, 457, 617, 412, 572, 459, 619)(414, 574, 461, 621, 416, 576, 463, 623)(418, 578, 465, 625, 420, 580, 467, 627)(422, 582, 469, 629, 424, 584, 471, 631)(426, 586, 473, 633, 428, 588, 475, 635)(430, 590, 477, 637, 432, 592, 479, 639)(435, 595, 470, 630, 450, 610, 472, 632)(439, 599, 466, 626, 455, 615, 468, 628)(442, 602, 474, 634, 443, 603, 476, 636)(445, 605, 478, 638, 446, 606, 480, 640)(448, 608, 464, 624, 451, 611, 462, 622)(453, 613, 460, 620, 456, 616, 458, 618) L = (1, 322)(2, 321)(3, 327)(4, 329)(5, 330)(6, 332)(7, 323)(8, 331)(9, 324)(10, 325)(11, 328)(12, 326)(13, 337)(14, 338)(15, 339)(16, 340)(17, 333)(18, 334)(19, 335)(20, 336)(21, 345)(22, 346)(23, 347)(24, 348)(25, 341)(26, 342)(27, 343)(28, 344)(29, 353)(30, 354)(31, 355)(32, 356)(33, 349)(34, 350)(35, 351)(36, 352)(37, 364)(38, 363)(39, 385)(40, 389)(41, 383)(42, 381)(43, 358)(44, 357)(45, 386)(46, 396)(47, 388)(48, 390)(49, 393)(50, 392)(51, 399)(52, 401)(53, 404)(54, 406)(55, 409)(56, 411)(57, 413)(58, 415)(59, 417)(60, 419)(61, 362)(62, 421)(63, 361)(64, 423)(65, 359)(66, 365)(67, 433)(68, 367)(69, 360)(70, 368)(71, 437)(72, 370)(73, 369)(74, 431)(75, 429)(76, 366)(77, 427)(78, 425)(79, 371)(80, 434)(81, 372)(82, 444)(83, 436)(84, 373)(85, 438)(86, 374)(87, 441)(88, 440)(89, 375)(90, 447)(91, 376)(92, 449)(93, 377)(94, 452)(95, 378)(96, 454)(97, 379)(98, 457)(99, 380)(100, 459)(101, 382)(102, 461)(103, 384)(104, 463)(105, 398)(106, 465)(107, 397)(108, 467)(109, 395)(110, 469)(111, 394)(112, 471)(113, 387)(114, 400)(115, 480)(116, 403)(117, 391)(118, 405)(119, 476)(120, 408)(121, 407)(122, 479)(123, 477)(124, 402)(125, 475)(126, 473)(127, 410)(128, 470)(129, 412)(130, 478)(131, 472)(132, 414)(133, 466)(134, 416)(135, 474)(136, 468)(137, 418)(138, 464)(139, 420)(140, 462)(141, 422)(142, 460)(143, 424)(144, 458)(145, 426)(146, 453)(147, 428)(148, 456)(149, 430)(150, 448)(151, 432)(152, 451)(153, 446)(154, 455)(155, 445)(156, 439)(157, 443)(158, 450)(159, 442)(160, 435)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640) local type(s) :: { ( 2, 160, 2, 160 ), ( 2, 160, 2, 160, 2, 160, 2, 160 ) } Outer automorphisms :: reflexible Dual of E20.1118 Graph:: bipartite v = 120 e = 320 f = 162 degree seq :: [ 4^80, 8^40 ] E20.1116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 80}) Quotient :: dipole Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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, Y1^-1 * Y2^-40 * Y1^-1 ] Map:: R = (1, 161, 2, 162, 6, 166, 4, 164)(3, 163, 9, 169, 13, 173, 8, 168)(5, 165, 11, 171, 14, 174, 7, 167)(10, 170, 16, 176, 21, 181, 17, 177)(12, 172, 15, 175, 22, 182, 19, 179)(18, 178, 25, 185, 29, 189, 24, 184)(20, 180, 27, 187, 30, 190, 23, 183)(26, 186, 32, 192, 37, 197, 33, 193)(28, 188, 31, 191, 38, 198, 35, 195)(34, 194, 41, 201, 45, 205, 40, 200)(36, 196, 43, 203, 46, 206, 39, 199)(42, 202, 48, 208, 53, 213, 49, 209)(44, 204, 47, 207, 54, 214, 51, 211)(50, 210, 57, 217, 61, 221, 56, 216)(52, 212, 59, 219, 62, 222, 55, 215)(58, 218, 64, 224, 105, 265, 65, 225)(60, 220, 63, 223, 82, 242, 67, 227)(66, 226, 73, 233, 118, 278, 80, 240)(68, 228, 111, 271, 76, 236, 107, 267)(69, 229, 113, 273, 74, 234, 109, 269)(70, 230, 114, 274, 72, 232, 115, 275)(71, 231, 116, 276, 79, 239, 117, 277)(75, 235, 119, 279, 78, 238, 120, 280)(77, 237, 121, 281, 85, 245, 122, 282)(81, 241, 123, 283, 84, 244, 124, 284)(83, 243, 125, 285, 89, 249, 126, 286)(86, 246, 127, 287, 88, 248, 128, 288)(87, 247, 129, 289, 93, 253, 130, 290)(90, 250, 131, 291, 92, 252, 132, 292)(91, 251, 133, 293, 97, 257, 134, 294)(94, 254, 135, 295, 96, 256, 136, 296)(95, 255, 137, 297, 101, 261, 138, 298)(98, 258, 139, 299, 100, 260, 140, 300)(99, 259, 141, 301, 106, 266, 142, 302)(102, 262, 144, 304, 104, 264, 145, 305)(103, 263, 146, 306, 143, 303, 147, 307)(108, 268, 151, 311, 112, 272, 152, 312)(110, 270, 155, 315, 148, 308, 156, 316)(149, 309, 159, 319, 150, 310, 160, 320)(153, 313, 157, 317, 154, 314, 158, 318)(321, 481, 323, 483, 330, 490, 338, 498, 346, 506, 354, 514, 362, 522, 370, 530, 378, 538, 386, 546, 429, 589, 437, 597, 442, 602, 446, 606, 450, 610, 454, 614, 458, 618, 462, 622, 467, 627, 476, 636, 478, 638, 470, 630, 428, 588, 424, 584, 418, 578, 416, 576, 410, 570, 408, 568, 401, 561, 398, 558, 390, 550, 396, 556, 402, 562, 382, 542, 374, 534, 366, 526, 358, 518, 350, 510, 342, 502, 334, 494, 326, 486, 333, 493, 341, 501, 349, 509, 357, 517, 365, 525, 373, 533, 381, 541, 425, 585, 438, 598, 433, 593, 436, 596, 441, 601, 445, 605, 449, 609, 453, 613, 457, 617, 461, 621, 466, 626, 475, 635, 477, 637, 469, 629, 432, 592, 422, 582, 420, 580, 414, 574, 412, 572, 406, 566, 404, 564, 395, 555, 392, 552, 388, 548, 380, 540, 372, 532, 364, 524, 356, 516, 348, 508, 340, 500, 332, 492, 325, 485)(322, 482, 327, 487, 335, 495, 343, 503, 351, 511, 359, 519, 367, 527, 375, 535, 383, 543, 427, 587, 435, 595, 440, 600, 444, 604, 448, 608, 452, 612, 456, 616, 460, 620, 465, 625, 472, 632, 480, 640, 474, 634, 430, 590, 463, 623, 419, 579, 421, 581, 411, 571, 413, 573, 403, 563, 405, 565, 391, 551, 394, 554, 393, 553, 385, 545, 377, 537, 369, 529, 361, 521, 353, 513, 345, 505, 337, 497, 329, 489, 324, 484, 331, 491, 339, 499, 347, 507, 355, 515, 363, 523, 371, 531, 379, 539, 387, 547, 431, 591, 434, 594, 439, 599, 443, 603, 447, 607, 451, 611, 455, 615, 459, 619, 464, 624, 471, 631, 479, 639, 473, 633, 468, 628, 423, 583, 426, 586, 415, 575, 417, 577, 407, 567, 409, 569, 397, 557, 399, 559, 389, 549, 400, 560, 384, 544, 376, 536, 368, 528, 360, 520, 352, 512, 344, 504, 336, 496, 328, 488) L = (1, 323)(2, 327)(3, 330)(4, 331)(5, 321)(6, 333)(7, 335)(8, 322)(9, 324)(10, 338)(11, 339)(12, 325)(13, 341)(14, 326)(15, 343)(16, 328)(17, 329)(18, 346)(19, 347)(20, 332)(21, 349)(22, 334)(23, 351)(24, 336)(25, 337)(26, 354)(27, 355)(28, 340)(29, 357)(30, 342)(31, 359)(32, 344)(33, 345)(34, 362)(35, 363)(36, 348)(37, 365)(38, 350)(39, 367)(40, 352)(41, 353)(42, 370)(43, 371)(44, 356)(45, 373)(46, 358)(47, 375)(48, 360)(49, 361)(50, 378)(51, 379)(52, 364)(53, 381)(54, 366)(55, 383)(56, 368)(57, 369)(58, 386)(59, 387)(60, 372)(61, 425)(62, 374)(63, 427)(64, 376)(65, 377)(66, 429)(67, 431)(68, 380)(69, 400)(70, 396)(71, 394)(72, 388)(73, 385)(74, 393)(75, 392)(76, 402)(77, 399)(78, 390)(79, 389)(80, 384)(81, 398)(82, 382)(83, 405)(84, 395)(85, 391)(86, 404)(87, 409)(88, 401)(89, 397)(90, 408)(91, 413)(92, 406)(93, 403)(94, 412)(95, 417)(96, 410)(97, 407)(98, 416)(99, 421)(100, 414)(101, 411)(102, 420)(103, 426)(104, 418)(105, 438)(106, 415)(107, 435)(108, 424)(109, 437)(110, 463)(111, 434)(112, 422)(113, 436)(114, 439)(115, 440)(116, 441)(117, 442)(118, 433)(119, 443)(120, 444)(121, 445)(122, 446)(123, 447)(124, 448)(125, 449)(126, 450)(127, 451)(128, 452)(129, 453)(130, 454)(131, 455)(132, 456)(133, 457)(134, 458)(135, 459)(136, 460)(137, 461)(138, 462)(139, 464)(140, 465)(141, 466)(142, 467)(143, 419)(144, 471)(145, 472)(146, 475)(147, 476)(148, 423)(149, 432)(150, 428)(151, 479)(152, 480)(153, 468)(154, 430)(155, 477)(156, 478)(157, 469)(158, 470)(159, 473)(160, 474)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.1117 Graph:: bipartite v = 42 e = 320 f = 240 degree seq :: [ 8^40, 160^2 ] E20.1117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 80}) Quotient :: dipole Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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, Y3^37 * Y2 * Y3^-1 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^80 ] Map:: polytopal R = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)(321, 481, 322, 482)(323, 483, 327, 487)(324, 484, 329, 489)(325, 485, 331, 491)(326, 486, 333, 493)(328, 488, 334, 494)(330, 490, 332, 492)(335, 495, 340, 500)(336, 496, 343, 503)(337, 497, 345, 505)(338, 498, 341, 501)(339, 499, 347, 507)(342, 502, 349, 509)(344, 504, 351, 511)(346, 506, 352, 512)(348, 508, 350, 510)(353, 513, 359, 519)(354, 514, 361, 521)(355, 515, 357, 517)(356, 516, 363, 523)(358, 518, 365, 525)(360, 520, 367, 527)(362, 522, 368, 528)(364, 524, 366, 526)(369, 529, 375, 535)(370, 530, 377, 537)(371, 531, 373, 533)(372, 532, 379, 539)(374, 534, 381, 541)(376, 536, 383, 543)(378, 538, 384, 544)(380, 540, 382, 542)(385, 545, 427, 587)(386, 546, 397, 557)(387, 547, 400, 560)(388, 548, 431, 591)(389, 549, 433, 593)(390, 550, 434, 594)(391, 551, 435, 595)(392, 552, 436, 596)(393, 553, 437, 597)(394, 554, 425, 585)(395, 555, 438, 598)(396, 556, 439, 599)(398, 558, 440, 600)(399, 559, 441, 601)(401, 561, 442, 602)(402, 562, 443, 603)(403, 563, 444, 604)(404, 564, 429, 589)(405, 565, 445, 605)(406, 566, 446, 606)(407, 567, 447, 607)(408, 568, 448, 608)(409, 569, 449, 609)(410, 570, 450, 610)(411, 571, 451, 611)(412, 572, 452, 612)(413, 573, 453, 613)(414, 574, 454, 614)(415, 575, 455, 615)(416, 576, 456, 616)(417, 577, 457, 617)(418, 578, 458, 618)(419, 579, 459, 619)(420, 580, 461, 621)(421, 581, 462, 622)(422, 582, 463, 623)(423, 583, 464, 624)(424, 584, 466, 626)(426, 586, 468, 628)(428, 588, 470, 630)(430, 590, 472, 632)(432, 592, 474, 634)(460, 620, 480, 640)(465, 625, 477, 637)(467, 627, 478, 638)(469, 629, 476, 636)(471, 631, 475, 635)(473, 633, 479, 639) L = (1, 323)(2, 325)(3, 328)(4, 321)(5, 332)(6, 322)(7, 335)(8, 337)(9, 338)(10, 324)(11, 340)(12, 342)(13, 343)(14, 326)(15, 329)(16, 327)(17, 346)(18, 347)(19, 330)(20, 333)(21, 331)(22, 350)(23, 351)(24, 334)(25, 336)(26, 354)(27, 355)(28, 339)(29, 341)(30, 358)(31, 359)(32, 344)(33, 345)(34, 362)(35, 363)(36, 348)(37, 349)(38, 366)(39, 367)(40, 352)(41, 353)(42, 370)(43, 371)(44, 356)(45, 357)(46, 374)(47, 375)(48, 360)(49, 361)(50, 378)(51, 379)(52, 364)(53, 365)(54, 382)(55, 383)(56, 368)(57, 369)(58, 386)(59, 387)(60, 372)(61, 373)(62, 425)(63, 427)(64, 376)(65, 377)(66, 429)(67, 431)(68, 380)(69, 397)(70, 394)(71, 404)(72, 384)(73, 401)(74, 400)(75, 399)(76, 390)(77, 385)(78, 396)(79, 389)(80, 381)(81, 388)(82, 406)(83, 393)(84, 392)(85, 403)(86, 391)(87, 410)(88, 398)(89, 408)(90, 395)(91, 414)(92, 405)(93, 412)(94, 402)(95, 418)(96, 409)(97, 416)(98, 407)(99, 422)(100, 413)(101, 420)(102, 411)(103, 428)(104, 417)(105, 442)(106, 424)(107, 436)(108, 415)(109, 441)(110, 460)(111, 434)(112, 421)(113, 435)(114, 437)(115, 438)(116, 433)(117, 440)(118, 443)(119, 444)(120, 445)(121, 446)(122, 439)(123, 447)(124, 448)(125, 449)(126, 450)(127, 451)(128, 452)(129, 453)(130, 454)(131, 455)(132, 456)(133, 457)(134, 458)(135, 459)(136, 461)(137, 462)(138, 463)(139, 464)(140, 419)(141, 466)(142, 468)(143, 470)(144, 472)(145, 423)(146, 474)(147, 432)(148, 478)(149, 426)(150, 480)(151, 465)(152, 475)(153, 430)(154, 476)(155, 467)(156, 471)(157, 479)(158, 473)(159, 469)(160, 477)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640) local type(s) :: { ( 8, 160 ), ( 8, 160, 8, 160 ) } Outer automorphisms :: reflexible Dual of E20.1116 Graph:: simple bipartite v = 240 e = 320 f = 42 degree seq :: [ 2^160, 4^80 ] E20.1118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 80}) Quotient :: dipole Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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^-2)^2, (Y3 * Y1)^4, Y1^-2 * Y3 * Y1^17 * Y3 * Y1^-21 ] Map:: R = (1, 161, 2, 162, 5, 165, 11, 171, 20, 180, 29, 189, 37, 197, 45, 205, 53, 213, 61, 221, 73, 233, 77, 237, 81, 241, 86, 246, 90, 250, 94, 254, 98, 258, 103, 263, 140, 300, 147, 307, 151, 311, 155, 315, 159, 319, 160, 320, 143, 303, 136, 296, 131, 291, 127, 287, 123, 283, 119, 279, 114, 274, 118, 278, 105, 265, 66, 226, 58, 218, 50, 210, 42, 202, 34, 194, 26, 186, 16, 176, 23, 183, 17, 177, 24, 184, 32, 192, 40, 200, 48, 208, 56, 216, 64, 224, 74, 234, 70, 230, 72, 232, 76, 236, 80, 240, 85, 245, 89, 249, 93, 253, 97, 257, 102, 262, 139, 299, 148, 308, 152, 312, 156, 316, 145, 305, 138, 298, 133, 293, 128, 288, 124, 284, 120, 280, 115, 275, 111, 271, 108, 268, 68, 228, 60, 220, 52, 212, 44, 204, 36, 196, 28, 188, 19, 179, 10, 170, 4, 164)(3, 163, 7, 167, 15, 175, 25, 185, 33, 193, 41, 201, 49, 209, 57, 217, 65, 225, 82, 242, 71, 231, 83, 243, 79, 239, 91, 251, 88, 248, 99, 259, 96, 256, 132, 292, 106, 266, 144, 304, 149, 309, 154, 314, 157, 317, 142, 302, 134, 294, 130, 290, 125, 285, 122, 282, 116, 276, 113, 273, 109, 269, 101, 261, 63, 223, 54, 214, 47, 207, 38, 198, 31, 191, 21, 181, 14, 174, 6, 166, 13, 173, 9, 169, 18, 178, 27, 187, 35, 195, 43, 203, 51, 211, 59, 219, 67, 227, 69, 229, 78, 238, 75, 235, 87, 247, 84, 244, 95, 255, 92, 252, 104, 264, 100, 260, 137, 297, 146, 306, 150, 310, 153, 313, 158, 318, 141, 301, 135, 295, 129, 289, 126, 286, 121, 281, 117, 277, 112, 272, 110, 270, 107, 267, 62, 222, 55, 215, 46, 206, 39, 199, 30, 190, 22, 182, 12, 172, 8, 168)(321, 481)(322, 482)(323, 483)(324, 484)(325, 485)(326, 486)(327, 487)(328, 488)(329, 489)(330, 490)(331, 491)(332, 492)(333, 493)(334, 494)(335, 495)(336, 496)(337, 497)(338, 498)(339, 499)(340, 500)(341, 501)(342, 502)(343, 503)(344, 504)(345, 505)(346, 506)(347, 507)(348, 508)(349, 509)(350, 510)(351, 511)(352, 512)(353, 513)(354, 514)(355, 515)(356, 516)(357, 517)(358, 518)(359, 519)(360, 520)(361, 521)(362, 522)(363, 523)(364, 524)(365, 525)(366, 526)(367, 527)(368, 528)(369, 529)(370, 530)(371, 531)(372, 532)(373, 533)(374, 534)(375, 535)(376, 536)(377, 537)(378, 538)(379, 539)(380, 540)(381, 541)(382, 542)(383, 543)(384, 544)(385, 545)(386, 546)(387, 547)(388, 548)(389, 549)(390, 550)(391, 551)(392, 552)(393, 553)(394, 554)(395, 555)(396, 556)(397, 557)(398, 558)(399, 559)(400, 560)(401, 561)(402, 562)(403, 563)(404, 564)(405, 565)(406, 566)(407, 567)(408, 568)(409, 569)(410, 570)(411, 571)(412, 572)(413, 573)(414, 574)(415, 575)(416, 576)(417, 577)(418, 578)(419, 579)(420, 580)(421, 581)(422, 582)(423, 583)(424, 584)(425, 585)(426, 586)(427, 587)(428, 588)(429, 589)(430, 590)(431, 591)(432, 592)(433, 593)(434, 594)(435, 595)(436, 596)(437, 597)(438, 598)(439, 599)(440, 600)(441, 601)(442, 602)(443, 603)(444, 604)(445, 605)(446, 606)(447, 607)(448, 608)(449, 609)(450, 610)(451, 611)(452, 612)(453, 613)(454, 614)(455, 615)(456, 616)(457, 617)(458, 618)(459, 619)(460, 620)(461, 621)(462, 622)(463, 623)(464, 624)(465, 625)(466, 626)(467, 627)(468, 628)(469, 629)(470, 630)(471, 631)(472, 632)(473, 633)(474, 634)(475, 635)(476, 636)(477, 637)(478, 638)(479, 639)(480, 640) L = (1, 323)(2, 326)(3, 321)(4, 329)(5, 332)(6, 322)(7, 336)(8, 337)(9, 324)(10, 335)(11, 341)(12, 325)(13, 343)(14, 344)(15, 330)(16, 327)(17, 328)(18, 346)(19, 347)(20, 350)(21, 331)(22, 352)(23, 333)(24, 334)(25, 354)(26, 338)(27, 339)(28, 353)(29, 358)(30, 340)(31, 360)(32, 342)(33, 348)(34, 345)(35, 362)(36, 363)(37, 366)(38, 349)(39, 368)(40, 351)(41, 370)(42, 355)(43, 356)(44, 369)(45, 374)(46, 357)(47, 376)(48, 359)(49, 364)(50, 361)(51, 378)(52, 379)(53, 382)(54, 365)(55, 384)(56, 367)(57, 386)(58, 371)(59, 372)(60, 385)(61, 421)(62, 373)(63, 394)(64, 375)(65, 380)(66, 377)(67, 425)(68, 389)(69, 388)(70, 427)(71, 428)(72, 429)(73, 430)(74, 383)(75, 431)(76, 432)(77, 433)(78, 434)(79, 435)(80, 436)(81, 437)(82, 438)(83, 439)(84, 440)(85, 441)(86, 442)(87, 443)(88, 444)(89, 445)(90, 446)(91, 447)(92, 448)(93, 449)(94, 450)(95, 451)(96, 453)(97, 454)(98, 455)(99, 456)(100, 458)(101, 381)(102, 461)(103, 462)(104, 463)(105, 387)(106, 465)(107, 390)(108, 391)(109, 392)(110, 393)(111, 395)(112, 396)(113, 397)(114, 398)(115, 399)(116, 400)(117, 401)(118, 402)(119, 403)(120, 404)(121, 405)(122, 406)(123, 407)(124, 408)(125, 409)(126, 410)(127, 411)(128, 412)(129, 413)(130, 414)(131, 415)(132, 480)(133, 416)(134, 417)(135, 418)(136, 419)(137, 479)(138, 420)(139, 477)(140, 478)(141, 422)(142, 423)(143, 424)(144, 475)(145, 426)(146, 476)(147, 474)(148, 473)(149, 472)(150, 471)(151, 470)(152, 469)(153, 468)(154, 467)(155, 464)(156, 466)(157, 459)(158, 460)(159, 457)(160, 452)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E20.1115 Graph:: simple bipartite v = 162 e = 320 f = 120 degree seq :: [ 2^160, 160^2 ] E20.1119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 80}) Quotient :: dipole Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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, Y2^3 * Y1 * Y2^-37 * Y1 ] Map:: R = (1, 161, 2, 162)(3, 163, 7, 167)(4, 164, 9, 169)(5, 165, 11, 171)(6, 166, 13, 173)(8, 168, 14, 174)(10, 170, 12, 172)(15, 175, 20, 180)(16, 176, 23, 183)(17, 177, 25, 185)(18, 178, 21, 181)(19, 179, 27, 187)(22, 182, 29, 189)(24, 184, 31, 191)(26, 186, 32, 192)(28, 188, 30, 190)(33, 193, 39, 199)(34, 194, 41, 201)(35, 195, 37, 197)(36, 196, 43, 203)(38, 198, 45, 205)(40, 200, 47, 207)(42, 202, 48, 208)(44, 204, 46, 206)(49, 209, 55, 215)(50, 210, 57, 217)(51, 211, 53, 213)(52, 212, 59, 219)(54, 214, 61, 221)(56, 216, 63, 223)(58, 218, 64, 224)(60, 220, 62, 222)(65, 225, 103, 263)(66, 226, 70, 230)(67, 227, 71, 231)(68, 228, 107, 267)(69, 229, 102, 262)(72, 232, 112, 272)(73, 233, 114, 274)(74, 234, 106, 266)(75, 235, 117, 277)(76, 236, 119, 279)(77, 237, 121, 281)(78, 238, 123, 283)(79, 239, 125, 285)(80, 240, 127, 287)(81, 241, 129, 289)(82, 242, 131, 291)(83, 243, 133, 293)(84, 244, 135, 295)(85, 245, 137, 297)(86, 246, 139, 299)(87, 247, 141, 301)(88, 248, 143, 303)(89, 249, 145, 305)(90, 250, 147, 307)(91, 251, 149, 309)(92, 252, 151, 311)(93, 253, 153, 313)(94, 254, 155, 315)(95, 255, 157, 317)(96, 256, 156, 316)(97, 257, 159, 319)(98, 258, 152, 312)(99, 259, 160, 320)(100, 260, 150, 310)(101, 261, 158, 318)(104, 264, 154, 314)(105, 265, 144, 304)(108, 268, 140, 300)(109, 269, 142, 302)(110, 270, 146, 306)(111, 271, 148, 308)(113, 273, 132, 292)(115, 275, 128, 288)(116, 276, 138, 298)(118, 278, 126, 286)(120, 280, 134, 294)(122, 282, 130, 290)(124, 284, 136, 296)(321, 481, 323, 483, 328, 488, 337, 497, 346, 506, 354, 514, 362, 522, 370, 530, 378, 538, 386, 546, 426, 586, 441, 601, 453, 613, 459, 619, 469, 629, 475, 635, 480, 640, 474, 634, 466, 626, 458, 618, 450, 610, 440, 600, 428, 588, 420, 580, 416, 576, 412, 572, 408, 568, 404, 564, 400, 560, 395, 555, 392, 552, 389, 549, 391, 551, 381, 541, 373, 533, 365, 525, 357, 517, 349, 509, 341, 501, 331, 491, 340, 500, 333, 493, 343, 503, 351, 511, 359, 519, 367, 527, 375, 535, 383, 543, 423, 583, 443, 603, 434, 594, 445, 605, 451, 611, 461, 621, 467, 627, 477, 637, 472, 632, 464, 624, 456, 616, 448, 608, 438, 598, 433, 593, 429, 589, 431, 591, 421, 581, 417, 577, 413, 573, 409, 569, 405, 565, 401, 561, 396, 556, 388, 548, 380, 540, 372, 532, 364, 524, 356, 516, 348, 508, 339, 499, 330, 490, 324, 484)(322, 482, 325, 485, 332, 492, 342, 502, 350, 510, 358, 518, 366, 526, 374, 534, 382, 542, 422, 582, 439, 599, 437, 597, 457, 617, 455, 615, 473, 633, 471, 631, 478, 638, 470, 630, 462, 622, 454, 614, 446, 606, 436, 596, 444, 604, 424, 584, 418, 578, 414, 574, 410, 570, 406, 566, 402, 562, 397, 557, 393, 553, 390, 550, 385, 545, 377, 537, 369, 529, 361, 521, 353, 513, 345, 505, 336, 496, 327, 487, 335, 495, 329, 489, 338, 498, 347, 507, 355, 515, 363, 523, 371, 531, 379, 539, 387, 547, 427, 587, 432, 592, 449, 609, 447, 607, 465, 625, 463, 623, 479, 639, 476, 636, 468, 628, 460, 620, 452, 612, 442, 602, 435, 595, 430, 590, 425, 585, 419, 579, 415, 575, 411, 571, 407, 567, 403, 563, 399, 559, 394, 554, 398, 558, 384, 544, 376, 536, 368, 528, 360, 520, 352, 512, 344, 504, 334, 494, 326, 486) L = (1, 322)(2, 321)(3, 327)(4, 329)(5, 331)(6, 333)(7, 323)(8, 334)(9, 324)(10, 332)(11, 325)(12, 330)(13, 326)(14, 328)(15, 340)(16, 343)(17, 345)(18, 341)(19, 347)(20, 335)(21, 338)(22, 349)(23, 336)(24, 351)(25, 337)(26, 352)(27, 339)(28, 350)(29, 342)(30, 348)(31, 344)(32, 346)(33, 359)(34, 361)(35, 357)(36, 363)(37, 355)(38, 365)(39, 353)(40, 367)(41, 354)(42, 368)(43, 356)(44, 366)(45, 358)(46, 364)(47, 360)(48, 362)(49, 375)(50, 377)(51, 373)(52, 379)(53, 371)(54, 381)(55, 369)(56, 383)(57, 370)(58, 384)(59, 372)(60, 382)(61, 374)(62, 380)(63, 376)(64, 378)(65, 423)(66, 390)(67, 391)(68, 427)(69, 422)(70, 386)(71, 387)(72, 432)(73, 434)(74, 426)(75, 437)(76, 439)(77, 441)(78, 443)(79, 445)(80, 447)(81, 449)(82, 451)(83, 453)(84, 455)(85, 457)(86, 459)(87, 461)(88, 463)(89, 465)(90, 467)(91, 469)(92, 471)(93, 473)(94, 475)(95, 477)(96, 476)(97, 479)(98, 472)(99, 480)(100, 470)(101, 478)(102, 389)(103, 385)(104, 474)(105, 464)(106, 394)(107, 388)(108, 460)(109, 462)(110, 466)(111, 468)(112, 392)(113, 452)(114, 393)(115, 448)(116, 458)(117, 395)(118, 446)(119, 396)(120, 454)(121, 397)(122, 450)(123, 398)(124, 456)(125, 399)(126, 438)(127, 400)(128, 435)(129, 401)(130, 442)(131, 402)(132, 433)(133, 403)(134, 440)(135, 404)(136, 444)(137, 405)(138, 436)(139, 406)(140, 428)(141, 407)(142, 429)(143, 408)(144, 425)(145, 409)(146, 430)(147, 410)(148, 431)(149, 411)(150, 420)(151, 412)(152, 418)(153, 413)(154, 424)(155, 414)(156, 416)(157, 415)(158, 421)(159, 417)(160, 419)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E20.1120 Graph:: bipartite v = 82 e = 320 f = 200 degree seq :: [ 4^80, 160^2 ] E20.1120 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 80}) Quotient :: dipole Aut^+ = C80 : C2 (small group id <160, 7>) Aut = $<320, 535>$ (small group id <320, 535>) |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^-40 * Y1^-1, (Y3 * Y2^-1)^80 ] Map:: R = (1, 161, 2, 162, 6, 166, 4, 164)(3, 163, 9, 169, 13, 173, 8, 168)(5, 165, 11, 171, 14, 174, 7, 167)(10, 170, 16, 176, 21, 181, 17, 177)(12, 172, 15, 175, 22, 182, 19, 179)(18, 178, 25, 185, 29, 189, 24, 184)(20, 180, 27, 187, 30, 190, 23, 183)(26, 186, 32, 192, 37, 197, 33, 193)(28, 188, 31, 191, 38, 198, 35, 195)(34, 194, 41, 201, 45, 205, 40, 200)(36, 196, 43, 203, 46, 206, 39, 199)(42, 202, 48, 208, 53, 213, 49, 209)(44, 204, 47, 207, 54, 214, 51, 211)(50, 210, 57, 217, 61, 221, 56, 216)(52, 212, 59, 219, 62, 222, 55, 215)(58, 218, 64, 224, 69, 229, 65, 225)(60, 220, 63, 223, 98, 258, 67, 227)(66, 226, 100, 260, 70, 230, 104, 264)(68, 228, 71, 231, 106, 266, 73, 233)(72, 232, 108, 268, 77, 237, 110, 270)(74, 234, 112, 272, 76, 236, 114, 274)(75, 235, 115, 275, 81, 241, 117, 277)(78, 238, 120, 280, 80, 240, 122, 282)(79, 239, 123, 283, 85, 245, 125, 285)(82, 242, 128, 288, 84, 244, 130, 290)(83, 243, 131, 291, 89, 249, 133, 293)(86, 246, 136, 296, 88, 248, 138, 298)(87, 247, 139, 299, 93, 253, 141, 301)(90, 250, 144, 304, 92, 252, 146, 306)(91, 251, 147, 307, 97, 257, 149, 309)(94, 254, 152, 312, 96, 256, 154, 314)(95, 255, 155, 315, 103, 263, 157, 317)(99, 259, 160, 320, 102, 262, 156, 316)(101, 261, 158, 318, 105, 265, 153, 313)(107, 267, 159, 319, 111, 271, 148, 308)(109, 269, 150, 310, 119, 279, 145, 305)(113, 273, 140, 300, 118, 278, 151, 311)(116, 276, 137, 297, 127, 287, 142, 302)(121, 281, 143, 303, 126, 286, 132, 292)(124, 284, 134, 294, 135, 295, 129, 289)(321, 481)(322, 482)(323, 483)(324, 484)(325, 485)(326, 486)(327, 487)(328, 488)(329, 489)(330, 490)(331, 491)(332, 492)(333, 493)(334, 494)(335, 495)(336, 496)(337, 497)(338, 498)(339, 499)(340, 500)(341, 501)(342, 502)(343, 503)(344, 504)(345, 505)(346, 506)(347, 507)(348, 508)(349, 509)(350, 510)(351, 511)(352, 512)(353, 513)(354, 514)(355, 515)(356, 516)(357, 517)(358, 518)(359, 519)(360, 520)(361, 521)(362, 522)(363, 523)(364, 524)(365, 525)(366, 526)(367, 527)(368, 528)(369, 529)(370, 530)(371, 531)(372, 532)(373, 533)(374, 534)(375, 535)(376, 536)(377, 537)(378, 538)(379, 539)(380, 540)(381, 541)(382, 542)(383, 543)(384, 544)(385, 545)(386, 546)(387, 547)(388, 548)(389, 549)(390, 550)(391, 551)(392, 552)(393, 553)(394, 554)(395, 555)(396, 556)(397, 557)(398, 558)(399, 559)(400, 560)(401, 561)(402, 562)(403, 563)(404, 564)(405, 565)(406, 566)(407, 567)(408, 568)(409, 569)(410, 570)(411, 571)(412, 572)(413, 573)(414, 574)(415, 575)(416, 576)(417, 577)(418, 578)(419, 579)(420, 580)(421, 581)(422, 582)(423, 583)(424, 584)(425, 585)(426, 586)(427, 587)(428, 588)(429, 589)(430, 590)(431, 591)(432, 592)(433, 593)(434, 594)(435, 595)(436, 596)(437, 597)(438, 598)(439, 599)(440, 600)(441, 601)(442, 602)(443, 603)(444, 604)(445, 605)(446, 606)(447, 607)(448, 608)(449, 609)(450, 610)(451, 611)(452, 612)(453, 613)(454, 614)(455, 615)(456, 616)(457, 617)(458, 618)(459, 619)(460, 620)(461, 621)(462, 622)(463, 623)(464, 624)(465, 625)(466, 626)(467, 627)(468, 628)(469, 629)(470, 630)(471, 631)(472, 632)(473, 633)(474, 634)(475, 635)(476, 636)(477, 637)(478, 638)(479, 639)(480, 640) L = (1, 323)(2, 327)(3, 330)(4, 331)(5, 321)(6, 333)(7, 335)(8, 322)(9, 324)(10, 338)(11, 339)(12, 325)(13, 341)(14, 326)(15, 343)(16, 328)(17, 329)(18, 346)(19, 347)(20, 332)(21, 349)(22, 334)(23, 351)(24, 336)(25, 337)(26, 354)(27, 355)(28, 340)(29, 357)(30, 342)(31, 359)(32, 344)(33, 345)(34, 362)(35, 363)(36, 348)(37, 365)(38, 350)(39, 367)(40, 352)(41, 353)(42, 370)(43, 371)(44, 356)(45, 373)(46, 358)(47, 375)(48, 360)(49, 361)(50, 378)(51, 379)(52, 364)(53, 381)(54, 366)(55, 383)(56, 368)(57, 369)(58, 386)(59, 387)(60, 372)(61, 389)(62, 374)(63, 393)(64, 376)(65, 377)(66, 397)(67, 391)(68, 380)(69, 390)(70, 392)(71, 394)(72, 395)(73, 396)(74, 398)(75, 399)(76, 400)(77, 401)(78, 402)(79, 403)(80, 404)(81, 405)(82, 406)(83, 407)(84, 408)(85, 409)(86, 410)(87, 411)(88, 412)(89, 413)(90, 414)(91, 415)(92, 416)(93, 417)(94, 419)(95, 421)(96, 422)(97, 423)(98, 382)(99, 431)(100, 385)(101, 439)(102, 427)(103, 425)(104, 384)(105, 429)(106, 418)(107, 433)(108, 420)(109, 436)(110, 424)(111, 438)(112, 388)(113, 441)(114, 426)(115, 430)(116, 444)(117, 428)(118, 446)(119, 447)(120, 434)(121, 449)(122, 432)(123, 437)(124, 452)(125, 435)(126, 454)(127, 455)(128, 442)(129, 457)(130, 440)(131, 445)(132, 460)(133, 443)(134, 462)(135, 463)(136, 450)(137, 465)(138, 448)(139, 453)(140, 468)(141, 451)(142, 470)(143, 471)(144, 458)(145, 473)(146, 456)(147, 461)(148, 476)(149, 459)(150, 478)(151, 479)(152, 466)(153, 475)(154, 464)(155, 469)(156, 472)(157, 467)(158, 477)(159, 480)(160, 474)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640) local type(s) :: { ( 4, 160 ), ( 4, 160, 4, 160, 4, 160, 4, 160 ) } Outer automorphisms :: reflexible Dual of E20.1119 Graph:: simple bipartite v = 200 e = 320 f = 82 degree seq :: [ 2^160, 8^40 ] E20.1121 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 42}) Quotient :: regular Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^42 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 78, 72, 69, 70, 73, 79, 87, 95, 100, 105, 109, 114, 138, 126, 120, 122, 128, 140, 147, 135, 123, 129, 141, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 89, 80, 76, 71, 75, 83, 92, 97, 102, 107, 111, 116, 157, 142, 134, 124, 132, 148, 163, 127, 151, 119, 149, 137, 166, 62, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 88, 82, 74, 81, 77, 86, 94, 99, 104, 108, 112, 118, 155, 146, 130, 144, 136, 154, 139, 160, 121, 158, 125, 164, 113, 63, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 64, 103, 98, 93, 84, 90, 85, 91, 96, 101, 106, 110, 115, 168, 167, 165, 150, 159, 152, 161, 162, 153, 131, 143, 133, 145, 156, 117, 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, 113)(63, 103)(67, 117)(68, 88)(69, 119)(70, 121)(71, 123)(72, 125)(73, 127)(74, 129)(75, 131)(76, 133)(77, 135)(78, 137)(79, 139)(80, 141)(81, 143)(82, 145)(83, 147)(84, 149)(85, 151)(86, 153)(87, 148)(89, 156)(90, 158)(91, 160)(92, 162)(93, 164)(94, 140)(95, 136)(96, 163)(97, 128)(98, 166)(99, 161)(100, 124)(101, 154)(102, 152)(104, 122)(105, 130)(106, 132)(107, 120)(108, 159)(109, 142)(110, 144)(111, 150)(112, 126)(114, 155)(115, 134)(116, 138)(118, 165)(146, 168)(157, 167) local type(s) :: { ( 4^42 ) } Outer automorphisms :: reflexible Dual of E20.1122 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 84 f = 42 degree seq :: [ 42^4 ] E20.1122 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 42}) Quotient :: regular Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^42 ] 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, 61, 38, 62)(39, 63, 43, 64)(40, 65, 42, 67)(41, 66, 46, 68)(44, 69, 45, 70)(47, 71, 48, 72)(49, 73, 50, 74)(51, 75, 52, 76)(53, 77, 54, 78)(55, 79, 56, 80)(57, 81, 58, 82)(59, 83, 60, 84)(85, 109, 86, 110)(87, 111, 88, 112)(89, 113, 90, 115)(91, 114, 92, 116)(93, 117, 94, 118)(95, 119, 96, 120)(97, 121, 98, 122)(99, 123, 100, 124)(101, 125, 102, 126)(103, 127, 104, 128)(105, 129, 106, 130)(107, 131, 108, 132)(133, 157, 134, 158)(135, 159, 136, 160)(137, 161, 138, 163)(139, 162, 140, 164)(141, 165, 142, 166)(143, 167, 144, 168)(145, 155, 146, 156)(147, 154, 148, 153)(149, 152, 150, 151) 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, 46)(36, 41)(39, 62)(40, 66)(42, 68)(43, 61)(44, 63)(45, 64)(47, 65)(48, 67)(49, 69)(50, 70)(51, 71)(52, 72)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80)(81, 85)(82, 86)(83, 92)(84, 91)(87, 110)(88, 109)(89, 114)(90, 116)(93, 111)(94, 112)(95, 113)(96, 115)(97, 117)(98, 118)(99, 119)(100, 120)(101, 121)(102, 122)(103, 123)(104, 124)(105, 125)(106, 126)(107, 127)(108, 128)(129, 133)(130, 134)(131, 140)(132, 139)(135, 158)(136, 157)(137, 162)(138, 164)(141, 159)(142, 160)(143, 161)(144, 163)(145, 165)(146, 166)(147, 167)(148, 168)(149, 155)(150, 156)(151, 154)(152, 153) local type(s) :: { ( 42^4 ) } Outer automorphisms :: reflexible Dual of E20.1121 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 42 e = 84 f = 4 degree seq :: [ 4^42 ] E20.1123 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 42}) Quotient :: edge Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^42 ] 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, 41, 36, 42)(39, 61, 44, 62)(40, 65, 47, 66)(43, 68, 45, 63)(46, 71, 48, 64)(49, 69, 50, 67)(51, 72, 52, 70)(53, 74, 54, 73)(55, 76, 56, 75)(57, 78, 58, 77)(59, 80, 60, 79)(81, 85, 82, 86)(83, 89, 84, 90)(87, 109, 92, 110)(88, 113, 95, 114)(91, 116, 93, 111)(94, 119, 96, 112)(97, 117, 98, 115)(99, 120, 100, 118)(101, 122, 102, 121)(103, 124, 104, 123)(105, 126, 106, 125)(107, 128, 108, 127)(129, 133, 130, 134)(131, 137, 132, 138)(135, 157, 140, 158)(136, 161, 143, 162)(139, 164, 141, 159)(142, 167, 144, 160)(145, 165, 146, 163)(147, 168, 148, 166)(149, 156, 150, 155)(151, 154, 152, 153)(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, 229)(206, 230)(207, 231)(208, 232)(209, 233)(210, 234)(211, 235)(212, 236)(213, 237)(214, 238)(215, 239)(216, 240)(217, 241)(218, 242)(219, 243)(220, 244)(221, 245)(222, 246)(223, 247)(224, 248)(225, 249)(226, 250)(227, 251)(228, 252)(253, 277)(254, 278)(255, 279)(256, 280)(257, 281)(258, 282)(259, 283)(260, 284)(261, 285)(262, 286)(263, 287)(264, 288)(265, 289)(266, 290)(267, 291)(268, 292)(269, 293)(270, 294)(271, 295)(272, 296)(273, 297)(274, 298)(275, 299)(276, 300)(301, 325)(302, 326)(303, 327)(304, 328)(305, 329)(306, 330)(307, 331)(308, 332)(309, 333)(310, 334)(311, 335)(312, 336)(313, 323)(314, 324)(315, 321)(316, 322)(317, 320)(318, 319) 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) :: { ( 84, 84 ), ( 84^4 ) } Outer automorphisms :: reflexible Dual of E20.1127 Transitivity :: ET+ Graph:: simple bipartite v = 126 e = 168 f = 4 degree seq :: [ 2^84, 4^42 ] E20.1124 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 42}) Quotient :: edge Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^42 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 110, 125, 137, 144, 154, 160, 165, 157, 149, 140, 131, 120, 114, 112, 104, 100, 96, 92, 88, 83, 78, 72, 69, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 107, 113, 121, 130, 141, 148, 158, 164, 161, 153, 145, 136, 126, 117, 123, 108, 102, 98, 94, 90, 86, 81, 75, 70, 74, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 111, 115, 119, 132, 139, 150, 156, 166, 163, 155, 147, 138, 128, 118, 129, 109, 103, 99, 95, 91, 87, 82, 76, 71, 77, 65, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 61, 105, 124, 116, 127, 135, 146, 152, 162, 168, 167, 159, 151, 143, 134, 122, 133, 142, 106, 101, 97, 93, 89, 85, 80, 73, 79, 84, 62, 54, 46, 38, 30, 22, 14)(169, 170, 174, 172)(171, 177, 181, 176)(173, 179, 182, 175)(178, 184, 189, 185)(180, 183, 190, 187)(186, 193, 197, 192)(188, 195, 198, 191)(194, 200, 205, 201)(196, 199, 206, 203)(202, 209, 213, 208)(204, 211, 214, 207)(210, 216, 221, 217)(212, 215, 222, 219)(218, 225, 229, 224)(220, 227, 230, 223)(226, 232, 273, 233)(228, 231, 252, 235)(234, 245, 292, 242)(236, 279, 247, 275)(237, 281, 241, 283)(238, 284, 239, 278)(240, 287, 248, 289)(243, 293, 244, 295)(246, 298, 253, 300)(249, 303, 250, 305)(251, 307, 257, 309)(254, 312, 255, 314)(256, 316, 261, 318)(258, 320, 259, 322)(260, 324, 265, 326)(262, 328, 263, 330)(264, 332, 269, 334)(266, 336, 267, 333)(268, 331, 274, 329)(270, 325, 271, 335)(272, 321, 310, 323)(276, 327, 277, 317)(280, 315, 301, 313)(282, 304, 290, 306)(285, 311, 286, 299)(288, 296, 302, 294)(291, 308, 297, 319) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4^4 ), ( 4^42 ) } Outer automorphisms :: reflexible Dual of E20.1128 Transitivity :: ET+ Graph:: simple bipartite v = 46 e = 168 f = 84 degree seq :: [ 4^42, 42^4 ] E20.1125 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 42}) Quotient :: edge Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^42 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 101)(63, 72)(67, 105)(68, 71)(69, 107)(70, 109)(73, 113)(74, 115)(75, 117)(76, 119)(77, 121)(78, 123)(79, 125)(80, 127)(81, 129)(82, 131)(83, 133)(84, 135)(85, 137)(86, 139)(87, 141)(88, 143)(89, 145)(90, 147)(91, 149)(92, 151)(93, 153)(94, 155)(95, 157)(96, 159)(97, 161)(98, 163)(99, 165)(100, 162)(102, 160)(103, 167)(104, 154)(106, 168)(108, 158)(110, 152)(111, 146)(112, 166)(114, 142)(116, 156)(118, 138)(120, 136)(122, 164)(124, 130)(126, 150)(128, 148)(132, 144)(134, 140)(169, 170, 173, 179, 188, 197, 205, 213, 221, 229, 247, 250, 254, 258, 262, 266, 271, 280, 276, 278, 282, 288, 298, 306, 314, 322, 330, 325, 319, 309, 303, 291, 285, 236, 228, 220, 212, 204, 196, 187, 178, 172)(171, 175, 183, 193, 201, 209, 217, 225, 233, 245, 243, 248, 252, 256, 260, 264, 268, 274, 279, 284, 292, 302, 310, 318, 326, 329, 335, 313, 323, 297, 307, 281, 293, 275, 230, 223, 214, 207, 198, 190, 180, 176)(174, 181, 177, 186, 195, 203, 211, 219, 227, 235, 239, 242, 246, 251, 255, 259, 263, 267, 272, 290, 286, 296, 304, 312, 320, 328, 334, 321, 331, 305, 315, 287, 299, 277, 269, 231, 222, 215, 206, 199, 189, 182)(184, 191, 185, 192, 200, 208, 216, 224, 232, 240, 237, 238, 241, 244, 249, 253, 257, 261, 265, 270, 294, 300, 308, 316, 324, 332, 336, 333, 327, 317, 311, 301, 295, 283, 289, 273, 234, 226, 218, 210, 202, 194) 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 ), ( 8^42 ) } Outer automorphisms :: reflexible Dual of E20.1126 Transitivity :: ET+ Graph:: simple bipartite v = 88 e = 168 f = 42 degree seq :: [ 2^84, 42^4 ] E20.1126 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 42}) Quotient :: loop Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^42 ] Map:: R = (1, 169, 3, 171, 8, 176, 4, 172)(2, 170, 5, 173, 11, 179, 6, 174)(7, 175, 13, 181, 9, 177, 14, 182)(10, 178, 15, 183, 12, 180, 16, 184)(17, 185, 21, 189, 18, 186, 22, 190)(19, 187, 23, 191, 20, 188, 24, 192)(25, 193, 29, 197, 26, 194, 30, 198)(27, 195, 31, 199, 28, 196, 32, 200)(33, 201, 37, 205, 34, 202, 38, 206)(35, 203, 44, 212, 36, 204, 39, 207)(40, 208, 57, 225, 41, 209, 59, 227)(42, 210, 68, 236, 43, 211, 61, 229)(45, 213, 65, 233, 46, 214, 63, 231)(47, 215, 70, 238, 48, 216, 67, 235)(49, 217, 75, 243, 50, 218, 73, 241)(51, 219, 79, 247, 52, 220, 77, 245)(53, 221, 83, 251, 54, 222, 81, 249)(55, 223, 87, 255, 56, 224, 85, 253)(58, 226, 91, 259, 60, 228, 89, 257)(62, 230, 93, 261, 72, 240, 95, 263)(64, 232, 98, 266, 66, 234, 97, 265)(69, 237, 101, 269, 71, 239, 102, 270)(74, 242, 104, 272, 76, 244, 105, 273)(78, 246, 108, 276, 80, 248, 109, 277)(82, 250, 113, 281, 84, 252, 114, 282)(86, 254, 117, 285, 88, 256, 118, 286)(90, 258, 121, 289, 92, 260, 122, 290)(94, 262, 125, 293, 96, 264, 126, 294)(99, 267, 129, 297, 100, 268, 130, 298)(103, 271, 134, 302, 112, 280, 133, 301)(106, 274, 137, 305, 107, 275, 138, 306)(110, 278, 142, 310, 111, 279, 141, 309)(115, 283, 145, 313, 116, 284, 144, 312)(119, 287, 149, 317, 120, 288, 148, 316)(123, 291, 154, 322, 124, 292, 153, 321)(127, 295, 158, 326, 128, 296, 157, 325)(131, 299, 162, 330, 132, 300, 161, 329)(135, 303, 166, 334, 136, 304, 165, 333)(139, 307, 168, 336, 140, 308, 167, 335)(143, 311, 163, 331, 152, 320, 164, 332)(146, 314, 160, 328, 147, 315, 159, 327)(150, 318, 156, 324, 151, 319, 155, 323) L = (1, 170)(2, 169)(3, 175)(4, 177)(5, 178)(6, 180)(7, 171)(8, 179)(9, 172)(10, 173)(11, 176)(12, 174)(13, 185)(14, 186)(15, 187)(16, 188)(17, 181)(18, 182)(19, 183)(20, 184)(21, 193)(22, 194)(23, 195)(24, 196)(25, 189)(26, 190)(27, 191)(28, 192)(29, 201)(30, 202)(31, 203)(32, 204)(33, 197)(34, 198)(35, 199)(36, 200)(37, 225)(38, 227)(39, 229)(40, 231)(41, 233)(42, 235)(43, 238)(44, 236)(45, 241)(46, 243)(47, 245)(48, 247)(49, 249)(50, 251)(51, 253)(52, 255)(53, 257)(54, 259)(55, 261)(56, 263)(57, 205)(58, 266)(59, 206)(60, 265)(61, 207)(62, 270)(63, 208)(64, 273)(65, 209)(66, 272)(67, 210)(68, 212)(69, 277)(70, 211)(71, 276)(72, 269)(73, 213)(74, 282)(75, 214)(76, 281)(77, 215)(78, 286)(79, 216)(80, 285)(81, 217)(82, 290)(83, 218)(84, 289)(85, 219)(86, 294)(87, 220)(88, 293)(89, 221)(90, 298)(91, 222)(92, 297)(93, 223)(94, 302)(95, 224)(96, 301)(97, 228)(98, 226)(99, 305)(100, 306)(101, 240)(102, 230)(103, 309)(104, 234)(105, 232)(106, 312)(107, 313)(108, 239)(109, 237)(110, 316)(111, 317)(112, 310)(113, 244)(114, 242)(115, 321)(116, 322)(117, 248)(118, 246)(119, 325)(120, 326)(121, 252)(122, 250)(123, 329)(124, 330)(125, 256)(126, 254)(127, 333)(128, 334)(129, 260)(130, 258)(131, 335)(132, 336)(133, 264)(134, 262)(135, 331)(136, 332)(137, 267)(138, 268)(139, 328)(140, 327)(141, 271)(142, 280)(143, 323)(144, 274)(145, 275)(146, 319)(147, 318)(148, 278)(149, 279)(150, 315)(151, 314)(152, 324)(153, 283)(154, 284)(155, 311)(156, 320)(157, 287)(158, 288)(159, 308)(160, 307)(161, 291)(162, 292)(163, 303)(164, 304)(165, 295)(166, 296)(167, 299)(168, 300) local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42 ) } Outer automorphisms :: reflexible Dual of E20.1125 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 42 e = 168 f = 88 degree seq :: [ 8^42 ] E20.1127 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 42}) Quotient :: loop Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^42 ] Map:: R = (1, 169, 3, 171, 10, 178, 18, 186, 26, 194, 34, 202, 42, 210, 50, 218, 58, 226, 66, 234, 109, 277, 116, 284, 121, 289, 125, 293, 129, 297, 133, 301, 137, 305, 141, 309, 146, 314, 155, 323, 165, 333, 162, 330, 157, 325, 150, 318, 108, 276, 104, 272, 98, 266, 96, 264, 90, 258, 88, 256, 81, 249, 78, 246, 70, 238, 68, 236, 60, 228, 52, 220, 44, 212, 36, 204, 28, 196, 20, 188, 12, 180, 5, 173)(2, 170, 7, 175, 15, 183, 23, 191, 31, 199, 39, 207, 47, 215, 55, 223, 63, 231, 107, 275, 114, 282, 119, 287, 123, 291, 127, 295, 131, 299, 135, 303, 139, 307, 144, 312, 151, 319, 167, 335, 164, 332, 159, 327, 154, 322, 110, 278, 143, 311, 99, 267, 101, 269, 91, 259, 93, 261, 83, 251, 85, 253, 71, 239, 74, 242, 73, 241, 64, 232, 56, 224, 48, 216, 40, 208, 32, 200, 24, 192, 16, 184, 8, 176)(4, 172, 11, 179, 19, 187, 27, 195, 35, 203, 43, 211, 51, 219, 59, 227, 67, 235, 111, 279, 115, 283, 120, 288, 124, 292, 128, 296, 132, 300, 136, 304, 140, 308, 145, 313, 152, 320, 168, 336, 163, 331, 160, 328, 153, 321, 148, 316, 103, 271, 106, 274, 95, 263, 97, 265, 87, 255, 89, 257, 77, 245, 79, 247, 69, 237, 80, 248, 65, 233, 57, 225, 49, 217, 41, 209, 33, 201, 25, 193, 17, 185, 9, 177)(6, 174, 13, 181, 21, 189, 29, 197, 37, 205, 45, 213, 53, 221, 61, 229, 105, 273, 118, 286, 113, 281, 117, 285, 122, 290, 126, 294, 130, 298, 134, 302, 138, 306, 142, 310, 147, 315, 156, 324, 166, 334, 161, 329, 158, 326, 149, 317, 112, 280, 102, 270, 100, 268, 94, 262, 92, 260, 86, 254, 84, 252, 75, 243, 72, 240, 76, 244, 82, 250, 62, 230, 54, 222, 46, 214, 38, 206, 30, 198, 22, 190, 14, 182) L = (1, 170)(2, 174)(3, 177)(4, 169)(5, 179)(6, 172)(7, 173)(8, 171)(9, 181)(10, 184)(11, 182)(12, 183)(13, 176)(14, 175)(15, 190)(16, 189)(17, 178)(18, 193)(19, 180)(20, 195)(21, 185)(22, 187)(23, 188)(24, 186)(25, 197)(26, 200)(27, 198)(28, 199)(29, 192)(30, 191)(31, 206)(32, 205)(33, 194)(34, 209)(35, 196)(36, 211)(37, 201)(38, 203)(39, 204)(40, 202)(41, 213)(42, 216)(43, 214)(44, 215)(45, 208)(46, 207)(47, 222)(48, 221)(49, 210)(50, 225)(51, 212)(52, 227)(53, 217)(54, 219)(55, 220)(56, 218)(57, 229)(58, 232)(59, 230)(60, 231)(61, 224)(62, 223)(63, 250)(64, 273)(65, 226)(66, 248)(67, 228)(68, 279)(69, 277)(70, 282)(71, 284)(72, 283)(73, 234)(74, 281)(75, 287)(76, 275)(77, 289)(78, 288)(79, 285)(80, 286)(81, 291)(82, 235)(83, 293)(84, 292)(85, 290)(86, 295)(87, 297)(88, 296)(89, 294)(90, 299)(91, 301)(92, 300)(93, 298)(94, 303)(95, 305)(96, 304)(97, 302)(98, 307)(99, 309)(100, 308)(101, 306)(102, 312)(103, 314)(104, 313)(105, 233)(106, 310)(107, 236)(108, 319)(109, 242)(110, 323)(111, 244)(112, 320)(113, 237)(114, 240)(115, 238)(116, 247)(117, 239)(118, 241)(119, 246)(120, 243)(121, 253)(122, 245)(123, 252)(124, 249)(125, 257)(126, 251)(127, 256)(128, 254)(129, 261)(130, 255)(131, 260)(132, 258)(133, 265)(134, 259)(135, 264)(136, 262)(137, 269)(138, 263)(139, 268)(140, 266)(141, 274)(142, 267)(143, 315)(144, 272)(145, 270)(146, 311)(147, 271)(148, 324)(149, 335)(150, 336)(151, 280)(152, 276)(153, 333)(154, 334)(155, 316)(156, 278)(157, 332)(158, 331)(159, 330)(160, 329)(161, 327)(162, 328)(163, 325)(164, 326)(165, 322)(166, 321)(167, 318)(168, 317) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E20.1123 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 168 f = 126 degree seq :: [ 84^4 ] E20.1128 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 42}) Quotient :: loop Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^42 ] Map:: polytopal non-degenerate R = (1, 169, 3, 171)(2, 170, 6, 174)(4, 172, 9, 177)(5, 173, 12, 180)(7, 175, 16, 184)(8, 176, 17, 185)(10, 178, 15, 183)(11, 179, 21, 189)(13, 181, 23, 191)(14, 182, 24, 192)(18, 186, 26, 194)(19, 187, 27, 195)(20, 188, 30, 198)(22, 190, 32, 200)(25, 193, 34, 202)(28, 196, 33, 201)(29, 197, 38, 206)(31, 199, 40, 208)(35, 203, 42, 210)(36, 204, 43, 211)(37, 205, 46, 214)(39, 207, 48, 216)(41, 209, 50, 218)(44, 212, 49, 217)(45, 213, 54, 222)(47, 215, 56, 224)(51, 219, 58, 226)(52, 220, 59, 227)(53, 221, 62, 230)(55, 223, 64, 232)(57, 225, 66, 234)(60, 228, 65, 233)(61, 229, 117, 285)(63, 231, 111, 279)(67, 235, 121, 289)(68, 236, 98, 266)(69, 237, 123, 291)(70, 238, 125, 293)(71, 239, 127, 295)(72, 240, 129, 297)(73, 241, 131, 299)(74, 242, 133, 301)(75, 243, 132, 300)(76, 244, 136, 304)(77, 245, 138, 306)(78, 246, 139, 307)(79, 247, 128, 296)(80, 248, 142, 310)(81, 249, 141, 309)(82, 250, 145, 313)(83, 251, 147, 315)(84, 252, 148, 316)(85, 253, 150, 318)(86, 254, 126, 294)(87, 255, 151, 319)(88, 256, 134, 302)(89, 257, 153, 321)(90, 258, 155, 323)(91, 259, 157, 325)(92, 260, 135, 303)(93, 261, 124, 292)(94, 262, 159, 327)(95, 263, 158, 326)(96, 264, 143, 311)(97, 265, 161, 329)(99, 267, 144, 312)(100, 268, 149, 317)(101, 269, 164, 332)(102, 270, 130, 298)(103, 271, 154, 322)(104, 272, 137, 305)(105, 273, 140, 308)(106, 274, 166, 334)(107, 275, 160, 328)(108, 276, 162, 330)(109, 277, 146, 314)(110, 278, 165, 333)(112, 280, 152, 320)(113, 281, 122, 290)(114, 282, 156, 324)(115, 283, 118, 286)(116, 284, 167, 335)(119, 287, 163, 331)(120, 288, 168, 336) L = (1, 170)(2, 173)(3, 175)(4, 169)(5, 179)(6, 181)(7, 183)(8, 171)(9, 186)(10, 172)(11, 188)(12, 176)(13, 177)(14, 174)(15, 193)(16, 191)(17, 192)(18, 195)(19, 178)(20, 197)(21, 182)(22, 180)(23, 185)(24, 200)(25, 201)(26, 184)(27, 203)(28, 187)(29, 205)(30, 190)(31, 189)(32, 208)(33, 209)(34, 194)(35, 211)(36, 196)(37, 213)(38, 199)(39, 198)(40, 216)(41, 217)(42, 202)(43, 219)(44, 204)(45, 221)(46, 207)(47, 206)(48, 224)(49, 225)(50, 210)(51, 227)(52, 212)(53, 229)(54, 215)(55, 214)(56, 232)(57, 233)(58, 218)(59, 235)(60, 220)(61, 255)(62, 223)(63, 222)(64, 279)(65, 265)(66, 226)(67, 266)(68, 228)(69, 238)(70, 241)(71, 243)(72, 237)(73, 247)(74, 249)(75, 251)(76, 239)(77, 254)(78, 240)(79, 256)(80, 244)(81, 245)(82, 242)(83, 261)(84, 259)(85, 260)(86, 263)(87, 246)(88, 264)(89, 250)(90, 248)(91, 253)(92, 267)(93, 268)(94, 252)(95, 270)(96, 271)(97, 258)(98, 257)(99, 272)(100, 273)(101, 262)(102, 275)(103, 276)(104, 277)(105, 278)(106, 269)(107, 280)(108, 281)(109, 282)(110, 283)(111, 274)(112, 284)(113, 286)(114, 287)(115, 288)(116, 290)(117, 231)(118, 320)(119, 336)(120, 330)(121, 234)(122, 331)(123, 316)(124, 294)(125, 325)(126, 300)(127, 301)(128, 303)(129, 327)(130, 292)(131, 318)(132, 309)(133, 310)(134, 312)(135, 293)(136, 313)(137, 296)(138, 295)(139, 332)(140, 298)(141, 304)(142, 321)(143, 305)(144, 299)(145, 323)(146, 302)(147, 306)(148, 307)(149, 326)(150, 291)(151, 334)(152, 308)(153, 329)(154, 314)(155, 236)(156, 311)(157, 297)(158, 315)(159, 319)(160, 317)(161, 289)(162, 324)(163, 322)(164, 285)(165, 328)(166, 230)(167, 333)(168, 335) local type(s) :: { ( 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E20.1124 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 84 e = 168 f = 46 degree seq :: [ 4^84 ] E20.1129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 42}) Quotient :: dipole Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |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)^42 ] Map:: R = (1, 169, 2, 170)(3, 171, 7, 175)(4, 172, 9, 177)(5, 173, 10, 178)(6, 174, 12, 180)(8, 176, 11, 179)(13, 181, 17, 185)(14, 182, 18, 186)(15, 183, 19, 187)(16, 184, 20, 188)(21, 189, 25, 193)(22, 190, 26, 194)(23, 191, 27, 195)(24, 192, 28, 196)(29, 197, 33, 201)(30, 198, 34, 202)(31, 199, 35, 203)(32, 200, 36, 204)(37, 205, 61, 229)(38, 206, 62, 230)(39, 207, 63, 231)(40, 208, 64, 232)(41, 209, 65, 233)(42, 210, 66, 234)(43, 211, 67, 235)(44, 212, 68, 236)(45, 213, 69, 237)(46, 214, 70, 238)(47, 215, 71, 239)(48, 216, 72, 240)(49, 217, 73, 241)(50, 218, 74, 242)(51, 219, 75, 243)(52, 220, 76, 244)(53, 221, 77, 245)(54, 222, 78, 246)(55, 223, 79, 247)(56, 224, 80, 248)(57, 225, 81, 249)(58, 226, 82, 250)(59, 227, 83, 251)(60, 228, 84, 252)(85, 253, 109, 277)(86, 254, 110, 278)(87, 255, 111, 279)(88, 256, 112, 280)(89, 257, 113, 281)(90, 258, 114, 282)(91, 259, 115, 283)(92, 260, 116, 284)(93, 261, 117, 285)(94, 262, 118, 286)(95, 263, 119, 287)(96, 264, 120, 288)(97, 265, 121, 289)(98, 266, 122, 290)(99, 267, 123, 291)(100, 268, 124, 292)(101, 269, 125, 293)(102, 270, 126, 294)(103, 271, 127, 295)(104, 272, 128, 296)(105, 273, 129, 297)(106, 274, 130, 298)(107, 275, 131, 299)(108, 276, 132, 300)(133, 301, 157, 325)(134, 302, 158, 326)(135, 303, 159, 327)(136, 304, 160, 328)(137, 305, 161, 329)(138, 306, 162, 330)(139, 307, 163, 331)(140, 308, 164, 332)(141, 309, 165, 333)(142, 310, 166, 334)(143, 311, 167, 335)(144, 312, 168, 336)(145, 313, 155, 323)(146, 314, 156, 324)(147, 315, 153, 321)(148, 316, 154, 322)(149, 317, 152, 320)(150, 318, 151, 319)(337, 505, 339, 507, 344, 512, 340, 508)(338, 506, 341, 509, 347, 515, 342, 510)(343, 511, 349, 517, 345, 513, 350, 518)(346, 514, 351, 519, 348, 516, 352, 520)(353, 521, 357, 525, 354, 522, 358, 526)(355, 523, 359, 527, 356, 524, 360, 528)(361, 529, 365, 533, 362, 530, 366, 534)(363, 531, 367, 535, 364, 532, 368, 536)(369, 537, 373, 541, 370, 538, 374, 542)(371, 539, 378, 546, 372, 540, 377, 545)(375, 543, 398, 566, 380, 548, 397, 565)(376, 544, 401, 569, 383, 551, 402, 570)(379, 547, 404, 572, 381, 549, 399, 567)(382, 550, 407, 575, 384, 552, 400, 568)(385, 553, 405, 573, 386, 554, 403, 571)(387, 555, 408, 576, 388, 556, 406, 574)(389, 557, 410, 578, 390, 558, 409, 577)(391, 559, 412, 580, 392, 560, 411, 579)(393, 561, 414, 582, 394, 562, 413, 581)(395, 563, 416, 584, 396, 564, 415, 583)(417, 585, 421, 589, 418, 586, 422, 590)(419, 587, 426, 594, 420, 588, 425, 593)(423, 591, 446, 614, 428, 596, 445, 613)(424, 592, 449, 617, 431, 599, 450, 618)(427, 595, 452, 620, 429, 597, 447, 615)(430, 598, 455, 623, 432, 600, 448, 616)(433, 601, 453, 621, 434, 602, 451, 619)(435, 603, 456, 624, 436, 604, 454, 622)(437, 605, 458, 626, 438, 606, 457, 625)(439, 607, 460, 628, 440, 608, 459, 627)(441, 609, 462, 630, 442, 610, 461, 629)(443, 611, 464, 632, 444, 612, 463, 631)(465, 633, 469, 637, 466, 634, 470, 638)(467, 635, 474, 642, 468, 636, 473, 641)(471, 639, 494, 662, 476, 644, 493, 661)(472, 640, 497, 665, 479, 647, 498, 666)(475, 643, 500, 668, 477, 645, 495, 663)(478, 646, 503, 671, 480, 648, 496, 664)(481, 649, 501, 669, 482, 650, 499, 667)(483, 651, 504, 672, 484, 652, 502, 670)(485, 653, 492, 660, 486, 654, 491, 659)(487, 655, 490, 658, 488, 656, 489, 657) L = (1, 338)(2, 337)(3, 343)(4, 345)(5, 346)(6, 348)(7, 339)(8, 347)(9, 340)(10, 341)(11, 344)(12, 342)(13, 353)(14, 354)(15, 355)(16, 356)(17, 349)(18, 350)(19, 351)(20, 352)(21, 361)(22, 362)(23, 363)(24, 364)(25, 357)(26, 358)(27, 359)(28, 360)(29, 369)(30, 370)(31, 371)(32, 372)(33, 365)(34, 366)(35, 367)(36, 368)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 493)(134, 494)(135, 495)(136, 496)(137, 497)(138, 498)(139, 499)(140, 500)(141, 501)(142, 502)(143, 503)(144, 504)(145, 491)(146, 492)(147, 489)(148, 490)(149, 488)(150, 487)(151, 486)(152, 485)(153, 483)(154, 484)(155, 481)(156, 482)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 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, 84, 2, 84 ), ( 2, 84, 2, 84, 2, 84, 2, 84 ) } Outer automorphisms :: reflexible Dual of E20.1132 Graph:: bipartite v = 126 e = 336 f = 172 degree seq :: [ 4^84, 8^42 ] E20.1130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 42}) Quotient :: dipole Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |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, Y2^42 ] Map:: R = (1, 169, 2, 170, 6, 174, 4, 172)(3, 171, 9, 177, 13, 181, 8, 176)(5, 173, 11, 179, 14, 182, 7, 175)(10, 178, 16, 184, 21, 189, 17, 185)(12, 180, 15, 183, 22, 190, 19, 187)(18, 186, 25, 193, 29, 197, 24, 192)(20, 188, 27, 195, 30, 198, 23, 191)(26, 194, 32, 200, 37, 205, 33, 201)(28, 196, 31, 199, 38, 206, 35, 203)(34, 202, 41, 209, 45, 213, 40, 208)(36, 204, 43, 211, 46, 214, 39, 207)(42, 210, 48, 216, 53, 221, 49, 217)(44, 212, 47, 215, 54, 222, 51, 219)(50, 218, 57, 225, 61, 229, 56, 224)(52, 220, 59, 227, 62, 230, 55, 223)(58, 226, 64, 232, 75, 243, 65, 233)(60, 228, 63, 231, 102, 270, 67, 235)(66, 234, 105, 273, 70, 238, 108, 276)(68, 236, 72, 240, 107, 275, 69, 237)(71, 239, 109, 277, 77, 245, 110, 278)(73, 241, 111, 279, 74, 242, 112, 280)(76, 244, 113, 281, 81, 249, 114, 282)(78, 246, 115, 283, 79, 247, 116, 284)(80, 248, 117, 285, 85, 253, 118, 286)(82, 250, 119, 287, 83, 251, 120, 288)(84, 252, 121, 289, 89, 257, 122, 290)(86, 254, 123, 291, 87, 255, 124, 292)(88, 256, 125, 293, 93, 261, 126, 294)(90, 258, 127, 295, 91, 259, 128, 296)(92, 260, 129, 297, 97, 265, 130, 298)(94, 262, 131, 299, 95, 263, 132, 300)(96, 264, 133, 301, 101, 269, 135, 303)(98, 266, 136, 304, 99, 267, 137, 305)(100, 268, 138, 306, 134, 302, 140, 308)(103, 271, 141, 309, 104, 272, 143, 311)(106, 274, 145, 313, 139, 307, 147, 315)(142, 310, 167, 335, 144, 312, 168, 336)(146, 314, 165, 333, 148, 316, 166, 334)(149, 317, 163, 331, 150, 318, 164, 332)(151, 319, 161, 329, 152, 320, 162, 330)(153, 321, 160, 328, 154, 322, 159, 327)(155, 323, 158, 326, 156, 324, 157, 325)(337, 505, 339, 507, 346, 514, 354, 522, 362, 530, 370, 538, 378, 546, 386, 554, 394, 562, 402, 570, 409, 577, 415, 583, 418, 586, 423, 591, 426, 594, 431, 599, 434, 602, 440, 608, 480, 648, 486, 654, 489, 657, 494, 662, 497, 665, 502, 670, 481, 649, 474, 642, 469, 637, 465, 633, 461, 629, 457, 625, 453, 621, 449, 617, 445, 613, 404, 572, 396, 564, 388, 556, 380, 548, 372, 540, 364, 532, 356, 524, 348, 516, 341, 509)(338, 506, 343, 511, 351, 519, 359, 527, 367, 535, 375, 543, 383, 551, 391, 559, 399, 567, 405, 573, 413, 581, 412, 580, 421, 589, 420, 588, 429, 597, 428, 596, 437, 605, 436, 604, 475, 643, 484, 652, 488, 656, 491, 659, 496, 664, 499, 667, 504, 672, 477, 645, 472, 640, 467, 635, 463, 631, 459, 627, 455, 623, 451, 619, 447, 615, 444, 612, 400, 568, 392, 560, 384, 552, 376, 544, 368, 536, 360, 528, 352, 520, 344, 512)(340, 508, 347, 515, 355, 523, 363, 531, 371, 539, 379, 547, 387, 555, 395, 563, 403, 571, 408, 576, 407, 575, 417, 585, 416, 584, 425, 593, 424, 592, 433, 601, 432, 600, 470, 638, 442, 610, 482, 650, 487, 655, 492, 660, 495, 663, 500, 668, 503, 671, 479, 647, 473, 641, 468, 636, 464, 632, 460, 628, 456, 624, 452, 620, 448, 616, 441, 609, 401, 569, 393, 561, 385, 553, 377, 545, 369, 537, 361, 529, 353, 521, 345, 513)(342, 510, 349, 517, 357, 525, 365, 533, 373, 541, 381, 549, 389, 557, 397, 565, 411, 579, 406, 574, 410, 578, 414, 582, 419, 587, 422, 590, 427, 595, 430, 598, 435, 603, 439, 607, 478, 646, 485, 653, 490, 658, 493, 661, 498, 666, 501, 669, 483, 651, 476, 644, 471, 639, 466, 634, 462, 630, 458, 626, 454, 622, 450, 618, 446, 614, 443, 611, 438, 606, 398, 566, 390, 558, 382, 550, 374, 542, 366, 534, 358, 526, 350, 518) L = (1, 339)(2, 343)(3, 346)(4, 347)(5, 337)(6, 349)(7, 351)(8, 338)(9, 340)(10, 354)(11, 355)(12, 341)(13, 357)(14, 342)(15, 359)(16, 344)(17, 345)(18, 362)(19, 363)(20, 348)(21, 365)(22, 350)(23, 367)(24, 352)(25, 353)(26, 370)(27, 371)(28, 356)(29, 373)(30, 358)(31, 375)(32, 360)(33, 361)(34, 378)(35, 379)(36, 364)(37, 381)(38, 366)(39, 383)(40, 368)(41, 369)(42, 386)(43, 387)(44, 372)(45, 389)(46, 374)(47, 391)(48, 376)(49, 377)(50, 394)(51, 395)(52, 380)(53, 397)(54, 382)(55, 399)(56, 384)(57, 385)(58, 402)(59, 403)(60, 388)(61, 411)(62, 390)(63, 405)(64, 392)(65, 393)(66, 409)(67, 408)(68, 396)(69, 413)(70, 410)(71, 417)(72, 407)(73, 415)(74, 414)(75, 406)(76, 421)(77, 412)(78, 419)(79, 418)(80, 425)(81, 416)(82, 423)(83, 422)(84, 429)(85, 420)(86, 427)(87, 426)(88, 433)(89, 424)(90, 431)(91, 430)(92, 437)(93, 428)(94, 435)(95, 434)(96, 470)(97, 432)(98, 440)(99, 439)(100, 475)(101, 436)(102, 398)(103, 478)(104, 480)(105, 401)(106, 482)(107, 438)(108, 400)(109, 404)(110, 443)(111, 444)(112, 441)(113, 445)(114, 446)(115, 447)(116, 448)(117, 449)(118, 450)(119, 451)(120, 452)(121, 453)(122, 454)(123, 455)(124, 456)(125, 457)(126, 458)(127, 459)(128, 460)(129, 461)(130, 462)(131, 463)(132, 464)(133, 465)(134, 442)(135, 466)(136, 467)(137, 468)(138, 469)(139, 484)(140, 471)(141, 472)(142, 485)(143, 473)(144, 486)(145, 474)(146, 487)(147, 476)(148, 488)(149, 490)(150, 489)(151, 492)(152, 491)(153, 494)(154, 493)(155, 496)(156, 495)(157, 498)(158, 497)(159, 500)(160, 499)(161, 502)(162, 501)(163, 504)(164, 503)(165, 483)(166, 481)(167, 479)(168, 477)(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, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E20.1131 Graph:: bipartite v = 46 e = 336 f = 252 degree seq :: [ 8^42, 84^4 ] E20.1131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 42}) Quotient :: dipole Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^42 ] Map:: polytopal R = (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)(337, 505, 338, 506)(339, 507, 343, 511)(340, 508, 345, 513)(341, 509, 347, 515)(342, 510, 349, 517)(344, 512, 350, 518)(346, 514, 348, 516)(351, 519, 356, 524)(352, 520, 359, 527)(353, 521, 361, 529)(354, 522, 357, 525)(355, 523, 363, 531)(358, 526, 365, 533)(360, 528, 367, 535)(362, 530, 368, 536)(364, 532, 366, 534)(369, 537, 375, 543)(370, 538, 377, 545)(371, 539, 373, 541)(372, 540, 379, 547)(374, 542, 381, 549)(376, 544, 383, 551)(378, 546, 384, 552)(380, 548, 382, 550)(385, 553, 391, 559)(386, 554, 393, 561)(387, 555, 389, 557)(388, 556, 395, 563)(390, 558, 397, 565)(392, 560, 399, 567)(394, 562, 400, 568)(396, 564, 398, 566)(401, 569, 405, 573)(402, 570, 435, 603)(403, 571, 437, 605)(404, 572, 407, 575)(406, 574, 440, 608)(408, 576, 443, 611)(409, 577, 445, 613)(410, 578, 447, 615)(411, 579, 449, 617)(412, 580, 451, 619)(413, 581, 453, 621)(414, 582, 455, 623)(415, 583, 457, 625)(416, 584, 459, 627)(417, 585, 461, 629)(418, 586, 463, 631)(419, 587, 465, 633)(420, 588, 467, 635)(421, 589, 469, 637)(422, 590, 471, 639)(423, 591, 473, 641)(424, 592, 475, 643)(425, 593, 477, 645)(426, 594, 479, 647)(427, 595, 481, 649)(428, 596, 483, 651)(429, 597, 485, 653)(430, 598, 487, 655)(431, 599, 489, 657)(432, 600, 491, 659)(433, 601, 493, 661)(434, 602, 495, 663)(436, 604, 497, 665)(438, 606, 499, 667)(439, 607, 501, 669)(441, 609, 503, 671)(442, 610, 504, 672)(444, 612, 494, 662)(446, 614, 498, 666)(448, 616, 490, 658)(450, 618, 492, 660)(452, 620, 502, 670)(454, 622, 496, 664)(456, 624, 500, 668)(458, 626, 478, 646)(460, 628, 482, 650)(462, 630, 474, 642)(464, 632, 486, 654)(466, 634, 476, 644)(468, 636, 488, 656)(470, 638, 480, 648)(472, 640, 484, 652) L = (1, 339)(2, 341)(3, 344)(4, 337)(5, 348)(6, 338)(7, 351)(8, 353)(9, 354)(10, 340)(11, 356)(12, 358)(13, 359)(14, 342)(15, 345)(16, 343)(17, 362)(18, 363)(19, 346)(20, 349)(21, 347)(22, 366)(23, 367)(24, 350)(25, 352)(26, 370)(27, 371)(28, 355)(29, 357)(30, 374)(31, 375)(32, 360)(33, 361)(34, 378)(35, 379)(36, 364)(37, 365)(38, 382)(39, 383)(40, 368)(41, 369)(42, 386)(43, 387)(44, 372)(45, 373)(46, 390)(47, 391)(48, 376)(49, 377)(50, 394)(51, 395)(52, 380)(53, 381)(54, 398)(55, 399)(56, 384)(57, 385)(58, 402)(59, 403)(60, 388)(61, 389)(62, 409)(63, 405)(64, 392)(65, 393)(66, 414)(67, 407)(68, 396)(69, 406)(70, 408)(71, 410)(72, 411)(73, 412)(74, 413)(75, 415)(76, 416)(77, 417)(78, 418)(79, 419)(80, 420)(81, 421)(82, 422)(83, 423)(84, 424)(85, 425)(86, 426)(87, 427)(88, 428)(89, 429)(90, 430)(91, 431)(92, 432)(93, 433)(94, 434)(95, 436)(96, 438)(97, 446)(98, 439)(99, 401)(100, 456)(101, 397)(102, 442)(103, 441)(104, 400)(105, 444)(106, 448)(107, 435)(108, 450)(109, 437)(110, 452)(111, 445)(112, 454)(113, 455)(114, 458)(115, 404)(116, 460)(117, 451)(118, 462)(119, 440)(120, 464)(121, 463)(122, 466)(123, 447)(124, 468)(125, 459)(126, 470)(127, 443)(128, 472)(129, 471)(130, 474)(131, 453)(132, 476)(133, 467)(134, 478)(135, 449)(136, 480)(137, 479)(138, 482)(139, 461)(140, 484)(141, 475)(142, 486)(143, 457)(144, 488)(145, 487)(146, 490)(147, 469)(148, 492)(149, 483)(150, 494)(151, 465)(152, 496)(153, 495)(154, 498)(155, 477)(156, 500)(157, 491)(158, 497)(159, 473)(160, 502)(161, 501)(162, 499)(163, 485)(164, 503)(165, 481)(166, 504)(167, 489)(168, 493)(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, 84 ), ( 8, 84, 8, 84 ) } Outer automorphisms :: reflexible Dual of E20.1130 Graph:: simple bipartite v = 252 e = 336 f = 46 degree seq :: [ 2^168, 4^84 ] E20.1132 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 42}) Quotient :: dipole Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |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, Y1^42 ] Map:: polytopal R = (1, 169, 2, 170, 5, 173, 11, 179, 20, 188, 29, 197, 37, 205, 45, 213, 53, 221, 61, 229, 125, 293, 158, 326, 151, 319, 142, 310, 136, 304, 133, 301, 134, 302, 137, 305, 143, 311, 132, 300, 122, 290, 118, 286, 109, 277, 103, 271, 93, 261, 86, 254, 75, 243, 81, 249, 76, 244, 82, 250, 90, 258, 99, 267, 107, 275, 68, 236, 60, 228, 52, 220, 44, 212, 36, 204, 28, 196, 19, 187, 10, 178, 4, 172)(3, 171, 7, 175, 15, 183, 25, 193, 33, 201, 41, 209, 49, 217, 57, 225, 65, 233, 129, 297, 165, 333, 159, 327, 153, 321, 144, 312, 140, 308, 135, 303, 139, 307, 147, 315, 126, 294, 162, 330, 113, 281, 121, 289, 97, 265, 108, 276, 79, 247, 92, 260, 70, 238, 91, 259, 72, 240, 94, 262, 87, 255, 110, 278, 104, 272, 123, 291, 62, 230, 55, 223, 46, 214, 39, 207, 30, 198, 22, 190, 12, 180, 8, 176)(6, 174, 13, 181, 9, 177, 18, 186, 27, 195, 35, 203, 43, 211, 51, 219, 59, 227, 67, 235, 131, 299, 164, 332, 160, 328, 152, 320, 146, 314, 138, 306, 145, 313, 141, 309, 150, 318, 157, 325, 119, 287, 128, 296, 105, 273, 115, 283, 88, 256, 100, 268, 73, 241, 85, 253, 69, 237, 84, 252, 78, 246, 102, 270, 96, 264, 117, 285, 112, 280, 63, 231, 54, 222, 47, 215, 38, 206, 31, 199, 21, 189, 14, 182)(16, 184, 23, 191, 17, 185, 24, 192, 32, 200, 40, 208, 48, 216, 56, 224, 64, 232, 127, 295, 168, 336, 167, 335, 166, 334, 163, 331, 156, 324, 148, 316, 154, 322, 149, 317, 155, 323, 161, 329, 130, 298, 124, 292, 116, 284, 111, 279, 101, 269, 95, 263, 83, 251, 77, 245, 71, 239, 74, 242, 80, 248, 89, 257, 98, 266, 106, 274, 114, 282, 120, 288, 66, 234, 58, 226, 50, 218, 42, 210, 34, 202, 26, 194)(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, 342)(3, 337)(4, 345)(5, 348)(6, 338)(7, 352)(8, 353)(9, 340)(10, 351)(11, 357)(12, 341)(13, 359)(14, 360)(15, 346)(16, 343)(17, 344)(18, 362)(19, 363)(20, 366)(21, 347)(22, 368)(23, 349)(24, 350)(25, 370)(26, 354)(27, 355)(28, 369)(29, 374)(30, 356)(31, 376)(32, 358)(33, 364)(34, 361)(35, 378)(36, 379)(37, 382)(38, 365)(39, 384)(40, 367)(41, 386)(42, 371)(43, 372)(44, 385)(45, 390)(46, 373)(47, 392)(48, 375)(49, 380)(50, 377)(51, 394)(52, 395)(53, 398)(54, 381)(55, 400)(56, 383)(57, 402)(58, 387)(59, 388)(60, 401)(61, 448)(62, 389)(63, 463)(64, 391)(65, 396)(66, 393)(67, 456)(68, 467)(69, 469)(70, 470)(71, 471)(72, 472)(73, 473)(74, 474)(75, 475)(76, 476)(77, 477)(78, 478)(79, 479)(80, 480)(81, 481)(82, 482)(83, 483)(84, 484)(85, 485)(86, 486)(87, 487)(88, 468)(89, 488)(90, 489)(91, 490)(92, 491)(93, 462)(94, 492)(95, 493)(96, 494)(97, 458)(98, 495)(99, 496)(100, 497)(101, 498)(102, 499)(103, 455)(104, 461)(105, 454)(106, 500)(107, 501)(108, 466)(109, 449)(110, 502)(111, 464)(112, 397)(113, 445)(114, 465)(115, 460)(116, 457)(117, 503)(118, 441)(119, 439)(120, 403)(121, 452)(122, 433)(123, 504)(124, 451)(125, 440)(126, 429)(127, 399)(128, 447)(129, 450)(130, 444)(131, 404)(132, 424)(133, 405)(134, 406)(135, 407)(136, 408)(137, 409)(138, 410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 417)(146, 418)(147, 419)(148, 420)(149, 421)(150, 422)(151, 423)(152, 425)(153, 426)(154, 427)(155, 428)(156, 430)(157, 431)(158, 432)(159, 434)(160, 435)(161, 436)(162, 437)(163, 438)(164, 442)(165, 443)(166, 446)(167, 453)(168, 459)(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, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E20.1129 Graph:: simple bipartite v = 172 e = 336 f = 126 degree seq :: [ 2^168, 84^4 ] E20.1133 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 42}) Quotient :: dipole Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |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, Y2^42 ] Map:: R = (1, 169, 2, 170)(3, 171, 7, 175)(4, 172, 9, 177)(5, 173, 11, 179)(6, 174, 13, 181)(8, 176, 14, 182)(10, 178, 12, 180)(15, 183, 20, 188)(16, 184, 23, 191)(17, 185, 25, 193)(18, 186, 21, 189)(19, 187, 27, 195)(22, 190, 29, 197)(24, 192, 31, 199)(26, 194, 32, 200)(28, 196, 30, 198)(33, 201, 39, 207)(34, 202, 41, 209)(35, 203, 37, 205)(36, 204, 43, 211)(38, 206, 45, 213)(40, 208, 47, 215)(42, 210, 48, 216)(44, 212, 46, 214)(49, 217, 55, 223)(50, 218, 57, 225)(51, 219, 53, 221)(52, 220, 59, 227)(54, 222, 61, 229)(56, 224, 63, 231)(58, 226, 64, 232)(60, 228, 62, 230)(65, 233, 119, 287)(66, 234, 96, 264)(67, 235, 106, 274)(68, 236, 123, 291)(69, 237, 125, 293)(70, 238, 126, 294)(71, 239, 127, 295)(72, 240, 128, 296)(73, 241, 129, 297)(74, 242, 130, 298)(75, 243, 131, 299)(76, 244, 132, 300)(77, 245, 133, 301)(78, 246, 134, 302)(79, 247, 135, 303)(80, 248, 136, 304)(81, 249, 137, 305)(82, 250, 138, 306)(83, 251, 139, 307)(84, 252, 140, 308)(85, 253, 141, 309)(86, 254, 142, 310)(87, 255, 121, 289)(88, 256, 143, 311)(89, 257, 144, 312)(90, 258, 145, 313)(91, 259, 146, 314)(92, 260, 147, 315)(93, 261, 148, 316)(94, 262, 149, 317)(95, 263, 150, 318)(97, 265, 151, 319)(98, 266, 152, 320)(99, 267, 153, 321)(100, 268, 117, 285)(101, 269, 154, 322)(102, 270, 155, 323)(103, 271, 156, 324)(104, 272, 157, 325)(105, 273, 158, 326)(107, 275, 159, 327)(108, 276, 160, 328)(109, 277, 161, 329)(110, 278, 162, 330)(111, 279, 163, 331)(112, 280, 165, 333)(113, 281, 122, 290)(114, 282, 166, 334)(115, 283, 124, 292)(116, 284, 167, 335)(118, 286, 164, 332)(120, 288, 168, 336)(337, 505, 339, 507, 344, 512, 353, 521, 362, 530, 370, 538, 378, 546, 386, 554, 394, 562, 402, 570, 457, 625, 470, 638, 464, 632, 461, 629, 463, 631, 468, 636, 477, 645, 485, 653, 490, 658, 495, 663, 499, 667, 460, 628, 449, 617, 448, 616, 440, 608, 438, 606, 426, 594, 422, 590, 409, 577, 419, 587, 410, 578, 420, 588, 428, 596, 404, 572, 396, 564, 388, 556, 380, 548, 372, 540, 364, 532, 355, 523, 346, 514, 340, 508)(338, 506, 341, 509, 348, 516, 358, 526, 366, 534, 374, 542, 382, 550, 390, 558, 398, 566, 453, 621, 483, 651, 474, 642, 466, 634, 462, 630, 465, 633, 472, 640, 481, 649, 488, 656, 493, 661, 497, 665, 458, 626, 500, 668, 447, 615, 450, 618, 437, 605, 441, 609, 421, 589, 427, 595, 407, 575, 424, 592, 408, 576, 425, 593, 423, 591, 439, 607, 400, 568, 392, 560, 384, 552, 376, 544, 368, 536, 360, 528, 350, 518, 342, 510)(343, 511, 351, 519, 345, 513, 354, 522, 363, 531, 371, 539, 379, 547, 387, 555, 395, 563, 403, 571, 459, 627, 484, 652, 476, 644, 467, 635, 475, 643, 469, 637, 478, 646, 486, 654, 491, 659, 496, 664, 501, 669, 503, 671, 451, 619, 456, 624, 443, 611, 446, 614, 430, 598, 435, 603, 412, 580, 417, 585, 405, 573, 415, 583, 414, 582, 433, 601, 432, 600, 401, 569, 393, 561, 385, 553, 377, 545, 369, 537, 361, 529, 352, 520)(347, 515, 356, 524, 349, 517, 359, 527, 367, 535, 375, 543, 383, 551, 391, 559, 399, 567, 455, 623, 492, 660, 487, 655, 480, 648, 471, 639, 479, 647, 473, 641, 482, 650, 489, 657, 494, 662, 498, 666, 502, 670, 504, 672, 454, 622, 452, 620, 445, 613, 444, 612, 434, 602, 431, 599, 416, 584, 413, 581, 406, 574, 411, 579, 418, 586, 429, 597, 436, 604, 442, 610, 397, 565, 389, 557, 381, 549, 373, 541, 365, 533, 357, 525) L = (1, 338)(2, 337)(3, 343)(4, 345)(5, 347)(6, 349)(7, 339)(8, 350)(9, 340)(10, 348)(11, 341)(12, 346)(13, 342)(14, 344)(15, 356)(16, 359)(17, 361)(18, 357)(19, 363)(20, 351)(21, 354)(22, 365)(23, 352)(24, 367)(25, 353)(26, 368)(27, 355)(28, 366)(29, 358)(30, 364)(31, 360)(32, 362)(33, 375)(34, 377)(35, 373)(36, 379)(37, 371)(38, 381)(39, 369)(40, 383)(41, 370)(42, 384)(43, 372)(44, 382)(45, 374)(46, 380)(47, 376)(48, 378)(49, 391)(50, 393)(51, 389)(52, 395)(53, 387)(54, 397)(55, 385)(56, 399)(57, 386)(58, 400)(59, 388)(60, 398)(61, 390)(62, 396)(63, 392)(64, 394)(65, 455)(66, 432)(67, 442)(68, 459)(69, 461)(70, 462)(71, 463)(72, 464)(73, 465)(74, 466)(75, 467)(76, 468)(77, 469)(78, 470)(79, 471)(80, 472)(81, 473)(82, 474)(83, 475)(84, 476)(85, 477)(86, 478)(87, 457)(88, 479)(89, 480)(90, 481)(91, 482)(92, 483)(93, 484)(94, 485)(95, 486)(96, 402)(97, 487)(98, 488)(99, 489)(100, 453)(101, 490)(102, 491)(103, 492)(104, 493)(105, 494)(106, 403)(107, 495)(108, 496)(109, 497)(110, 498)(111, 499)(112, 501)(113, 458)(114, 502)(115, 460)(116, 503)(117, 436)(118, 500)(119, 401)(120, 504)(121, 423)(122, 449)(123, 404)(124, 451)(125, 405)(126, 406)(127, 407)(128, 408)(129, 409)(130, 410)(131, 411)(132, 412)(133, 413)(134, 414)(135, 415)(136, 416)(137, 417)(138, 418)(139, 419)(140, 420)(141, 421)(142, 422)(143, 424)(144, 425)(145, 426)(146, 427)(147, 428)(148, 429)(149, 430)(150, 431)(151, 433)(152, 434)(153, 435)(154, 437)(155, 438)(156, 439)(157, 440)(158, 441)(159, 443)(160, 444)(161, 445)(162, 446)(163, 447)(164, 454)(165, 448)(166, 450)(167, 452)(168, 456)(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, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E20.1134 Graph:: bipartite v = 88 e = 336 f = 210 degree seq :: [ 4^84, 84^4 ] E20.1134 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 42}) Quotient :: dipole Aut^+ = (C42 x C2) : C2 (small group id <168, 38>) Aut = D8 x D42 (small group id <336, 198>) |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)^42 ] Map:: polytopal R = (1, 169, 2, 170, 6, 174, 4, 172)(3, 171, 9, 177, 13, 181, 8, 176)(5, 173, 11, 179, 14, 182, 7, 175)(10, 178, 16, 184, 21, 189, 17, 185)(12, 180, 15, 183, 22, 190, 19, 187)(18, 186, 25, 193, 29, 197, 24, 192)(20, 188, 27, 195, 30, 198, 23, 191)(26, 194, 32, 200, 37, 205, 33, 201)(28, 196, 31, 199, 38, 206, 35, 203)(34, 202, 41, 209, 45, 213, 40, 208)(36, 204, 43, 211, 46, 214, 39, 207)(42, 210, 48, 216, 53, 221, 49, 217)(44, 212, 47, 215, 54, 222, 51, 219)(50, 218, 57, 225, 61, 229, 56, 224)(52, 220, 59, 227, 62, 230, 55, 223)(58, 226, 64, 232, 83, 251, 65, 233)(60, 228, 63, 231, 106, 274, 67, 235)(66, 234, 109, 277, 75, 243, 118, 286)(68, 236, 79, 247, 115, 283, 71, 239)(69, 237, 111, 279, 74, 242, 112, 280)(70, 238, 113, 281, 72, 240, 114, 282)(73, 241, 116, 284, 80, 248, 117, 285)(76, 244, 119, 287, 77, 245, 120, 288)(78, 246, 121, 289, 85, 253, 122, 290)(81, 249, 123, 291, 82, 250, 124, 292)(84, 252, 125, 293, 89, 257, 126, 294)(86, 254, 127, 295, 87, 255, 128, 296)(88, 256, 129, 297, 93, 261, 130, 298)(90, 258, 131, 299, 91, 259, 132, 300)(92, 260, 133, 301, 97, 265, 134, 302)(94, 262, 135, 303, 95, 263, 136, 304)(96, 264, 137, 305, 101, 269, 138, 306)(98, 266, 139, 307, 99, 267, 140, 308)(100, 268, 141, 309, 105, 273, 143, 311)(102, 270, 144, 312, 103, 271, 145, 313)(104, 272, 146, 314, 142, 310, 148, 316)(107, 275, 149, 317, 108, 276, 151, 319)(110, 278, 153, 321, 147, 315, 155, 323)(150, 318, 168, 336, 152, 320, 167, 335)(154, 322, 166, 334, 156, 324, 165, 333)(157, 325, 164, 332, 158, 326, 163, 331)(159, 327, 162, 330, 160, 328, 161, 329)(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, 346)(4, 347)(5, 337)(6, 349)(7, 351)(8, 338)(9, 340)(10, 354)(11, 355)(12, 341)(13, 357)(14, 342)(15, 359)(16, 344)(17, 345)(18, 362)(19, 363)(20, 348)(21, 365)(22, 350)(23, 367)(24, 352)(25, 353)(26, 370)(27, 371)(28, 356)(29, 373)(30, 358)(31, 375)(32, 360)(33, 361)(34, 378)(35, 379)(36, 364)(37, 381)(38, 366)(39, 383)(40, 368)(41, 369)(42, 386)(43, 387)(44, 372)(45, 389)(46, 374)(47, 391)(48, 376)(49, 377)(50, 394)(51, 395)(52, 380)(53, 397)(54, 382)(55, 399)(56, 384)(57, 385)(58, 402)(59, 403)(60, 388)(61, 419)(62, 390)(63, 407)(64, 392)(65, 393)(66, 406)(67, 415)(68, 396)(69, 416)(70, 413)(71, 410)(72, 412)(73, 421)(74, 409)(75, 408)(76, 418)(77, 417)(78, 425)(79, 405)(80, 414)(81, 423)(82, 422)(83, 411)(84, 429)(85, 420)(86, 427)(87, 426)(88, 433)(89, 424)(90, 431)(91, 430)(92, 437)(93, 428)(94, 435)(95, 434)(96, 441)(97, 432)(98, 439)(99, 438)(100, 478)(101, 436)(102, 444)(103, 443)(104, 483)(105, 440)(106, 398)(107, 486)(108, 488)(109, 401)(110, 490)(111, 404)(112, 451)(113, 454)(114, 445)(115, 442)(116, 447)(117, 448)(118, 400)(119, 449)(120, 450)(121, 452)(122, 453)(123, 455)(124, 456)(125, 457)(126, 458)(127, 459)(128, 460)(129, 461)(130, 462)(131, 463)(132, 464)(133, 465)(134, 466)(135, 467)(136, 468)(137, 469)(138, 470)(139, 471)(140, 472)(141, 473)(142, 446)(143, 474)(144, 475)(145, 476)(146, 477)(147, 492)(148, 479)(149, 480)(150, 493)(151, 481)(152, 494)(153, 482)(154, 495)(155, 484)(156, 496)(157, 498)(158, 497)(159, 500)(160, 499)(161, 502)(162, 501)(163, 504)(164, 503)(165, 489)(166, 491)(167, 485)(168, 487)(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, 84 ), ( 4, 84, 4, 84, 4, 84, 4, 84 ) } Outer automorphisms :: reflexible Dual of E20.1133 Graph:: simple bipartite v = 210 e = 336 f = 88 degree seq :: [ 2^168, 8^42 ] E20.1135 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 6}) Quotient :: halfedge Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ X2^2, X1^6, (X2 * X1^-2 * X2 * X1^-1)^2, (X2 * X1^-1)^6, (X2 * X1^-1 * X2 * X1^2 * X2 * X1^-1)^2, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 29, 18, 8)(6, 13, 25, 48, 28, 14)(9, 19, 36, 66, 39, 20)(12, 23, 44, 78, 47, 24)(16, 31, 58, 98, 61, 32)(17, 33, 62, 80, 45, 34)(21, 40, 71, 112, 73, 41)(22, 42, 74, 115, 77, 43)(26, 50, 38, 70, 88, 51)(27, 52, 89, 117, 75, 53)(30, 56, 95, 140, 97, 57)(35, 65, 105, 130, 85, 49)(37, 68, 76, 118, 111, 69)(46, 81, 123, 114, 72, 82)(54, 92, 135, 167, 121, 79)(55, 93, 137, 181, 139, 94)(59, 86, 64, 91, 125, 99)(60, 100, 145, 183, 138, 101)(63, 87, 131, 177, 148, 104)(67, 108, 152, 196, 153, 109)(83, 126, 171, 204, 160, 116)(84, 127, 173, 215, 174, 128)(90, 122, 168, 213, 178, 134)(96, 142, 187, 150, 106, 132)(102, 147, 191, 222, 186, 141)(103, 129, 175, 218, 180, 136)(107, 151, 195, 224, 190, 146)(110, 154, 179, 217, 189, 144)(113, 119, 163, 207, 194, 157)(120, 164, 209, 188, 210, 165)(124, 161, 205, 185, 214, 170)(133, 166, 211, 182, 143, 172)(149, 184, 206, 162, 158, 193)(155, 199, 221, 227, 212, 197)(156, 200, 223, 228, 220, 198)(159, 201, 225, 219, 192, 202)(169, 203, 226, 216, 176, 208) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 35)(19, 37)(20, 38)(23, 45)(24, 46)(25, 49)(28, 54)(29, 55)(31, 59)(32, 60)(33, 63)(34, 64)(36, 67)(39, 56)(40, 72)(41, 58)(42, 75)(43, 76)(44, 79)(47, 83)(48, 84)(50, 86)(51, 87)(52, 90)(53, 91)(57, 96)(61, 102)(62, 103)(65, 106)(66, 107)(68, 99)(69, 110)(70, 101)(71, 113)(73, 108)(74, 116)(77, 119)(78, 120)(80, 122)(81, 124)(82, 125)(85, 129)(88, 132)(89, 133)(92, 136)(93, 138)(94, 131)(95, 141)(97, 143)(98, 144)(100, 146)(104, 127)(105, 149)(109, 147)(111, 155)(112, 156)(114, 158)(115, 159)(117, 161)(118, 162)(121, 166)(123, 169)(126, 172)(128, 168)(130, 176)(134, 164)(135, 179)(137, 182)(139, 184)(140, 185)(142, 188)(145, 171)(148, 192)(150, 194)(151, 189)(152, 197)(153, 180)(154, 198)(157, 199)(160, 203)(163, 208)(165, 205)(167, 212)(170, 201)(173, 216)(174, 217)(175, 219)(177, 207)(178, 220)(181, 221)(183, 210)(186, 204)(187, 223)(190, 214)(191, 215)(193, 202)(195, 218)(196, 213)(200, 206)(209, 227)(211, 228)(222, 225)(224, 226) local type(s) :: { ( 6^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 38 e = 114 f = 38 degree seq :: [ 6^38 ] E20.1136 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 6, 6}) Quotient :: halfedge Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ X2^2, X1^6, X1^6, X1^2 * X2 * X1^-3 * X2 * X1, (X1^-1 * X2)^6, X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 ] Map:: polytopal 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, 63, 44, 66, 41)(27, 42, 62, 39, 61, 43)(35, 53, 58, 37, 57, 54)(36, 55, 60, 38, 59, 56)(48, 72, 101, 76, 86, 73)(49, 74, 100, 71, 99, 75)(51, 77, 98, 69, 97, 78)(52, 79, 93, 70, 90, 64)(65, 91, 120, 89, 119, 92)(67, 94, 118, 87, 117, 95)(68, 96, 80, 88, 112, 83)(81, 108, 114, 84, 113, 109)(82, 110, 116, 85, 115, 111)(102, 132, 169, 131, 168, 133)(103, 134, 167, 129, 166, 135)(104, 136, 105, 130, 163, 127)(106, 137, 165, 128, 164, 138)(107, 139, 155, 121, 154, 140)(122, 156, 195, 152, 194, 157)(123, 158, 124, 153, 191, 150)(125, 159, 193, 151, 192, 160)(126, 161, 185, 145, 184, 162)(141, 179, 187, 146, 186, 180)(142, 181, 143, 147, 188, 148)(144, 182, 190, 149, 189, 183)(170, 212, 225, 210, 223, 201)(171, 200, 172, 211, 224, 208)(173, 199, 220, 209, 228, 213)(174, 214, 218, 205, 219, 204)(175, 203, 226, 206, 217, 202)(176, 215, 177, 207, 222, 196)(178, 216, 227, 197, 221, 198) 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, 64)(41, 65)(42, 67)(43, 68)(45, 69)(46, 70)(47, 71)(50, 76)(53, 80)(54, 81)(55, 82)(56, 72)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(66, 93)(73, 102)(74, 103)(75, 104)(77, 105)(78, 106)(79, 107)(90, 121)(91, 122)(92, 123)(94, 124)(95, 125)(96, 126)(97, 127)(98, 128)(99, 129)(100, 130)(101, 131)(108, 141)(109, 142)(110, 143)(111, 144)(112, 145)(113, 146)(114, 147)(115, 148)(116, 149)(117, 150)(118, 151)(119, 152)(120, 153)(132, 170)(133, 171)(134, 172)(135, 173)(136, 174)(137, 175)(138, 176)(139, 177)(140, 178)(154, 196)(155, 197)(156, 198)(157, 199)(158, 200)(159, 201)(160, 202)(161, 203)(162, 204)(163, 205)(164, 206)(165, 207)(166, 208)(167, 209)(168, 210)(169, 211)(179, 214)(180, 213)(181, 216)(182, 215)(183, 212)(184, 217)(185, 218)(186, 219)(187, 220)(188, 221)(189, 222)(190, 223)(191, 224)(192, 225)(193, 226)(194, 227)(195, 228) local type(s) :: { ( 6^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 38 e = 114 f = 38 degree seq :: [ 6^38 ] E20.1137 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ X1^2, X2^6, (X2^-2 * X1 * X2^-1)^2, (X2^-1 * X1)^6, (X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1)^2, X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 ] Map:: polytopal R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 24)(14, 28)(15, 29)(16, 31)(18, 25)(19, 35)(20, 36)(22, 37)(23, 39)(26, 43)(27, 44)(30, 47)(32, 50)(33, 51)(34, 52)(38, 59)(40, 62)(41, 63)(42, 64)(45, 68)(46, 70)(48, 74)(49, 75)(53, 80)(54, 81)(55, 82)(56, 57)(58, 84)(60, 88)(61, 89)(65, 94)(66, 95)(67, 96)(69, 97)(71, 93)(72, 100)(73, 101)(76, 105)(77, 106)(78, 107)(79, 85)(83, 112)(86, 115)(87, 116)(90, 120)(91, 121)(92, 122)(98, 129)(99, 130)(102, 134)(103, 135)(104, 136)(108, 141)(109, 142)(110, 143)(111, 144)(113, 147)(114, 148)(117, 152)(118, 153)(119, 154)(123, 159)(124, 160)(125, 161)(126, 162)(127, 163)(128, 164)(131, 168)(132, 169)(133, 170)(137, 175)(138, 176)(139, 177)(140, 178)(145, 184)(146, 185)(149, 189)(150, 190)(151, 191)(155, 196)(156, 197)(157, 198)(158, 199)(165, 204)(166, 192)(167, 188)(171, 187)(172, 201)(173, 200)(174, 195)(179, 194)(180, 193)(181, 203)(182, 202)(183, 186)(205, 228)(206, 220)(207, 219)(208, 218)(209, 225)(210, 224)(211, 223)(212, 222)(213, 221)(214, 227)(215, 226)(216, 217)(229, 231, 236, 246, 238, 232)(230, 233, 240, 253, 242, 234)(235, 243, 258, 249, 260, 244)(237, 247, 262, 245, 261, 248)(239, 250, 266, 256, 268, 251)(241, 254, 270, 252, 269, 255)(257, 273, 297, 278, 299, 274)(259, 276, 301, 275, 300, 277)(263, 281, 305, 279, 304, 282)(264, 283, 307, 280, 306, 284)(265, 285, 311, 290, 313, 286)(267, 288, 315, 287, 314, 289)(271, 293, 319, 291, 318, 294)(272, 295, 321, 292, 320, 296)(298, 326, 356, 325, 355, 327)(302, 330, 360, 328, 359, 331)(303, 332, 308, 329, 361, 333)(309, 336, 366, 334, 365, 337)(310, 338, 368, 335, 367, 339)(312, 341, 374, 340, 373, 342)(316, 345, 378, 343, 377, 346)(317, 347, 322, 344, 379, 348)(323, 351, 384, 349, 383, 352)(324, 353, 386, 350, 385, 354)(357, 393, 434, 391, 433, 394)(358, 395, 362, 392, 435, 396)(363, 399, 437, 397, 436, 400)(364, 401, 439, 398, 438, 402)(369, 407, 441, 403, 440, 408)(370, 409, 371, 404, 442, 405)(372, 410, 444, 406, 443, 411)(375, 414, 446, 412, 445, 415)(376, 416, 380, 413, 447, 417)(381, 420, 449, 418, 448, 421)(382, 422, 451, 419, 450, 423)(387, 428, 453, 424, 452, 429)(388, 430, 389, 425, 454, 426)(390, 431, 456, 427, 455, 432) L = (1, 229)(2, 230)(3, 231)(4, 232)(5, 233)(6, 234)(7, 235)(8, 236)(9, 237)(10, 238)(11, 239)(12, 240)(13, 241)(14, 242)(15, 243)(16, 244)(17, 245)(18, 246)(19, 247)(20, 248)(21, 249)(22, 250)(23, 251)(24, 252)(25, 253)(26, 254)(27, 255)(28, 256)(29, 257)(30, 258)(31, 259)(32, 260)(33, 261)(34, 262)(35, 263)(36, 264)(37, 265)(38, 266)(39, 267)(40, 268)(41, 269)(42, 270)(43, 271)(44, 272)(45, 273)(46, 274)(47, 275)(48, 276)(49, 277)(50, 278)(51, 279)(52, 280)(53, 281)(54, 282)(55, 283)(56, 284)(57, 285)(58, 286)(59, 287)(60, 288)(61, 289)(62, 290)(63, 291)(64, 292)(65, 293)(66, 294)(67, 295)(68, 296)(69, 297)(70, 298)(71, 299)(72, 300)(73, 301)(74, 302)(75, 303)(76, 304)(77, 305)(78, 306)(79, 307)(80, 308)(81, 309)(82, 310)(83, 311)(84, 312)(85, 313)(86, 314)(87, 315)(88, 316)(89, 317)(90, 318)(91, 319)(92, 320)(93, 321)(94, 322)(95, 323)(96, 324)(97, 325)(98, 326)(99, 327)(100, 328)(101, 329)(102, 330)(103, 331)(104, 332)(105, 333)(106, 334)(107, 335)(108, 336)(109, 337)(110, 338)(111, 339)(112, 340)(113, 341)(114, 342)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456) local type(s) :: { ( 12, 12 ), ( 12^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 152 e = 228 f = 38 degree seq :: [ 2^114, 6^38 ] E20.1138 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ X1^2, X2^6, (X2^-2 * X1 * X2^-1 * X1)^2, (X2^-1 * X1)^6, (X2^-1 * X1 * X2^2 * X1 * X2^-1 * X1)^2, X2^-1 * X1 * X2^2 * X1 * X2^-2 * X1 * X2^2 * X1 * X2^-2 * X1 * X2 * X1 ] Map:: polytopal R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 24)(14, 28)(15, 29)(16, 31)(18, 35)(19, 36)(20, 38)(22, 42)(23, 44)(25, 48)(26, 49)(27, 51)(30, 54)(32, 60)(33, 52)(34, 62)(37, 68)(39, 46)(40, 71)(41, 43)(45, 79)(47, 81)(50, 87)(53, 90)(55, 74)(56, 85)(57, 94)(58, 95)(59, 89)(61, 99)(63, 103)(64, 97)(65, 105)(66, 75)(67, 107)(69, 111)(70, 78)(72, 113)(73, 109)(76, 116)(77, 117)(80, 121)(82, 125)(83, 119)(84, 127)(86, 129)(88, 133)(91, 135)(92, 131)(93, 124)(96, 139)(98, 132)(100, 143)(101, 144)(102, 115)(104, 147)(106, 150)(108, 152)(110, 120)(112, 156)(114, 158)(118, 161)(122, 165)(123, 166)(126, 169)(128, 172)(130, 174)(134, 178)(136, 180)(137, 177)(138, 182)(140, 185)(141, 186)(142, 184)(145, 190)(146, 168)(148, 192)(149, 193)(151, 195)(153, 197)(154, 176)(155, 159)(157, 196)(160, 202)(162, 205)(163, 206)(164, 204)(167, 210)(170, 212)(171, 213)(173, 215)(175, 217)(179, 216)(181, 201)(183, 221)(187, 222)(188, 208)(189, 223)(191, 224)(194, 220)(198, 219)(199, 218)(200, 214)(203, 225)(207, 226)(209, 227)(211, 228)(229, 231, 236, 246, 238, 232)(230, 233, 240, 253, 242, 234)(235, 243, 258, 285, 260, 244)(237, 247, 265, 297, 267, 248)(239, 250, 271, 304, 273, 251)(241, 254, 278, 316, 280, 255)(245, 261, 289, 328, 291, 262)(249, 268, 300, 342, 301, 269)(252, 274, 308, 350, 310, 275)(256, 281, 319, 364, 320, 282)(257, 283, 266, 298, 321, 284)(259, 286, 324, 368, 325, 287)(263, 292, 332, 376, 334, 293)(264, 294, 333, 377, 336, 295)(270, 302, 279, 317, 343, 303)(272, 305, 346, 390, 347, 306)(276, 311, 354, 398, 356, 312)(277, 313, 355, 399, 358, 314)(288, 326, 369, 415, 370, 327)(290, 329, 373, 340, 299, 330)(296, 337, 381, 426, 382, 338)(307, 348, 391, 435, 392, 349)(309, 351, 395, 362, 318, 352)(315, 359, 403, 446, 404, 360)(322, 357, 401, 434, 409, 365)(323, 361, 405, 447, 411, 366)(331, 374, 389, 432, 419, 375)(335, 379, 414, 429, 387, 344)(339, 383, 427, 431, 388, 345)(341, 378, 422, 441, 406, 385)(353, 396, 367, 412, 439, 397)(363, 400, 442, 421, 384, 407)(371, 410, 437, 394, 433, 416)(372, 413, 436, 393, 430, 417)(380, 424, 440, 455, 450, 425)(386, 428, 438, 456, 449, 423)(402, 444, 420, 451, 454, 445)(408, 448, 418, 452, 453, 443) L = (1, 229)(2, 230)(3, 231)(4, 232)(5, 233)(6, 234)(7, 235)(8, 236)(9, 237)(10, 238)(11, 239)(12, 240)(13, 241)(14, 242)(15, 243)(16, 244)(17, 245)(18, 246)(19, 247)(20, 248)(21, 249)(22, 250)(23, 251)(24, 252)(25, 253)(26, 254)(27, 255)(28, 256)(29, 257)(30, 258)(31, 259)(32, 260)(33, 261)(34, 262)(35, 263)(36, 264)(37, 265)(38, 266)(39, 267)(40, 268)(41, 269)(42, 270)(43, 271)(44, 272)(45, 273)(46, 274)(47, 275)(48, 276)(49, 277)(50, 278)(51, 279)(52, 280)(53, 281)(54, 282)(55, 283)(56, 284)(57, 285)(58, 286)(59, 287)(60, 288)(61, 289)(62, 290)(63, 291)(64, 292)(65, 293)(66, 294)(67, 295)(68, 296)(69, 297)(70, 298)(71, 299)(72, 300)(73, 301)(74, 302)(75, 303)(76, 304)(77, 305)(78, 306)(79, 307)(80, 308)(81, 309)(82, 310)(83, 311)(84, 312)(85, 313)(86, 314)(87, 315)(88, 316)(89, 317)(90, 318)(91, 319)(92, 320)(93, 321)(94, 322)(95, 323)(96, 324)(97, 325)(98, 326)(99, 327)(100, 328)(101, 329)(102, 330)(103, 331)(104, 332)(105, 333)(106, 334)(107, 335)(108, 336)(109, 337)(110, 338)(111, 339)(112, 340)(113, 341)(114, 342)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456) local type(s) :: { ( 12, 12 ), ( 12^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 152 e = 228 f = 38 degree seq :: [ 2^114, 6^38 ] E20.1139 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ (X1^-1 * X2^-1)^2, X1^6, X2^6, (X2 * X1^-1 * X2)^2, X1^-1 * X2^-1 * X1^3 * X2^-1 * X1^-1 * X2 * X1^-1 * X2, X2 * X1^-1 * X2^-1 * X1^4 * X2^2 * X1^-1, X1^-1 * X2^-1 * X1^4 * X2^-1 * X1^-2 * X2^2 * X1^-1, X1^-1 * X2^-1 * X1^2 * X2^-1 * X1^2 * X2 * X1^-1 * X2 * X1^2 * X2^-1 * X1 * X2^-1 * X1^-1, X1^-1 * X2^-1 * X1^2 * X2^2 * X1^2 * X2 * X1^-2 * X2 * X1^-2 * X2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 6, 16, 13, 4)(3, 9, 23, 47, 28, 11)(5, 14, 33, 44, 20, 7)(8, 21, 45, 71, 38, 17)(10, 25, 52, 80, 46, 22)(12, 29, 57, 95, 60, 31)(15, 30, 59, 98, 63, 34)(18, 39, 72, 105, 65, 35)(19, 41, 74, 114, 73, 40)(24, 50, 86, 129, 84, 48)(26, 42, 69, 103, 87, 51)(27, 54, 91, 135, 93, 55)(32, 36, 66, 106, 100, 61)(37, 68, 108, 153, 107, 67)(43, 76, 118, 165, 120, 77)(49, 85, 130, 173, 124, 81)(53, 90, 134, 183, 132, 88)(56, 82, 125, 174, 139, 94)(58, 64, 102, 147, 142, 96)(62, 101, 146, 169, 121, 78)(70, 110, 157, 210, 159, 111)(75, 117, 164, 217, 162, 115)(79, 122, 170, 214, 160, 112)(83, 127, 176, 212, 175, 126)(89, 133, 184, 222, 166, 119)(92, 123, 171, 226, 188, 136)(97, 143, 195, 219, 192, 140)(99, 141, 193, 227, 196, 144)(104, 149, 202, 185, 204, 150)(109, 156, 209, 180, 207, 154)(113, 161, 215, 182, 205, 151)(116, 163, 218, 172, 211, 158)(128, 177, 225, 198, 213, 178)(131, 181, 220, 167, 223, 179)(137, 189, 199, 148, 201, 186)(138, 187, 203, 155, 208, 190)(145, 152, 206, 228, 216, 197)(168, 221, 194, 200, 191, 224)(229, 231, 238, 254, 243, 233)(230, 235, 247, 270, 250, 236)(232, 240, 258, 279, 252, 237)(234, 245, 265, 297, 268, 246)(239, 255, 242, 262, 281, 253)(241, 260, 278, 315, 286, 257)(244, 263, 292, 331, 295, 264)(248, 271, 249, 274, 303, 269)(251, 276, 311, 287, 259, 277)(256, 284, 318, 291, 320, 282)(261, 283, 317, 280, 316, 290)(266, 298, 267, 301, 337, 296)(272, 306, 345, 308, 347, 304)(273, 305, 344, 302, 343, 307)(275, 309, 351, 326, 354, 310)(285, 324, 359, 314, 289, 325)(288, 327, 355, 312, 356, 313)(293, 332, 294, 335, 376, 330)(299, 340, 384, 342, 386, 338)(300, 339, 383, 336, 382, 341)(319, 364, 413, 362, 322, 365)(321, 366, 329, 360, 410, 361)(323, 368, 405, 357, 407, 369)(328, 373, 409, 370, 422, 371)(333, 379, 429, 381, 431, 377)(334, 378, 428, 375, 427, 380)(346, 394, 447, 392, 349, 395)(348, 396, 350, 390, 444, 391)(352, 400, 353, 403, 442, 399)(358, 406, 438, 404, 372, 408)(363, 414, 433, 411, 430, 415)(367, 419, 432, 416, 434, 417)(374, 418, 455, 412, 443, 426)(385, 439, 401, 437, 388, 440)(387, 441, 389, 435, 424, 436)(393, 448, 425, 445, 423, 449)(397, 453, 420, 450, 421, 451)(398, 452, 402, 446, 456, 454) L = (1, 229)(2, 230)(3, 231)(4, 232)(5, 233)(6, 234)(7, 235)(8, 236)(9, 237)(10, 238)(11, 239)(12, 240)(13, 241)(14, 242)(15, 243)(16, 244)(17, 245)(18, 246)(19, 247)(20, 248)(21, 249)(22, 250)(23, 251)(24, 252)(25, 253)(26, 254)(27, 255)(28, 256)(29, 257)(30, 258)(31, 259)(32, 260)(33, 261)(34, 262)(35, 263)(36, 264)(37, 265)(38, 266)(39, 267)(40, 268)(41, 269)(42, 270)(43, 271)(44, 272)(45, 273)(46, 274)(47, 275)(48, 276)(49, 277)(50, 278)(51, 279)(52, 280)(53, 281)(54, 282)(55, 283)(56, 284)(57, 285)(58, 286)(59, 287)(60, 288)(61, 289)(62, 290)(63, 291)(64, 292)(65, 293)(66, 294)(67, 295)(68, 296)(69, 297)(70, 298)(71, 299)(72, 300)(73, 301)(74, 302)(75, 303)(76, 304)(77, 305)(78, 306)(79, 307)(80, 308)(81, 309)(82, 310)(83, 311)(84, 312)(85, 313)(86, 314)(87, 315)(88, 316)(89, 317)(90, 318)(91, 319)(92, 320)(93, 321)(94, 322)(95, 323)(96, 324)(97, 325)(98, 326)(99, 327)(100, 328)(101, 329)(102, 330)(103, 331)(104, 332)(105, 333)(106, 334)(107, 335)(108, 336)(109, 337)(110, 338)(111, 339)(112, 340)(113, 341)(114, 342)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456) local type(s) :: { ( 4^6 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 76 e = 228 f = 114 degree seq :: [ 6^76 ] E20.1140 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ X1^2, X2^6, (X2^-2 * X1 * X2^-1)^2, (X2^-1 * X1)^6, (X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1)^2, X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 ] Map:: polytopal non-degenerate R = (1, 229, 2, 230)(3, 231, 7, 235)(4, 232, 9, 237)(5, 233, 11, 239)(6, 234, 13, 241)(8, 236, 17, 245)(10, 238, 21, 249)(12, 240, 24, 252)(14, 242, 28, 256)(15, 243, 29, 257)(16, 244, 31, 259)(18, 246, 25, 253)(19, 247, 35, 263)(20, 248, 36, 264)(22, 250, 37, 265)(23, 251, 39, 267)(26, 254, 43, 271)(27, 255, 44, 272)(30, 258, 47, 275)(32, 260, 50, 278)(33, 261, 51, 279)(34, 262, 52, 280)(38, 266, 59, 287)(40, 268, 62, 290)(41, 269, 63, 291)(42, 270, 64, 292)(45, 273, 68, 296)(46, 274, 70, 298)(48, 276, 74, 302)(49, 277, 75, 303)(53, 281, 80, 308)(54, 282, 81, 309)(55, 283, 82, 310)(56, 284, 57, 285)(58, 286, 84, 312)(60, 288, 88, 316)(61, 289, 89, 317)(65, 293, 94, 322)(66, 294, 95, 323)(67, 295, 96, 324)(69, 297, 97, 325)(71, 299, 93, 321)(72, 300, 100, 328)(73, 301, 101, 329)(76, 304, 105, 333)(77, 305, 106, 334)(78, 306, 107, 335)(79, 307, 85, 313)(83, 311, 112, 340)(86, 314, 115, 343)(87, 315, 116, 344)(90, 318, 120, 348)(91, 319, 121, 349)(92, 320, 122, 350)(98, 326, 129, 357)(99, 327, 130, 358)(102, 330, 134, 362)(103, 331, 135, 363)(104, 332, 136, 364)(108, 336, 141, 369)(109, 337, 142, 370)(110, 338, 143, 371)(111, 339, 144, 372)(113, 341, 147, 375)(114, 342, 148, 376)(117, 345, 152, 380)(118, 346, 153, 381)(119, 347, 154, 382)(123, 351, 159, 387)(124, 352, 160, 388)(125, 353, 161, 389)(126, 354, 162, 390)(127, 355, 163, 391)(128, 356, 164, 392)(131, 359, 168, 396)(132, 360, 169, 397)(133, 361, 170, 398)(137, 365, 175, 403)(138, 366, 176, 404)(139, 367, 177, 405)(140, 368, 178, 406)(145, 373, 184, 412)(146, 374, 185, 413)(149, 377, 189, 417)(150, 378, 190, 418)(151, 379, 191, 419)(155, 383, 196, 424)(156, 384, 197, 425)(157, 385, 198, 426)(158, 386, 199, 427)(165, 393, 204, 432)(166, 394, 192, 420)(167, 395, 188, 416)(171, 399, 187, 415)(172, 400, 201, 429)(173, 401, 200, 428)(174, 402, 195, 423)(179, 407, 194, 422)(180, 408, 193, 421)(181, 409, 203, 431)(182, 410, 202, 430)(183, 411, 186, 414)(205, 433, 228, 456)(206, 434, 220, 448)(207, 435, 219, 447)(208, 436, 218, 446)(209, 437, 225, 453)(210, 438, 224, 452)(211, 439, 223, 451)(212, 440, 222, 450)(213, 441, 221, 449)(214, 442, 227, 455)(215, 443, 226, 454)(216, 444, 217, 445) L = (1, 231)(2, 233)(3, 236)(4, 229)(5, 240)(6, 230)(7, 243)(8, 246)(9, 247)(10, 232)(11, 250)(12, 253)(13, 254)(14, 234)(15, 258)(16, 235)(17, 261)(18, 238)(19, 262)(20, 237)(21, 260)(22, 266)(23, 239)(24, 269)(25, 242)(26, 270)(27, 241)(28, 268)(29, 273)(30, 249)(31, 276)(32, 244)(33, 248)(34, 245)(35, 281)(36, 283)(37, 285)(38, 256)(39, 288)(40, 251)(41, 255)(42, 252)(43, 293)(44, 295)(45, 297)(46, 257)(47, 300)(48, 301)(49, 259)(50, 299)(51, 304)(52, 306)(53, 305)(54, 263)(55, 307)(56, 264)(57, 311)(58, 265)(59, 314)(60, 315)(61, 267)(62, 313)(63, 318)(64, 320)(65, 319)(66, 271)(67, 321)(68, 272)(69, 278)(70, 326)(71, 274)(72, 277)(73, 275)(74, 330)(75, 332)(76, 282)(77, 279)(78, 284)(79, 280)(80, 329)(81, 336)(82, 338)(83, 290)(84, 341)(85, 286)(86, 289)(87, 287)(88, 345)(89, 347)(90, 294)(91, 291)(92, 296)(93, 292)(94, 344)(95, 351)(96, 353)(97, 355)(98, 356)(99, 298)(100, 359)(101, 361)(102, 360)(103, 302)(104, 308)(105, 303)(106, 365)(107, 367)(108, 366)(109, 309)(110, 368)(111, 310)(112, 373)(113, 374)(114, 312)(115, 377)(116, 379)(117, 378)(118, 316)(119, 322)(120, 317)(121, 383)(122, 385)(123, 384)(124, 323)(125, 386)(126, 324)(127, 327)(128, 325)(129, 393)(130, 395)(131, 331)(132, 328)(133, 333)(134, 392)(135, 399)(136, 401)(137, 337)(138, 334)(139, 339)(140, 335)(141, 407)(142, 409)(143, 404)(144, 410)(145, 342)(146, 340)(147, 414)(148, 416)(149, 346)(150, 343)(151, 348)(152, 413)(153, 420)(154, 422)(155, 352)(156, 349)(157, 354)(158, 350)(159, 428)(160, 430)(161, 425)(162, 431)(163, 433)(164, 435)(165, 434)(166, 357)(167, 362)(168, 358)(169, 436)(170, 438)(171, 437)(172, 363)(173, 439)(174, 364)(175, 440)(176, 442)(177, 370)(178, 443)(179, 441)(180, 369)(181, 371)(182, 444)(183, 372)(184, 445)(185, 447)(186, 446)(187, 375)(188, 380)(189, 376)(190, 448)(191, 450)(192, 449)(193, 381)(194, 451)(195, 382)(196, 452)(197, 454)(198, 388)(199, 455)(200, 453)(201, 387)(202, 389)(203, 456)(204, 390)(205, 394)(206, 391)(207, 396)(208, 400)(209, 397)(210, 402)(211, 398)(212, 408)(213, 403)(214, 405)(215, 411)(216, 406)(217, 415)(218, 412)(219, 417)(220, 421)(221, 418)(222, 423)(223, 419)(224, 429)(225, 424)(226, 426)(227, 432)(228, 427) local type(s) :: { ( 6^4 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple bipartite v = 114 e = 228 f = 76 degree seq :: [ 4^114 ] E20.1141 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ (X1^-1 * X2^-1)^2, X1^6, X2^6, (X2 * X1^-1 * X2)^2, X1^-1 * X2^-1 * X1^3 * X2^-1 * X1^-1 * X2 * X1^-1 * X2, X2 * X1^-1 * X2^-1 * X1^4 * X2^2 * X1^-1, X1^-1 * X2^-1 * X1^4 * X2^-1 * X1^-2 * X2^2 * X1^-1, X1^-1 * X2^-1 * X1^2 * X2^-1 * X1^2 * X2 * X1^-1 * X2 * X1^2 * X2^-1 * X1 * X2^-1 * X1^-1, X1^-1 * X2^-1 * X1^2 * X2^2 * X1^2 * X2 * X1^-2 * X2 * X1^-2 * X2 * X1^-1 ] Map:: R = (1, 229, 2, 230, 6, 234, 16, 244, 13, 241, 4, 232)(3, 231, 9, 237, 23, 251, 47, 275, 28, 256, 11, 239)(5, 233, 14, 242, 33, 261, 44, 272, 20, 248, 7, 235)(8, 236, 21, 249, 45, 273, 71, 299, 38, 266, 17, 245)(10, 238, 25, 253, 52, 280, 80, 308, 46, 274, 22, 250)(12, 240, 29, 257, 57, 285, 95, 323, 60, 288, 31, 259)(15, 243, 30, 258, 59, 287, 98, 326, 63, 291, 34, 262)(18, 246, 39, 267, 72, 300, 105, 333, 65, 293, 35, 263)(19, 247, 41, 269, 74, 302, 114, 342, 73, 301, 40, 268)(24, 252, 50, 278, 86, 314, 129, 357, 84, 312, 48, 276)(26, 254, 42, 270, 69, 297, 103, 331, 87, 315, 51, 279)(27, 255, 54, 282, 91, 319, 135, 363, 93, 321, 55, 283)(32, 260, 36, 264, 66, 294, 106, 334, 100, 328, 61, 289)(37, 265, 68, 296, 108, 336, 153, 381, 107, 335, 67, 295)(43, 271, 76, 304, 118, 346, 165, 393, 120, 348, 77, 305)(49, 277, 85, 313, 130, 358, 173, 401, 124, 352, 81, 309)(53, 281, 90, 318, 134, 362, 183, 411, 132, 360, 88, 316)(56, 284, 82, 310, 125, 353, 174, 402, 139, 367, 94, 322)(58, 286, 64, 292, 102, 330, 147, 375, 142, 370, 96, 324)(62, 290, 101, 329, 146, 374, 169, 397, 121, 349, 78, 306)(70, 298, 110, 338, 157, 385, 210, 438, 159, 387, 111, 339)(75, 303, 117, 345, 164, 392, 217, 445, 162, 390, 115, 343)(79, 307, 122, 350, 170, 398, 214, 442, 160, 388, 112, 340)(83, 311, 127, 355, 176, 404, 212, 440, 175, 403, 126, 354)(89, 317, 133, 361, 184, 412, 222, 450, 166, 394, 119, 347)(92, 320, 123, 351, 171, 399, 226, 454, 188, 416, 136, 364)(97, 325, 143, 371, 195, 423, 219, 447, 192, 420, 140, 368)(99, 327, 141, 369, 193, 421, 227, 455, 196, 424, 144, 372)(104, 332, 149, 377, 202, 430, 185, 413, 204, 432, 150, 378)(109, 337, 156, 384, 209, 437, 180, 408, 207, 435, 154, 382)(113, 341, 161, 389, 215, 443, 182, 410, 205, 433, 151, 379)(116, 344, 163, 391, 218, 446, 172, 400, 211, 439, 158, 386)(128, 356, 177, 405, 225, 453, 198, 426, 213, 441, 178, 406)(131, 359, 181, 409, 220, 448, 167, 395, 223, 451, 179, 407)(137, 365, 189, 417, 199, 427, 148, 376, 201, 429, 186, 414)(138, 366, 187, 415, 203, 431, 155, 383, 208, 436, 190, 418)(145, 373, 152, 380, 206, 434, 228, 456, 216, 444, 197, 425)(168, 396, 221, 449, 194, 422, 200, 428, 191, 419, 224, 452) L = (1, 231)(2, 235)(3, 238)(4, 240)(5, 229)(6, 245)(7, 247)(8, 230)(9, 232)(10, 254)(11, 255)(12, 258)(13, 260)(14, 262)(15, 233)(16, 263)(17, 265)(18, 234)(19, 270)(20, 271)(21, 274)(22, 236)(23, 276)(24, 237)(25, 239)(26, 243)(27, 242)(28, 284)(29, 241)(30, 279)(31, 277)(32, 278)(33, 283)(34, 281)(35, 292)(36, 244)(37, 297)(38, 298)(39, 301)(40, 246)(41, 248)(42, 250)(43, 249)(44, 306)(45, 305)(46, 303)(47, 309)(48, 311)(49, 251)(50, 315)(51, 252)(52, 316)(53, 253)(54, 256)(55, 317)(56, 318)(57, 324)(58, 257)(59, 259)(60, 327)(61, 325)(62, 261)(63, 320)(64, 331)(65, 332)(66, 335)(67, 264)(68, 266)(69, 268)(70, 267)(71, 340)(72, 339)(73, 337)(74, 343)(75, 269)(76, 272)(77, 344)(78, 345)(79, 273)(80, 347)(81, 351)(82, 275)(83, 287)(84, 356)(85, 288)(86, 289)(87, 286)(88, 290)(89, 280)(90, 291)(91, 364)(92, 282)(93, 366)(94, 365)(95, 368)(96, 359)(97, 285)(98, 354)(99, 355)(100, 373)(101, 360)(102, 293)(103, 295)(104, 294)(105, 379)(106, 378)(107, 376)(108, 382)(109, 296)(110, 299)(111, 383)(112, 384)(113, 300)(114, 386)(115, 307)(116, 302)(117, 308)(118, 394)(119, 304)(120, 396)(121, 395)(122, 390)(123, 326)(124, 400)(125, 403)(126, 310)(127, 312)(128, 313)(129, 407)(130, 406)(131, 314)(132, 410)(133, 321)(134, 322)(135, 414)(136, 413)(137, 319)(138, 329)(139, 419)(140, 405)(141, 323)(142, 422)(143, 328)(144, 408)(145, 409)(146, 418)(147, 427)(148, 330)(149, 333)(150, 428)(151, 429)(152, 334)(153, 431)(154, 341)(155, 336)(156, 342)(157, 439)(158, 338)(159, 441)(160, 440)(161, 435)(162, 444)(163, 348)(164, 349)(165, 448)(166, 447)(167, 346)(168, 350)(169, 453)(170, 452)(171, 352)(172, 353)(173, 437)(174, 446)(175, 442)(176, 372)(177, 357)(178, 438)(179, 369)(180, 358)(181, 370)(182, 361)(183, 430)(184, 443)(185, 362)(186, 433)(187, 363)(188, 434)(189, 367)(190, 455)(191, 432)(192, 450)(193, 451)(194, 371)(195, 449)(196, 436)(197, 445)(198, 374)(199, 380)(200, 375)(201, 381)(202, 415)(203, 377)(204, 416)(205, 411)(206, 417)(207, 424)(208, 387)(209, 388)(210, 404)(211, 401)(212, 385)(213, 389)(214, 399)(215, 426)(216, 391)(217, 423)(218, 456)(219, 392)(220, 425)(221, 393)(222, 421)(223, 397)(224, 402)(225, 420)(226, 398)(227, 412)(228, 454) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 38 e = 228 f = 152 degree seq :: [ 12^38 ] E20.1142 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x ((C19 : C3) : C2) (small group id <228, 7>) Aut = C2 x ((C19 : C3) : C2) (small group id <228, 7>) |r| :: 1 Presentation :: [ (X2 * X1)^2, X2^6, (X1^-1 * X2 * X1^-1)^2, X1^6, X1^-1 * X2 * X1^3 * X2^-1 * X1^-2, X1^-1 * X2^3 * X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1, X1^-1 * X2^-1 * X1 * X2^2 * X1^-1 * X2^-2 * X1 * X2^-2 * X1 * X2^3 * X1^-1, X1^-1 * X2^-2 * X1 * X2^2 * X1^-1 * X2^3 * X1^-1 * X2 * X1^-1 * X2^-2 * X1^-1, X1^-1 * X2^3 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^-2 * X1^-1, X2 * X1^-1 * X2^-1 * X1 * X2^2 * X1 * X2^-1 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1 ] Map:: R = (1, 229, 2, 230, 6, 234, 16, 244, 13, 241, 4, 232)(3, 231, 9, 237, 23, 251, 35, 263, 18, 246, 11, 239)(5, 233, 14, 242, 31, 259, 36, 264, 20, 248, 7, 235)(8, 236, 21, 249, 12, 240, 29, 257, 38, 266, 17, 245)(10, 238, 25, 253, 51, 279, 64, 292, 48, 276, 27, 255)(15, 243, 34, 262, 43, 271, 65, 293, 61, 289, 32, 260)(19, 247, 40, 268, 71, 299, 59, 287, 33, 261, 42, 270)(22, 250, 46, 274, 69, 297, 57, 285, 78, 306, 44, 272)(24, 252, 49, 277, 28, 256, 39, 267, 70, 298, 47, 275)(26, 254, 53, 281, 90, 318, 102, 330, 87, 315, 54, 282)(30, 258, 45, 273, 68, 296, 37, 265, 66, 294, 58, 286)(41, 269, 73, 301, 113, 341, 95, 323, 110, 338, 74, 302)(50, 278, 85, 313, 105, 333, 67, 295, 104, 332, 83, 311)(52, 280, 88, 316, 55, 283, 82, 310, 125, 353, 86, 314)(56, 284, 84, 312, 124, 352, 81, 309, 108, 336, 94, 322)(60, 288, 97, 325, 117, 345, 76, 304, 63, 291, 99, 327)(62, 290, 100, 328, 109, 337, 72, 300, 111, 339, 75, 303)(77, 305, 118, 346, 152, 380, 107, 335, 80, 308, 120, 348)(79, 307, 121, 349, 96, 324, 103, 331, 147, 375, 106, 334)(89, 317, 133, 361, 172, 400, 123, 351, 171, 399, 131, 359)(91, 319, 135, 363, 92, 320, 130, 358, 181, 409, 134, 362)(93, 321, 132, 360, 180, 408, 129, 357, 174, 402, 138, 366)(98, 326, 142, 370, 156, 384, 112, 340, 158, 386, 143, 371)(101, 329, 146, 374, 164, 392, 141, 369, 193, 421, 144, 372)(114, 342, 160, 388, 115, 343, 155, 383, 210, 438, 159, 387)(116, 344, 157, 385, 209, 437, 154, 382, 145, 373, 163, 391)(119, 347, 166, 394, 199, 427, 148, 376, 201, 429, 167, 395)(122, 350, 170, 398, 206, 434, 165, 393, 221, 449, 168, 396)(126, 354, 149, 377, 202, 430, 150, 378, 128, 356, 176, 404)(127, 355, 177, 405, 139, 367, 153, 381, 207, 435, 173, 401)(136, 364, 188, 416, 225, 453, 179, 407, 227, 455, 186, 414)(137, 365, 187, 415, 222, 450, 185, 413, 223, 451, 189, 417)(140, 368, 169, 397, 205, 433, 151, 379, 200, 428, 192, 420)(161, 389, 217, 445, 183, 411, 208, 436, 190, 418, 215, 443)(162, 390, 216, 444, 184, 412, 214, 442, 182, 410, 218, 446)(175, 403, 211, 439, 194, 422, 204, 432, 195, 423, 213, 441)(178, 406, 219, 447, 197, 425, 203, 431, 228, 456, 212, 440)(191, 419, 220, 448, 198, 426, 226, 454, 196, 424, 224, 452) L = (1, 231)(2, 235)(3, 238)(4, 240)(5, 229)(6, 245)(7, 247)(8, 230)(9, 232)(10, 254)(11, 256)(12, 258)(13, 259)(14, 260)(15, 233)(16, 263)(17, 265)(18, 234)(19, 269)(20, 271)(21, 272)(22, 236)(23, 275)(24, 237)(25, 239)(26, 243)(27, 283)(28, 284)(29, 241)(30, 278)(31, 287)(32, 288)(33, 242)(34, 282)(35, 292)(36, 244)(37, 295)(38, 297)(39, 246)(40, 248)(41, 250)(42, 303)(43, 304)(44, 305)(45, 249)(46, 302)(47, 309)(48, 251)(49, 311)(50, 252)(51, 314)(52, 253)(53, 255)(54, 320)(55, 321)(56, 317)(57, 257)(58, 324)(59, 323)(60, 326)(61, 318)(62, 261)(63, 262)(64, 330)(65, 264)(66, 266)(67, 267)(68, 334)(69, 335)(70, 333)(71, 337)(72, 268)(73, 270)(74, 343)(75, 344)(76, 340)(77, 347)(78, 341)(79, 273)(80, 274)(81, 351)(82, 276)(83, 354)(84, 277)(85, 286)(86, 357)(87, 279)(88, 359)(89, 280)(90, 362)(91, 281)(92, 365)(93, 364)(94, 367)(95, 285)(96, 368)(97, 289)(98, 290)(99, 372)(100, 371)(101, 291)(102, 293)(103, 294)(104, 296)(105, 378)(106, 379)(107, 376)(108, 298)(109, 382)(110, 299)(111, 384)(112, 300)(113, 387)(114, 301)(115, 390)(116, 389)(117, 392)(118, 306)(119, 307)(120, 396)(121, 395)(122, 308)(123, 310)(124, 401)(125, 400)(126, 403)(127, 312)(128, 313)(129, 407)(130, 315)(131, 410)(132, 316)(133, 322)(134, 413)(135, 414)(136, 319)(137, 329)(138, 418)(139, 419)(140, 406)(141, 325)(142, 327)(143, 423)(144, 424)(145, 328)(146, 417)(147, 427)(148, 331)(149, 332)(150, 432)(151, 431)(152, 434)(153, 336)(154, 436)(155, 338)(156, 439)(157, 339)(158, 345)(159, 442)(160, 443)(161, 342)(162, 350)(163, 447)(164, 448)(165, 346)(166, 348)(167, 451)(168, 452)(169, 349)(170, 446)(171, 352)(172, 444)(173, 454)(174, 353)(175, 355)(176, 440)(177, 441)(178, 356)(179, 358)(180, 445)(181, 453)(182, 438)(183, 360)(184, 361)(185, 369)(186, 428)(187, 363)(188, 366)(189, 429)(190, 437)(191, 449)(192, 455)(193, 450)(194, 370)(195, 430)(196, 435)(197, 373)(198, 374)(199, 415)(200, 375)(201, 380)(202, 425)(203, 377)(204, 381)(205, 416)(206, 426)(207, 422)(208, 383)(209, 456)(210, 411)(211, 404)(212, 385)(213, 386)(214, 393)(215, 402)(216, 388)(217, 391)(218, 399)(219, 420)(220, 405)(221, 412)(222, 394)(223, 409)(224, 421)(225, 397)(226, 398)(227, 408)(228, 433) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 38 e = 228 f = 152 degree seq :: [ 12^38 ] ## Checksum: 1142 records. ## Written on: Sun Oct 20 00:57:02 CEST 2019